Steel Construction Manual [Digital ed.] 1564240606, 9781564240606

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Steel construction manual

american institute of

steel construction

fourteenth edition

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1 Dimensions and Properties

2 General Design Considerations

3 Design of Flexural Members

4 Design of Compression Members

5 Design of Tension Members

6 Design of Members Subject to Combined Forces

7 Design Considerations for Bolts

8 Design Considerations for Welds

9 Design of Connecting Elements

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10 Design of Simple Shear Connections

11 Design of Partially Restrained Moment Connections

12 Design of Fully Restrained Moment Connections

13 Design of Bracing Connections and Truss Connections

14 Design of Beam Bearing Plates, Col. Base Plates, Anchor Rods, and Col. Splices

15 Design of Hanger Connections, Bracket Plates, and Crane-Rail Connections

16 Specifications and Codes

17 Miscellaneous Data and Mathematical Information

Index and General Nomenclature

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STEEL CONSTRUCTION MANUAL

AMERICAN INSTITUTE OF

STEEL CONSTRUCTION

FOURTEENTH EDITION

AISC_Prelims_14th Ed._February 25, 2013 14-11-10 9:30 AM Page vi

(Black plate)

vi

AISC © 2011 by American Institute of Steel Construction ISBN 1-56424-060-6 All rights reserved. This book or any part thereof must not be reproduced in any form without the written permission of the publisher. The AISC logo is a registered trademark of AISC. The information presented in this publication has been prepared in accordance with recognized engineering principles and is for general information only. While it is believed to be accurate, this information should not be used or relied upon for any specific application without competent professional examination and verification of its accuracy, suitability, and applicability by a licensed professional engineer, designer, or architect. The publication of the material contained herein is not intended as a representation or warranty on the part of the American Institute of Steel Construction or of any other person named herein, that this information is suitable for any general or particular use or of freedom from infringement of any patent or patents. Anyone making use of this information assumes all liability arising from such use. Caution must be exercised when relying upon other specifications and codes developed by other bodies and incorporated by reference herein since such material may be modified or amended from time to time subsequent to the printing of this edition. The Institute bears no responsibility for such material other than to refer to it and incorporate it by reference at the time of the initial publication of this edition. Printed in the United States of America First Printing: March 2011 Second Printing: February 2012 Third Printing: February 2013 Fourth Printing: February 2015

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FOREWORD

The American Institute of Steel Construction, founded in 1921, is the nonprofit technical standards developer and trade organization for the fabricated structural steel industry in the United States. AISC is headquartered in Chicago and has a long tradition of service to the steel construction industry providing timely and reliable information. The continuing financial support and active participation of Members in the engineering, research and development activities of the Institute make possible the publishing of this Steel Construction Manual. Those Members include the following: Full Members engaged in the fabrication, production and sale of structural steel; Associate Members, who include erectors, detailers, service consultants, software developers and steel product manufacturers; Professional Members, who are structural or civil engineers and architects, including architectural and engineering educators; Affiliate Members, who include general contractors, building inspectors and code officials; and Student Members. The Institute’s objective is to make structural steel the material of choice, by being the leader in structural-steel-related technical and market-building activities, including specification and code development, research, education, technical assistance, quality certification, standardization and market development. To accomplish this objective, the Institute publishes manuals, design guides and specifications. Best known and most widely used is the Steel Construction Manual, which holds a highly respected position in engineering literature. The Manual is based on the Specification for Structural Steel Buildings and the Code of Standard Practice for Steel Buildings and Bridges. Both standards are included in the Manual for easy reference. The Institute also publishes technical information and timely articles in its Engineering Journal, Design Guide series, Modern Steel Construction magazine, and other design aids, research reports and journal articles. Nearly all of the information AISC publishes is available for download from the AISC web site at www.aisc.org.

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PREFACE

This Manual is the 14th Edition of the AISC Steel Construction Manual, which was first published in 1927. It replaces the 13th Edition Manual originally published in 2005. The following specifications, codes and standards are printed in Part 16 of this Manual: • 2010 AISC Specification for Structural Steel Buildings • 2009 RCSC Specification for Structural Joints Using High-Strength Bolts • 2010 AISC Code of Standard Practice for Steel Buildings and Bridges The following resources supplement the Manual and are available on the AISC web site at www.aisc.org: • AISC Design Examples, which illustrate the application of tables and specification provisions that are included in this Manual. • AISC Shapes Database V14.0 and V14.0H. • Background and supporting literature (references) for the AISC Steel Construction Manual. The following major changes and improvements have been made in this revision: • All tabular information and discussions have been updated to comply with the 2010 Specification for Structural Buildings and the standards and other documents referenced therein. • Shape information has been updated to ASTM A6-09 throughout the Manual, including a new HP shape series. • Eccentrically loaded weld tables have been revised to indicate the strongest weld permitted by the three methods listed in Chapter J of the specification and supplemented to provide strengths for L-shaped welds loaded from either side. • The procedure for the design of bracket plates in Part 15 has been revised. • In Part 10, the procedure for the design of conventional single plate shear connections has been revised to accommodate the increased bolt shear strengths of the 2010 Specification for Structural Steel Buildings. • In Part 10, for extended single plate shear connections, information is provided to determine if stiffening plates (stabilizers) are required. In addition, many other improvements have been made throughout this Manual and the number of accompanying design examples has been expanded. By the AISC Committee on Manuals and Textbooks, William A. Thornton, Chairman Mark V. Holland, Vice-Chairman Abbas Aminmansour Charles J. Carter Harry A. Cole Brad Davis Robert O. Disque Bo Dowswell

Edward M. Egan Marshall T. Ferrell Lanny J. Flynn Patrick J. Fortney Louis F. Geschwindner W. Scott Goodrich Christopher M. Hewitt W. Steven Hofmeister

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Bill R. Lindley, II Ronald L. Meng Larry S. Muir Thomas M. Murray Charles R. Page Davis G. Parsons, II Rafael Sabelli Clifford W. Schwinger

William N. Scott William T. Segui Victor Shneur Marc L. Sorenson Gary C. Violette Michael A. West Ronald G. Yeager Cynthia J. Duncan, Secretary

The committee gratefully acknowledges the contributions made to this Manual by the AISC Committee on Specifications and the following individuals: Leigh C. Arber, Areti Carter, Janet T. Cummins, Amanuel Gebremeskel, Kurt Gustafson, Richard C. Kaehler, Daniel J. Kaufman, Rostislav Kucher, Brent L. Leu, Margaret A. Matthew, Frederick J. Palmer, Vijaykumar Patel, Elizabeth A. Rehwoldt, Thomas J. Schlafly, Zachary W. Stutts and Sriramulu Vinnakota.

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SCOPE

The specification requirements and other design recommendations and considerations summarized in this Manual apply in general to the design and construction of steel buildings and other structures. The design of seismic force resisting systems also must meet the requirements in the AISC Seismic Provisions for Structural Steel Buildings, except in the following cases for which use of the AISC Seismic Provisions is not required: • Buildings and other structures in seismic design category (SDC) A • Buildings and other structures in SDC B or C with R = 3 systems [steel systems not specifically detailed for seismic resistance per ASCE/SEI 7 Table 12.2-1 (ASCE, 2010)] • Nonbuilding structures similar to buildings with R = 11/2 braced-frame systems or R = 1 moment-frame systems; see ASCE/SEI 7 Table 15.4-1 • Nonbuilding structures not similar to buildings (see ASCE/SEI 7 Table 15.4-2), which are designed to meet the requirements in other standards entirely Conversely, use of the AISC Seismic Provisions is required in the following cases: • Buildings and other structures in SDC B or C when one of the exemptions for steel seismic force resisting systems above does not apply • Buildings and other structures in SDC B or C that use composite seismic force resisting systems (those containing composite steel-and-concrete members and those composed of steel members in combination with reinforced concrete members) • Buildings in SDC D, E or F • Nonbuilding structures in SDC D, E or F when the exemption above does not apply The AISC Seismic Design Manual provides guidance on the use of the AISC Seismic Provisions. The Manual consists of seventeen parts addressing various topics related to steel building design and construction. Part 1 provides the dimensions and properties for structural products commonly used. For proper material specifications for these products, as well as general specification requirements and other design considerations, see Part 2. For the design of members, see Parts 3 through 6. For the design of connections, see Parts 7 through 15. For AISC Specifications and Codes, see Part 16. For other miscellaneous information, see Part 17.

REFERENCE ASCE (2010), Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 7-10, American Society of Civil Engineers, Reston, VA.

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PART 1 DIMENSIONS AND PROPERTIES

SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–3 STRUCTURAL PRODUCTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–3 W-, M-, S- and HP-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–3 Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–4 Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–4 Structural Tees (WT-, MT- and ST-Shapes) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–5 Hollow Structural Sections (HSS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–5 Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–6 Double Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–6 Double Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–7 W-Shapes and S-Shapes with Cap Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–7 Plate Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–8 Raised-Pattern Floor Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–9 Crane Rails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–9 Other Structural Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–9 STANDARD MILL PRACTICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–9 Hot-Rolled Structural Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–9 Hollow Structural Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–9 Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–10 Plate Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–10 PART 1 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–11 TABLES OF DESIGN DIMENSIONS, DETAILING DIMENSIONS, AND AXIAL, STRONG-AXIS FLEXURAL, AND WEAK-AXIS FLEXURAL PROPERTIES . . . . 1–12 Table 1-1.

W-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–12

Table 1-2.

M-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–30

Table 1-3.

S-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–32

Table 1-4.

HP-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–34

Table 1-5.

C-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–36

Table 1-6.

MC-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–38

Table 1-7.

Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–42 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Table 1-7A.

Workable Gages in Angle Legs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1–48

Table 1-7B.

Compactness Criteria for Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . .1–49

Table 1-8.

WT-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–50

Table 1-9.

MT-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–70

Table 1-10.

ST-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–72

Table 1-11.

Rectangular HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–74

Table 1-12.

Square HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–92

Table 1-12A. Rectangular and Square HSS Compactness Criteria . . . . . . . . . . . . .1–95 Table 1-13.

Round HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–96

Table 1-14.

Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–101

Table 1-15.

Double Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–102

Table 1-16.

2C-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–110

Table 1-17.

2MC-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–111

Table 1-18.

Weights of Raised-Pattern Floor Plates . . . . . . . . . . . . . . . . . . . . . . 1–113

Table 1-19.

W-Shapes with Cap Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–114

Table 1-20.

S-Shapes with Cap Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–116

Table 1-21.

Crane Rails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–118

Table 1-22.

ASTM A6 Tolerances for W-Shapes and HP-Shapes . . . . . . . . . . . 1–119

Table 1-23.

ASTM A6 Tolerances for S-Shapes, M-Shapes and Channels . . . . 1–121

Table 1-24.

ASTM A6 Tolerances for WT-, MT- and ST-Shapes . . . . . . . . . . . 1–122

Table 1-25.

ASTM A6 Tolerances for Angles, 3 in. and Larger . . . . . . . . . . . . 1–123

Table 1-26.

ASTM A6 Tolerances for Angles, < 3 in. . . . . . . . . . . . . . . . . . . . . 1–124

Table 1-27.

Tolerances for Rectangular and Square HSS . . . . . . . . . . . . . . . . . 1–125

Table 1-28.

Tolerances for Round HSS and Pipe . . . . . . . . . . . . . . . . . . . . . . . . 1–126

Table 1-29.

Rectangular Sheared Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–127

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SCOPE The dimensions and properties for structural products commonly used in steel building design and construction are given in this Part. Although the dimensions and properties tabulated in Part 1 reflect “commonly” used structural products, some of the shapes listed are not commonly produced or stocked. These shapes are usually only produced to order, and will likely be subject to mill production schedules and minimum order quantities. For availability of shapes, go to www.aisc.org. For torsional and flexural-torsional properties of rolled shapes see AISC Design Guide 9, Torsional Analysis of Structural Steel Members (Seaburg and Carter, 1997). For surface areas, box perimeters and areas, W/D ratios and A/D ratios, see AISC Design Guide 19, Fire Resistance of Structural Steel Framing (Ruddy et al., 2003).

STRUCTURAL PRODUCTS W-, M-, S- and HP-Shapes Four types of H-shaped (or I-shaped) members are covered in this Manual: • W-shapes, which have essentially parallel inner and outer flange surfaces. • M-shapes, which are H-shaped members that are not classified in ASTM A6 as W-, Sor HP-shapes. M-shapes may have a sloped inside flange face or other cross-section features that do not meet the criteria for W-, S- or HP-shapes. • S-shapes (also known as American standard beams), which have a slope of approximately 162/3% (2 on 12) on the inner flange surfaces. • HP-shapes (also known as bearing piles), which are similar to W-shapes except their webs and flanges are of equal thickness and the depth and flange width are nominally equal for a given designation. These shapes are designated by the mark W, M, S or HP, nominal depth (in.) and nominal weight (lb/ft). For example, a W24×55 is a W-shape that is nominally 24 in. deep and weighs 55 lb/ft. The following dimensional and property information is given in this Manual for the W-, M-, S- and HP-shapes covered in ASTM A6: • Design dimensions, detailing dimensions, axial properties and flexural properties are given in Tables 1-1, 1-2, 1-3 and 1-4 for W-, M-, S- and HP-shapes, respectively. • SI-equivalent designations are given in Table 17-1 for W-shapes and in Table 17-2 for M-, S- and HP-shapes. Tabulated decimal values are appropriate for use in design calculations, whereas fractional values are appropriate for use in detailing. All decimal and fractional values are similar with one exception: Because of the variation in fillet sizes used in shape production, the decimal value, kdes, is conservatively presented based on the smallest fillet used in production, and the fractional value, kdet, is conservatively presented based on the largest fillet used in production. For the definitions of the tabulated variables, refer to the Nomenclature section at the back of this Manual. When appropriate, this Manual presents tabulated values for the workable gage of a section. The term workable gage refers to the gage for fasteners in the flange that provides for entering and tightening clearances and edge distance and spacing requirements. When AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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the listed value is footnoted, the actual size, combination, and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. Other gages that provide for entering and tightening clearances and edge distance and spacing requirements can also be used.

Channels Two types of channels are covered in this Manual: • C-shapes (also known as American standard channels), which have a slope of approximately 162/3% (2 on 12) on the inner flange surfaces. • MC-shapes (also known as miscellaneous channels), which have a slope other than 162/3% (2 on 12) on the inner flange surfaces. These shapes are designated by the mark C or MC, nominal depth (in.) and nominal weight (lb/ft). For example, a C12×25 is a C-shape that is nominally 12 in. deep and weighs 25 lb/ft. The following dimensional and property information is given in this Manual for the channels covered in ASTM A6: • Design dimensions, detailing dimensions, and axial, flexural and torsional properties are given in Tables 1-5 and 1-6 for C- and MC-shapes, respectively. • SI-equivalent designations are given in Table 17-3. For the definitions of the tabulated variables, refer to the Nomenclature section at the back of this Manual.

Angles Angles (also known as L-shapes) have legs of equal thickness and either equal or unequal leg sizes. Angles are designated by the mark L, leg sizes (in.) and thickness (in.). For example, an L4×3×1/2 is an angle with one 4-in. leg, one 3-in. leg, and 1/2-in. thickness. The following dimensional and property information is given in this Manual for the angles covered in ASTM A6: • Design dimensions, detailing dimensions, and axial, flexural and flexural-torsional properties are given in Table 1-7. The effects of leg-to-leg and toe fillet radii have been considered in the determination of these section properties. The Sz value that is given in Table 1-7 is based on the largest perpendicular distance measured from the z-axis to the center of the thickness at the tip of the angle toe(s) or heel. Additional properties of single angles are provided in the digital shapes database available at www.aisc.org. These properties are used for calculations involving z and w principal axes. For unequal leg angles, the database includes I, and values of S at the toe of the short leg, the heel, and the toe of the long leg, for the w and z principal axes. For equal leg angles, the database includes I, and values of S at the toe of the leg and the heel, for w and z principal axes. • Workable gages on angle legs are tabulated in Table 1-7A. • Compactness criteria for angles are tabulated in Table 1-7B. • SI-equivalent designations are given in Table 17-4. For the definitions of the tabulated variables, refer to the Nomenclature section at the back of this Manual. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Structural Tees (WT-, MT- and ST-Shapes) Three types of structural tees are covered in this Manual: • WT-shapes, which are made from W-shapes • MT-shapes, which are made from M-shapes • ST-shapes, which are made from S-shapes These shapes are designated by the mark WT, MT or ST, nominal depth (in.) and nominal weight (lb/ft). WT-, MT- and ST-shapes are split (sheared or thermal-cut) from W-, M- and S-shapes, respectively, and have half the nominal depth and weight of that shape. For example, a WT12×27.5 is a structural tee split from a W-shape (W24×55), is nominally 12 in. deep and weighs 27.5 lb/ft. Although off-center splitting or splitting on two lines can be obtained by special order, the resulting nonstandard shape is not covered in this Manual. The following dimensional and property information is given in this Manual for the structural tees cut from the W-, M- and S-shapes covered in ASTM A6: • Design dimensions, detailing dimensions, and axial, flexural and torsional properties are given in Tables 1-8, 1-9 and 1-10 for WT-, MT- and ST-shapes, respectively. • SI-equivalent designations are given in Table 17-5 for WT-shapes and in Table 17-6 for MT- and ST-shapes. For the definitions of the tabulated variables, refer to the Nomenclature section at the back of this Manual.

Hollow Structural Sections (HSS) Three types of HSS are covered in this Manual: • Rectangular HSS, which have an essentially rectangular cross section, except for rounded corners, and uniform wall thickness, except at the weld seam(s) • Square HSS, which have an essentially square cross section, except for rounded corners, and uniform wall thickness, except at the weld seam(s) • Round HSS, which have an essentially round cross section and uniform wall thickness, except at the weld seam(s) In each case, ASTM A500 covers only electric-resistance-welded (ERW) HSS with a maximum periphery of 64 in. The coverage of HSS in this Manual is similarly limited. Rectangular HSS are designated by the mark HSS, overall outside dimensions (in.), and wall thickness (in.), with all dimensions expressed as fractional numbers. For example, an HSS10×10×1/2 is nominally 10 in. by 10 in. with a 1/2-in. wall thickness. Round HSS are designated by the term HSS, nominal outside diameter (in.), and wall thickness (in.) with both dimensions expressed to three decimal places. For example, an HSS10.000×0.500 is nominally 10 in. in diameter with a 1/2-in. nominal wall thickness. Per AISC Specification Section B4.2, the wall thickness used in design, tdes, is taken as 0.93 times the nominal wall thickness, tnom. The rationale for this requirement is explained in the corresponding Specification Commentary Section B4.2. In calculating the tabulated b/t and h/t ratios, the outside corner radii are taken as 1.5tdes for rectangular and square HSS, per AISC Specification Section B4.1. In other tabulated design dimensions, the corner radii are taken as 2tdes. In the tabulated workable flat dimenAMERICAN INSTITUTE OF STEEL CONSTRUCTION

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sions of rectangular (and square) HSS, the outside corner radii are taken as 2.25tnom. The term workable flat refers to a reasonable flat width or depth of material for use in making connections to HSS. The workable flat dimension is provided as a reflection of current industry practice, although the tolerances of ASTM A500 allow a greater maximum corner radius of 3tnom. The following dimensional and property information is given in this Manual for the HSS covered in ASTM A500, A501, A618 or A847: • Design dimensions, detailing dimensions, and axial, strong-axis flexural, weak-axis flexural, torsional, and flexural-torsional properties are given in Tables 1-11 and 1-12 for rectangular and square HSS, respectively. • Design dimensions, detailing dimensions, and axial, flexural and torsional properties are given in Table 1-13 for round HSS. • SI-equivalent designations are given in Tables 17-7, 17-8 and 17-9 for rectangular, square and round HSS, respectively. • Compactness criteria of rectangular and square HSS are given in Table 1-12A. For the definitions of the tabulated variables, refer to the Nomenclature section at the back of this Manual.

Pipe Pipes have an essentially round cross section and uniform thickness, except at the weld seam(s) for welded pipe. Pipes up to and including NPS 12 are designated by the term Pipe, nominal diameter (in.) and weight class (Std., x-Strong, xx-Strong). NPS stands for nominal pipe size. For example, Pipe 5 Std. denotes a pipe with a 5-in. nominal diameter and a 0.258-in. wall thickness, which corresponds to the standard weight series. Pipes with wall thicknesses that do not correspond to the foregoing weight classes are designated by the term Pipe, outside diameter (in.), and wall thickness (in.) with both expressed to three decimal places. For example, Pipe 14.000×0.375 and Pipe 5.563×0.500 are proper designations. Per AISC Specification Section B4.2, the wall thickness used in design, tdes, is taken as 0.93 times the nominal wall thickness, tnom. The rationale for this requirement is explained in the corresponding Specification Commentary Section B4.2. The following dimensional and property information is given in this Manual for the pipes covered in ASTM A53: • Design dimensions, detailing dimensions, and axial, flexural and torsional properties are given in Table 1-14. • SI-equivalent designations are given in Table 17-10. For the definitions of the tabulated variables, refer to the Nomenclature section at the back of this Manual.

Double Angles Double angles (also known as 2L-shapes) are made with two angles that are interconnected through their back-to-back legs along the length of the member, either in contact for the full length or separated by spacers at the points of interconnection.

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These shapes are designated by the mark 2L, the sizes and thickness of their legs (in.), and their orientation when the angle legs are not of equal size (LLBB or SLBB).1 For example, a 2L4×3×1/2 LLBB has two angles with one 4-in. leg and one 3-in. leg and the 4-in. legs are back-to-back; a 2L4×3×1/2 SLBB is similar, except the 3-in. legs are back-to-back. In both cases, the legs are 1/2-in. thick. The following dimensional and property information is given in this Manual for the double angles built-up from the angles covered in ASTM A6: • Design dimensions, detailing dimensions, and axial, strong-axis flexural, weak-axis flexural, torsional, and flexural-torsional properties are given in Table 1-15 for equalleg, LLBB and SLBB angles. In each case, angle separations of zero in., 3/ 8 in. and 3 /4 in. are covered. The effects of leg-to-leg and toe fillet radii have been considered in the determination of these section properties. For workable gages on legs of angles, see Table 1-7A. For the definitions of the tabulated variables, refer to the Nomenclature section at the back of this Manual.

Double Channels Double channels (also known as 2C- and 2MC-shapes) are made with two channels that are interconnected through their back-to-back webs along the length of the member, either in contact for the full length or separated by spacers at the points of interconnection. These shapes are designated by the mark 2C or 2MC, nominal depth (in.), and nominal weight per channel (lb/ft). For example, a 2C12×25 is a double channel that consists of two channels that are each nominally 12 in. deep and each weigh 25 lb/ft. The following dimensional and property information is given in this Manual for the double channels built-up from the channels covered in ASTM A6: • Design dimensions, detailing dimensions, and axial, strong-axis flexural, and weakaxis flexural properties are given in Tables 1-16 and 1-17 for 2C- and 2MC-shapes, respectively. In each case, channel separations of zero, 3/ 8 in. and 3/ 4 in. are covered. For the definitions of the tabulated variables, refer to the Nomenclature section at the back of this Manual.

W-Shapes and S-Shapes with Cap Channels Common combined sections made with W- or S-shapes and channels (C- or MC-shapes) are tabulated in this Manual. In either case, the channel web is interconnected to the W-shape or S-shape top flange, respectively, with the flange toes down. The interconnection of the two elements must be designed for the horizontal shear, q, where q=

VQ I

(1-1)

1 LLBB stands for long legs back-to-back. SLBB stands for short legs back-to-back. Alternatively, the orientations LLV and SLV, which stand for long legs vertical and short legs vertical, respectively, can be used.

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where I = moment of inertia of the combined cross section, in.4 Q = first moment of the channel area about the neutral axis of the combined cross section, in.3 V = vertical shear, kips q = horizontal shear, kips/in. The effects of other forces, such as crane horizontal and lateral forces, may also require consideration, when applicable. The following dimensional and property information is given in this Manual for combined sections built-up from the W-shapes, S-shapes and cap channels covered in ASTM A6: • Design dimensions, detailing dimensions, and axial, strong-axis flexural, and weakaxis flexural properties of W-shapes with cap channels are given in Table 1-19. • Design dimensions, detailing dimensions, and axial, strong-axis flexural, and weakaxis flexural properties of S-shapes with cap channels are given in Table 1-20. For the definitions of the tabulated variables, refer to the Nomenclature section at the back of this Manual.

Plate Products Plate products may be ordered as sheet, strip or bar material. Sheet and strip are distinguished from structural bars and plates by their dimensional characteristics, as outlined in Table 2-3 and Table 2-5. The historical classification system for structural bars and plates suggests that there is only a physical difference between them based upon size and production procedure. In raw form, flat stock has historically been classified as a bar if it is less than or equal to 8 in. wide and as a plate if it is greater than 8 in. wide. Bars are rolled between horizontal and vertical rolls and trimmed to length by shearing or thermal cutting on the ends only. Plates are generally produced using one of two methods: 1. Sheared plates are rolled between horizontal rolls and trimmed to width and length by shearing or thermal cutting on the edges and ends; or 2. Stripped plates are sheared or thermal cut from wider sheared plates. There is very little, if any, structural difference between plates and bars. Consequently, the term plate is becoming a universally applied term today and a PL1/2 in.×41/2 in.×1ft 3 in., for example, might be fabricated from plate or bar stock. For structural plates, the preferred practice is to specify thickness in 1/16-in. increments up to 3/ 8-in. thickness, 1/8-in. increments over 3/ 8-in. to 1-in. thickness, and 1/4-in. increments over 1-in. thickness. The current extreme width for sheared plates is 200 in. Because mill practice regarding plate widths vary, individual mills should be consulted to determine preferences. For bars, the preferred practice is to specify width in 1/4-in. increments, and thickness and diameter in 1/8-in. increments.

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Raised-Pattern Floor Plates Weights of raised-pattern floor plates are given in Table 1-18. Raised-pattern floor plates are commonly available in widths up to 120 in. For larger plate widths, see literature available from floor plate producers.

Crane Rails Although crane rails are not listed as structural steel in the AISC Code of Standard Practice Section 2.1, this information is provided because some fabricators may choose to provide crane rails. Crane rails are designated by unit weight in lb/yard. Dimensions and properties for the crane rails shown are given in Table 1-21. Crane rails can be either heat treated or end hardened to reduce wear. For additional information or for profiles and properties of crane rails not listed, manufacturer’s catalogs should be consulted. For crane-rail connections, see Part 15.

Other Structural Products The following other structural products are covered in this Manual as indicated: • High-strength bolts, common bolts, washers, nuts and direct-tension-indicator washers are covered in Part 7. • Welding filler metals and fluxes are covered in Part 8. • Forged steel structural hardware items, such as clevises, turnbuckles, sleeve nuts, recessed-pin nuts, and cotter pins are covered in Part 15. • Anchor rods and threaded rods are covered in Part 14.

STANDARD MILL PRACTICES The production of structural products is subject to unavoidable variations relative to the theoretical dimensions and profiles, due to many factors, including roll wear, roll dressing practices and temperature effects. Such variations are limited by the dimensional and profile tolerances as summarized below.

Hot-Rolled Structural Shapes Acceptable dimensional tolerances for hot-rolled structural shapes (W-, M-, S- and HPshapes), channels (C- and MC-shapes), and angles are given in ASTM A6 Section 12 and summarized in Tables 1-22 through 1-26. Supplementary information, including permissible variations for sheet and strip and for other grades of steel, can also be found in literature from steel plate producers and the Association of Iron and Steel Technology.

Hollow Structural Sections Acceptable dimensional tolerances for HSS are given in ASTM A500 Section 11, A501 Section 12, A618 Section 8, or A847 Section 10, as applicable, and summarized in Tables 1-27 and 1-28, for rectangular and round HSS, respectively. Supplementary information

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can also be found in literature from HSS producers and the Steel Tube Institute, such as Recommended Methods to Check Dimensional Tolerances on Hollow Structural Sections (HSS) Made to ASTM A500.

Pipe Acceptable dimensional tolerances for pipes are given in ASTM A53 Section 10 and summarized in Table 1-28. Supplementary information can also be found in literature from pipe producers.

Plate Products Acceptable dimensional tolerances for plate products are given in ASTM A6 Section 12 and summarized in Table 1-29. Note that plate thickness can be specified in inches or by weight per square foot, and separate tolerances apply to each method. No decimal edge thickness can be assured for plate specified by the latter method. Supplementary information, including permissible variations for sheet and strip and for other grades of steel, can also be found in literature from steel plate producers and the Association of Iron and Steel Technology.

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PART 1 REFERENCES

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PART 1 REFERENCES Ruddy, J.L., Marlo, J.P., Ioannides, S.A. and Alfawakhiri, F. (2003), Fire Resistance of Structural Steel Framing, Design Guide 19, AISC, Chicago, IL. Seaburg, P.A. and Carter, C.J. (1997), Torsional Analysis of Structural Steel Members, Design Guide 9, AISC, Chicago, IL.

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Table 1-1

W-Shapes Dimensions Web

Flange

Shape

Area, A

Depth, d

W44×335 c ×290 c ×262 c ×230 c,v

in.2 98.5 85.4 77.2 67.8

in. 44.0 44 43.6 435/8 43.3 431/4 42.9 427/8

in. in. in. 1/2 1.03 1 15.9 16 7/16 15.8 157/8 0.865 7/8 0.785 13/16 7/16 15.8 15 3/4 0.710 11/16 3/8 15.8 153/4

W40×593 h ×503 h ×431h ×397 h ×372 h ×362 h ×324 ×297 c ×277 c ×249 c ×215 c ×199 c

174 148 127 117 110 106 95.3 87.3 81.5 73.5 63.5 58.8

43.0 42.1 41.3 41.0 40.6 40.6 40.2 39.8 39.7 39.4 39.0 38.7

43 42 411/4 41 405/8 401/2 401/8 397/8 393/4 393/8 39 385/8

1.79 1.54 1.34 1.22 1.16 1.12 1.00 0.930 0.830 0.750 0.650 0.650

113/16 19/16 15/16 11/4 13/16 11/8 1 15/16 13/16 3/4 5/8 5/8

W40×392 h 116 ×331h 97.7 ×327 h 95.9 ×294 86.2 ×278 82.3 ×264 77.4 ×235 c 69.1 ×211c 62.1 ×183 c 53.3 ×167 c 49.3 ×149 c,v 43.8

41.6 40.8 40.8 40.4 40.2 40.0 39.7 39.4 39.0 38.6 38.2

415/8 403/4 403/4 403/8 401/8 40 393/4 393/8 39 385/8 381/4

1.42 1.22 1.18 1.06 1.03 0.960 0.830 0.750 0.650 0.650 0.630

17/16 11/4 13/16 11/16 1 15/16 13/16 3/4 5/8 5/8 5/8

c h v

Thickness, tw

tw ᎏ 2

15/16 13/16 11/16 5/8 5/8 9/16 1/2 1/2 7/16 3/8 5/16 5/16 3/4 5/8 5/8 9/16 1/2 1/2 7/16 3/8 5/16 5/16 5/16

Width, bf

Distance

Thickness, tf

kdes

kdet

in. 1.77 13/4 1.58 19/16 1.42 17/16 1.22 11/4

in. 2.56 2.36 2.20 2.01

in. 25/8 27/16 21/4 21/16

Workable Gage in. in. in. 15/16 383/4 51/2 11/4 13/16 13/16

k

k1

T

16.7 16.4 16.2 16.1 16.1 16.0 15.9 15.8 15.8 15.8 15.8 15.8

163/4 16 3/8 161/4 161/8 161/8 16 157/8 157/8 157/8 153/4 153/4 153/4

3.23 2.76 2.36 2.20 2.05 2.01 1.81 1.65 1.58 1.42 1.22 1.07

31/4 23/4 23/8 23/16 21/16 2 113/16 15/8 19/16 17/16 11/4 11/16

4.41 3.94 3.54 3.38 3.23 3.19 2.99 2.83 2.76 2.60 2.40 2.25

41/2 4 35/8 31/2 35/16 31/4 31/16 215/16 27/8 211/16 21/2 25/16

21/8 34 2 17/8 113/16 113/16 13/4 111/16 111/16 15/8 19/16 19/16 19/16

71/2

12.4 12.2 12.1 12.0 12.0 11.9 11.9 11.8 11.8 11.8 11.8

123/8 121/8 121/8 12 12 117/8 117/8 113/4 113/4 113/4 113/4

2.52 2.13 2.13 1.93 1.81 1.73 1.58 1.42 1.20 1.03 0.830

21/2 21/8 21/8 115/16 113/16 13/4 19/16 17/16 13/16 1 13/16

3.70 3.31 3.31 3.11 2.99 2.91 2.76 2.60 2.38 2.21 2.01

313/16 33/8 33/8 33/16 31/16 3 27/8 211/16 21/2 25/16 21/8

115/16 34 113/16 113/16 13/4 13/4 111/16 15/8 19/16 19/16 19/16 11/2

71/2

Shape is slender for compression with Fy = 50 ksi. Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi.

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Table 1-1 (continued)

W-Shapes Properties W44-W40 Nominal Wt.

Compact Section Criteria

Axis X-X

Axis Y-Y

rts

I in.4 1200 1040 923 796

S in.3 150 132 117 101

r in. 3.49 3.49 3.47 3.43

Z in.3 236 205 182 157

in. 4.24 4.20 4.17 4.13

Cw

in. 42.2 42.0 41.9 41.7

in.4 74.7 50.9 37.3 24.9

in.6 535000 461000 405000 346000

335 290 262 230

4.50 5.02 5.57 6.45

38.0 45.0 49.6 54.8

593 503 431 397 372 362 324 297 277 249 215 199

2.58 2.98 3.44 3.66 3.93 3.99 4.40 4.80 5.03 5.55 6.45 7.39

19.1 22.3 25.5 28.0 29.5 30.5 34.2 36.8 41.2 45.6 52.6 52.6

50400 41600 34800 32000 29600 28900 25600 23200 21900 19600 16700 14900

2340 1980 1690 1560 1460 1420 1280 1170 1100 993 859 770

17.0 16.8 16.6 16.6 16.5 16.5 16.4 16.3 16.4 16.3 16.2 16.0

2760 2320 1960 1800 1680 1640 1460 1330 1250 1120 964 869

2520 2040 1690 1540 1420 1380 1220 1090 1040 926 803 695

302 249 208 191 177 173 153 138 132 118 101 88.2

3.80 3.72 3.65 3.64 3.60 3.60 3.58 3.54 3.58 3.55 3.54 3.45

481 394 328 300 277 270 239 215 204 182 156 137

4.63 4.50 4.41 4.38 4.33 4.33 4.27 4.22 4.25 4.21 4.19 4.12

39.8 39.3 38.9 38.8 38.6 38.6 38.4 38.2 38.1 38.0 37.8 37.6

445 277 177 142 116 109 79.4 61.2 51.5 38.1 24.8 18.3

997000 789000 638000 579000 528000 513000 448000 399000 379000 334000 284000 246000

392 331 327 294 278 264 235 211 183 167 149

2.45 2.86 2.85 3.11 3.31 3.45 3.77 4.17 4.92 5.76 7.11

24.1 28.0 29.0 32.2 33.3 35.6 41.2 45.6 52.6 52.6 54.3

29900 24700 24500 21900 20500 19400 17400 15500 13200 11600 9800

1440 1210 1200 1080 1020 971 875 786 675 600 513

16.1 15.9 16.0 15.9 15.8 15.8 15.9 15.8 15.7 15.3 15.0

1710 1430 1410 1270 1190 1130 1010 906 774 693 598

803 644 640 562 521 493 444 390 331 283 229

130 106 105 93.5 87.1 82.6 74.6 66.1 56.0 47.9 38.8

2.64 2.57 2.58 2.55 2.52 2.52 2.54 2.51 2.49 2.40 2.29

212 172 170 150 140 132 118 105 88.3 76.0 62.2

3.30 3.21 3.21 3.16 3.13 3.12 3.11 3.07 3.04 2.98 2.89

39.1 38.7 38.7 38.5 38.4 38.3 38.1 38.0 37.8 37.6 37.4

172 105 103 76.6 65.0 56.1 41.3 30.4 19.3 14.0 9.36

306000 241000 239000 208000 192000 181000 161000 141000 118000 99700 80000

h ᎏ tw

Z in.3 1620 1410 1270 1100

J

I S in.4 in.3 31100 1410 27000 1240 24100 1110 20800 971

b ᎏf lb/ft 2tf

r in. 17.8 17.8 17.7 17.5

ho

Torsional Properties

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Table 1-1 (continued)

W-Shapes Dimensions Web Area, A

Shape

Depth, d

in.2 W36×652 h 192 ×529 h 156 ×487 h 143 ×441h 130 ×395 h 116 ×361h 106 ×330 96.9 ×302 89.0 ×282 c 82.9 ×262 c 77.2 ×247 c 72.5 ×231c 68.2

in. 41.1 41 39.8 393/4 39.3 393/8 38.9 387/8 38.4 383/8 38.0 38 37.7 375/8 37.3 373/8 37.1 371/8 36.9 367/8 36.7 365/8 36.5 361/2

W36×256 ×232 c ×210 c ×194 c ×182 c ×170 c ×160 c ×150 c ×135 c,v

37.4 37.1 36.7 36.5 36.3 36.2 36.0 35.9 35.6

75.3 68.0 61.9 57.0 53.6 50.0 47.0 44.3 39.9

h

373/8 371/8 363/4 361/2 363/8 361/8 36 357/8 351/2

Thickness, tw

Flange tw ᎏ 2

in. in. in. 1.97 2 1 17.6 175/8 13/16 17.2 171/4 1.61 15/8 3/4 1.50 11/2 17.1 171/8 11/16 17.0 17 1.36 13/8 5/8 1.22 11/4 16.8 167/8 9/16 16.7 163/4 1.12 11/8 1/2 1.02 1 16.6 165/8 0.945 15/16 1/2 16.7 165/8 7/16 16.6 165/8 0.885 7/8 0.840 13/16 7/16 16.6 161/2 0.800 13/16 7/16 16.5 161/2 3/8 0.760 3/4 16.5 161/2 0.960 0.870 0.830 0.765 0.725 0.680 0.650 0.625 0.600

15/16

1/2

7/8

7/16

13/16

7/16

3/4

3/8

3/4 11/16

3/8 3/8

5/8

5/16

5/8

5/16

5/8

11/4

5/16 5/8

W33×387 114 ×354 h 104 ×318 93.7 ×291 85.6 ×263 77.4 ×241c 71.1 ×221c 65.3 ×201c 59.1

36.0 35.6 35.2 34.8 34.5 34.2 33.9 33.7

36 351/2 351/8 347/8 341/2 341/8 337/8 335/8

1.26 1.16 13/16 1.04 11/16 0.960 15/16 0.870 7/8 0.830 13/16 0.775 3/4 0.715 11/16

3/8 3/8

W33×169 c ×152 c ×141c ×130 c ×118 c,v

33.8 33.5 33.3 33.1 32.9

337/8 331/2 331/4 331/8 327/8

0.670 0.635 0.605 0.580 0.550

11/16

3/8

5/8

5/16

5/8

5/16

9/16

5/16

9/16

5/16

c h v

49.5 44.9 41.5 38.3 34.7

Width, bf

5/8 9/16 1/2 7/16 7/16

Distance

k

Thickness, tf

kdes

kdet

in. 3.54 39/16 2.91 215/16 2.68 211/16 2.44 27/16 2.20 23/16 2.01 2 1.85 17/8 1.68 111/16 1.57 19/16 1.44 17/16 1.35 13/8 1.26 11/4

in. 4.49 3.86 3.63 3.39 3.15 2.96 2.80 2.63 2.52 2.39 2.30 2.21

in. 413/16 43/16 4 33/4 37/16 35/16 31/8 3 27/8 23/4 25/8 29/16

in. 23/16 2 17/8 17/8 113/16 13/4 13/4 111/16 15/8 15/8 15/8 19/16

k1

Workable Gage in. in. 313/8 71/2

T

12.2 12.1 12.2 12.1 12.1 12.0 12.0 12.0 12.0

121/4 121/8 121/8 121/8 121/8 12 12 12 12

1.73 1.57 1.36 1.26 1.18 1.10 1.02 0.940 0.790

13/4 19/16 13/8 11/4 13/16 11/8 1 15/16 13/16

2.48 2.32 2.11 2.01 1.93 1.85 1.77 1.69 1.54

25/8 27/16 25/16 23/16 21/8 2 115/16 17/8 111/16

15/16 321/8 11/4 11/4 13/16 13/16 13/16 11/8 11/8 11/8

51/2

16.2 16.1 16.0 15.9 15.8 15.9 15.8 15.7

161/4 161/8 16 157/8 153/4 157/8 153/4 153/4

2.28 2.09 1.89 1.73 1.57 1.40 1.28 1.15

21/4 21/16 17/8 13/4 19/16 13/8 11/4 11/8

3.07 2.88 2.68 2.52 2.36 2.19 2.06 1.94

33/16 215/16 23/4 25/8 27/16 21/4 21/8 2

17/16 295/8 13/8 15/16 15/16 11/4 11/4 13/16 13/16

51/2

11.5 11.6 11.5 11.5 11.5

111/2 115/8 111/2 111/2 111/2

1.22 11/4 1.06 11/16 0.960 15/16 0.855 7/8 0.740 3/4

1.92 1.76 1.66 1.56 1.44

21/8 115/16 113/16 13/4 15/8

13/16 295/8 11/8 11/8 11/8 11/8

51/2

Shape is slender for compression with Fy = 50 ksi. Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi.

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Table 1-1 (continued)

W-Shapes Properties W36-W33 Nominal Wt.

Compact Section Criteria

Axis X-X

652 529 487 441 395 361 330 302 282 262 247 231

2.48 2.96 3.19 3.48 3.83 4.16 4.49 4.96 5.29 5.75 6.11 6.54

16.3 19.9 21.4 23.6 26.3 28.6 31.4 33.9 36.2 38.2 40.1 42.2

I in.4 50600 39600 36000 32100 28500 25700 23300 21100 19600 17900 16700 15600

256 232 210 194 182 170 160 150 135

3.53 3.86 4.48 4.81 5.12 5.47 5.88 6.37 7.56

33.8 37.3 39.1 42.4 44.8 47.7 49.9 51.9 54.1

16800 15000 13200 12100 11300 10500 9760 9040 7800

895 809 719 664 623 581 542 504 439

387 354 318 291 263 241 221 201

3.55 3.85 4.23 4.60 5.03 5.66 6.20 6.85

23.7 25.7 28.7 31.0 34.3 35.9 38.5 41.7

24300 22000 19500 17700 15900 14200 12900 11600

1350 1240 1110 1020 919 831 759 686

14.6 14.5 14.5 14.4 14.3 14.1 14.1 14.0

169 152 141 130 118

4.71 5.48 6.01 6.73 7.76

44.7 47.2 49.6 51.7 54.5

9290 8160 7450 6710 5900

549 487 448 406 359

13.7 13.5 13.4 13.2 13.0

b ᎏf lb/ft 2tf

h ᎏ tw

S in.3 2460 1990 1830 1650 1490 1350 1240 1130 1050 972 913 854

r in. 16.2 16.0 15.8 15.7 15.7 15.6 15.5 15.4 15.4 15.3 15.2 15.1

Axis Y-Y

Z in.3 2910 2330 2130 1910 1710 1550 1410 1280 1190 1100 1030 963

14.9 1040 14.8 936 14.6 833 14.6 767 14.5 718 14.5 668 14.4 624 14.3 581 14.0 509

I in.4 3230 2490 2250 1990 1750 1570 1420 1300 1200 1090 1010 940

S in.3 367 289 263 235 208 188 171 156 144 132 123 114

r in. 4.10 4.00 3.96 3.92 3.88 3.85 3.83 3.82 3.80 3.76 3.74 3.71

rts

ho

J

Z in.3 581 454 412 368 325 293 265 241 223 204 190 176

in. 4.96 4.80 4.74 4.69 4.61 4.58 4.53 4.53 4.50 4.46 4.42 4.40

in. 37.6 36.9 36.6 36.5 36.2 36.0 35.9 35.6 35.5 35.5 35.4 35.2

2.65 137 2.62 122 2.58 107 2.56 97.7 2.55 90.7 2.53 83.8 2.50 77.3 2.47 70.9 2.38 59.7

3.24 3.21 3.18 3.15 3.13 3.11 3.09 3.06 2.99

35.7 35.5 35.3 35.2 35.1 35.1 35.0 35.0 34.8

4.49 4.44 4.40 4.34 4.31 4.29 4.25 4.21

33.7 33.5 33.3 33.1 32.9 32.8 32.6 32.6

3.03 3.01 2.98 2.94 2.89

32.6 32.4 32.3 32.2 32.2

528 468 411 375 347 320 295 270 225

86.5 77.2 67.5 61.9 57.6 53.2 49.1 45.1 37.7

1560 1420 1270 1160 1040 940 857 773

1620 1460 1290 1160 1040 933 840 749

200 181 161 146 131 118 106 95.2

3.77 3.74 3.71 3.68 3.66 3.62 3.59 3.56

629 559 514 467 415

310 273 246 218 187

53.9 47.2 42.7 37.9 32.6

2.50 2.47 2.43 2.39 2.32

312 282 250 226 202 182 164 147 84.4 73.9 66.9 59.5 51.3

Torsional Properties

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.4 593 327 258 194 142 109 84.3 64.3 52.7 41.6 34.7 28.7 52.9 39.6 28.0 22.2 18.5 15.1 12.4 10.1 7.00 148 115 84.4 65.1 48.7 36.2 27.8 20.8 17.7 12.4 9.70 7.37 5.30

Cw in.6 1130000 846000 754000 661000 575000 509000 456000 412000 378000 342000 316000 292000 168000 148000 128000 116000 107000 98500 90200 82200 68100 459000 408000 357000 319000 281000 251000 224000 198000 82400 71700 64400 56600 48300

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DIMENSIONS AND PROPERTIES

Table 1-1 (continued)

W-Shapes Dimensions Web Shape

Area, A

Depth, d

Thickness, tw

in.2 W30×391 h 115 ×357 h 105 ×326 h 95.9 ×292 86.0 ×261 77.0 ×235 69.3 ×211 62.3 ×191 c 56.1 ×173 c 50.9

in. 33.2 331/4 32.8 323/4 32.4 323/8 32.0 32 31.6 315/8 31.3 311/4 30.9 31 30.7 305/8 30.4 301/2

W30×148 c ×132 c ×124 c ×116 c ×108 c ×99 c ×90 c,v

43.6 38.8 36.5 34.2 31.7 29.0 26.3

30.7 30.3 30.2 30.0 29.8 29.7 29.5

305/8 301/4 301/8 30 297/8 295/8 291/2

0.650 0.615 0.585 0.565 0.545 0.520 0.470

W27×539 h 159 ×368 h 109 ×336 h 99.2 ×307 h 90.2 ×281 83.1 ×258 76.1 ×235 69.4 ×217 63.9 ×194 57.1 ×178 52.5 ×161c 47.6 ×146 c 43.2

32.5 30.4 30.0 29.6 29.3 29.0 28.7 28.4 28.1 27.8 27.6 27.4

321/2 303/8 30 295/8 291/4 29 285/8 283/8 281/8 273/4 275/8 273/8

1.97 1.38 1.26 1.16 1.06 0.980 0.910 0.830 0.750 0.725 0.660 0.605

W27×129 c ×114 c ×102 c ×94 c ×84 c

27.6 27.3 27.1 26.9 26.7

275/8 271/4 271/8 267/8 263/4

0.610 0.570 0.515 0.490 0.460

37.8 33.6 30.0 27.6 24.7

Flange tw ᎏ 2

Width, bf

in. in. in. 11/16 15.6 155/8 1.36 13/8 5/8 1.24 11/4 15.5 151/2 9/16 15.4 153/8 1.14 11/8 1/2 1.02 1 15.3 151/4 0.930 15/16 1/2 15.2 151/8 0.830 13/16 7/16 15.1 15 3/8 0.775 3/4 15.1 151/8 0.710 11/16 3/8 15.0 15 5/16 15.0 15 0.655 5/8 5/8

5/16

5/8

5/16

9/16

5/16

9/16

5/16

9/16

5/16

1/2

1/4

1/2

1/4

2 1 11/16 13/8 5/8 11/4 13/16 5/8 11/16 9/16 1/2 1 15/16 1/2 13/16 7/16 3/4 3/8 3/4 3/8 11/16 3/8 5/8 5/16 5/8

5/16

9/16

5/16

1/2

1/4

1/2

1/4

7/16

1/4

Distance

k

Thickness, tf

kdes

kdet

in. 2.44 2 7/16 2.24 21/4 2.05 21/16 1.85 17/8 1.65 15/8 1.50 11/2 1.32 15/16 1.19 13/16 1.07 11/16

in. 3.23 3.03 2.84 2.64 2.44 2.29 2.10 1.97 1.85

in. 33/8 31/8 215/16 23/4 29/16 23/8 21/4 21/16 2

in. 11/2 17/16 13/8 15/16 15/16 11/4 13/16 13/16 11/8

k1

Workable Gage in. in. 261/2 51/2

T

10.5 10.5 10.5 10.5 10.5 10.5 10.4

101/2 101/2 101/2 101/2 101/2 101/2 103/8

1.18 13/16 1.00 1 0.930 15/16 0.850 7/8 0.760 3/4 0.670 11/16 0.610 5/8

1.83 1.65 1.58 1.50 1.41 1.32 1.26

21/16 17/8 113/16 13/4 111/16 19/16 11/2

11/8 261/2 11/8 11/8 11/8 11/8 11/16 11/16

51/2

15.3 14.7 14.6 14.4 14.4 14.3 14.2 14.1 14.0 14.1 14.0 14.0

151/4 145/8 141/2 141/2 143/8 141/4 141/4 141/8 14 141/8 14 14

3.54 2.48 2.28 2.09 1.93 1.77 1.61 1.50 1.34 1.19 1.08 0.975

3 9/16 21/2 21/4 21/16 115/16 13/4 15/8 11/2 15/16 13/16 11/16 1

4.33 3.27 3.07 2.88 2.72 2.56 2.40 2.29 2.13 1.98 1.87 1.76

47/16 33/8 33/16 3 213/16 211/16 21/2 23/8 21/4 21/16 2 17/8

113/16 235/8 51/2 g 11/2 51/2 17/16 17/16 13/8 15/16 15/16 11/4 13/16 13/16 13/16 11/8

10.0 10.1 10.0 10.0 10.0

10 101/8 10 10 10

1.10 11/8 0.930 15/16 0.830 13/16 0.745 3/4 0.640 5/8

1.70 1.53 1.43 1.34 1.24

2 113/16 13/4 15/8 19/16

11/8 235/8 11/8 11/16 11/16 11/16

51/2

Shape is slender for compression with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. v Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi. c

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

1–17

Table 1-1 (continued)

W-Shapes Properties W30-W27 Nominal Wt.

Compact Section Criteria

b ᎏf lb/ft 2tf

h ᎏ tw

391 357 326 292 261 235 211 191 173

3.19 3.45 3.75 4.12 4.59 5.02 5.74 6.35 7.04

19.7 21.6 23.4 26.2 28.7 32.2 34.5 37.7 40.8

148 132 124 116 108 99 90

4.44 5.27 5.65 6.17 6.89 7.80 8.52

41.6 43.9 46.2 47.8 49.6 51.9 57.5

539 368 336 307 281 258 235 217 194 178 161 146

2.15 2.96 3.19 3.46 3.72 4.03 4.41 4.71 5.24 5.92 6.49 7.16

12.1 17.3 18.9 20.6 22.5 24.4 26.2 28.7 31.8 32.9 36.1 39.4

129 114 102 94 84

4.55 5.41 6.03 6.70 7.78

39.7 42.5 47.1 49.5 52.7

Axis X-X

I S in.4 in.3 20700 1250 18700 1140 16800 1040 14900 930 13100 829 11700 748 10300 665 9200 600 8230 541

Axis Y-Y

rts

ho

J

r in. 13.4 13.3 13.2 13.2 13.1 13.0 12.9 12.8 12.7

Z in.3 1450 1320 1190 1060 943 847 751 675 607

I in.4 1550 1390 1240 1100 959 855 757 673 598

S in.3 198 179 162 144 127 114 100 89.5 79.8

r in. 3.67 3.64 3.60 3.58 3.53 3.51 3.49 3.46 3.42

Z in.3 310 279 252 223 196 175 155 138 123

in. 4.37 4.31 4.26 4.22 4.16 4.13 4.11 4.06 4.03

in. 30.8 30.6 30.4 30.2 30.0 29.8 29.6 29.5 29.3

436 380 355 329 299 269 245

12.4 12.2 12.1 12.0 11.9 11.7 11.7

500 437 408 378 346 312 283

227 196 181 164 146 128 115

43.3 37.2 34.4 31.3 27.9 24.5 22.1

2.28 2.25 2.23 2.19 2.15 2.10 2.09

68.0 58.4 54.0 49.2 43.9 38.6 34.7

2.77 2.75 2.73 2.70 2.67 2.62 2.60

29.5 29.3 29.3 29.2 29.0 29.0 28.9

25600 1570 16200 1060 14600 972 13100 887 11900 814 10800 745 9700 677 8910 627 7860 559 7020 505 6310 458 5660 414

12.7 12.2 12.1 12.0 12.0 11.9 11.8 11.8 11.7 11.6 11.5 11.5

1890 1240 1130 1030 936 852 772 711 631 570 515 464

2110 1310 1180 1050 953 859 769 704 619 555 497 443

277 179 162 146 133 120 108 100 88.1 78.8 70.9 63.5

3.65 3.48 3.45 3.41 3.39 3.36 3.33 3.32 3.29 3.25 3.23 3.20

437 279 252 227 206 187 168 154 136 122 109 97.7

4.41 4.15 4.10 4.04 4.00 3.96 3.92 3.89 3.85 3.83 3.79 3.76

29.0 27.9 27.7 27.5 27.4 27.2 27.1 26.9 26.8 26.6 26.5 26.4

11.2 11.0 11.0 10.9 10.7

395 343 305 278 244

184 159 139 124 106

36.8 31.5 27.8 24.8 21.2

2.21 2.18 2.15 2.12 2.07

57.6 49.3 43.4 38.8 33.2

2.66 2.65 2.62 2.59 2.54

26.5 26.4 26.3 26.2 26.1

6680 5770 5360 4930 4470 3990 3610

4760 4080 3620 3270 2850

345 299 267 243 213

Torsional Properties

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.4 173 134 103 75.2 54.1 40.3 28.4 21.0 15.6 14.5 9.72 7.99 6.43 4.99 3.77 2.84 496 170 131 101 79.5 61.6 47.0 37.6 27.1 20.1 15.1 11.3 11.1 7.33 5.28 4.03 2.81

Cw in.6 366000 324000 287000 250000 215000 190000 166000 146000 129000 49400 42100 38600 34900 30900 26800 24000 443000 255000 226000 199000 178000 159000 141000 128000 111000 98400 87300 77200 32500 27600 24000 21300 17900

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DIMENSIONS AND PROPERTIES

Table 1-1 (continued)

W-Shapes Dimensions Web Shape

Area, A

Depth, d

in.2 W24×370 h 109 ×335 h 98.3 ×306 h 89.7 x279 h 81.9 ×250 73.5 ×229 67.2 ×207 60.7 ×192 56.5 ×176 51.7 ×162 47.8 ×146 43.0 ×131 38.6 ×117 c 34.4 ×104 c 30.7

in. 28.0 28 27.5 271/2 27.1 271/8 26.7 263/4 26.3 263/8 26.0 26 25.7 253/4 25.5 251/2 25.2 251/4 25.0 25 24.7 243/4 24.5 241/2 24.3 241/4 24.1 24

W24×103 c ×94 c ×84 c ×76 c ×68 c

24.5 24.3 24.1 23.9 23.7

Flange

kdes

kdet

in. in. in. 3/4 1.52 11/2 13.7 135/8 11/16 13.5 131/2 1.38 13/8 5/8 1.26 11/4 13.4 133/8 1.16 13/16 5/8 13.3 131/4 1.04 11/16 9/16 13.2 131/8 0.960 15/16 1/2 13.1 131/8 7/16 13.0 13 0.870 7/8 0.810 13/16 7/16 13.0 13 3/8 0.750 3/4 12.9 127/8 0.705 11/16 3/8 13.0 13 5/16 12.9 127/8 0.650 5/8 5/16 12.9 127/8 0.605 5/8 0.550 9/16 5/16 12.8 123/4 1/4 0.500 1/2 12.8 123/4

in. 2.72 23/4 2.48 21/2 2.28 21/4 2.09 21/16 1.89 17/8 1.73 13/4 1.57 19/16 1.46 17/16 1.34 15/16 1.22 11/4 1.09 11/16 0.960 15/16 0.850 7/8 0.750 3/4

in. 3.22 2.98 2.78 2.59 2.39 2.23 2.07 1.96 1.84 1.72 1.59 1.46 1.35 1.25

in. 35/8 33/8 33/16 3 213/16 25/8 21/2 23/8 21/4 21/8 2 17/8 13/4 15/8

Workable Gage in. in. in. 19/16 203/4 51/2 11/2 17/16 17/16 13/8 15/16 11/4 11/4 13/16 13/16 11/8 11/8 11/8 11/16

0.980 1 0.875 7/8 0.770 3/4 0.680 11/16 0.585 9/16

1.48 1.38 1.27 1.18 1.09

17/8 13/4 111/16 19/16 11/2

11/8 203/4 11/16 11/16 11/16 11/16

tw ᎏ 2

0.550 0.515 0.470 0.440 0.415

9/16

5/16

1/2

1/4

1/2

1/4

7/16

1/4

7/16

1/4

W24×62 ×55 c,v

18.2 23.7 0.430 16.2 23.6 235/8 0.395

7/16

1/4

3/8

3/16

W21×201 ×182 ×166 ×147 ×132 ×122 ×111 ×101c

59.3 53.6 48.8 43.2 38.8 35.9 32.6 29.8

15/16

1/2

13/16

7/16

3/4

3/8

3/4

3/8 5/16

c

30.3 27.7 24.7 22.4 20.1

241/2 241/4 241/8 237/8 233/4 233/4

23.0 22.7 22.5 22.1 21.8 21.7 21.5 21.4

23 223/4 221/2 22 217/8 215/8 211/2 213/8

Distance

Thickness, tf

Thickness, tw

0.910 0.830 0.750 0.720 0.650 0.600 0.550 0.500

5/8 5/8 9/16

5/16

1/2

1/4

5/16

Width, bf

9.00 9.07 9.02 8.99 8.97

9 91/8 9 9 9

7.04 7 7.01 7 12.6 12.5 12.4 12.5 12.4 12.4 12.3 12.3

125/8 121/2 123/8 121/2 121/2 123/8 123/8 121/4

0.590 0.505

9/16

1.63 1.48 1.36 1.15 1.04 0.960 0.875 0.800

15/8 11/2 13/8 11/8 11/16 15/16 7/8 13/16

1/2

k

k1

T

51/2

1.09 11/2 11/16 203/4 31/2 g 1.01 17/16 1 203/4 31/2 g 2.13 1.98 1.86 1.65 1.54 1.46 1.38 1.30

21/2 23/8 21/4 2 115/16 113/16 13/4 111/16

15/16 11/4 13/16 13/16 11/8 11/8 11/8 11/16

18

51/2

Shape is slender for compression with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. v Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi. c

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 19

DIMENSIONS AND PROPERTIES

1–19

Table 1-1 (continued)

W-Shapes Properties W24-W21 Nominal Wt.

Compact Section Criteria

Axis X-X

370 335 306 279 250 229 207 192 176 162 146 131 117 104

2.51 2.73 2.94 3.18 3.49 3.79 4.14 4.43 4.81 5.31 5.92 6.70 7.53 8.50

14.2 15.6 17.1 18.6 20.7 22.5 24.8 26.6 28.7 30.6 33.2 35.6 39.2 43.1

I in.4 13400 11900 10700 9600 8490 7650 6820 6260 5680 5170 4580 4020 3540 3100

103 94 84 76 68

4.59 5.18 5.86 6.61 7.66

39.2 41.9 45.9 49.0 52.0

3000 2700 2370 2100 1830

245 222 196 176 154

62 5.97 50.1 55 6.94 54.6

1550 1350 5310 4730 4280 3630 3220 2960 2670 2420

b ᎏf lb/ft 2tf

201 182 166 147 132 122 111 101

3.86 4.22 4.57 5.44 6.01 6.45 7.05 7.68

h ᎏ tw

20.6 22.6 25.0 26.1 28.9 31.3 34.1 37.5

Axis Y-Y

S in.3 957 864 789 718 644 588 531 491 450 414 371 329 291 258

r Z in. in.3 11.1 1130 11.0 1020 10.9 922 10.8 835 10.7 744 10.7 675 10.6 606 10.5 559 10.5 511 10.4 468 10.3 418 10.2 370 10.1 327 10.1 289 10.0 9.87 9.79 9.69 9.55

I in.4 1160 1030 919 823 724 651 578 530 479 443 391 340 297 259

280 254 224 200 177

119 109 94.4 82.5 70.4

131 114

9.23 153 9.11 134

34.5 29.1

461 417 380 329 295 273 249 227

9.47 9.40 9.36 9.17 9.12 9.09 9.05 9.02

530 476 432 373 333 307 279 253

542 483 435 376 333 305 274 248

rts

J

Cw

in. 25.3 25.0 24.8 24.6 24.4 24.3 24.1 24.0 23.9 23.8 23.6 23.5 23.5 23.4

in.4 201 152 117 90.5 66.6 51.3 38.3 30.8 23.9 18.5 13.4 9.50 6.72 4.72

in.6 186000 161000 142000 125000 108000 96100 84100 76300 68400 62600 54600 47100 40800 35200

23.5 23.4 23.3 23.2 23.1

7.07 5.26 3.70 2.68 1.87

16600 15000 12800 11100 9430

1.75 23.1 1.72 23.1

1.71 1.18

4620 3870

40.9 30.7 23.6 15.4 11.3 8.98 6.83 5.21

62000 54400 48500 41100 36000 32700 29200 26200

S in.3 170 152 137 124 110 99.4 88.8 81.8 74.3 68.4 60.5 53.0 46.5 40.7

r in. 3.27 3.23 3.20 3.17 3.14 3.11 3.08 3.07 3.04 3.05 3.01 2.97 2.94 2.91

Z in.3 267 238 214 193 171 154 137 126 115 105 93.2 81.5 71.4 62.4

in. 3.92 3.86 3.81 3.76 3.71 3.67 3.62 3.60 3.57 3.57 3.53 3.49 3.46 3.42

26.5 24.0 20.9 18.4 15.7

1.99 1.98 1.95 1.92 1.87

41.5 37.5 32.6 28.6 24.5

2.40 2.40 2.37 2.33 2.30

9.80 1.38 8.30 1.34

15.7 13.3

86.1 77.2 70.0 60.1 53.5 49.2 44.5 40.3

3.02 133 3.00 119 2.99 108 2.95 92.6 2.93 82.3 2.92 75.6 2.90 68.2 2.89 61.7

ho

Torsional Properties

3.55 3.51 3.48 3.46 3.43 3.40 3.37 3.35

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

21.4 21.2 21.1 21.0 20.8 20.7 20.6 20.6

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1–20

DIMENSIONS AND PROPERTIES

Table 1-1 (continued)

W-Shapes Dimensions Web Shape

Area, A

Depth, d

W21×93 ×83 c ×73 c ×68 c ×62 c ×55 c ×48 c,f

in.2 27.3 24.4 21.5 20.0 18.3 16.2 14.1

in. 21.6 215/8 21.4 213/8 21.2 211/4 21.1 211/8 21.0 21 20.8 203/4 20.6 205/8

W21×57 c ×50 c ×44 c

16.7 21.1 21 0.405 14.7 20.8 207/8 0.380 13.0 20.7 205/8 0.350

W18×311 h ×283 h ×258 h ×234 h ×211 ×192 ×175 ×158 ×143 ×130 ×119 ×106 ×97 ×86 ×76 c

91.6 83.3 76.0 68.6 62.3 56.2 51.4 46.3 42.0 38.3 35.1 31.1 28.5 25.3 22.3

22.3 21.9 21.5 21.1 20.7 20.4 20.0 19.7 19.5 19.3 19.0 18.7 18.6 18.4 18.2

223/8 217/8 211/2 21 205/8 203/8 20 193/4 191/2 191/4 19 183/4 185/8 183/8 181/4

W18×71 ×65 ×60 c ×55 c ×50 c

20.9 19.1 17.6 16.2 14.7

18.5 18.4 18.2 18.1 18.0

181/2 183/8 181/4 181/8 18

W18×46 c ×40 c ×35 c

Flange

Thickness, tw

tw ᎏ 2

Width, bf

in. 0.580 9/16 0.515 1/2 0.455 7/16 0.430 7/16 0.400 3/8 0.375 3/8 0.350 3/8

in. 5/16 1/4 1/4 1/4 3/16 3/16 3/16

3/8

3/16

3/8

3/16

3/8

3/16

1.52 1.40 1.28 1.16 1.06 0.960 0.890 0.810 0.730 0.670 0.655 0.590 0.535 0.480 0.425

11/2 13/8 11/4 13/16 11/16 15/16 7/8 13/16 3/4 11/16 5/8 9/16 9/16 1/2 7/16

3/4

0.495 0.450 0.415 0.390 0.355

1/2

1/4

7/16

1/4

7/16

1/4

3/8

3/16

3/8

3/16

13.5 18.1 18 0.360 11.8 17.9 177/8 0.315 10.3 17.7 173/4 0.300

3/8

3/16

5/16

3/16

5/16

3/16

11/16 5/8 5/8 9/16 1/2 7/16 7/16 3/8 3/8 5/16 5/16 5/16 1/4 1/4

Distance

k

Thickness, tf

kdes

kdet

in. 8.42 83/8 8.36 83/8 8.30 81/4 8.27 81/4 8.24 81/4 8.22 81/4 8.14 81/8

in. 0.930 0.835 0.740 0.685 0.615 0.522 0.430

in. 1.43 1.34 1.24 1.19 1.12 1.02 0.930

in. 15/8 11/2 17/16 13/8 15/16 13/16 11/8

6.56 61/2 6.53 61/2 6.50 61/2

0.650 0.535 0.450

5/8

12 117/8 113/4 115/8 111/2 111/2 113/8 111/4 111/4 111/8 111/4 111/4 111/8 111/8 11

2.74 2.50 2.30 2.11 1.91 1.75 1.59 1.44 1.32 1.20 1.06 0.940 0.870 0.770 0.680

23/4 21/2 25/16 21/8 115/16 13/4 19/16 17/16 15/16 13/16 11/16 15/16 7/8 3/4 11/16

75/8 75/8 71/2 71/2 71/2

0.810 0.750 0.695 0.630 0.570

13/16

0.605 0.525 0.425

5/8

12.0 11.9 11.8 11.7 11.6 11.5 11.4 11.3 11.2 11.2 11.3 11.2 11.1 11.1 11.0 7.64 7.59 7.56 7.53 7.50

6.06 6 6.02 6 6.00 6

15/16 13/16 3/4 11/16 5/8 1/2 7/16

9/16 7/16

3/4 11/16 5/8 9/16

1/2 7/16

1.15 15/16 1.04 11/4 0.950 11/8 3.24 3.00 2.70 2.51 2.31 2.15 1.99 1.84 1.72 1.60 1.46 1.34 1.27 1.17 1.08

37/16 33/16 3 23/4 29/16 27/16 27/16 23/8 23/16 21/16 115/16 113/16 13/4 15/8 19/16

1.21 1.15 1.10 1.03 0.972

11/2 17/16 13/8 15/16 11/4

1.01 11/4 0.927 13/16 0.827 11/8

k1 in. 15/16

Workable Gage in. in. 183/8 51/2

T

7/8 7/8 7/8 13/16 13/16 13/16

183/8

31/2

13/8 151/2 15/16 11/4 13/16 13/16 11/8 11/4 151/8 11/4 13/16 13/16 13/16 11/8 11/8 11/16 11/16

51/2

13/16 13/16 13/16

7/8

151/2

31/2g

7/8 13/16 13/16 13/16 13/16

151/2 31/2 g

13/16 3/4

Shape is slender for compression with Fy = 50 ksi. Shape exceeds compact limit for flexure with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. c f

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A:14th Ed_

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Page 21

DIMENSIONS AND PROPERTIES

1–21

Table 1-1 (continued)

W-Shapes Properties W21-W18 Nominal Wt.

Compact Section Criteria

Axis X-X

Axis Y-Y

32.3 36.4 41.2 43.6 46.9 50.0 53.6

I in.4 2070 1830 1600 1480 1330 1140 959

S in.3 192 171 151 140 127 110 93.0

r in. 8.70 8.67 8.64 8.60 8.54 8.40 8.24

57 5.04 46.3 50 6.10 49.4 44 7.22 53.6

1170 984 843

111 94.5 81.6

8.36 129 8.18 110 8.06 95.4

b ᎏf lb/ft 2tf

93 83 73 68 62 55 48

4.53 5.00 5.60 6.04 6.70 7.87 9.47

h ᎏ tw

Z in.3 221 196 172 160 144 126 107

311 283 258 234 211 192 175 158 143 130 119 106 97 86 76

2.19 2.38 2.56 2.76 3.02 3.27 3.58 3.92 4.25 4.65 5.31 5.96 6.41 7.20 8.11

10.4 11.3 12.5 13.8 15.1 16.7 18.0 19.8 22.0 23.9 24.5 27.2 30.0 33.4 37.8

6970 6170 5510 4900 4330 3870 3450 3060 2750 2460 2190 1910 1750 1530 1330

624 565 514 466 419 380 344 310 282 256 231 204 188 166 146

8.72 8.61 8.53 8.44 8.35 8.28 8.20 8.12 8.09 8.03 7.90 7.84 7.82 7.77 7.73

754 676 611 549 490 442 398 356 322 290 262 230 211 186 163

71 65 60 55 50

4.71 5.06 5.44 5.98 6.57

32.4 35.7 38.7 41.1 45.2

1170 1070 984 890 800

127 117 108 98.3 88.9

7.50 7.49 7.47 7.41 7.38

146 133 123 112 101

46 5.01 44.6 40 5.73 50.9 35 7.06 53.5

712 612 510

78.8 68.4 57.6

7.25 7.21 7.04

90.7 78.4 66.5

I in.4 92.9 81.4 70.6 64.7 57.5 48.4 38.7 30.6 24.9 20.7 795 704 628 558 493 440 391 347 311 278 253 220 201 175 152 60.3 54.8 50.1 44.9 40.1 22.5 19.1 15.3

S in.3 22.1 19.5 17.0 15.7 14.0 11.8 9.52

rts

ho

Torsional Properties

J

Cw

r in. 1.84 1.83 1.81 1.80 1.77 1.73 1.66

Z in.3 34.7 30.5 26.6 24.4 21.7 18.4 14.9

in. 2.24 2.21 2.19 2.17 2.15 2.11 2.05

in. 20.7 20.6 20.5 20.4 20.4 20.3 20.2

in.4 6.03 4.34 3.02 2.45 1.83 1.24 0.803

in.6 9940 8630 7410 6760 5960 4980 3950

9.35 1.35 7.64 1.30 6.37 1.26

14.8 12.2 10.2

1.68 20.5 1.64 20.3 1.60 20.3

1.77 1.14 0.770

3190 2570 2110

132 118 107 95.8 85.3 76.8 68.8 61.4 55.5 49.9 44.9 39.4 36.1 31.6 27.6

2.95 2.91 2.88 2.85 2.82 2.79 2.76 2.74 2.72 2.70 2.69 2.66 2.65 2.63 2.61

207 185 166 149 132 119 106 94.8 85.4 76.7 69.1 60.5 55.3 48.4 42.2

3.53 3.47 3.42 3.37 3.32 3.28 3.24 3.20 3.17 3.13 3.13 3.10 3.08 3.05 3.02

19.6 19.4 19.2 19.0 18.8 18.7 18.4 18.3 18.2 18.1 17.9 17.8 17.7 17.6 17.5

176 134 103 78.7 58.6 44.7 33.8 25.2 19.2 14.5 10.6 7.48 5.86 4.10 2.83

76200 65900 57600 50100 43400 38000 33300 29000 25700 22700 20300 17400 15800 13600 11700

15.8 14.4 13.3 11.9 10.7

1.70 1.69 1.68 1.67 1.65

24.7 22.5 20.6 18.5 16.6

2.05 2.03 2.02 2.00 1.98

17.7 17.7 17.5 17.5 17.4

3.49 2.73 2.17 1.66 1.24

4700 4240 3850 3430 3040

1.22 0.810 0.506

1720 1440 1140

7.43 1.29 6.35 1.27 5.12 1.22

11.7 1.58 17.5 10.0 1.56 17.4 8.06 1.51 17.3

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 22

1–22

DIMENSIONS AND PROPERTIES

Table 1-1 (continued)

W-Shapes Dimensions Web Shape

Area, A

Depth, d

W16×100 ×89 ×77 ×67 c

in.2 29.4 26.2 22.6 19.6

in. 17.0 17 16.8 163/4 16.5 161/2 16.3 163/8

W16×57 ×50 c ×45 c ×40 c ×36 c

16.8 14.7 13.3 11.8 10.6

16.4 16.3 16.1 16.0 15.9

W16×31c ×26 c,v W14×730 h ×665 h ×605 h ×550 h ×500 h ×455 h ×426 h ×398 h ×370 h ×342 h ×311 h ×283 h ×257 ×233 ×211 ×193 ×176 ×159 ×145

163/8 161/4 161/8 16 157/8

22.4 21.6 20.9 20.2 19.6 19.0 18.7 18.3 17.9 17.5 17.1 16.7 16.4 16.0 15.7 15.5 15.2 15.0 14.8

223/8 215/8 207/8 201/4 195/8 19 185/8 181/4 177/8 171/2 171/8 163/4 163/8 16 153/4 151/2 151/4 15 143/4

Distance

k

tw ᎏ 2

Width, bf

Thickness, tf

kdes

kdet

in. 0.585 9/16 0.525 1/2 0.455 7/16 0.395 3/8

in. 5/16 1/4 1/4 3/16

in. 10.4 103/8 10.4 103/8 10.3 101/4 10.2 101/4

in. 0.985 1 0.875 7/8 0.760 3/4 0.665 11/16

in. 1.39 1.28 1.16 1.07

in. 17/8 13/4 15/8 19/16

in. 11/8 11/16 11/16 1

1.12 1.03 0.967 0.907 0.832

13/8 15/16 11/4 13/16 11/8

7/8

0.430 0.380 0.345 0.305 0.295

9.13 15.9 157/8 0.275 7.68 15.7 153/4 0.250 215 196 178 162 147 134 125 117 109 101 91.4 83.3 75.6 68.5 62.0 56.8 51.8 46.7 42.7

Flange

Thickness, tw

3.07 2.83 2.60 2.38 2.19 2.02 1.88 1.77 1.66 1.54 1.41 1.29 1.18 1.07 0.980 0.890 0.830 0.745 0.680

7/16

1/4

3/8

3/16

3/8

3/16

5/16

3/16

5/16

3/16

1/4

1/8

1/4

1/8

31/16 213/16 25/8 23/8 23/16 2 17/8 13/4 111/16 19/16 17/16 15/16 13/16 11/16 1 7/8 13/16 3/4 11/16

19/16 17/16 15/16 13/16 11/8 1 15/16 7/8 13/16 13/16 3/4 11/16 5/8 9/16 1/2 7/16 7/16 3/8 3/8

71/8 71/8 7 7 7

0.715 0.630 0.565 0.505 0.430

11/16

5.53 51/2 5.50 51/2

0.440 0.345

7/16

7.12 7.07 7.04 7.00 6.99

17.9 17.7 17.4 17.2 17.0 16.8 16.7 16.6 16.5 16.4 16.2 16.1 16.0 15.9 15.8 15.7 15.7 15.6 15.5

177/8 175/8 173/8 171/4 17 167/8 163/4 165/8 161/2 163/8 161/4 161/8 16 157/8 153/4 153/4 155/8 155/8 151/2

4.91 4.52 4.16 3.82 3.50 3.21 3.04 2.85 2.66 2.47 2.26 2.07 1.89 1.72 1.56 1.44 1.31 1.19 1.09

5/8 9/16 1/2 7/16

3/8

415/16 41/2 43/16 313/16 31/2 33/16 31/16 27/8 211/16 21/2 21/4 21/16 17/8 13/4 19/16 17/16 15/16 13/16 11/16

0.842 11/8 0.747 11/16 5.51 5.12 4.76 4.42 4.10 3.81 3.63 3.44 3.26 3.07 2.86 2.67 2.49 2.32 2.16 2.04 1.91 1.79 1.69

63/16 513/16 57/16 51/8 413/16 41/2 45/16 41/8 315/16 33/4 39/16 33/8 33/16 3 27/8 23/4 25/8 21/2 23/8

k1

Workable Gage in. in. 131/4 51/2

T

135/8 31/2 g

13/16 13/16 13/16 3/4 3/4 3/4

135/8 135/8

31/2 31/2

23/4 10 3-71/2-3g 5 2 /8 3-71/2-3g 21/2 3-71/2-3 23/8 25/16 21/4 21/8 21/8 21/16 2 115/16 17/8 113/16 13/4 111/16 111/16 15/8 19/16 19/16

Shape is slender for compression with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. v Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi. c

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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7:26 AM

Page 23

DIMENSIONS AND PROPERTIES

1–23

Table 1-1 (continued)

W-Shapes Properties W16-W14 Nominal Wt.

Compact Section Criteria

Axis X-X

100 89 77 67

5.29 5.92 6.77 7.70

24.3 27.0 31.2 35.9

I in.4 1490 1300 1110 954

57 50 45 40 36

4.98 5.61 6.23 6.93 8.12

33.0 37.4 41.1 46.5 48.1

758 659 586 518 448

92.2 81.0 72.7 64.7 56.5

6.72 105 6.68 92.0 6.65 82.3 6.63 73.0 6.51 64.0

43.1 37.2 32.8 28.9 24.5

31 6.28 51.6 26 7.97 56.8

375 301

47.2 38.4

6.41 6.26

12.4 9.59

b ᎏf lb/ft 2tf

730 665 605 550 500 455 426 398 370 342 311 283 257 233 211 193 176 159 145

1.82 1.95 2.09 2.25 2.43 2.62 2.75 2.92 3.10 3.31 3.59 3.89 4.23 4.62 5.06 5.45 5.97 6.54 7.11

h ᎏ tw

S in.3 175 155 134 117

3.71 14300 1280 4.03 12400 1150 4.39 10800 1040 4.79 9430 931 5.21 8210 838 5.66 7190 756 6.08 6600 706 6.44 6000 656 6.89 5440 607 7.41 4900 558 8.09 4330 506 8.84 3840 459 9.71 3400 415 10.7 3010 375 11.6 2660 338 12.8 2400 310 13.7 2140 281 15.3 1900 254 16.8 1710 232

r in. 7.10 7.05 7.00 6.96

Axis Y-Y

Z in.3 198 175 150 130

54.0 44.2

8.17 1660 7.98 1480 7.80 1320 7.63 1180 7.48 1050 7.33 936 7.26 869 7.16 801 7.07 736 6.98 672 6.88 603 6.79 542 6.71 487 6.63 436 6.55 390 6.50 355 6.43 320 6.38 287 6.33 260

I in.4 186 163 138 119

4720 4170 3680 3250 2880 2560 2360 2170 1990 1810 1610 1440 1290 1150 1030 931 838 748 677

rts

J

Cw

in. 16.0 15.9 15.7 15.6

in.4 7.73 5.45 3.57 2.39

in.6 11900 10200 8590 7300

15.7 15.7 15.5 15.5 15.5

2.22 1.52 1.11 0.794 0.545

2660 2270 1990 1730 1460

7.03 1.42 15.5 5.48 1.38 15.4

0.461 0.262

739 565

S in.3 35.7 31.4 26.9 23.2

r in. 2.51 2.49 2.47 2.46

Z in.3 54.9 48.1 41.1 35.5

in. 2.92 2.88 2.85 2.82

12.1 10.5 9.34 8.25 7.00

1.60 1.59 1.57 1.57 1.52

18.9 16.3 14.5 12.7 10.8

1.92 1.89 1.87 1.86 1.83

4.49 1.17 3.49 1.12 527 472 423 378 339 304 283 262 241 221 199 179 161 145 130 119 107 96.2 87.3

4.69 4.62 4.55 4.49 4.43 4.38 4.34 4.31 4.27 4.24 4.20 4.17 4.13 4.10 4.07 4.05 4.02 4.00 3.98

ho

Torsional Properties

816 730 652 583 522 468 434 402 370 338 304 274 246 221 198 180 163 146 133

5.68 5.57 5.44 5.35 5.26 5.17 5.11 5.05 5.00 4.95 4.87 4.80 4.75 4.69 4.64 4.59 4.55 4.51 4.47

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

17.5 1450 17.1 1120 16.7 869 16.4 669 16.1 514 15.8 395 15.7 331 15.5 273 15.2 222 15.0 178 14.8 136 14.6 104 14.5 79.1 14.3 59.5 14.1 44.6 14.1 34.8 13.9 26.5 13.8 19.7 13.7 15.2

362000 305000 258000 219000 187000 160000 144000 129000 116000 103000 89100 77700 67800 59000 51500 45900 40500 35600 31700

AISC_PART 01A:14th Ed_

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7:27 AM

Page 24

1–24

DIMENSIONS AND PROPERTIES

Table 1-1 (continued)

W-Shapes Dimensions Web Shape

Area, A

Depth, d

W14×132 ×120 ×109 ×99 f ×90 f

in.2 38.8 35.3 32.0 29.1 26.5

in. 14.7 145/8 14.5 141/2 14.3 143/8 14.2 141/8 14.0 14

W14×82 ×74 ×68 ×61

24.0 21.8 20.0 17.9

14.3 14.2 14.0 13.9

Width, bf

Thickness, tf

kdes

kdet

in. 0.645 5/8 0.590 9/16 0.525 1/2 0.485 1/2 0.440 7/16

in. 5/16 5/16 1/4 1/4 1/4

in. 14.7 143/4 14.7 145/8 14.6 145/8 14.6 145/8 14.5 141/2

in. 1.03 1 0.940 15/16 0.860 7/8 0.780 3/4 0.710 11/16

in. 1.63 1.54 1.46 1.38 1.31

10.1 10.1 10.0 10.0

1.45 1.38 1.31 1.24

1/2

1/4

7/16

1/4

7/16 3/8

1/4 3/16

W14×53 ×48 ×43 c

15.6 13.9 0.370 14.1 13.8 133/4 0.340 12.6 13.7 135/8 0.305

3/8

3/16

5/16

3/16

5/16

3/16

W14×38 c ×34 c ×30 c

11.2 14.1 141/8 0.310 10.0 14.0 14 0.285 8.85 13.8 137/8 0.270

5/16

3/16

5/16

3/16

1/4

1/8

W14×26 c ×22 c

7.69 13.9 137/8 0.255 6.49 13.7 133/4 0.230

1/4

1/8

1/4

1/8

13/4 15/8 11/2 13/8 15/16 13/16 11/16 15/16 7/8 13/16 11/16 5/8 9/16 1/2 1/2 7/16 3/8

7/8

137/8

98.9 89.5 81.9 74.1 67.7 61.8 56.0 50.0 44.7 39.9 35.2 31.2 28.2 25.6 23.2 21.1 19.1

16.8 16.3 15.9 15.4 15.1 14.7 14.4 14.0 13.7 13.4 13.1 12.9 12.7 12.5 12.4 12.3 12.1

167/8 163/8 157/8 153/8 15 143/4 143/8 14 133/4 133/8 131/8 127/8 123/4 121/2 123/8 121/4 121/8

Distance

k

tw ᎏ 2

0.510 0.450 0.415 0.375

W12×336 h ×305 h ×279 h ×252 h ×230 h ×210 ×190 ×170 ×152 ×136 ×120 ×106 ×96 ×87 ×79 ×72 ×65 f

141/4 141/8 14 137/8

Flange

Thickness, tw

1.78 1.63 1.53 1.40 1.29 1.18 1.06 0.960 0.870 0.790 0.710 0.610 0.550 0.515 0.470 0.430 0.390

13/16 3/4 11/16 11/16 5/8 9/16 1/2 7/16 7/16 3/8 5/16 5/16 1/4 1/4 1/4 3/16

0.855 0.785 0.720 0.645

7/8

8.06 8 8.03 8 8.00 8

0.660 0.595 0.530

11/16

6.77 63/4 6.75 63/4 6.73 63/4

0.515 0.455 0.385

1/2

5.03 5 5.00 5

0.420 0.335

7/16

2.96 2.71 2.47 2.25 2.07 1.90 1.74 1.56 1.40 1.25 1.11 0.990 0.900 0.810 0.735 0.670 0.605

215/16 211/16 21/2 21/4 21/16 17/8 13/4 19/16 13/8 11/4 11/8 1 7/8 13/16 3/4 11/16 5/8

13.4 13.2 13.1 13.0 12.9 12.8 12.7 12.6 12.5 12.4 12.3 12.2 12.2 12.1 12.1 12.0 12.0

101/8 101/8 10 10

133/8 131/4 131/8 13 127/8 123/4 125/8 125/8 121/2 123/8 123/8 121/4 121/8 121/8 121/8 12 12

13/16 3/4 5/8

5/8 1/2

7/16 3/8

5/16

k1

T

in. 25/16 21/4 23/16 21/16 2

in. 19/16 11/2 11/2 17/16 17/16

in. 10

111/16 15/8 19/16 11/2

11/16 107/8 11/16 11/16 1

Workable Gage in. 51/2

51/2

1.25 11/2 1 1.19 17/16 1 1.12 13/8 1

107/8

0.915 11/4 0.855 13/16 0.785 11/8

13/16

115/8 31/2 g 31/2 31/2

0.820 11/8 0.735 11/16

3/4

3.55 3.30 3.07 2.85 2.67 2.50 2.33 2.16 2.00 1.85 1.70 1.59 1.50 1.41 1.33 1.27 1.20

37/8 35/8 33/8 31/8 215/16 213/16 25/8 27/16 25/16 21/8 2 17/8 113/16 111/16 15/8 19/16 11/2

3/4 3/4

3/4

51/2

115/8 23/4 g 115/8 23/4 g

111/16 91/8 15/8 15/8 11/2 11/2 17/16 13/8 15/16 11/4 11/4 13/16 11/8 11/8 11/16 11/16 11/16 1

51/2

Shape is slender for compression with Fy = 50 ksi. Shape exceeds compact limit for flexure with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. c f

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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7:27 AM

Page 25

DIMENSIONS AND PROPERTIES

1–25

Table 1-1 (continued)

W-Shapes Properties W14-W12 Nominal Wt.

Compact Section Criteria

Axis X-X

Axis Y-Y

rts

ho

Torsional Properties

J

Cw

in. 13.7 13.6 13.4 13.4 13.3

in.4 12.3 9.37 7.12 5.37 4.06

in.6 25500 22700 20200 18000 16000

13.4 13.4 13.3 13.3

5.07 3.87 3.01 2.19

6710 5990 5380 4710

2.22 13.2 2.20 13.2 2.18 13.2

1.94 1.45 1.05

2540 2240 1950

132 120 109 99 90

7.15 7.80 8.49 9.34 10.2

17.7 19.3 21.7 23.5 25.9

I in.4 1530 1380 1240 1110 999

82 74 68 61

5.92 6.41 6.97 7.75

22.4 25.4 27.5 30.4

881 795 722 640

123 112 103 92.1

6.05 6.04 6.01 5.98

53 6.11 30.9 48 6.75 33.6 43 7.54 37.4

541 484 428

77.8 70.2 62.6

5.89 5.85 5.82

87.1 78.4 69.6

57.7 51.4 45.2

14.3 1.92 12.8 1.91 11.3 1.89

38 6.57 39.6 34 7.41 43.1 30 8.74 45.4

385 340 291

54.6 48.6 42.0

5.87 5.83 5.73

61.5 54.6 47.3

26.7 23.3 19.6

7.88 1.55 6.91 1.53 5.82 1.49

12.1 1.82 13.6 10.6 1.80 13.5 8.99 1.77 13.4

0.798 0.569 0.380

1230 1070 887

26 5.98 48.1 22 7.46 53.3

245 199

35.3 29.0

5.65 5.54

40.2 33.2

3.55 1.08 2.80 1.04

5.54 1.30 13.5 4.39 1.27 13.4

0.358 0.208

405 314

4060 3550 3110 2720 2420 2140 1890 1650 1430 1240 1070 933 833 740 662 597 533

483 435 393 353 321 292 263 235 209 186 163 145 131 118 107 97.4 87.9

6.41 6.29 6.16 6.06 5.97 5.89 5.82 5.74 5.66 5.58 5.51 5.47 5.44 5.38 5.34 5.31 5.28

b ᎏf lb/ft 2tf

336 305 279 252 230 210 190 170 152 136 120 106 96 87 79 72 65

2.26 2.45 2.66 2.89 3.11 3.37 3.65 4.03 4.46 4.96 5.57 6.17 6.76 7.48 8.22 8.99 9.92

h ᎏ tw

5.47 5.98 6.35 6.96 7.56 8.23 9.16 10.1 11.2 12.3 13.7 15.9 17.7 18.9 20.7 22.6 24.9

S in.3 209 190 173 157 143

r in. 6.28 6.24 6.22 6.17 6.14

Z in.3 234 212 192 173 157

I in.4 548 495 447 402 362

S in.3 74.5 67.5 61.2 55.2 49.9

r Z in. in.3 3.76 113 3.74 102 3.73 92.7 3.71 83.6 3.70 75.6

in. 4.23 4.20 4.17 4.14 4.10

139 126 115 102

148 134 121 107

29.3 26.6 24.2 21.5

2.48 2.48 2.46 2.45

44.8 40.5 36.9 32.8

2.85 2.83 2.80 2.78

22.0 19.6 17.3

8.91 7.00

603 1190 537 1050 481 937 428 828 386 742 348 664 311 589 275 517 243 454 214 398 186 345 164 301 147 270 132 241 119 216 108 195 96.8 174

177 159 143 127 115 104 93.0 82.3 72.8 64.2 56.0 49.3 44.4 39.7 35.8 32.4 29.1

3.47 3.42 3.38 3.34 3.31 3.28 3.25 3.22 3.19 3.16 3.13 3.11 3.09 3.07 3.05 3.04 3.02

274 244 220 196 177 159 143 126 111 98.0 85.4 75.1 67.5 60.4 54.3 49.2 44.1

4.13 4.05 4.00 3.93 3.87 3.81 3.77 3.70 3.66 3.61 3.56 3.52 3.49 3.46 3.43 3.41 3.38

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

13.8 13.6 13.4 13.2 13.0 12.8 12.7 12.4 12.3 12.2 12.0 11.9 11.8 11.7 11.7 11.6 11.5

243 185 143 108 83.8 64.7 48.8 35.6 25.8 18.5 12.9 9.13 6.85 5.10 3.84 2.93 2.18

57000 48600 42000 35800 31200 27200 23600 20100 17200 14700 12400 10700 9410 8270 7330 6540 5780

AISC_PART 01A:14th Ed_

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1–26

DIMENSIONS AND PROPERTIES

Table 1-1 (continued)

W-Shapes Dimensions Web Shape

Area, A

Depth, d

Thickness, tw

Flange tw ᎏ 2

Width, bf

W12×58 ×53

in. in. in.2 17.0 12.2 121/4 0.360 3/8 15.6 12.1 12 0.345 3/8

in. in. 3/16 10.0 10 3/16 10.0 10

W12×50 ×45 ×40

14.6 12.2 121/4 0.370 13.1 12.1 12 0.335 11.7 11.9 12 0.295

3/8

3/16

5/16

3/16

5/16

3/16

8.08 81/8 8.05 8 8.01 8

5/16

3/16

61/2

1/4

1/8

1/4

1/8

0.260 0.235 0.220 0.200

1/4

1/8

1/4

1/8

1/4 3/16

1/8 1/8 3/8

11/16

3/8

5/8

5/16

1/2

1/4

1/2

1/4

7/16 3/8

1/4 3/16

c

W12×35 ×30 c ×26 c

W12×22 c ×19 c ×16 c ×14c,v

121/2

10.3 12.5 0.300 8.79 12.3 123/8 0.260 7.65 12.2 121/4 0.230 6.48 12.3 5.57 12.2 4.71 12.0 4.16 11.9

121/4 121/8 12 117/8

W10×112 ×100 ×88 ×77 ×68 ×60 ×54 ×49

32.9 29.3 26.0 22.7 19.9 17.7 15.8 14.4

0.755 0.680 0.605 0.530 0.470 0.420 0.370 0.340

3/4

5/16

3/16

W10×45 ×39 ×33

13.3 10.1 101/8 0.350 11.5 9.92 97/8 0.315 9.71 9.73 93/4 0.290

3/8

3/16

5/16

3/16

5/16

3/16 3/16

1/4

1/8

11.4 11.1 10.8 10.6 10.4 10.2 10.1 10.0

113/8 111/8 107/8 105/8 103/8 101/4 101/8 10

101/2

W10×30 ×26 ×22 c

8.84 10.5 0.300 7.61 10.3 103/8 0.260 6.49 10.2 101/8 0.240

5/16 1/4

1/8

W10×19 ×17 c ×15 c ×12 c,f

5.62 10.2 101/4 4.99 10.1 101/8 4.41 9.99 10 3.54 9.87 97/8

1/4

1/8

1/4

1/8

1/4

1/8

3/16

1/8

0.250 0.240 0.230 0.190

Distance

Thickness, tf

5/8

6.56 6.52 61/2 6.49 61/2

0.520 0.440 0.380

1/2

4.03 4.01 3.99 3.97

0.425 0.350 0.265 0.225

7/16

10.4 10.3 10.3 10.2 10.1 10.1 10.0 10.0

103/8 103/8 101/4 101/4 101/8 101/8 10 10

9/16 1/2

7/16 3/8

3/8 1/4 1/4

11/4

1.25 1.12 11/8 0.990 1 0.870 7/8 0.770 3/4 0.680 11/16 0.615 5/8 0.560 9/16 0.620 0.530 0.435

5/8

5.81 5.77 53/4 5.75 53/4

0.510 0.440 0.360

1/2

4.02 4.01 4.00 3.96

0.395 0.330 0.270 0.210

3/8

8.02 8 7.99 8 7.96 8 53/4

4 4 4 4

kdes

kdet

in. in. in. 0.640 5/8 1.24 11/2 0.575 9/16 1.18 13/8 0.640 0.575 0.515

4 4 4 4

k

1/2 7/16

7/16 3/8

5/16 1/4 3/16

1.14 11/2 1.08 13/8 1.02 13/8 13/16

0.820 0.740 11/8 0.680 11/16 0.725 0.650 0.565 0.525 1.75 1.62 1.49 1.37 1.27 1.18 1.12 1.06

T

in. 15/16

in. 91/4 91/4

Workable Gage in. 51/2 51/2

15/16

91/4

51/2

101/8

31/2

15/16

15/16 7/8 3/4 3/4 3/4

15/16

5/8

7/8

9/16

13/16

9/16

3/4

9/16

103/8 21/4 g

115/16

1 71/2 113/16 1 111/16 15/16 19/16 7/8 17/16 7/8 13/16 13/8 15/16 13/16 13/16 11/4

1.12 15/16 1.03 13/16 0.935 11/8 11/8

0.810 0.740 11/16 0.660 15/16 0.695 0.630 0.570 0.510

k1

13/16

51/2

71/2

51/2

81/4

23/4 g

83/8

21/4 g

13/16 3/4 11/16 11/16 5/8

15/16

5/8

7/8

9/16

13/16

9/16

3/4

9/16

Shape is slender for compression with Fy = 50 ksi. Shape exceeds compact limit for flexure with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. v Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi. c f

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A_14th Ed._Nov. 19, 2012 14-11-10 9:42 AM Page 27

(Black plate)

1–27

DIMENSIONS AND PROPERTIES

Table 1-1 (continued)

W-Shapes Properties W12-W10 Nominal Wt.

Compact Section Criteria

Axis X-X

Axis Y-Y

rts

J

Cw

in. in. 2.81 11.6 2.79 11.5

in.4 2.10 1.58

in.6 3570 3160

2.25 11.6 2.23 11.5 2.21 11.4

1.71 1.26 0.906

1880 1650 1440

11.5 1.79 12.0 9.56 1.77 11.9 8.17 1.75 11.8

0.741 0.457 0.300

879 720 607

0.293 0.180 0.103 0.0704

164 131 96.9 80.4

h ᎏ tw

lb/ft 58 7.82 27.0 53 8.69 28.1

I in.4 475 425

S in.3 78.0 70.6

r in. 5.28 5.23

Z in.3 86.4 77.9

I in.4 107 95.8

S r in.3 in. 21.4 2.51 19.2 2.48

Z in.3 32.5 29.1

50 6.31 26.8 45 7.00 29.6 40 7.77 33.6

391 348 307

64.2 57.7 51.5

5.18 5.15 5.13

71.9 64.2 57.0

56.3 50.0 44.1

13.9 1.96 12.4 1.95 11.0 1.94

21.3 19.0 16.8

35 6.31 36.2 30 7.41 41.8 26 8.54 47.2

285 238 204

45.6 38.6 33.4

5.25 5.21 5.17

51.2 43.1 37.2

24.5 20.3 17.3

7.47 1.54 6.24 1.52 5.34 1.51

22 19 16 14

4.74 5.72 7.53 8.82

41.8 46.2 49.4 54.3

156 130 103 88.6

25.4 21.3 17.1 14.9

4.91 4.82 4.67 4.62

29.3 24.7 20.1 17.4

112 100 88 77 68 60 54 49

4.17 4.62 5.18 5.86 6.58 7.41 8.15 8.93

10.4 11.6 13.0 14.8 16.7 18.7 21.2 23.1

716 623 534 455 394 341 303 272

126 112 98.5 85.9 75.7 66.7 60.0 54.6

45 6.47 22.5 39 7.53 25.0 33 9.15 27.1

248 209 171

49.1 42.1 35.0

4.32 4.27 4.19

54.9 46.8 38.8

30 5.70 29.5 26 6.56 34.0 22 7.99 36.9

170 144 118

32.4 27.9 23.2

4.38 4.35 4.27

36.6 31.3 26.0

18.8 16.2 13.8 10.9

4.14 4.05 3.95 3.90

21.6 18.7 16.0 12.6

19 17 15 12

b ᎏf 2tf

5.09 6.08 7.41 9.43

35.4 36.9 38.5 46.6

96.3 81.9 68.9 53.8

4.66 147 4.60 130 4.54 113 4.49 97.6 4.44 85.3 4.39 74.6 4.37 66.6 4.35 60.4

4.66 3.76 2.82 2.36 236 207 179 154 134 116 103 93.4

2.31 1.88 1.41 1.19

3.66 2.98 2.26 1.90

1.04 1.02 0.983 0.961

11.9 11.9 11.7 11.7

2.68 2.65 2.63 2.60 2.59 2.57 2.56 2.54

69.2 61.0 53.1 45.9 40.1 35.0 31.3 28.3

3.08 10.2 15.1 3.04 10.0 10.9 2.99 9.81 7.53 2.95 9.73 5.11 2.92 9.63 3.56 2.88 9.52 2.48 2.85 9.49 1.82 2.84 9.44 1.39

6020 5150 4330 3630 3100 2640 2320 2070

53.4 45.0 36.6

13.3 2.01 11.3 1.98 9.20 1.94

20.3 17.2 14.0

2.27 2.24 2.20

9.48 9.39 9.30

1.51 0.976 0.583

1200 992 791

16.7 14.1 11.4

5.75 1.37 4.89 1.36 3.97 1.33

8.84 1.60 7.50 1.58 6.10 1.55

9.99 9.86 9.84

0.622 0.402 0.239

414 345 275

2.14 1.78 1.45 1.10

3.35 2.80 2.30 1.74

9.81 9.77 9.72 9.66

0.233 0.156 0.104 0.0547

104 85.1 68.3 50.9

4.29 3.56 2.89 2.18

45.3 40.0 34.8 30.1 26.4 23.0 20.6 18.7

0.848 0.822 0.773 0.753

ho

Torsional Properties

0.874 0.845 0.810 0.785

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.06 1.04 1.01 0.983

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DIMENSIONS AND PROPERTIES

Table 1-1 (continued)

W-Shapes Dimensions Web

c f g

Shape

Area, A

W8×67 ×58 ×48 ×40 ×35 ×31f

in.2 19.7 17.1 14.1 11.7 10.3 9.13

Depth, d in. 9.00 8.75 8.50 8.25 8.12 8.00

9 83/4 81/2 81/4 81/8 8

Flange

Thickness, tw

tw ᎏ 2

Width, bf

in. 0.570 9/16 0.510 1/2 0.400 3/8 0.360 3/8 0.310 5/16 0.285 5/16

in. 5/16 1/4 3/16 3/16 3/16 3/16

Distance

kdes

kdet

in. 8.28 81/4 8.22 81/4 8.11 81/8 8.07 81/8 8.02 8 8.00 8

in. 0.935 0.810 0.685 0.560 0.495 0.435

in. 1.33 1.20 1.08 0.954 0.889 0.829

in. 15/8 11/2 13/8 11/4 13/16 11/8

6.54 61/2 6.50 61/2

0.465 0.400

7/16

5.27 51/4 5.25 51/4

0.400 0.330

3/8

4.02 4 4.00 4 3.94 4

0.315 0.255 0.205

5/16

6.08 61/8 6.02 6 5.99 6

0.455 0.365 0.260

7/16

4.03 4.00 3.94 3.94

4 4 4 4

0.405 0.280 0.215 0.195

3/8

15/16 13/16 11/16 9/16 1/2 7/16

W8×28 ×24

8.25 8.06 8 0.285 7.08 7.93 77/8 0.245

5/16

3/16

1/4

1/8

W8×21 ×18

6.16 8.28 81/4 0.250 5.26 8.14 81/8 0.230

1/4

1/8

1/4

1/8

W8×15 ×13 ×10 c,f

4.44 8.11 81/8 0.245 3.84 7.99 8 0.230 2.96 7.89 77/8 0.170

1/4

1/8

1/4

1/8

3/16

1/8

W6×25 ×20 ×15 f

7.34 6.38 63/8 0.320 5.87 6.20 61/4 0.260 4.43 5.99 6 0.230

5/16

3/16

1/4

1/8

1/4

1/8

W6×16 ×12 ×9 f ×8.5 f

4.74 3.55 2.68 2.52

0.260 0.230 0.170 0.170

1/4

1/8

1/4

1/8

3/16

1/8

3/16

1/8

W5×19 ×16

5.56 5.15 51/8 0.270 4.71 5.01 5 0.240

1/4

1/8 1/8

5.03 5 5.00 5

0.430 0.360

7/16

1/4

W4×13

3.83 4.16 41/8 0.280

1/4

1/8

4.06 4

0.345

6.28 6.03 5.90 5.83

61/4 6 57/8 57/8

k

Thickness, tf

k1

T

in.

in. 53/4

Workable Gage in. 51/2

15/16 7/8 13/16 13/16 13/16 3/4

0.859 0.794

15/16

5/8

7/8

9/16

61/8 61/8

4 4

0.700 0.630

7/8 13/16

9/16 9/16

61/2 61/2

23/4 g 23/4 g

0.615 0.555 0.505

13/16

9/16

61/2

21/4 g

3/4

9/16

11/16

1/2

0.705 0.615 0.510

15/16

9/16

41/2

31/2

7/8

9/16

3/4

9/16

0.655 0.530 0.465 0.445

7/8

9/16 9/16

41/2

21/4 g

3/4 11/16

1/2

11/16

1/2

0.730 0.660

13/16

7/16

3/8

3/4

7/16

31/2 31/2

23/4 g 23/4 g

3/8

0.595

3/4

1/2

25/8

21/4 g

3/8

5/16

1/4 3/16

3/8 1/4

1/4 3/16 3/16

Shape is slender for compression with Fy = 50 ksi. Shape exceeds compact limit for flexure with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

1–29

Table 1-1 (continued)

W-Shapes Properties W8-W4 Nominal Wt.

Compact Section Criteria

b ᎏf lb/ft 2tf

h ᎏ tw

Axis X-X

I in.4 272 228 184 146 127 110

Axis Y-Y

S in.3 60.4 52.0 43.2 35.5 31.2 27.5

r in. 3.72 3.65 3.61 3.53 3.51 3.47

Z in.3 70.1 59.8 49.0 39.8 34.7 30.4

I in.4 88.6 75.1 60.9 49.1 42.6 37.1 21.7 18.3

S in.3 21.4 18.3 15.0 12.2 10.6 9.27

r in. 2.12 2.10 2.08 2.04 2.03 2.02

rts Z in.3 32.7 27.9 22.9 18.5 16.1 14.1

ho

Torsional Properties

J

Cw

in. 2.43 2.39 2.35 2.31 2.28 2.26

in. 8.07 7.94 7.82 7.69 7.63 7.57

in.4 5.05 3.33 1.96 1.12 0.769 0.536

in.6 1440 1180 931 726 619 530

6.63 1.62 5.63 1.61

10.1 1.84 8.57 1.81

7.60 7.53

0.537 0.346

312 259

9.77 7.97

3.71 1.26 3.04 1.23

5.69 1.46 4.66 1.43

7.88 7.81

0.282 0.172

152 122

13.6 11.4 8.87

3.41 2.73 2.09

1.70 0.876 1.37 0.843 1.06 0.841

2.67 1.06 2.15 1.03 1.66 1.01

7.80 7.74 7.69

0.137 0.0871 0.0426

51.8 40.8 30.9

16.7 2.70 13.4 2.66 9.72 2.56

18.9 14.9 10.8

17.1 13.3 9.32

5.61 1.52 4.41 1.50 3.11 1.45

8.56 1.74 6.72 1.70 4.75 1.66

5.93 5.84 5.73

0.461 0.240 0.101

150 113 76.5

32.1 22.1 16.4 14.9

10.2 7.31 5.56 5.10

2.60 2.49 2.47 2.43

11.7 8.30 6.23 5.73

4.43 2.99 2.20 1.99

2.20 1.50 1.11 1.01

3.39 2.32 1.72 1.56

1.13 1.08 1.06 1.05

5.88 5.75 5.69 5.64

0.223 0.0903 0.0405 0.0333

38.2 24.7 17.7 15.8

5.85 13.7 6.94 15.4

26.3 21.4

10.2 2.17 8.55 2.13

11.6 9.63

9.13 7.51

3.63 1.28 3.00 1.26

5.53 1.45 4.58 1.43

4.72 4.65

0.316 0.192

50.9 40.6

5.88 10.6

11.3

5.46 1.72

6.28

3.86

1.90 1.00

2.92 1.16

3.82

0.151

14.0

67 58 48 40 35 31

4.43 5.07 5.92 7.21 8.10 9.19

11.1 12.4 15.9 17.6 20.5 22.3

28 24

7.03 22.3 8.12 25.9

98.0 82.7

24.3 20.9

3.45 3.42

27.2 23.1

21 18

6.59 27.5 7.95 29.9

75.3 61.9

18.2 15.2

3.49 3.43

20.4 17.0

15 13 10

6.37 28.1 7.84 29.9 9.61 40.5

48.0 39.6 30.8

11.8 3.29 9.91 3.21 7.81 3.22

25 20 15

6.68 15.5 8.25 19.1 11.5 21.6

53.4 41.4 29.1

16 12 9 8.5

4.98 7.14 9.16 10.1

19.1 21.6 29.2 29.1

19 16 13

0.967 0.918 0.905 0.890

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-2

M-Shapes Dimensions Web Shape

Area, A

Depth, d

Flange

Thickness, tw ᎏ 2 tw

in. in. in.2 M12.5×12.4 c,v 3.63 12.5 121/2 0.155 1/8 ×11.6 c,v 3.40 12.5 121/2 0.155 1/8

in. 1/16 1/16

Distance

Width, bf

Thickness, tf

k

k1

T

Workable Gage

in. 3.75 33/4 3.50 31/2

in. 0.228 1/4 0.211 3/16

in.

in.

9/16

3/8

in. 113/8 113/8

in. — —

9/16

3/8

M12×11.8 c 3.47 12.0 12 ×10.8 c 3.18 12.0 12

0.177 0.160

3/16

1/8

31/8 31/8

0.225 0.210

3/16

9/16 9/16

3/8

1/8

3.07 3.07

1/4

3/16

3/8

107/8 107/8

— —

M12×10 c,v

2.95 12.0 12

0.149

1/8

1/16

3.25

31/4

0.180

3/16

1/2

3/8

11

—

M10×9 c ×8 c

2.65 10.0 10 2.37 9.95 10

0.157 0.141

3/16

1/8

0.206 0.182

9/16

3/8

1/16

23/4 23/4

3/16

1/8

2.69 2.69

3/16

9/16

9.99 10

0.130

1/8

1/16

2.69

23/4

0.173

3/16

0.135 0.129

1/8

1/16

2.28 2.28

21/4 21/4

0.189 0.177

1/16

1.84 2.00

17/8 2

M10×7.5 c,v 2.22 M8×6.5 c ×6.2 c

1.92 1.82

8.00 8 8.00 8

1/8

1/16

M6×4.4 c ×3.7 c

1.29 1.09

6.00 6 0.114 1/8 5.92 57/8 0.0980 1/8

1/16

M5×18.9 t

5.56

5.00 5

M4×6 f ×4.08 ×3.45 ×3.2

1.75 1.27 1.01 1.01

3.80 4.00 4.00 4.00

M3×2.9

33/4 4 4 4

0.914 3.00 3

3/8

87/8 87/8

— —

7/16

5/16

91/8

—

3/16

9/16

3/8

3/16

7/16

1/4

67/8 71/8

— —

0.171 0.129

3/16

3/8

1/4

1/8

5/16

1/4

51/4 51/4

— —

0.316

5/ 16

3/ 16

5.00

5

0.416

7/16

13/16

1/2

33/8

23/4g

0.130 0.115 0.0920 0.0920

1/8

1/ 16

3/8

9/16

3/8

1/16

1/8

1/2

3/8

1/16

1/16

0.160 0.170 0.130 0.130

3/16

1/16

33/4 21/4 21/4 21/4

1/2

1/ 16

3.80 2.25 2.25 2.25

3/16

1/8

1/8

1/2

3/8

23/4 27/8 3 3

— — — —

0.0900

1/16

1/16

2.25

21/4

0.130

1/8

1/2

3/8

2

—

Shape is slender for compression with Fy = 36 ksi. Shape exceeds compact limit for flexure with Fy = 36 ksi. g The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. t Shape has tapered flanges while other M-shapes have parallel flange surfaces. v Shape does not meet the h/tw limit for shear in AISC Specification Section G2.1(b)(i) with Fy = 36 ksi. — Indicates flange is too narrow to establish a workable gage. c f

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

1–31

Table 1-2 (continued)

M-Shapes Properties

Nominal Wt.

Compact Section Criteria

Axis X-X

M-SHAPES

Axis Y-Y

rts

ho

J ᎏ S x ho

Torsional Properties

lb/ft 12.4 11.6

J Cw I S r Z I S r Z in.4 in.3 in. in.3 in.4 in.3 in. in.3 in. in. in.4 in.6 8.22 74.8 89.3 14.2 4.96 16.5 2.01 1.07 0.744 1.68 0.933 12.3 0.000283 0.0493 76.0 8.29 74.8 80.3 12.8 4.86 15.0 1.51 0.864 0.667 1.37 0.852 12.3 0.000263 0.0414 57.1

11.8 10.8

6.81 62.5 72.2 12.0 4.56 14.3 1.09 0.709 0.559 1.15 7.30 69.2 66.7 11.1 4.58 13.2 1.01 0.661 0.564 1.07

0.731 11.8 0.732 11.8

0.000355 0.0500 37.7 0.000300 0.0393 35.0

10

9.03 74.7 61.7 10.3 4.57 12.2 1.03 0.636 0.592 1.02

0.768 11.8

0.000240 0.0292 35.9

b ᎏf 2t f

h ᎏ tw

9 8

6.53 58.4 39.0 7.39 65.0 34.6

7.79 3.83 9.22 0.672 0.500 0.503 0.809 0.650 9.79 0.000411 0.0314 16.1 6.95 3.82 8.20 0.593 0.441 0.500 0.711 0.646 9.77 0.000328 0.0224 14.2

7.5

7.77 71.0 33.0

6.60 3.85 7.77 0.562 0.418 0.503 0.670 0.646 9.82 0.000289 0.0187 13.5

6.5 6.2

6.03 53.8 18.5 6.44 56.5 17.6

4.63 3.11 5.43 0.376 0.329 0.443 0.529 0.563 7.81 0.000509 0.0184 4.39 3.10 5.15 0.352 0.308 0.439 0.495 0.560 7.82 0.000455 0.0156

4.4 3.7

5.39 47.0 7.75 54.7

18.9 6 4.08 3.45 3.2 2.9

7.23 2.41 2.36 2.80 0.180 0.195 0.372 0.311 0.467 5.83 0.000707 0.00990 1.53 5.96 2.01 2.34 2.33 0.173 0.173 0.398 0.273 0.499 5.79 0.000459 0.00530 1.45

6.01 11.2 24.2 11.9 6.62 8.65 8.65

22.0 26.4 33.9 33.9

8.65 23.6

5.73 5.38

4.72 3.53 2.86 2.86

9.67 2.08 11.1 8.70 3.48

1.25

5.33

1.44

4.58 0.00709 0.313

2.48 1.77 1.43 1.43

0.915 0.506 0.496 0.496

1.18 0.453 0.346 0.346

1.04 0.593 0.580 0.580

3.64 3.83 3.87 3.87

1.64 1.67 1.68 1.68

2.74 2.00 1.60 1.60

1.47 0.325 0.248 0.248

0.771 0.289 0.221 0.221

0.00208 0.00218 0.00148 0.00148

0.0184 0.0147 0.00820 0.00820

45.7 4.87 1.19 0.930 0.930

1.50 1.00 1.28 1.12 0.248 0.221 0.521 0.344 0.597 2.87 0.00275 0.00790 0.511

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A:14th Ed_

1/20/11

7:27 AM

Page 32

1–32

DIMENSIONS AND PROPERTIES

Table 1-3

S-Shapes Dimensions Web Shape

Area, A

Depth, d

Flange

Distance

Thickness, tw

tw ᎏ 2

Width, bf

Thickness, tf

in. 0.800 13/16 0.620 5/8

in. 7/16

in. 8.05 8 7.87 77/8

1.09 1.09

7.25 71/4 7.13 71/8 7.00 7

0.870 0.870 0.870

7/8

7.20 71/4 7.06 7

0.920 0.920

15/16

S24×121 ×106

in.2 35.5 31.1

24.5 24.5

in. 241/2 241/2

S24×100 ×90 ×80

29.3 26.5 23.5

24.0 24.0 24.0

24 24 24

0.745 0.625 0.500

3/4

3/8

5/8

5/16

1/2

1/4

S20×96 ×86

28.2 25.3

20.3 20.3

201/4 201/4

0.800 0.660

13/16

7/16

11/16

3/8

S20×75 ×66

22.0 19.4

20.0 20.0

20 20

0.635 0.505

5/8

5/16 1/4

6.39 63/8 6.26 61/4

0.795 0.795

13/16

1/2

S18×70 ×54.7

20.5 16.0

18.0 18.0

18 18

0.711 0.461

11/16

3/8 1/4

6.25 61/4 6.00 6

0.691 0.691

11/16

7/16

S15×50 ×42.9

14.7 12.6

15.0 15.0

15 15

0.550 0.411

9/16

5/16 1/4

5.64 55/8 5.50 51/2

0.622 0.622

5/8

7/16

S12×50 ×40.8

14.7 11.9

12.0 12.0

12 12

0.687 0.462

11/16

3/8 1/4

5.48 51/2 5.25 51/4

0.659 0.659

11/16

7/16

S12×35 ×31.8

10.2 12.0 9.31 12.0

12 12

0.428 0.350

7/16

1/4 3/16

5.08 51/8 5.00 5

0.544 0.544

9/16

3/8

S10×35 ×25.4

10.3 10.0 7.45 10.0

10 10

0.594 0.311

5/8

5/16 3/16

4.94 5 4.66 45/8

0.491 0.491

1/2

5/16

4.17 41/8 4.00 4

0.425 0.425

7/16

5/16

in. 11/16 11/16 7/8 7/8

15/16

13/16

11/16

5/8

11/16

9/16

1/2

k

T

Workable Gage

in. 2 2

in. 201/2 201/2

in. 4 4

13/4 13/4 13/4

201/2 201/2 201/2

4 4 4

13/4 13/4

163/4 163/4

4 4

15/8 15/8

163/4 163/4

31/2g 31/2g

11/2 11/2

15 15

31/2g 31/2g

13/8 13/8

121/4 121/4

31/2g 31/2g

17/16 17/16

91/8 91/8

3g 3g

13/16 13/16

95/8 95/8

3g 3g

11/8 11/8

73/4 73/4

23/4g 23/4g

1 1

6 6

21/4g 21/4g

S8×23 ×18.4

6.76 5.40

8.00 8 8.00 8

0.441 0.271

7/16

1/4

1/4

1/8

S6×17.25 ×12.5

5.05 3.66

6.00 6 6.00 6

0.465 0.232

7/16

1/4

0.359 0.359

13/16

1/8

3.57 35/8 3.33 33/8

3/8

1/4

3/8

13/16

43/8 43/8

— —

S5×10

2.93

5.00 5

0.214

3/16

1/8

3.00 3

0.326

5/16

3/4

31/2

—

3/16

2.80 2.66 25/8

0.293 0.293

5/16

3/4

21/2

5/16

3/4

21/2

— —

2.51 21/2 2.33 23/8

0.260 0.260

1/4

5/8

1/4

5/8

13/4 13/4

— —

S4×9.5 ×7.7

2.79 2.26

4.00 4 4.00 4

0.326 0.193

5/16 3/16

1/8

S3×7.5 ×5.7

2.20 1.66

3.00 3 3.00 3

0.349 0.170

3/8

3/16

3/16

1/8

23/4

g

7/16

The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. — Indicates flange is too narrow to establish a workable gage.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A:14th Ed_

1/20/11

7:27 AM

Page 33

DIMENSIONS AND PROPERTIES

1–33

Table 1-3 (continued)

S-Shapes Properties S-SHAPES Nominal Wt.

Compact Section Criteria

Axis X-X

Axis Y-Y

rts

ho

Torsional Properties

lb/ft 121 106

I in.4 3.69 25.9 3160 3.61 33.4 2940

S in.3 258 240

r Z in. in.3 9.43 306 9.71 279

I in.4 83.0 76.8

J S r Z in.3 in. in.3 in. in. in.4 20.6 1.53 36.3 1.94 23.4 12.8 19.5 1.57 33.4 1.93 23.4 10.1

100 90 80

4.16 27.8 2380 4.09 33.1 2250 4.02 41.4 2100

199 187 175

9.01 239 9.21 222 9.47 204

47.4 44.7 42.0

13.1 12.5 12.0

1.27 24.0 1.30 22.4 1.34 20.8

1.66 23.1 1.66 23.1 1.67 23.1

7.59 6.05 4.89

6350 5980 5620

96 86

3.91 21.1 1670 3.84 25.6 1570

165 155

7.71 198 7.89 183

49.9 46.6

13.9 13.2

1.33 24.9 1.36 23.1

1.71 19.4 1.71 19.4

8.40 6.65

4690 4370

75 66

4.02 26.6 1280 3.93 33.5 1190

128 119

7.62 152 7.83 139

29.5 27.5

9.25 1.16 16.7 8.78 1.19 15.4

1.49 19.2 1.49 19.2

4.59 3.58

2720 2530

70 54.7

4.52 21.5 4.34 33.2

923 801

103 89.0

6.70 124 7.07 104

24.0 20.7

7.69 1.08 14.3 6.91 1.14 12.1

1.42 17.3 1.42 17.3

4.10 2.33

1800 1550

50 42.9

4.53 22.7 4.42 30.4

485 446

64.7 59.4

5.75 5.95

77.0 69.2

15.6 14.3

5.53 1.03 10.0 1.32 14.4 5.19 1.06 9.08 1.31 14.4

2.12 1.54

805 737

50 40.8

4.16 13.7 3.98 20.6

303 270

50.6 45.1

4.55 4.76

60.9 52.7

15.6 13.5

5.69 1.03 10.3 1.32 11.3 5.13 1.06 8.86 1.30 11.3

2.77 1.69

501 433

35 31.8

4.67 23.1 4.60 28.3

228 217

38.1 36.2

4.72 4.83

44.6 41.8

9.84 9.33

3.88 0.980 6.80 1.22 11.5 3.73 1.00 6.44 1.21 11.5

1.05 0.878

323 306

35 25.4

5.03 13.4 4.75 25.6

147 123

29.4 24.6

3.78 4.07

35.4 28.3

8.30 6.73

3.36 0.899 6.19 1.16 2.89 0.950 4.99 1.14

9.51 1.29 9.51 0.603

188 152

23 18.4

4.91 14.1 4.71 22.9

16.2 14.4

3.09 3.26

19.2 16.5

4.27 3.69

2.05 0.795 3.67 0.999 7.58 0.550 1.84 0.827 3.18 0.985 7.58 0.335

61.2 52.9 18.2 14.3

b ᎏf 2t f

h ᎏ tw

64.7 57.5

17.25 4.97 9.67 12.5 4.64 19.4

26.2 22.0

8.74 2.28 7.34 2.45

10.5 8.45

2.29 1.80

1.28 0.673 2.35 0.859 5.64 0.371 1.08 0.702 1.86 0.831 5.64 0.167

10

12.3

4.90 2.05

5.66

1.19

0.795 0.638 1.37 0.754 4.67 0.114

4.61 16.8

Cw in.6 11400 10500

6.52

9.5 7.7

4.77 8.33 4.54 14.1

6.76 6.05

3.38 1.56 3.03 1.64

4.04 3.50

0.887 0.635 0.564 1.13 0.698 3.71 0.120 0.748 0.562 0.576 0.970 0.676 3.71 0.0732

3.05 2.57

7.5 5.7

4.83 5.38 4.48 11.0

2.91 2.50

1.94 1.15 1.67 1.23

2.35 1.94

0.578 0.461 0.513 0.821 0.638 2.74 0.0896 0.447 0.383 0.518 0.656 0.605 2.74 0.0433

1.08 0.838

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A:14th Ed._

2/17/12

7:13 AM

Page 34

1–34

DIMENSIONS AND PROPERTIES

Table 1-4

HP-Shapes Dimensions Web Depth, d

Flange

Shape

Area, A

HP18×204 ×181 ×157f ×135f

in.2 60.2 53.2 46.2 39.9

18.3 18.0 17.7 17.5

in. 181/4 18 17 3/4 17 1/2

HP16×183 ×162 ×141 ×121f ×101f ×88c,f

54.1 47.7 41.7 35.8 29.9 25.8

16.5 16.3 16.0 15.8 15.5 15.3

161/2 161/4 16 153/4 151/2 153/8

1.13 1 1/8 1.00 1 0.875 7/8 0.750 3/4 0.625 5/8 0.540 9/16

HP14×117 f ×102 f ×89 f ×73 c,f

34.4 30.1 26.1 21.4

14.2 14.0 13.8 13.6

141/4 14 137/8 135/8

0.805 0.705 0.615 0.505

13/16

7/16

11/16

3/8

5/8

5/16

1/2

1/4

12.3 12.1 11.9 11.8

121/4

0.685 121/8 0.605 12 0.515 113/4 0.435

11/16

3/8

5/8

5/16

1/2 7/16

1/4 1/4

Thickness, tw ᎏ 2 tw in. 1.13 1 1/8 1.00 1 0.870 7/8 0.750 3/4

Width, bf

in. 9/16 1/2 7/16 3/8 9/16 1/2 7/16 3/8 5/16 5/16

18.1 18.0 17.9 17.8

in. 181/8 18 17 7/8 17 3/4

Distance

Thickness, tf

k

in. 1.13 11/8 1.00 1 0.870 7/8 0.750 3/4

in. 2 5/16 2 3/16 21/16 115/16

in. in. 13/4 131/2 111/16 15/8 19/16

in. 7 1/2

2 5/16 2 3/16 21/16 115/16 113/16 13/4

13/4 113/4 111/16 15/8 19/16 11/2 17/16

51/2

11/2 13/8 15/16 13/16

11/16 111/4 1 15/16 7/8

51/2

13/8 15/16 11/4 11/8

1

91/2

51/2

16.3 16.1 16.0 15.9 15.8 15.7

161/2 161/8 16 15 7/8 15 3/4 1511/16

1.13 11/8 1.00 1 0.875 7/8 0.750 3/4 0.625 5/8 0.540 9/16

14.9 14.8 14.7 14.6

147/8 143/4 143/4 145/8

0.805 0.705 0.615 0.505

13/16

121/4

12.3 12.2 121/4 12.1 121/8 12.0 12

0.685 0.610 0.515 0.435

11/16

11/16 5/8 1/2

k1

T

Workable Gage

HP12×84 ×74f ×63 f ×53 c,f

24.6 21.8 18.4 15.5

HP10×57 ×42 f

16.7 12.4

9.99 10 0.565 9.70 93/4 0.415

9/16

5/16

0.565 0.420

7/16

11/4 11/8

15/16

1/4

10.2 101/4 10.1 101/8

9/16

7/16

13/16

71/2 71/2

51/2 51/2

HP8×36 f

10.6

8.02

7/16

1/4

8.16 81/8

0.445

7/16

11/8

7/8

53/4

51/2

c f

8

0.445

5/8 1/2 7/16

Shape is slender for compression with Fy = 50 ksi. Shape exceeds compact limit for flexure with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

15/16 7/8 7/8

AISC_PART 01A:14th Ed_

1/20/11

7:28 AM

Page 35

DIMENSIONS AND PROPERTIES

1–35

Table 1-4 (continued)

HP-Shapes Properties

Nominal Wt.

Compact Section Criteria

Axis X-X

Axis Y-Y

lb/ft 204 8.01 181 9.00 157 10.3 135 11.9

12.1 13.6 15.6 18.2

I in.4 3480 3020 2570 2200

183 7.21 162 8.05 141 9.14 121 10.6 101 12.6 88 14.5

10.5 11.9 13.6 15.9 19.0 22.0

2510 2190 1870 1590 1300 1110

304 269 234 201 168 145

6.81 6.78 6.70 6.66 6.59 6.56

349 306 264 226 187 161

818 100 697 86.6 599 74.9 504 63.4 412 52.2 349 44.5

117 9.25 102 10.5 89 11.9 73 14.4

14.2 1220 172 16.2 1050 150 18.5 904 131 22.6 729 107

5.96 5.92 5.88 5.84

194 169 146 118

443 380 326 261

14.2 16.1 18.9 22.3

5.14 120 5.11 105 5.06 88.3 5.03 74.0

213 186 153 127

b ᎏf 2tf

84 8.97 74 10.0 63 11.8 53 13.8

h ᎏ tw

S in.3 380 336 290 251

r in. 7.60 7.53 7.46 7.43

Z I S in.3 in.4 in.3 433 1120 124 379 974 108 327 833 93.1 281 706 79.3

r in. 4.31 4.28 4.25 4.21

650 106 569 93.8 472 79.1 393 66.7

Z in.3 191 167 143 122

ho

J ᎏ S x ho

J

Cw

in. 17.2 17.0 16.8 16.8

0.00451 0.00362 0.00285 0.00216

in.4 29.5 20.7 13.9 9.12

in.6 82500 70400 59000 49500

3.89 156 3.82 134 3.79 116 3.75 97.6 3.71 80.1 3.68 68.2

4.54 4.45 4.40 4.34 4.27 4.21

15.4 15.3 15.1 15.1 14.9 14.8

0.00576 0.00457 0.00365 0.00275 0.00203 0.00161

26.9 18.8 12.9 8.35 5.07 3.45

48300 40800 34300 28500 22800 19000

59.5 51.4 44.3 35.8

3.59 3.56 3.53 3.49

91.4 78.8 67.7 54.6

4.15 4.10 4.05 4.00

13.4 13.3 13.2 13.1

0.00348 0.00270 0.00207 0.00143

8.02 5.39 3.59 2.01

19900 16800 14200 11200

34.6 30.4 25.3 21.1

2.94 2.92 2.88 2.86

53.2 46.6 38.7 32.2

3.41 3.38 3.33 3.29

11.6 11.5 11.4 11.4

0.00345 0.00276 0.00202 0.00148

4.24 2.98 1.83 1.12

7140 6160 5000 4080

2.45 2.41

30.3 2.84 21.8 2.77

9.43 0.00355 1.97 9.28 0.00202 0.813

2240 1540

9.88 1.95

15.2 2.26

7.58 0.00341 0.770

578

294 210

58.8 4.18 43.4 4.13

66.5 101 19.7 48.3 71.7 14.2

36

119

29.8 3.36

33.6

40.3

rts

Torsional Properties

in. 5.03 4.96 4.92 4.85

57 9.03 13.9 42 12.0 18.9 9.16 14.2

HP-SHAPES

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A:14th Ed_

1/20/11

7:28 AM

Page 36

1–36

DIMENSIONS AND PROPERTIES

Table 1-5

C-Shapes Dimensions Web Shape

Area, A

Depth, d

Thickness, tw

in.2 in. in. C15×50 14.7 15.0 15 0.716 11/16 ×40 11.8 15.0 15 0.520 1/2 ×33.9 10.0 15.0 15 0.400 3/8 C12×30 8.81 12.0 ×25 7.34 12.0 ×20.7 6.08 12.0

12 0.510 12 0.387 12 0.282

C10×30 ×25 ×20 ×15.3

10 10 10 10

8.81 7.35 5.87 4.48

10.0 10.0 10.0 10.0

Flange tw ᎏ 2

1/4 3/16

1/2

1/4

3/8

3/16

5/16

3/16

0.673 11/16 0.526 1/2 0.379 3/8 0.240 1/4 7/16

3/8 1/4 3/16 1/8

5.87 9.00 4.40 9.00 3.94 9.00

9 0.448 9 0.285 5/16 9 0.233 1/4

1/4

C8×18.75 5.51 8.00 ×13.75 4.03 8.00 ×11.5 3.37 8.00

8 0.487 1/2 8 0.303 5/16 8 0.220 1/4

1/4

C7×14.75 4.33 7.00 ×12.25 3.59 7.00 ×9.8 2.87 7.00

7 0.419 7/16 7 0.314 5/16 7 0.210 3/16

1/4

C6×13 ×10.5 ×8.2

3.82 6.00 3.07 6.00 2.39 6.00

6 0.437 7/16 6 0.314 5/16 6 0.200 3/16

1/4

C5×9 ×6.7

2.64 5.00 1.97 5.00

5 0.325 5 0.190

5/16

3/16

3/16

1/8

C4×7.25 ×6.25 ×5.4 ×4.5

2.13 1.77 1.58 1.38

4.00 4.00 4.00 4.00

4 4 4 4

0.321 5/16 0.247 1/4 0.184 3/16 0.125 1/8

3/16

C3×6 ×5 ×4.1 ×3.5

1.76 1.47 1.20 1.09

3.00 3.00 3.00 3.00

3 3 3 3

0.356 3/8 0.258 1/4 0.170 3/16 0.132 1/8

3/16

C9×20 ×15 ×13.4

Average Thickness, tf

k

T

Workable Gage

in.

in. 17/16 17/16 17/16

in. 121/8 121/8 121/8

in. 21/4 2 2

in. 3/8

3/16 1/8

3/16 1/8

3/16 1/8

3/16 1/8

1/8 1/8 1/16

1/8 1/8 1/16

Distance

Width, bf 3.72 3.52 3.40

33/4 31/2 33/8

in. 0.650 5/8 0.650 5/8 0.650 5/8

3.17 3.05 2.94

31/8 3 3

0.501 0.501 0.501

1/2

3.03 2.89 2.74 2.60

3 27/8 23/4 25/8

0.436 0.436 0.436 0.436

7/16

2.65 2.49 2.43

25/8

0.413 0.413 0.413

7/16

21/2 23/8

2.53 2.34 2.26

21/2 23/8 21/4

0.390 0.390 0.390

3/8

15/16

3/8

15/16

3/8

15/16

2.30 2.19 2.09

21/4 21/4 21/8

0.366 0.366 0.366

3/8

7/8

3/8

7/8

3/8

7/8

2.16 2.03 1.92

21/8 2 17/8

0.343 0.343 0.343

5/16

13/16

5/16

13/16

5/16

13/16

1.89 1.75

17/8

3/4

13/4

0.320 0.320

5/16 5/16

3/4

1.72 1.65 1.58 1.58

13/4 13/4 15/8 15/8

0.296 0.272 0.296 0.296

5/16

3/4

5/16

3/4

5/16

3/4

5/16

3/4

1.60 1.50 1.41 1.37

15/8 11/2 13/8 13/8

0.273 0.273 0.273 0.273

1/4

11/16

1/4

11/16

1/4

11/16

1/4

11/16

1/2 1/2

7/16 7/16 7/16

7/16 7/16

rts

ho

in. in. 1.17 14.4 1.15 14.4 1.13 14.4

11/8 11/8 11/8

93/4 13/4g 93/4 13/4g 93/4 13/4g

1 1 1 1

8 8 8 8

13/4g 13/4g 11/2g 11/2g

0.924 0.911 0.894 0.868

1 1 1

7 7 7

11/2g 13/8g 13/8g

0.850 8.59 0.825 8.59 0.814 8.59

61/8 61/8 61/8

11/2g 13/8g 13/8g

0.800 7.61 0.774 7.61 0.756 7.61

51/4 51/4 51/4

11/4g 11/4g 11/4g

0.738 6.63 0.722 6.63 0.698 6.63

43/8 43/8 43/8

13/8g 11/8g 11/8g

0.689 5.66 0.669 5.66 0.643 5.66

31/2 31/2

11/8g —

0.616 4.68 0.584 4.68

21/2 21/2 21/2 21/2

1g — — —

0.563 0.546 0.528 0.524

3.70 3.73 3.70 3.70

15/8 15/8 15/8 15/8

— — — —

0.519 0.496 0.469 0.456

2.73 2.73 2.73 2.73

g

1.01 11.5 1.00 11.5 0.983 11.5

The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. — Indicates flange is too narrow to establish a workable gage.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.56 9.56 9.56 9.56

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DIMENSIONS AND PROPERTIES

1–37

Table 1-5 (continued)

C-Shapes Properties C-SHAPES Torsional Properties

Nom- Shear inal Ctr, eo Wt.

Axis X-X

Axis Y-Y

J xp Z in.3 in. in.4 8.14 0.490 2.65 6.84 0.392 1.45 6.19 0.332 1.01

Cw

–r o

I lb/ft in. in.4 50 0.583 404 40 0.767 348 33.9 0.896 315

S r Z I S r x– in.3 in. in.3 in.4 in.3 in. in. 53.8 5.24 68.5 11.0 3.77 0.865 0.799 46.5 5.43 57.5 9.17 3.34 0.883 0.778 42.0 5.61 50.8 8.07 3.09 0.901 0.788

30 25 20.7

0.618 162 0.746 144 0.870 129

27.0 24.0 21.5

4.29 33.8 4.43 29.4 4.61 25.6

5.12 2.05 0.762 0.674 4.32 0.367 0.861 151 4.45 1.87 0.779 0.674 3.82 0.306 0.538 130 3.86 1.72 0.797 0.698 3.47 0.253 0.369 112

4.54 0.919 4.72 0.909 4.93 0.899

30 25 20 15.3

0.368 0.494 0.636 0.796

20.7 18.2 15.8 13.5

3.43 3.52 3.67 3.88

3.93 3.34 2.80 2.27

20 15 13.4

0.515 60.9 13.5 0.681 51.0 11.3 0.742 47.8 10.6

103 91.1 78.9 67.3

26.7 23.1 19.4 15.9

0.668 0.675 0.690 0.711

0.649 0.617 0.606 0.634

3.78 3.18 2.70 2.34

0.441 0.367 0.294 0.224

H

in. 5.49 0.937 5.71 0.927 5.94 0.920

1.22 0.687 0.368 0.209

79.5 68.3 56.9 45.5

3.63 3.76 3.93 4.19

2.41 1.17 0.640 0.583 2.46 0.326 0.427 1.91 1.01 0.659 0.586 2.04 0.245 0.208 1.75 0.954 0.666 0.601 1.94 0.219 0.168

39.4 31.0 28.2

3.46 0.899 3.69 0.882 3.79 0.875

18.75 0.431 43.9 11.0 2.82 13.9 1.97 1.01 0.598 0.565 2.17 0.344 0.434 13.75 0.604 36.1 9.02 2.99 11.0 1.52 0.848 0.613 0.554 1.73 0.252 0.186 11.5 0.697 32.5 8.14 3.11 9.63 1.31 0.775 0.623 0.572 1.57 0.211 0.130

25.1 19.2 16.5

3.05 0.894 3.26 0.874 3.41 0.862

3.22 16.9 3.40 13.6 3.48 12.6

1.65 1.47 1.31 1.15

in.6 492 410 358

0.921 0.912 0.900 0.884

14.75 0.441 27.2 12.25 0.538 24.2 9.8 0.647 21.2

7.78 2.51 9.75 1.37 0.772 0.561 0.532 1.63 0.309 0.267 13.1 6.92 2.59 8.46 1.16 0.696 0.568 0.525 1.42 0.257 0.161 11.2 6.07 2.72 7.19 0.957 0.617 0.578 0.541 1.26 0.205 0.0996 9.15

2.75 0.875 2.86 0.862 3.02 0.845

13 10.5 8.2

5.78 2.13 7.29 1.05 0.638 0.524 0.514 1.35 0.318 0.237 5.04 2.22 6.18 0.860 0.561 0.529 0.500 1.14 0.256 0.128 4.35 2.34 5.16 0.687 0.488 0.536 0.512 0.987 0.199 0.0736

7.19 5.91 4.70

2.37 0.858 2.48 0.842 2.65 0.824

0.380 17.3 0.486 15.1 0.599 13.1

9 6.7

0.427 0.552

8.89 3.56 1.84 4.39 0.624 0.444 0.486 0.478 0.913 0.264 0.109 7.48 2.99 1.95 3.55 0.470 0.372 0.489 0.484 0.757 0.215 0.0549

2.93 2.22

2.10 0.815 2.26 0.790

7.25 6.25 5.4 4.5

0.386 0.434 0.501 0.587

4.58 4.00 3.85 3.65

2.29 2.00 1.92 1.83

1.47 1.50 1.56 1.63

2.84 2.43 2.29 2.12

0.425 0.345 0.312 0.289

0.337 0.284 0.277 0.265

0.447 0.441 0.444 0.457

0.459 0.435 0.457 0.493

0.695 0.569 0.565 0.531

0.266 0.221 0.231 0.321

0.0817 0.0487 0.0399 0.0322

1.24 1.03 0.921 0.871

1.75 1.79 1.88 2.01

0.767 0.764 0.742 0.710

6 5 4.1 3.5

0.322 0.392 0.461 0.493

2.07 1.85 1.65 1.57

1.38 1.23 1.10 1.04

1.09 1.12 1.18 1.20

1.74 1.52 1.32 1.24

0.300 0.241 0.191 0.169

0.263 0.228 0.196 0.182

0.413 0.405 0.398 0.394

0.455 0.439 0.437 0.443

0.543 0.464 0.399 0.364

0.294 0.245 0.262 0.296

0.0725 0.0425 0.0269 0.0226

0.462 0.379 0.307 0.276

1.40 1.45 1.53 1.57

0.690 0.673 0.655 0.646

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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1–38

DIMENSIONS AND PROPERTIES

Table 1-6

MC-Shapes Dimensions Web Area, A

Shape

Depth, d

Flange

Thickness, tw ᎏ 2 tw

Width, bf

Distance

Average Thickness, tf

k

T

Workable Gage

rts

ho

MC18×58 ×51.9 ×45.8 ×42.7

in.2 17.1 15.3 13.5 12.6

in. 18.0 18.0 18.0 18.0

18 18 18 18

in. in. in. 0.700 11/16 3/8 4.20 41/4 0.600 5/8 5/16 4.10 41/8 0.500 1/2 1/4 4.00 4 0.450 7/16 1/4 3.95 4

in. 0.625 5/8 0.625 5/8 0.625 5/8 0.625 5/8

in. in. 17/16 151/8 17/16 17/16 17/16

in. 21/2

in. 1.35 1.35 1.34 1.34

in. 17.4 17.4 17.4 17.4

MC13×50 ×40 ×35 ×31.8

14.7 11.7 10.3 9.35

13.0 13.0 13.0 13.0

13 13 13 13

0.787 13/16 0.560 9/16 0.447 7/16 0.375 3/8

7/16

17/16 101/8 17/16 17/16 17/16

21/2

1.41 1.38 1.35 1.34

12.4 12.4 12.4 12.4

MC12×50 ×45 ×40 ×35 ×31

14.7 13.2 11.8 10.3 9.12

12.0 12.0 12.0 12.0 12.0

12 12 12 12 12

0.835 13/16 0.710 11/16 0.590 9/16 0.465 7/16 0.370 3/8

7/16

21/2

11/16

15/16 15/16 15/16 15/16 15/16

1.37 1.35 1.33 1.30 1.28

11.3 11.3 11.3 11.3 11.3

3/4

101/2 101/2

—

73/8

21/2g

MC12×14.3 MC12×10.6

c

4.18 12.0

12 0.250 1/4

3.10 12.0

12 0.190 3/16 13/16

4.41 4.19 4.07 4.00

43/8 41/8 41/8 4

0.610 0.610 0.610 0.610

5/8

41/8 4 37/8 33/4 35/8

0.700 0.700 0.700 0.700 0.700

11/16

3/16

4.14 4.01 3.89 3.77 3.67

1/8

2.12 21/8 0.313

5/16

1/8

1.50 11/2 0.309

5/16

3/4

4.32 0.575 4.10 41/8 0.575 3.95 4 0.575

9/16

15/16

9/16

15/16 15/16

1.44 73/8 21/2g 1.40 73/8 21/2g 1.36

9.43 9.43 9.43

3.41 33/8 0.575 3.32 33/8 0.575

9/16

15/16 15/16

73/8 73/8

2g 2g

1.17 1.14

9.43 9.43

3/4

81/2 87/8

— —

0.486 9.72 0.363 9.80

11/4 11/4

61/2 61/2

2g 2g

1.20 1.18

8.45 8.45

13/16 13/16

55/8 55/8

2g 2g

1.20 1.18

7.48 7.48

11/8 11/8

53/4 53/4

2g 2g

1.03 1.02

7.50 7.50

5/16 1/4 3/16

3/8 5/16 1/4

12.1 10.0 9.87 10.0 8.37 10.0

10 0.796 10 0.575 9/16 10 0.425 7/16

7/16

MC10×25 ×22

7.34 10.0 6.45 10.0

10 0.380 3/8 10 0.290 5/16

3/16

MC10×8.4 c ×6.5 c

2.46 10.0 1.95 10.0

10 0.170 3/16 10 0.152 1/8

1/8

MC10×41.1 ×33.6 ×28.5

5/16 1/4

3/16

1/16

43/8

7.47 7.02

9.00 9.00

9 0.450 7/16 9 0.400 3/8

1/4

MC8×22.8 ×21.4

6.70 6.28

8.00 8.00

8 0.427 7/16 8 0.375 3/8

1/4

MC8×20 ×18.7

5.87 5.50

8.00 8.00

8 0.400 3/8 8 0.353 3/8

3/16 3/16

3.03 3 2.98 3

MC8×8.5

2.50

8.00

8 0.179 3/16

1/8

1.87 17/8 0.311

3/16

5/8 5/8

11/16 11/16 11/16

9/16

9/16

1.50 11/2 0.280 1/4 1.17 11/8 0.202 3/16

MC9×25.4 ×23.9

3/16

5/8

3.50 31/2 0.550 3.45 31/2 0.550

9/16 9/16

3.50 31/2 0.525 1/2 3.45 31/2 0.525 1/2 0.500 1/2 0.500 1/2 5/16

9/16

13/16

93/8

21/4

11/4g 0.672 11.7 0.478 11.7

63/8 11/8g 0.624 7.69

Shape is slender for compression with Fy = 36 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. — Indicates flange is too narrow to establish a workable gage. c

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 39

DIMENSIONS AND PROPERTIES

1–39

Table 1-6 (continued)

MC-Shapes Properties MC18-MC8 Nom- Shear inal Ctr, eo Wt.

Torsional Properties Axis X-X

Axis Y-Y

J

Cw

–r o

S in.3 75.0 69.6 64.2 61.5

r in. 6.29 6.41 6.55 6.64

Z in.3 95.4 87.3 79.2 75.1

I in.4 17.6 16.3 14.9 14.3

S in.3 5.28 5.02 4.77 4.64

r in. 1.02 1.03 1.05 1.07

Z x– in. in.3 0.862 10.7 0.858 9.86 0.866 9.14 0.877 8.82

in. 0.474 0.424 0.374 0.349

in.4 in.6 2.81 1070 2.03 985 1.45 897 1.23 852

in. 6.56 6.70 6.87 6.97

0.944 0.939 0.933 0.930

xp

H

lb/ft 58 51.9 45.8 42.7

in. 0.695 0.797 0.909 0.969

I in.4 675 627 578 554

50 40 35 31.8

0.815 1.03 1.16 1.24

314 273 252 239

48.3 41.9 38.8 36.7

4.62 4.82 4.95 5.05

60.8 51.2 46.5 43.4

16.4 13.7 12.3 11.4

4.77 4.24 3.97 3.79

1.06 1.08 1.09 1.10

0.974 10.2 0.963 8.66 0.980 8.04 1.00 7.69

0.566 0.452 0.396 0.360

2.96 1.55 1.13 0.937

558 462 412 380

5.07 5.32 5.50 5.64

0.875 0.859 0.849 0.842

50 45 40 35 31

0.741 0.844 0.952 1.07 1.17

269 251 234 216 202

44.9 41.9 39.0 36.0 33.7

4.28 4.36 4.46 4.59 4.71

56.5 52.0 47.7 43.2 39.7

17.4 15.8 14.2 12.6 11.3

5.64 5.30 4.98 4.64 4.37

1.09 1.09 1.10 1.11 1.11

1.05 10.9 1.04 10.1 1.04 9.31 1.05 8.62 1.08 8.15

0.613 0.550 0.490 0.428 0.425

3.23 2.33 1.69 1.24 1.00

411 373 336 297 267

4.77 4.88 5.01 5.18 5.34

0.859 0.851 0.842 0.831 0.822

14.3 0.435 76.1 12.7 10.6 0.284 55.3

4.27 15.9

9.22 4.22 11.6

1.00 0.574 0.489 0.377 1.21 0.174 0.117

32.8

4.37 0.965

0.378 0.307 0.349 0.269 0.635 0.129 0.0596

11.7

4.27 0.983

41.1 0.864 157 33.6 1.06 139 28.5 1.21 126

31.5 27.8 25.3

3.61 39.3 15.7 3.75 33.7 13.1 3.89 30.0 11.3

25 22

22.0 20.5

3.87 26.2 3.99 23.9

1.03 110 1.12 102

8.4 0.332 31.9 6.5 0.182 22.9

4.85 1.14 1.09 4.35 1.15 1.09 3.99 1.16 1.12

9.49 0.604 2.26 8.28 0.494 1.20 7.59 0.419 0.791

269 224 193

4.26 0.790 4.47 0.770 4.68 0.752

7.25 2.96 0.993 0.953 5.65 0.367 0.638 6.40 2.75 0.997 0.990 5.29 0.467 0.510

124 110

4.46 0.803 4.62 0.791

6.39 3.61 7.92 0.326 0.268 0.364 0.284 0.548 0.123 0.0413 4.59 3.43 5.90 0.133 0.137 0.262 0.194 0.284 0.0975 0.0191

25.4 0.986 87.9 19.5 23.9 1.04 84.9 18.9

3.43 23.5 3.48 22.5

7.57 2.99 1.01 0.970 5.70 0.415 0.691 7.14 2.89 1.01 0.981 5.51 0.390 0.599

22.8 1.04 21.4 1.09

63.8 15.9 61.5 15.4

3.09 19.1 3.13 18.2

7.01 2.81 1.02 1.01 6.58 2.71 1.02 1.02

20 0.843 54.4 13.6 18.7 0.889 52.4 13.1

3.04 16.4 3.09 15.6

8.5 0.542 23.3

7.00 3.68 0.972 2.76 3.46 0.988 104 98.0

4.08 0.770 4.15 0.763

5.37 0.419 0.572 5.18 0.452 0.495

75.2 70.8

3.84 0.715 3.91 0.707

4.42 2.02 0.867 0.840 3.86 0.367 0.441 4.15 1.95 0.868 0.849 3.72 0.344 0.380

47.8 45.0

3.58 0.779 3.65 0.773

5.82 3.05 6.95 0.624 0.431 0.500 0.428 0.875 0.156 0.0587

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.21 3.24 0.910

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Page 40

1–40

DIMENSIONS AND PROPERTIES

Table 1-6 (continued)

MC-Shapes Dimensions Web Shape

Area, A

Depth, d

Flange

Thickness, tw ᎏ 2 tw

Distance

Average Thickness, tf

k

T

Workable Gage

rts

ho

in. in. 3.60 35/8 0.500 1/2 3.45 31/2 0.500 1/2

in. 11/8 11/8

in. 43/4 43/4

in. 2g 2g

in. 1.23 1.19

in. 6.50 6.50

3.50 31/2 0.475 1/2 3.50 31/2 0.385 3/8

11/16 7/8

37/8 41/4

2g 2g

1.20 1.20

5.53 5.62

0.475 1/2 0.475 1/2

11/16 11/16

37/8 37/8

13/4g 1.03 13/4g 1.01

5.53 5.53

11/2g 0.856 5.63

Width, bf

MC7×22.7 ×19.1

in.2 6.67 5.61

in. in. 7.00 7 0.503 1/2 7.00 7 0.352 3/8

MC6×18 ×15.3

5.29 4.49

6.00 6.00

6 0.379 3/8 6 0.340 5/16

3/16

MC6×16.3 ×15.1

4.79 4.44

6.00 6.00

6 0.375 3/8 6 0.316 5/16

3/16 3/16

3.00 3 2.94 3

MC6×12

3.53

6.00

6 0.310 5/16

3/16

2.50 21/2 0.375

3/8

7/8

41/4

MC6×7 ×6.5

2.09 1.95

6.00 6.00

6 0.179 3/16 6 0.155 1/8

1/8

1.88 17/8 0.291 1.85 17/8 0.291

5/16

3/4

1/16

5/16

3/4

41/2 41/2

— —

0.638 5.71 0.631 5.71

MC4×13.8

4.03

4.00

4 0.500 1/2

1/4

2.50 21/2 0.500 1/2

2

—

0.851 3.50

13/8

—

0.657 2.65

MC3×7.1

2.11

3.00

3 0.312

5/16

in. 1/4 3/16

3/16

3/16

1.94 2

0.351

3/8

1 13/16

g

The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. — Indicates flange is too narrow to establish a workable gage.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A:14th Ed_

1/20/11

7:28 AM

Page 41

DIMENSIONS AND PROPERTIES

1–41

Table 1-6 (continued)

MC-Shapes Properties MC7-MC3 Nom- Shear inal Ctr, eo Wt.

Torsional Properties Axis X-X

Axis Y-Y

J xp Z in.3 in. in.4 5.38 0.477 0.625 4.85 0.579 0.407

in.6 58.3 49.3

in. 3.53 0.659 3.70 0.638

9.89 2.37 11.7 5.88 2.47 1.05 1.12 8.44 2.38 9.91 4.91 2.01 1.05 1.05

4.68 0.644 0.379 3.85 0.511 0.223

34.6 30.0

3.46 0.563 3.41 0.579

16.3 0.930 26.0 15.1 0.982 24.9

8.66 2.33 10.4 3.77 1.82 0.887 0.927 3.47 0.465 0.336 8.30 2.37 9.83 3.46 1.73 0.883 0.940 3.30 0.543 0.285

22.1 20.5

3.11 0.643 3.18 0.634

12

6.24 2.30 7.47 1.85 1.03 0.724 0.704 1.97 0.294 0.155

11.3

2.80 0.740

lb/ft in. 22.7 1.01 19.1 1.15 18 1.17 15.3 1.16

29.7 25.3

0.725 18.7

7 0.583 11.4 6.5 0.612 11.0

3.81 2.34 4.50 0.603 0.439 0.537 0.501 0.865 0.174 0.0464 3.66 2.38 4.28 0.565 0.422 0.539 0.513 0.836 0.191 0.0412

Cw

–r o

I S r x– in.4 in.3 in. in. 7.24 2.83 1.04 1.04 6.06 2.55 1.04 1.08

I S r Z in.4 in.3 in. in.3 47.4 13.5 2.67 16.4 43.1 12.3 2.77 14.5

H

4.00 2.63 0.830 3.75 2.68 0.824

13.8 0.643

8.85 4.43 1.48 5.53 2.13 1.29 0.727 0.849 2.40 0.508 0.373

4.84 2.23 0.550

7.1 0.574

2.72 1.81 1.14 2.24 0.666 0.518 0.562 0.653 0.998 0.414 0.0928

0.915 1.76 0.516

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 42

1–42

DIMENSIONS AND PROPERTIES

Table 1-7

Angles Properties Flexural-Torsional Properties

Axis X-X

k

Wt.

Area, A

L8×8×11/8 ×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2

in. 13/4 15/8 11/2 13/8 11/4 13/16 11/8

lb/ft 56.9 51.0 45.0 38.9 32.7 29.6 26.4

in.2 16.8 15.1 13.3 11.5 9.69 8.77 7.84

in.4 98.1 89.1 79.7 69.9 59.6 54.2 48.8

in.3 17.5 15.8 14.0 12.2 10.3 9.33 8.36

in. 2.41 2.43 2.45 2.46 2.48 2.49 2.49

in. 2.40 2.36 2.31 2.26 2.21 2.19 2.17

in.3 31.6 28.5 25.3 22.0 18.6 16.8 15.1

in. 1.05 0.944 0.831 0.719 0.606 0.548 0.490

in.4 7.13 5.08 3.46 2.21 1.30 0.961 0.683

in.6 32.5 23.4 16.1 10.4 6.16 4.55 3.23

in. 4.29 4.32 4.36 4.39 4.42 4.43 4.45

L8×6×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16

11/2 13/8 11/4 11/8 11/16 1 15/16

44.2 39.1 33.8 28.5 25.7 23.0 20.2

13.1 11.5 9.99 8.41 7.61 6.80 5.99

80.9 72.4 63.5 54.2 49.4 44.4 39.3

15.1 13.4 11.7 9.86 8.94 8.01 7.06

2.49 2.50 2.52 2.54 2.55 2.55 2.56

2.65 2.60 2.55 2.50 2.48 2.46 2.43

27.3 24.3 21.1 17.9 16.2 14.6 12.9

1.45 1.43 1.34 1.27 1.24 1.20 1.15

4.34 2.96 1.90 1.12 0.823 0.584 0.396

16.3 11.3 7.28 4.33 3.20 2.28 1.55

3.88 3.92 3.95 3.98 3.99 4.01 4.02

L8×4×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16

11/2 13/8 11/4 11/8 11/16 1 15/16

37.4 33.1 28.7 24.2 21.9 19.6 17.2

11.1 9.79 8.49 7.16 6.49 5.80 5.11

69.7 62.6 55.0 47.0 42.9 38.6 34.2

14.0 12.5 10.9 9.20 8.34 7.48 6.59

2.51 2.53 2.55 2.56 2.57 2.58 2.59

3.03 2.99 2.94 2.89 2.86 2.84 2.81

24.3 21.7 18.9 16.1 14.6 13.1 11.6

2.45 2.41 2.34 2.27 2.23 2.20 2.16

3.68 2.51 1.61 0.955 0.704 0.501 0.340

12.9 8.89 5.75 3.42 2.53 1.80 1.22

3.75 3.78 3.80 3.83 3.84 3.86 3.87

L7×4×3/4 ×5/8 ×1/2 ×7/16 ×3/8

11/4 11/8 1 15/16 7/8

26.2 22.1 17.9 15.7 13.6

7.74 6.50 5.26 4.63 4.00

37.8 32.4 26.6 23.6 20.5

8.39 7.12 5.79 5.11 4.42

2.21 2.23 2.25 2.26 2.27

2.50 2.45 2.40 2.38 2.35

14.8 12.5 10.2 9.03 7.81

1.84 1.80 1.74 1.71 1.67

1.47 0.868 0.456 0.310 0.198

3.97 2.37 1.25 0.851 0.544

3.31 3.34 3.37 3.38 3.40

L6×6×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16 ×3/8 ×5/16

11/2 13/8 11/4 11/8 11/16 1 15/16 7/8 13/16

37.4 33.1 28.7 24.2 21.9 19.6 17.2 14.9 12.4

11.0 9.75 8.46 7.13 6.45 5.77 5.08 4.38 3.67

35.4 31.9 28.1 24.1 22.0 19.9 17.6 15.4 13.0

8.55 7.61 6.64 5.64 5.12 4.59 4.06 3.51 2.95

1.79 1.81 1.82 1.84 1.85 1.86 1.86 1.87 1.88

1.86 1.81 1.77 1.72 1.70 1.67 1.65 1.62 1.60

15.4 13.7 11.9 10.1 9.18 8.22 7.25 6.27 5.26

0.917 0.813 0.705 0.594 0.538 0.481 0.423 0.365 0.306

3.68 2.51 1.61 0.955 0.704 0.501 0.340 0.218 0.129

9.24 6.41 4.17 2.50 1.85 1.32 0.899 0.575 0.338

3.18 3.21 3.24 3.28 3.29 3.31 3.32 3.34 3.35

Shape

I

S

r

y–

yp

Z

Note: For workable gages, refer to Table 1-7A. For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

J

Cw

–r o

AISC_PART 01A_14th Ed._Nov. 19, 2012 14-11-10 9:50 AM Page 43

(Black plate)

1–43

DIMENSIONS AND PROPERTIES

Table 1-7 (continued)

Angles Properties

L8-L6

Axis Y-Y

I

S

r

L8×8×11/8 ×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2

in.4 98.1 89.1 79.7 69.9 59.6 54.2 48.8

in.3 17.5 15.8 14.0 12.2 10.3 9.33 8.36

in. 2.41 2.43 2.45 2.46 2.48 2.49 2.49

in. 2.40 2.36 2.31 2.26 2.21 2.19 2.17

in.3 31.6 28.5 25.3 22.0 18.6 16.8 15.1

in. 1.05 0.944 0.831 0.719 0.606 0.548 0.490

in.4 40.7 36.8 32.7 28.5 24.2 21.9 19.8

in.3 12.0 11.0 10.0 8.90 7.72 7.09 6.44

L8×6×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16

38.8 34.9 30.8 26.4 24.1 21.7 19.3

8.92 7.94 6.92 5.88 5.34 4.79 4.23

1.72 1.74 1.75 1.77 1.78 1.79 1.80

1.65 1.60 1.56 1.51 1.49 1.46 1.44

16.2 14.4 12.5 10.5 9.52 8.52 7.50

0.819 0.719 0.624 0.526 0.476 0.425 0.374

21.3 18.9 16.6 14.1 12.8 11.5 10.2

L8×4×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16

11.6 10.5 9.37 8.11 7.44 6.75 6.03

3.94 3.51 3.07 2.62 2.38 2.15 1.90

1.03 1.04 1.05 1.06 1.07 1.08 1.09

1.04 0.997 0.949 0.902 0.878 0.854 0.829

7.73 6.77 5.82 4.86 4.39 3.91 3.42

0.694 0.612 0.531 0.448 0.406 0.363 0.319

L7×4×3/4 ×5/8 ×1/2 ×7/16 ×3/8

9.00 7.79 6.48 5.79 5.06

3.01 2.56 2.10 1.86 1.61

1.08 1.10 1.11 1.12 1.12

1.00 0.958 0.910 0.886 0.861

5.60 4.69 3.77 3.31 2.84

0.553 0.464 0.376 0.331 0.286

8.55 7.61 6.64 5.64 5.12 4.59 4.06 3.51 2.95

1.79 1.81 1.82 1.84 1.85 1.86 1.86 1.87 1.88

1.86 1.81 1.77 1.72 1.70 1.67 1.65 1.62 1.60

15.4 13.7 11.9 10.1 9.18 8.22 7.25 6.27 5.26

Shape

L6×6×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16 ×3/8 ×5/16

35.4 31.9 28.1 24.1 22.0 19.9 17.6 15.4 13.0

Qs

Axis Z-Z

x–

Z

xp

I

S

r

Tan ␣

Fy = 36 ksi

in. 1.56 1.56 1.57 1.57 1.58 1.58 1.59

1.00 1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 0.997 0.959 0.912

7.60 6.71 5.82 4.91 4.45 3.98 3.51

1.28 1.28 1.29 1.29 1.30 1.30 1.31

0.542 0.546 0.550 0.554 0.556 0.557 0.559

1.00 1.00 1.00 0.997 0.959 0.912 0.850

7.83 6.97 6.14 5.24 4.78 4.32 3.84

3.48 3.06 2.65 2.24 2.03 1.82 1.61

0.844 0.846 0.850 0.856 0.859 0.863 0.867

0.247 0.252 0.257 0.262 0.264 0.266 0.268

1.00 1.00 1.00 0.997 0.959 0.912 0.850

5.63 4.81 3.94 3.50 3.04

2.57 2.16 1.76 1.55 1.34

0.855 0.860 0.866 0.869 0.873

0.324 0.329 0.334 0.337 0.339

1.00 1.00 0.965 0.912 0.840

0.917 14.9 0.813 13.3 0.705 11.6 0.594 9.81 0.538 8.90 0.481 8.06 0.423 7.05 0.365 6.21 0.306 5.20

5.70 5.18 4.63 4.04 3.73 3.40 3.05 2.69 2.30

1.17 1.17 1.17 1.17 1.18 1.18 1.18 1.19 1.19

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 1.00 1.00 0.973 0.912 0.826

Note: For workable gages, refer to Table 1-7A. For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A:14th Ed_

1/20/11

7:28 AM

Page 44

1–44

DIMENSIONS AND PROPERTIES

Table 1-7 (continued)

Angles Properties Flexural-Torsional Properties

Axis X-X Shape

k

Wt.

Area, A

in. 13/8 11/4 11/8 11/16 1 15/16 7/8 13/16

lb/ft 27.2 23.6 20.0 18.1 16.2 14.3 12.3 10.3

in.2 8.00 6.94 5.86 5.31 4.75 4.18 3.61 3.03

I

r

y–

Z

yp

J

Cw

–r o

in.3 7.13 6.23 5.29 4.81 4.31 3.81 3.30 2.77

in. 1.86 1.88 1.89 1.90 1.91 1.92 1.93 1.94

in. 2.12 2.07 2.03 2.00 1.98 1.95 1.93 1.90

in.3 12.7 11.1 9.44 8.59 7.71 6.81 5.89 4.96

in. 1.43 1.37 1.31 1.28 1.25 1.22 1.19 1.15

in.4 2.03 1.31 0.775 0.572 0.407 0.276 0.177 0.104

in.6 4.04 2.64 1.59 1.18 0.843 0.575 0.369 0.217

in. 2.82 2.85 2.88 2.90 2.91 2.93 2.94 2.96

4.50 16.6 3.44 12.9 2.89 10.9

4.23 3.23 2.72

1.92 1.93 1.94

2.07 2.02 2.00

7.49 5.74 4.84

1.50 1.41 1.38

0.386 0.168 0.0990

0.779 0.341 0.201

2.88 2.90 2.92

27.2 23.6 20.0 16.2 14.3 12.3 10.3

8.00 6.98 5.90 4.79 4.22 3.65 3.07

17.8 15.7 13.6 11.3 10.0 8.76 7.44

5.16 4.52 3.85 3.15 2.78 2.41 2.04

1.49 1.50 1.52 1.53 1.54 1.55 1.56

1.56 1.52 1.47 1.42 1.40 1.37 1.35

9.31 8.14 6.93 5.66 5.00 4.33 3.65

0.800 0.698 0.590 0.479 0.422 0.365 0.307

2.07 1.33 0.792 0.417 0.284 0.183 0.108

3.53 2.32 1.40 0.744 0.508 0.327 0.193

2.64 2.67 2.70 2.73 2.74 2.76 2.77

19.8 16.8 13.6 10.4 8.70 7.00

5.85 13.9 4.93 12.0 4.00 10.0 3.05 7.75 2.56 6.58 2.07 5.36

4.26 3.63 2.97 2.28 1.92 1.55

1.55 1.56 1.58 1.59 1.60 1.61

1.74 1.69 1.65 1.60 1.57 1.55

7.60 6.50 5.33 4.09 3.45 2.78

1.10 1.06 1.00 0.933 0.904 0.860

1.09 0.651 0.343 0.150 0.0883 0.0464

1.52 0.918 0.491 0.217 0.128 0.0670

2.36 2.39 2.42 2.45 2.47 2.48

3/4 11/16

12.8 11.3 9.80 8.20 6.60

3.75 3.31 2.86 2.41 1.94

9.43 8.41 7.35 6.24 5.09

2.89 2.56 2.22 1.87 1.51

1.58 1.59 1.60 1.61 1.62

1.74 1.72 1.69 1.67 1.64

5.12 4.53 3.93 3.32 2.68

1.25 1.22 1.19 1.14 1.12

0.322 0.220 0.141 0.0832 0.0438

0.444 0.304 0.196 0.116 0.0606

2.38 2.39 2.41 2.42 2.43

L4×4×3/4 11/8 ×5/8 1 7/8 ×1/2 13/16 ×7/16 3/4 ×3/8 11/16 ×5/16 5/8 ×1/4

18.5 15.7 12.8 11.3 9.80 8.20 6.60

5.44 4.61 3.75 3.30 2.86 2.40 1.93

7.62 6.62 5.52 4.93 4.32 3.67 3.00

2.79 2.38 1.96 1.73 1.50 1.27 1.03

1.18 1.20 1.21 1.22 1.23 1.24 1.25

1.27 1.22 1.18 1.15 1.13 1.11 1.08

5.02 4.28 3.50 3.10 2.69 2.26 1.82

0.680 0.576 0.469 0.413 0.358 0.300 0.241

1.02 0.610 0.322 0.220 0.141 0.0832 0.0438

1.12 0.680 0.366 0.252 0.162 0.0963 0.0505

2.10 2.13 2.16 2.18 2.19 2.21 2.22

L6×4×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16 ×3/8 ×5/16

L6×31/2×1/2 1 15.3 7/8 ×3/8 11.7 ×5/16 13/16 9.80 L5×5×7/8 ×3/4 ×5/8 ×1/2 ×7/16 ×3/8 ×5/16

13/8 11/4 11/8 1 15/16 7/8 13/16

L5×31/2×3/4 13/16 ×5/8 11/16 15/16 ×1/2 13/16 ×3/8 3/4 ×5/16 11/16 ×1/4 L5×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4

15/16 7/8 13/16

in.4 27.7 24.5 21.0 19.2 17.3 15.4 13.4 11.4

S

Note: For workable gages, refer to Table 1-7A. For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A_14th Ed._Nov. 19, 2012 14-11-10 9:55 AM Page 45

(Black plate)

1–45

DIMENSIONS AND PROPERTIES

Table 1-7 (continued)

Angles Properties

L6-L4

Axis Y-Y

I

S

r

L6×4×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16 ×3/8 ×5/16

in.4 9.70 8.63 7.48 6.86 6.22 5.56 4.86 4.13

in.3 3.37 2.95 2.52 2.29 2.06 1.83 1.58 1.34

in. 1.10 1.12 1.13 1.14 1.14 1.15 1.16 1.17

in. 1.12 1.07 1.03 1.00 0.981 0.957 0.933 0.908

in.3 6.26 5.42 4.56 4.13 3.69 3.24 2.79 2.33

in. 0.667 0.578 0.488 0.443 0.396 0.348 0.301 0.253

in.4 5.82 5.08 4.32 3.93 3.54 3.14 2.73 2.31

in.3 2.91 2.51 2.12 1.92 1.72 1.51 1.31 1.10

L6×31/2×1/2 ×3/8 ×5/16

4.24 3.33 2.84

1.59 1.22 1.03

0.968 0.984 0.991

0.829 0.781 0.756

2.88 2.18 1.82

0.375 0.287 0.241

2.59 2.01 1.70

L5×5×7/8 ×3/4 ×5/8 ×1/2 ×7/16 ×3/8 ×5/16

17.8 15.7 13.6 11.3 10.0 8.76 7.44

5.16 4.52 3.85 3.15 2.78 2.41 2.04

1.49 1.50 1.52 1.53 1.54 1.55 1.56

1.56 1.52 1.47 1.42 1.40 1.37 1.35

9.31 8.14 6.93 5.66 5.00 4.33 3.65

0.800 0.698 0.590 0.479 0.422 0.365 0.307

L5×31/2×3/4 ×5/8 ×1/2 ×3/8 ×5/16 ×1/4

5.52 4.80 4.02 3.15 2.69 2.20

2.20 1.88 1.55 1.19 1.01 0.816

0.974 0.987 1.00 1.02 1.02 1.03

0.993 0.947 0.901 0.854 0.829 0.804

4.07 3.43 2.79 2.12 1.77 1.42

L5×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4

2.55 2.29 2.01 1.72 1.41

1.13 1.00 0.874 0.739 0.600

0.824 0.831 0.838 0.846 0.853

0.746 0.722 0.698 0.673 0.648

L4×4×3/4 ×5/8 ×1/2 ×7/16 ×3/8 ×5/16 ×1/4

7.62 6.62 5.52 4.93 4.32 3.67 3.00

2.79 2.38 1.96 1.73 1.50 1.27 1.03

1.18 1.20 1.21 1.22 1.23 1.24 1.25

1.27 1.22 1.18 1.15 1.13 1.11 1.08

Shape

Qs

Axis Z-Z

x–

Z

xp

I

S

r

Tan ␣

Fy = 36 ksi

in. 0.854 0.856 0.859 0.861 0.864 0.867 0.870 0.874

0.421 0.428 0.435 0.438 0.440 0.443 0.446 0.449

1.00 1.00 1.00 1.00 1.00 0.973 0.912 0.826

1.34 1.02 0.859

0.756 0.763 0.767

0.343 0.349 0.352

1.00 0.912 0.826

7.60 6.55 5.62 4.64 4.04 3.55 3.00

3.43 3.08 2.70 2.29 2.06 1.83 1.58

0.971 0.972 0.975 0.980 0.983 0.986 0.990

1.00 1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 1.00 0.983 0.912

0.585 0.493 0.400 0.305 0.256 0.207

3.23 2.74 2.26 1.73 1.47 1.19

1.90 1.60 1.29 0.985 0.827 0.667

0.744 0.746 0.750 0.755 0.758 0.761

0.464 0.472 0.479 0.485 0.489 0.491

1.00 1.00 1.00 0.983 0.912 0.804

2.08 1.82 1.57 1.31 1.05

0.375 0.331 0.286 0.241 0.194

1.55 1.37 1.20 1.01 0.825

0.953 0.840 0.726 0.610 0.491

0.642 0.644 0.646 0.649 0.652

0.357 0.361 0.364 0.368 0.371

1.00 1.00 0.983 0.912 0.804

5.02 4.28 3.50 3.10 2.69 2.26 1.82

0.680 0.576 0.469 0.413 0.358 0.300 0.241

3.25 2.76 2.25 1.99 1.73 1.46 1.19

1.81 1.59 1.35 1.22 1.08 0.936 0.776

0.774 0.774 0.776 0.777 0.779 0.781 0.783

1.00 1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 1.00 0.997 0.912

Note: For workable gages, refer to Table 1-7A. For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A:14th Ed_

1/20/11

7:28 AM

Page 46

1–46

DIMENSIONS AND PROPERTIES

Table 1-7 (continued)

Angles Properties Flexural-Torsional Properties

Axis X-X

Area, A

I

S

in. lb/ft 7/8 11.9 3/4 9.10 11/16 7.70 5/8 6.20

in.2 3.50 2.68 2.25 1.82

in.4 5.30 4.15 3.53 2.89

in.3 1.92 1.48 1.25 1.01

in. 1.23 1.25 1.25 1.26

L4×3×5/8 1 13.6 7/8 ×1/2 11.1 3/4 ×3/8 8.50 11/16 ×5/16 7.20 5/8 ×1/4 5.80

3.99 3.25 2.49 2.09 1.69

6.01 5.02 3.94 3.36 2.75

2.28 1.87 1.44 1.22 0.988

11.1 9.80 8.50 7.20 5.80

3.25 2.89 2.50 2.10 1.70

3.63 3.25 2.86 2.44 2.00

10.2 9.10 7.90 6.60 5.40

3.02 2.67 2.32 1.95 1.58

9.40 7.20 6.10 4.90

Shape

L4×31/2×1/2 ×3/8 ×5/16 ×1/4

L31/2×31/2×1/2 ×7/16 ×3/8 ×5/16 ×1/4 L31/2×3×1/2

×7/16 ×3/8 ×5/16 ×1/4

L31/2×21/2×1/2 ×3/8 ×5/16 ×1/4 L3×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4 ×3/16 L3×21/2×1/2 ×7/16 ×3/8 ×5/16 ×1/4 ×3/16

k

7/8 13/16 3/4 11/16 5/8 7/8 13/16 3/4 11/16 5/8 7/8 3/4 11/16 5/8 7/8 13/16 3/4 11/16 5/8 9/16 7/8 13/16 3/4 11/16 5/8 9/16

Wt.

y–

Z

yp

J

Cw

–r o

in. 1.24 1.20 1.17 1.14

in.3 3.46 2.66 2.24 1.81

in. 0.500 0.427 0.400 0.360

in.4 0.301 0.132 0.0782 0.0412

in.6 0.302 0.134 0.0798 0.0419

in. 2.03 2.06 2.08 2.09

1.23 1.24 1.26 1.27 1.27

1.37 1.32 1.27 1.25 1.22

4.08 3.36 2.60 2.19 1.77

0.808 0.750 0.680 0.656 0.620

0.529 0.281 0.123 0.0731 0.0386

0.472 0.255 0.114 0.0676 0.0356

1.91 1.94 1.97 1.98 1.99

1.48 1.32 1.15 0.969 0.787

1.05 1.06 1.07 1.08 1.09

1.05 1.03 1.00 0.979 0.954

2.66 2.36 2.06 1.74 1.41

0.464 0.413 0.357 0.300 0.243

0.281 0.192 0.123 0.0731 0.0386

0.238 0.164 0.106 0.0634 0.0334

1.87 1.89 1.90 1.92 1.93

3.45 3.10 2.73 2.33 1.92

1.45 1.29 1.12 0.951 0.773

1.07 1.08 1.09 1.09 1.10

1.12 1.09 1.07 1.05 1.02

2.61 2.32 2.03 1.72 1.39

0.480 0.449 0.407 0.380 0.340

0.260 0.178 0.114 0.0680 0.0360

0.191 0.132 0.0858 0.0512 0.0270

1.75 1.76 1.78 1.79 1.80

2.77 2.12 1.79 1.45

3.24 2.56 2.20 1.81

1.41 1.09 0.925 0.753

1.08 1.10 1.11 1.12

1.20 1.15 1.13 1.10

2.52 1.96 1.67 1.36

0.730 0.673 0.636 0.600

0.234 0.103 0.0611 0.0322

0.159 0.0714 0.0426 0.0225

1.66 1.69 1.71 1.72

9.40 8.30 7.20 6.10 4.90 3.71

2.76 2.43 2.11 1.78 1.44 1.09

2.20 1.98 1.75 1.50 1.23 0.948

1.06 0.946 0.825 0.699 0.569 0.433

0.895 0.903 0.910 0.918 0.926 0.933

0.929 0.907 0.884 0.860 0.836 0.812

1.91 1.70 1.48 1.26 1.02 0.774

0.460 0.405 0.352 0.297 0.240 0.182

0.230 0.157 0.101 0.0597 0.0313 0.0136

0.144 1.59 0.100 1.60 0.0652 1.62 0.0390 1.64 0.0206 1.65 0.00899 1.67

8.50 7.60 6.60 5.60 4.50 3.39

2.50 2.22 1.93 1.63 1.32 1.00

2.07 1.87 1.65 1.41 1.16 0.899

1.03 0.921 0.803 0.681 0.555 0.423

0.910 0.917 0.924 0.932 0.940 0.947

0.995 0.972 0.949 0.925 0.900 0.874

1.86 1.66 1.45 1.23 1.000 0.761

0.500 0.463 0.427 0.392 0.360 0.333

0.213 0.146 0.0943 0.0560 0.0296 0.0130

0.112 1.46 0.0777 1.48 0.0507 1.49 0.0304 1.51 0.0161 1.52 0.00705 1.54

r

Note: For workable gages, refer to Table 1-7A. For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A_14th Ed._Nov. 19, 2012 14-11-10 10:03 AM Page 47

(Black plate)

1–47

DIMENSIONS AND PROPERTIES

Table 1-7 (continued)

Angles Properties

L4-L3

Axis Y-Y

I

S

r

L4×31/2×1/2 ×3/8 ×5/16 ×1/4

in.4 3.76 2.96 2.52 2.07

in.3 1.50 1.16 0.980 0.794

in. 1.04 1.05 1.06 1.07

in. 0.994 0.947 0.923 0.897

in.3 2.69 2.06 1.74 1.40

in. 0.438 0.335 0.281 0.228

in.4 1.79 1.39 1.16 0.953

in.3 1.17 0.938 0.811 0.653

L4×3×5/8 ×1/2 ×3/8 ×5/16 ×1/4

2.85 2.40 1.89 1.62 1.33

1.34 1.10 0.851 0.721 0.585

0.845 0.858 0.873 0.880 0.887

0.867 0.822 0.775 0.750 0.725

2.45 1.99 1.52 1.28 1.03

0.499 0.406 0.311 0.261 0.211

1.59 1.30 1.00 0.849 0.692

L31/2×31/2×1/2 ×7/16 ×3/8 ×5/16 ×1/4

3.63 3.25 2.86 2.44 2.00

1.48 1.32 1.15 0.969 0.787

1.05 1.06 1.07 1.08 1.09

1.05 1.03 1.00 0.979 0.954

2.66 2.36 2.06 1.74 1.41

0.464 0.413 0.357 0.300 0.243

L31/2×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4

2.32 2.09 1.84 1.58 1.30

1.09 0.971 0.847 0.718 0.585

0.877 0.885 0.892 0.900 0.908

0.869 0.846 0.823 0.798 0.773

1.97 1.75 1.52 1.28 1.04

L31/2×21/2×1/2 ×3/8 ×5/16 ×1/4

1.36 1.09 0.937 0.775

0.756 0.589 0.501 0.410

0.701 0.716 0.723 0.731

0.701 0.655 0.632 0.607

L3×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4 ×3/16

2.20 1.98 1.75 1.50 1.23 0.948

1.06 0.946 0.825 0.699 0.569 0.433

0.895 0.903 0.910 0.918 0.926 0.933

L3×21/2×1/2 ×7/16 ×3/8 ×5/16 ×1/4 ×3/16

1.29 1.17 1.03 0.888 0.734 0.568

0.736 0.656 0.573 0.487 0.397 0.303

0.718 0.724 0.731 0.739 0.746 0.753

Shape

Qs

Axis Z-Z

x–

Z

xp

I

S

r

Tan ␣

Fy = 36 ksi

in. 0.716 0.719 0.721 0.723

0.750 0.755 0.757 0.759

1.00 1.00 0.997 0.912

1.13 0.927 0.705 0.591 0.476

0.631 0.633 0.636 0.638 0.639

0.534 0.542 0.551 0.554 0.558

1.00 1.00 1.00 0.997 0.912

1.51 1.33 1.17 0.984 0.802

1.01 0.920 0.821 0.714 0.598

0.679 0.681 0.683 0.685 0.688

1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 0.965

0.431 0.381 0.331 0.279 0.226

1.15 1.02 0.894 0.758 0.622

0.851 0.774 0.692 0.602 0.487

0.618 0.620 0.622 0.624 0.628

0.713 0.717 0.720 0.722 0.725

1.00 1.00 1.00 1.00 0.965

1.39 1.07 0.900 0.728

0.396 0.303 0.256 0.207

0.781 0.609 0.518 0.426

0.649 0.496 0.419 0.340

0.532 0.535 0.538 0.541

0.485 0.495 0.500 0.504

1.00 1.00 1.00 0.965

0.929 0.907 0.884 0.860 0.836 0.812

1.91 1.70 1.48 1.26 1.02 0.774

0.460 0.405 0.352 0.297 0.240 0.182

0.922 0.817 0.716 0.606 0.490 0.373

0.703 0.639 0.570 0.496 0.415 0.326

0.580 0.580 0.581 0.583 0.585 0.586

1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 1.00 0.912

0.746 0.724 0.701 0.677 0.653 0.627

1.34 1.19 1.03 0.873 0.707 0.536

0.417 0.370 0.322 0.272 0.220 0.167

0.665 0.594 0.514 0.435 0.355 0.271

0.568 0.517 0.463 0.404 0.327 0.247

0.516 0.516 0.517 0.518 0.520 0.521

0.666 0.671 0.675 0.679 0.683 0.687

1.00 1.00 1.00 1.00 1.00 0.912

Note: For workable gages, refer to Table 1-7A. For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 48

1–48

DIMENSIONS AND PROPERTIES

Table 1-7 (continued)

Angles Properties Flexural-Torsional Properties

Axis X-X Shape

L3×2×1/2 ×3/8 ×5/16 ×1/4 ×3/16 L21/2×21/2×1/2

×3/8 ×5/16 ×1/4 ×3/16

L21/2×2×3/8 ×5/16 ×1/4 ×3/16 L21/2×11/2×1/4

×3/16

L2×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

k

Wt.

Area, A

in.

lb/ft 7.70 5.90 5.00 4.10 3.07

in.2 2.26 1.75 1.48 1.20 0.917

in.4 1.92 1.54 1.32 1.09 0.847

in.3 1.00 0.779 0.662 0.541 0.414

in. 0.922 0.937 0.945 0.953 0.961

in. 1.08 1.03 1.01 0.980 0.952

in.3 1.78 1.39 1.19 0.969 0.743

in. 0.740 0.667 0.632 0.600 0.555

in.4 0.192 0.0855 0.0510 0.0270 0.0119

in.6 in. 0.0908 1.39 0.0413 1.42 0.0248 1.43 0.0132 1.45 0.00576 1.46

7.70 5.90 5.00 4.10 3.07

2.26 1.73 1.46 1.19 0.901

1.22 0.972 0.837 0.692 0.535

0.716 0.558 0.474 0.387 0.295

0.735 0.749 0.756 0.764 0.771

0.803 0.758 0.735 0.711 0.687

1.29 1.01 0.853 0.695 0.529

0.452 0.346 0.292 0.238 0.180

0.188 0.0833 0.0495 0.0261 0.0114

0.0791 0.0362 0.0218 0.0116 0.00510

1.30 1.33 1.35 1.36 1.38

5.30 4.50 3.62 2.75

1.55 1.32 1.07 0.818

0.914 0.790 0.656 0.511

0.546 0.465 0.381 0.293

0.766 0.774 0.782 0.790

0.826 0.803 0.779 0.754

0.982 0.839 0.688 0.529

0.433 0.388 0.360 0.319

0.0746 0.0444 0.0235 0.0103

0.0268 0.0162 0.00868 0.00382

1.22 1.23 1.25 1.26

3.19 2.44

0.947 0.594 0.364 0.792 0.724 0.464 0.280 0.801

0.866 0.839

0.644 0.606 0.0209 0.00694 0.497 0.569 0.00921 0.00306

1.19 1.20

4.70 3.92 3.19 2.44 1.65

1.37 1.16 0.944 0.722 0.491

0.632 0.609 0.586 0.561 0.534

0.629 0.537 0.440 0.338 0.230

1.05 1.06 1.08 1.09 1.10

13/16 11/16 5/8 9/16 1/2 3/4 5/8 9/16 1/2 7/16 5/8 9/16 1/2 7/16 1/2 7/16 5/8 9/16 1/2 7/16 3/8

I

S

r

y–

Z

yp

J

0.476 0.414 0.346 0.271 0.189

0.348 0.298 0.244 0.188 0.129

0.591 0.598 0.605 0.612 0.620

0.343 0.290 0.236 0.181 0.123

Cw

0.0658 0.0393 0.0209 0.00921 0.00293

0.0174 0.0106 0.00572 0.00254 0.000789

–r o

Table 1-7A

Workable Gages in Angle Legs, in. Leg

8

g g1 g2

41/2 3 3

7

6

4 21/2 3

31/2 21/4 21/2

5

4

3 2 13/4

21/2

31/2

3

21/2

2

2

13/4

13/8

11/8

13/4 11/2 13/8 11/4 1

7/8

7/8

Note: Other gages are permitted to suit specific requirements subject to clearances and edge distance limitations.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3/4

1 5/8

AISC_PART 01A_14th Ed._Nov. 19, 2012 14-11-10 10:09 AM Page 49

(Black plate)

1–49

DIMENSIONS AND PROPERTIES

Table 1-7 (continued)

Angles Properties

L3-L2

Axis Y-Y

I

S

r

L3×2×1/2 ×3/8 ×5/16 ×1/4 ×3/16

in.4 0.667 0.539 0.467 0.390 0.305

in.3 0.470 0.368 0.314 0.258 0.198

in. 0.543 0.555 0.562 0.569 0.577

in. 0.580 0.535 0.511 0.487 0.462

in.3 0.887 0.679 0.572 0.463 0.351

in. 0.377 0.292 0.247 0.200 0.153

in.4 0.409 0.319 0.271 0.223 0.173

in.3 0.411 0.313 0.264 0.214 0.163

L21/2×21/2×1/2 ×3/8 ×5/16 ×1/4 ×3/16

1.22 0.972 0.837 0.692 0.535

0.716 0.558 0.474 0.387 0.295

0.735 0.749 0.756 0.764 0.771

0.803 0.758 0.735 0.711 0.687

1.29 1.01 0.853 0.695 0.529

0.452 0.346 0.292 0.238 0.180

0.526 0.400 0.338 0.276 0.209

L21/2×2×3/8 ×5/16 ×1/4 ×3/16

0.513 0.446 0.372 0.292

0.361 0.309 0.253 0.195

0.574 0.581 0.589 0.597

0.578 0.555 0.532 0.508

0.657 0.557 0.454 0.347

0.310 0.264 0.214 0.164

0.273 0.233 0.192 0.148

L21/2×11/2×1/4 ×3/16

0.160 0.126

0.142 0.110

0.411 0.418

0.372 0.347

0.261 0.198

L2×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.476 0.414 0.346 0.271 0.189

0.348 0.298 0.244 0.188 0.129

0.591 0.598 0.605 0.612 0.620

0.632 0.609 0.586 0.561 0.534

0.629 0.537 0.440 0.338 0.230

Shape

Qs

Axis Z-Z

x–

Z

xp

I

S

r

Tan ␣

Fy = 36 ksi

in. 0.425 0.426 0.428 0.431 0.435

0.413 0.426 0.432 0.437 0.442

1.00 1.00 1.00 1.00 0.912

0.459 0.373 0.326 0.274 0.216

0.481 0.481 0.481 0.482 0.482

1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 0.983

0.295 0.260 0.213 0.163

0.419 0.420 0.423 0.426

0.612 0.618 0.624 0.628

1.00 1.00 1.00 0.983

0.189 0.145

0.0977 0.119 0.321 0.0754 0.0914 0.324

0.354 0.360

1.00 0.983

0.343 0.290 0.236 0.181 0.123

0.203 0.172 0.142 0.109 0.0756

1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 0.912

0.227 0.200 0.171 0.137 0.0994

0.386 0.386 0.387 0.389 0.391

Table 1-7B

Compactness Criteria for Angles Compression

t

nonslender up to

Flexure compact up to

Compression

noncompact up to

t

nonslender up to

Width of angle leg, in. 11/8 1 7/8 3/4 5/8 9/16 1/2

8

7 6

8

7

Flexure compact up to

noncompact up to

Width of angle leg, in. — — — — — — 8

7/16 3/8 5/16 1/4 3/16 1/8

5 4 4 3 2 11/2

Note: Compactness criteria given for Fy = 36 ksi. Cv = 1.0 for all angles.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

6 5 4 31/2 21/2 11/2

8 8 8 6 4 3

AISC_PART 01A:14th Ed_

1/20/11

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Page 50

1–50

DIMENSIONS AND PROPERTIES

Table 1-8

WT-Shapes Dimensions Stem Area, A

Shape

h v

2

in.

Thickness, tw

tw ᎏ 2

Flange Area

Width, bf

2

Distance

Thickness, tf

in.

in.

in.

in.

in.

in.

22.0 21.8 21.7 21.5

22 213/4 215/8 211/2

1.03 1 0.865 7/8 0.785 13/16 0.710 11/16

1/2

22.6 18.9 17.0 15.2

15.9 15.8 15.8 15.8

16 157/8 153/4 153/4

1.77 1.58 1.42 1.22

13/4 19/16 17/16 11/4

2.56 2.36 2.20 2.01

25/8 27/16 21/4 21/16

51/2

h

WT20×296.5 ×251.5 h ×215.5 h ×198.5 h ×186 h ×181c,h ×162 c ×148.5 c ×138.5 c ×124.5 c ×107.5 c,v ×99.5 c,v

87.2 74.0 63.3 58.3 54.7 53.2 47.7 43.6 40.7 36.7 31.8 29.2

21.5 21.0 20.6 20.5 20.3 20.3 20.1 19.9 19.8 19.7 19.5 19.3

211/2 21 205/8 201/2 203/8 201/4 201/8 197/8 197/8 193/4 191/2 193/8

1.79 1.54 1.34 1.22 1.16 1.12 1.00 0.930 0.830 0.750 0.650 0.650

113/16 19/16 15/16 11/4 13/16 11/8 1 15/16 13/16 3/4 5/8 5/8

15/16 13/16

38.5 32.3 11/16 27.6 5/8 25.0 5/8 23.6 9/16 22.7 1/2 20.1 1/2 18.5 7/16 16.5 3/8 14.8 5/16 12.7 5/16 12.6

16.7 16.4 16.2 16.1 16.1 16.0 15.9 15.8 15.8 15.8 15.8 15.8

163/4 163/8 161/4 161/8 161/8 16 157/8 157/8 157/8 153/4 153/4 153/4

3.23 2.76 2.36 2.20 2.05 2.01 1.81 1.65 1.58 1.42 1.22 1.07

31/4 23/4 23/8 23/16 21/16 2 113/16 15/8 19/16 17/16 11/4 11/16

4.41 3.94 3.54 3.38 3.23 3.19 2.99 2.83 2.76 2.60 2.40 2.25

41/2 4 35/8 31/2 35/16 31/4 31/16 215/16 27/8 211/16 21/2 25/16

71/2

WT20×196 h ×165.5 h ×163.5 h ×147 c ×139 c ×132 c ×117.5 c ×105.5 c ×91.5 c,v ×83.5 c,v ×74.5 c,v

57.8 48.8 47.9 43.1 41.0 38.7 34.6 31.1 26.7 24.5 21.9

20.8 20.4 20.4 20.2 20.1 20.0 19.8 19.7 19.5 19.3 19.1

203/4 203/8 203/8 201/4 201/8 20 197/8 195/8 191/2 191/4 191/8

1.42 1.22 1.18 1.06 1.03 0.960 0.830 0.750 0.650 0.650 0.630

17/16 11/4 13/16 11/16 1 15/16 13/16 3/4 5/8 5/8 5/8

3/4

12.4 12.2 12.1 12.0 12.0 11.9 11.9 11.8 11.8 11.8 11.8

123/8 121/8 121/8 12 12 117/8 117/8 113/4 113/4 113/4 113/4

2.52 2.13 2.13 1.93 1.81 1.73 1.58 1.42 1.20 1.03 0.830

21/2 21/8 21/8 115/16 113/16 13/4 19/16 17/16 13/16 1 13/16

3.70 3.31 3.31 3.11 2.99 2.91 2.76 2.60 2.38 2.21 2.01

313/16 33/8 33/8 33/16 31/16 3 27/8 211/16 21/2 25/16 21/8

71/2

7/16 3/8

5/8 5/8 9/16 1/2 1/2 7/16 3/8 5/16 5/16 5/16

29.4 24.9 24.1 21.4 20.6 19.2 16.5 14.8 12.7 12.5 12.0

in.

kdes

49.2 42.6 38.5 33.9

7/16

in.

kdet

Workable Gage

k

WT22×167.5 c ×145 c ×131c ×115 c,v

in.

c

Depth, d

Shape is slender for compression with Fy = 50 ksi. Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Shear strength controlled by buckling effects (Cv < 1.0) with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 51

DIMENSIONS AND PROPERTIES

1–51

Table 1-8 (continued)

WT-Shapes Properties

Nominal Wt.

Compact Section Criteria

Axis X-X

WT22-WT20

Qs

Axis Y-Y

I

S

r

y–

Z

yp

I

S

r

Z

in.4

in.3

in.

in.

in.3

in.

in.4

in.3

in.

in.3

2170 131 1830 111 1640 99.4 1440 88.6

6.63 6.54 6.53 6.53

5.53 5.26 5.19 5.17

234 196 176 157

1.54 1.35 1.22 1.07

600 521 462 398

75.2 65.9 58.6 50.5

12.0 13.6 15.4 16.8 17.5 18.1 20.1 21.4 23.9 26.3 30.0 29.7

3310 2730 2290 2070 1930 1870 1650 1500 1360 1210 1030 988

209 174 148 134 126 122 108 98.9 88.6 79.4 68.0 66.5

6.16 6.07 6.01 5.96 5.95 5.92 5.88 5.87 5.78 5.75 5.71 5.81

5.66 5.38 5.18 5.03 4.98 4.91 4.77 4.71 4.50 4.41 4.28 4.47

379 314 266 240 225 217 192 176 157 140 120 117

2.61 1260 2.25 1020 1.95 843 1.81 771 1.70 709 1.66 691 1.50 609 1.38 546 1.29 522 1.16 463 1.01 398 0.929 347

151 124 104 95.7 88.3 86.3 76.6 69.0 65.9 58.8 50.5 44.1

14.6 16.7 17.3 19.1 19.5 20.8 23.9 26.3 30.0 29.7 30.3

2270 1880 1840 1630 1550 1450 1260 1120 955 899 815

153 128 125 111 106 99.2 85.7 76.7 65.7 63.7 59.7

6.27 6.21 6.19 6.14 6.14 6.11 6.04 6.01 5.98 6.05 6.10

5.94 5.74 5.66 5.51 5.51 5.41 5.17 5.08 4.97 5.19 5.45

275 231 224 199 191 178 153 137 117 115 108

2.33 2.00 1.98 1.80 1.71 1.63 1.45 1.31 1.13 1.10 1.72

lb/ft 167.5 145 131 115

b ᎏf 2tf

d ᎏ tw

4.50 5.02 5.57 6.45

21.4 25.2 27.6 30.3

296.5 251.5 215.5 198.5 186 181 162 148.5 138.5 124.5 107.5 99.5

2.58 2.98 3.44 3.66 3.93 3.99 4.40 4.80 5.03 5.55 6.45 7.39

196 165.5 163.5 147 139 132 117.5 105.5 91.5 83.5 74.5

2.45 2.86 2.85 3.11 3.31 3.45 3.77 4.17 4.92 5.76 7.11

401 322 320 281 261 246 222 195 165 141 114

64.9 52.9 52.7 46.7 43.5 41.3 37.3 33.0 28.0 23.9 19.4

Fy = 50 ksi

3.49 118 3.49 102 3.47 90.9 3.43 78.3

0.824 0.630 0.525 0.436

3.80 3.72 3.65 3.63 3.60 3.60 3.57 3.54 3.58 3.55 3.54 3.45

240 197 164 150 138 135 119 107 102 90.8 77.8 68.2

1.00 1.00 1.00 1.00 1.00 0.991 0.890 0.824 0.697 0.579 0.445 0.454

2.64 106 2.57 85.7 2.58 85.0 2.55 75.0 2.52 69.9 2.52 66.0 2.54 59.0 2.51 52.1 2.49 44.0 2.40 37.8 2.29 30.9

1.00 1.00 1.00 0.940 0.920 0.854 0.697 0.579 0.445 0.454 0.436

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Torsional Properties

J

Cw

in.4

in.6

37.2 25.4 18.6 12.4

438 275 200 139

221 2340 138 1400 88.2 881 70.6 677 57.7 558 54.2 511 39.6 362 30.5 279 25.7 218 19.0 158 12.4 101 9.12 83.5 85.4 52.5 51.4 38.2 32.4 27.9 20.6 15.2 9.65 6.99 4.66

796 484 449 322 282 233 156 113 71.2 62.9 51.9

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DIMENSIONS AND PROPERTIES

Table 1-8 (continued)

WT-Shapes Dimensions Stem Area, A

Shape

Depth, d

2

in.

in.

96.2 77.8 71.7 64.9 58.1 53.0 48.4 44.5 41.5 38.5 36.3 34.1

20.5 19.9 19.7 19.4 19.2 19.0 18.8 18.7 18.6 18.4 18.3 18.2

201/2 197/8 195/8 193/8 191/4 19 187/8 185/8 181/2 183/8 183/8 181/4

1.97 1.61 1.50 1.36 1.22 1.12 1.02 0.945 0.885 0.840 0.800 0.760

WT18×128 c ×116 c ×105 c ×97 c ×91c ×85 c ×80 c ×75 c ×67.5 c,v

37.6 34.0 30.9 28.5 26.8 25.0 23.5 22.1 19.9

18.7 18.6 18.3 18.2 18.2 18.1 18.0 17.9 17.8

183/4 181/2 183/8 181/4 181/8 181/8 18 177/8 173/4

0.960 0.870 0.830 0.765 0.725 0.680 0.650 0.625 0.600

WT16.5×193.5 ×177 h ×159 ×145.5 c ×131.5 c ×120.5 c ×110.5 c ×100.5 c

h v

in.

WT18×326 h ×264.5 h ×243.5 h ×220.5 h ×197.5 h ×180.5h ×165 c ×151c ×141c ×131c ×123.5 c ×115.5c

h

c

Thickness, tw

57.0 52.1 46.8 42.8 38.7 35.6 32.6 29.7

18.0 17.8 17.6 17.4 17.3 17.1 17.0 16.8

18 173/4 175/8 173/8 171/4 171/8 17 167/8

tw ᎏ 2

in.

Flange Area 2

in.

1/2

7/8

7/16

13/16

7/16

3/4

3/8

3/4 11/16

3/8 3/8

5/8

5/16

5/8

5/16

5/8

11/4

1.26 1.16 13/16 1.04 11/16 0.960 15/16 0.870 7/8 0.830 13/16 0.775 3/4 0.715 11/16

5/16 5/8 5/8 9/16 1/2 7/16 7/16 3/8 3/8

Thickness, tf

in.

in.

kdet

Workable Gage

kdes in.

in.

in.

17.6 17.2 17.1 17.0 16.8 16.7 16.6 16.7 16.6 16.6 16.5 16.5

175/8 171/4 171/8 17 167/8 163/4 165/8 165/8 165/8 161/2 161/2 161/2

3.54 2.91 2.68 2.44 2.20 2.01 1.85 1.68 1.57 1.44 1.35 1.26

39/16 215/16 211/16 27/16 23/16 2 17/8 111/16 19/16 17/16 13/8 11/4

4.49 3.86 3.63 3.39 3.15 2.96 2.80 2.63 2.52 2.39 2.30 2.21

413/16 43/16 4 33/4 37/16 35/16 31/8 3 27/8 23/4 25/8 29/16

71/2

18.0 16.1 15.2 14.0 13.2 12.3 11.7 11.2 10.7

12.2 12.1 12.2 12.1 12.1 12.0 12.0 12.0 12.0

121/4 121/8 121/8 121/8 121/8 12 12 12 12

1.73 1.57 1.36 1.26 1.18 1.10 1.02 0.940 0.790

13/4 19/16 13/8 11/4 13/16 11/8 1 15/16 13/16

2.48 2.32 2.11 2.01 1.93 1.85 1.77 1.69 1.54

25/8 27/16 25/16 23/16 21/8 2 115/16 17/8 111/16

51/2

22.6 20.6 18.3 16.7 15.0 14.2 13.1 12.0

16.2 16.1 16.0 15.9 15.8 15.9 15.8 15.7

161/4 161/8 16 157/8 153/4 157/8 153/4 153/4

2.28 2.09 1.89 1.73 1.57 1.40 1.28 1.15

21/4 21/16 17/8 13/4 19/16 13/8 11/4 11/8

3.07 2.88 2.68 2.52 2.36 2.19 2.06 1.94

33/16 215/16 23/4 25/8 27/16 21/4 21/8 2

5 1/2

2 1 40.4 13/16 32.0 15/8 3/4 29.5 11/2 11/16 26.4 13/8 5/8 23.4 11/4 9/16 21.3 11/8 1/2 19.2 1 15/16 1/2 17.6 7/8 7/16 16.4 7/16 15.5 13/16 13/16 7/16 14.7 3/4 3/8 13.9 15/16

Width, bf

Distance

k

Shape is slender for compression with Fy = 50 ksi. Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Shear strength controlled by buckling effects (Cv < 1.0) with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A:14th Ed_

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Page 53

DIMENSIONS AND PROPERTIES

1–53

Table 1-8 (continued)

WT-Shapes Properties

Nominal Wt.

Compact Section Criteria

Axis X-X

WT18-WT16.5

Qs

Axis Y-Y

Fy = 50

Torsional Properties

J

Cw

in.4

in.6

295 163 128 96.6 70.7 54.1 42.0 32.1 26.3 20.8 17.3 14.3

3070 1600 1250 914 652 491 372 285 231 185 155 129

d ᎏ tw

I

S

r

y–

Z

yp

I

S

r

Z

lb/ft 326 264.5 243.5 220.5 197.5 180.5 165 151 141 131 123.5 115.5

b ᎏf 2tf

in.4

in.3

in.

in.

in.3

in.

in.4

in.3

in.

in.3

2.48 2.96 3.19 3.48 3.83 4.16 4.49 4.96 5.29 5.75 6.11 6.54

10.4 12.4 13.1 14.3 15.7 17.0 18.4 19.8 21.0 21.9 22.9 23.9

3160 2440 2220 1980 1740 1570 1410 1280 1190 1110 1040 978

208 164 150 134 119 107 97.0 88.8 82.6 77.5 73.3 69.1

5.74 5.60 5.57 5.52 5.47 5.43 5.39 5.37 5.36 5.36 5.36 5.36

5.35 4.96 4.84 4.69 4.53 4.42 4.30 4.22 4.16 4.14 4.12 4.10

383 298 272 242 213 192 173 158 146 137 129 122

2.73 2.26 2.10 1.91 1.73 1.59 1.46 1.33 1.25 1.16 1.10 1.03

1610 1240 1120 997 877 786 711 648 599 545 507 470

184 145 131 117 104 94.0 85.5 77.8 72.2 65.8 61.4 57.0

4.10 4.00 3.96 3.92 3.88 3.85 3.83 3.82 3.80 3.76 3.74 3.71

290 227 206 184 162 146 132 120 112 102 94.8 88.0

1.00 1.00 1.00 1.00 1.00 1.00 0.976 0.905 0.844 0.799 0.748 0.697

128 116 105 97 91 85 80 75 67.5

3.53 3.86 4.48 4.81 5.12 5.47 5.88 6.37 7.56

19.5 1210 21.4 1080 22.0 985 23.8 901 25.1 845 26.6 786 27.7 740 28.6 698 29.7 637

87.4 78.5 73.1 67.0 63.1 58.9 55.8 53.1 49.7

5.66 5.63 5.65 5.62 5.62 5.61 5.61 5.62 5.66

4.92 4.82 4.87 4.80 4.77 4.73 4.74 4.78 4.96

156 140 131 120 113 105 100 95.5 90.1

1.54 1.40 1.27 1.18 1.11 1.04 0.980 0.923 1.23

264 234 206 187 174 160 147 135 113

43.2 38.6 33.8 30.9 28.8 26.6 24.6 22.5 18.9

2.65 2.62 2.58 2.56 2.55 2.53 2.50 2.47 2.38

68.5 60.9 53.4 48.8 45.3 41.8 38.6 35.4 29.8

0.920 0.824 0.794 0.702 0.635 0.566 0.522 0.489 0.454

26.4 19.7 13.9 11.1 9.20 7.51 6.17 5.04 3.48

205 151 119 92.7 77.6 63.2 53.6 46.0 37.3

193.5 177 159 145.5 131.5 120.5 110.5 100.5

3.55 3.85 4.23 4.60 5.03 5.66 6.20 6.85

14.3 15.3 16.9 18.1 19.9 20.6 21.9 23.5

1460 107 1320 96.8 1160 85.8 1060 78.3 943 70.2 872 65.8 799 60.8 725 55.5

5.07 5.03 4.99 4.96 4.93 4.96 4.95 4.95

4.27 4.15 4.02 3.93 3.83 3.84 3.81 3.77

193 174 154 140 125 116 107 97.8

1.76 1.62 1.46 1.35 1.23 1.12 1.03 0.940

810 729 645 581 517 466 420 375

100 90.6 80.7 73.1 65.5 58.8 53.2 47.6

3.77 3.74 3.71 3.68 3.65 3.62 3.59 3.56

156 141 125 113 101 90.8 82.1 73.3

1.00 1.00 1.00 0.991 0.900 0.864 0.799 0.718

73.9 57.1 42.1 32.5 24.3 18.0 13.9 10.4

615 468 335 256 188 146 113 84.9

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ksi

AISC_PART 01A:14th Ed_

1/20/11

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Page 54

1–54

DIMENSIONS AND PROPERTIES

Table 1-8 (continued)

WT-Shapes Dimensions Stem Area, A

Shape

Depth, d

2

Area

Width, bf

2

Thickness, tf

kdes

in.

in.

in.

in.

in.

in.

167/8 163/4 165/8 161/2 163/8

0.670 0.635 0.605 0.580 0.550

11/16

3/8 5/16

5/8

5/16

9/16

5/16

9/16

5/16

11.5 11.6 11.5 11.5 11.5

111/2 115/8 111/2 111/2 111/2

1.22 11/4 1.06 11/16 0.960 15/16 0.855 7/8 0.740 3/4

1.92 1.76 1.66 1.56 1.44

21/8 115/16 113/16 13/4 15/8

51/2

5/8

11.3 10.6 10.1 9.60 9.04

WT15×195.5 h ×178.5 h ×163 h ×146 ×130.5 ×117.5 c ×105.5 c ×95.5 c ×86.5 c

57.6 52.5 48.0 43.0 38.5 34.7 31.1 28.0 25.4

16.6 16.4 16.2 16.0 15.8 15.7 15.5 15.3 15.2

165/8 163/8 161/4 16 153/4 155/8 151/2 153/8 151/4

1.36 1.24 1.14 1.02 0.930 0.830 0.775 0.710 0.655

13/8 11/4 11/8 1 15/16 13/16 3/4 11/16 5/8

11/16

22.6 20.3 18.5 16.3 14.7 13.0 12.0 10.9 10.0

15.6 15.5 15.4 15.3 15.2 15.1 15.1 15.0 15.0

155/8 151/2 153/8 151/4 151/8 15 151/8 15 15

2.44 2.24 2.05 1.85 1.65 1.50 1.32 1.19 1.07

3.23 3.03 2.84 2.64 2.44 2.29 2.10 1.97 1.85

33/8 31/8 215/16 23/4 29/16 23/8 21/4 21/16 2

51/2

WT15×74c ×66 c ×62 c ×58 c ×54c ×49.5 c ×45 c,v

21.8 19.5 18.2 17.1 15.9 14.5 13.2

15.3 15.2 15.1 15.0 14.9 14.8 14.8

153/8 151/8 151/8 15 147/8 147/8 143/4

0.650 0.615 0.585 0.565 0.545 0.520 0.470

5/8

5/16 5/16

9/16

5/16

9/16

5/16

9/16 1/2

5/16 1/4

1/2

1/4

10.0 9.32 8.82 8.48 8.13 7.71 6.94

10.5 10.5 10.5 10.5 10.5 10.5 10.4

101/2 101/2 101/2 101/2 101/2 101/2 103/8

1.18 13/16 1.00 1 0.930 15/16 0.850 7/8 0.760 3/4 0.670 11/16 0.610 5/8

1.83 1.65 1.58 1.50 1.41 1.32 1.26

21/16 17/8 113/16 13/4 111/16 19/16 11/2

51/2

5/8

79.3 54.2 49.5 45.2 41.5 38.1 34.7 32.0 28.6 26.3 23.8 21.6

16.3 15.2 15.0 14.8 14.6 14.5 14.3 14.2 14.1 13.9 13.8 13.7

161/4 151/4 15 143/4 145/8 141/2 143/8 141/4 14 137/8 133/4 133/4

1.97 1.38 1.26 1.16 1.06 0.980 0.910 0.830 0.750 0.725 0.660 0.605

2 1 32.0 11/16 21.0 13/8 5/8 18.9 11/4 13/16 5/8 17.2 11/16 9/16 15.5 1/2 14.2 1 15/16 1/2 13.0 13/16 7/16 11.8 3/4 3/8 10.5 3/4 3/8 10.1 11/16 3/8 9.10 5/8 5/16 8.28

15.3 14.7 14.6 14.4 14.4 14.3 14.2 14.1 14.0 14.1 14.0 14.0

151/4 145/8 141/2 141/2 143/8 141/4 141/4 141/8 14 141/8 14 14

3.54 2.48 2.28 2.09 1.93 1.77 1.61 1.50 1.34 1.19 1.08 0.975

39/16 21/2 21/4 21/16 115/16 13/4 15/8 11/2 15/16 13/16 11/16 1

4.33 3.27 3.07 2.88 2.72 2.56 2.40 2.29 2.13 1.98 1.87 1.76

47/16 33/8 33/16 3 213/16 211/16 21/2 23/8 21/4 21/16 2 17/8

51/2g 51/2

h

WT13.5×269.5 ×184h ×168 h ×153.5 h ×140.5 ×129 ×117.5 ×108.5 ×97 c ×89 c ×80.5 c ×73 c

5/8 9/16 1/2 1/2 7/16 3/8 3/8 5/16

in.

kdet

Workable Gage

16.9 16.7 16.7 16.5 16.4

in.

in.

tw ᎏ 2

Distance

k

24.7 22.5 20.7 19.1 17.4

WT16.5×84.5 c ×76 c ×70.5 c ×65 c ×59 c,v

in.

Thickness, tw

Flange

27/16 21/4 21/16 17/8 15/8 11/2 15/16 13/16 11/16

Shape is slender for compression with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. v Shear strength controlled by buckling effects (Cv < 1.0) with Fy = 50 ksi. c

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A:14th Ed_

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7:29 AM

Page 55

DIMENSIONS AND PROPERTIES

1–55

Table 1-8 (continued)

WT-Shapes Properties

Nominal Wt.

Compact Section Criteria

Axis X-X

WT16.5-WT13.5

Qs

Axis Y-Y

Fy = 50

Torsional Properties

J

Cw

in.4

in.6

d ᎏ tw

I

S

r

y–

Z

yp

I

S

r

Z

lb/ft 84.5 76 70.5 65 59

b ᎏf 2tf

in.4

in.3

in.

in.

in.3

in.

in.4

in.3

in.

in.3

4.71 5.48 6.01 6.73 7.76

25.2 26.3 27.6 28.4 29.8

649 592 552 513 469

51.1 47.4 44.7 42.1 39.2

5.12 5.14 5.15 5.18 5.20

4.21 4.26 4.29 4.36 4.47

90.8 84.5 79.8 75.6 70.8

1.08 0.967 0.901 0.832 0.862

155 136 123 109 93.5

27.0 23.6 21.3 18.9 16.3

2.50 2.47 2.43 2.38 2.32

42.1 36.9 33.4 29.7 25.6

0.630 0.579 0.525 0.496 0.451

8.81 6.16 4.84 3.67 2.64

55.4 43.0 35.4 29.3 23.4

195.5 178.5 163 146 130.5 117.5 105.5 95.5 86.5

3.19 3.45 3.75 4.12 4.59 5.02 5.74 6.35 7.01

12.2 13.2 14.2 15.7 17.0 18.9 20.0 21.5 23.2

1220 1090 981 861 765 674 610 549 497

96.9 87.2 78.8 69.6 62.4 55.1 50.5 45.7 41.7

4.61 4.56 4.52 4.48 4.46 4.41 4.43 4.42 4.42

4.00 3.87 3.76 3.62 3.54 3.41 3.39 3.34 3.31

177 159 143 125 112 98.2 89.5 80.8 73.5

1.85 1.70 1.56 1.41 1.27 1.15 1.03 0.935 0.851

774 693 622 549 480 427 378 336 299

99.2 89.6 81.0 71.9 63.3 56.8 50.1 44.7 39.9

3.67 3.64 3.60 3.58 3.53 3.51 3.49 3.46 3.42

155 140 126 111 97.9 87.5 77.2 68.9 61.4

1.00 1.00 1.00 1.00 1.00 0.951 0.895 0.819 0.733

86.3 66.6 51.2 37.5 26.9 20.1 14.1 10.5 7.78

636 478 361 257 184 133 96.4 71.2 53.0

74 66 62 58 54 49.5 45

4.44 5.27 5.65 6.17 6.89 7.80 8.52

23.5 24.7 25.8 26.5 27.3 28.5 31.5

466 421 396 373 349 322 290

40.6 37.4 35.3 33.7 32.0 30.0 27.1

4.63 4.66 4.66 4.67 4.69 4.71 4.69

3.84 3.90 3.90 3.94 4.01 4.09 4.04

72.2 66.8 63.1 60.4 57.7 54.4 49.0

1.04 0.921 0.867 0.815 0.757 0.912 0.835

114 98.0 90.4 82.1 73.0 63.9 57.3

21.7 18.6 17.2 15.6 13.9 12.2 11.0

2.28 2.25 2.23 2.19 2.15 2.10 2.09

33.9 29.2 27.0 24.6 21.9 19.3 17.3

0.718 0.657 0.601 0.570 0.537 0.493 0.403

7.24 4.85 3.98 3.21 2.49 1.88 1.41

37.6 28.5 23.9 20.5 17.3 14.3 10.5

269.5 184 168 153.5 140.5 129 117.5 108.5 97 89 80.5 73

2.15 2.96 3.19 3.46 3.72 4.03 4.41 4.71 5.24 5.92 6.49 7.16

8.30 1530 128 11.0 939 81.7 11.9 839 73.4 12.8 753 66.4 13.8 677 59.9 14.8 613 54.7 15.7 556 50.0 17.1 502 45.2 18.8 444 40.3 19.2 414 38.2 20.9 372 34.4 22.6 336 31.2

4.39 4.16 4.12 4.08 4.04 4.02 4.00 3.96 3.94 3.97 3.95 3.95

4.34 3.71 3.58 3.47 3.35 3.27 3.20 3.10 3.02 3.04 2.98 2.94

242 151 135 121 109 98.9 89.9 81.1 71.8 67.7 60.8 55.0

138 89.3 80.8 72.9 66.4 60.2 54.2 49.9 44.1 39.4 35.4 31.7

3.65 3.48 3.45 3.41 3.39 3.36 3.33 3.32 3.29 3.25 3.23 3.20

218 140 126 113 103 93.3 83.8 77.0 67.8 60.8 54.5 48.8

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.956 0.935 0.849 0.763

2.60 1060 1.85 655 1.70 587 1.56 527 1.44 477 1.33 430 1.22 384 1.13 352 1.02 309 0.932 278 0.849 248 0.772 222

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ksi

247 1740 84.5 532 65.4 401 50.5 304 39.6 232 30.7 178 23.4 135 18.8 105 13.5 74.3 10.0 57.7 7.53 42.7 5.62 31.7

AISC_PART 01A:14th Ed_

1/20/11

7:29 AM

Page 56

1–56

DIMENSIONS AND PROPERTIES

Table 1-8 (continued)

WT-Shapes Dimensions Stem Shape

Area, A

Depth, d

2

in.

Thickness, tw

Area

Width, bf

2

Distance

Thickness, tf

kdes

in.

in.

in.

in.

in.

in.

13.8 13.6 13.5 13.5 13.4

137/8 135/8 131/2 131/2 133/8

0.610 0.570 0.515 0.490 0.460

5/8

5/16 5/16

1/2

1/4

1/2

1/4

7/16

1/4

10.0 10.1 10.0 10.0 10.0

10 101/8 10 10 10

1.10 11/8 0.930 15/16 0.830 13/16 0.745 3/4 0.640 5/8

1.70 1.53 1.43 1.34 1.24

2 113/16 13/4 15/8 19/16

51/2

9/16

8.43 7.78 6.98 6.60 6.14

WT12×185 h ×167.5 h ×153 h ×139.5 h ×125 ×114.5 ×103.5 ×96 ×88 ×81 ×73 c ×65.5 c ×58.5 c ×52 c

54.5 49.1 44.9 41.0 36.8 33.6 30.3 28.2 25.8 23.9 21.5 19.3 17.2 15.3

14.0 13.8 13.6 13.4 13.2 13.0 12.9 12.7 12.6 12.5 12.4 12.2 12.1 12.0

14 133/4 135/8 133/8 131/8 13 127/8 123/4 125/8 121/2 123/8 121/4 121/8 12

1.52 1.38 1.26 1.16 1.04 0.960 0.870 0.810 0.750 0.705 0.650 0.605 0.550 0.500

11/2 13/8 11/4 13/16 11/16 15/16 7/8 13/16 3/4 11/16 5/8 5/8 9/16 1/2

3/4

21.3 19.0 17.1 15.5 13.7 12.5 11.2 10.3 9.47 8.81 8.04 7.41 6.67 6.02

13.7 13.5 13.4 13.3 13.2 13.1 13.0 13.0 12.9 13.0 12.9 12.9 12.8 12.8

135/8 131/2 133/8 131/4 131/8 131/8 13 13 127/8 13 127/8 127/8 123/4 123/4

2.72 2.48 2.28 2.09 1.89 1.73 1.57 1.46 1.34 1.22 1.09 0.960 0.850 0.750

23/4 21/2 21/4 21/16 17/8 13/4 19/16 17/16 15/16 11/4 11/16 15/16 7/8 3/4

3.22 2.98 2.78 2.59 2.39 2.23 2.07 1.96 1.84 1.72 1.59 1.46 1.35 1.25

35/8 33/8 33/16 3 213/16 25/8 21/2 23/8 21/4 21/8 2 17/8 13/4 15/8

51/2

WT12×51.5c ×47 c ×42 c ×38 c ×34 c

15.1 13.8 12.4 11.2 10.0

12.3 12.2 12.1 12.0 11.9

121/4 121/8 12 12 117/8

0.550 0.515 0.470 0.440 0.415

9/16

5/16 1/4

1/2

1/4

7/16

1/4

7/16

1/4

0.980 1 0.875 7/8 0.770 3/4 0.680 11/16 0.585 9/16

1.48 1.38 1.27 1.18 1.09

17/8 13/4 111/16 19/16 11/2

51/2

1/2

9.11 11.9 117/8 0.430 8.10 11.8 113/4 0.395

7/16

1/4

3/8

3/16

in.

WT12×31c ×27.5 c,v

11/16 5/8 5/8 9/16 1/2 7/16 7/16 3/8 3/8 5/16 5/16 5/16 1/4

in.

kdet

Workable Gage

k

18.9 16.8 15.0 13.8 12.4

WT13.5×64.5 c ×57 c ×51c ×47 c ×42 c

in.

tw ᎏ 2

Flange

6.75 6.26 5.66 5.26 4.92

9.00 9.07 9.02 8.99 8.97

9 91/8 9 9 9

5.10 4.66

7.04 7 7.01 7

0.590 0.505

9/16 1/2

1.09 11/2 1.01 17/16

Shape is slender for compression with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. v Shear strength controlled by buckling effects (Cv < 1.0) with Fy = 50 ksi. c

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

51/2g 51/2g 31/2 31/2

AISC_PART 01A:14th Ed_

1/20/11

7:29 AM

Page 57

DIMENSIONS AND PROPERTIES

1–57

Table 1-8 (continued)

WT-Shapes Properties

Nominal Wt.

Compact Section Criteria

Axis X-X

WT13.5-WT12

Qs

Axis Y-Y

Fy = 50

Torsional Properties

J

Cw

in.4

in.6

5.55 3.65 2.63 2.01 1.40

24.0 17.5 12.6 10.2 7.79

d ᎏ tw

I

S

r

y–

Z

yp

I

S

r

Z

lb/ft 64.5 57 51 47 42

b ᎏf 2tf

in.4

in.3

in.

in.

in.3

in.

in.4

in.3

in.

in.3

4.55 5.41 6.03 6.70 7.78

22.6 23.9 26.2 27.6 29.1

323 289 258 239 216

31.0 28.3 25.3 23.8 21.9

4.13 4.15 4.14 4.16 4.18

3.39 3.42 3.37 3.41 3.48

55.1 50.4 45.0 42.4 39.2

0.945 0.832 0.750 0.692 0.621

92.2 79.3 69.6 62.0 52.8

18.4 15.8 13.9 12.4 10.6

2.21 2.18 2.15 2.12 2.07

28.8 24.6 21.7 19.4 16.6

185 167.5 153 139.5 125 114.5 103.5 96 88 81 73 65.5 58.5 52

2.51 2.73 2.94 3.18 3.49 3.79 4.14 4.43 4.81 5.31 5.92 6.70 7.53 8.50

9.20 10.0 10.8 11.6 12.7 13.5 14.8 15.7 16.8 17.7 19.1 20.2 22.0 24.0

779 686 611 546 478 431 382 350 319 293 264 238 212 189

74.7 66.3 59.4 53.6 47.2 42.9 38.3 35.2 32.2 29.9 27.2 24.8 22.3 20.0

3.78 3.73 3.69 3.65 3.61 3.58 3.55 3.53 3.51 3.50 3.50 3.52 3.51 3.51

3.57 140 3.42 123 3.29 110 3.18 98.8 3.05 86.5 2.96 78.1 2.87 69.3 2.80 63.5 2.74 57.8 2.70 53.3 2.66 48.2 2.65 43.9 2.62 39.2 2.59 35.1

1.99 1.82 1.67 1.54 1.39 1.28 1.17 1.09 1.00 0.921 0.833 0.750 0.672 0.600

85.1 75.9 68.6 61.9 54.9 49.7 44.4 40.9 37.2 34.2 30.3 26.5 23.2 20.3

3.27 133 3.23 119 3.20 107 3.17 96.3 3.14 85.2 3.11 77.0 3.08 68.6 3.07 63.1 3.04 57.3 3.05 52.6 3.01 46.6 2.97 40.7 2.94 35.7 2.91 31.2

1.00 100 1.00 75.6 1.00 58.4 1.00 45.1 1.00 33.2 1.00 25.5 1.00 19.1 1.00 15.3 1.00 11.9 1.00 9.22 0.940 6.70 0.885 4.74 0.794 3.35 0.692 2.35

51.5 47 42 38 34

4.59 5.18 5.86 6.61 7.66

22.4 23.7 25.7 27.3 28.7

204 186 166 151 137

22.0 20.3 18.3 16.9 15.6

3.67 3.67 3.67 3.68 3.70

3.01 2.99 2.97 3.00 3.06

39.2 36.1 32.5 30.1 27.9

0.841 0.764 0.685 0.622 0.560

13.3 12.0 10.5 9.18 7.85

1.99 1.98 1.95 1.92 1.87

0.773 0.707 0.606 0.537 0.486

31 5.97 27.7 27.5 6.94 29.9

131 117

15.6 14.1

3.79 3.80

3.46 3.50

28.4 1.28 25.6 1.53

581 513 460 412 362 326 289 265 240 221 195 170 149 130 59.7 54.5 47.2 41.3 35.2 17.2 14.5

4.90 1.38 4.15 1.34

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

20.7 18.7 16.3 14.3 12.3

ksi

0.763 0.697 0.583 0.525 0.473

7.85 0.522 6.65 0.448

553 405 305 230 165 125 91.3 72.5 55.8 43.8 31.9 23.1 16.4 11.6

3.53 12.3 2.62 9.57 1.84 6.90 1.34 5.30 0.932 4.08 0.850 0.588

3.92 2.93

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1–58

DIMENSIONS AND PROPERTIES

Table 1-8 (continued)

WT-Shapes Dimensions Stem Area, A

Shape

Depth, d

2

in.

Thickness, tw

Area

in.

in.

29.6 26.8 24.4 21.6 19.4 17.9 16.3 14.9

11.5 11.4 11.2 11.0 10.9 10.8 10.8 10.7

111/2 113/8 111/4 11 107/8 107/8 103/4 105/8

0.910 0.830 0.750 0.720 0.650 0.600 0.550 0.500

15/16

1/2

13/16

7/16

3/4

3/8

3/4

3/8

5/8

5/16

5/8

5/16

9/16

5/16 1/4

10.5 9.43 8.43 7.94 7.09 6.50 5.92 5.34

WT10.5×46.5 c ×41.5 c ×36.5 c ×34 c ×31c ×27.5 c ×24 c,f,v

13.7 12.2 10.7 10.0 9.13 8.10 7.07

10.8 10.7 10.6 10.6 10.5 10.4 10.3

103/4 103/4 105/8 105/8 101/2 103/8 101/4

0.580 0.515 0.455 0.430 0.400 0.375 0.350

9/16

c

WT10.5×28.5 ×25 c ×22 c,v

WT9×155.5 h ×141.5 h ×129 h ×117 h ×105.5 ×96 ×87.5 ×79 ×71.5 ×65 ×59.5 ×53 ×48.5 ×43 c ×38 c

101/2

8.37 10.5 0.405 7.36 10.4 103/8 0.380 6.49 10.3 103/8 0.350 45.8 41.7 38.0 34.3 31.2 28.1 25.7 23.2 21.0 19.2 17.6 15.6 14.2 12.7 11.1

11.2 10.9 10.7 10.5 10.3 10.2 10.0 9.86 9.75 9.63 9.49 9.37 9.30 9.20 9.11

111/8 107/8 103/4 101/2 103/8 101/8 10 97/8 93/4 95/8 91/2 93/8 91/4 91/4 91/8

1.52 1.40 1.28 1.16 1.06 0.960 0.890 0.810 0.730 0.670 0.655 0.590 0.535 0.480 0.425

1/2

1/2

5/16 1/4

7/16

1/4

7/16

1/4

3/8

3/16

3/8

3/16

3/8

3/16

3/8

3/16

3/8

3/16

3/8

3/16

11/2 13/8 11/4 13/16 11/16 15/16 7/8 13/16 3/4 11/16 5/8 9/16 9/16 1/2 7/16

3/4 11/16 5/8 5/8 9/16 1/2 7/16 7/16 3/8 3/8 5/16 5/16 5/16 1/4 1/4

Width, bf

2

WT10.5×100.5 ×91 ×83 ×73.5 ×66 ×61 ×55.5 c ×50.5 c

in.

in.

tw ᎏ 2

Flange

6.27 5.52 4.83 4.54 4.20 3.90 3.61 4.26 3.96 3.62 17.0 15.3 13.7 12.2 11.0 9.77 8.92 7.99 7.11 6.45 6.21 5.53 4.97 4.41 3.87

Thickness, tf

in. 12.6 12.5 12.4 12.5 12.4 12.4 12.3 12.3 8.42 8.36 8.30 8.27 8.24 8.22 8.14

Distance

in.

125/8 121/2 123/8 121/2 121/2 123/8 123/8 121/4

1.63 1.48 1.36 1.15 1.04 0.960 0.875 0.800

15/8 11/2 13/8 11/8 11/16 15/16 7/8 13/16

83/8 83/8 81/4 81/4 81/4 81/4 81/8

0.930 0.835 0.740 0.685 0.615 0.522 0.430

15/16

61/2

6.56 0.650 6.53 61/2 0.535 6.50 61/2 0.450 12.0 11.9 11.8 11.7 11.6 11.5 11.4 11.3 11.2 11.2 11.3 11.2 11.1 11.1 11.0

12 117/8 113/4 115/8 111/2 111/2 113/8 111/4 111/4 111/8 111/4 111/4 111/8 111/8 11

2.74 2.50 2.30 2.11 1.91 1.75 1.59 1.44 1.32 1.20 1.06 0.940 0.870 0.770 0.680

13/16 3/4 11/16 5/8 1/2 7/16 5/8 9/16 7/16

23/4 21/2 25/16 21/8 115/16 13/4 19/16 17/16 15/16 13/16 11/16 15/16 7/8 3/4 11/16

kdet

Workable Gage

k kdes in.

in.

in.

2.13 1.98 1.86 1.65 1.54 1.46 1.38 1.30

21/2 23/8 21/4 2 115/16 113/16 13/4 111/16

51/2

1.43 1.34 1.24 1.19 1.12 1.02 0.930

15/8 11/2 17/16 13/8 15/16 13/16 11/8

51/2

1.15 15/16 1.04 11/4 0.950 11/8

31/2 31/2g 31/2g

3.24 3.00 2.70 2.51 2.31 2.15 1.99 1.84 1.72 1.60 1.46 1.34 1.27 1.17 1.08

37/16 33/16 3 23/4 29/16 27/16 27/16 23/8 23/16 21/16 115/16 113/16 13/4 15/8 19/16

Shape is slender for compression with Fy = 50 ksi. Shape exceeds compact limit for flexure with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. v Shear strength controlled by buckling effects (Cv < 1.0) with Fy = 50 ksi. c f

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

51/2

AISC_PART 01A:14th Ed_

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DIMENSIONS AND PROPERTIES

1–59

Table 1-8 (continued)

WT-Shapes Properties

Nominal Wt.

Compact Section Criteria

Axis X-X

WT10.5-WT9

Qs

Axis Y-Y

Fy = 50

Torsional Properties

J

Cw

in.4

in.6

20.4 15.3 11.8 7.69 5.62 4.47 3.40 2.60

85.4 63.0 47.3 32.5 23.4 18.4 13.8 10.4

d ᎏ tw

I

S

r

y–

Z

yp

I

S

r

Z

lb/ft 100.5 91 83 73.5 66 61 55.5 50.5

b ᎏf 2tf

in.4

in.3

in.

in.

in.3

in.

in.4

in.3

in.

in.3

3.86 4.22 4.57 5.44 6.01 6.45 7.05 7.68

12.6 13.7 14.9 15.3 16.8 18.0 19.6 21.4

285 253 226 204 181 166 150 135

31.9 28.5 25.5 23.7 21.1 19.3 17.5 15.8

3.10 3.07 3.04 3.08 3.06 3.04 3.03 3.01

2.57 2.48 2.39 2.39 2.33 2.28 2.23 2.18

58.6 52.1 46.3 42.4 37.6 34.3 31.0 27.9

1.18 1.07 0.983 0.864 0.780 0.724 0.662 0.605

43.1 38.6 35.0 30.0 26.7 24.6 22.2 20.2

3.02 3.00 2.99 2.95 2.93 2.91 2.90 2.89

66.5 59.5 53.9 46.3 41.1 37.8 34.1 30.8

1.00 1.00 1.00 1.00 1.00 1.00 0.915 0.824

46.5 41.5 36.5 34 31 27.5 24

4.53 5.00 5.60 6.04 6.70 7.87 9.47

18.6 20.8 23.3 24.7 26.3 27.7 29.4

144 127 110 103 93.8 84.4 74.9

17.9 15.7 13.8 12.9 11.9 10.9 9.90

3.25 3.22 3.21 3.20 3.21 3.23 3.26

2.74 2.66 2.60 2.59 2.58 2.64 2.74

31.8 28.0 24.4 22.9 21.1 19.4 17.8

0.812 0.728 0.647 0.606 0.554 0.493 0.459

46.4 40.7 35.3 32.4 28.7 24.2 19.4

11.0 9.74 8.51 7.83 6.97 5.89 4.76

1.84 1.83 1.81 1.80 1.77 1.73 1.66

17.3 15.2 13.3 12.2 10.9 9.18 7.44

0.966 0.854 0.728 0.657 0.579 0.522 0.463

3.01 2.16 1.51 1.22 0.913 0.617 0.400

9.33 6.50 4.42 3.62 2.78 2.08 1.52

90.4 11.8 3.29 80.3 10.7 3.30 71.1 9.68 3.31

2.85 2.93 2.98

21.2 0.638 19.4 0.771 17.6 1.06

15.3 12.5 10.3

7.40 0.597 6.08 0.533 5.07 0.463

0.884 0.570 0.383

2.50 1.89 1.40

2.93 2.80 2.68 2.55 2.44 2.34 2.26 2.17 2.09 2.02 2.03 1.97 1.91 1.86 1.80

90.6 80.2 71.0 62.4 55.0 48.5 43.6 38.5 34.0 30.5 28.7 25.2 22.6 19.9 17.3

28.5 5.04 25.9 25 6.10 27.4 22 7.22 29.4 155.5 141.5 129 117 105.5 96 87.5 79 71.5 65 59.5 53 48.5 43 38

2.19 2.38 2.56 2.76 3.02 3.27 3.58 3.92 4.25 4.65 5.31 5.96 6.41 7.20 8.11

7.37 7.79 8.36 9.05 9.72 10.6 11.2 12.2 13.4 14.4 14.5 15.9 17.4 19.2 21.4

383 337 298 261 229 202 181 160 142 127 119 104 93.8 82.4 71.8

46.6 41.5 37.0 32.7 29.1 25.8 23.4 20.8 18.5 16.7 15.9 14.1 12.7 11.2 9.83

2.89 2.85 2.80 2.75 2.72 2.68 2.66 2.63 2.60 2.58 2.60 2.59 2.56 2.55 2.54

1.91 1.75 1.61 1.48 1.34 1.23 1.13 1.02 0.937 0.856 0.778 0.695 0.640 0.570 0.505

271 241 217 188 166 152 137 124

398 352 314 279 246 220 196 174 156 139 126 110 100 87.6 76.2

4.67 1.35 3.82 1.30 3.18 1.26 66.2 59.2 53.4 47.9 42.7 38.4 34.4 30.7 27.7 24.9 22.5 19.7 18.0 15.8 13.8

2.95 104 2.91 92.5 2.88 83.1 2.85 74.4 2.82 66.1 2.79 59.4 2.76 53.1 2.74 47.4 2.72 42.7 2.70 38.3 2.69 34.5 2.66 30.2 2.65 27.6 2.63 24.2 2.61 21.1

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ksi

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.935 0.824

87.2 66.5 51.1 39.1 29.1 22.3 16.8 12.5 9.58 7.23 5.30 3.73 2.92 2.04 1.41

339 251 189 140 102 75.7 56.5 41.2 30.7 22.8 17.4 12.1 9.29 6.42 4.37

AISC_PART 01A:14th Ed_

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1–60

DIMENSIONS AND PROPERTIES

Table 1-8 (continued)

WT-Shapes Dimensions Stem Shape

Area, A 2

in. WT9×35.5 c ×32.5 c ×30 c ×27.5 c ×25 c WT9×23 c ×20 c ×17.5 c,v

10.4 9.55 8.82 8.10 7.34

Depth, d in. 9.24 9.18 9.12 9.06 9.00

6.77 9.03 5.88 8.95 5.15 8.85

Thickness, tw in.

tw ᎏ 2

Flange Area

Width, bf

2

in.

in.

0.495 0.450 0.415 0.390 0.355

1/2

1/4

7/16

1/4

7/16

1/4

3/8

3/16

3/8

3/16

4.57 4.13 3.78 3.53 3.19

7.64 7.59 7.56 7.53 7.50

9 0.360 9 0.315 87/8 0.300

3/8

3/16

5/16

3/16

5/16

3/16

3.25 2.82 2.66

6.06 6 6.02 6 6.00 6

1/2

5/16 1/4

7/16

1/4

91/4 91/8 91/8 9 9

WT8×50 ×44.5 ×38.5 c ×33.5 c

14.7 13.1 11.3 9.81

8.49 8.38 8.26 8.17

81/2 83/8 81/4 81/8

0.585 0.525 0.455 0.395

9/16

3/8

3/16

WT8×28.5 c ×25 c ×22.5 c ×20 c ×18 c

8.39 7.37 6.63 5.89 5.29

8.22 8.13 8.07 8.01 7.93

81/4 81/8 81/8 8 77/8

0.430 0.380 0.345 0.305 0.295

7/16

1/4

3/8

3/16

3/8

3/16

5/16

3/16

5/16

3/16

WT8×15.5 c ×13 c,v

4.56 7.94 3.84 7.85

1/4

1/8

1/4

1/8

8 0.275 77/8 0.250

4.96 4.40 3.76 3.23

Thickness, tf

in.

10.4 10.4 10.3 10.2

Distance

in. 75/8 75/8 71/2 71/2 71/2

103/8 103/8 101/4 101/4 71/8 71/8 7 7 7

0.810 0.750 0.695 0.630 0.570

13/16

0.605 0.525 0.425

5/8

3/4 11/16 5/8 9/16

1/2 7/16

0.985 1 0.875 7/8 0.760 3/4 0.665 11/16

3.53 3.09 2.78 2.44 2.34

7.12 7.07 7.04 7.00 6.99

0.715 0.630 0.565 0.505 0.430

2.18 1.96

5.53 51/2 0.440 5.50 51/2 0.345

11/16 5/8 9/16 1/2 7/16 7/16 3/8

k kdes

kdet

in.

in.

in.

1.21 1.15 1.10 1.03 0.972

11/2 17/16 13/8 15/16 11/4

31/2g

1.01 11/4 0.927 13/16 0.827 11/8

31/2g

1.39 1.28 1.16 1.07

17/8 13/4 15/8 19/16

51/2

1.12 1.03 0.967 0.907 0.832

13/8 15/16 11/4 13/16 11/8

31/2g

0.842 11/8 0.747 11/16

31/2 31/2

Shape is slender for compression with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. v Shear strength controlled by buckling effects (Cv < 1.0) with Fy = 50 ksi. c

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Workable Gage

31/2 31/2

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Page 61

DIMENSIONS AND PROPERTIES

1–61

Table 1-8 (continued)

WT-Shapes Properties

Nominal Wt. lb/ft 35.5 32.5 30 27.5 25

Compact Section Criteria b ᎏf 2tf

d ᎏ tw

4.71 5.06 5.44 5.98 6.57

18.7 20.4 22.0 23.2 25.4

Axis X-X

WT9-WT8

Qs

Axis Y-Y

J

Cw

in.4

in.6

0.961 0.875 0.794 0.733 0.620

1.74 1.36 1.08 0.830 0.619

3.96 3.01 2.35 1.84 1.36

5.84 0.635 4.97 0.496 4.02 0.460

0.609 0.404 0.252

1.20 0.788 0.598

I

S

r

y–

Z

yp

I

S

r

Z

in.4

in.3

in.

in.

in.3

in.

in.4

in.3

in.

in.3

2.74 2.72 2.71 2.71 2.70

2.26 2.20 2.16 2.16 2.12

20.0 18.0 16.5 15.3 13.8

0.683 0.629 0.583 0.538 0.489

30.1 27.4 25.0 22.5 20.0

7.89 7.22 6.63 5.97 5.35

1.70 1.69 1.68 1.67 1.65

12.3 11.2 10.3 9.26 8.28

7.77 2.77 6.73 2.76 6.21 2.79

2.33 2.29 2.39

13.9 0.558 12.0 0.489 11.2 0.450

11.3 9.55 7.67

3.71 1.29 3.17 1.27 2.56 1.22

78.2 11.2 70.7 10.1 64.7 9.29 59.5 8.63 53.5 7.79

23 5.01 25.1 20 5.73 28.4 17.5 7.06 29.5

52.1 44.8 40.1

50 44.5 38.5 33.5

5.29 5.92 6.77 7.70

14.5 16.0 18.2 20.7

76.8 11.4 67.2 10.1 56.9 8.59 48.6 7.36

2.28 2.27 2.24 2.22

1.76 1.70 1.63 1.56

20.7 18.1 15.3 13.0

0.706 0.631 0.549 0.481

93.1 81.3 69.2 59.5

28.5 25 22.5 20 18

4.98 5.61 6.23 6.93 8.12

19.1 21.4 23.4 26.3 26.9

48.7 42.3 37.8 33.1 30.6

7.77 6.78 6.10 5.35 5.05

2.41 2.40 2.39 2.37 2.41

1.94 1.89 1.86 1.81 1.88

13.8 12.0 10.8 9.43 8.93

0.589 0.521 0.471 0.421 0.378

21.6 18.6 16.4 14.4 12.2

15.5 6.28 28.9 13 7.97 31.4

27.5 23.5

4.64 2.45 4.09 2.47

2.02 2.09

8.27 0.413 7.36 0.372

6.20 4.79

17.9 15.7 13.4 11.6 6.06 5.26 4.67 4.12 3.50

2.51 2.49 2.47 2.46 1.60 1.59 1.57 1.56 1.52

2.24 1.17 1.74 1.12

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Torsional Properties

27.4 24.0 20.5 17.7

Fy = 50 ksi

1.00 1.00 0.986 0.859

3.85 2.72 1.78 1.19

0.940 0.824 0.723 0.579 0.553

1.10 0.760 0.555 0.396 0.272

1.99 1.34 0.974 0.673 0.516

3.51 0.479 2.73 0.406

0.230 0.130

0.366 0.243

9.42 8.15 7.22 6.36 5.42

10.4 7.19 4.61 3.01

AISC_PART 01A:14th Ed_

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Page 62

1–62

DIMENSIONS AND PROPERTIES

Table 1-8 (continued)

WT-Shapes Dimensions Stem Shape

Area, A 2

in.

Depth, d in.

Thickness, tw in.

tw ᎏ 2

in.

WT7×365 h ×332.5 h ×302.5 h ×275 h ×250 h ×227.5 h ×213 h ×199 h ×185 h ×171h ×155.5 h ×141.5 h ×128.5 ×116.5 ×105.5 ×96.5 ×88 ×79.5 ×72.5

107 97.8 89.0 80.9 73.5 66.9 62.7 58.4 54.4 50.3 45.7 41.6 37.8 34.2 31.0 28.4 25.9 23.4 21.3

11.2 10.8 10.5 10.1 9.80 9.51 9.34 9.15 8.96 8.77 8.56 8.37 8.19 8.02 7.86 7.74 7.61 7.49 7.39

111/4 107/8 101/2 101/8 93/4 91/2 93/8 91/8 9 83/4 81/2 83/8 81/4 8 77/8 73/4 75/8 71/2 73/8

3.07 2.83 2.60 2.38 2.19 2.02 1.88 1.77 1.66 1.54 1.41 1.29 1.18 1.07 0.980 0.890 0.830 0.745 0.680

31/16 213/16 25/8 23/8 23/16 2 17/8 13/4 111/16 19/16 17/16 15/16 13/16 11/16 1 7/8 13/16 3/4 11/16

WT7×66 ×60 ×54.5 ×49.5 f ×45 f

19.4 17.7 16.0 14.6 13.2

7.33 7.24 7.16 7.08 7.01

73/8 71/4 71/8 71/8 7

0.645 0.590 0.525 0.485 0.440

5/8

5/16

9/16

5/16

1/2

1/4

1/2

1/4

7/16

1/4

WT7×41 ×37 ×34 ×30.5 c

12.0 10.9 10.0 8.96

7.16 7.09 7.02 6.95

71/8 71/8 7 7

0.510 0.450 0.415 0.375

1/2

1/4

7/16

1/4

7/16

1/4

3/8

3/16

7 0.370 67/8 0.340 67/8 0.305

3/8

3/16

5/16

3/16

5/16

3/16

WT7×26.5 c ×24 c ×21.5 c

7.80 6.96 7.07 6.90 6.31 6.83

Flange Area

Width, bf

2

in.

Distance

Thickness, tf

kdet

in.

in.

in.

177/8 175/8 173/8 171/4 17 167/8 163/4 165/8 161/2 163/8 161/4 161/8 16 157/8 153/4 153/4 155/8 155/8 151/2

4.91 4.52 4.16 3.82 3.50 3.21 3.04 2.85 2.66 2.47 2.26 2.07 1.89 1.72 1.56 1.44 1.31 1.19 1.09

415/16 41/2 43/16 313/16 31/2 33/16 31/16 27/8 211/16 21/2 21/4 21/16 17/8 13/4 19/16 17/16 15/16 13/16 11/16

5.51 5.12 4.76 4.42 4.10 3.81 3.63 3.44 3.26 3.07 2.86 2.67 2.49 2.32 2.16 2.04 1.91 1.79 1.69

63/16 513/16 57/16 51/8 413/16 41/2 45/16 41/8 315/16 33/4 39/16 33/8 33/16 3 27/8 23/4 25/8 21/2 23/8

71/2g 71/2g 71/2

4.73 4.27 3.76 3.43 3.08

14.7 14.7 14.6 14.6 14.5

143/4 145/8 145/8 145/8 141/2

1.03 1 0.940 15/16 0.860 7/8 0.780 3/4 0.710 11/16

1.63 1.54 1.46 1.38 1.31

25/16 21/4 23/16 21/16 2

51/2

3.65 3.19 2.91 2.60

10.1 10.1 10.0 10.0

101/8 101/8 10 10

0.855 0.785 0.720 0.645

7/8

1.45 1.38 1.31 1.24

111/16 15/8 19/16 11/2

51/2

0.660 0.595 0.530

11/16

2.58 2.34 2.08

8.06 8 8.03 8 8.00 8

in.

kdes

Workable Gage

17.9 17.7 17.4 17.2 17.0 16.8 16.7 16.6 16.5 16.4 16.2 16.1 16.0 15.9 15.8 15.7 15.7 15.6 15.5

19/16 34.4 17/16 30.6 15/16 27.1 13/16 24.1 11/8 21.5 1 19.2 15/16 17.5 7/8 16.2 13/16 14.8 13/16 13.5 3/4 12.1 11/16 10.8 5/8 9.62 9/16 8.58 1/2 7.70 7/16 6.89 7/16 6.32 3/8 5.58 3/8 5.03

in.

k

13/16 3/4 5/8

5/8 1/2

1.25 11/2 1.19 17/16 1.12 13/8

Shape is slender for compression with Fy = 50 ksi. Shape exceeds compact limit for flexure with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. c f

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

51/2

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DIMENSIONS AND PROPERTIES

1–63

Table 1-8 (continued)

WT-Shapes Properties

Nominal Wt.

Compact Section Criteria

Axis X-X

WT7

Qs

Axis Y-Y

J

Cw

in.4

in.6

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

714 555 430 331 254 196 164 135 110 88.3 67.5 51.8 39.3 29.6 22.2 17.3 13.2 9.84 7.56

5250 3920 2930 2180 1620 1210 991 801 640 502 375 281 209 154 113 87.2 65.2 47.9 36.3

56.5 51.2 46.3 41.8 37.8

1.00 1.00 1.00 1.00 1.00

6.13 4.67 3.55 2.68 2.03

26.6 20.0 15.0 11.1 8.31

22.4 20.2 18.4 16.4

1.00 1.00 1.00 0.971

2.53 1.93 1.50 1.09

5.63 4.19 3.21 2.29

0.967 0.723 0.522

1.46 1.07 0.751

b ᎏf 2tf

d ᎏ tw

I

S

r

y–

Z

yp

I

S

r

Z

in.4

in.3

in.

in.

in.3

in.

in.4

in.3

in.

in.3

1.82 1.95 2.09 2.25 2.43 2.62 2.75 2.92 3.10 3.31 3.59 3.89 4.23 4.62 5.06 5.45 5.97 6.54 7.11

3.65 3.82 4.04 4.24 4.47 4.71 4.97 5.17 5.40 5.69 6.07 6.49 6.94 7.50 8.02 8.70 9.17 10.1 10.9

739 622 524 442 375 321 287 257 229 203 176 153 133 116 102 89.8 80.5 70.2 62.5

95.4 82.1 70.6 60.9 52.7 45.9 41.4 37.6 33.9 30.4 26.7 23.5 20.7 18.2 16.2 14.4 13.0 11.4 10.2

2.62 2.52 2.43 2.34 2.26 2.19 2.14 2.10 2.05 2.01 1.96 1.92 1.88 1.84 1.81 1.78 1.76 1.73 1.71

3.47 3.25 3.05 2.85 2.67 2.51 2.40 2.30 2.19 2.09 1.97 1.86 1.75 1.65 1.57 1.49 1.43 1.35 1.29

211 182 157 136 117 102 91.7 82.9 74.4 66.2 57.7 50.4 43.9 38.2 33.4 29.4 26.3 22.8 20.2

3.00 2.77 2.55 2.35 2.16 1.99 1.88 1.76 1.65 1.54 1.41 1.29 1.18 1.08 0.980 0.903 0.827 0.751 0.688

2360 2080 1840 1630 1440 1280 1180 1090 994 903 807 722 645 576 513 466 419 374 338

264 236 211 189 169 152 141 131 121 110 99.4 89.7 80.7 72.5 65.0 59.3 53.5 48.1 43.7

4.69 4.62 4.55 4.49 4.43 4.38 4.34 4.31 4.27 4.24 4.20 4.17 4.13 4.10 4.07 4.05 4.02 4.00 3.98

408 365 326 292 261 234 217 201 185 169 152 137 123 110 98.9 90.1 81.3 73.0 66.2

66 7.15 60 7.80 54.5 8.49 49.5 9.34 45 10.2

11.4 12.3 13.6 14.6 15.9

57.8 51.7 45.3 40.9 36.5

9.57 8.61 7.56 6.88 6.16

1.73 1.71 1.68 1.67 1.66

1.29 1.24 1.17 1.14 1.09

18.6 16.5 14.4 12.9 11.5

0.658 0.602 0.548 0.500 0.456

274 247 223 201 181

37.2 33.7 30.6 27.6 25.0

3.76 3.74 3.73 3.71 3.70

41 37 34 30.5

5.92 6.41 6.97 7.75

14.0 15.8 16.9 18.5

41.2 36.0 32.6 28.9

7.14 6.25 5.69 5.07

1.85 1.82 1.81 1.80

1.39 1.32 1.29 1.25

13.2 11.5 10.4 9.15

0.593 0.541 0.498 0.448

74.1 66.9 60.7 53.7

14.6 13.3 12.1 10.7

2.48 2.48 2.46 2.45

26.5 24 21.5

6.11 18.8 6.75 20.3 7.54 22.4

27.6 24.9 21.9

4.94 1.88 4.49 1.88 3.98 1.86

1.38 1.35 1.31

8.87 0.484 8.00 0.440 7.05 0.395

28.8 25.7 22.6

lb/ft 365 332.5 302.5 275 250 227.5 213 199 185 171 155.5 141.5 128.5 116.5 105.5 96.5 88 79.5 72.5

7.15 1.92 6.40 1.91 5.65 1.89

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Torsional Properties

Fy = 50 ksi

11.0 0.956 9.80 0.880 8.64 0.773

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Page 64

1–64

DIMENSIONS AND PROPERTIES

Table 1-8 (continued)

WT-Shapes Dimensions Stem Shape

Area, A 2

Depth, d

Area

Width, bf

Thickness, tf

in.

in.

2

in.

in.

5.58 7.05 5.00 6.99 4.42 6.92

7 0.310 7 0.285 67/8 0.270

5/16

3/16

1/4

3/16 1/8

6.77 63/4 0.515 6.75 63/4 0.455 6.73 63/4 0.385

1/2

5/16

2.19 1.99 1.87

WT7×13 c ×11c,v

3.85 6.96 3.25 6.87

7 0.255 67/8 0.230

1/4

1/8 1/8

1.77 1.58

5.03 5 5.00 5

0.420 0.335

7/16

1/4

13/4 15/8 11/2 13/8 15/16 13/16 11/16 15/16 7/8 13/16 11/16 5/8 9/16 1/2 1/2 7/16 3/8

7/8

2.96 2.71 2.47 2.25 2.07 1.90 1.74 1.56 1.40 1.25 1.11 0.990 0.900 0.810 0.735 0.670 0.605

215/16 211/16 21/2 21/4 21/16 17/8 13/4 19/16 13/8 11/4 11/8 1 7/8 13/16 3/4 11/16 5/8

0.640 0.575

5/8

2.26 2.02 1.76

8.08 81/8 0.640 8.05 8 0.575 8.01 8 0.515

5/8

1.88 1.60 1.41

6.56 61/2 0.520 6.52 61/2 0.440 6.49 61/2 0.380

1/2

WT6×168 h ×152.5 h ×139.5 h ×126 h ×115 h ×105 ×95 ×85 ×76 ×68 ×60 ×53 ×48 ×43.5 ×39.5 ×36 ×32.5 f

49.5 44.7 41.0 37.1 33.8 30.9 28.0 25.0 22.4 20.0 17.6 15.6 14.1 12.8 11.6 10.6 9.54

8.41 8.16 7.93 7.71 7.53 7.36 7.19 7.02 6.86 6.71 6.56 6.45 6.36 6.27 6.19 6.13 6.06

in.

tw ᎏ 2

Distance

WT7×19 c ×17 c ×15 c

in.

in.

Thickness, tw

Flange

83/8 81/8 77/8 73/4 71/2 73/8 71/4 7 67/8 63/4 61/2 61/2 63/8 61/4 61/4 61/8 6

1.78 1.63 1.53 1.40 1.29 1.18 1.06 0.960 0.870 0.790 0.710 0.610 0.550 0.515 0.470 0.430 0.390

14.9 13.3 3/4 12.1 11/16 10.7 11/16 9.67 5/8 8.68 9/16 7.62 1/2 6.73 7/16 5.96 7/16 5.30 3/8 4.66 5/16 3.93 5/16 3.50 1/4 3.23 1/4 2.91 1/4 2.63 3/16 2.36 13/16

WT6×29 ×26.5

8.52 6.10 7.78 6.03

61/8 0.360 6 0.345

3/8

3/16

3/8

3/16

WT6×25 ×22.5 ×20 c

7.30 6.10 6.56 6.03 5.84 5.97

61/8 0.370 6 0.335 6 0.295

3/8

3/16

5/16

3/16

5/16

3/16

WT6×17.5 c ×15 c ×13 c

5.17 6.25 4.40 6.17 3.82 6.11

61/4 0.300 61/8 0.260 61/8 0.230

5/16 1/4

3/16 1/8

1/4

1/8

13.4 13.2 13.1 13.0 12.9 12.8 12.7 12.6 12.5 12.4 12.3 12.2 12.2 12.1 12.1 12.0 12.0

133/8 131/4 131/8 13 127/8 123/4 125/8 125/8 121/2 123/8 123/8 121/4 121/8 121/8 121/8 12 12

2.19 10.0 10 2.08 10.0 10

7/16 3/8

5/16

9/16

9/16 1/2

7/16 3/8

k kdes

kdet

in.

in.

f

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

0.915 11/4 0.855 13/16 0.785 11/8

31/2g 31/2 31/2

0.820 11/8 0.735 11/16

2 3/4g 2 3/4g

3.55 3.30 3.07 2.85 2.67 2.50 2.33 2.16 2.00 1.85 1.70 1.59 1.50 1.41 1.33 1.27 1.20

37/8 35/8 33/8 31/8 215/16 213/16 25/8 27/16 25/16 21/8 2 17/8 113/16 111/16 15/8 19/16 11/2

51/2

1.24 11/2 1.18 13/8

51/2 51/2

1.14 11/2 1.08 13/8 1.02 13/8

51/2

0.820 13/16 0.740 11/8 0.680 11/16

31/2

Shape is slender for compression with Fy = 50 ksi. Shape exceeds compact limit for flexure with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. v Shear strength controlled by buckling effects (Cv < 1.0) with Fy = 50 ksi. c

Workable Gage

AISC_PART 01A:14th Ed_

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7:30 AM

Page 65

DIMENSIONS AND PROPERTIES

1–65

Table 1-8 (continued)

WT-Shapes Properties

Nominal Wt.

Compact Section Criteria

Axis X-X

WT7-WT6

Qs

Axis Y-Y

J

Cw

in.4

in.6

6.07 0.758 5.32 0.667 4.49 0.611

0.398 0.284 0.190

0.554 0.400 0.287

2.76 0.537 2.19 0.448

0.179 0.104

0.207 0.134

I

S

r

y–

Z

yp

I

S

r

Z

lb/ft 19 17 15

d ᎏ tw

in.4

in.3

in.

in.

in.3

in.

in.4

in.3

in.

in.3

6.57 22.7 7.41 24.5 8.74 25.6

23.3 20.9 19.0

4.22 2.04 3.83 2.04 3.55 2.07

1.54 1.53 1.58

7.45 0.412 6.74 0.371 6.25 0.329

13.3 3.94 1.55 11.6 3.45 1.53 9.79 2.91 1.49

13 11

5.98 27.3 7.46 29.9

17.3 14.8

3.31 2.12 2.91 2.14

1.72 1.76

5.89 0.383 5.20 0.325

4.45 1.77 1.08 3.50 1.40 1.04

168 152.5 139.5 126 115 105 95 85 76 68 60 53 48 43.5 39.5 36 32.5

b ᎏf 2tf

2.26 2.45 2.66 2.89 3.11 3.37 3.65 4.03 4.46 4.96 5.57 6.17 6.76 7.48 8.22 8.99 9.92

4.72 5.01 5.18 5.51 5.84 6.24 6.78 7.31 7.89 8.49 9.24 10.6 11.6 12.2 13.2 14.3 15.5

190 162 141 121 106 92.1 79.0 67.8 58.5 50.6 43.4 36.3 32.0 28.9 25.8 23.2 20.6

31.2 27.0 24.1 20.9 18.5 16.4 14.2 12.3 10.8 9.46 8.22 6.92 6.12 5.60 5.03 4.54 4.06

1.96 1.90 1.86 1.81 1.77 1.73 1.68 1.65 1.62 1.59 1.57 1.53 1.51 1.50 1.49 1.48 1.47

2.31 2.16 2.05 1.92 1.82 1.72 1.62 1.52 1.43 1.35 1.28 1.19 1.13 1.10 1.06 1.02 0.985

68.4 59.1 51.9 44.8 39.4 34.5 29.8 25.6 22.0 19.0 16.2 13.6 11.9 10.7 9.49 8.48 7.50

1.84 1.69 1.56 1.42 1.31 1.21 1.10 0.994 0.896 0.805 0.716 0.637 0.580 0.527 0.480 0.439 0.398

593 525 469 414 371 332 295 259 227 199 172 151 135 120 108 97.5 87.2

88.6 79.3 71.3 63.6 57.5 51.9 46.5 41.2 36.4 32.1 28.0 24.7 22.2 19.9 17.9 16.2 14.5

3.47 137 3.42 122 3.38 110 3.34 97.9 3.31 88.4 3.28 79.7 3.25 71.2 3.22 62.9 3.19 55.6 3.16 48.9 3.13 42.7 3.11 37.5 3.09 33.7 3.07 30.2 3.05 27.1 3.04 24.6 3.02 22.0

29 26.5

7.82 16.9 8.69 17.5

19.1 17.7

3.76 1.50 3.54 1.51

1.03 1.02

6.97 0.426 6.46 0.389

53.5 10.7 2.51 47.9 9.58 2.48

16.2 14.5

25 22.5 20

6.31 16.5 7.00 18.0 7.77 20.2

18.7 16.6 14.4

3.79 1.60 3.39 1.59 2.95 1.57

1.17 1.13 1.09

6.88 0.452 6.10 0.408 5.28 0.365

28.2 25.0 22.0

6.97 1.96 6.21 1.95 5.50 1.94

17.5 15 13

6.31 20.8 7.41 23.7 8.54 26.6

16.0 13.5 11.7

3.23 1.76 2.75 1.75 2.40 1.75

1.30 1.27 1.25

5.71 0.394 4.83 0.337 4.20 0.295

12.2 3.73 1.54 10.2 3.12 1.52 8.66 2.67 1.51

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Torsional Properties

Fy = 50 ksi

1.00 120 1.00 92.0 1.00 70.9 1.00 53.5 1.00 41.6 1.00 32.1 1.00 24.3 1.00 17.7 1.00 12.8 1.00 9.21 1.00 6.42 1.00 4.55 1.00 3.42 1.00 2.54 1.00 1.91 1.00 1.46 1.00 1.09 1.00 1.00

481 356 267 195 148 112 82.1 58.3 41.3 28.9 19.7 13.6 10.1 7.34 5.43 4.07 2.97

1.05 0.788

2.08 1.53

10.6 1.00 9.47 1.00 8.38 0.885

0.855 0.627 0.452

1.23 0.885 0.620

5.73 0.854 4.78 0.707 4.08 0.566

0.369 0.228 0.150

0.437 0.267 0.174

AISC_PART 01A:14th Ed_

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Page 66

1–66

DIMENSIONS AND PROPERTIES

Table 1-8 (continued)

WT-Shapes Dimensions Stem Area, A

Shape

2

Depth, d

in.

tw ᎏ 2

Area

in.

in.

3.24 2.79 2.36 2.08

6.16 6.08 6.00 5.96

61/8 61/8 6 6

0.260 0.235 0.220 0.200

1/4

1/8

1/4

1/8

1/4

1/8

3/16

1/8

1.60 1.43 1.32 1.19

WT5×56 ×50 ×44 ×38.5 ×34 ×30 ×27 ×24.5

16.5 14.7 13.0 11.3 10.0 8.84 7.90 7.21

5.68 5.55 5.42 5.30 5.20 5.11 5.05 4.99

55/8 51/2 53/8 51/4 51/4 51/8 5 5

0.755 0.680 0.605 0.530 0.470 0.420 0.370 0.340

3/4

3/8 3/8

11/16 5/8 1/2

5/16 1/4

1/2

1/4

7/16

1/4

3/8

3/16

5/16

3/16

WT5×22.5 ×19.5 ×16.5

6.63 5.05 5.73 4.96 4.85 4.87

5 0.350 5 0.315 47/8 0.290

3/8

3/16

5/16

3/16

5/16

3/16

WT5×15 ×13 c ×11c

4.42 5.24 3.81 5.17 3.24 5.09

51/4 0.300 51/8 0.260 51/8 0.240

5/16 1/4

3/16 1/8

1/4

1/8

WT5×9.5 ×8.5 c ×7.5 c ×6 c,f

2.81 2.50 2.21 1.77

5.12 5.06 5.00 4.94

51/8

0.250 5 0.240 5 0.230 47/8 0.190

1/4

1/8

1/4

1/8

1/4

1/8

3/16

1/8

WT4×33.5 ×29 ×24 ×20 ×17.5 ×15.5 f

9.84 8.54 7.05 5.87 5.14 4.56

4.50 4.38 4.25 4.13 4.06 4.00

41/2 43/8 41/4 41/8 4 4

0.570 0.510 0.400 0.360 0.310 0.285

9/16 1/2

5/16 1/4

3/8

3/16

3/8

3/16

5/16

3/16

5/16

WT4×14 ×12

4.12 4.03 3.54 3.97

4 4

0.285 0.245

5/16

c

1/4

Width, bf

2

WT6×11c ×9.5 c ×8 c ×7 c,v

in.

in.

Thickness, tw

Flange

4.29 3.77 3.28 2.81 2.44 2.15 1.87 1.70

Thickness, tf

in. 4.03 4.01 3.99 3.97 10.4 10.3 10.3 10.2 10.1 10.1 10.0 10.0

Distance

in. 4 4 4 4

103/8 103/8 101/4 101/4 101/8 101/8 10 10

0.425 0.350 0.265 0.225

7/16 3/8 1/4 1/4

1.25 11/4 1.12 11/8 0.990 1 0.870 7/8 0.770 3/4 0.680 11/16 0.615 5/8 0.560 9/16

1.77 1.56 1.41

8.02 8 7.99 8 7.96 8

0.620 0.530 0.435

5/8

1.57 1.34 1.22

5.81 53/4 0.510 5.77 53/4 0.440 5.75 53/4 0.360

1/2

1.28 1.21 1.15 0.938

4.02 4.01 4.00 3.96

4 4 4 4

0.395 0.330 0.270 0.210

3/8

8.28 8.22 8.11 8.07 8.02 8.00

81/4 81/4 81/8 81/8 8 8

0.935 0.810 0.685 0.560 0.495 0.435

15/16

3/16

2.57 2.23 1.70 1.49 1.26 1.14

3/16 1/8

1.15 6.54 61/2 0.465 0.971 6.50 61/2 0.400

1/2 7/16

7/16 3/8

5/16 1/4 3/16

13/16 11/16 9/16 1/2 7/16 7/16 3/8

k kdes

kdet

in.

in.

in.

15/16

21/4g

0.725 0.650 0.565 0.525 1.75 1.62 1.49 1.37 1.27 1.18 1.12 1.06

7/8 13/16 3/4

115/16 113/16 111/16 19/16 17/16 13/8 15/16 11/4

f

g

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

51/2

1.12 15/16 1.03 13/16 0.935 11/8 0.810 11/8 0.740 11/16 0.660 15/16

23/4g

15/16

21/4g

0.695 0.630 0.570 0.510 1.33 1.20 1.08 0.954 0.889 0.829

7/8 13/16 3/4

15/8 11/2 13/8 11/4 13/16 11/8

0.859 0.794

Shape is slender for compression with Fy = 50 ksi. Shape exceeds compact limit for flexure with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. v Shear strength controlled by buckling effects (Cv < 1.0) with Fy = 50 ksi. c

Workable Gage

15/16 7/8

51/2

31/2 31/2

AISC_PART 01A:14th Ed_

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Page 67

DIMENSIONS AND PROPERTIES

1–67

Table 1-8 (continued)

WT-Shapes Properties

Nominal Wt.

Compact Section Criteria

Axis X-X

WT6-WT4

Qs

Axis Y-Y

J

Cw

in.4

in.6

0.707 0.597 0.537 0.451

0.146 0.0899 0.0511 0.0350

0.137 0.0934 0.0678 0.0493

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

7.50 5.41 3.75 2.55 1.78 1.23 0.909 0.693

1.00 1.00 1.00

0.753 0.487 0.291

0.981 0.616 0.356

4.41 3.75 3.05

1.00 0.900 0.834

0.310 0.201 0.119

0.273 0.173 0.107

1.67 1.40 1.15 0.869

0.870 0.839 0.809 0.592

0.116 0.0776 0.0518 0.0272

0.0796 0.0610 0.0475 0.0255

1.00 1.00 1.00 1.00 1.00 1.00

2.51 1.66 0.977 0.558 0.384 0.267

3.56 2.28 1.30 0.715 0.480 0.327

1.00 1.00

0.268 0.173

0.230 0.144

d ᎏ tw

I

S

r

y–

Z

yp

I

S

r

Z

lb/ft 11 9.5 8 7

b ᎏf 2tf

in.4

in.3

in.

in.

in.3

in.

in.4

in.3

in.

in.3

4.74 5.72 7.53 8.82

23.7 25.9 27.3 29.8

11.7 10.1 8.70 7.67

2.59 2.28 2.04 1.83

1.90 1.90 1.92 1.92

1.63 1.65 1.74 1.76

2.33 1.88 1.41 1.18

1.15 0.939 0.706 0.593

0.847 0.821 0.773 0.753

1.83 1.49 1.13 0.947

56 50 44 38.5 34 30 27 24.5

4.17 4.62 5.18 5.86 6.58 7.41 8.15 8.93

7.52 8.16 8.96 10.0 11.1 12.2 13.6 14.7

28.6 24.5 20.8 17.4 14.9 12.9 11.1 10.0

6.40 5.56 4.77 4.05 3.49 3.04 2.64 2.39

1.32 1.29 1.27 1.24 1.22 1.21 1.19 1.18

1.21 13.4 0.791 118 1.13 11.4 0.711 103 1.06 9.65 0.631 89.3 0.990 8.06 0.555 76.8 0.932 6.85 0.493 66.7 0.884 5.87 0.438 58.1 0.836 5.05 0.395 51.7 0.807 4.52 0.361 46.7

22.5 19.5 16.5

6.47 14.4 7.53 15.7 9.15 16.8

10.2 2.47 1.24 8.84 2.16 1.24 7.71 1.93 1.26

0.907 0.876 0.869

4.65 0.413 3.99 0.359 3.48 0.305

15 13 11

5.70 17.5 6.56 19.9 7.99 21.2

9.28 2.24 1.45 7.86 1.91 1.44 6.88 1.72 1.46

1.10 1.06 1.07

4.01 0.380 3.39 0.330 3.02 0.282

8.35 2.87 1.37 7.05 2.44 1.36 5.71 1.99 1.33

9.5 8.5 7.5 6

5.09 6.08 7.41 9.43

20.5 21.1 21.7 26.0

6.68 6.06 5.45 4.35

1.74 1.62 1.50 1.22

1.54 1.56 1.57 1.57

1.28 1.32 1.37 1.36

3.10 2.90 2.71 2.20

0.349 0.311 0.305 0.322

2.15 1.78 1.45 1.09

33.5 29 24 20 17.5 15.5

4.43 5.07 5.92 7.21 8.10 9.19

7.89 10.9 8.59 9.12 10.6 6.85 11.5 5.73 13.1 4.82 14.0 4.28

3.05 2.61 1.97 1.69 1.43 1.28

1.05 1.03 0.986 0.988 0.968 0.969

0.936 0.874 0.777 0.735 0.688 0.668

6.29 5.25 3.94 3.25 2.71 2.39

0.594 0.520 0.435 0.364 0.321 0.285

14 12

7.03 14.1 8.12 16.2

4.23 1.28 1.01 0.734 3.53 1.08 0.999 0.695

4.63 4.11 3.72 3.32

0.402 0.348 0.639 0.760

2.38 0.315 1.98 0.272

26.7 22.5 18.3

22.6 20.0 17.4 15.1 13.2 11.5 10.3 9.34

2.67 2.65 2.63 2.60 2.58 2.57 2.56 2.54

34.6 30.5 26.5 22.9 20.0 17.5 15.6 14.1

6.65 2.01 10.1 5.64 1.98 8.57 4.60 1.94 7.00

1.07 0.887 0.723 0.551

44.3 10.7 37.5 9.13 30.5 7.51 24.5 6.08 21.3 5.31 18.5 4.64

0.874 0.844 0.810 0.785

2.12 16.3 2.10 13.9 2.08 11.4 2.04 9.24 2.03 8.05 2.02 7.03

10.8 3.31 1.62 9.14 2.81 1.61

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Torsional Properties

5.04 4.28

Fy = 50 ksi

16.9 11.9 8.02 5.31 3.62 2.46 1.78 1.33

AISC_PART 01A:14th Ed_

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DIMENSIONS AND PROPERTIES

Table 1-8 (continued)

WT-Shapes Dimensions Stem Shape

Area, A 2

f g

in.

Thickness, tw in.

tw ᎏ 2

Flange Area 2

Distance

Width, bf

Thickness, tf

in.

in.

in.

in.

WT4×10.5 ×9

3.08 4.14 2.63 4.07

41/8 0.250 41/8 0.230

1/4

1/8

3/8

1/4

1/8

1.04 5.27 51/4 0.400 0.936 5.25 51/4 0.330

WT4×7.5 ×6.5 ×5 c,f

2.22 4.06 1.92 4.00 1.48 3.95

4 4 4

1/4

1/8 1/8

3/16

1/8

0.993 4.02 4 0.919 4.00 4 0.671 3.94 4

0.315 0.255 0.205

5/16

1/4

WT3×12.5 ×10 ×7.5 f

3.67 3.19 2.94 3.10 2.21 3.00

31/4

0.320 31/8 0.260 3 0.230

5/16

3/16

1/4

1/8

1/4

1/8

1.02 6.08 0.806 6.02 6 0.689 5.99 6

0.455 0.365 0.260

7/16

WT3×8 ×6 ×4.5 f ×4.25 f

2.37 1.78 1.34 1.26

3.14 3.02 2.95 2.92

31/8 3 3 27/8

0.260 0.230 0.170 0.170

1/4

1/8 1/8

3/16

1/8

3/16

1/8

0.816 0.693 0.502 0.496

0.405 0.280 0.215 0.195

3/8

1/4

WT2.5×9.5 ×8

2.78 2.58 2.35 2.51

25/8

0.270 21/2 0.240

1/4

1/8

1/4

1/8

0.695 5.03 5 0.601 5.00 5

0.430 0.360

7/16

WT2×6.5

1.91 2.08

21/8 0.280

1/4

1/8

0.582 4.06 4

0.345

in.

c

Depth, d

0.245 0.230 0.170

61/8

4.03 4.00 3.94 3.94

4 4 4 4

k kdes

kdet

in.

in.

in.

0.700 0.630

7/8 13/16

23/4g 23/4g

0.615 0.555 0.505

13/16

21/4g

0.705 0.615 0.510

15/16

0.655 0.530 0.465 0.445

7/8

0.730 0.660

13/16

3/8

3/4

23/4 23/4

3/8

0.595

3/4

21/4

5/16

1/4 3/16

3/8 1/4

1/4 3/16 3/16

Shape is slender for compression with Fy = 50 ksi. Shape exceeds compact limit for flexure with Fy = 50 ksi. The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Workable Gage

3/4 11/16

31/2

7/8 3/4

21/4g

3/4 11/16 11/16

AISC_PART 01A:14th Ed_

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DIMENSIONS AND PROPERTIES

1–69

Table 1-8 (continued)

WT-Shapes Properties

Nominal Wt.

Compact Section Criteria

Axis X-X

WT4-WT2

Qs

Axis Y-Y

Fy = 50

Torsional Properties

J

Cw

in.4

in.6

I

S

r

y–

Z

yp

I

S

r

Z

lb/ft 10.5 9

d ᎏ tw

in.4

in.3

in.

in.

in.3

in.

in.4

in.3

in.

in.3

6.59 16.6 7.95 17.7

3.90 3.41

1.18 1.12 1.05 1.14

0.831 2.11 0.292 0.834 1.86 0.251

4.88 3.98

1.85 1.26 1.52 1.23

7.5 6.5 5

6.37 16.6 7.84 17.4 9.61 23.2

3.28 2.89 2.15

1.07 1.22 0.974 1.23 0.717 1.20

0.998 1.91 0.276 1.03 1.74 0.240 0.953 1.27 0.188

1.70 1.36 1.05

0.849 0.876 1.33 1.00 0.682 0.843 1.07 1.00 0.531 0.840 0.826 0.733

0.0679 0.0382 0.0433 0.0269 0.0212 0.0114

12.5 6.68 10.0 10 8.25 11.9 7.5 11.5 13.0

2.29 1.76 1.41

0.886 0.789 0.610 1.68 0.302 0.693 0.774 0.560 1.29 0.244 0.577 0.797 0.558 1.03 0.185

8.53 6.64 4.66

2.81 1.52 2.21 1.50 1.56 1.45

4.28 1.00 3.36 1.00 2.37 1.00

0.229 0.171 0.120 0.0858 0.0504 0.0342

1.69 1.32 0.950 0.905

0.685 0.564 0.408 0.397

2.21 1.50 1.10 0.995

1.10 0.748 0.557 0.505

1.69 1.16 0.856 0.778

0.111 0.0449 0.0202 0.0166

8 6 4.5 4.25

b ᎏf 2tf

4.98 7.14 9.16 10.1

12.1 13.1 17.4 17.2

0.844 0.862 0.842 0.848

0.676 0.677 0.623 0.637

1.25 1.01 0.720 0.700

0.294 0.222 0.170 0.160

0.966 0.918 0.905 0.890

ksi

2.84 1.00 2.33 1.00

1.00 1.00 1.00 1.00

0.141 0.0916 0.0855 0.0562

0.0426 0.0178 0.00736 0.00620

9.5 8

5.85 9.56 1.01 0.485 0.604 0.487 0.970 0.276 6.94 10.5 0.845 0.413 0.599 0.458 0.801 0.235

4.56 3.75

1.81 1.28 1.50 1.26

2.76 1.00 2.28 1.00

0.157 0.0775 0.0958 0.0453

6.5

5.88 7.43 0.526 0.321 0.524 0.440 0.616 0.236

1.93

0.950 1.00

1.46 1.00

0.0750 0.0233

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01A:14th Ed_

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7:31 AM

Page 70

1–70

DIMENSIONS AND PROPERTIES

Table 1-9

MT-Shapes Dimensions Stem Shape

c,v

MT6.25×6.2 ×5.8 c,v c

MT6×5.9 ×5.4 c,v ×5 c,v c

Area, A

Depth, d

in.2

in.

Thickness, tw in.

Flange

tw ᎏ 2

Area

Width, bf

in.

in.2

in.

1.82 1.70

6.27 6.25

61/4

1/8

1/16

61/4

0.155 0.155

1/8

1/16

1.74 1.59 1.48

6.00 5.99 5.99

6 6 6

0.177 0.160 0.149

3/16

1/8

3/16

1/8

1/8

1/16 1/8

Distance

Thickness, tf in.

k

Workable Gage

in.

in.

0.971 3.75 0.969 3.50

33/4 31/2

0.228 0.211

1/4

9/16

—

3/16

9/16

1.06 3.07 0.958 3.07 0.892 3.25

31/8 31/8 31/4

0.225 0.210 0.180

1/4

9/16

3/16

9/16

3/16

1/2 9/16

— — —

1.33 1.19

5.00 4.98

5 5

0.157 0.141

3/16

1/16

23/4

0.206 0.182

3/16

1/8

0.785 2.69 0.701 2.69

23/4

3/16

9/16

— —

MT5×3.75 c,v 1.11

5.00

5

0.130

1/8

1/16

0.649 2.69

23/4

0.173

3/16

7/16

—

1/16

0.540 2.28 0.516 2.28

21/4

9/16

21/4

0.189 0.177

3/16 3/16

7/16

— —

MT5×4.5 ×4 c

c,v

0.959 4.00 0.911 4.00

4 4

0.135 0.129

1/8 1/8

1/16

MT3×2.2c 0.647 3.00 ×1.85 c 0.545 2.96

3 3

0.114 0.0980

1/8

1/16 1/16

0.342 1.84 0.290 2.00

17/8 2

0.171 0.129

3/16

1/8

1/8

3/8 5/16

— — 23/4g

MT4×3.25 ×3.1c

MT2.5×9.45 t MT2×3

f

2.50

21/2 0.316

5/16

3/16

0.790 5.00

5

0.416

7/16

13/16

0.875 1.90

17/8 0.130

1/8

1/16

0.247 3.80

33/4

0.160

3/16

1/2

2.78

Shape is slender for compression with Fy = 36 ksi. Shape exceeds compact limit for flexure with Fy = 36 ksi. g The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. t This shape has tapered flanges while all other MT-shapes have parallel flange surfaces. v Shape does not meet the h/tw limit for shear in AISC Specification Section G2.1(a) with Fy = 36 ksi. — Indicates flange is too narrow to establish a workable gage. c

f

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

—

AISC_PART 01A:14th Ed_

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Page 71

DIMENSIONS AND PROPERTIES

1–71

Table 1-9 (continued)

MT-Shapes Properties MT-SHAPES

Nominal Wt.

lb/ft

Compact Section Criteria b ᎏf 2tf

d ᎏ tw

Axis X-X

I

S 4

in.

r

y–

Qs

Axis Y-Y

yp

Z

3

3

in.

in.

in.

in.

in.

I

S 4

in.

r 3

in.

in.

Z in.

Fy = 36 3

ksi

Torsional Properties

J

Cw 4

in.

in.6

6.2 5.8

8.22 40.4 7.29 8.29 40.3 6.94

1.61 1.57

2.01 2.03

1.74 1.84

2.92 2.86

0.372 1.00 0.536 0.808 0.756 0.432

0.746 0.839 0.341 0.0246 0.669 0.684 0.342 0.0206

0.0284 0.0268

5.9 5.4 5

6.82 33.9 6.61 7.31 37.4 6.03 9.03 40.2 5.62

1.61 1.46 1.36

1.96 1.95 1.96

1.89 1.86 1.86

2.89 2.63 2.45

1.13 1.05 1.08

0.543 0.354 0.506 0.330 0.517 0.318

0.561 0.575 0.484 0.0249 0.566 0.532 0.397 0.0196 0.594 0.509 0.344 0.0145

0.0337 0.0250 0.0202

4.5 4

6.53 31.8 3.47 7.39 35.3 3.08

1.00 1.62 0.894 1.62

1.54 1.52

1.81 1.61

0.808 0.336 0.250 0.809 0.296 0.220

0.505 0.403 0.550 0.0156 0.502 0.354 0.446 0.0112

0.0138 0.00989

3.75 7.77 38.4 2.91

0.836 1.63

1.51

1.51

0.759 0.281 0.209

0.505 0.334 0.377 0.00932 0.00792

3.25 6.03 29.6 1.57 3.1 6.44 31.0 1.50

0.558 1.29 0.533 1.29

1.18 1.18

1.01 0.472 0.188 0.165 0.967 0.497 0.176 0.154

0.444 0.264 0.634 0.00917 0.00463 0.441 0.247 0.578 0.00778 0.00403

2.2 5.38 26.3 0.579 0.268 0.949 0.841 0.483 0.190 0.0897 0.0973 0.374 0.155 0.778 0.00494 0.00124 1.85 7.75 30.2 0.483 0.226 0.945 0.827 0.409 0.174 0.0863 0.0863 0.400 0.136 0.609 0.00265 0.000754 9.45 6.01 3

11.9

7.91 1.05

0.528 0.617 0.512 1.03

0.276 4.35

1.74

14.6 0.208 0.133 0.493 0.341 0.241 0.112 0.732 0.385

1.26

2.66

1.00

0.926 0.588 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

0.156

0.0732

0.00919 0.00193

AISC_PART 01B:14th Ed._

1/20/11

7:33 AM

Page 72

1–72

DIMENSIONS AND PROPERTIES

Table 1-10

ST-Shapes Dimensions Stem Shape

Area, A

Depth, d

ST12×60.5 ×53

in.2 17.8 15.6

12.3 12.3

ST12×50 ×45 ×40 c

14.7 13.2 11.7

12.0 12.0 12.0

12 12 12

ST10×48 ×43

14.1 12.7

10.2 10.2

ST10×37.5 ×33

11.0 10.0 9.70 10.0

ST9×35 10.3 ×27.35 8.02

Thickness, tw

in. in. 121/4 0.800 13/16 121/4 0.620 5/8

tw 2 in. 7/16 5/16

Flange Area

Width, bf

Distance

Thickness, tf

Workable Gage

in.2 9.80 7.60

8.05 7.87

8 77/8

1.09 1.09

11/16 11/16

2 2

in. 4 4

8.94 7.50 6.00

7.25 7.13 7.00

71/4 71/8 7

0.870 0.870 0.870

7/8

13/4 13/4 13/4

4 4 4

8.12 6.70

7.20 7.06

71/4 7

0.920 0.920

15/16

13/4 13/4

4 4

15/8 15/8

31/2g 31/2g

11/2 11/2

31/2g 31/2g

13/8 13/8

31/2g 31/2g

17/16 17/16

3g 3g

13/16 13/16

3g 3g

11/8 11/8

23/4g 23/4g

in.

in.

in.

3/4

3/8

5/8

5/16

1/2

1/4

101/8 0.800 101/8 0.660

13/16

7/16

11/16

3/8

10 10

0.635 0.505

5/8

5/16 1/4

6.35 5.05

6.39 6.26

63/8 61/4

0.795 0.795

13/16

1/2

9.00 9 9.00 9

0.711 0.461

11/16

3/8 1/4

6.40 4.15

6.25 6.00

61/4 6

0.691 0.691

11/16

7/16

0.745 0.625 0.500

k

7/8 7/8

15/16

13/16

11/16

ST7.5×25 ×21.45

7.34 6.30

7.50 71/2 7.50 71/2

0.550 0.411

9/16

5/16 1/4

4.13 3.08

5.64 5.50

55/8 51/2

0.622 0.622

5/8

7/16

ST6×25 ×20.4

7.33 5.96

6.00 6 6.00 6

0.687 0.462

11/16

3/8 1/4

4.12 2.77

5.48 5.25

51/2 51/4

0.659 0.659

11/16

7/16

ST6×17.5 ×15.9

5.12 4.65

6.00 6 6.00 6

0.428 0.350

7/16

1/4 3/16

2.57 2.10

5.08 5.00

51/8 5

0.544 0.544

9/16

3/8

ST5×17.5 ×12.7

5.14 3.72

5.00 5 5.00 5

0.594 0.311

5/8

5/16 3/16

2.97 1.56

4.94 4.66

5 45/8

0.491 0.491

1/2

5/16

ST4×11.5 ×9.2

3.38 2.70

4.00 4 4.00 4

0.441 0.271

7/16

1/4 1/8

1.76 1.08

4.17 4.00

41/8 4

0.425 0.425

7/16

1/4

7/16

1 1

21/4g 21/4g

ST3×8.6 ×6.25

2.53 1.83

3.00 3 3.00 3

0.465 0.232

7/16

1/4

35/8 33/8

0.359 0.359

13/16

1/8

1.40 3.57 0.696 3.33

3/8

1/4

3/8

13/16

— —

1.46

2.50 21/2

0.214

3/16

1/8

0.535 3.00

3

0.326

5/16

3/4

—

1.40 1.13

2.00 2 2.00 2

0.326 0.193

5/16

3/16

23/4 25/8

0.293 0.293

3/4

1/8

0.652 2.80 0.386 2.66

5/16

3/16

5/16

3/4

— —

0.349 0.170

3/8

3/16

21/2 23/8

0.260 0.260

5/8

1/8

0.524 2.51 0.255 2.33

1/4

3/16

1/4

5/8

ST2.5×5 ST2×4.75 ×3.85 ST1.5×3.75 ×2.85 c g

1.10 1.50 11/2 0.830 1.50 11/2

5/8

11/16

9/16

1/2

Shape is slender for compression with Fy = 36 ksi The actual size, combination and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility.

— Indicates flange is too narrow to establish a workable gage.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

— —

AISC_PART 01B_14th Ed._Nov. 19, 2012 14-12-04 2:33 PM Page 73

(Black plate)

DIMENSIONS AND PROPERTIES

1–73

Table 1-10 (continued)

ST-Shapes Properties ST-SHAPES Compact Nom- Section inal Criteria Wt. b d I S ᎏf ᎏ tw lb/ft 2tf in.4 in.3 60.5 3.69 15.4 259 30.1 53 3.61 19.8 216 24.1

yp y– r Z I S r Z Fy = 36 J Cw ksi in. in. in.3 in. in.4 in.3 in. in.3 in.4 in.6 3.82 3.63 54.5 1.26 41.5 10.3 1.53 18.1 1.00 6.38 27.5 3.72 3.28 43.3 1.02 38.4 9.76 1.57 16.7 1.00 5.05 15.0

50 45 40

4.17 16.1 215 4.10 19.2 190 4.02 24.0 162

26.3 22.6 18.6

3.83 3.79 3.72

3.84 47.5 3.60 41.1 3.30 33.6

2.16 23.7 1.42 22.3 0.909 21.0

6.55 1.27 12.0 6.27 1.30 11.2 6.00 1.34 10.4

1.00 3.76 1.00 3.01 0.876 2.44

19.5 12.1 6.94

48 43

3.91 12.7 143 3.84 15.4 124

20.3 17.2

3.18 3.13

3.13 36.9 2.91 31.1

1.35 25.0 0.972 23.3

6.93 1.33 12.5 6.59 1.36 11.6

1.00 1.00

4.16 3.30

15.0 9.17

37.5 4.02 15.7 109 15.8 33 3.94 19.8 92.9 12.9

3.15 3.10

3.07 28.6 2.81 23.4

1.34 14.8 0.841 13.7

4.62 1.16 4.39 1.19

8.36 1.00 7.70 1.00

2.28 1.78

7.21 4.02

35 4.52 12.7 27.35 4.34 19.5

84.5 14.0 62.3 9.60

2.87 2.79

2.94 25.1 2.51 17.3

1.78 12.0 0.737 10.4

3.84 1.08 3.45 1.14

7.17 1.00 6.06 1.00

2.02 1.16

7.03 2.26

25 4.53 13.6 21.45 4.42 18.2

40.5 32.9

7.72 5.99

2.35 2.29

2.25 14.0 2.01 10.8

0.826 7.79 0.605 7.13

2.76 1.03 2.59 1.06

4.99 1.00 4.54 1.00

1.05 0.765

2.02 0.995

25 4.17 8.73 25.1 20.4 3.98 13.0 18.9

6.04 4.27

1.85 1.78

1.84 11.0 0.758 7.79 1.58 7.71 0.577 6.74

2.84 1.03 2.57 1.06

5.16 1.00 4.43 1.00

1.36 0.842

1.97 0.787

17.5 4.67 14.0 15.9 4.60 17.1

3.95 3.30

1.83 1.78

1.65 1.51

7.12 0.543 4.92 5.94 0.480 4.66

1.94 0.980 3.40 1.00 1.87 1.00 3.22 1.00

0.524 0.438

0.556 0.364

17.5 5.03 8.42 12.5 3.62 12.7 4.75 16.1 7.79 2.05

1.56 1.45

1.56 1.20

6.58 0.673 4.15 3.70 0.403 3.36

1.68 0.899 3.10 1.00 1.44 0.950 2.49 1.00

0.633 0.300

0.725 0.173

11.5 4.91 9.07 9.2 4.71 14.8

1.22 1.14

1.15 3.19 0.439 2.13 0.942 2.07 0.336 1.84

1.02 0.795 1.84 1.00 0.922 0.827 1.59 1.00

0.271 0.167

0.168 0.0642

8.6 4.97 6.45 6.25 4.64 12.9

17.2 14.8

5.00 1.76 3.49 1.14

Axis X-X

Qs

Axis Y-Y

Torsional Properties

2.12 1.02 0.915 0.915 1.85 0.394 1.14 0.642 0.673 1.17 1.00 1.26 0.547 0.831 0.692 1.01 0.271 0.901 0.541 0.702 0.930 1.00

0.181 0.0772 0.0830 0.0197

0.671 0.348 0.677 0.570 0.650 0.239 0.597 0.398 0.638 0.686 1.00

0.0568 0.01000

4.75 4.78 6.13 0.462 0.319 0.575 0.553 0.592 0.250 0.444 0.317 0.564 0.565 1.00 3.85 4.54 10.4 0.307 0.198 0.522 0.448 0.381 0.204 0.374 0.281 0.576 0.485 1.00

0.0590 0.00995 0.0364 0.00457

3.75 4.83 4.30 0.200 0.187 0.426 0.432 0.351 0.219 0.289 0.230 0.513 0.411 1.00 2.85 4.48 8.82 0.114 0.0970 0.370 0.329 0.196 0.171 0.223 0.192 0.518 0.328 1.00

0.0432 0.00496 0.0216 0.00189

5

4.60 11.7

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DIMENSIONS AND PROPERTIES

Table 1-11

Rectangular HSS Dimensions and Properties Design Wall Thickness, t

Nominal Wt.

HSS20×12×5/8 ×1/2 ×3/8 ×5/16

in. 0.581 0.465 0.349 0.291

lb/ft 127.37 103.30 78.52 65.87

HSS20×8×5/8 ×1/2 ×3/8 ×5/16

0.581 0.465 0.349 0.291

HSS20×4×1/2 ×3/8 ×5/16 ×1/4

Shape

Area, A

Axis X-X

b/t

h/t

in.2 35.0 28.3 21.5 18.1

17.7 22.8 31.4 38.2

31.4 40.0 54.3 65.7

in.4 1880 1550 1200 1010

in.3 188 155 120 101

in. 7.33 7.39 7.45 7.48

in.3 230 188 144 122

110.36 89.68 68.31 57.36

30.3 24.6 18.7 15.7

10.8 14.2 19.9 24.5

31.4 40.0 54.3 65.7

1440 1190 926 786

144 119 92.6 78.6

6.89 6.96 7.03 7.07

185 152 117 98.6

0.465 0.349 0.291 0.233

76.07 58.10 48.86 39.43

20.9 16.0 13.4 10.8

5.60 8.46 10.7 14.2

40.0 54.3 65.7 82.8

838 657 560 458

83.8 65.7 56.0 45.8

6.33 6.42 6.46 6.50

115 89.3 75.6 61.5

HSS18×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4

0.581 0.465 0.349 0.291 0.233

93.34 76.07 58.10 48.86 39.43

25.7 20.9 16.0 13.4 10.8

7.33 9.90 14.2 17.6 22.8

28.0 35.7 48.6 58.9 74.3

923 770 602 513 419

103 85.6 66.9 57.0 46.5

6.00 6.07 6.15 6.18 6.22

135 112 86.4 73.1 59.4

HSS16×12×5/8 ×1/2 ×3/8 ×5/16

0.581 0.465 0.349 0.291

110.36 89.68 68.31 57.36

30.3 24.6 18.7 15.7

17.7 22.8 31.4 38.2

24.5 31.4 42.8 52.0

1090 904 702 595

136 113 87.7 74.4

6.00 6.06 6.12 6.15

165 135 104 87.7

HSS16×8×5/8 ×1/2 ×3/8 ×5/16 ×1/4

0.581 0.465 0.349 0.291 0.233

93.34 76.07 58.10 48.86 39.43

25.7 20.9 16.0 13.4 10.8

10.8 14.2 19.9 24.5 31.3

24.5 31.4 42.8 52.0 65.7

815 679 531 451 368

102 84.9 66.3 56.4 46.1

5.64 5.70 5.77 5.80 5.83

129 106 82.1 69.4 56.4

HSS16×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

0.581 0.465 0.349 0.291 0.233 0.174

76.33 62.46 47.90 40.35 32.63 24.73

21.0 17.2 13.2 11.1 8.96 6.76

3.88 5.60 8.46 10.7 14.2 20.0

24.5 31.4 42.8 52.0 65.7 89.0

539 455 360 308 253 193

67.3 56.9 45.0 38.5 31.6 24.2

5.06 5.15 5.23 5.27 5.31 5.35

92.9 77.3 60.2 51.1 41.7 31.7

I

Note: For compactness criteria, refer to Table 1-12A.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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r

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DIMENSIONS AND PROPERTIES

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Table 1-11 (continued)

Rectangular HSS Dimensions and Properties HSS20-HSS16 Workable Flat

Axis Y-Y Shape

HSS20×12×5/8 ×1/2 ×3/8 ×5/16 HSS20×8×5/8 ×1/2 ×3/8 ×5/16

I in.4 851 705 547 464 338 283 222 189

S

r

Z

in.3 142 117 91.1 77.3

in. 4.930 4.99 5.04 5.07

in.3 162 132 102 85.8

84.6 70.8 55.6 47.4

3.34 3.39 3.44 3.47

Depth Width

Torsion

J

C

Surface Area

in. in. in.4 173/16 93/16 1890 173/4 93/4 1540 185/16 105/16 1180 185/8 105/8 997

in.3 257 209 160 134

ft 2/ft 5.17 5.20 5.23 5.25

96.4 79.5 61.5 52.0

173/16 173/4 185/16 185/8

53/16 53/4 65/16 65/8

916 757 586 496

167 137 105 88.3

4.50 4.53 4.57 4.58

HSS20×4×1/2 ×3/8 ×5/16 ×1/4

58.7 47.6 41.2 34.3

29.3 23.8 20.6 17.1

1.68 1.73 1.75 1.78

34.0 26.8 22.9 18.7

173/4 185/16 185/8 187/8

— 25/16 25/8 27/8

195 156 134 111

63.8 49.9 42.4 34.7

3.87 3.90 3.92 3.93

HSS18×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4

158 134 106 91.3 75.1

52.7 44.6 35.5 30.4 25.0

2.48 2.53 2.58 2.61 2.63

61.0 50.7 39.5 33.5 27.3

153/16 153/4 165/16 169/16 167/8

33/16 33/4 45/16 49/16 47/8

462 387 302 257 210

109 89.9 69.5 58.7 47.7

3.83 3.87 3.90 3.92 3.93

133/16 93/16 1370 133/4 93/4 1120 145/16 105/16 862 145/8 105/8 727

204 166 127 107

4.50 4.53 4.57 4.58

132 108 83.4 70.4 57.0

3.83 3.87 3.90 3.92 3.93

60.5 50.7 39.7 33.8 27.6 21.1

3.17 3.20 3.23 3.25 3.27 3.28

HSS16x12×5/8 ×1/2 ×3/8 ×5/16

700 581 452 384

117 96.8 75.3 64.0

4.80 4.86 4.91 4.94

135 111 85.5 72.2

HSS16×8×5/8 ×1/2 ×3/8 ×5/16 ×1/4

274 230 181 155 127

68.6 57.6 45.3 38.7 31.7

3.27 3.32 3.37 3.40 3.42

79.2 65.5 50.8 43.0 35.0

133/16 133/4 145/16 145/8 147/8

53/16 53/4 65/16 65/8 67/8

681 563 436 369 300

27.0 23.5 19.1 16.6 13.8 10.8

1.60 1.65 1.71 1.73 1.76 1.78

32.5 27.4 21.7 18.5 15.2 11.7

133/16 133/4 145/16 145/8 147/8 153/16

— — 25/16 25/8 27/8 33/16

174 150 120 103 85.2 65.5

HSS16×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

54.1 47.0 38.3 33.2 27.7 21.5

— Indicates flat depth or width is too small to establish a workable flat.

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DIMENSIONS AND PROPERTIES

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties Design Wall Thickness, t

Nominal Wt.

HSS14×10×5/8 ×1/2 ×3/8 ×5/16 ×1/4

in. 0.581 0.465 0.349 0.291 0.233

lb/ft 93.34 76.07 58.10 48.86 39.43

HSS14×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

0.581 0.465 0.349 0.291 0.233 0.174

HSS14×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

Shape

Area, A

Axis X-X

b/t

h/t

in.2 25.7 20.9 16.0 13.4 10.8

14.2 18.5 25.7 31.4 39.9

21.1 27.1 37.1 45.1 57.1

76.33 62.46 47.90 40.35 32.63 24.73

21.0 17.2 13.2 11.1 8.96 6.76

7.33 9.90 14.2 17.6 22.8 31.5

0.581 0.465 0.349 0.291 0.233 0.174

67.82 55.66 42.79 36.10 29.23 22.18

18.7 15.3 11.8 9.92 8.03 6.06

HSS12×10×1/2 ×3/8 ×5/16 ×1/4

0.465 0.349 0.291 0.233

69.27 53.00 44.60 36.03

HSS12×8×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

0.581 0.465 0.349 0.291 0.233 0.174

HSS12×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

0.581 0.465 0.349 0.291 0.233 0.174

I

S

r

in.4 687 573 447 380 310

in.3 98.2 81.8 63.9 54.3 44.3

in. 5.17 5.23 5.29 5.32 5.35

in.3 120 98.8 76.3 64.6 52.4

21.1 27.1 37.1 45.1 57.1 77.5

478 402 317 271 222 170

68.3 57.4 45.3 38.7 31.7 24.3

4.77 4.84 4.91 4.94 4.98 5.01

88.7 73.6 57.3 48.6 39.6 30.1

3.88 5.60 8.46 10.7 14.2 20.0

21.1 27.1 37.1 45.1 57.1 77.5

373 317 252 216 178 137

53.3 45.3 36.0 30.9 25.4 19.5

4.47 4.55 4.63 4.67 4.71 4.74

73.1 61.0 47.8 40.6 33.2 25.3

19.0 14.6 12.2 9.90

18.5 25.7 31.4 39.9

22.8 31.4 38.2 48.5

395 310 264 216

65.9 51.6 44.0 36.0

4.56 4.61 4.64 4.67

78.8 61.1 51.7 42.1

76.33 62.46 47.90 40.35 32.63 24.73

21.0 17.2 13.2 11.1 8.96 6.76

10.8 14.2 19.9 24.5 31.3 43.0

17.7 22.8 31.4 38.2 48.5 66.0

397 333 262 224 184 140

66.1 55.6 43.7 37.4 30.6 23.4

4.34 4.41 4.47 4.50 4.53 4.56

82.1 68.1 53.0 44.9 36.6 27.8

67.82 55.66 42.79 36.10 29.23 22.18

18.7 15.3 11.8 9.92 8.03 6.06

7.33 9.90 14.2 17.6 22.8 31.5

17.7 22.8 31.4 38.2 48.5 66.0

321 271 215 184 151 116

53.4 45.2 35.9 30.7 25.2 19.4

4.14 4.21 4.28 4.31 4.34 4.38

68.8 57.4 44.8 38.1 31.1 23.7

Note: For compactness criteria, refer to Table 1-12A.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

1–77

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties HSS14-HSS12 Workable Flat

Axis Y-Y Shape

I

S

r

Z

Depth Width

Torsion

J

C

Surface Area

HSS14×10×5/8 ×1/2 ×3/8 ×5/16 ×1/4

in.4 407 341 267 227 186

in.3 81.5 68.1 53.4 45.5 37.2

in. 3.98 4.04 4.09 4.12 4.14

in.3 95.1 78.5 60.7 51.4 41.8

in. 113/16 113/4 125/16 129/16 127/8

in. 73/16 73/4 85/16 89/16 87/8

in.4 832 685 528 446 362

in.3 146 120 91.8 77.4 62.6

ft 2/ft 3.83 3.87 3.90 3.92 3.93

HSS14×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

124 105 84.1 72.3 59.6 45.9

41.2 35.1 28.0 24.1 19.9 15.3

2.43 2.48 2.53 2.55 2.58 2.61

48.4 40.4 31.6 26.9 22.0 16.7

113/16 113/4 125/16 129/16 127/8 133/16

33/16 33/4 45/16 49/16 47/8 53/16

334 279 219 186 152 116

83.7 69.3 53.7 45.5 36.9 28.0

3.17 3.20 3.23 3.25 3.27 3.28

HSS14×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

47.2 41.2 33.6 29.2 24.4 19.0

23.6 20.6 16.8 14.6 12.2 9.48

1.59 1.64 1.69 1.72 1.74 1.77

28.5 24.1 19.1 16.4 13.5 10.3

111/4 113/4 121/4 125/8 127/8 131/8

— — 21/4 25/8 27/8 31/8

148 127 102 87.7 72.4 55.8

52.6 44.1 34.6 29.5 24.1 18.4

2.83 2.87 2.90 2.92 2.93 2.95

298 234 200 164

59.7 46.9 40.0 32.7

3.96 4.01 4.04 4.07

69.6 54.0 45.7 37.2

93/4 105/16 109/16 107/8

73/4 85/16 89/16 87/8

545 421 356 289

102 78.3 66.1 53.5

3.53 3.57 3.58 3.60

HSS12×8×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

210 178 140 120 98.8 75.7

52.5 44.4 35.1 30.1 24.7 18.9

3.16 3.21 3.27 3.29 3.32 3.35

61.9 51.5 40.1 34.1 27.8 21.1

93/16 93/4 105/16 109/16 107/8 111/8

53/16 53/4 65/16 69/16 67/8 71/8

454 377 293 248 202 153

97.7 80.4 62.1 52.4 42.5 32.2

3.17 3.20 3.23 3.25 3.27 3.28

HSS12×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

107 91.1 72.9 62.8 51.9 40.0

35.5 30.4 24.3 20.9 17.3 13.3

2.39 2.44 2.49 2.52 2.54 2.57

42.1 35.2 27.7 23.6 19.3 14.7

93/16 93/4 105/16 109/16 107/8 113/16

33/16 33/4 45/16 49/16 47/8 53/16

271 227 178 152 124 94.6

71.1 59.0 45.8 38.8 31.6 24.0

2.83 2.87 2.90 2.92 2.93 2.95

HSS12×10×1/2 ×3/8 ×5/16 ×1/4

— Indicates flat depth or width is too small to establish a workable flat.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties Design Wall Thickness, t

Nominal Wt.

Area, A

b/t

h/t

I

S

r

Z

HSS12×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

in. 0.581 0.465 0.349 0.291 0.233 0.174

lb/ft 59.32 48.85 37.69 31.84 25.82 19.63

in.2 16.4 13.5 10.4 8.76 7.10 5.37

3.88 5.60 8.46 10.7 14.2 20.0

17.7 22.8 31.4 38.2 48.5 66.0

in.4 245 210 168 144 119 91.8

in.3 40.8 34.9 28.0 24.1 19.9 15.3

in. 3.87 3.95 4.02 4.06 4.10 4.13

in.3 55.5 46.7 36.7 31.3 25.6 19.6

HSS12×31/2×3/8 ×5/16

0.349 0.291

36.41 30.78

10.0 8.46

7.03 9.03

31.4 38.2

156 134

26.0 22.4

3.94 3.98

34.7 29.6

HSS12×3×5/16 ×1/4 ×3/16

0.291 0.233 0.174

29.72 24.12 18.35

8.17 6.63 5.02

7.31 9.88 14.2

38.2 48.5 66.0

124 103 79.6

20.7 17.2 13.3

3.90 3.94 3.98

27.9 22.9 17.5

HSS12×2×5/16 ×1/4 ×3/16

0.291 0.233 0.174

27.59 22.42 17.08

7.59 6.17 4.67

3.87 5.58 8.49

38.2 48.5 66.0

104 86.9 67.4

17.4 14.5 11.2

3.71 3.75 3.80

24.5 20.1 15.5

HSS10×8×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

0.581 0.465 0.349 0.291 0.233 0.174

67.82 55.66 42.79 36.10 29.23 22.18

18.7 15.3 11.8 9.92 8.03 6.06

10.8 14.2 19.9 24.5 31.3 43.0

14.2 18.5 25.7 31.4 39.9 54.5

253 214 169 145 119 91.4

50.5 42.7 33.9 29.0 23.8 18.3

3.68 3.73 3.79 3.82 3.85 3.88

62.2 51.9 40.5 34.4 28.1 21.4

HSS10×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

0.581 0.465 0.349 0.291 0.233 0.174

59.32 48.85 37.69 31.84 25.82 19.63

16.4 13.5 10.4 8.76 7.10 5.37

7.33 9.90 14.2 17.6 22.8 31.5

14.2 18.5 25.7 31.4 39.9 54.5

201 171 137 118 96.9 74.6

40.2 34.3 27.4 23.5 19.4 14.9

3.50 3.57 3.63 3.66 3.69 3.73

51.3 43.0 33.8 28.8 23.6 18.0

HSS10×5×3/8 ×5/16 ×1/4 ×3/16

0.349 0.291 0.233 0.174

35.13 29.72 24.12 18.35

9.67 8.17 6.63 5.02

11.3 14.2 18.5 25.7

25.7 31.4 39.9 54.5

120 104 85.8 66.2

24.1 20.8 17.2 13.2

3.53 3.56 3.60 3.63

30.4 26.0 21.3 16.3

Shape

Axis X-X

Note: For compactness criteria, refer to Table 1-12A.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

1–79

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties HSS12-HSS10 Axis Y-Y Shape

I

Torsion

Workable Flat

S

r

Z

Depth Width

J

C

Surface Area

HSS12×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

in.4 40.4 35.3 28.9 25.2 21.0 16.4

in.3 20.2 17.7 14.5 12.6 10.5 8.20

in. 1.57 1.62 1.67 1.70 1.72 1.75

in.3 24.5 20.9 16.6 14.2 11.7 9.00

in. 93/16 93/4 105/16 105/8 107/8 113/16

in. — — 25/16 25/8 27/8 33/16

in.4 122 105 84.1 72.4 59.8 46.1

in.3 44.6 37.5 29.5 25.2 20.6 15.7

ft 2/ft 2.50 2.53 2.57 2.58 2.60 2.62

HSS12×31/2×3/8 ×5/16

21.3 18.6

12.2 10.6

1.46 1.48

14.0 12.1

105/16 105/8

— —

64.7 56.0

25.5 21.8

2.48 2.50

HSS12×3×5/16 ×1/4 ×3/16

13.1 11.1 8.72

8.73 7.38 5.81

1.27 1.29 1.32

10.0 8.28 6.40

105/8 107/8 113/16

— — 23/16

41.3 34.5 26.8

18.4 15.1 11.6

2.42 2.43 2.45

HSS12×2×5/16 ×1/4 ×3/16

5.10 4.41 3.55

5.10 4.41 3.55

0.820 0.845 0.872

6.05 5.08 3.97

105/8 107/8 113/16

— — —

17.6 15.1 12.0

11.6 9.64 7.49

2.25 2.27 2.28

HSS10×8×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

178 151 120 103 84.7 65.1

44.5 37.8 30.0 25.7 21.2 16.3

3.09 3.14 3.19 3.22 3.25 3.28

53.3 44.5 34.8 29.6 24.2 18.4

73/16 73/4 85/16 85/8 87/8 93/16

53/16 53/4 65/16 65/8 67/8 73/16

346 288 224 190 155 118

80.4 66.4 51.4 43.5 35.3 26.7

2.83 2.87 2.90 2.92 2.93 2.95

HSS10×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

89.4 76.8 61.8 53.3 44.1 34.1

29.8 25.6 20.6 17.8 14.7 11.4

2.34 2.39 2.44 2.47 2.49 2.52

35.8 30.1 23.7 20.2 16.6 12.7

73/16 73/4 85/16 85/8 87/8 93/16

33/16 33/4 45/16 45/8 47/8 53/16

209 176 139 118 96.7 73.8

58.6 48.7 37.9 32.2 26.2 19.9

2.50 2.53 2.57 2.58 2.60 2.62

HSS10×5×3/8 ×5/16 ×1/4 ×3/16

40.6 35.2 29.3 22.7

16.2 14.1 11.7 9.09

2.05 2.07 2.10 2.13

18.7 16.0 13.2 10.1

85/16 85/8 87/8 93/16

35/16 35/8 37/8 43/16

100 86.0 70.7 54.1

31.2 26.5 21.6 16.5

2.40 2.42 2.43 2.45

— Indicates flat depth or width is too small to establish a workable flat.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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1/20/11

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DIMENSIONS AND PROPERTIES

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties Design Wall Thickness, t

Nominal Wt.

Area, A

b/t

h/t

I

S

r

Z

HSS10×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

in. 0.581 0.465 0.349 0.291 0.233 0.174 0.116

lb/ft 50.81 42.05 32.58 27.59 22.42 17.08 11.56

in.2 14.0 11.6 8.97 7.59 6.17 4.67 3.16

3.88 5.60 8.46 10.7 14.2 20.0 31.5

14.2 18.5 25.7 31.4 39.9 54.5 83.2

in.4 149 129 104 90.1 74.7 57.8 39.8

in.3 29.9 25.8 20.8 18.0 14.9 11.6 7.97

in. 3.26 3.34 3.41 3.44 3.48 3.52 3.55

in.3 40.3 34.1 27.0 23.1 19.0 14.6 10.0

HSS10×31/2×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.465 0.349 0.291 0.233 0.174 0.116

40.34 31.31 26.53 21.57 16.44 11.13

11.1 8.62 7.30 5.93 4.50 3.04

4.53 7.03 9.03 12.0 17.1 27.2

18.5 25.7 31.4 39.9 54.5 83.2

118 96.1 83.2 69.1 53.6 37.0

23.7 19.2 16.6 13.8 10.7 7.40

3.26 3.34 3.38 3.41 3.45 3.49

31.9 25.3 21.7 17.9 13.7 9.37

HSS10×3×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.349 0.291 0.233 0.174 0.116

30.03 25.46 20.72 15.80 10.71

8.27 7.01 5.70 4.32 2.93

5.60 7.31 9.88 14.2 22.9

25.7 31.4 39.9 54.5 83.2

88.0 76.3 63.6 49.4 34.2

17.6 15.3 12.7 9.87 6.83

3.26 3.30 3.34 3.38 3.42

23.7 20.3 16.7 12.8 8.80

HSS10×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.349 0.291 0.233 0.174 0.116

27.48 23.34 19.02 14.53 9.86

7.58 6.43 5.24 3.98 2.70

2.73 3.87 5.58 8.49 14.2

25.7 31.4 39.9 54.5 83.2

71.7 62.6 52.5 41.0 28.5

14.3 12.5 10.5 8.19 5.70

3.08 3.12 3.17 3.21 3.25

20.3 17.5 14.4 11.1 7.65

HSS9×7×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

0.581 0.465 0.349 0.291 0.233 0.174

59.32 48.85 37.69 31.84 25.82 19.63

16.4 13.5 10.4 8.76 7.10 5.37

9.05 12.1 17.1 21.1 27.0 37.2

12.5 16.4 22.8 27.9 35.6 48.7

174 149 119 102 84.1 64.7

38.7 33.0 26.4 22.6 18.7 14.4

3.26 3.32 3.38 3.41 3.44 3.47

48.3 40.5 31.8 27.1 22.2 16.9

Shape

Axis X-X

Note: For compactness criteria, refer to Table 1-12A.

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DIMENSIONS AND PROPERTIES

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Table 1-11 (continued)

Rectangular HSS Dimensions and Properties HSS10-HSS9 Axis Y-Y Shape

Depth Width

I

S

r

Z

HSS10×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

in.4 33.5 29.5 24.3 21.2 17.7 13.9 9.65

in.3 16.8 14.7 12.1 10.6 8.87 6.93 4.83

in. 1.54 1.59 1.64 1.67 1.70 1.72 1.75

in.3 20.6 17.6 14.0 12.1 10.0 7.66 5.26

in. 73/16 73/4 85/16 85/8 87/8 93/16 97/16

HSS10×31/2×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

21.4 17.8 15.6 13.1 10.3 7.22

12.2 10.2 8.92 7.51 5.89 4.12

1.39 1.44 1.46 1.49 1.51 1.54

14.7 11.8 10.2 8.45 6.52 4.48

HSS10×3×3/8 ×5/16 ×1/4 ×3/16 ×1/8

12.4 11.0 9.28 7.33 5.16

8.28 7.30 6.19 4.89 3.44

1.22 1.25 1.28 1.30 1.33

HSS10×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

4.70 4.24 3.67 2.97 2.14

4.70 4.24 3.67 2.97 2.14

0.787 0.812 0.838 0.864 0.890

HSS9×7×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

117 100 80.4 69.2 57.2 44.1

33.5 28.7 23.0 19.8 16.3 12.6

Torsion

Workable Flat

2.68 2.73 2.78 2.81 2.84 2.87

Surface Area

J

C

in. — — 25/16 25/8 27/8 33/16 37/16

in.4 95.7 82.6 66.5 57.3 47.4 36.5 25.1

in.3 36.7 31.0 24.4 20.9 17.1 13.1 8.90

ft 2/ft 2.17 2.20 2.23 2.25 2.27 2.28 2.30

73/4 85/16 85/8 87/8 93/16 97/16

— — — — 211/16 215/16

63.2 51.5 44.6 37.0 28.6 19.8

26.5 21.1 18.0 14.8 11.4 7.75

2.12 2.15 2.17 2.18 2.20 2.22

9.73 8.42 6.99 5.41 3.74

85/16 85/8 87/8 93/16 97/16

— — — 23/16 27/16

37.8 33.0 27.6 21.5 14.9

17.7 15.2 12.5 9.64 6.61

2.07 2.08 2.10 2.12 2.13

5.76 5.06 4.26 3.34 2.33

85/16 85/8 87/8 93/16 97/16

— — — — —

15.9 14.2 12.2 9.74 6.90

11.0 9.56 7.99 6.22 4.31

1.90 1.92 1.93 1.95 1.97

63/16 63/4 75/16 75/8 77/8 83/16

43/16 43/4 55/16 55/8 57/8 63/16

62.0 51.5 40.0 33.9 27.6 20.9

2.50 2.53 2.57 2.58 2.60 2.62

40.5 34.0 26.7 22.8 18.7 14.3

— Indicates flat depth or width is too small to establish a workable flat.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

235 197 154 131 107 81.7

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DIMENSIONS AND PROPERTIES

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties Design Wall Thickness, t

Nominal Wt.

Area, A

b/t

h/t

I

S

r

Z

HSS9×5×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

in. 0.581 0.465 0.349 0.291 0.233 0.174

lb/ft 50.81 42.05 32.58 27.59 22.42 17.08

in.2 14.0 11.6 8.97 7.59 6.17 4.67

5.61 7.75 11.3 14.2 18.5 25.7

12.5 16.4 22.8 27.9 35.6 48.7

in.4 133 115 92.5 79.8 66.1 51.1

in.3 29.6 25.5 20.5 17.7 14.7 11.4

in. 3.08 3.14 3.21 3.24 3.27 3.31

in.3 38.5 32.5 25.7 22.0 18.1 13.8

HSS9×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16

0.465 0.349 0.291 0.233 0.174

35.24 27.48 23.34 19.02 14.53

9.74 7.58 6.43 5.24 3.98

3.45 5.60 7.31 9.88 14.2

16.4 22.8 27.9 35.6 48.7

80.8 66.3 57.7 48.2 37.6

18.0 14.7 12.8 10.7 8.35

2.88 2.96 3.00 3.04 3.07

24.6 19.7 16.9 14.0 10.8

HSS8×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

0.581 0.465 0.349 0.291 0.233 0.174

50.81 42.05 32.58 27.59 22.42 17.08

14.0 11.6 8.97 7.59 6.17 4.67

7.33 9.90 14.2 17.6 22.8 31.5

10.8 14.2 19.9 24.5 31.3 43.0

114 98.2 79.1 68.3 56.6 43.7

28.5 24.6 19.8 17.1 14.2 10.9

2.85 2.91 2.97 3.00 3.03 3.06

36.1 30.5 24.1 20.6 16.9 13.0

HSS8×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.581 0.465 0.349 0.291 0.233 0.174 0.116

42.30 35.24 27.48 23.34 19.02 14.53 9.86

11.7 9.74 7.58 6.43 5.24 3.98 2.70

3.88 5.60 8.46 10.7 14.2 20.0 31.5

10.8 14.2 19.9 24.5 31.3 43.0 66.0

82.0 71.8 58.7 51.0 42.5 33.1 22.9

20.5 17.9 14.7 12.8 10.6 8.27 5.73

2.64 2.71 2.78 2.82 2.85 2.88 2.92

27.4 23.5 18.8 16.1 13.3 10.2 7.02

HSS8×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.465 0.349 0.291 0.233 0.174 0.116

31.84 24.93 21.21 17.32 13.25 9.01

8.81 6.88 5.85 4.77 3.63 2.46

3.45 5.60 7.31 9.88 14.2 22.9

14.2 19.9 24.5 31.3 43.0 66.0

58.6 48.5 42.4 35.5 27.8 19.3

14.6 12.1 10.6 8.88 6.94 4.83

2.58 2.65 2.69 2.73 2.77 2.80

20.0 16.1 13.9 11.5 8.87 6.11

Shape

Axis X-X

Note: For compactness criteria, refer to Table 1-12A.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

1–83

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties HSS9-HSS8 Axis Y-Y Shape

I

Torsion

Workable Flat

S

r

Z

Depth Width

J

C

Surface Area

HSS9×5×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

in.4 52.0 45.2 36.8 32.0 26.6 20.7

in.3 20.8 18.1 14.7 12.8 10.6 8.28

in. 1.92 1.97 2.03 2.05 2.08 2.10

in.3 25.3 21.5 17.1 14.6 12.0 9.25

in. 63/16 63/4 75/16 75/8 77/8 83/16

in. 23/16 23/4 35/16 35/8 37/8 43/16

in.4 128 109 86.9 74.4 61.2 46.9

in.3 42.5 35.6 27.9 23.8 19.4 14.8

ft 2/ft 2.17 2.20 2.23 2.25 2.27 2.28

HSS9×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16

13.2 11.2 9.88 8.38 6.64

8.81 7.45 6.59 5.59 4.42

1.17 1.21 1.24 1.27 1.29

10.8 8.80 7.63 6.35 4.92

63/4 75/16 75/8 77/8 83/16

— — — — 23/16

40.0 33.1 28.9 24.2 18.9

19.7 15.8 13.6 11.3 8.66

1.87 1.90 1.92 1.93 1.95

HSS8×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

72.3 62.5 50.6 43.8 36.4 28.2

24.1 20.8 16.9 14.6 12.1 9.39

2.27 2.32 2.38 2.40 2.43 2.46

29.5 24.9 19.8 16.9 13.9 10.7

53/16 53/4 65/16 65/8 67/8 73/16

33/16 33/4 45/16 45/8 47/8 53/16

150 127 100 85.8 70.3 53.7

46.0 38.4 30.0 25.5 20.8 15.8

2.17 2.20 2.23 2.25 2.27 2.28

HSS8×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

26.6 23.6 19.6 17.2 14.4 11.3 7.90

13.3 11.8 9.80 8.58 7.21 5.65 3.95

1.51 1.56 1.61 1.63 1.66 1.69 1.71

16.6 14.3 11.5 9.91 8.20 6.33 4.36

53/16 53/4 65/16 65/8 67/8 73/16 77/16

— — 25/16 25/8 27/8 33/16 37/16

70.3 61.1 49.3 42.6 35.3 27.2 18.7

28.7 24.4 19.3 16.5 13.6 10.4 7.10

1.83 1.87 1.90 1.92 1.93 1.95 1.97

HSS8×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

11.7 10.0 8.81 7.49 5.94 4.20

7.81 6.63 5.87 4.99 3.96 2.80

1.15 1.20 1.23 1.25 1.28 1.31

9.64 7.88 6.84 5.70 4.43 3.07

53/4 65/16 65/8 67/8 73/16 77/16

— — — — 23/16 27/16

34.3 28.5 24.9 20.8 16.2 11.3

17.4 14.0 12.1 10.0 7.68 5.27

1.70 1.73 1.75 1.77 1.78 1.80

— Indicates flat depth or width is too small to establish a workable flat.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties Design Wall Thickness, t

Nominal Wt.

Area, A

b/t

h/t

I

S

r

Z

HSS8×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

in. 0.349 0.291 0.233 0.174 0.116

lb/ft 22.37 19.08 15.62 11.97 8.16

in.2 6.18 5.26 4.30 3.28 2.23

2.73 3.87 5.58 8.49 14.2

19.9 24.5 31.3 43.0 66.0

in.4 38.2 33.7 28.5 22.4 15.7

in.3 9.56 8.43 7.12 5.61 3.93

in. 2.49 2.53 2.57 2.61 2.65

in.3 13.4 11.6 9.68 7.51 5.19

HSS7×5×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.465 0.349 0.291 0.233 0.174 0.116

35.24 27.48 23.34 19.02 14.53 9.86

9.74 7.58 6.43 5.24 3.98 2.70

7.75 11.3 14.2 18.5 25.7 40.1

12.1 17.1 21.1 27.0 37.2 57.3

60.6 49.5 43.0 35.9 27.9 19.3

17.3 14.1 12.3 10.2 7.96 5.52

2.50 2.56 2.59 2.62 2.65 2.68

21.9 17.5 15.0 12.4 9.52 6.53

HSS7×4×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.465 0.349 0.291 0.233 0.174 0.116

31.84 24.93 21.21 17.32 13.25 9.01

8.81 6.88 5.85 4.77 3.63 2.46

5.60 8.46 10.7 14.2 20.0 31.5

12.1 17.1 21.1 27.0 37.2 57.3

50.7 41.8 36.5 30.5 23.8 16.6

14.5 11.9 10.4 8.72 6.81 4.73

2.40 2.46 2.50 2.53 2.56 2.59

18.8 15.1 13.1 10.8 8.33 5.73

HSS7×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.465 0.349 0.291 0.233 0.174 0.116

28.43 22.37 19.08 15.62 11.97 8.16

7.88 6.18 5.26 4.30 3.28 2.23

3.45 5.60 7.31 9.88 14.2 22.9

12.1 17.1 21.1 27.0 37.2 57.3

40.7 34.1 29.9 25.2 19.8 13.8

11.6 9.73 8.54 7.19 5.65 3.95

2.27 2.35 2.38 2.42 2.45 2.49

15.8 12.8 11.1 9.22 7.14 4.93

HSS7×2×1/4 ×3/16 ×1/8

0.233 0.174 0.116

13.91 10.70 7.31

3.84 2.93 2.00

5.58 8.49 14.2

27.0 37.2 57.3

19.8 15.7 11.1

5.67 4.49 3.16

2.27 2.31 2.35

7.64 5.95 4.13

HSS6×5×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.465 0.349 0.291 0.233 0.174 0.116

31.84 24.93 21.21 17.32 13.25 9.01

8.81 6.88 5.85 4.77 3.63 2.46

7.75 11.3 14.2 18.5 25.7 40.1

9.90 14.2 17.6 22.8 31.5 48.7

41.1 33.9 29.6 24.7 19.3 13.4

13.7 11.3 9.85 8.25 6.44 4.48

2.16 2.22 2.25 2.28 2.31 2.34

17.2 13.8 11.9 9.87 7.62 5.24

Shape

Axis X-X

Note: For compactness criteria, refer to Table 1-12A.

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DIMENSIONS AND PROPERTIES

1–85

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties HSS8-HSS6 Axis Y-Y Shape

HSS8×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

Torsion

Workable Flat Depth Width

I

S

r

Z

in.4 3.73 3.38 2.94 2.39 1.72

in.3 3.73 3.38 2.94 2.39 1.72

in. 0.777 0.802 0.827 0.853 0.879

in.3 4.61 4.06 3.43 2.70 1.90

in. 65/16 65/8 67/8 73/16 77/16

Surface Area

J

C

in. — — — — —

in.4 12.1 10.9 9.36 7.48 5.30

in.3 8.65 7.57 6.35 4.95 3.44

ft 2/ft 1.57 1.58 1.60 1.62 1.63

HSS7×5×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

35.6 29.3 25.5 21.3 16.6 11.6

14.2 11.7 10.2 8.53 6.65 4.63

1.91 1.97 1.99 2.02 2.05 2.07

17.3 13.8 11.9 9.83 7.57 5.20

43/4 55/16 55/8 57/8 63/16 67/16

23/4 35/16 35/8 37/8 43/16 47/16

75.8 60.6 52.1 42.9 32.9 22.5

27.2 21.4 18.3 15.0 11.4 7.79

1.87 1.90 1.92 1.93 1.95 1.97

HSS7×4×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

20.7 17.3 15.2 12.8 10.0 7.03

10.4 8.63 7.58 6.38 5.02 3.51

1.53 1.58 1.61 1.64 1.66 1.69

12.6 10.2 8.83 7.33 5.67 3.91

43/4 55/16 55/8 57/8 61/8 67/16

— 25/16 25/8 27/8 31/8 37/16

50.5 41.0 35.4 29.3 22.7 15.6

21.1 16.8 14.4 11.8 9.07 6.20

1.70 1.73 1.75 1.77 1.78 1.80

HSS7×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

10.2 8.71 7.74 6.60 5.24 3.71

6.80 5.81 5.16 4.40 3.50 2.48

1.14 1.19 1.21 1.24 1.26 1.29

8.46 6.95 6.05 5.06 3.94 2.73

43/4 55/16 55/8 57/8 63/16 67/16

— — — — 23/16 27/16

28.6 23.9 20.9 17.5 13.7 9.48

15.0 12.1 10.5 8.68 6.69 4.60

1.53 1.57 1.58 1.60 1.62 1.63

HSS7×2×1/4 ×3/16 ×1/8

2.58 2.10 1.52

2.58 2.10 1.52

0.819 0.845 0.871

3.02 2.39 1.68

57/8 63/16 67/16

— — —

7.95 6.35 4.51

5.52 4.32 3.00

1.43 1.45 1.47

12.3 10.2 8.91 7.47 5.84 4.07

1.87 1.92 1.95 1.98 2.01 2.03

15.2 12.2 10.5 8.72 6.73 4.63

33/4 45/16 45/8 47/8 53/16 57/16

23/4 35/16 35/8 37/8 43/16 47/16

23.0 18.2 15.6 12.8 9.76 6.66

1.70 1.73 1.75 1.77 1.78 1.80

HSS6×5×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

30.8 25.5 22.3 18.7 14.6 10.2

— Indicates flat depth or width is too small to establish a workable flat.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

59.8 48.1 41.4 34.2 26.3 18.0

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DIMENSIONS AND PROPERTIES

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties Design Wall Thickness, t

Nominal Wt.

Area, A

b/t

h/t

I

S

r

Z

HSS6×4×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

in. 0.465 0.349 0.291 0.233 0.174 0.116

lb/ft 28.43 22.37 19.08 15.62 11.97 8.16

in.2 7.88 6.18 5.26 4.30 3.28 2.23

5.60 8.46 10.7 14.2 20.0 31.5

9.90 14.2 17.6 22.8 31.5 48.7

in.4 34.0 28.3 24.8 20.9 16.4 11.4

in.3 11.3 9.43 8.27 6.96 5.46 3.81

in. 2.08 2.14 2.17 2.20 2.23 2.26

in.3 14.6 11.9 10.3 8.53 6.60 4.56

HSS6×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.465 0.349 0.291 0.233 0.174 0.116

25.03 19.82 16.96 13.91 10.70 7.31

6.95 5.48 4.68 3.84 2.93 2.00

3.45 5.60 7.31 9.88 14.2 22.9

9.90 14.2 17.6 22.8 31.5 48.7

26.8 22.7 20.1 17.0 13.4 9.43

8.95 7.57 6.69 5.66 4.47 3.14

1.97 2.04 2.07 2.10 2.14 2.17

12.1 9.90 8.61 7.19 5.59 3.87

HSS6×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.349 0.291 0.233 0.174 0.116

17.27 14.83 12.21 9.42 6.46

4.78 4.10 3.37 2.58 1.77

2.73 3.87 5.58 8.49 14.2

14.2 17.6 22.8 31.5 48.7

17.1 15.3 13.1 10.5 7.42

5.71 5.11 4.37 3.49 2.47

1.89 1.93 1.97 2.01 2.05

7.93 6.95 5.84 4.58 3.19

HSS5×4×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.465 0.349 0.291 0.233 0.174 0.116

25.03 19.82 16.96 13.91 10.70 7.31

6.95 5.48 4.68 3.84 2.93 2.00

5.60 8.46 10.7 14.2 20.0 31.5

7.75 11.3 14.2 18.5 25.7 40.1

21.2 17.9 15.8 13.4 10.6 7.42

8.49 7.17 6.32 5.35 4.22 2.97

1.75 1.81 1.84 1.87 1.90 1.93

10.9 8.96 7.79 6.49 5.05 3.50

HSS5×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.465 0.349 0.291 0.233 0.174 0.116

21.63 17.27 14.83 12.21 9.42 6.46

6.02 4.78 4.10 3.37 2.58 1.77

3.45 5.60 7.31 9.88 14.2 22.9

7.75 11.3 14.2 18.5 25.7 40.1

16.4 14.1 12.6 10.7 8.53 6.03

6.57 5.65 5.03 4.29 3.41 2.41

1.65 1.72 1.75 1.78 1.82 1.85

8.83 7.34 6.42 5.38 4.21 2.93

Shape

Axis X-X

Note: For compactness criteria, refer to Table 1-12A.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

1–87

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties HSS6-HSS5 Workable Flat

Axis Y-Y Shape

I

S

r

Z

HSS6×4×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

in.4 17.8 14.9 13.2 11.1 8.76 6.15

in.3 8.89 7.47 6.58 5.56 4.38 3.08

in. 1.50 1.55 1.58 1.61 1.63 1.66

in.3 11.0 8.94 7.75 6.45 5.00 3.46

in. 33/4 45/16 45/8 47/8 53/16 57/16

HSS6×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

8.69 7.48 6.67 5.70 4.55 3.23

5.79 4.99 4.45 3.80 3.03 2.15

1.12 1.17 1.19 1.22 1.25 1.27

7.28 6.03 5.27 4.41 3.45 2.40

HSS6×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

2.77 2.52 2.21 1.80 1.31

2.77 2.52 2.21 1.80 1.31

0.760 0.785 0.810 0.836 0.861

HSS5×4×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

14.9 12.6 11.1 9.46 7.48 5.27

7.43 6.30 5.57 4.73 3.74 2.64

HSS5×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

7.18 6.25 5.60 4.81 3.85 2.75

4.78 4.16 3.73 3.21 2.57 1.83

Depth Width

Torsion

Surface Area

J

C

in. — 25/16 25/8 27/8 33/16 37/16

in.4 40.3 32.8 28.4 23.6 18.2 12.6

in.3 17.8 14.2 12.2 10.1 7.74 5.30

ft 2/ft 1.53 1.57 1.58 1.60 1.62 1.63

33/4 45/16 45/8 47/8 53/16 57/16

— — — — 23/16 27/16

23.1 19.3 16.9 14.2 11.1 7.73

12.7 10.3 8.91 7.39 5.71 3.93

1.37 1.40 1.42 1.43 1.45 1.47

3.46 3.07 2.61 2.07 1.46

45/16 45/8 47/8 53/16 57/16

— — — — —

8.42 7.60 6.55 5.24 3.72

6.35 5.58 4.70 3.68 2.57

1.23 1.25 1.27 1.28 1.30

1.46 1.52 1.54 1.57 1.60 1.62

9.35 7.67 6.67 5.57 4.34 3.01

23/4 35/16 35/8 37/8 43/16 47/16

— 25/16 25/8 27/8 33/16 37/16

30.3 24.9 21.7 18.0 14.0 9.66

14.5 11.7 10.1 8.32 6.41 4.39

1.37 1.40 1.42 1.43 1.45 1.47

1.09 1.14 1.17 1.19 1.22 1.25

6.10 5.10 4.48 3.77 2.96 2.07

23/4 35/16 35/8 37/8 43/16 47/16

— — — — 23/16 27/16

17.6 14.9 13.1 11.0 8.64 6.02

10.3 8.44 7.33 6.10 4.73 3.26

1.20 1.23 1.25 1.27 1.28 1.30

— Indicates flat depth or width is too small to establish a workable flat.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties Design Wall Thickness, t

Nominal Wt.

Area, A

b/t

h/t

HSS5×21/2×1/4 ×3/16 ×1/8

in. 0.233 0.174 0.116

lb/ft 11.36 8.78 6.03

in.2 3.14 2.41 1.65

7.73 11.4 18.6

18.5 25.7 40.1

HSS5×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.349 0.291 0.233 0.174 0.116

14.72 12.70 10.51 8.15 5.61

4.09 3.52 2.91 2.24 1.54

2.73 3.87 5.58 8.49 14.2

HSS4×3×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.349 0.291 0.233 0.174 0.116

14.72 12.70 10.51 8.15 5.61

4.09 3.52 2.91 2.24 1.54

HSS4×21/2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.349 0.291 0.233 0.174 0.116

13.44 11.64 9.66 7.51 5.18

HSS4×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.349 0.291 0.233 0.174 0.116

HSS31/2×21/2×3/8 ×5/16 ×1/4 ×3/16 ×1/8 HSS31/2×2×1/4 ×3/16 ×1/8

Shape

Axis X-X

I

S

r

Z

in.4 9.40 7.51 5.34

in.3 3.76 3.01 2.14

in. 1.73 1.77 1.80

in.3 4.83 3.79 2.65

11.3 14.2 18.5 25.7 40.1

10.4 9.35 8.08 6.50 4.65

4.14 3.74 3.23 2.60 1.86

1.59 1.63 1.67 1.70 1.74

5.71 5.05 4.27 3.37 2.37

5.60 7.31 9.88 14.2 22.9

8.46 10.7 14.2 20.0 31.5

7.93 7.14 6.15 4.93 3.52

3.97 3.57 3.07 2.47 1.76

1.39 1.42 1.45 1.49 1.52

5.12 4.51 3.81 3.00 2.11

3.74 3.23 2.67 2.06 1.42

4.16 5.59 7.73 11.4 18.6

8.46 10.7 14.2 20.0 31.5

6.77 6.13 5.32 4.30 3.09

3.38 3.07 2.66 2.15 1.54

1.35 1.38 1.41 1.44 1.47

4.48 3.97 3.38 2.67 1.88

12.17 10.58 8.81 6.87 4.75

3.39 2.94 2.44 1.89 1.30

2.73 3.87 5.58 8.49 14.2

8.46 10.7 14.2 20.0 31.5

5.60 5.13 4.49 3.66 2.65

2.80 2.56 2.25 1.83 1.32

1.29 1.32 1.36 1.39 1.43

3.84 3.43 2.94 2.34 1.66

0.349 0.291 0.233 0.174 0.116

12.17 10.58 8.81 6.87 4.75

3.39 2.94 2.44 1.89 1.30

4.16 5.59 7.73 11.4 18.6

7.03 9.03 12.0 17.1 27.2

4.75 4.34 3.79 3.09 2.23

2.72 2.48 2.17 1.76 1.28

1.18 1.22 1.25 1.28 1.31

3.59 3.20 2.74 2.18 1.54

0.233 0.174 0.116

7.96 6.23 4.33

2.21 1.71 1.19

5.58 8.49 14.2

12.0 17.1 27.2

3.17 2.61 1.90

1.81 1.49 1.09

1.20 1.23 1.27

2.36 1.89 1.34

Note: For compactness criteria, refer to Table 1-12A.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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1/20/11

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DIMENSIONS AND PROPERTIES

1–89

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties HSS5-HSS31/2 Workable Flat

Axis Y-Y Shape

Depth Width

Torsion

S

r

Z

HSS5×21/2×1/4 ×3/16 ×1/8

in.4 3.13 2.53 1.82

in.3 2.50 2.03 1.46

in. 0.999 1.02 1.05

in.3 2.95 2.33 1.64

in. 37/8 43/16 47/16

in. — — —

in.4 7.93 6.26 4.40

in.3 4.99 3.89 2.70

ft 2/ft 1.18 1.20 1.22

HSS5×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

2.28 2.10 1.84 1.51 1.10

2.28 2.10 1.84 1.51 1.10

0.748 0.772 0.797 0.823 0.848

2.88 2.57 2.20 1.75 1.24

35/16 35/8 37/8 43/16 47/16

— — — — —

6.61 5.99 5.17 4.15 2.95

5.20 4.59 3.88 3.05 2.13

1.07 1.08 1.10 1.12 1.13

HSS4×3×3/8 ×5/16 ×1/4 ×3/16 ×1/8

5.01 4.52 3.91 3.16 2.27

3.34 3.02 2.61 2.10 1.51

1.11 1.13 1.16 1.19 1.21

4.18 3.69 3.12 2.46 1.73

25/16 25/8 27/8 33/16 37/16

— — — — —

10.6 9.41 7.96 6.26 4.38

6.59 5.75 4.81 3.74 2.59

1.07 1.08 1.10 1.12 1.13

HSS4×21/2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

3.17 2.89 2.53 2.06 1.49

2.54 2.32 2.02 1.65 1.19

0.922 0.947 0.973 0.999 1.03

3.20 2.85 2.43 1.93 1.36

25/16 25/8 27/8 31/8 37/16

— — — — —

7.57 6.77 5.78 4.59 3.23

5.32 4.67 3.93 3.08 2.14

0.983 1.00 1.02 1.03 1.05

1.80 1.67 1.48 1.22 0.898

1.80 1.67 1.48 1.22 0.898

0.729 0.754 0.779 0.804 0.830

2.31 2.08 1.79 1.43 1.02

25/16 25/8 27/8 33/16 37/16

— — — — —

4.83 4.40 3.82 3.08 2.20

4.04 3.59 3.05 2.41 1.69

0.900 0.917 0.933 0.950 0.967

2.77 2.54 2.23 1.82 1.33

2.21 2.03 1.78 1.46 1.06

0.904 0.930 0.956 0.983 1.01

2.82 2.52 2.16 1.72 1.22

— 21/8 23/8 211/16 215/16

— — — — —

6.16 5.53 4.75 3.78 2.67

4.57 4.03 3.40 2.67 1.87

0.900 0.917 0.933 0.950 0.967

1.30 1.08 0.795

1.30 1.08 0.795

0.766 0.792 0.818

1.58 1.27 0.912

23/8 211/16 215/16

— — —

3.16 2.55 1.83

2.64 2.09 1.47

0.850 0.867 0.883

HSS4×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8 HSS31/2×21/2×3/8 ×5/16 ×1/4 ×3/16 ×1/8 HSS31/2×2×1/4 ×3/16 ×1/8

—Indicates flat depth or width is too small to establish a workable flat.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

J

C

Surface Area

I

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Page 90

1–90

DIMENSIONS AND PROPERTIES

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties Design Wall Thickness, t

Nominal Wt.

Area, A

b/t

h/t

HSS31/2×11/2×1/4 ×3/16 ×1/8

in. 0.233 0.174 0.116

lb/ft 7.11 5.59 3.90

in.2 1.97 1.54 1.07

3.44 5.62 9.93

12.0 17.1 27.2

in.4 2.55 2.12 1.57

HSS3×21/2×5/16 ×1/4 ×3/16 ×1/8

0.291 0.233 0.174 0.116

9.51 7.96 6.23 4.33

2.64 2.21 1.71 1.19

5.59 7.73 11.4 18.6

7.31 9.88 14.2 22.9

HSS3×2×5/16 ×1/4 ×3/16 ×1/8

0.291 0.233 0.174 0.116

8.45 7.11 5.59 3.90

2.35 1.97 1.54 1.07

3.87 5.58 8.49 14.2

HSS3×11/2×1/4 ×3/16 ×1/8

0.233 0.174 0.116

6.26 4.96 3.48

1.74 1.37 0.956

HSS3×1×3/16 ×1/8

0.174 0.116

4.32 3.05

HSS21/2×2×1/4 ×3/16 ×1/8

0.233 0.174 0.116

HSS21/2×11/2×1/4 ×3/16 ×1/8

Shape

Axis X-X

I

r

Z

in.3 1.46 1.21 0.896

in. 1.14 1.17 1.21

in.3 1.98 1.60 1.15

2.92 2.57 2.11 1.54

1.94 1.72 1.41 1.03

1.05 1.08 1.11 1.14

2.51 2.16 1.73 1.23

7.31 9.88 14.2 22.9

2.38 2.13 1.77 1.30

1.59 1.42 1.18 0.867

1.01 1.04 1.07 1.10

2.11 1.83 1.48 1.06

3.44 5.62 9.93

9.88 14.2 22.9

1.68 1.42 1.06

1.12 0.945 0.706

0.982 1.02 1.05

1.51 1.24 0.895

1.19 0.840

2.75 5.62

14.2 22.9

1.07 0.817

0.713 0.545

0.947 0.987

0.989 0.728

6.26 4.96 3.48

1.74 1.37 0.956

5.58 8.49 14.2

7.73 11.4 18.6

1.33 1.12 0.833

1.06 0.894 0.667

0.874 0.904 0.934

1.37 1.12 0.809

0.233 0.174 0.116

5.41 4.32 3.05

1.51 1.19 0.840

3.44 5.62 9.93

7.73 11.4 18.6

1.03 0.882 0.668

0.822 0.705 0.535

0.826 0.860 0.892

1.11 0.915 0.671

HSS21/2×1×3/16 ×1/8

0.174 0.116

3.68 2.63

1.02 0.724

2.75 5.62

11.4 18.6

0.646 0.503

0.517 0.403

0.796 0.834

0.713 0.532

HSS21/4×2×3/16 ×1/8

0.174 0.116

4.64 3.27

1.28 0.898

8.49 14.2

9.93 16.4

0.859 0.646

0.764 0.574

0.819 0.848

0.952 0.693

HSS2×11/2×3/16 ×1/8

0.174 0.116

3.68 2.63

1.02 0.724

5.62 9.93

8.49 14.2

0.495 0.383

0.495 0.383

0.697 0.728

0.639 0.475

HSS2×1×3/16 ×1/8

0.174 0.116

3.04 2.20

0.845 0.608

2.75 5.62

8.49 14.2

0.350 0.280

0.350 0.280

0.643 0.679

0.480 0.366

Note: For compactness criteria, refer to Table 1-12A.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

S

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DIMENSIONS AND PROPERTIES

1–91

Table 1-11 (continued)

Rectangular HSS Dimensions and Properties HSS31/2 -HSS2 Workable Flat

Axis Y-Y Shape

I

S

r

Z

Depth Width

Torsion

J

C

Surface Area

in.4 0.638 0.544 0.411

in.3 0.851 0.725 0.548

in. 0.569 0.594 0.619

in.3 1.06 0.867 0.630

in. 23/8 211/16 215/16

in. — — —

in.4 1.79 1.49 1.09

in.3 1.88 1.51 1.08

ft 2/ft 0.767 0.784 0.800

2.18 1.93 1.59 1.16

1.74 1.54 1.27 0.931

0.908 0.935 0.963 0.990

2.20 1.90 1.52 1.09

— — 23/16 27/16

— — — —

4.34 3.74 3.00 2.13

3.39 2.87 2.27 1.59

0.833 0.850 0.867 0.883

HSS3×2×5/16 ×1/4 ×3/16 ×1/8

1.24 1.11 0.932 0.692

1.24 1.11 0.932 0.692

0.725 0.751 0.778 0.804

1.58 1.38 1.12 0.803

— — 23/16 27/16

— — — —

2.87 2.52 2.05 1.47

2.60 2.23 1.78 1.25

0.750 0.767 0.784 0.800

HSS3×11/2×1/4 ×3/16 ×1/8

0.543 0.467 0.355

0.725 0.622 0.474

0.559 0.584 0.610

0.911 0.752 0.550

17/8 23/16 27/16

— — —

1.44 1.21 0.886

1.58 1.28 0.920

0.683 0.700 0.717

HSS3×1×3/16 ×1/8

0.173 0.138

0.345 0.276

0.380 0.405

0.432 0.325

23/16 27/16

— —

0.526 0.408

0.792 0.585

0.617 0.633

HSS21/2×2×1/4 ×3/16 ×1/8

0.930 0.786 0.589

0.930 0.786 0.589

0.731 0.758 0.785

1.17 0.956 0.694

— — —

— — —

1.90 1.55 1.12

1.82 1.46 1.04

0.683 0.700 0.717

HSS21/2×11/2×1/4 ×3/16 ×1/8

0.449 0.390 0.300

0.599 0.520 0.399

0.546 0.572 0.597

0.764 0.636 0.469

— — —

— — —

1.10 0.929 0.687

1.29 1.05 0.759

0.600 0.617 0.633

HSS21/2×1×3/16 ×1/8

0.143 0.115

0.285 0.230

0.374 0.399

0.360 0.274

— —

— —

0.412 0.322

0.648 0.483

0.534 0.550

HSS21/4×2×3/16 ×1/8

0.713 0.538

0.713 0.538

0.747 0.774

0.877 0.639

— —

— —

1.32 0.957

1.30 0.927

0.659 0.675

HSS2×11/2×3/16 ×1/8

0.313 0.244

0.417 0.325

0.554 0.581

0.521 0.389

— —

— —

0.664 0.496

0.822 0.599

0.534 0.550

0.112 0.0922

0.225 0.184

0.365 0.390

0.288 0.223

— —

— —

0.301 0.238

0.505 0.380

0.450 0.467

HSS31/2×11/2×1/4 ×3/16 ×1/8 HSS3×21/2×5/16 ×1/4 ×3/16 ×1/8

HSS2×1×3/16 ×1/8

— Indicates flat depth or width is too small to establish a workable flat.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 92

1–92

DIMENSIONS AND PROPERTIES

Table 1-12

Square HSS Dimensions and Properties HSS16-HSS8

Shape

Design Wall Nom- Area, Thick- inal A ness, Wt. t

b/t

h/t

I

S

r

Z

HSS16×16×5/8 ×1/2 ×3/8 ×5/16

in. 0.581 0.465 0.349 0.291

lb/ft 127.37 103.30 78.52 65.87

in.2 35.0 28.3 21.5 18.1

24.5 31.4 42.8 52.0

in.4 in.3 24.5 1370 171 31.4 1130 141 42.8 873 109 52.0 739 92.3

in. 6.25 6.31 6.37 6.39

in.3 200 164 126 106

HSS14×14×5/8 ×1/2 ×3/8 ×5/16

0.581 0.465 0.349 0.291

110.36 89.68 68.31 57.36

30.3 24.6 18.7 15.7

21.1 27.1 37.1 45.1

21.1 27.1 37.1 45.1

897 743 577 490

128 106 82.5 69.9

5.44 151 5.49 124 5.55 95.4 5.58 80.5

HSS12×12×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

0.581 0.465 0.349 0.291 0.233 0.174

93.34 76.07 58.10 48.86 39.43 29.84

25.7 20.9 16.0 13.4 10.8 8.15

17.7 22.8 31.4 38.2 48.5 66.0

17.7 22.8 31.4 38.2 48.5 66.0

548 457 357 304 248 189

91.4 76.2 59.5 50.7 41.4 31.5

4.62 109 4.68 89.6 4.73 69.2 4.76 58.6 4.79 47.6 4.82 36.0

HSS10×10×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

0.581 0.465 0.349 0.291 0.233 0.174

76.33 62.46 47.90 40.35 32.63 24.73

21.0 17.2 13.2 11.1 8.96 6.76

14.2 18.5 25.7 31.4 39.9 54.5

14.2 18.5 25.7 31.4 39.9 54.5

304 256 202 172 141 108

60.8 51.2 40.4 34.5 28.3 21.6

3.80 3.86 3.92 3.94 3.97 4.00

HSS9×9×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.581 0.465 0.349 0.291 0.233 0.174 0.116

67.82 55.66 42.79 36.10 29.23 22.18 14.96

18.7 15.3 11.8 9.92 8.03 6.06 4.09

12.5 16.4 22.8 27.9 35.6 48.7 74.6

12.5 16.4 22.8 27.9 35.6 48.7 74.6

216 183 145 124 102 78.2 53.5

47.9 40.6 32.2 27.6 22.7 17.4 11.9

HSS8×8×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.581 0.465 0.349 0.291 0.233 0.174 0.116

59.32 48.85 37.69 31.84 25.82 19.63 13.26

16.4 13.5 10.4 8.76 7.10 5.37 3.62

10.8 14.2 19.9 24.5 31.3 43.0 66.0

10.8 14.2 19.9 24.5 31.3 43.0 66.0

146 125 100 85.6 70.7 54.4 37.4

36.5 31.2 24.9 21.4 17.7 13.6 9.34

Workable Flat

Torsion

J

in.3 276 224 171 144

ft 2/ft 5.17 5.20 5.23 5.25

113/16 1430 113/4 1170 125/16 900 125/8 759

208 170 130 109

4.50 4.53 4.57 4.58

93/16 93/4 105/16 105/8 107/8 113/16

885 728 561 474 384 290

151 123 94.6 79.7 64.5 48.6

3.83 3.87 3.90 3.92 3.93 3.95

73.2 60.7 47.2 40.1 32.7 24.8

73/16 73/4 85/16 85/8 87/8 93/16

498 412 320 271 220 167

102 84.2 64.8 54.8 44.4 33.6

3.17 3.20 3.23 3.25 3.27 3.28

3.40 3.45 3.51 3.54 3.56 3.59 3.62

58.1 48.4 37.8 32.1 26.2 20.0 13.6

63/16 63/4 75/16 75/8 77/8 83/16 87/16

356 296 231 196 159 121 82.0

81.6 67.4 52.1 44.0 35.8 27.1 18.3

2.83 2.87 2.90 2.92 2.93 2.95 2.97

2.99 3.04 3.10 3.13 3.15 3.18 3.21

44.7 37.5 29.4 25.1 20.5 15.7 10.7

53/16 53/4 65/16 65/8 67/8 73/16 77/16

244 204 160 136 111 84.5 57.3

63.2 52.4 40.7 34.5 28.1 21.3 14.4

2.50 2.53 2.57 2.58 2.60 2.62 2.63

Note: For compactness criteria, refer to Table 1-12A.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in. 133/16 133/4 145/16 145/8

in.4 2170 1770 1350 1140

C

Surface Area

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DIMENSIONS AND PROPERTIES

1–93

Table 1-12 (continued)

Square HSS Dimensions and Properties

Shape

Design Wall Nom- Area, Thick- inal A ness, Wt. t

b/t

h/t

I

S

r

Z

HSS7-HSS41/2 Torsion

Workable Flat

J

C

Surface Area

HSS7×7×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

in. 0.581 0.465 0.349 0.291 0.233 0.174 0.116

lb/ft 50.81 42.05 32.58 27.59 22.42 17.08 11.56

in.2 14.0 11.6 8.97 7.59 6.17 4.67 3.16

9.05 12.1 17.1 21.1 27.0 37.2 57.3

9.05 12.1 17.1 21.1 27.0 37.2 57.3

in.4 93.4 80.5 65.0 56.1 46.5 36.0 24.8

in.3 26.7 23.0 18.6 16.0 13.3 10.3 7.09

in. 2.58 2.63 2.69 2.72 2.75 2.77 2.80

in.3 33.1 27.9 22.1 18.9 15.5 11.9 8.13

in. 43/16 43/4 55/16 55/8 57/8 63/16 67/16

in.4 158 133 105 89.7 73.5 56.1 38.2

in.3 47.1 39.3 30.7 26.1 21.3 16.2 11.0

ft 2/ft 2.17 2.20 2.23 2.25 2.27 2.28 2.30

HSS6×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.581 0.465 0.349 0.291 0.233 0.174 0.116

42.30 35.24 27.48 23.34 19.02 14.53 9.86

11.7 9.74 7.58 6.43 5.24 3.98 2.70

7.33 9.90 14.2 17.6 22.8 31.5 48.7

7.33 9.90 14.2 17.6 22.8 31.5 48.7

55.2 48.3 39.5 34.3 28.6 22.3 15.5

18.4 16.1 13.2 11.4 9.54 7.42 5.15

2.17 2.23 2.28 2.31 2.34 2.37 2.39

23.2 19.8 15.8 13.6 11.2 8.63 5.92

33/16 33/4 45/16 45/8 47/8 53/16 57/16

94.9 81.1 64.6 55.4 45.6 35.0 23.9

33.4 28.1 22.1 18.9 15.4 11.8 8.03

1.83 1.87 1.90 1.92 1.93 1.95 1.97

HSS51/2×51/2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.349 0.291 0.233 0.174 0.116

24.93 21.21 17.32 13.25 9.01

6.88 5.85 4.77 3.63 2.46

12.8 15.9 20.6 28.6 44.4

12.8 15.9 20.6 28.6 44.4

29.7 25.9 21.7 17.0 11.8

10.8 9.43 7.90 6.17 4.30

2.08 2.11 2.13 2.16 2.19

13.1 11.3 9.32 7.19 4.95

313/16 41/8 43/8 411/16 415/16

49.0 42.2 34.8 26.7 18.3

18.4 15.7 12.9 9.85 6.72

1.73 1.75 1.77 1.78 1.80

HSS5×5×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.465 0.349 0.291 0.233 0.174 0.116

28.43 22.37 19.08 15.62 11.97 8.16

7.88 6.18 5.26 4.30 3.28 2.23

7.75 11.3 14.2 18.5 25.7 40.1

7.75 11.3 14.2 18.5 25.7 40.1

26.0 10.4 21.7 8.68 19.0 7.62 16.0 6.41 12.6 5.03 8.80 3.52

1.82 1.87 1.90 1.93 1.96 1.99

13.1 10.6 9.16 7.61 5.89 4.07

23/4 35/16 35/8 37/8 43/16 47/16

44.6 36.1 31.2 25.8 19.9 13.7

18.7 14.9 12.8 10.5 8.08 5.53

1.53 1.57 1.58 1.60 1.62 1.63

HSS41/2×41/2×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.465 0.349 0.291 0.233 0.174 0.116

25.03 19.82 16.96 13.91 10.70 7.31

6.95 5.48 4.68 3.84 2.93 2.00

6.68 9.89 12.5 16.3 22.9 35.8

6.68 9.89 12.5 16.3 22.9 35.8

18.1 15.3 13.5 11.4 9.02 6.35

1.61 1.67 1.70 1.73 1.75 1.78

10.2 8.36 7.27 6.06 4.71 3.27

21/4 213/16 31/8 33/8 311/16 315/16

31.3 14.8 25.7 11.9 22.3 10.2 18.5 8.44 14.4 6.49 9.92 4.45

1.37 1.40 1.42 1.43 1.45 1.47

8.03 6.79 6.00 5.08 4.01 2.82

Note: For compactness criteria, refer to Table 1-12A.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-12 (continued)

Square HSS Dimensions and Properties HSS4-HSS2

Shape

Design Wall Nom- Area, Thick- inal A ness, Wt. t

I

S

r

Z

Workable Flat

Torsion

Surface Area

b/t

h/t

5.60 8.46 10.7 14.2 20.0 31.5

5.60 8.46 10.7 14.2 20.0 31.5

in.4 11.9 10.3 9.14 7.80 6.21 4.40

in.3 5.97 5.13 4.57 3.90 3.10 2.20

in. 1.41 1.47 1.49 1.52 1.55 1.58

in.3 7.70 6.39 5.59 4.69 3.67 2.56

in. — 25/16 25/8 27/8 33/16 37/16

HSS31/2×31/2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.349 14.72 4.09 7.03 7.03 0.291 12.70 3.52 9.03 9.03 0.233 10.51 2.91 12.0 12.0 0.174 8.15 2.24 17.1 17.1 0.116 5.61 1.54 27.2 27.2

6.49 5.84 5.04 4.05 2.90

3.71 3.34 2.88 2.31 1.66

1.26 1.29 1.32 1.35 1.37

4.69 4.14 3.50 2.76 1.93

— 11.2 21/8 9.89 23/8 8.35 211/16 6.56 215/16 4.58

6.77 5.90 4.92 3.83 2.65

1.07 1.08 1.10 1.12 1.13

HSS3×3×3/8 ×5/16 ×1/4 ×3/16 ×1/8

0.349 12.17 3.39 5.60 5.60 0.291 10.58 2.94 7.31 7.31 0.233 8.81 2.44 9.88 9.88 0.174 6.87 1.89 14.2 14.2 0.116 4.75 1.30 22.9 22.9

3.78 3.45 3.02 2.46 1.78

2.52 2.30 2.01 1.64 1.19

1.06 1.08 1.11 1.14 1.17

3.25 2.90 2.48 1.97 1.40

— — — 23/16 27/16

6.64 5.94 5.08 4.03 2.84

4.74 4.18 3.52 2.76 1.92

0.900 0.917 0.933 0.950 0.967

0.291 0.233 0.174 0.116

1.82 1.63 1.35 0.998

1.46 1.30 1.08 0.799

0.880 0.908 0.937 0.965

1.88 1.63 1.32 0.947

— — — —

3.20 2.79 2.25 1.61

2.74 2.35 1.86 1.31

0.750 0.767 0.784 0.800

HSS21/4×21/4×1/4 0.233 ×3/16 0.174 ×1/8 0.116

6.26 1.74 6.66 6.66 1.13 1.01 0.806 1.28 4.96 1.37 9.93 9.93 0.953 0.847 0.835 1.04 3.48 0.956 16.4 16.4 0.712 0.633 0.863 0.755

— — —

1.96 1.60 1.15

1.85 1.48 1.05

0.683 0.700 0.717

HSS2×2×1/4 0.233 ×3/16 0.174 ×1/8 0.116

5.41 1.51 5.58 5.58 0.747 0.747 0.704 0.964 4.32 1.19 8.49 8.49 0.641 0.641 0.733 0.797 3.05 0.840 14.2 14.2 0.486 0.486 0.761 0.584

— — —

1.31 1.41 0.600 1.09 1.14 0.617 0.796 0.817 0.633

HSS4×4×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

HSS21/2×21/2×5/16 ×1/4 ×3/16 ×1/8

in. 0.465 0.349 0.291 0.233 0.174 0.116

lb/ft 21.63 17.27 14.83 12.21 9.42 6.46

8.45 7.11 5.59 3.90

in.2 6.02 4.78 4.10 3.37 2.58 1.77

2.35 5.59 5.59 1.97 7.73 7.73 1.54 11.4 11.4 1.07 18.6 18.6

Note: For compactness criteria, refer to Table 1-12A. — Indicates flat depth or width is too small to establish a workable flat.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

J

C

in.4 in.3 21.0 11.2 17.5 9.14 15.3 7.91 12.8 6.56 10.0 5.07 6.91 3.49

ft 2/ft 1.20 1.23 1.25 1.27 1.28 1.30

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DIMENSIONS AND PROPERTIES

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Table 1-12A

Rectangular and Square HSS Compactness Criteria Compactness Criteria for Rectangular and Square HSS Nominal Wall Thickness, in.

5/8 1/2 3/8 5/16 1/4 3/16 1/8

Compression

Shear

Flexure

nonslender up to

compact up to

compact up to

Cv = 1.0 up to

Flange Width, in.

Flange Width, in.

Web Height, in.

Web Height, in.

20 16 12 10 8 6 4

18 14 10 9 7 5 31/2

20 20 20 18 14 10 7

20 20 20 18 14 10 7

Note: Compactness criteria given for Fy = 46 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-13

Round HSS Dimensions and Properties HSS20-HSS10

Shape

Design Wall Thickness, t

Nominal Wt.

Area, A

Torsion

D/t

I

S

r

Z J

C

HSS20×0.500 ×0.375f

in. 0.465 0.349

lb/ft in.2 104.00 28.5 78.67 21.5

43.0 57.3

in.4 1360 1040

in.3 136 104

in. 6.91 6.95

in.3 177 135

in.4 2720 2080

in.3 272 208

HSS18×0.500 ×0.375f

0.465 0.349

93.54 25.6 70.66 19.4

38.7 51.6

985 754

109 83.8

6.20 6.24

143 109

1970 1510

219 168

HSS16×0.625 ×0.500 ×0.438 ×0.375 ×0.312f ×0.250f

0.581 0.465 0.407 0.349 0.291 0.233

103.00 82.85 72.87 62.64 52.32 42.09

28.1 22.7 19.9 17.2 14.4 11.5

27.5 34.4 39.3 45.8 55.0 68.7

838 685 606 526 443 359

105 85.7 75.8 65.7 55.4 44.8

5.46 5.49 5.51 5.53 5.55 5.58

138 112 99.0 85.5 71.8 57.9

1680 1370 1210 1050 886 717

209 171 152 131 111 89.7

HSS14×0.625 ×0.500 ×0.375 ×0.312 ×0.250f

0.581 0.465 0.349 0.291 0.233

89.36 72.16 54.62 45.65 36.75

24.5 19.8 15.0 12.5 10.1

24.1 30.1 40.1 48.1 60.1

552 453 349 295 239

78.9 64.8 49.8 42.1 34.1

4.75 4.79 4.83 4.85 4.87

105 85.2 65.1 54.7 44.2

1100 907 698 589 478

158 130 100 84.2 68.2

HSS12.750×0.500 ×0.375 ×0.250f

0.465 0.349 0.233

65.48 17.9 49.61 13.6 33.41 9.16

27.4 36.5 54.7

339 262 180

53.2 41.0 28.2

4.35 4.39 4.43

70.2 53.7 36.5

678 523 359

106 82.1 56.3

HSS10.750×0.500 ×0.375 ×0.250

0.465 0.349 0.233

54.79 15.0 41.59 11.4 28.06 7.70

23.1 30.8 46.1

199 154 106

37.0 28.7 19.8

3.64 3.68 3.72

49.2 37.8 25.8

398 309 213

74.1 57.4 39.6

HSS10×0.625 ×0.500 ×0.375 ×0.312 ×0.250 ×0.188f

0.581 0.465 0.349 0.291 0.233 0.174

62.64 17.2 50.78 13.9 38.58 10.6 32.31 8.88 26.06 7.15 19.72 5.37

17.2 21.5 28.7 34.4 42.9 57.5

191 159 123 105 85.3 64.8

38.3 31.7 24.7 20.9 17.1 13.0

3.34 3.38 3.41 3.43 3.45 3.47

51.6 42.3 32.5 27.4 22.2 16.8

383 317 247 209 171 130

76.6 63.5 49.3 41.9 34.1 25.9

f

Shape exceeds compact limit for flexure with Fy = 42 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

1–97

Table 1-13 (continued)

Round HSS Dimensions and Properties

Shape

f

Design Wall Thickness, t

Nominal Wt.

HSS9.625HSS6.875 Torsion

Area, A

D/t

I

S

r

Z J

C

HSS9.625×0.500 ×0.375 ×0.312 ×0.250 ×0.188f

in. 0.465 0.349 0.291 0.233 0.174

lb/ft in.2 48.77 13.4 37.08 10.2 31.06 8.53 25.06 6.87 18.97 5.17

20.7 27.6 33.1 41.3 55.3

in.4 141 110 93.0 75.9 57.7

in.3 29.2 22.8 19.3 15.8 12.0

in. 3.24 3.28 3.30 3.32 3.34

in.3 39.0 30.0 25.4 20.6 15.5

in.4 281 219 186 152 115

in.3 58.5 45.5 38.7 31.5 24.0

HSS8.625×0.625 ×0.500 ×0.375 ×0.322 ×0.250 ×0.188f

0.581 0.465 0.349 0.300 0.233 0.174

53.45 14.7 43.43 11.9 33.07 9.07 28.58 7.85 22.38 6.14 16.96 4.62

14.8 18.5 24.7 28.8 37.0 49.6

119 100 77.8 68.1 54.1 41.3

27.7 23.1 18.0 15.8 12.5 9.57

2.85 2.89 2.93 2.95 2.97 2.99

37.7 31.0 23.9 20.8 16.4 12.4

239 199 156 136 108 82.5

55.4 46.2 36.1 31.6 25.1 19.1

HSS7.625×0.375 ×0.328

0.349 0.305

29.06 25.59

7.98 7.01

21.8 25.0

52.9 47.1

13.9 12.3

2.58 2.59

18.5 16.4

106 94.1

27.8 24.7

HSS7.500×0.500 ×0.375 ×0.312 ×0.250 ×0.188

0.465 0.349 0.291 0.233 0.174

37.42 10.3 28.56 7.84 23.97 6.59 19.38 5.32 14.70 4.00

16.1 21.5 25.8 32.2 43.1

63.9 50.2 42.9 35.2 26.9

17.0 13.4 11.4 9.37 7.17

2.49 2.53 2.55 2.57 2.59

23.0 17.9 15.1 12.3 9.34

128 100 85.8 70.3 53.8

34.1 26.8 22.9 18.7 14.3

HSS7×0.500 ×0.375 ×0.312 ×0.250 ×0.188 ×0.125f

0.465 0.349 0.291 0.233 0.174 0.116

34.74 26.56 22.31 18.04 13.69 9.19

9.55 7.29 6.13 4.95 3.73 2.51

15.1 20.1 24.1 30.0 40.2 60.3

51.2 40.4 34.6 28.4 21.7 14.9

14.6 11.6 9.88 8.11 6.21 4.25

2.32 2.35 2.37 2.39 2.41 2.43

19.9 15.5 13.1 10.7 8.11 5.50

102 80.9 69.1 56.8 43.5 29.7

29.3 23.1 19.8 16.2 12.4 8.49

HSS6.875×0.500 ×0.375 ×0.312 ×0.250 ×0.188

0.465 0.349 0.291 0.233 0.174

34.07 26.06 21.89 17.71 13.44

9.36 7.16 6.02 4.86 3.66

14.8 19.7 23.6 29.5 39.5

48.3 38.2 32.7 26.8 20.6

14.1 11.1 9.51 7.81 5.99

2.27 2.31 2.33 2.35 2.37

19.1 14.9 12.6 10.3 7.81

96.7 76.4 65.4 53.7 41.1

28.1 22.2 19.0 15.6 12.0

Shape exceeds compact limit for flexure with Fy = 42 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-13 (continued)

Round HSS Dimensions and Properties

HSS6.625HSS5 Design Wall Thickness, t

Nominal Wt.

Area, A

D/t

HSS6.625×0.500 ×0.432 ×0.375 ×0.312 ×0.280 ×0.250 ×0.188 ×0.125f

in. 0.465 0.402 0.349 0.291 0.260 0.233 0.174 0.116

lb/ft 32.74 28.60 25.06 21.06 18.99 17.04 12.94 8.69

in.2 9.00 7.86 6.88 5.79 5.20 4.68 3.53 2.37

14.2 16.5 19.0 22.8 25.5 28.4 38.1 57.1

in.4 42.9 38.2 34.0 29.1 26.4 23.9 18.4 12.6

in.3 13.0 11.5 10.3 8.79 7.96 7.22 5.54 3.79

in. 2.18 2.20 2.22 2.24 2.25 2.26 2.28 2.30

HSS6×0.500 ×0.375 ×0.312 ×0.280 ×0.250 ×0.188 ×0.125f

0.465 0.349 0.291 0.260 0.233 0.174 0.116

29.40 22.55 18.97 17.12 15.37 11.68 7.85

8.09 6.20 5.22 4.69 4.22 3.18 2.14

12.9 17.2 20.6 23.1 25.8 34.5 51.7

31.2 24.8 21.3 19.3 17.6 13.5 9.28

10.4 8.28 7.11 6.45 5.86 4.51 3.09

HSS5.563×0.500 ×0.375 ×0.258 ×0.188 ×0.134

0.465 0.349 0.240 0.174 0.124

27.06 20.80 14.63 10.80 7.78

7.45 5.72 4.01 2.95 2.12

12.0 15.9 23.2 32.0 44.9

24.4 19.5 14.2 10.7 7.84

HSS5.500×0.500 ×0.375 ×0.258

0.465 0.349 0.240

26.73 20.55 14.46

7.36 5.65 3.97

11.8 15.8 22.9

HSS5×0.500 ×0.375 ×0.312 ×0.258 ×0.250 ×0.188 ×0.125

0.465 0.349 0.291 0.240 0.233 0.174 0.116

24.05 18.54 15.64 13.08 12.69 9.67 6.51

6.62 5.10 4.30 3.59 3.49 2.64 1.78

10.8 14.3 17.2 20.8 21.5 28.7 43.1

Shape

f

Torsion

I

S

r

Z J

C

in.3 17.7 15.6 13.8 11.7 10.5 9.52 7.24 4.92

in.4 85.9 76.4 68.0 58.2 52.7 47.9 36.7 25.1

in.3 25.9 23.1 20.5 17.6 15.9 14.4 11.1 7.59

1.96 2.00 2.02 2.03 2.04 2.06 2.08

14.3 11.2 9.49 8.57 7.75 5.91 4.02

62.4 49.7 42.6 38.7 35.2 27.0 18.6

20.8 16.6 14.2 12.9 11.7 9.02 6.19

8.77 7.02 5.12 3.85 2.82

1.81 1.85 1.88 1.91 1.92

12.1 9.50 6.80 5.05 3.67

48.8 39.0 28.5 21.4 15.7

17.5 14.0 10.2 7.70 5.64

23.5 18.8 13.7

8.55 6.84 5.00

1.79 1.83 1.86

11.8 9.27 6.64

47.0 37.6 27.5

17.1 13.7 10.0

17.2 13.9 12.0 10.2 9.94 7.69 5.31

6.88 5.55 4.79 4.08 3.97 3.08 2.12

1.61 1.65 1.67 1.69 1.69 1.71 1.73

9.60 7.56 6.46 5.44 5.30 4.05 2.77

34.4 27.7 24.0 20.4 19.9 15.4 10.6

13.8 11.1 9.58 8.15 7.95 6.15 4.25

Shape exceeds compact limit for flexure with Fy = 42 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

1–99

Table 1-13 (continued)

Round HSS Dimensions and Properties

HSS4.500HSS2.500

Design Wall Thickness, t

Nominal Wt.

Area, A

D/t

HSS4.500×0.375 ×0.337 ×0.237 ×0.188 ×0.125

in. 0.349 0.313 0.220 0.174 0.116

lb/ft 16.54 15.00 10.80 8.67 5.85

in.2 4.55 4.12 2.96 2.36 1.60

12.9 14.4 20.5 25.9 38.8

in.4 9.87 9.07 6.79 5.54 3.84

in.3 4.39 4.03 3.02 2.46 1.71

in. 1.47 1.48 1.52 1.53 1.55

in.3 6.03 5.50 4.03 3.26 2.23

in.4 19.7 18.1 13.6 11.1 7.68

in.3 8.78 8.06 6.04 4.93 3.41

HSS4×0.313 ×0.250 ×0.237 ×0.226 ×0.220 ×0.188 ×0.125

0.291 0.233 0.220 0.210 0.205 0.174 0.116

12.34 10.00 9.53 9.12 8.89 7.66 5.18

3.39 2.76 2.61 2.50 2.44 2.09 1.42

13.7 17.2 18.2 19.0 19.5 23.0 34.5

5.87 4.91 4.68 4.50 4.41 3.83 2.67

2.93 2.45 2.34 2.25 2.21 1.92 1.34

1.32 1.33 1.34 1.34 1.34 1.35 1.37

4.01 3.31 3.15 3.02 2.96 2.55 1.75

11.7 9.82 9.36 9.01 8.83 7.67 5.34

5.87 4.91 4.68 4.50 4.41 3.83 2.67

HSS3.500×0.313 ×0.300 ×0.250 ×0.216 ×0.203 ×0.188 ×0.125

0.291 0.279 0.233 0.201 0.189 0.174 0.116

10.66 10.26 8.69 7.58 7.15 6.66 4.51

2.93 2.82 2.39 2.08 1.97 1.82 1.23

12.0 12.5 15.0 17.4 18.5 20.1 30.2

3.81 3.69 3.21 2.84 2.70 2.52 1.77

2.18 2.11 1.83 1.63 1.54 1.44 1.01

1.14 1.14 1.16 1.17 1.17 1.18 1.20

3.00 2.90 2.49 2.19 2.07 1.93 1.33

7.61 7.38 6.41 5.69 5.41 5.04 3.53

4.35 4.22 3.66 3.25 3.09 2.88 2.02

HSS3×0.250 ×0.216 ×0.203 ×0.188 ×0.152 ×0.134 ×0.125

0.233 0.201 0.189 0.174 0.141 0.124 0.116

7.35 6.43 6.07 5.65 4.63 4.11 3.84

2.03 1.77 1.67 1.54 1.27 1.12 1.05

12.9 14.9 15.9 17.2 21.3 24.2 25.9

1.95 1.74 1.66 1.55 1.30 1.16 1.09

1.30 1.16 1.10 1.03 0.865 0.774 0.730

0.982 0.992 0.996 1.00 1.01 1.02 1.02

1.79 1.58 1.50 1.39 1.15 1.03 0.965

3.90 3.48 3.31 3.10 2.59 2.32 2.19

2.60 2.32 2.21 2.06 1.73 1.55 1.46

HSS2.875×0.250 ×0.203 ×0.188 ×0.125

0.233 0.189 0.174 0.116

7.02 5.80 5.40 3.67

1.93 1.59 1.48 1.01

12.3 15.2 16.5 24.8

1.70 1.45 1.35 0.958

1.18 1.01 0.941 0.667

0.938 0.952 0.957 0.976

1.63 1.37 1.27 0.884

3.40 2.89 2.70 1.92

2.37 2.01 1.88 1.33

HSS2.500×0.250 ×0.188 ×0.125

0.233 0.174 0.116

6.01 4.65 3.17

1.66 1.27 0.869

10.7 14.4 21.6

1.08 0.865 0.619

0.862 0.692 0.495

0.806 0.825 0.844

1.20 0.943 0.660

2.15 1.73 1.24

1.72 1.38 0.990

Shape

Torsion

I

S

r

Z J

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

C

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1–100

DIMENSIONS AND PROPERTIES

Table 1-13 (continued)

Round HSS Dimensions and Properties

HSS2.375HSS1.660 Design Wall Thickness, t

Nominal Wt.

Area, A

D/t

HSS2.375×0.250 ×0.218 ×0.188 ×0.154 ×0.125

in. 0.233 0.203 0.174 0.143 0.116

lb/ft 5.68 5.03 4.40 3.66 3.01

in.2 1.57 1.39 1.20 1.00 0.823

10.2 11.7 13.6 16.6 20.5

in.4 0.910 0.824 0.733 0.627 0.527

in.3 0.766 0.694 0.617 0.528 0.443

in. 0.762 0.771 0.781 0.791 0.800

in.3 1.07 0.960 0.845 0.713 0.592

HSS1.900×0.188 ×0.145 ×0.120

0.174 0.135 0.111

3.44 2.72 2.28

0.943 0.749 0.624

10.9 14.1 17.1

0.355 0.293 0.251

0.374 0.309 0.264

0.613 0.626 0.634

0.520 0.421 0.356

0.710 0.586 0.501

0.747 0.617 0.527

HSS1.660×0.140

0.130

2.27

0.625

12.8

0.184

0.222

0.543

0.305

0.368

0.444

Shape

Torsion

I

S

r

Z J

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.4 1.82 1.65 1.47 1.25 1.05

C in.3 1.53 1.39 1.23 1.06 0.887

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DIMENSIONS AND PROPERTIES

1–101

Table 1-14

Pipe Dimensions and Properties PIPE

Shape

Nom- Dimensions Nominal Design Wall Wall inal Outside Inside Area DiaDia- Thick- ThickWt. meter meter ness ness lb/ft in. in. in. in. in.2

D/t

I

S

r

J

Z

in.4

in.3

in.

in.4

in.3

Standard Weight (Std.) Pipe 12 Std. Pipe 10 Std. Pipe 8 Std. Pipe 6 Std. Pipe 5 Std. Pipe 4 Std. Pipe 31/ 2 Std. Pipe 3 Std. Pipe 21/ 2 Std. Pipe 2 Std. Pipe 11/ 2 Std. Pipe 11/4 Std. Pipe 1 Std. Pipe 3/4 Std. Pipe 1/ 2 Std.

49.6 12.8 40.5 10.8 28.6 8.63 19.0 6.63 14.6 5.56 10.8 4.50 9.12 4.00 7.58 3.50 5.80 2.88 3.66 2.38 2.72 1.90 2.27 1.66 1.68 1.32 1.13 1.05 0.850 0.840

12.0 10.0 7.98 6.07 5.05 4.03 3.55 3.07 2.47 2.07 1.61 1.38 1.05 0.824 0.622

0.375 0.365 0.322 0.280 0.258 0.237 0.226 0.216 0.203 0.154 0.145 0.140 0.133 0.113 0.109

0.349 13.7 0.340 11.5 0.300 7.85 0.261 5.20 0.241 4.01 0.221 2.96 0.211 2.50 0.201 2.07 0.189 1.61 0.143 1.02 0.135 0.749 0.130 0.625 0.124 0.469 0.105 0.312 0.101 0.234

36.5 31.6 28.8 25.4 23.1 20.4 19.0 17.4 15.2 16.6 14.1 12.8 10.6 10.0 8.32

262 41.0 151 28.1 68.1 15.8 26.5 7.99 14.3 5.14 6.82 3.03 4.52 2.26 2.85 1.63 1.45 1.01 0.627 0.528 0.293 0.309 0.184 0.222 0.0830 0.126 0.0350 0.0671 0.0160 0.0388

4.39 523 3.68 302 2.95 136 2.25 52.9 1.88 28.6 1.51 13.6 1.34 9.04 1.17 5.69 0.952 2.89 0.791 1.25 0.626 0.586 0.543 0.368 0.423 0.166 0.336 0.0700 0.264 0.0320

53.7 36.9 20.8 10.6 6.83 4.05 3.03 2.19 1.37 0.713 0.421 0.305 0.177 0.0942 0.0555

339 199 100 38.3 19.5 9.12 5.94 3.70 1.83 0.827 0.372 0.231 0.101 0.0430 0.0190

53.2 37.0 23.1 11.6 7.02 4.05 2.97 2.11 1.27 0.696 0.392 0.278 0.154 0.0818 0.0462

4.35 678 3.64 398 2.89 199 2.20 76.6 1.85 39.0 1.48 18.2 1.31 11.9 1.14 7.40 0.930 3.66 0.771 1.65 0.610 0.744 0.528 0.462 0.410 0.202 0.325 0.0860 0.253 0.0380

70.2 49.2 31.0 15.6 9.50 5.53 4.07 2.91 1.77 0.964 0.549 0.393 0.221 0.119 0.0686

35.8 19.2 11.6 6.53 3.31 1.94 1.07

2.78 308 2.08 127 1.74 64.4 1.39 29.4 1.06 11.6 0.854 5.56 0.711 2.54

49.9 27.4 16.7 9.50 4.89 2.91 1.60

Extra Strong (x-Strong) Pipe 12 x-Strong Pipe 10 x-Strong Pipe 8 x-Strong Pipe 6 x-Strong Pipe 5 x-Strong Pipe 4 x-Strong Pipe 31/ 2 x-Strong Pipe 3 x-Strong Pipe 21/ 2 x-Strong Pipe 2 x-Strong Pipe 11/ 2 x-Strong Pipe 11/4 x-Strong Pipe 1 x-Strong Pipe 3/4 x-Strong Pipe 1/ 2 x-Strong

65.5 54.8 43.4 28.6 20.8 15.0 12.5 10.3 7.67 5.03 3.63 3.00 2.17 1.48 1.09

12.8 10.8 8.63 6.63 5.56 4.50 4.00 3.50 2.88 2.38 1.90 1.66 1.32 1.05 0.840

11.8 9.75 7.63 5.76 4.81 3.83 3.36 2.90 2.32 1.94 1.50 1.28 0.957 0.742 0.546

Pipe 8 xx-Strong Pipe 6 xx-Strong Pipe 5 xx-Strong Pipe 4 xx-Strong Pipe 3 xx-Strong Pipe 21/ 2 xx-Strong Pipe 2 xx-Strong

72.5 53.2 38.6 27.6 18.6 13.7 9.04

8.63 6.63 5.56 4.50 3.50 2.88 2.38

6.88 4.90 4.06 3.15 2.30 1.77 1.50

0.500 0.500 0.500 0.432 0.375 0.337 0.318 0.300 0.276 0.218 0.200 0.191 0.179 0.154 0.147

0.465 17.5 0.465 15.1 0.465 11.9 0.403 7.83 0.349 5.73 0.315 4.14 0.296 3.43 0.280 2.83 0.257 2.10 0.204 1.40 0.186 1.00 0.178 0.837 0.166 0.602 0.143 0.407 0.137 0.303

27.4 23.1 18.5 16.4 15.9 14.3 13.5 12.5 11.2 11.7 10.2 9.33 7.92 7.34 6.13

Double-Extra Strong (xx-Strong) 0.875 0.864 0.750 0.674 0.600 0.552 0.436

0.816 20.0 0.805 14.7 0.699 10.7 0.628 7.66 0.559 5.17 0.514 3.83 0.406 2.51

10.6 8.23 7.96 7.17 6.26 5.59 5.85

154 63.5 32.2 14.7 5.79 2.78 1.27

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-15

Double Angles Properties SLBB LLBB

Shape

Area

LLBB Separation, s, in.

SLBB Qs

LLBB Qs

Axis Y-Y Radius of Gyration SLBB Separation, s, in.

Angles Angles in SepaContact rated

rx

Angles Angles in SepaContact rated

rx

in.2

0

3/8

3/4

0

3/8

3/4

2L8×8×11/8 ×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2

33.6 30.2 26.6 23.0 19.4 17.5 15.7

3.41 3.39 3.36 3.34 3.32 3.31 3.30

3.54 3.52 3.50 3.47 3.45 3.44 3.43

3.68 3.66 3.63 3.61 3.58 3.57 3.56

3.41 3.39 3.36 3.34 3.32 3.31 3.30

3.54 3.52 3.50 3.47 3.45 3.44 3.43

3.68 3.66 3.63 3.61 3.58 3.57 3.56

1.00 1.00 1.00 1.00 1.00 1.00 0.998

1.00 1.00 1.00 1.00 0.997 0.959 0.912

2.41 2.43 2.45 2.46 2.48 2.49 2.49

1.00 1.00 1.00 1.00 1.00 1.00 0.998

1.00 1.00 1.00 1.00 0.997 0.959 0.912

2.41 2.43 2.45 2.46 2.48 2.49 2.49

2L8×6×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16

26.2 23.0 20.0 16.8 15.2 13.6 12.0

2.39 2.37 2.35 2.33 2.32 2.31 2.30

2.52 2.50 2.47 2.45 2.44 2.43 2.42

2.66 2.63 2.61 2.59 2.58 2.56 2.55

3.63 3.61 3.59 3.57 3.55 3.54 3.53

3.77 3.75 3.72 3.70 3.69 3.68 3.66

3.91 3.89 3.86 3.84 3.83 3.81 3.80

1.00 1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 0.997 0.959 0.912 0.850

2.49 2.50 2.52 2.54 2.55 2.55 2.56

1.00 1.00 1.00 1.00 1.00 0.998 0.938

1.00 1.00 1.00 0.997 0.959 0.912 0.850

1.72 1.74 1.75 1.77 1.78 1.79 1.80

2L8×4×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16

22.2 19.6 17.0 14.3 13.0 11.6 10.2

1.46 1.44 1.42 1.39 1.38 1.38 1.37

1.60 1.57 1.55 1.52 1.51 1.50 1.49

1.75 1.72 1.69 1.66 1.65 1.63 1.62

3.94 3.91 3.89 3.86 3.85 3.83 3.82

4.08 4.06 4.03 4.00 3.99 3.97 3.96

4.23 4.21 4.18 4.15 4.13 4.12 4.10

1.00 1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 0.997 0.959 0.912 0.850

2.51 2.53 2.55 2.56 2.57 2.58 2.59

1.00 1.00 1.00 1.00 1.00 0.998 0.938

1.00 1.00 1.00 0.997 0.959 0.912 0.850

1.03 1.04 1.05 1.06 1.07 1.08 1.09

2L7×4×3/4 ×5/8 ×1/2 ×7/16 ×3/8

15.5 13.0 10.5 9.26 8.00

1.48 1.45 1.44 1.43 1.42

1.61 1.58 1.56 1.55 1.54

1.75 1.73 1.70 1.68 1.67

3.34 3.31 3.29 3.28 3.26

3.48 3.46 3.43 3.42 3.40

3.63 3.60 3.57 3.56 3.54

1.00 1.00 1.00 1.00 1.00

1.00 1.00 0.965 0.912 0.840

2.21 2.23 2.25 2.26 2.27

1.00 1.00 1.00 0.998 0.928

1.00 1.00 0.965 0.912 0.840

1.08 1.10 1.11 1.12 1.12

2L6×6×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16 ×3/8 ×5/16

22.0 19.5 16.9 14.3 12.9 11.5 10.2 8.76 7.34

2.58 2.56 2.54 2.52 2.51 2.50 2.49 2.48 2.47

2.72 2.70 2.67 2.65 2.64 2.63 2.62 2.60 2.59

2.86 2.84 2.81 2.79 2.78 2.76 2.75 2.74 2.72

2.58 2.56 2.54 2.52 2.51 2.50 2.49 2.48 2.47

2.72 2.70 2.67 2.65 2.64 2.63 2.62 2.60 2.59

2.86 2.84 2.81 2.79 2.78 2.76 2.75 2.74 2.72

1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.998 0.914

1.00 1.00 1.00 1.00 1.00 1.00 0.973 0.912 0.826

1.79 1.81 1.82 1.84 1.85 1.86 1.86 1.87 1.88

1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.998 0.914

1.00 1.00 1.00 1.00 1.00 1.00 0.973 0.912 0.826

1.79 1.81 1.82 1.84 1.85 1.86 1.86 1.87 1.88

Note: For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

in.

AISC_PART 01B:14th Ed._

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Page 103

DIMENSIONS AND PROPERTIES

1–103

Table 1-15 (continued)

Double Angles Properties

2L8-2L6

Flexural-Torsional Properties Long Legs Vertical Short Legs Vertical Back to Back of Angles, in. Back to Back of Angles, in.

Shape

3/8

0

3/4

3/8

0

Single Angle Properties

Area, A

3/4

rz

r–o

H

r–o

H

r–o

H

r–o

H

r–o

H

r–o

H

in.2

in.

2L8×8×11/8 ×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2

4.56 4.56 4.56 4.56 4.56 4.56 4.56

0.837 0.834 0.831 0.829 0.826 0.825 0.824

4.66 4.66 4.66 4.66 4.66 4.65 4.65

0.844 0.841 0.838 0.836 0.833 0.832 0.831

4.77 4.77 4.76 4.76 4.76 4.75 4.75

0.851 0.848 0.845 0.843 0.840 0.839 0.837

4.56 4.56 4.56 4.56 4.56 4.56 4.56

0.837 0.834 0.831 0.829 0.826 0.825 0.824

4.66 4.66 4.66 4.66 4.66 4.65 4.65

0.844 0.841 0.838 0.836 0.833 0.832 0.831

4.77 4.77 4.76 4.76 4.76 4.75 4.75

0.851 0.848 0.845 0.843 0.840 0.839 0.837

16.8 15.1 13.3 11.5 9.69 8.77 7.84

1.56 1.56 1.57 1.57 1.58 1.58 1.59

2L8×6×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16

4.06 4.07 4.07 4.08 4.09 4.09 4.09

0.721 0.718 0.714 0.712 0.710 0.709 0.708

4.14 4.14 4.15 4.16 4.16 4.16 4.16

0.732 0.728 0.725 0.722 0.720 0.719 0.718

4.23 4.23 4.23 4.24 4.24 4.24 4.24

0.742 0.739 0.735 0.732 0.731 0.729 0.728

4.18 4.17 4.17 4.16 4.15 4.15 4.15

0.924 0.922 0.919 0.917 0.916 0.915 0.913

4.30 4.29 4.28 4.27 4.27 4.26 4.26

0.929 0.926 0.924 0.921 0.920 0.919 0.918

4.43 4.42 4.40 4.39 4.39 4.38 4.38

0.933 0.930 0.928 0.926 0.924 0.923 0.922

13.1 11.5 9.99 8.41 7.61 6.80 5.99

1.28 1.28 1.29 1.29 1.30 1.30 1.31

2L8×4×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16

3.86 3.87 3.88 3.89 3.90 3.90 3.91

0.568 0.566 0.564 0.562 0.562 0.561 0.561

3.91 3.92 3.93 3.94 3.94 3.95 3.95

0.580 0.577 0.575 0.573 0.572 0.571 0.571

3.97 3.98 3.99 3.99 4.00 4.00 4.00

0.594 0.590 0.587 0.585 0.584 0.583 0.582

4.11 4.09 4.07 4.05 4.04 4.03 4.02

0.983 0.981 0.980 0.979 0.978 0.978 0.977

4.25 4.22 4.20 4.18 4.17 4.16 4.15

0.984 0.982 0.981 0.980 0.980 0.979 0.978

4.39 4.37 4.35 4.32 4.31 4.30 4.29

0.985 0.984 0.983 0.981 0.981 0.980 0.980

11.1 9.79 8.49 7.16 6.49 5.80 5.11

0.844 0.846 0.850 0.856 0.859 0.863 0.867

2L7×4×3/4 ×5/8 ×1/2 ×7/16 ×3/8

3.41 3.42 3.43 3.43 3.44

0.611 0.608 0.606 0.605 0.605

3.47 3.47 3.48 3.49 3.49

0.624 0.621 0.618 0.617 0.616

3.53 3.54 3.55 3.55 3.55

0.639 0.635 0.632 0.630 0.629

3.57 3.55 3.53 3.53 3.52

0.969 0.967 0.965 0.964 0.963

3.70 3.68 3.66 3.66 3.65

0.971 0.969 0.968 0.967 0.966

3.84 3.82 3.80 3.79 3.78

0.973 0.971 0.970 0.969 0.968

7.74 6.50 5.26 4.63 4.00

0.855 0.860 0.866 0.869 0.873

2L6×6×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16 ×3/8 ×5/16

3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42

0.843 0.839 0.835 0.831 0.829 0.827 0.826 0.824 0.823

3.53 3.53 3.52 3.52 3.52 3.52 3.52 3.51 3.51

0.852 0.848 0.844 0.840 0.838 0.836 0.835 0.833 0.832

3.64 3.63 3.63 3.62 3.62 3.62 3.62 3.61 3.61

0.861 0.857 0.853 0.849 0.847 0.846 0.844 0.842 0.841

3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42

0.843 0.839 0.835 0.831 0.829 0.827 0.826 0.824 0.823

3.53 3.53 3.52 3.52 3.52 3.52 3.52 3.51 3.51

0.852 0.848 0.844 0.840 0.838 0.836 0.835 0.833 0.832

3.64 3.63 3.63 3.62 3.62 3.62 3.62 3.61 3.61

0.861 0.857 0.853 0.849 0.847 0.846 0.844 0.842 0.841

11.0 9.75 8.46 7.13 6.45 5.77 5.08 4.38 3.67

1.17 1.17 1.17 1.17 1.18 1.18 1.18 1.19 1.19

Note: For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01B:14th Ed._

1/20/11

7:34 AM

Page 104

1–104

DIMENSIONS AND PROPERTIES

Table 1-15 (continued)

Double Angles Properties SLBB LLBB

Shape

Area

LLBB Separation, s, in.

SLBB Qs

LLBB Qs

Axis Y-Y Radius of Gyration SLBB Separation, s, in.

Angles Angles in SepaContact rated

rx

Angles Angles in SepaContact rated

rx

in.2

0

3/8

3/4

0

3/8

3/4

2L6×4×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16 ×3/8 ×5/16

16.0 13.9 11.7 10.6 9.50 8.36 7.22 6.06

1.57 1.55 1.53 1.52 1.51 1.50 1.49 1.48

1.71 1.68 1.66 1.65 1.64 1.62 1.61 1.60

1.86 1.83 1.80 1.79 1.77 1.76 1.75 1.74

2.82 2.80 2.77 2.76 2.75 2.74 2.73 2.72

2.96 2.94 2.91 2.90 2.89 2.88 2.86 2.85

3.11 3.08 3.06 3.04 3.03 3.02 3.00 2.99

2L6×31/2×1/2 ×3/8 ×5/16

9.00 6.88 5.78

1.27 1.26 1.25

1.40 1.38 1.37

1.54 1.52 1.50

2.82 2.80 2.78

2.96 2.94 2.92

3.11 1.00 3.08 1.00 3.06 1.00

1.00 1.92 0.912 1.93 0.826 1.94

1.00 1.00 0.968 0.998 0.912 0.984 0.914 0.826 0.991

2L5×5×7/8 ×3/4 ×5/8 ×1/2 ×7/16 ×3/8 ×5/16

16.0 14.0 11.8 9.58 8.44 7.30 6.14

2.16 2.13 2.11 2.09 2.08 2.07 2.06

2.30 2.27 2.25 2.22 2.21 2.20 2.19

2.44 2.41 2.39 2.36 2.35 2.34 2.32

2.16 2.13 2.11 2.09 2.08 2.07 2.06

2.30 2.27 2.25 2.22 2.21 2.20 2.19

2.44 2.41 2.39 2.36 2.35 2.34 2.32

1.00 1.00 1.00 1.00 1.00 1.00 0.998

1.00 1.00 1.00 1.00 1.00 0.983 0.912

1.49 1.50 1.52 1.53 1.54 1.55 1.56

1.00 1.00 1.00 1.00 1.00 1.00 0.998

1.00 1.00 1.00 1.00 1.00 0.983 0.912

1.49 1.50 1.52 1.53 1.54 1.55 1.56

2L5×31/2×3/4 ×5/8 ×1/2 ×3/8 ×5/16 ×1/4

11.7 9.86 8.00 6.10 5.12 4.14

1.39 1.37 1.35 1.33 1.32 1.31

1.53 1.50 1.48 1.46 1.44 1.43

1.68 1.65 1.62 1.59 1.58 1.57

2.33 2.30 2.28 2.26 2.25 2.23

2.47 2.45 2.42 2.39 2.38 2.37

2.62 2.59 2.57 2.54 2.52 2.51

1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 0.983 0.912 0.804

1.55 1.56 1.58 1.59 1.60 1.61

1.00 1.00 1.00 1.00 0.998 0.894

1.00 1.00 1.00 0.983 0.912 0.804

0.974 0.987 1.00 1.02 1.02 1.03

2L5×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4

7.50 6.62 5.72 4.82 3.88

1.11 1.10 1.09 1.08 1.07

1.24 1.23 1.22 1.21 1.19

1.39 1.38 1.36 1.35 1.33

2.35 2.34 2.33 2.32 2.30

2.50 2.48 2.47 2.46 2.44

2.64 2.63 2.62 2.60 2.58

1.00 1.00 1.00 1.00 1.00

1.00 1.00 0.983 0.912 0.804

1.58 1.59 1.60 1.61 1.62

1.00 1.00 1.00 0.998 0.894

1.00 1.00 0.983 0.912 0.804

0.824 0.831 0.838 0.846 0.853

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 1.00 0.973 0.912 0.826

Note: For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in. 1.86 1.88 1.89 1.90 1.91 1.92 1.93 1.94

1.00 1.00 1.00 1.00 1.00 1.00 0.998 0.914

1.00 1.00 1.00 1.00 1.00 0.973 0.912 0.826

in. 1.10 1.12 1.13 1.14 1.14 1.15 1.16 1.17

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DIMENSIONS AND PROPERTIES

1–105

Table 1-15 (continued)

Double Angles Properties Flexural-Torsional Properties Long Legs Vertical Short Legs Vertical Back to Back of Angles, in. Back to Back of Angles, in.

Shape

3/8

0 2L6×4×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16 ×3/8 ×5/16

2L6-2L5

3/4

3/8

0

Single Angle Properties

Area, A

3/4

rz

r–o

H

r–o

H

r–o

H

r–o

H

r–o

H

r–o

H

in.2

in.

2.96 2.97 2.98 2.98 2.99 2.99 2.99 3.00

0.678 0.673 0.669 0.667 0.665 0.663 0.662 0.661

3.04 3.04 3.05 3.05 3.05 3.06 3.06 3.06

0.694 0.688 0.684 0.682 0.679 0.678 0.676 0.674

3.12 3.12 3.13 3.13 3.13 3.13 3.13 3.13

0.710 0.705 0.700 0.697 0.695 0.693 0.691 0.689

3.10 3.09 3.08 3.07 3.07 3.06 3.06 3.05

0.952 0.949 0.946 0.945 0.943 0.942 0.940 0.939

3.23 3.22 3.21 3.20 3.19 3.19 3.18 3.17

0.956 0.953 0.950 0.949 0.948 0.946 0.945 0.944

3.37 3.35 3.34 3.33 3.32 3.31 3.31 3.30

0.959 0.957 0.954 0.953 0.952 0.950 0.949 0.948

8.00 6.94 5.86 5.31 4.75 4.18 3.61 3.03

0.854 0.856 0.859 0.861 0.864 0.867 0.870 0.874

2L6x31/2×1/2 2.94 0.615 2.99 0.630 3.06 0.646 3.04 0.964 3.17 0.967 3.31 0.969 4.50 0.756 ×3/8 2.95 0.613 3.00 0.627 3.07 0.642 3.02 0.962 3.15 0.965 3.29 0.967 3.44 0.763 ×5/16 2.95 0.612 3.00 0.625 3.07 0.641 3.02 0.960 3.14 0.964 3.28 0.966 2.89 0.767 2L5×5×7/8 ×3/4 ×5/8 ×1/2 ×7/16 ×3/8 ×5/16

2.85 2.85 2.85 2.85 2.85 2.84 2.84

0.845 0.840 0.835 0.830 0.828 0.826 0.825

2.96 2.95 2.95 2.94 2.94 2.94 2.94

0.856 0.851 0.846 0.842 0.839 0.838 0.836

3.07 3.06 3.06 3.05 3.05 3.04 3.04

0.866 0.861 0.857 0.852 0.850 0.848 0.847

2.85 2.85 2.85 2.85 2.85 2.84 2.84

0.845 0.840 0.835 0.830 0.828 0.826 0.825

2.96 2.95 2.95 2.94 2.94 2.94 2.94

0.856 0.851 0.846 0.842 0.839 0.838 0.836

3.07 3.06 3.06 3.05 3.05 3.04 3.04

0.866 0.861 0.857 0.852 0.850 0.848 0.847

8.00 6.98 5.90 4.79 4.22 3.65 3.07

0.971 0.972 0.975 0.980 0.983 0.986 0.990

2L5x31/2×3/4 ×5/8 ×1/2 ×3/8 ×5/16 ×1/4

2.49 2.49 2.50 2.51 2.51 2.52

0.699 0.693 0.688 0.683 0.682 0.680

2.57 2.57 2.58 2.58 2.58 2.58

0.717 0.711 0.705 0.700 0.698 0.696

2.66 2.66 2.66 2.66 2.66 2.66

0.736 0.730 0.724 0.718 0.716 0.714

2.60 2.59 2.58 2.56 2.56 2.55

0.943 0.940 0.936 0.933 0.931 0.929

2.73 2.71 2.70 2.69 2.68 2.67

0.949 0.945 0.942 0.938 0.937 0.935

2.86 2.85 2.83 2.81 2.81 2.80

0.953 0.950 0.947 0.944 0.942 0.941

5.85 4.93 4.00 3.05 2.56 2.07

0.744 0.746 0.750 0.755 0.758 0.761

2L5×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4

2.44 2.45 2.45 2.46 2.46

0.628 0.626 0.624 0.623 0.622

2.51 2.51 2.51 2.52 2.52

0.646 0.644 0.642 0.640 0.638

2.58 2.58 2.59 2.59 2.59

0.667 0.664 0.661 0.659 0.657

2.54 2.54 2.53 2.52 2.51

0.962 0.961 0.959 0.958 0.957

2.68 2.67 2.66 2.65 2.64

0.966 0.964 0.963 0.962 0.961

2.81 2.80 2.79 2.78 2.77

0.969 0.968 0.967 0.965 0.964

3.75 3.31 2.86 2.41 1.94

0.642 0.644 0.646 0.649 0.652

Note: For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 106

1–106

DIMENSIONS AND PROPERTIES

Table 1-15 (continued)

Double Angles Properties SLBB LLBB

Shape

Area

LLBB Separation, s, in.

SLBB Qs

LLBB Qs

Axis Y-Y Radius of Gyration SLBB Separation, s, in.

Angles Angles in SepaContact rated

rx

Angles Angles in SepaContact rated

rx

in.2

0

3/8

3/4

0

3/8

3/4

2L4×4×3/4 ×5/8 ×1/2 ×7/16 ×3/8 ×5/16 ×1/4

10.9 9.22 7.50 6.60 5.72 4.80 3.86

1.73 1.71 1.69 1.68 1.67 1.66 1.65

1.88 1.85 1.83 1.81 1.80 1.79 1.78

2.03 2.00 1.97 1.96 1.94 1.93 1.91

1.73 1.71 1.69 1.68 1.67 1.66 1.65

1.88 1.85 1.83 1.81 1.80 1.79 1.78

2.03 2.00 1.97 1.96 1.94 1.93 1.91

1.00 1.00 1.00 1.00 1.00 1.00 0.998

1.00 1.00 1.00 1.00 1.00 0.997 0.912

1.18 1.20 1.21 1.22 1.23 1.24 1.25

1.00 1.00 1.00 1.00 1.00 1.00 0.998

1.00 1.00 1.00 1.00 1.00 0.997 0.912

1.18 1.20 1.21 1.22 1.23 1.24 1.25

2L4×31/2×1/2 ×3/8 ×5/16 ×1/4

7.00 5.36 4.50 3.64

1.44 1.42 1.40 1.39

1.57 1.55 1.53 1.52

1.72 1.69 1.68 1.66

1.75 1.73 1.72 1.70

1.89 1.86 1.85 1.83

2.03 2.00 1.99 1.97

1.00 1.00 1.00 1.00

1.00 1.00 0.997 0.912

1.23 1.25 1.25 1.26

1.00 1.00 1.00 0.998

1.00 1.00 0.997 0.912

1.04 1.05 1.06 1.07

2L4×3×5/8 ×1/2 ×3/8 ×5/16 ×1/4

7.98 6.50 4.98 4.18 3.38

1.21 1.19 1.17 1.16 1.15

1.35 1.32 1.30 1.29 1.27

1.50 1.47 1.44 1.43 1.41

1.84 1.81 1.79 1.78 1.76

1.98 1.95 1.93 1.91 1.90

2.13 2.10 2.07 2.06 2.04

1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 0.997 0.912

1.23 1.24 1.26 1.27 1.27

1.00 1.00 1.00 1.00 0.998

1.00 1.00 1.00 0.997 0.912

0.845 0.858 0.873 0.880 0.887

2L31/2×31/2×1/2 ×7/16 ×3/8 ×5/16 ×1/4

6.50 5.78 5.00 4.20 3.40

1.49 1.48 1.47 1.46 1.44

1.63 1.61 1.60 1.59 1.57

1.77 1.76 1.74 1.73 1.72

1.49 1.48 1.47 1.46 1.44

1.63 1.61 1.60 1.59 1.57

1.77 1.76 1.74 1.73 1.72

1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 0.965

1.05 1.06 1.07 1.08 1.09

1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 0.965

1.05 1.06 1.07 1.08 1.09

2L31/2×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4

6.04 5.34 4.64 3.90 3.16

1.23 1.22 1.21 1.20 1.19

1.37 1.36 1.35 1.33 1.32

1.52 1.51 1.49 1.48 1.46

1.55 1.54 1.52 1.51 1.50

1.69 1.67 1.66 1.65 1.63

1.84 1.82 1.81 1.79 1.78

1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 0.965

1.07 1.08 1.09 1.09 1.10

1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 0.965

0.877 0.885 0.892 0.900 0.908

2L31/2×21/2×1/2 ×3/8 ×5/16 ×1/4

5.54 4.24 3.58 2.90

0.992 0.970 0.960 0.950

1.13 1.11 1.09 1.08

1.28 1.25 1.24 1.22

1.62 1.59 1.58 1.57

1.76 1.73 1.72 1.70

1.91 1.88 1.87 1.85

1.00 1.00 1.00 1.00

1.00 1.00 1.00 0.965

1.08 1.10 1.11 1.12

1.00 1.00 1.00 1.00

1.00 1.00 1.00 0.965

0.701 0.716 0.723 0.731

Note: For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

in.

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Page 107

DIMENSIONS AND PROPERTIES

1–107

Table 1-15 (continued)

Double Angles 2L4-2L31/2

Properties Flexural-Torsional Properties Long Legs Vertical Short Legs Vertical Back to Back of Angles, in. Back to Back of Angles, in.

Shape

3/8

0

3/4

3/8

0

Single Angle Properties

Area, A

3/4

rz

r–o

H

r–o

H

r–o

H

r–o

H

r–o

H

r–o

H

in.2

in.

2L4×4×3/4 ×5/8 ×1/2 ×7/16 ×3/8 ×5/16 ×1/4

2.28 2.28 2.28 2.28 2.28 2.28 2.28

0.847 0.841 0.834 0.832 0.829 0.826 0.824

2.39 2.39 2.38 2.38 2.38 2.37 2.37

0.861 0.854 0.848 0.846 0.843 0.840 0.838

2.51 2.50 2.49 2.49 2.49 2.48 2.48

0.874 0.868 0.862 0.859 0.856 0.854 0.851

2.28 2.28 2.28 2.28 2.28 2.28 2.28

0.847 0.841 0.834 0.832 0.829 0.826 0.824

2.39 2.39 2.38 2.38 2.38 2.37 2.37

0.861 0.854 0.848 0.846 0.843 0.840 0.838

2.51 2.50 2.49 2.49 2.49 2.48 2.48

0.874 0.868 0.862 0.859 0.856 0.854 0.851

5.44 4.61 3.75 3.30 2.86 2.40 1.93

0.774 0.774 0.776 0.777 0.779 0.781 0.783

2L4×31/2×1/2 ×3/8 ×5/16 ×1/4

2.14 2.14 2.14 2.14

0.784 0.778 0.775 0.773

2.23 2.23 2.23 2.22

0.802 0.795 0.792 0.790

2.33 2.33 2.33 2.32

0.819 0.813 0.810 0.807

2.16 2.16 2.16 2.15

0.882 0.876 0.874 0.871

2.28 2.27 2.26 2.26

0.893 0.888 0.885 0.883

2.40 2.39 2.38 2.37

0.904 0.899 0.896 0.894

3.50 2.68 2.25 1.82

0.716 0.719 0.721 0.723

2L4×3×5/8 ×1/2 ×3/8 ×5/16 ×1/4

2.02 2.02 2.03 2.03 2.03

0.728 0.721 0.715 0.712 0.710

2.11 2.11 2.11 2.11 2.11

0.750 0.743 0.736 0.733 0.730

2.21 2.20 2.20 2.20 2.20

0.773 0.765 0.757 0.754 0.751

2.10 2.09 2.08 2.07 2.06

0.930 0.925 0.920 0.918 0.915

2.22 2.21 2.20 2.19 2.18

0.938 0.933 0.928 0.926 0.924

2.36 2.34 2.32 2.32 2.31

0.945 0.940 0.936 0.934 0.932

3.99 3.25 2.49 2.09 1.69

0.631 0.633 0.636 0.638 0.639

2L31/2×31/2×1/2 ×7/16 ×3/8 ×5/16 ×1/4

1.99 1.99 1.99 1.99 1.99

0.838 0.835 0.832 0.829 0.826

2.10 2.09 2.09 2.09 2.08

0.854 0.851 0.848 0.845 0.842

2.21 2.21 2.20 2.20 2.19

0.869 0.866 0.863 0.860 0.857

1.99 1.99 1.99 1.99 1.99

0.838 0.835 0.832 0.829 0.826

2.10 2.09 2.09 2.09 2.08

0.854 0.851 0.848 0.845 0.842

2.21 2.21 2.20 2.20 2.19

0.869 0.866 0.863 0.860 0.857

3.25 2.89 2.50 2.10 1.70

0.679 0.681 0.683 0.685 0.688

2L31/2×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4

1.85 1.85 1.85 1.85 1.85

0.780 0.776 0.773 0.770 0.767

1.94 1.94 1.94 1.94 1.94

0.801 0.797 0.794 0.790 0.787

2.05 2.05 2.05 2.04 2.04

0.822 0.818 0.814 0.811 0.807

1.88 1.88 1.88 1.87 1.87

0.892 0.889 0.885 0.883 0.880

2.00 1.99 1.99 1.98 1.98

0.904 0.901 0.898 0.895 0.893

2.13 2.12 2.11 2.11 2.10

0.915 0.912 0.910 0.907 0.905

3.02 2.67 2.32 1.95 1.58

0.618 0.620 0.622 0.624 0.628

2L31/2×21/2×1/2 ×3/8 ×5/16 ×1/4

1.75 1.75 1.76 1.76

0.706 0.698 0.695 0.693

1.83 1.83 1.83 1.83

0.732 0.724 0.720 0.717

1.93 1.93 1.92 1.92

0.759 0.750 0.746 0.742

1.82 1.81 1.80 1.80

0.938 0.933 0.930 0.928

1.95 1.93 1.92 1.92

0.946 0.941 0.939 0.937

2.08 2.07 2.06 2.05

0.953 0.949 0.947 0.944

2.77 2.12 1.79 1.45

0.532 0.535 0.538 0.541

Note: For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 01B:14th Ed._

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Page 108

1–108

DIMENSIONS AND PROPERTIES

Table 1-15 (continued)

Double Angles Properties SLBB LLBB

Shape

Area

LLBB Separation, s, in.

SLBB Qs

LLBB Qs

Axis Y-Y Radius of Gyration SLBB Separation, s, in.

Angles Angles in SepaContact rated

rx

Angles Angles in SepaContact rated

rx

in.2

0

3/8

3/4

0

3/8

3/4

2L3×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4 ×3/16

5.52 4.86 4.22 3.56 2.88 2.18

1.29 1.28 1.27 1.26 1.25 1.24

1.43 1.42 1.41 1.39 1.38 1.37

1.58 1.57 1.55 1.54 1.52 1.51

1.29 1.28 1.27 1.26 1.25 1.24

1.43 1.42 1.41 1.39 1.38 1.37

1.58 1.57 1.55 1.54 1.52 1.51

1.00 1.00 1.00 1.00 1.00 0.998

1.00 1.00 1.00 1.00 1.00 0.912

0.895 0.903 0.910 0.918 0.926 0.933

1.00 1.00 1.00 1.00 1.00 0.998

1.00 1.00 1.00 1.00 1.00 0.912

0.895 0.903 0.910 0.918 0.926 0.933

2L3×21/2×1/2 ×7/16 ×3/8 ×5/16 ×1/4 ×3/16

5.00 4.44 3.86 3.26 2.64 2.00

1.04 1.02 1.01 1.00 0.991 0.980

1.18 1.16 1.15 1.14 1.12 1.11

1.33 1.32 1.30 1.29 1.27 1.25

1.35 1.34 1.32 1.31 1.30 1.29

1.49 1.48 1.46 1.45 1.44 1.42

1.64 1.63 1.61 1.60 1.58 1.57

1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 1.00 0.912

0.910 0.917 0.924 0.932 0.940 0.947

1.00 1.00 1.00 1.00 1.00 0.998

1.00 1.00 1.00 1.00 1.00 0.912

0.718 0.724 0.731 0.739 0.746 0.753

2L3×2×1/2 ×3/8 ×5/16 ×1/4 ×3/16

4.52 3.50 2.96 2.40 1.83

0.795 0.771 0.760 0.749 0.739

0.940 0.911 0.897 0.883 0.869

1.10 1.07 1.05 1.03 1.02

1.42 1.39 1.38 1.37 1.35

1.56 1.54 1.52 1.51 1.49

1.72 1.69 1.67 1.66 1.64

1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 0.912

0.922 0.937 0.945 0.953 0.961

1.00 1.00 1.00 1.00 0.998

1.00 1.00 1.00 1.00 0.912

0.543 0.555 0.562 0.569 0.577

2L21/2×21/2×1/2 ×3/8 ×5/16 ×1/4 ×3/16

4.52 3.46 2.92 2.38 1.80

1.09 1.07 1.05 1.04 1.03

1.23 1.21 1.19 1.18 1.17

1.39 1.36 1.34 1.33 1.31

1.09 1.07 1.05 1.04 1.03

1.23 1.21 1.19 1.18 1.17

1.39 1.36 1.34 1.33 1.31

1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 0.983

0.735 0.749 0.756 0.764 0.771

1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 0.983

0.735 0.749 0.756 0.764 0.771

2L21/2×2×3/8 ×5/16 ×1/4 ×3/16

3.10 2.64 2.14 1.64

0.815 0.804 0.794 0.784

0.957 0.943 0.930 0.916

1.11 1.10 1.08 1.07

1.13 1.12 1.10 1.09

1.27 1.26 1.24 1.23

1.42 1.41 1.39 1.38

1.00 1.00 1.00 1.00

1.00 1.00 1.00 0.983

0.766 0.774 0.782 0.790

1.00 1.00 1.00 1.00

1.00 1.00 1.00 0.983

0.574 0.581 0.589 0.597

2L21/2×11/2×1/4 ×3/16

1.89 1.45

0.554 0.694 0.852 1.17 0.543 0.679 0.834 1.16

1.32 1.30

1.47 1.00 1.45 1.00

1.00 0.792 1.00 0.983 0.801 1.00

1.00 0.411 0.983 0.418

2.74 2.32 1.89 1.44 0.982

0.865 0.853 0.842 0.831 0.818

1.01 0.996 0.982 0.967 0.951

1.17 1.15 1.14 1.12 1.10

1.00 1.00 1.00 1.00 0.912

1.00 1.00 1.00 1.00 0.912

2L2×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

1.01 0.996 0.982 0.967 0.951

1.17 1.15 1.14 1.12 1.10

0.865 0.853 0.842 0.831 0.818

1.00 1.00 1.00 1.00 0.998

Note: For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

0.591 0.598 0.605 0.612 0.620

1.00 1.00 1.00 1.00 0.998

in.

0.591 0.598 0.605 0.612 0.620

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Page 109

DIMENSIONS AND PROPERTIES

1–109

Table 1-15 (continued)

Double Angles Properties

2L3-2L2

Flexural-Torsional Properties Long Legs Vertical Short Legs Vertical Back to Back of Angles, in. Back to Back of Angles, in.

Shape

3/8

0

3/4

3/8

0

Single Angle Properties

Area, A

3/4

rz

r–o

H

r–o

H

r–o

H

r–o

H

r–o

H

r–o

H

in.2

in.

2L3×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4 ×3/16

1.71 1.71 1.71 1.71 1.71 1.71

0.842 0.838 0.834 0.830 0.827 0.823

1.82 1.82 1.81 1.81 1.81 1.80

0.861 0.857 0.853 0.849 0.845 0.842

1.94 1.94 1.93 1.93 1.92 1.91

0.878 0.874 0.870 0.866 0.863 0.859

1.71 1.71 1.71 1.71 1.71 1.71

0.842 0.838 0.834 0.830 0.827 0.823

1.82 1.82 1.81 1.81 1.81 1.80

0.861 0.857 0.853 0.849 0.845 0.842

1.94 1.94 1.93 1.93 1.92 1.91

0.878 0.874 0.870 0.866 0.863 0.859

2.76 2.43 2.11 1.78 1.44 1.09

0.580 0.580 0.581 0.583 0.585 0.586

2L3×21/2×1/2 ×7/16 ×3/8 ×5/16 ×1/4 ×3/16

1.57 1.57 1.57 1.57 1.57 1.57

0.774 0.769 0.764 0.760 0.756 0.753

1.66 1.66 1.66 1.66 1.66 1.65

0.800 0.795 0.790 0.785 0.781 0.778

1.78 1.77 1.77 1.76 1.76 1.75

0.824 0.819 0.815 0.810 0.806 0.802

1.61 1.60 1.60 1.59 1.59 1.58

0.905 0.901 0.897 0.893 0.890 0.887

1.73 1.72 1.72 1.71 1.70 1.70

0.918 0.914 0.911 0.907 0.904 0.901

1.86 1.85 1.85 1.84 1.83 1.82

0.929 0.926 0.923 0.920 0.917 0.914

2.50 2.22 1.93 1.63 1.32 1.00

0.516 0.516 0.517 0.518 0.520 0.521

2L3×2×1/2 ×3/8 ×5/16 ×1/4 ×3/16

1.47 1.48 1.48 1.48 1.49

0.684 0.675 0.671 0.668 0.666

1.55 1.55 1.56 1.56 1.55

0.717 0.707 0.702 0.698 0.695

1.66 1.65 1.65 1.65 1.64

0.751 0.739 0.734 0.730 0.726

1.55 1.54 1.53 1.52 1.52

0.955 0.949 0.946 0.944 0.941

1.69 1.67 1.66 1.65 1.64

0.962 0.957 0.954 0.952 0.950

1.83 1.81 1.80 1.79 1.78

0.968 0.963 0.961 0.959 0.957

2.26 1.75 1.48 1.20 0.917

0.425 0.426 0.428 0.431 0.435

2L21/2×21/2×1/2 ×3/8 ×5/16 ×1/4 ×3/16

1.43 1.42 1.42 1.42 1.42

0.850 0.839 0.834 0.829 0.825

1.54 1.53 1.53 1.52 1.52

0.871 0.861 0.856 0.852 0.847

1.67 1.65 1.65 1.64 1.63

0.890 0.881 0.876 0.872 0.868

1.43 1.42 1.42 1.42 1.42

0.850 0.839 0.834 0.829 0.825

1.54 1.53 1.53 1.52 1.52

0.871 0.861 0.856 0.852 0.847

1.67 1.65 1.65 1.64 1.63

0.890 0.881 0.876 0.872 0.868

2.26 1.73 1.46 1.19 0.901

0.481 0.481 0.481 0.482 0.482

2L21/2×2×3/8 ×5/16 ×1/4 ×3/16

1.29 1.29 1.29 1.29

0.754 0.748 0.744 0.740

1.38 1.38 1.38 1.38

0.786 0.781 0.775 0.771

1.49 1.49 1.49 1.48

0.817 0.812 0.806 0.801

1.32 1.32 1.32 1.31

0.913 0.909 0.904 0.901

1.45 1.44 1.43 1.43

0.927 0.923 0.920 0.916

1.59 1.58 1.57 1.56

0.939 0.936 0.933 0.929

1.55 1.32 1.07 0.818

0.419 0.420 0.423 0.426

2L21/2×11/2×1/4 1.22 0.630 1.29 0.669 1.38 0.712 1.27 0.962 1.40 0.969 1.55 0.975 0.947 0.321 ×3/16 1.22 0.627 1.29 0.665 1.38 0.706 1.26 0.959 1.39 0.967 1.53 0.973 0.724 0.324 2L2×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

1.14 1.14 1.13 1.13 1.13

0.847 0.841 0.835 0.830 0.826

1.25 1.25 1.24 1.24 1.23

0.874 0.868 0.862 0.857 0.853

1.38 1.37 1.37 1.36 1.35

0.897 0.891 0.886 0.882 0.877

1.14 1.14 1.13 1.13 1.13

0.847 0.841 0.835 0.830 0.826

1.25 1.25 1.24 1.24 1.23

0.874 0.868 0.862 0.857 0.853

Note: For compactness criteria, refer to Table 1-7B.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.38 1.37 1.37 1.36 1.35

0.897 0.891 0.886 0.882 0.877

1.37 1.16 0.944 0.722 0.491

0.386 0.386 0.387 0.389 0.391

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DIMENSIONS AND PROPERTIES

Table 1-16

2C-Shapes Properties 2C-SHAPES

Shape

Axis Y-Y Separation, s, in.

Area, A in.2

3/8

0

I in.4

S in.3

r in.

Z in.3

29.4 40.7 23.6 32.6 20.0 28.5

2C12×30 ×25 ×20.7

17.6 18.2 14.7 15.6 12.2 13.6

5.75 1.02 11.9 23.3 5.11 1.03 9.89 19.8 4.64 1.06 8.49 17.2

2C10×30 ×25 ×20 ×15.3

17.6 14.7 11.7 8.96

5.04 4.25 3.62 3.13

2C9×20 ×15 ×13.4

11.7 8.80 8.80 6.86 7.88 6.34

11.0 1.18 23.5 9.25 1.18 18.4 8.38 1.20 15.8

I in.4

2C15×50 ×40 ×33.9

15.3 12.3 9.91 8.14

Axis X-X

0.931 11.4 0.914 9.06 0.918 7.11 0.953 5.68

S in.3

3/4

r in.

Z in.3

I in.4

S in.3

50.5 12.9 1.31 29.0 62.4 15.3 40.2 10.9 1.31 22.8 49.6 12.7 35.1 9.78 1.33 19.5 43.1 11.4

20.2 16.2 13.0 10.6

r in.

Z in.3

rx in.

1.46 34.5 1.45 27.2 1.47 23.3

5.24 5.43 5.61

6.94 1.15 15.2 29.6 6.12 1.16 12.6 25.0 5.51 1.19 10.8 21.7

8.36 1.30 18.5 7.32 1.31 15.4 6.55 1.34 13.0

4.29 4.43 4.61

6.27 5.27 4.44 3.80

7.73 6.48 5.43 4.59

3.43 3.52 3.67 3.88

1.07 14.7 26.3 1.05 11.8 21.1 1.05 9.32 16.9 1.09 7.36 13.7

3.32 0.866 6.84 11.8 4.15 1.00 2.76 0.882 5.17 9.10 3.41 1.02 2.61 0.897 4.74 8.39 3.20 1.03

9.05 15.6 6.82 12.0 6.21 11.0

1.22 18.0 1.20 14.6 1.20 11.5 1.23 9.04

5.15 1.15 11.2 3.22 4.19 1.17 8.48 3.40 3.92 1.18 7.69 3.48

2C8×18.75 11.0 7.46 ×13.75 8.06 5.51 ×11.5 6.74 4.82

2.95 0.823 6.23 10.2 3.75 0.962 8.29 13.7 4.71 1.11 10.4 2.82 2.35 0.826 4.48 7.47 2.95 0.962 5.99 10.0 3.68 1.11 7.51 2.99 2.13 0.846 3.86 6.50 2.66 0.982 5.12 8.66 3.29 1.13 6.38 3.11

2C7×14.75 ×12.25 ×9.8

8.66 5.18 7.18 4.30 5.74 3.59

2.25 0.773 4.61 1.96 0.773 3.78 1.72 0.791 3.11

7.21 2.90 0.912 6.23 9.85 3.68 1.07 5.97 2.51 0.911 5.13 8.14 3.17 1.06 4.95 2.17 0.929 4.18 6.72 2.73 1.08

7.85 2.51 6.48 2.59 5.26 2.72

2C6×13 ×10.5 ×8.2

7.64 4.11 6.14 3.26 4.78 2.63

1.91 0.734 3.92 1.60 0.728 3.08 1.37 0.741 2.45

5.85 2.50 0.876 5.35 8.13 3.21 1.03 4.63 2.08 0.867 4.24 6.43 2.67 1.02 3.72 1.76 0.881 3.34 5.14 2.24 1.04

6.77 2.13 5.39 2.22 4.24 2.34

2C5×9 ×6.7

5.28 2.45 3.94 1.86

1.30 0.682 2.52 1.06 0.688 1.91

3.59 1.73 0.824 3.51 5.09 2.25 0.982 4.50 1.84 2.71 1.40 0.831 2.65 3.84 1.81 0.989 3.83 1.95

2C4×7.25 ×6.25 ×5.4 ×4.5

4.26 3.54 3.16 2.76

1.75 1.36 1.29 1.25

1.02 0.824 0.812 0.789

0.641 0.620 0.637 0.673

1.96 1.54 1.44 1.36

2.63 2.06 1.94 1.86

1.38 1.12 1.10 1.05

0.786 0.763 0.783 0.820

2.75 2.20 2.04 1.88

3.81 3.01 2.82 2.66

1.82 1.49 1.44 1.36

0.946 0.922 0.943 0.981

3.55 2.87 2.63 2.40

1.47 1.50 1.56 1.63

2C3×6 ×5 ×4.1 ×3.5

3.52 2.94 2.40 2.18

1.33 1.05 0.842 0.766

0.833 0.699 0.597 0.558

0.614 0.597 0.591 0.593

1.60 1.29 1.05 0.966

2.06 1.63 1.32 1.20

1.15 0.969 0.827 0.772

0.764 0.746 0.741 0.743

2.26 1.84 1.50 1.37

3.03 2.43 1.97 1.80

1.54 1.30 1.10 1.03

0.927 0.909 0.905 0.908

2.92 2.39 1.95 1.78

1.09 1.12 1.18 1.20

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

1–111

Table 1-17

2MC-Shapes Properties 2MC18-2MC7 Axis Y-Y Separation, s, in.

Area, A

Shape

3/8

0

in.2

I in.4

S in.3

r in.

Z in.3

I in.4

2MC18×58 ×51.9 ×45.8 ×42.7

34.2 30.6 27.0 25.2

60.6 55.0 50.1 47.8

14.4 13.4 12.5 12.1

1.33 1.34 1.36 1.38

29.5 26.3 23.4 22.1

72.8 65.9 59.8 57.0

2MC13×50 ×40 ×35 ×31.8

29.4 23.4 20.6 18.7

60.7 49.1 44.3 41.5

13.8 11.7 10.9 10.4

1.44 1.45 1.47 1.49

28.6 22.7 20.2 18.7

2MC12×50 ×45 ×40 ×35 ×31

29.4 26.4 23.6 20.6 18.2

67.2 59.9 53.7 48.0 44.0

16.2 14.9 13.8 12.7 12.0

1.51 1.51 1.51 1.53 1.55

30.9 27.5 24.5 21.6 19.7

2MC12×14.3 c

2MC12×10.6

2MC10×8.4c ×6.5c

r in.

Z in.3

I in.4

16.6 15.4 14.3 13.8

1.46 1.47 1.49 1.51

35.9 32.0 28.4 26.8

87.5 79.0 71.4 67.9

72.5 58.4 52.6 49.2

15.8 13.4 12.3 11.7

1.57 1.58 1.60 1.62

34.1 27.2 24.1 22.2

79.8 71.1 63.7 56.8 52.1

18.5 16.9 15.6 14.4 13.5

1.65 1.64 1.65 1.66 1.69

36.4 32.4 29.0 25.5 23.1

S in.3

rx

r in.

Z in.3

in.

19.1 17.6 16.3 15.7

1.60 1.61 1.63 1.64

42.3 37.7 33.5 31.6

6.29 6.41 6.55 6.64

86.3 69.4 62.3 58.2

18.0 15.2 14.0 13.3

1.71 1.72 1.74 1.76

39.7 31.6 27.9 25.7

4.62 4.82 4.95 5.05

94.5 84.1 75.3 67.1 61.4

20.9 19.2 17.7 16.2 15.2

1.79 1.79 1.79 1.81 1.83

41.9 37.4 33.4 29.4 26.5

4.28 4.36 4.46 4.59 4.71

1.50 0.618 3.15

4.66

2.02 0.747 4.72 6.73 2.70

0.897

6.29 4.27

6.20 1.21

0.804 0.441 1.67

2.05

1.21 0.575 2.83 3.33 1.78

0.733

3.99 4.22

14.7 27.8 12.9 25.4

13.9 12.1 11.0

1.58 26.4 1.58 21.5 1.61 18.7

70.7 58.2 51.1

8.18 1.38 14.0 7.67 1.40 12.8

33.6 30.7

15.7 13.6 12.3

1.71 30.9 83.1 17.7 1.72 25.2 68.3 15.3 1.75 21.9 59.8 13.8

1.85 1.86 1.89

35.5 28.9 25.0

3.61 3.75 3.89

9.36 1.51 16.8 40.4 10.7 8.76 1.54 15.2 36.8 10.0

1.66 1.69

19.5 17.6

3.87 3.99

4.92 1.05 0.700 0.462 1.40 1.75 1.03 0.596 2.32 2.79 1.49 0.753 3.90 0.414 0.354 0.326 0.757 0.835 0.615 0.463 1.49 1.53 0.990 0.626

3.24 3.61 2.22 3.43

2MC9×25.4 14.9 29.2 ×23.9 14.0 27.8

8.34 1.40 14.5 8.05 1.41 13.8

35.2 33.4

9.53 1.53 17.3 42.2 10.9 9.19 1.54 16.4 40.1 10.5

1.68 1.69

20.1 19.0

3.43 3.48

2MC8×22.8 13.4 27.7 ×21.4 12.6 26.3

7.91 1.44 13.5 7.63 1.45 12.8

33.2 31.6

9.01 1.58 16.0 39.7 10.2 8.68 1.59 15.2 37.7 9.86

1.72 1.73

18.6 17.5

3.09 3.13

2MC8×20 11.7 17.1 ×18.7 11.0 16.2

5.66 1.21 5.45 1.21

6.61 1.34 12.1 26.2 6.35 1.35 11.4 24.8

1.49 1.50

14.3 13.5

3.04 3.09

2MC8×8.5

1.15 0.658 2.14

5.00 2.16

2MC7×22.7 13.3 29.0 ×19.1 11.2 25.1 c

S in.3

3/4

8.36 3.19

2MC10×41.1 24.2 60.0 ×33.6 19.7 49.5 ×28.5 16.7 43.5 2MC10×25 ×22

Axis X-X

9.88 21.2 9.34 20.1

8.06 1.47 13.9 7.27 1.50 12.1

3.14 34.7 30.0

7.70 7.39

1.52 0.793 3.08 4.47 1.99

0.946

9.16 1.61 16.4 41.3 10.4 8.25 1.64 14.2 35.7 9.34

1.76 1.78

Shape is slender for compression with Fy = 36 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.02 3.05 18.9 16.3

2.67 2.77

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DIMENSIONS AND PROPERTIES

Table 1-17 (continued)

2MC-Shapes Properties 2MC6-2MC3

Shape

Axis Y-Y Separation, s, in.

Area, A in.2

3/8

0

I in.4

S in.3

Axis X-X

r in.

Z in.3

I in.4

S in.3

3/4

r in.

Z in.3

rx

I in.4

S in.3

r in.

Z in.3

in.

2MC6×18 10.6 25.0 ×15.3 8.98 19.7

7.13 1.54 11.8 29.8 5.63 1.48 9.43 23.6

8.07 1.68 13.8 35.3 6.39 1.62 11.1 28.1

9.11 7.24

1.83 1.77

15.8 12.8

2.37 2.38

2MC6×16.3 9.58 15.8 ×15.1 8.88 14.8

5.26 1.28 5.02 1.29

8.88 19.4 8.35 18.2

6.10 1.42 10.7 23.8 5.82 1.43 10.0 22.3

7.05 6.71

1.58 1.58

12.5 11.7

2.33 2.37

2MC6×12

7.06 7.21

2.89 1.01

4.97

9.32

3.47 1.15

4.15

1.30

7.62 2.30

2MC6×7 ×6.5

4.18 2.25 3.90 2.15

1.20 0.734 2.09 1.16 0.744 2.00

3.19 3.04

1.55 0.873 2.88 4.41 1.96 1.49 0.883 2.73 4.20 1.89

1.03 1.04

3.66 2.34 3.46 2.38

2MC4×13.8 8.06 10.1

4.03 1.12

2MC3×7.1

1.62 0.862 2.76

4.22 3.13

6.84 12.9 4.31

6.29 11.9

4.81 1.27

8.35 16.3

5.68

1.42

9.87 1.48

2.03 1.01

3.55 5.79 2.50

1.17

4.34 1.14

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

1–113

Table 1-18

Weights of Raised-Pattern Floor Plates

Gauge No.

Wt., lb/ft 2

18 16 14 13 12

2.40 3.00 3.75 4.50 5.25

Nominal Thickness, in. 1/8 3/16 1/4 5/16 3/8 7/16

Wt., lb/ft 2

Nominal Thickness, in.

6.16 8.71 11.3 13.8 16.4 18.9

Note: Thickness is measured near the edge of the plate, exclusive of raised pattern.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1/2 9/16 5/8 3/4 7/8

1

Wt., lb/ft 2 21.5 24.0 26.6 31.7 36.8 41.9

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1–114

DIMENSIONS AND PROPERTIES

Table 1-19

W-Shapes with Cap Channels Properties Axis X-X W-Shape

Channel

Total Wt.

Total Area

I

I S1 = ᎏ y

I S2 = ᎏ y

in.3

in.3

1

lb/ft

in.2

in.4

r

2

in.

W36×150

MC18×42.7 C15×33.9

193 184

56.8 54.2

12000 11500

553 546

831 764

14.6 14.6

W33×141

MC18×42.7 C15×33.9

184 175

54.1 51.5

10000 9580

490 484

750 689

13.6 13.6

W33×118

MC18×42.7 C15×33.9

161 152

47.2 44.6

8280 7900

400 395

656 596

13.2 13.3

W30×116

MC18×42.7 C15×33.9

159 150

46.8 44.1

6900 6590

365 360

598 544

12.1 12.2

W30×99

MC18×42.7 C15×33.9

142 133

41.6 39.0

5830 5550

304 300

533 481

11.8 11.9

W27×94

C15×33.9

128

37.6

4530

268

435

11.0

W27×84

C15×33.9

118

34.7

4050

237

403

10.8

W24×84

C15×33.9 C12×20.7

118 105

34.7 30.8

3340 3030

217 211

367 302

9.82 9.92

W24×68

C15×33.9 C12×20.7

102 88.7

30.0 26.1

2710 2440

173 168

321 258

9.51 9.67

W21×68

C15×33.9 C12×20.7

102 88.7

30.0 26.1

2180 1970

156 152

287 232

8.52 8.67

W21×62

C15×33.9 C12×20.7

95.9 82.7

28.2 24.3

2000 1800

142 138

272 218

8.41 8.59

W18×50

C15×33.9 C12×20.7

83.9 70.7

24.6 20.7

1250 1120

100 97.3

211 166

7.12 7.35

W16×36

C15×33.9 C12×20.7

69.9 56.7

20.5 16.6

748 670

64.5 62.8

160 123

6.04 6.34

W14×30

C12×20.7 C10×15.3

50.7 45.3

14.9 13.3

447 420

46.7 46.0

98.1 84.5

5.47 5.61

W12×26

C12×20.7 C10×15.3

46.7 41.3

13.7 12.1

318 299

36.8 36.3

82.1 70.5

4.81 4.96

Note: Compactness criteria not addressed in this table.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

1–115

Table 1-19 (continued)

W-Shapes with Cap Channels Properties Axis X-X W-Shape

Channel

Axis Y-Y

y1

y2

Z

yp

I

S

r

Z

in.

in.

in.3

in.

in.4

in.3

in.

in.3

W36×150

MC18×42.7 C15×33.9

21.8 21.1

14.5 15.1

738 716

28.0 25.9

824 584

91.5 77.9

3.81 3.28

146 122

W33×141

MC18×42.7 C15×33.9

20.4 19.8

13.3 13.9

652 635

27.0 24.9

800 561

88.9 74.8

3.85 3.30

142 118

W33×118

MC18×42.7 C15×33.9

20.7 20.0

12.6 13.3

544 529

27.8 25.5

741 502

82.3 66.9

3.96 3.35

126 102

W30×116

MC18×42.7 C15×33.9

18.9 18.3

11.5 12.1

492 480

26.1 23.8

718 479

79.8 63.8

3.92 3.29

124 100

W30×99

MC18×42.7 C15×33.9

19.2 18.5

10.9 11.5

412 408

26.4 24.4

682 442

75.8 59.0

4.05 3.37

114 89.4

W27×94

C15×33.9

16.9

10.4

357

23.6

439

58.5

3.41

89.6

W27×84

C15×33.9

17.1

10.0

316

23.9

420

56.0

3.48

83.9

W24×84

C15×33.9 C12×20.7

15.4 14.3

9.10 10.0

286 275

21.6 18.5

409 223

54.5 37.2

3.43 2.69

83.4 58.2

W24×68

C15×33.9 C12×20.7

15.7 14.5

8.46 9.49

232 224

21.7 19.2

385 199

51.3 33.2

3.58 2.76

75.3 50.1

W21×68

C15×33.9 C12×20.7

13.9 12.9

7.59 8.49

207 200

19.3 17.6

379 194

50.6 32.3

3.56 2.72

75.1 50.0

W21×62

C15×33.9 C12×20.7

14.1 13.0

7.33 8.26

189 183

19.4 18.1

372 186

49.6 31.1

3.63 2.77

72.5 47.3

W18×50

C15×33.9 C12×20.7

12.5 11.5

5.92 6.76

133 127

16.9 16.1

354 169

47.3 28.2

3.79 2.85

67.3 42.2

W16×36

C15×33.9 C12×20.7

11.6 10.7

4.67 5.47

86.8 83.2

15.2 14.6

339 153

45.2 25.6

4.06 3.04

61.6 36.4

W14×30

C12×20.7 C10×15.3

9.57 9.11

4.55 4.97

62.0 60.3

12.9 12.6

149 86.8

24.8 17.4

3.16 2.55

34.6 24.9

W12×26

C12×20.7 C10×15.3

8.63 8.22

3.87 4.24

48.2 47.0

11.6 11.3

146 84.5

24.4 16.9

3.27 2.64

33.7 24.1

Note: Compactness criteria not addressed in this table.

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DIMENSIONS AND PROPERTIES

Table 1-20

S-Shapes with Cap Channels Properties Axis X-X S-Shape

Channel

Total Wt.

Total Area

I

I S1 = ᎏ y

I S2 = ᎏ y

in.3

in.3

1

lb/ft

in.2

in.4

r

2

in.

S24×80

C12×20.7 C10×15.3

101 95.3

29.5 27.9

2750 2610

191 188

278 252

9.66 9.67

S20×66

C12×20.7 C10×15.3

86.7 81.3

25.5 23.9

1620 1530

132 129

202 181

7.97 8.00

S15×42.9

C10×15.3 C8×11.5

58.2 54.4

17.1 16.0

615 583

65.7 64.7

105 93.9

6.00 6.04

S12×31.8

C10×15.3 C8×11.5

47.1 43.3

13.8 12.7

314 297

40.2 39.6

71.2 63.0

4.77 4.84

S10×25.4

C10×15.3 C8×11.5

40.7 36.9

11.9 10.8

185 175

27.5 27.1

52.7 46.3

3.94 4.02

Note: Compactness criteria not addressed in this table.

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DIMENSIONS AND PROPERTIES

1–117

Table 1-20 (continued)

S-Shapes with Cap Channels Properties Axis X-X S-Shape

Channel

Axis Y-Y

y1

y2

Z

yp

I

S

r

Z

in.

in.

in.3

in.

in.4

in.3

in.

in.3

S24×80

C12×20.7 C10×15.3

14.4 13.9

9.90 10.4

256 246

18.1 16.5

171 109

28.5 21.8

2.41 1.98

46.4 36.8

S20×66

C12×20.7 C10×15.3

12.3 11.8

7.99 8.44

180 173

16.0 14.4

156 94.7

26.1 18.9

2.48 1.99

41.0 31.3

S15×42.9

C10×15.3 C8×11.5

9.37 9.01

5.87 6.21

87.6 86.5

12.8 11.6

81.5 46.8

16.3 11.7

2.18 1.71

25.0 18.7

S12×31.8

C10×15.3 C8×11.5

7.82 7.50

4.42 4.72

54.0 52.4

10.6 10.3

76.5 41.8

15.3 10.5

2.36 1.82

22.3 16.1

S10×25.4

C10×15.3 C8×11.5

6.73 6.45

3.51 3.77

37.2 36.1

73.9 39.2

14.8 9.81

2.49 1.90

20.9 14.6

9.03 8.82

Note: Compactness criteria not addressed in this table.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-21

Crane Rails Dimensions and Properties

ASCE CRANE RAILS

ASTM PROFILE 104

ASTM PROFILE 135

ASTM PROFILE 175

n

in.

in.

17/32 11/64 5/8 7/32 11/16

1/4

49/64

9/32

13/16

9/32

7/8

19/64

57/64 19/64 31/32 5/16

11/16 11/16 11/4 19/64

1/2 15/32 5/8 1/2

c

r

in.

in. 12 12 12 12 12 12 12 12 12 14 Flat 18

111/16 17/8 21/8 23/8 27/16 21/2 29/16 23/4 21/2 37/16 4.3 41/4

t in.

h

R

in.

in. 12 12 12 12 12 12 12 12 31/2 12 Vert. Vert.

21/64

123/32

25/64

155/64 21/16 217/64 215/32 25/8 23/4 25/64 27/16 213/16 23/4 37/64

7/16 31/64 33/64 35/64 9/16 9/16 1 11/4 11/4 11/2

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Axis X-X S

l

Base

171/128 123/32 1115/128 23/64 23/16 217/64 265/128 27/16 215/32 25/8 221/32

in. 31/8 31/2 37/8 41/4 45/8 5 53/16 53/4 5 53/16 6 6

m

Web

Head

in. 125/64

b

Head

Area

Base Gage, g

Depth, d

Classification

Crane

Std.

ASCE ASTM A759

Wt.

lb/yd in. 30 31/8 40 31/2 50 37/8 60 41/4 70 45/8 — 80 5 85 53/16 100 53/4 104 5 135 53/4 171 6 175 6 Light

TYPE

ASTM PROFILE 171

y

in.2 3.00 3.94 4.90 5.93 6.81 7.86 8.33 9.84 10.3 13.3 16.8 17.1

in.4 4.10 6.54 10.1 14.6 19.7 26.4 30.1 44.0 29.8 50.8 73.4 70.5

in.3 2.55 3.59 5.10 6.64 8.19 10.1 11.1 14.6 10.7 17.3 24.5 23.4

in.3 — 3.89 — 7.12 8.87 11.1 12.2 16.1 13.5 18.1 24.4 23.6

in. — 1.68 1.88 2.05 2.22 2.38 2.47 2.73 2.21 2.81 3.01 2.98

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DIMENSIONS AND PROPERTIES

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Table 1-22

ASTM A6 Tolerances for W-Shapes and HP-Shapes

Permissible Cross-Sectional Variations Nominal Depth, in.

A Depth at Web Centerline, in.

B Flange Width, in.

T + T′ Flanges Out of Square, Max. in.

Ea Web Off Center, in.

C, Max. Depth at any Cross-Section over Theoretical Depth, in.

Over

Under

Over

Under

To 12, incl.

1/ 8

1/ 8

1/ 4

3/ 16

1/ 4

3/ 16

1/ 4

Over 12

1/ 8

1/ 8

1/ 4

3/ 16

5/ 16

3/ 16

1/ 4

Permissible Variations in Length Variations from Specified Length for Lengths Given, in. Nominal Depth b, in.

30 ft and Under Over

Beams 24 in. and under Beams over 24 in. All columns

Sizes

/8

1

1

/2

/2

1/

Under

plus 1/16 for each additional 5 ft or fraction thereof

3

/8

1 2 plus /16 for each additional 5 ft or fraction thereof

1

/2

Mill Straightness Tolerancesc Permissible Variation in Straightness, in. Length Camber

Flange width less than 6 in.

All

Area and Weight

3/8

/8

All

Ends Out of Square

Over

3

3

Flange width equal to or greater than 6 in.

Certain sections with a flange width approx. equal to depth & specified on order as columnsd

Over 30 ft

Under

45 ft and under

Sweep

(total length, ft) in. × 10 1/8 in. × (total length, ft) 1/8 in. × (total length, ft) 10 5 (total length, ft) 1/8 in. × with 3/8 in. max. 10 1/8

[

in. + 1/8 in. × (total length, ft – 45) 10 Other Permissible Rolling Variations Over 45 ft

3/8

]

−2.5 to +3.0% from the theoretical cross-sectional area or the specified nominal weighte 1/64

in., per in. of depth, or of flange width if it is greater than the depth

a

Variation of 5/16 in. max. for sections over 426 lb/ft. b For shapes specified in the order for use as bearing piles, the permitted variations are plus 5 in. and minus 0 in. c The tolerances herein are taken from ASTM A6 and apply to the straightness of members received from the rolling mill, measured as illustrated in Figure 1-1. d Applies only to W8×31and heavier, W10×49 and heavier, W12×65 and heavier, W14×90 and heavier, HP8×36, HP10×57, HP12×74 and heavier, and HP14×102 and heavier. If other sections are specified on the order as columns, the tolerance will be subject to negotiation with the manufacturer. e For shapes with a nominal weight ≥ 100 lb/ft, the permitted variation is ±2.5% from the theoretical or specified amount.

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Page 120

DIMENSIONS AND PROPERTIES

W-Shapes

Channels

Angles

S- and M-Shapes

Tees

Fig. 1-1. Positions for measuring straightness. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Table 1-23

ASTM A6 Tolerances for S-Shapes, M-Shapes and Channels

*Back of square and centerline of web to be parallel when measuring “out-of-square”

Permissible Cross-Sectional Variations Nominal Depth, in.

Shape

Aa Depth, in.

B Flange Width, in.

Over

Under

Over

Under

3 to 7, incl.

3/ 32

1/ 16

1/ 8

1/ 8

Over 7 to 14, incl.

1/ 8

3/ 32

5/ 32

5/ 32

Over 14 to 24, incl.

3/ 16

1/ 8

3/ 16

3/ 16

S shapes and M shapes

Channels

3 to 7, incl.

3/ 32

1/ 16

1/ 8

1/ 8

Over 7 to 14, incl.

1/ 8

3/ 32

1/ 8

5/ 32

Over 14

3/ 16

1/ 8

1/ 8

3/ 16

T + T ′b

Flanges Out of Square, per in. of B, in.

E Web Off Center, in.

1/ 32

3/ 16

1/ 32

—

Permissible Variations in Length Variations from Specified Length for Lengths Givenc, in. Shape

5 to 10 ft, excl.

10 to 20 ft, excl.

20 to 30 ft, incl.

Over 30 to 40 ft, incl.

Over 40 to 65 ft, incl.

Over 65 ft

All

1

11/ 2

13/4

21/ 4

23/4

—

Mill Straightness Tolerancesd Camber

Sweep

1/8

in. ×

(total length, ft) 5

Due to the extreme variations in flexibility of these shapes, permitted variations for sweep are subject to negotiation between the manufacturer and purchaser for the individual sections involved.

Other Permissible Rolling Variations Area and Weight Ends Out of Square

−2.5 to +3.0% from the theoretical cross-sectional area or the specified nominal weighte S-Shapes, M-Shapes and Channels 1/64 in., per in. of depth

— Indicates that there is no requirement. a A is measured at center line of web for S-shapes and M-shapes and at back of web for channels. b T + T ′ applies when flanges of channels are toed in or out. c The permitted variation under the specified length is 0 in. for all lengths. There are no requirements for lengths over 65 ft. d The tolerances herein are taken from ASTM A6 and apply to the straightness of members received from the rolling mill, measured as illustrated in Figure 1-1. e For shapes with a nominal weight ≥ 100 lb/ft, the permitted variation is ±2.5% from the theoretical or specified amount.

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DIMENSIONS AND PROPERTIES

Table 1-24

ASTM A6 Tolerances for WT-, MT- and ST-Shapes

Permissible Variations in Depth Dimension A may be approximately one-half beam depth or any dimension resulting from off-center splitting or splitting on two lines, as specified in the order. Specified Depth, A, in. Variations in Depth A, Over and Under 1/8 To 6, excl. 3/16 6 to 16, excl. 1/4 16 to 20, excl. 5/16 20 to 24, excl. 3/8 24 and over The above variations in depths of tees include the permissible variations in depth for the beams before splitting

Mill Straightness Tolerancesa Camber and Sweep

1/8

in. ×

(total length, ft) 5

Other Permissible Rolling Variations Other permissible variations in cross section as well as permissible variations in length, area, weight, ends out-of-square, and sweep for WTs will correspond to those of the beam before splitting. — Indicates that there is no requirement. a The tolerances herein are taken from ASTM A6 and apply to the straightness of members received from the rolling mill, measured as illustrated in Figure 1-1. For tolerance on induced camber and sweep, see AISC Code of Standard Practice Section 6.4.4.

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DIMENSIONS AND PROPERTIES

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Table 1-25

ASTM A6 Tolerances for Angles, 3 in. and Larger

Permissible Cross-Sectional Variations

Shape

Angles

3 to 4, incl. Over 4 to 6, incl. Over 6

5 to 10 ft, excl. 1

T Out of Square per in. of B, in.

B Leg Size, in.

Nominal Leg Sizea, in. Over 1/8 1/8 3/16

Under 3/32 1/8 1/8

3/128b

Permissible Variations in Length Variations Over Specified Length for Lengths Givenc, in. 10 to 20 ft, excl. 20 to 30 ft, incl. Over 30 to 40 ft, incl. Over 40 to 65 ft, incl. 11/2 13/4 21/4 23/4 Mill Straightness Tolerancesd

Camber Sweep

1/8

in. ×

(total length, ft) , applied to either leg 5

Due to the extreme variations in flexibility of these shapes, permitted variations for sweep are subject to negotiation between the manufacturer and purchaser for the individual sections involved.

Other Permissible Rolling Variations Area and Weight Ends Out of Square a

−2.5 to +3.0% from the theoretical cross-sectional area or the specified nominal weight 3/128

in. per in. of leg length, or 11/2°. Variations based on the longer leg of unequal angle.

For unequal leg angles, longer leg determines classification.

b 3/128 in. per in. = 11/2° c The permitted variation d

under the specified length is 0 in. for all lengths. There are no requirements for lengths over 65 ft. The tolerances herein are taken from ASTM A6 and apply to the straightness of members received from the rolling mill, measured as illustrated in Figure 1-1.

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DIMENSIONS AND PROPERTIES

Table 1-26

ASTM A6 Tolerances for Angles, < 3 in.

Permissible Cross-Sectional Variations Variations in Thickness for Thicknesses Given, Over and Under, in.

Specified Leg Sizea, in. 3/ 16

and Under

Over 3/16 to 3/8 incl.

Over 3/8

B Leg Size, Over and Under, in.

1 and Under

0.008

0.010

—

1/ 32

Over 1 to 2, incl.

0.010

0.010

0.012

3/ 64

0.015

1/ 16

Over 2 to 3, excl.

0.012

0.015

T Out of Square per Inch of B, in. 3/ b 128

Permissible Variations in Length Variations Over Specified Length for Lengths Givenc, in. Section

5 to 10 ft, excl.

All bar-size angles

5/ 8

10 to 20 ft, excl.

20 to 30 ft, incl.

Over 30 to 40 ft, incl.

40 to 65 ft, incl.

1

11/2

2

21/2

Mill Straightness Tolerancesd Camber Sweep

1/ 4

in. in any 5 ft, or 1/4 in. ×

(total length, ft) , applied to either leg 5

Due to the extreme variations in flexibility of these shapes, permitted variations for sweep are subject to negotiation between the manufacturer and purchaser for the individual sections involved.

Other Permissible Rolling Variations Ends Out of Square

3/ 128

in. per in. of leg length, or 11/2°. Variations based on the longer leg of unequal angle.

— Indicates that there is no requirement. a For unequal angles, longer leg determines classification. b 3/128 in. per in. = 11/2° c The permitted variation under the specified length is 0 in. for all lengths. There are no requirements for lengths over 65 ft. d The tolerances herein are taken from ASTM A6 and apply to the straightness of members received from the rolling mill, measured as illustrated in Figure 1-1.

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DIMENSIONS AND PROPERTIES

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Table 1-27

Tolerances for Rectangular and Square HSS ASTM A500, ASTM A501, ASTM A618 and ASTM A847 The outside dimensions, measured across the flats at positions at least 2 in. from either end, shall not vary from the specified dimensions by more than the applicable amount given in the following table:

Outside Dimensions

Largest Outside Dimension Across Flats, in.

Permissible Variation Over and Under Specified Dimensionsa,b, in.

21/ 2 and under Over 21/ 2 to 31/ 2, incl. Over 31/ 2 to 51/ 2, incl. Over 51/ 2

0.020 0.025 0.030 1%c

HSS are commonly produced in random lengths, in multiple lengths, and in specific lengths. When specific lengths are ordered for HSS, the length tolerances shall be in accordance with the following table: Length tolerance for specific lengths, in. Length

Over 22 ft f

22 ft and under Over

Under

Over

Under

1/ 2

1/4

3/4

1/4

Wall Thickness

ASTM A500 and ASTM A847 only: The tolerance for wall thickness exclusive of the weld area shall be plus and minus 10% of the nominal wall thickness specified. The wall thickness is to be measured at the center of the flat.

Weight

ASTM A501 only: The weight of HSS, as specified in ASTM A501 Tables 3 and 4, shall not be less than the specified value by more than 3.5%.

Mass Straightness Squareness of Sides Radius of Corners

ASTM A618 only: The mass shall not be less than the specified value by more than 3.5%. The permissible variation for straightness shall be 1/8 in. times the number of ft of total length divided by 5. Adjacent sides may deviate from 90° by a tolerance of ± 2° maximum. The radius of any outside corner of the section shall not exceed 3 times the specified wall thicknessd. The tolerances for twist with respect to axial alignment of the section shall be as shown in the following table:

Twist

Specified Dimension of Longer Side, in.

Maximum Twist per 3 ft of length, in.

11/ 2 and under Over 11/ 2 to 21/ 2, incl. Over 21/ 2 to 4, incl. Over 4 to 6, incl. Over 6 to 8, incl. Over 8

0.050 0.062 0.075 0.087 0.100 0.112

Twist shall be determined by holding one end of the HSS down on a flat surface plate, measuring the height that each corner on the bottom side of the tubing extends above the surface plate near the opposite end of the HSS, and calculating the difference in the measured heights of such cornerse. a

The respective outside dimension tolerances include the allowances for convexity and concavity. ASTM A500 and ASTM A847 HSS only: The tolerances given are for the large flat dimension only. For HSS having a ratio of outside large to small flat dimension less than 1.5, the tolerance on the small flat dimesion shall be identical to those given. For HSS having a ratio of outside large to small flat dimension in the range of 1.5 to 3.0 inclusive, the tolerance on the small flat dimesion shall be 1.5 times those given. For HSS having a ratio of outside large to small flat dimension greater than 3.0, the tolerance on the small flat dimension shall be 2.0 times those given. c This value is 0.01 times the large flat dimension. ASTM A501 only: Over 51/2 to 10 incl., this value is 0.01 times large flat dimension; over 10, this value is 0.02 times the large flat dimension. d ASTM A501 HSS only: The radius of any outside corner must not exceed 3 times the calculated nominal wall thickness. e ASTM A500, ASTM A501, and ASTM A847 HSS only: For heavier sections it shall be permissible to use a suitable measuring device to determine twist. Twist measurements shall not be taken within 2 in. of the ends of the HSS. f ASTM A501 and A618: The upper limit on specific length is 44 ft. b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-28

Tolerances for Round HSS and Pipe

ASTM A53

Weight

The weight as specified in ASTM A53 Table X2.2 and Table X2.3 or as calculated from the relevant equation in ASME B36.10M shall not vary by more than ± 10%. Note that the weight tolerance is determined from the weights of the customary lifts of pipe as produced for shipment by the mill, divided by the number of ft of pipe in the lift. On pipe sizes over 4 in. where individual lengths may be weighed, the weight tolerance is applicable to the individual length.

Diameter

For pipe 2 in. and over in nominal diameter, the outside diameter shall not vary more than ± 1% from the outside diameter specified.

Thickness

The minimum wall thickness at any point shall not be more than 12.5% under the nominal wall thickness specified.

ASTM A500 and ASTM A847 Diametera

Thickness

For HSS 1.900 in. and under in specified diameter, the outside diameter shall not vary more than ± 0.5%, rounded to the nearest 0.005 in., from the specified diameter. For HSS 2.000 in. and over in specified diameter, the outside diameter shall not vary more than ± 0.75%, rounded to the nearest 0.005 in., from the specified diameter. The wall thickness at any point, excluding the weld seam of welded tubing, shall not be more than 10% under or over the specified wall thickness.

ASTM A501 and ASTM A618 Outside Dimensions

For HSS 11/ 2 in. and under in nominal size, the outside diameter shall not vary more than 1/ 64 in. over nor more than 1/ 32 in. under the specified diameter. For round hot-formed HSS 2 in. and over in nominal size, the outside diameter shall not vary more than ± 1% from the specified diameter.

Weight (A501 only)

The weight of HSS, as specified in ASTM A501 Table 5, shall not be less than the specified value by more than 3.5%.

Mass (A618 only)

The mass of HSS shall not be less than the specified value by more than 3.5%. The mass tolerance shall be determined from individual lengths or, for HSS 41/ 2 in. and under in outside diameter, shall be determined from masses of customary lifts produced by the mill.

ASTM A500, ASTM A501, ASTM A618 and ASTM A847 HSS are commonly produced in random mill lengths, in multiple lengths, and in specific lengths. When specific lengths are ordered for HSS, the length tolerances shall be in accordance with the following table: Length tolerance for specific cut lengths, in.

Length

Straightness a b

Over 22 ft b

22 ft and under Over

Under

Over

Under

1/ 2

1/ 4

3/4

1/ 4

The permissible variation for straightness of HSS shall be 1/ 8 in. times the number of ft of total length divided by 5.

The outside diameter measurements shall be taken at least 2 in. from the end of the HSS. ASTM A501 and A618: The upper limit and specific length is 44 ft.

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DIMENSIONS AND PROPERTIES

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Table 1-29

Rectangular Plates Permissible Variations from Flatness(Carbon Steel Only) Variations from Flatness for Specified Widths, in.

Specified Thickness, in.

To 36, excl.

36 to 48, excl.

48 to 60, excl.

60 to 72, excl.

72 to 84, excl.

84 to 96, excl.

96 to 108, excl.

108 to 120, excl.

To 1/4, excl.

9/16

3/4

15/16

11/4

13/8

11/2

15/8

13/4

12

/

58 /

34 /

15 16 /

11/8

11/4

1 3/8

11/2

12

/

9 16 /

58 /

58 /

34 /

78

/

1

11/8

7 16

/

12

/

9 16 /

58 /

58 /

34 /

1

1

to 1, excl.

7 16

/

12

/

9 16 /

58 /

58 /

58 /

34 /

78

1 to 2, excl.

38 /

12

/

12

/

9 16 /

9 16 /

58 /

58 /

58 /

2 to 4, excl.

5 16 /

38 /

7 16

/

12

/

12

/

12

/

12

/

9 16 /

4 to 6, excl.

38 /

7 16

/

12

/

12

/

9 16 /

9 16 /

58 /

34 /

6 to 8, excl.

7 16

12

12

58 /

11 16

34 /

78

78

1/4

to 3/8, excl.

3/8

to 1/ 2, excl.

1/ 2

to 3/4, excl.

3/4

/

/

/

/

/

/

/

Notes: 1. The longer dimension specified is considered the length, and permissible variations in flatness along the length shall not exceed the tabular amount for the specified width for plates up to 12 ft in length, or in any 12 ft for longer plates. 2. The flatness variations across the width shall not exceed the tabular amount for the specified width. 3. When the longer dimension is under 36 in., the permissible variation shall not exceed 1/4 in. When the longer dimension is from 36 to 72 in., inclusive, the permissible variation should not exceed 75% of the tabular amount for the specified width, but in no case less than 1/4 in. 4. These variations apply to plates which have a specified minimum tensile strength of not more than 60 ksi or comparable chemistry or hardness. The limits in the table are increased 50% for plates specified to a higher minimum tensile strength or comparable chemistry or hardness. 5. For plates 8 in. and over in thickness or 120 in. and over in width, see ASTM A6 Table 13. 6. Plates must be in a horizontal position on a flat surface when flatness is measured.

Permissible Variations in Cambera for Carbon Steel Sheared and Gas Cut Rectangular Plates Maximum permissible camber, in. (all thicknesses) = 1/8 in. ×

(total length, ft) 5

Permissible Variations in in Cambera for High-Strength Low-Alloy and Alloy Steel Sheared, Special-Cut, or Gas-Cut Rectangular Plates Specified Dimension, in.

Permitted Camber, in.

Thickness

Width

To 2, incl.

All

1/8

in. ×

(total length, ft) 5

To 30, incl.

3/16

in. ×

(total length, ft) 5

Over 30 to 60, incl.

1/4

in. ×

(total length, ft) 5

Over 2 to 15, incl.

a

Camber as it relates to plates is the horizontal edge curvature in the length, measured over the entire length of the plate in the flat position.

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AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–4 APPLICABLE SPECIFICATIONS, CODES AND STANDARDS . . . . . . . . . . . . . . . . 2–4 Specifications, Codes and Standards for Structural Steel Buildings . . . . . . . . . . . . . 2–4 Additional Requirements for Seismic Applications . . . . . . . . . . . . . . . . . . . . . . . 2–4 Other AISC Reference Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–5 OSHA REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–6 Columns and Column Base Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–6 Safety Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–6 Beams and Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–7 Cantilevers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–7 Joists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–7 Walking/Working Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–8 Controlling Contractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–8 USING THE 2010 AISC SPECIFICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–8 Load and Resistance Factor Design (LRFD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–9 Allowable Strength Design (ASD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–9 DESIGN FUNDAMENTALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–10 Loads, Load Factors and Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–10 Load and Resistance Factor Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–10 Allowable Strength Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–11 Superposition of Loads in Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . . 2–12 Nominal Strengths, Resistance Factors, Safety Factors and Available Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–12 Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–12 Structural Integrity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–13 Progressive Collapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–14 Required Strength, Stability, Effective Length, and Second-Order Effects . . . . . . 2–14 Simplified Determination of Required Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–16 Table 2-1. Multipliers for Use With the Simplified Method . . . . . . . . . . . . . . . . 2–17 STABILITY BRACING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–17 Simple-Span Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–17 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Beam Ends Supported on Bearing Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–17 Beams and Girders Framing Continuously Over Columns . . . . . . . . . . . . . . . . . . . 2–19 PROPERLY SPECIFYING MATERIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–25 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–25 Material Specifications

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–25

Other Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–25 Anchor rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–25 Raised-Pattern Floor Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–25 Sheet and Strip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–26 Filler Metal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–26 Steel Headed Stud Anchors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–26 Open-Web Steel Joists

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–26

Castellated Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–26 Steel Castings and Forgings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–26 Forged Steel Structural Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–26 Crane Rails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–27 CONTRACT DOCUMENT INFORMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–27 Design Drawings, Specifications and Other Contract Documents . . . . . . . . . . . . . 2–27 Required Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–28 Information Required Only When Specified . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–28 Approvals Required . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–29 Establishing Criteria for Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–29 Simple Shear Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–30 Moment Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–31 Horizontal and Vertical Bracing Connections

. . . . . . . . . . . . . . . . . . . . . . . . . . 2–31

Strut and Tie Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–32 Truss Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–32 Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–32 CONSTRUCTABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–32 TOLERANCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–33 Mill Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–33 Fabrication Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–33 Erection Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–33 Building Façade Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–34

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QUALITY CONTROL AND QUALITY ASSURANCE . . . . . . . . . . . . . . . . . . . . . . . 2–36 CAMBERING, CURVING AND STRAIGHTENING . . . . . . . . . . . . . . . . . . . . . . . . 2–37 Beam Camber and Sweep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–37 Cold Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–37 Hot Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–37 Truss Camber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–38 Straightening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2–38 FIRE PROTECTION AND ENGINEERING

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–38

CORROSION PROTECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–38 RENOVATION AND RETROFIT OF EXISTING STRUCTURES . . . . . . . . . . . . . . 2–38 THERMAL EFFECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–39 Expansion and Contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–39 Elevated-Temperature Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–40 FATIGUE AND FRACTURE CONTROL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–40 Avoiding Brittle Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–40 Avoiding Lamellar Tearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–42 WIND AND SEISMIC DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–42 Wind and Low-Seismic Applications High-Seismic Applications

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–42

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–42

PART 2 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–44 TABLES FOR THE GENERAL DESIGN AND SPECIFICATION OF MATERIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–47 Table 2-2. Summary Comparison of Methods for Stability Analysis and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–47 Table 2-3. AISI Standard Nomenclature for Flat-Rolled Carbon Steel . . . . . . . . . . 2–47 Table 2-4. Applicable ASTM Specifications for Various Structural Shapes . . . . . . 2–48 Table 2-5. Applicable ASTM Specifications for Plate and Bars . . . . . . . . . . . . . . . 2–49 Table 2-6. Applicable ASTM Specifications for Various Types of Structural Fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–50 Table 2-7. Metal Fastener Compatibility to Resist Corrosion . . . . . . . . . . . . . . . . . 2–51 Table 2-8. Summary of Surface Preparation Specifications . . . . . . . . . . . . . . . . . . 2–52

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SCOPE The specification requirements and other design considerations summarized in this Part apply in general to the design and construction of steel buildings. The specifications, codes and standards listed below are referenced throughout this manual.

APPLICABLE SPECIFICATIONS, CODES AND STANDARDS Specifications, Codes and Standards for Structural Steel Buildings Subject to the requirements in the applicable building code and the contract documents, the design, fabrication and erection of structural steel buildings is governed as indicated in the AISC Specification Sections A1 and B2 as follows: 1. ASCE/SEI 7: Minimum Design Loads for Buildings and Other Structures, ASCE/ SEI 7-10 (ASCE, 2010). Available from the American Society of Civil Engineers, ASCE/SEI 7 provides the general requirements for loads, load factors and load combinations. 2. AISC Specification: The 2010 AISC Specification for Structural Steel Buildings (ANSI/ AISC 360-10), included in Part 16 of this Manual and available at www.aisc.org, provides the general requirements for design and construction (AISC, 2010a). 3. AISC Code of Standard Practice: The 2010 AISC Code of Standard Practice for Steel Buildings and Bridges (AISC, 2010c) included in Part 16 of this manual and available at www.aisc.org, provides the standard of custom and usage for the fabrication and erection of structural steel. Other referenced standards include: 1. RCSC Specification: The 2009 RCSC Specification for Structural Joints Using High-Strength Bolts, reprinted in Part 16 of this Manual with the permission of the Research Council on Structural Connections and available at www.boltcouncil.org, provides the additional requirements specific to bolted joints with high-strength bolts (RCSC, 2009). 2. AWS D1.1: Structural Welding Code – Steel, AWS D1.1:2010 (AWS, 2010). Available from the American Welding Society, AWS D1.1 provides additional requirements specific to welded joints. Requirements for the proper specification of welds can be found in AWS A2.4: Standard Symbols for Welding, Brazing, and Nondestructive Examination (AWS, 2007). 3. ACI 318: Building Code Requirements for Structural Concrete and Commentary (ACI, 2008). Available from the American Concrete Institute, ACI 318 provides additional requirements for reinforced concrete, including composite design and the design of steel-to-concrete anchorage. Various other specifications and standards from ASME, ASTM and ACI are also referenced in AISC Specification Section A2.

Additional Requirements for Seismic Applications The 2010 AISC Seismic Provisions for Structural Steel Buildings (AISC, 2010b) apply as indicated in Section A1.1 of the 2010 AISC Specification and in the Scope provided at the front of this Manual. The AISC Seismic Provisions are available at www.aisc.org. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2–5

Other AISC Reference Documents The following other AISC publications may be of use in the design and construction of structural steel buildings: 1. AISC Detailing for Steel Construction, Third Edition, covers the standard practices and recommendations for steel detailing, including preparation of shop and erection drawings (AISC, 2009). 2. The AISC Seismic Design Manual (AISC, 2006) provides guidance on steel design in seismic applications, in accordance with the 2005 AISC Seismic Provisions for Structural Steel Buildings. 3. The AISC Design Examples is a web-based companion to this Manual and can be found at www.aisc.org (AISC, 2011). It includes design examples outlining the application of design aids and AISC Specification provisions developed in coordination with this Manual. Additionally, the following AISC Design Guides are available at www.aisc.org for in-depth coverage of specific topics in steel design: 1. Base Plate and Anchor Rod Design, Design Guide 1 (Fisher and Kloiber, 2006) 2. Steel and Composite Beams with Web Openings, Design Guide 2 (Darwin, 1990) 3. Serviceability Design Considerations for Steel Buildings, Design Guide 3 (West et al., 2003) 4. Extended End-Plate Moment Connections—Seismic and Wind Applications, Design Guide 4 (Murray and Sumner, 2003) 5. Low- and Medium-Rise Steel Buildings, Design Guide 5 (Allison, 1991). 6. Load and Resistance Factor Design of W-Shapes Encased in Concrete, Design Guide 6 (Griffis, 1992) 7. Industrial Buildings—Roofs to Anchor Rods, Design Guide 7 (Fisher, 2004) 8. Partially Restrained Composite Connections, Design Guide 8 (Leon et al., 1996) 9. Torsional Analysis of Structural Steel Members, Design Guide 9 (Seaburg and Carter, 1997) 10. Erection Bracing of Low-Rise Structural Steel Buildings, Design Guide 10 (Fisher and West, 1997) 11. Floor Vibrations Due to Human Activity, Design Guide 11 (Murray et al., 1997) 12. Modification of Existing Welded Steel Moment Frame Connections for Seismic Resistance, Design Guide 12 (Gross et al., 1999) 13. Stiffening of Wide-Flange Columns at Moment Connections: Wind and Seismic Applications, Design Guide 13 (Carter, 1999) 14. Staggered Truss Framing Systems, Design Guide 14 (Wexler and Lin, 2002) 15. AISC Rehabilitation and Retrofit Guide—A Reference for Historic Shapes and Specifications, Design Guide 15 (Brockenbrough, 2002) 16. Flush and Extended Multiple-Row Moment End-Plate Connections, Design Guide 16 (Murray and Shoemaker, 2002) 17. High Strength Bolts—A Primer for Structural Engineers, Design Guide 17 (Kulak, 2002) 18. Steel-Framed Open-Deck Parking Structures, Design Guide 18 (Churches et al. 2003) 19. Fire Resistance of Structural Steel Framing, Design Guide 19 (Ruddy et al., 2003) 20. Steel Plate Shear Walls, Design Guide 20 (Sabelli and Bruneau, 2006) AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Welded Connections—A Primer for Engineers, Design Guide 21 (Miller, 2006) Façade Attachments to Steel-Framed Buildings, Design Guide 22 (Parker, 2008) Constructability of Structural Steel Buildings, Design Guide 23 (Ruby, 2008) Hollow Structural Section Connections, Design Guide 24 (Packer et al., 2010) Web-Tapered Frame Design, Design Guide 25 (Kaehler et al., 2010)

OSHA REQUIREMENTS OSHA Safety and Health Standards for the Construction Industry, 29 CFR 1926 Part R Safety Standards for Steel Erection (OSHA, 2001) must be addressed in the design, detailing, fabrication and erection of steel structures. These regulations became effective on July 18, 2001. Following is a brief summary of selected provisions and related recommendations. The full text of the regulations should be consulted and can be found at www.osha.gov. See also Barger and West (2001) for further information.

Columns and Column Base Plates 1. All column base plates must be designed and fabricated with a minimum of four anchor rods. 2. Posts (which weigh less than 300 lb) are distinguished from columns and excluded from the four-anchor-rod requirement. 3. Columns, column base plates, and their foundations must be designed to resist a minimum eccentric gravity load of 300 lb located 18 in. from the extreme outer face of the column in each direction at the top of the column shaft. 4. Column splices must be designed to meet the same load-resisting characteristics as columns. 5. Double connections through column webs or at beams that frame over the tops of columns must be designed to have at least one installed bolt remain in place to support the first beam while the second beam is being erected. Alternatively, the fabricator must supply a seat or equivalent device with a means of positive attachment to support the first beam while the second beam is being erected. These features should be addressed in the construction documents. Items 1 through 4 are prescriptive, and alternative means such as guying are time consuming and costly. There are several methods to address the condition in item 5, as shown in Chapter 2 of AISC Detailing for Steel Construction.

Safety Cables 1. On multi-story structures, perimeter safety cables (two lines) are required at final interior and exterior perimeters of floors as soon as the deck is installed. 2. Perimeter columns must extend 48 in. above the finished floor (unless constructability does not allow) to allow the installation of perimeter safety cables. 3. The regulations prohibit field welding of attachments for installation of perimeter safety cables once the column has been erected. 4. Provision of some method of attaching the perimeter cable is required, but responsibility is not assigned either to the fabricator or to the erector. While this will be subject AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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to normal business arrangements between the fabricator and the erector, holes for these cables are often punched or drilled in columns by the fabricator. The primary consideration in the design of the frame based on these rules is that the position of the column splice is set with respect to the floor.

Beams and Bracing 1. Solid-web members (beams) must be connected with a minimum of two bolts or their equivalent before the crane load line is released. 2. Bracing members must be connected with a minimum of one bolt or its equivalent before the crane load line is released. The OSHA regulations allow an alternative to these minimums, if an “equivalent as specified by the project structural engineer of record” is provided. If the project requirements do not permit the use of bolts as described in items 1 and 2, then the “equivalent” means should be provided in the construction documents. It is recommended that the “equivalent” means should utilize bolts and removable connection material, and should provide requirements for the final condition of the connection. Solutions that employ shoring or the need to hold the member on the crane should be avoided.

Cantilevers 1. The erector is responsible for the stability of cantilevers and their temporary supports until the final cantilever connection is completed. OSHA 1926.756(a)(2) requires that a competent person shall determine if more than two bolts are necessary to ensure the stability of cantilevered members. Cantilever connections must be evaluated for the loads imposed on them during erection and consideration must be made for the intermediate states of completion, including the connection of the backspan member opposing the cantilever. Certain cantilever connections can facilitate the erector’s work in this regard, such as shop attaching short cantilevers, one piece cantilever/backspan beams carried through or over the column at the cantilever and field bolted flange plates or end plate connections to the supporting member. To the extent allowed by the contract documents, the selection of details is up to the fabricator, subject to normal business relations between the fabricator and the erector.

Joists 1. Unless panelized, all joists 40 ft long and longer and their bearing members must have holes to allow for initial connections by bolting. 2. Establishment of bridging terminus points for joists is mandated according to OSHA and manufacturer guidelines. 3. A vertical stabilizer plate to receive the joist bottom chord must be provided at columns. Minimum sizes are given and the stabilizer plate must have a hole for the attachment of guying or plumbing cables. These features should be addressed in the construction documents and shop drawings. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Walking/Working Surfaces 1. Framed metal deck openings must have structural members configured with projecting elements turned down to allow continuous decking, except where not allowed by design constraints or constructability. The openings in the metal deck are not to be cut until the hole is needed. 2. Steel headed stud anchors, threaded studs, reinforcing bars and deformed anchors that will project vertically from or horizontally across the top flange of the member are not to be attached to the top flanges of beams, joists or beam attachments until after the metal decking or other walking/working surface has been installed. Framing at openings with down turned elements and shop versus field attachment of anchors should be addressed in the construction documents and the shop drawings.

Controlling Contractor 1. The controlling contractor must provide adequate site access and adequate storage. 2. The controlling contractor must notify the erector of repairs or modifications to anchor rods in writing. Such modifications and repairs must be approved by the owner’s designated representative for design. 3. The controlling contractor must give notice that the supporting foundations have achieved sufficient strength to allow safe steel erection. 4. The controlling contractor must either provide overhead protection or prohibit other trades from working under steel erection activities. These provisions establish relationships among the erector, controlling contractor and owner’s representative for design that all parties need to be aware of.

USING THE 2010 AISC SPECIFICATION The 2010 AISC Specification for Structural Steel Buildings (ANSI/AISC 360-10) continues the format established in the 2005 edition of the Specification (AISC, 2005), ANSI/AISC 360-05, which unified the design provisions formerly presented in the 1989 Specification for Structural Steel Buildings—Allowable Stress Design and Plastic Design and the 1999 Load and Resistance Factor Design Specification for Structural Steel Buildings. The 2005 Specification for Structural Steel Buildings also integrated into a single document the information previously provided in the 1993 Load and Resistance Factor Design Specification for Single-Angle Members and the 1997 Specification for the Design of Steel Hollow Structural Sections. The 2010 AISC Specification, in combination with the 2010 Seismic Provisions for Structural Steel Buildings (ANSI/AISC 341-10), brings together all of the provisions needed for the design of structural steel in buildings and other structures. The 2010 AISC Specification continues to present two approaches for the design of structural steel members and connections. Chapter B establishes the general requirements for analysis and design. It states that “designs shall be made according to the provisions for Load and Resistance Factor Design (LRFD) or to the provisions for Allowable Strength Design (ASD).” These two approaches are equally valid for any structure for which the Specification is applicable. There is no preference stated or implied in the provisions.

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The required strength of structural members and connections may be determined by elastic, inelastic or plastic analysis for the load combinations associated with LRFD and by elastic analysis for load combinations associated with ASD and as stipulated by the applicable building code. In all cases, the available strength must exceed the required strength. The AISC Specification gives provisions for determining the available strength as summarized below.

Load and Resistance Factor Design (LRFD) The load combinations appropriate for LRFD are given in the applicable building code or, in its absence, ASCE/SEI 7 Section 2.3. For LRFD, the available strength is referred to as the design strength. All of the LRFD provisions are structured so that the design strength must equal or exceed the required strength. This is presented in AISC Specification Section B3.3 as Ru ≤ φRn

(2–1)

In this equation, Ru is the required strength determined by analysis for the LRFD load combinations, Rn is the nominal strength determined according to the AISC Specification provisions, and φ is the resistance factor given by the AISC Specification for a particular limit state. Throughout this Manual, tabulated values of φRn, the design strength, are given for LRFD. These values are tabulated as blue numbers in columns with the heading LRFD. If there is a desire to use the LRFD provisions in the form of stresses, the strength provisions can be transformed into stress provisions by factoring out the appropriate section property. In many cases, the provisions are already given directly in terms of stress.

Allowable Strength Design (ASD) Allowable strength design is similar to what is known as allowable stress design in that they are both carried out at the same load level. Thus, the same load combinations are used. The difference is that for strength design, the primary provisions are given in terms of forces or moments rather than stresses. In every situation, these strength provisions can be transformed into stress provisions by factoring out the appropriate section property. In many cases, the provisions are already given directly in terms of stress. The load combinations appropriate for ASD are given by the applicable building code or, in its absence, ASCE/SEI 7 Section 2.4. For ASD, the available strength is referred to as the allowable strength. All of the ASD provisions are structured so that the allowable strength must equal or exceed the required strength. This is presented in AISC Specification Section B3.4 as Ra ≤

Rn Ω

(2–2)

In this equation, Ra is the required strength determined by analysis for the ASD load combinations, Rn is the nominal strength determined according to the AISC Specification provisions and Ω is the safety factor given by the Specification for a particular limit state. Throughout this Manual, tabulated values of Rn /Ω, the allowable strength, are given for ASD. These values are tabulated as black numbers on a green background in columns with the heading ASD.

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DESIGN FUNDAMENTALS It is commonly believed that ASD is an elastic design method based entirely on a stress format without limit states and LRFD is an inelastic design method based entirely on a strength format with limit states. Traditional ASD was based on limit-states principles too, but without the use of the term. Additionally, either method can be formulated in a stress or strength basis, and both take advantage of inelastic behavior. The AISC Specification highlights how similar LRFD and ASD are in its formulation, with identical provisions throughout for LRFD and ASD. Design according to the AISC Specification, whether it is according to LRFD or ASD, is based on limit states design principles, which define the boundaries of structural usefulness. Strength limit states relate to load carrying capability and safety. Serviceability limit states relate to performance under normal service conditions. Structures must be proportioned so that no applicable strength or serviceability limit state is exceeded. Normally, several limit states will apply in the determination of the nominal strength of a structural member or connection. The controlling limit state is normally the one that results in the least available strength. As an example, the controlling limit state for bending of a simple beam may be yielding, local buckling, or lateral-torsional buckling for strength and deflection, or vibration for serviceability. The tabulated values may either reflect a single limit state or a combination of several limit states. This will be clearly stated in the introduction to the particular tables.

Loads, Load Factors and Load Combinations Based on AISC Specification Sections B3.3 and B3.4, the required strength (either Pu, Mu, Vu, etc. for LRFD or Pa, Ma, Va, etc. for ASD) is determined for the appropriate load magnitudes, load factors and load combinations given in the applicable building code. These are usually based on ASCE/SEI 7, which may be used when there is no applicable building code. The common loads found in building structures are: D L Lr S R W E

= = = = = = =

dead load live load due to occupancy roof live load snow load nominal load due to initial rainwater or ice exclusive of the ponding contribution wind load earthquake load

Load and Resistance Factor Design For LRFD, the required strength is determined from the following factored combinations,1 which are based on ASCE/SEI 7 Section 2.3: 1. 2. 3. 4.

1.4D 1.2D + 1.6L + 0.5(Lr or S or R) 1.2D + 1.6(Lr or S or R) + (0.5L or 0.5W) 1.2D + 1.0W + 0.5L + 0.5(Lr or S or R)

(2-3a) (2-3b) (2-3c) (2-3d)

1 Exception: Per ASCE/SEI 7, the load factor on L in combinations 3, 4 and 5 shall equal 1.0 for garages, areas occupied as places of public assembly, and all areas where the live load is greater than 100 psf.

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5. 1.2D + 1.0E + 0.5L + 0.2S 6. 0.9D + 1.0W 7. 0.9D + 1.0E

(2-3e) (2-3f) (2-3g)

The load combinations for LRFD recognize that, when several transient loads act in combination, only one assumes its maximum lifetime value,2 while the other(s) are at their “arbitrary-point-in-time” (APT) values. Each combination models the total design loading condition when a different load is at its maximum. Thus, the maximum-lifetime load effect is amplified by an amount that is proportional to its relative variability and the APT load effect(s) are factored to their mean value(s). With this approach, the margin of safety varies with the load combination yielding a more uniform reliability than would be expected when nominal loads are combined directly. Dead load, D, is present in each load combination with a load factor of 1.2, except in load combination 1, where it is the dominant (only) load effect, and load combinations 6 and 7, where it is reduced for calculation of the overturning or uplift effect. The 1.2 load factor accounts for the statistical variability of the dead load. The designer must independently account for other contributions to dead load, such as the weight of additional concrete, if any, added to adjust for concrete ponding effects (Ruddy, 1986) or differing framing elevations.

Allowable Strength Design For ASD, the required strength is determined from the following combinations, which are also based on ASCE/SEI 7 Section 2.4: 1. 2. 3. 4. 5. 6a. 6b. 7. 8.

D D+L D + (Lr or S or R) D + 0.75L + 0.75(Lr or S or R) D + (0.6W or 0.7E) D + 0.75L + 0.75(0.6W) + 0.75(Lr or S or R) D + 0.75L + 0.75(0.7E) + 0.75S 0.6D + 0.6W 0.6D + 0.7E

(2-4a) (2-4b) (2-4c) (2-4d) (2-4e) (2-4f) (2-4g) (2-4h) (2-4i)

The load combinations for ASD combine the code-specified nominal loads directly with no factors for those cases where loads with minimal variation with time are combined, cases 1, 2 and 3. For those cases where multiple time-variable loads are included, a 0.75 reduction factor is applied to the time-variable loads only. Since all of the safety in an ASD design comes through the introduction of the safety factor on the resistance side of the equation, each load case uses the same safety factor for a given limit state. In ASD, when considering members subjected to gravity loading only, it is clear that the controlling load combination is the one that adds the larger live load to the dead load. Thus, for a floor that does not carry roof load, the controlling combination will be D + L while for a roof the controlling combination will be D + (Lr or S or R). For gravity columns, after live load reductions have been accounted for, the floor and roof live loads may be reduced to 0.75 of their nominal values. A similar reduction is permitted for live loads in combination with lateral loads. 2

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Superposition of Loads in Load Combinations Whether the loads themselves or the effects of those loads are used in these combinations, LRFD or ASD, the results are the same, provided the principle of superposition is valid. This is true when deflections are small and the stress-strain behavior is nominally elastic. However, when second-order effects are significant or the behavior is inelastic, superposition is not valid and the loads, rather than the load effects, should be used in these combinations.

Nominal Strengths, Resistance Factors, Safety Factors and Available Strengths The AISC Specification requires that the available strength must be greater than or equal to the required strength for any element. The available strength is a function of the nominal strength given by the Specification and the corresponding resistance factor or safety factor. As discussed earlier, the required strength can be determined either with LRFD or ASD load combinations. The available strength for LRFD is the design strength, which is calculated as the product of the resistance factor φ and the nominal strength (φPn, φMn, φVn, etc.) The available strength for ASD is the allowable strength, which is calculated as the quotient of the nominal strength and the corresponding safety factor Ω (Pn / Ω, Mn / Ω, Vn / Ω, etc.). In LRFD, the margin of safety for the loads is contained in the load factors, and resistance factors, φ, to account for unavoidable variations in materials, design equations, fabrication and erection. In ASD, a single margin of safety for all of these effects is contained in the safety factor, Ω. The resistance factors, φ, and safety factors, Ω, in the AISC Specification are based upon research, as discussed in the AISC Specification Commentary to Chapter B, and the experience and judgment of the AISC Committee on Specifications. In general, φ is less than unity and Ω is greater than unity. The higher the variability in the test data for a given nominal strength, the lower its φ factor and the higher its Ω factor will be. Some examples of φ and Ω factors for steel members are as follows: φ = 0.90 for limit states involving yielding φ = 0.75 for limit states involving rupture Ω = 1.67 for limit states involving yielding Ω = 2.00 for limit states involving rupture The general relationship between the safety factor, Ω, and the resistance factor, φ, is Ω=

1.5 φ

(2–5)

Serviceability Serviceability requirements of the AISC Specification are found in Section B3.9 and Chapter L. The serviceability limit states should be selected appropriately for the specific application as discussed in the Specification Commentary to Chapter L. Serviceability limit states and the appropriate load combinations for checking their conformance to

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serviceability requirements can be found in ASCE/SEI 7 Appendix C and its Commentary. It should be noted that the load combinations in ASCE/SEI 7 Section 2.3 for LRFD and Section 2.4 for ASD are both for strength design, and are not necessarily appropriate for consideration of serviceability. Guidance is also available in the Commentary to the AISC Specification, both in general and for specific criteria, including camber, deflection, drift, vibrations, wind-induced motion, expansion and contraction, and connection slip. Additionally, the applicable building code may provide some further guidance or establish requirements. See also the serviceability discussions in Parts 3 through 6, AISC Design Guide 3, Serviceability Design Considerations for Steel Buildings (West et al., 2003) and AISC Design Guide 11, Floor Vibrations Due to Human Activity (Murray et al., 1997).

Structural Integrity Structural integrity as introduced into building codes and the 2010 AISC Specification Section B3.2, is a set of prescriptive requirements for connections that, when met, are intended to provide an unknown, but satisfactory, level of performance of the finished structure. The term structural integrity has often been used interchangeably with progressive collapse, but these two concepts have widely varying interpretations that can influence design in a variety of ways. The term progressive collapse does not appear in the International Building Code (ICC, 2009) or in the 2010 AISC Specification. Progressive collapse requirements generally are intended to prevent the collapse of a structure beyond a localized area of the structure where a structural element has been compromised. Progressive collapse requirements are often mandated for government facilities, or by owners for structures which have a high probability of being subject to terrorist attack. Structural integrity has always been one of the goals for the structural engineer in engineering design, and for the committees writing design standards. However, it has only been since the collapse of the buildings at the World Trade Center that requirements with the stated purpose of addressing structural integrity have appeared in U.S. building codes. The first building code to incorporate specific structural integrity requirements was the 2008 New York City Building Code which was quickly followed by requirements in the 2009 International Building Code. Although the requirements of these two building codes are both prescriptive in nature, there are some differences in requirements and their application. The AISC Specification Section B3.2 addresses the requirements of the 2009 International Building Code. The 2009 International Building Code stipulates minimum integrity provisions for buildings classified as high-rise and assigned to Occupancy Categories III or IV. High-rise buildings are defined as those having an occupied floor greater than 75 ft above fire department vehicle access. The structural integrity requirements state that column splices must resist a minimum tension force and beam end connections must resist a minimum axial tension force. The nominal axial tension strength of the beam end connection must equal or exceed either the required vertical shear strength for ASD or 2/3 the required vertical shear strength for LRFD. These required strengths can be reduced by 50% if the beam supports a composite deck with the prescribed steel anchors (Geschwindner and Gustafson, 2010). The International Building Code structural integrity requirements for the axial tension capacity of the beam end connections use a nominal strength basis reflecting the intent of the code to avoid brittle rupture failures of the connection components, rather than limiting AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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deformations or yielding of those components. Section B3.2 of the 2010 AISC Specification is based on this difference in limit state requirements for resistance to the prescriptive structural integrity loads, as compared to those limit states required when designing for traditional load combinations.

Progressive Collapse Progressive collapse is defined in ASCE/SEI 7-10 (ASCE, 2010) as “the spread of an initial local failure from element to element resulting, eventually, in the collapse of an entire structure or a disproportionately large part of it.” Progressive collapse requirements often involve assessment of the structure’s ability to accommodate loss of a member that has been compromised through redistribution of forces throughout the remaining structure. Design for progressive collapse poses a particularly challenging problem since it is difficult to identify the load cases to be examined or the members that may be compromised. Two main sources of requirements for evaluation of structures for progressive collapse are the Department of Defense and the General Services Administration. For facilities covered by the Department of Defense, all new and existing buildings of three stories or more must be designed to avoid progressive collapse. The specific requirements are published in United Facilities Criteria 4-023-03, “Design of Buildings to Resist Progressive Collapse” (DOD, 2009). For federal facilities under the jurisdiction of the General Services Administration, threat independent guidelines have been developed. The publication “Progressive Collapse Analysis and Design Guidelines for New Federal Office Buildings and Major Modernization Projects” (USGSA, 2003) provides an explicit process that any structural engineer could use to evaluate the progressive collapse potential of a multi-story facility.

Required Strength, Stability, Effective Length, and Second-Order Effects As previously discussed, the AISC Specification requires that the required strength must be less than or equal to the available strength in the design of every member and connection. Chapter C also requires that stability shall be provided for the structure as a whole and each of its elements. Any method that considers the influence of second-order effects, also known as P-delta effects, may be used. Thus, required strengths must be determined including second-order effects, as described in Specification Section C2.1. Note that Specification Section C2.1(2) permits an amplified first-order analysis as one method of second-order analysis, as provided in Appendix 8. Second-order effects are the additional forces, moments and displacements resulting from the applied loads acting in their displaced positions as well as the changes from the undeformed to the deformed geometry of the structure. Second-order effects are obtained by considering equilibrium of the structure within its deformed geometry. There are numerous ways of accounting for these effects. The commentary to AISC Specification Chapter C provides some guidance on methods of second-order analysis and suggests several benchmark problems for checking the adequacy of analysis methods. Since 1963, there have been provisions in the AISC Specifications to account for secondorder effects. Initially these provisions were embedded in the interaction equations. In past ASD Specifications, second-order effects were accounted for by the term

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1 1−

fa Fe′

found in the interaction equation. In past LRFD Specifications, the factors B1 and B2 from Chapter C of those specifications were used to amplify moments to account for secondorder effects. B1 was used to account for the second-order effects due to member curvature and B2 was used to account for second-order effects due to sidesway. In both Specifications, more exact methods were permitted. AISC Specification Section C1 and Appendix 7 provide three approaches that may be followed. • The direct analysis method is provided in Chapter C. This is the most comprehensive and, as the name suggests, most direct approach to incorporating all necessary factors in the analysis. Through the use of notional loads, reduced stiffness, and a secondorder analysis, the design can be carried out with the forces and moments from the analysis and an effective length equal to the member length, K = 1.0. Section C2 of the AISC Specification details the requirements for determination of required strengths using this method. • The effective length method is given in AISC Specification Appendix 7, Section 7.2. In this method, all gravity-only load cases have a minimum lateral load equal to 0.2% of the story gravity load applied. A second order analysis is carried out and the member strengths of columns and beam-columns are determined using effective lengths, determined by elastic buckling analysis, or more commonly, the alignment charts in the Commentary to the Specification when the associated assumptions are satisfied. The Specification permits K = 1.0 when the ratio of second order drift to first order drift is less than or equal to 1.1. • The first-order analysis method is given in AISC Specification Appendix 7, Section 7.3. With this approach, second-order effects are captured through the application of an additional lateral load equal to at least 0.42% of the story gravity load applied in each load case. No further second-order analysis is necessary. The required strengths are taken as the forces and moments obtained from the analysis and the effective length factor is K = 1.0. When a second-order analysis is called for in the above methods, AISC Specification Section C1 allows any method that properly considers P-delta effects. One such method is amplified first-order elastic analysis provided in Specification Appendix 8. This is a modified carry over of the B1-B2 approach used in previous LRFD Specifications, which was an extension of the simple approach taken in past ASD Specifications. The AISC Specification fully integrates the provisions for stability with the specified methods of design. For all framing systems, when using the direct analysis method, AISC Specification Section C3 provides that the effective length factor, K, for all members can be taken as 1.0 unless a lesser value can be justified by analysis. For the effective length method, AISC Specification Appendix 7, Section 7.2.3(a) provides that in braced frames, the effective length factor, K, may be taken as 1.0. For moment frames, Appendix 7, Section 7.2.3(b) requires that a critical buckling analysis to determine the critical buckling stress, Fe, be performed or effective length factors, K, be used. For the first-order analysis method,

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Appendix Section 7.3.3 stipulates that the effective length factor, K, be taken as unity for all members. This is discussed in more detail in the Commentary to Appendix 7.

Simplified Determination of Required Strength When a fast, conservative solution is desired, the following simplification of the effective length method can be used with the aid of Table 2-1. The features of each of the other methods of design for stability are summarized and compared in Table 2-2. An approximate second-order analysis approach is provided in AISC Specification Appendix 8. Where the member amplification (P-δ) factor is small, that is, less than B2, it is conservative to amplify the total moment and force by B2. Thus, Equations A-8-1 and A-8-2 become Mr = B1Mnt + B2Mlt = B2Mu

(2-6)

Pr = Pnt + B2 Plt = B2Pu

(2-7)

To use this simplified method, B1 cannot exceed B2. For members not subject to transverse loading between their ends, it is very unlikely that B1 would be greater than 1.0. In addition, the simplified approach is not valid if the amplification factor, B2, is greater than 1.5, because with the exception of taking B1 = B2, this simplified method meets the provisions of the effective length method in AISC Specification Appendix 7. It is up to the engineer to ensure that the frame is proportioned appropriately to use this simplified approach. In most designs it is not advisable to have a final structure where the second order amplification is greater than 1.5, although it is acceptable. In those cases, one should consider stiffening the structure. Step 1: Perform a first-order elastic analysis. Gravity load cases must include a minimum lateral load at each story equal to 0.002 times the story gravity load where the story gravity load is the load introduced at that story, independent of any loads from above. Step 2: Establish the design story drift limit and determine the lateral load that produces that drift. This is intended to be a measure of the lateral stiffness of the structure. Step 3: Determine the ratio of the total story gravity load to the lateral load determined in Step 2. For an ASD design, this ratio must be multiplied by 1.6 before entering Table 2-1. This ratio is part of the determination of the calculation on the elastic critical buckling strength, Pe story, in AISC Specification Equation A-8-7, which includes the parameter Rm. Rm is a minimum of 0.85 for rigid frames and 1.0 for all other frames. Step 4: Multiply all of the forces and moments from the first-order analysis by the value obtained from Table 2-1. Use the resulting forces and moments as the required strengths for the designs of all members and connections. Note that B2 must be computed for each story and in each principal direction. Step 5: For all cases where the multiplier is 1.1 or less, shown shaded in Table 2-1, the effective length may be taken as the member length, K = 1.0. For cases where the multiplier is greater than 1.1 but does not exceed 1.5, determine the effective length factor through analysis, such as with the alignment charts of the AISC Specification

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TABLE 2-1

Multipliers for Use With the Simplified Method Load Ratio from Step 3 (times 1.6 for ASD, 1.0 for LRFD)

Design Story Drift Limit

0

5

10

20

30

40

H/100 H/200 H/300 H/400 H/500

1 1 1 1 1

1.1 1 1 1 1

1.1 1.1 1 1 1

1.3 1.1 1.1 1.1 1

1.5/1.4 1.2 1.1 1.1 1.1

1.3 1.2 1.1 1.1

K=1

50

60

80

100

120

When ratio exceeds 1.5, simplified method requires a stiffer 1.4/1.3 1.5/1.4 structure. 1.2 1.3 1.5/1.4 1.2 1.2 1.3 1.4/1.3 1.5 1.1 1.2 1.2 1.3 1.4

Note: Where two values are provided, the value in bold is the value associated with Rm = 0.85.

Commentary. For cases where no value is shown for the multiplier, the structure must be stiffened in order to use this simplified approach. Note that the multipliers are the same value for both Rm = 0.85 and 1.0 in most instances due to rounding. Where this is not the case, two values are given consistent with the two values of Rm, respectively. Step 6: Ensure that the drift limit set in Step 2 is not exceeded and revise design as needed.

STABILITY BRACING Beams, girders and trusses must be restrained against rotation about their longitudinal axes at points of support (a basic assumption stated in the General Provisions of AISC Specification Section F1). Additionally, stability bracing with adequate strength and stiffness must be provided consistent with that assumed at braced points in the analysis for frames, columns and beams (see AISC Specification Appendix 6). Some guidance for special cases follows.

Simple-Span Beams In general, adequate lateral bracing is provided to the compression flange of a simple-span beam by the connections of infill beams, joists, concrete slabs, metal deck, concrete slabs on metal deck, and similar framing elements.

Beam Ends Supported on Bearing Plates The stability of a beam end supported on a bearing plate can be provided in one of several ways (see Figure 2-1): 1. The beam end can be built into solid concrete or masonry using anchorage devices. 2. The beam top flange can be stabilized through interconnection with a floor or roof system, provided that system is itself anchored to prevent its translation relative to the beam bearing.

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(a) Stability provided with transverse stiffeners

(b) Stability provided with an end plate

Fig. 2-1. Beam end supported on bearing plate.

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3. A top-flange stability connection can be provided. 4. An end-plate or transverse stiffeners located over the bearing plate extending to near the top-flange k-distance can be provided. Such stiffeners must be welded to the top of the bottom flange and to the beam web, but need not extend to or be welded to the top flange. In each case, the beam and bearing plate must also be anchored to the support. For the design of beam bearing plates, see Part 14. In atypical framing situations, such as when very deep beams are used, the strength and stiffness requirements in AISC Specification Appendix 6 can be applied to ensure the stability of the assembly. It may also be possible to demonstrate in a limited number of cases, such as with beams with thick webs and relatively shallow depths, that the beam has been properly designed without providing the details described above. In this case, the beam and bearing plate must still be anchored to the support. In any case, it should be noted that the assembly must also meet the requirements in AISC Specification Section J10.

Beams and Girders Framing Continuously Over Columns Roof framing is commonly configured with cantilevered beams that frame continuously over the tops of columns to support drop-in beams between the cantilevered segments (Rongoe, 1996; CISC, 1989). It is also commonly desirable to provide an assembly in which the intersection of the beam and column can be considered a braced point for the design of both the continuous cantilevering beam and the column top. The required stability can be provided in several ways (see Figure 2-2): 1. When an infill beam frames into the continuous beam at the column top, the required stability normally can be provided by using connection element(s) for the infill beam that cover three-quarters or more of the T-dimension of the continuous beam. Alternatively, connection elements that cover less than three-quarters of the T-dimension of the continuous beam can be used in conjunction with partial-depth stiffeners in the beam web along with a moment connection between the column top and beam bottom to maintain alignment of the beam/column assembly. A cap plate of reasonable proportions and four bolts will normally suffice. In either case, note that OSHA requires that, if two framing infill beams share common holes through a column web or the web of a beam that frames continuously over the top of a column,3 the beam erected first must remain attached while connecting the second. 2. When joists frame into the continuous beam or girder, the required stability normally can be provided by using bottom chord extensions connected to the column top. The resulting continuity moments must be reported to the joist supplier for their use in the design of the joists and bridging. Note that the continuous beam must still be checked for the concentrated force due to the column reaction per AISC Specification Section J10.

3

This requirement applies only at the location of the column, not at locations away from the column.

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The position of the bottom chord extension relative to the column cap plate will affect the bottom chord connection detail. When the extension aligns with the cap plate, the load path and force transfer is direct. When the extension is below the column cap plate, the column must be designed to stabilize the beam bottom flange and the connection between the extension and the column must develop the continuity/brace force. When the extension is above the column top, the beam web must have the necessary strength and stiffness to adequately brace the beam bottom/column top.

Fig. 2-2a. Beam framing continuously over column top, stability provided with connections of infill beams.

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3. If connection of the joist bottom chord extensions to the column must be avoided, the required stability can be provided with a diagonal brace that satisfies the strength and stiffness requirements in AISC Specification Appendix 6. Providing a relatively shallow angle with respect to the horizontal can minimize gravity-load effects in the diagonal brace. Alternatively, the required stability can be provided with stiffeners in the beam web along with a moment connection between the column top and beam bottom to maintain alignment of the beam/column assembly. A cap plate of reasonable proportions and four bolts will normally suffice. In atypical framing situations, such as when very deep girders are used, the strength and stiffness requirements in AISC Specification Appendix 6 can be applied for both the beam

Fig. 2-2b. Beam framing continuously over column top, stability provided with welded joist-chord extensions at column top.

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and the column to ensure the stability of the assembly. It may also be possible to demonstrate in a limited number of cases, such as with continuous beams with thick webs and relatively shallow depths, that the column and beam have been properly designed without providing infill beam connections, connected joist extensions, stiffeners, or diagonal braces as described above. In this case, a properly designed moment connection is still required between the beam bottom flange and the column top. In any case, it should be noted that the assembly must also meet the requirements in AISC Specification Section J10.

Fig. 2-2c. Beam framing continuously over column top, stability provided with welded joist-chord extensions above column top.

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Fig. 2-2d. Beam framing continuously over column top, stability provided with transverse stiffeners, joist chord extensions located at column top not welded.

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Fig. 2-2e. Beam framing continuously over column top, stability provided with stiffener plates, joist-chord extensions located above column top not welded.

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PROPERLY SPECIFYING MATERIALS Availability The general availability of structural shapes, HSS and pipe can be determined by checking the AISC database of available structural steel shapes at www.aisc.org/SteelAvailability. Generally, where many producers are listed, it is an indication that the particular shape is commonly available. However, except for the larger shapes, when only one or two producers are listed, it is prudent to consider contacting a steel fabricator to determine availability.

Material Specifications Applicable material specifications are as shown in the following tables: • Structural shapes in Table 2-3 • Plate and bar products in Table 2-4 • Fastening products in Table 2-5 Preferred material specifications are indicated in black shading. Other applicable material specifications are as shown in grey shading. The availability of grades other than the preferred material specification should be confirmed prior to their specification. Cross-sectional dimensions and production tolerances are addressed as indicated under “Standard Mill Practices” in Part 1.

Other Products Anchor rods Although the AISC Specification permits other materials for use as anchor rods, ASTM F1554 is the preferred specification, since all anchor rod production requirements are together in a single specification. ASTM F1554 provides three grades, namely 36 ksi, 55 ksi and 105 ksi. All Grade 36 rods are weldable. Grade 55 rods are weldable only when they are made per Supplementary Requirement S1. The project specifications must indicate if the material is to conform to Supplementary Requirement S1. As a heat-treated material, Grade 105 rods cannot be welded. Grade 105 should be used only for limited applications that require its high strength. For more information, refer to AISC Design Guide 1, Base Plate and Anchor Rod Design (Fisher and Kloiber, 2006).

Raised-Pattern Floor Plates ASTM A786 is the standard specification for rolled steel floor plates. As floor-plate design is seldom controlled by strength considerations, ASTM A786 “commercial grade” is commonly specified. If so, per ASTM A786-05 Section 5.1.3, “the product will be supplied 0.33% maximum carbon by heat analysis, and without specified mechanical properties.” Alternatively, if a defined strength level is desired, ASTM A786 raised-pattern floor plate can be ordered to a defined plate specification, such as ASTM A36, A572 or A588; see ASTM A786 Sections 5.1.3, 7.1 and 8.

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Sheet and Strip Sheet and strip products, which are generally thinner than structural plate and bar products are produced to such ASTM specifications as A570, A606 or A607 (see Table 2-3),

Filler Metal The appropriate filler metal for structural steel is as summarized in ANSI/AWS D1.1: 2010 Table 3.1 for the various combinations of base metal specification and grade and electrode specification. Weld strengths in this Manual are based upon a tensile strength level of 70 ksi.

Steel Headed Stud Anchors As specified in ANSI/AWS D1.1 Chapter 7 (Section 7.2.6 and Table 7.1), Type B shear stud connectors (referred to in the AISC Specification as steel headed stud anchors) made from ASTM A108 material are used for the interconnection of steel and concrete elements in composite construction (Fu = 65 ksi).

Open Web Steel Joists The AISC Code of Standard Practice does not include steel joists in its definition of structural steel. Steel joists are designed and fabricated per the requirements of specifications published by the Steel Joist Institute. Refer to SJI literature for further information.

Castellated Beams Castellated beams, also known as cellular beams, are members constructed by cutting along a staggered pattern down the web of a wide-flange member, offsetting the resulting pieces such that the deepest points of the cut are in contact, and welding the two pieces together, thereby creating a member with holes along its web. Castellated beams are currently designed and fabricated as a proprietary product. For more information, contact the manufacturer.

Steel Castings and Forgings Steel castings are specified as ASTM A27 Grade 65-35 or ASTM A216 Grade 80-35. Steel forgings are specified as ASTM A668.

Forged Steel Structural Hardware Forged steel structural hardware products, such as clevises, turnbuckles, eye nuts and sleeve nuts, are occasionally used in building design and construction. These products are generally forged according to ASTM A668 Class A requirements. ASTM A29, Grade 1035 material is commonly used in the manufacture of clevises and turnbuckles. ASTM A29, Grade 1030 material is commonly used in the manufacture of steel eye nuts and steel eye bolts. ASTM A29 Grade 1018 material is commonly used in the manufacture of sleeve nuts. Other products, such as steel rod ends, steel yoke ends and pins, cotter pins, and coupling nuts are commonly provided generically as “carbon steel.” The dimensional and strength characteristics of these devices are fully described in the literature provided by their manufacturer. Note that manufacturers usually provide strength characteristics in terms of a “safe working load” with a safety factor as high as 5, assuming AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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that the product will be used in rigging or similar applications subject to dynamic loading. The manufacturer’s safe working load may be overly conservative for permanent installations and similar applications subject to static loading only. If desired, the published safe working load can be converted into an available strength with reliability consistent with that of other statically loaded structural materials. In this case, the nominal strength, Rn, is determined as: Rn = (safe working load) ⫻ (manufacturer’s safety factor)

(2-8)

and the available strength, φRn or Rn /Ω, is determined using φ = 0.50 (LRFD)

Ω = 3.00 (ASD)

Crane Rails Crane rails are furnished to ASTM A759, ASTM A1, and/or manufacturer’s specifications and tolerances. Most manufacturers chamfer the top and sides of the crane-rail head at the ends unless specified otherwise to reduce chipping of the running surfaces. Often, crane rails are ordered as end-hardened, which improves the resistance of the crane-rail ends to impact that occurs as the moving wheel contacts it during crane operation. Alternatively, the entire rail can be ordered as heat-treated. When maximum wheel loading or controlled cooling is needed, refer to manufacturers’ catalogs. Purchase orders for crane rails should be noted “for crane service.” Light 40-lb rails are available in 30-ft lengths, 60-lb rails in 30-, 33- or 39-ft lengths, standard rails in 33- or 39-ft lengths and crane rails up to 80 ft. Consult manufacturer for availability of other lengths. Rails should be arranged so that joints on opposite sides of the crane runway will be staggered with respect to each other and with due consideration to the wheelbase of the crane. Rail joints should not occur at crane girder splices. Odd lengths that must be included to complete a run or obtain the necessary stagger should be not less than 10 ft long. Rails are furnished with standard drilling in both standard and odd lengths unless stipulated otherwise on the order.

CONTRACT DOCUMENT INFORMATION Design Drawings, Specifications and Other Contract Documents CASE Document 962D, A Guideline Addressing Coordination and Completeness of Structural Construction Documents (CASE, 2003), provides comprehensive guidance on the preparation of structural design drawings. Most provisions in the AISC Specification, RCSC Specification, AWS D1.1, and the AISC Code of Standard Practice are written in mandatory language. Some provisions require the communication of information in the contract documents, some provisions are invoked only when specified in the contract documents, and some provisions require the approval of the owner’s designated representative for design if they are to be used. Following is a summary of these provisions in the AISC Specification, RCSC Specification, and AISC Code of Standard Practice. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Required Information The following communication of information is required in the contract documents: 1. Required drawing information, per AISC Code of Standard Practice Sections 3.1 and 3.1.1 through 3.1.6. and RCSC Specification Section 1.4 (bolting products and joint type) 2. Drawing numbers and revision numbers, per AISC Code of Standard Practice Section 3.5 3. Structural system description, per AISC Code of Standard Practice Section 7.10.1 4. Installation schedule for nonstructural steel elements in the structural system, per AISC Code of Standard Practice Section 7.10.2 5. Project schedule, per AISC Code of Standard Practice Section 9.5.1

Information Required Only When Specified The following provisions are invoked only when specified in the contract documents: 1. Special material notch-toughness requirements, per AISC Specification Section A3.1c and Section A3.1d 2. Special connections requiring pretension, per AISC Specification Section J1.10 3. Bolted joint requirements, per AISC Specification Section J3.1 and RCSC Specification Section 1.4 4. Special cambering considerations, per AISC Specification Section L2 5. Special contours and finishing requirements for thermal cutting, per AISC Specification Sections M2.2 and M2.3, respectively 6. Corrosion protection requirements, if any, per AISC Specification Section M3 and AISC Code of Standard Practice Sections 6.5, 6.5.2 and 6.5.3 7. Responsibility for field touch-up painting, if painting is specified, per AISC Specification Section M4.6 and AISC Code of Standard Practice Section 6.5.4 8. Special quality control and inspection requirements, per AISC Specification Chapter N and AISC Code of Standard Practice Sections 8.1.3, 8.2 and 8.3 9. Evaluation procedures, per AISC Specification Section B6 10. Fatigue requirements, if any, per AISC Specification Section B3.9 11. Tolerance requirements other than those specified in the AISC Code of Standard Practice, per Code of Standard Practice Section 1.9 12. Designation of each connection as Option 1, 2 or 3, and identification of requirements for substantiating connection information, if any, per AISC Code of Standard Practice Section 3.1.2 13. Specific instructions to address items differently, if any, from requirements in the AISC Code of Standard Practice, per Code of Standard Practice Section 1.1 14. Submittal schedule for shop and erection drawings, per AISC Code of Standard Practice Section 4.2 15. Mill order timing, special mill testing, and special mill tolerances, per AISC Code of Standard Practice Sections 5.1, 5.2 and 5.2, respectively 16. Removal of backing bars and runoff tabs, per AISC Code of Standard Practice Section 6.3.2 17. Special erection mark requirements, per AISC Code of Standard Practice Section 6.6.1 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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18. Special delivery and erection sequences, per AISC Code of Standard Practice Sections 6.7.1 and 7.1, respectively 19. Special field splice requirements, per AISC Code of Standard Practice Section 6.7.4 20. Specials loads to be considered during erection, per AISC Code of Standard Practice Section 7.10.3 21. Special safety protection treatments, per AISC Code of Standard Practice Section 7.11.1 22. Identification of adjustable items, per AISC Code of Standard Practice Section 7.13.1.3 23. Cuts, alterations and holes for other trades, per AISC Code of Standard Practice Section 7.15 24. Revisions to the contract, per AISC Code of Standard Practice Section 9.3 25. Special terms of payment, per AISC Code of Standard Practice Section 9.6 26. Identification of architecturally exposed structural steel, per AISC Code of Standard Practice Section 10

Approvals Required The following provisions require the approval of the owner’s designated representative for design if they are to be used: 1. Bolted-joint-related approvals per RCSC Specification Commentary Section 1.4 2. Use of electronic or other copies of the design drawings by the fabricator, per AISC Code of Standard Practice Section 4.3 3. Use of stock materials not conforming to a specified ASTM specification, per AISC Code of Standard Practice Section 5.2.3 4. Correction of errors, per AISC Code of Standard Practice Section 7.14 5. Inspector-recommended deviations from contract documents, per AISC Code of Standard Practice Section 8.5.6 6. Contract price adjustment, per AISC Code of Standard Practice Section 9.4.2

Establishing Criteria for Connections AISC Code of Standard Practice Section 3.1.2 provides the following three methods for the establishment of connection requirements. In the first method, the complete design of all connections is shown in the structural design drawings. In this case, AISC Code of Standard Practice Commentary Section 3.1.2 provides a summary of the information that must be included in the structural design drawings. This method has the advantage that there is no need to provide connection loads, since the connections are completely designed in the structural design drawings. Additionally, it favors greater accuracy in the bidding process, since the connections are fully described in the contract documents. In the second method, the fabricator is allowed to select or complete the connections while preparing the shop and erection drawings, using the information provided by the owner’s designated representative for design per AISC Code of Standard Practice Section 3.1.2. In this case, AISC Code of Standard Practice Commentary Section 3.1.2 clarifies the intention that connections that can be selected or completed by the fabricator include those for which tables appear in the contract documents or the Manual. Other connections should be shown in detail in the structural design drawings. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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In the third method, connections are designated in the contract documents to be designed by a licensed professional engineer working for the fabricator. The AISC Code of Standard Practice sets forth detailed provisions that, in the absence of contract provisions to the contrary, serve as the basis of the relationships among the parties. One feature of these provisions is that the fabricator is required to provide representative examples of connection design documentation early in the process, and the owner’s designated representative for design is obliged is to review these submittals for conformity with the requirements of the contract documents. These early submittals are required in an attempt to avoid additional costs and/or delays as the approval process proceeds through subsequent shop drawings with connections developed from the original representative samples. Methods one and two have the advantage that the fabricator’s standard connections normally can be used, which often leads to project economy. However, the loads or other connection design criteria must be provided in the structural design drawings. Design loads and required strengths for connections should be provided in the structural design drawings and the design method used in the design of the frame (ASD or LRFD) must be indicated on the drawings. In all three methods, the resulting shop and erection drawings must be submitted to the owner’s designated representative for design for review and approval. As stated in the AISC Code of Standard Practice Section 4.4.1, the approval of shop and erection drawings constitutes “confirmation that the Fabricator has correctly interpreted the Contract Documents” and that the reviewer has “reviewed and approved the Connection details shown in the Shop and Erection Drawings.” Following is additional guidance for the communication of connection criteria to the connection designer.

Simple Shear Connections The full force envelope should be given for each simple shear connection. Because of the potential for overestimation and underestimation inherent in approximate methods (Thornton, 1995), actual beam end reactions should be indicated on the design drawings. The most effective method to communicate this information is to place a numeric value at each end of each span in the framing plans. In the past, beam end reactions were sometimes specified as a percentage of the tabulated uniform load in Manual Part 3. This practice can result in either over- or under-specification of connection reactions and should not be used. The inappropriateness of this practice is illustrated in the following examples. Over-estimation: 1. When beams are selected for serviceability considerations or for shape repetition, the uniform load tables will often result in heavier connections than would be required by the actual design loads. 2. When beams have relatively short spans, the uniform load tables will often result in heavier connections than would be required by the actual design loads. If not addressed with the accurate load, many times the heavier connections will require extension of the connection below the bottom flange of the supported member, requiring that the flange on one or both sides of the web to be cut and chipped, a costly process.

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Under-estimation: 1. When beams support other framing beams or other concentrated loads occur on girders supporting beams, the end reactions can be higher than 50% of the total uniform load. 2. For composite beams, the end reactions can be higher than 50% of the total uniform load. The percentage requirement can be increased for this condition, but the resulting approach is still subject to the above considerations.

Moment Connections The full force envelope should be given for each moment connection. If the owner’s designated representative for design can select the governing load combination, its effect alone should be provided. Otherwise, the effects of all appropriate load combinations should be indicated. Additionally, the maximum moment imbalance should also be given for use in the check of panel-zone web shear. Because of the potential for overestimation—and underestimation—inherent in approximate methods, it is recommended that the actual beam end reactions (moment, shear and other reactions, if any) be indicated in the structural design drawings. The most effective method to do so may be by tabulation for each joint and load combination. Although not recommended, beam end reactions are sometimes specified by more general criteria, such as by function of the beam strength. It should be noted, however, that there are several situations in which this approach is not appropriate. For example: 1. When beams are selected for serviceability considerations or for shape repetition, this approach will often result in heavier connections than would be required by the actual design loads. 2. When the column(s) or other members that frame at the joint could not resist the forces and moments determined from the criteria so specified, this approach will often result in heavier connections than would be required by the actual design loads. In some cases, the structural analysis may require that the actual connections be configured to match the assumptions used in the model. For example, it may be appropriate to release weak-axis moments in a beam-column joint where only strong-axis beam moment strength is required. Such requirements should be indicated in the structural design drawings.

Horizontal and Vertical Bracing Connections The full force envelope should be given for each bracing-member end connection. If the owner’s designated representative for design can select the governing load combination for the connection, its effect alone should be provided. Otherwise, the effects of all appropriate load combinations should be indicated in tabular form. This approach will allow a clear understanding of all of the forces on any given joint. Because of the potential for overestimation—and underestimation—inherent in approximate methods, it is recommended that the actual reactions at the bracing member end (axial force and other reactions, if any) be indicated in the structural design drawings. It is also recommended that transfer forces, if any, be so indicated. The most effective method to do so may be by tabulation for each bracing member end and load combination.

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Although not recommended, bracing member end reactions can be specified by more general criteria, such as by maximum member forces (tension or compression) or as a function of the member strength. It should be noted, however, that there are several situations in which such approaches are not appropriate. For example: 1. The specification of maximum member forces does not permit a check of the member forces at a joint if there are different load combinations governing the member designs at that joint. Nor does it reflect the possibility of load reversal as it may influence the design. 2. The specification of a percentage of member strength may not properly account for the interaction of forces at a joint or the transfer force through the joint. Additionally, it may not allow for a cross-check of all forces at a joint. In either case, this approach will often result in heavier connections than would be required by the actual design loads. Bracing connections may involve the interaction of gravity and lateral loads on the frame. In some cases, such as V- and inverted V-bracing (also known as Chevron bracing), gravity loads alone may govern design of the braces and their connections. Thus, clarity in the specification of loads and reactions is critical to properly consider the potential interaction of gravity and lateral loads at floors and roofs.

Strut and Tie Connections Floor and roof members in braced bays and adjacent bays may function as struts or ties in addition to carrying gravity loads. Therefore the recommendations for simple shear connections and bracing connections above apply in combination.

Truss Connections The recommendations for horizontal and vertical bracing connections above also apply in general to bracing connections with the following additional comments. Note that it is not necessary to specify a minimum connection strength as a percent of the member strength as a default. However, when trusses are shop assembled or field assembled on the ground for subsequent erection, consideration should be given to the loads that will be induced during handling, shipping and erection.

Column Splices Column splices may resist moments, shears and tensions in addition to gravity forces. Typical column splices are discussed in Part 14. As in the case of the other connections discussed above, unless the column splices are fully designed in the construction documents, forces and moments for the splice designs should be provided in the construction documents. Since column splices are located away from the girder/column joint and moments vary in the height of the column, an accurate assessment of the forces and moments at the column splices will usually significantly reduce their cost and complexity.

CONSTRUCTABILITY Constructability is a relatively new word for a well established idea. The design, detailing, fabrication and erection of structural steel is a process which in the end needs to result in a safe and economical steel frame. Building codes and the AISC Specification address strength and AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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structural integrity. Constructability addresses the need for global economy in the fabricated and erected steel frame. Constructability must be “designed in,” influencing decision making at all steps of the design process, from framing system selection, though member design, to connection selection and design. Constructability demands attention to detail and requires the designer to think ahead to the fabrication and erection of the steel frame. The goal is to design a steel frame that is relatively easy to detail, fabricate and erect. AISC provides guidance to the design community through its many publications and presentations, including the recently published Design Guide 23, Constructability of Structural Steel Buildings (Ruby, 2008). Constructability focuses on such issues as framing layout, the number of pieces in an area of framing, three-dimensional connection geometry, swinging in clearances, access to bolts, and access to welds. It involves the acknowledgement that numerous, seemingly small decisions can have an effect on the overall economy of the final erected steel frame. Fabricators and erectors have the knowledge that can assist in the design of constructible steel frames. Designers should seek their counsel.

TOLERANCES The effects of mill, fabrication and erection tolerances all require consideration in the design and construction of structural steel buildings. However, the accumulation of the mill tolerances and fabrication tolerances shall not cause the erection tolerances to be exceeded, per AISC Code of Standard Practice Section 7.12.

Mill Tolerances Mill tolerances are those variations that could be present in the product as-delivered from the rolling mill. These tolerances are given as follows: 1. For structural shapes and plates, see ASTM A6. 2. For HSS, see ASTM A500 (or other applicable ASTM specification for HSS). 3. For pipe, see ASTM A53. A summary of standard mill practices is also given in Part 1.

Fabrication Tolerances Fabrication tolerances are generally provided in AISC Specification Section M2 and AISC Code of Standard Practice Section 6.4. Additional requirements that govern fabrication are as follows: 1. Compression joint fit-up, per AISC Specification Section M4.4 2. Roughness limits for finished surfaces, per AISC Code of Standard Practice Section 6.2.2 3. Straightness of projecting elements of connection materials, per AISC Code of Standard Practice Section 6.3.1 4. Finishing requirements at locations of removal of run-off tabs and similar devices, per AISC Code of Standard Practice Section 6.3.2

Erection Tolerances Erection tolerances are generally provided in AISC Specification Section M4 and AISC Code of Standard Practice Section 7.13. Note that the tolerances specified therein are AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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predicated upon the proper installation of the following items by the owner’s designated representative for construction: 1. 2. 3. 4.

Building lines and benchmarks, per AISC Code of Standard Practice Section 7.4 Anchorage devices, per AISC Code of Standard Practice Section 7.5 Bearing devices, per AISC Code of Standard Practice Section 7.6 Grout, per AISC Code of Standard Practice Section 7.7

Building Façade Tolerances The preceding mill, fabrication and erection tolerances can be maintained with standard equipment and workmanship. However, the accumulated tolerances for the structural steel and the building façade must be accounted for in the design so that the two systems can be properly mated in the field. In the steel frame, this is normally accomplished by specifying adjustable connections in the contract documents, per AISC Code of Standard Practice Section 7.13.1.3. This section has three subsections. Subsection (a) addresses the vertical position of the adjustable items, subsection (b) addresses the horizontal position of the adjustable items, and subsection (c) addresses alignment of adjustable items at abutting ends. The required adjustability normally can be determined from the range of adjustment in the building façade anchor connections, tolerances for the erection of the building façade, and the accumulation of mill, fabrication and erection tolerances at the mid-span point of the spandrel beam. The actual locations of the column bases, the actual slope of the columns and the actual sweep of the spandrel beam all affect the accumulation of tolerances in the structural steel at this critical location. These conditions must be reflected in details that will allow successful erection of the steel frame and the façade, if each of these systems is properly constructed within its permitted tolerance envelope. Figures 2-3a, 2-4a and 2-5a illustrate details that are not recommended because they do not provide for adjustment. Figures 2-3b, 2-4b and 2-5b illustrate recommended alternative details that do provide for adjustability. Note that diagonal structural and stability bracing elements have been omitted in these details to improve the clarity of presentation regarding adjustability. Also, note that all elements beyond the slab edge are normally not structural steel, per AISC Code of Standard Practice Section 2.2, and are shown for the purposes of illustration only. The bolted details in Figures 2-4b and 2-5b can be used to provide field adjustability with slotted holes as shown. Further adjustability can be provided in these details, if necessary, by removing the bolts and clamping the connection elements for field welding. Alternatively, when the slab edge angle or plate in Figure 2-4b is shown as field welded and identified as adjustable in the contract documents, it can be provided to within a horizontal tolerance of ± 3/8 in., per AISC Code of Standard Practice Section 7.13.1.3. However, if the item was not shown as field welded and identified as adjustable in the contract documents, it would likely be attached in the shop or attached in the field to facilitate the concrete pour and not be suitable to provide for the necessary adjustment. The details in Figures 2-3b and 2-4b do not readily permit vertical adjustment of the adjustable material. However, the vertical position tolerance of ± 3/8 in. is less than the tolerance for the position of the spandrel member itself, see AISC Code of Standard Practice Section 7.13.1.2(b). The manufacturing tolerance for camber in the spandrel member is set by ASTM A6, as summarized in Table 1-22. The ASTM A6 limit for camber is 1/8 in. per 10 ft of length, thus, in most situations AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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the vertical position tolerance in AISC Code of Standard Practice Section 7.13.1.3(b) should be achieved indirectly. In general, spandrel members should not be cambered. Deflection of spandrel members should be controlled by member stiffness. Figure 2-5b shows a detail in which both horizontal and vertical adjustment can be achieved. With adjustable connections specified in design and provided in fabrication, actions taken on the job site will allow for a successful façade installation. Per the AISC Code of Standard Practice definition of established column line (see Code of Standard Practice Glossary),

(a) Without adjustment (not recommended)

(b) With adjustment (recommended)

Fig. 2-3. Attaching cold-formed steel façade systems to structural steel framing.

(a) Without adjustment (not recommended)

(b) With adjustment (recommended)

Fig. 2-4. Attaching curtain wall façade systems to structural steel framing. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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(a) Without adjustment (not recommended)

(b) With adjustment (recommended)

Fig. 2-5. Attaching masonry façade systems to structural steel framing.

proper placement of this line by the owner’s designated representative for construction based upon the actual column-center locations will assure that all subcontractors are working from the same information. When sufficient adjustment cannot be accommodated within the adjustable connections provided, a common solution is to allow the building façade to deviate (or drift) from the theoretical location to follow the as-built locations of the structural steel framing and concrete floor slabs. A survey of the as-built locations of these elements can be used to adjust the placement of the building façade accordingly. In this case, the adjustable connections can serve to ensure that no abrupt changes occur in the façade.

QUALITY CONTROL AND QUALITY ASSURANCE Prior to 2010, quality control and quality assurance were addressed in the contract documents, Chapter M of the AISC Specification, and building codes. In the 2010 AISC Specification, Chapter N, entitled Quality Control and Quality Assurance, has been added. This chapter distinguishes between quality control, which is the responsibility of the fabricator and erector, and quality assurance, which is the responsibility of the owner, usually through third party inspectors. The new provisions bring together requirements from diverse sources of quality control (QC) and quality assurance (QA), so that plans for QC and QA can be established on a project specific basis. Chapter N provides tabulated lists of inspection tasks for both QC and QA. As in the case of the AISC Seismic Provisions, these tasks are characterized as either “observe” or “perform.” Tasks identified as “observe” are general and random. Tasks identified as “perform” are specific to the final acceptance of an item in the work. The characterization of tasks as observe and perform is a substitute for the AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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distinction between periodic and continuous inspection used in other codes and standards, such as the International Building Code.

CAMBERING, CURVING AND STRAIGHTENING Beam Camber and Sweep Camber denotes a curve in the vertical plane. Sweep denotes a curve in the horizontal plane. Camber and sweep occur naturally in members as received from the mill. The deviation of the member from straight must be within the mill tolerances specified in ASTM A6/A6M. When required by the contract documents, cambering and curving to a specified amount can be provided by the fabricator per AISC Code of Standard Practice Sections 6.4.2 and 6.4.4, either by cold bending or by hot bending. Cambering and curving induce residual stresses similar to those that develop in rolled structural shapes as elements of the shape cool from the rolling temperature at different rates. These residual stresses do not affect the available strength of structural members, since the effect of residual stresses is considered in the provisions of the AISC Specification.

Cold Bending The inelastic deformations required in common cold bending operations, such as for beam cambering, normally fall well short of the strain-hardening range. Specific limitations on cold-bending capabilities should be obtained from those that provide the service and from Cold Bending of Wide-Flange Shapes for Construction (Bjorhovde, 2006). However, the following general guidelines may be useful in the absence of other information: 1. The minimum radius for camber induced by cold bending in members up to a nominal depth of 30 in. is between 10 and 14 times the depth of the member. Deeper members may require a larger minimum radius. 2. Cold bending may be used to provide curving in members to practically any radius desired. 3. A minimum length of 25 ft is commonly practical due to manufacturing/fabrication equipment. When curvatures and the resulting inelastic deformations are significant and corrective measures are required, the effects of cold work on the strength and ductility of the structural steels largely can be eliminated by thermal stress relief or annealing.

Hot Bending The controlled application of heat can be used in the shop and field to provide camber or curvature. The member is rapidly heated in selected areas that tend to expand, but are restrained by the adjacent cooler areas, causing inelastic deformations in the heated areas and a change in the shape of the cooled member. The mechanical properties of steels are largely unaffected by such heating operations, provided the maximum temperature does not exceed the temperature limitations given in AISC Specification Section M2.1. Temperature-indicating crayons or other suitable means should be used during the heating process to ensure proper regulation of the temperature. Heat curving induces residual stresses that are similar to those that develop in hot-rolled structural shapes as they cool from the rolling temperature because all parts of the shape do not cool at the same rate. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Truss Camber Camber is provided in trusses, when required, by the fabricator per AISC Code of Standard Practice Section 6.4.5, by geometric relocation of panel points and adjustment of member lengths based upon the camber requirements as specified in the contract documents.

Straightening All structural shapes are straightened at the mill after rolling, either by rotary or gag straightening, to meet the aforementioned mill tolerances. Similar processes and/or the controlled application of heat can be used in the shop or field to straighten a curved or distorted member. These processes are normally applied in a manner similar to those used to induce camber and curvature and described above.

FIRE PROTECTION AND ENGINEERING Provisions for structural design for fire conditions are found in Appendix 4 of the AISC Specification. Complete coverage of fire protection and engineering for steel structures is included in AISC Design Guide 19, Fire Resistance of Structural Steel Framing (Ruddy et al., 2003).

CORROSION PROTECTION In building structures, corrosion protection is not required for steel that will be enclosed by building finish, coated with a contact-type fireproofing, or in contact with concrete. When enclosed, the steel is trapped in a controlled environment and the products required for corrosion are quickly exhausted, as indicated in AISC Specification Commentary Section M3. A similar situation exists when steel is fireproofed or in contact with concrete. Accordingly, shop primer or paint is not required unless specified in the contract documents, per AISC Specification Section M3.1. Per AISC Code of Standard Practice Section 6.5, steel that is to remain unpainted need only be cleaned of heavy deposits of oil and grease by appropriate means after fabrication. Corrosion protection is required, however, in exterior exposed applications. Likewise, steel must be protected from corrosion in aggressively corrosive applications, such as a paper processing plant, a structure with oceanfront exposure, or when temperature changes can cause condensation. Corrosion should also be considered when connecting steel to dissimilar metals. Guidance on steel compatibility with metal fasteners is provided in Table 2-7. When surface preparation other than the cleaning described above is required, an appropriate grade of cleaning should be specified in the contract documents according to the Society for Protective Coatings (SSPC). A summary of the SSPC surface preparation specifications (SSPC, 2000) is provided in Table 2-8. SSPC SP 2 is the normal grade of cleaning when cleaning is required. For further information, refer to the publications of SSPC, the American Galvanizers Association (AGA), and the National Association of Corrosion Engineers International (NACE).

RENOVATION AND RETROFIT OF EXISTING STRUCTURES The provisions in AISC Specification Section B6 govern the evaluation of existing structures. Historical data on available steel grades and hot-rolled structural shapes, including AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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dimensions and properties, is available in AISC Design Guide 15, Rehabilitation and Retrofit Guide (Brockenbrough, 2002) and the companion database of historic shape properties from 1873-1999 available at www.aisc.org. See also Ricker (1988) and Tide (1990).

THERMAL EFFECTS Expansion and Contraction The average coefficient of expansion, ε, for structural steel between 70 °F and 100 °F is 0.0000065 for each °F (Camp et al., 1951). This value is a reasonable approximation of the coefficient of thermal expansion for temperatures less than 70 °F. For temperatures from 100 to 1, 200 °F, the change in length per unit length per °F, ε, is: ε = (6.1 + 0.0019t)10-6

(2-9)

where t is the initial temperature in °F. The coefficients of expansion for other building materials can be found in Table 17-11. Although buildings are typically constructed of flexible materials, expansion joints are often required in roofs and the supporting structure when horizontal dimensions are large. The maximum distance between expansion joints is dependent upon many variables, including ambient temperature during construction and the expected temperature range during the lifetime of the building. Figure 2-6 (Federal Construction Council, 1974) provides guidance based on design temperature change for maximum spacing of structural expansion joints in beam-andcolumn-framed buildings with pinned column bases and heated interiors. The report includes data for numerous cities and gives five modification factors to be applied as appropriate:

Fig. 2-6. Recommended maximum expansion-joint spacing. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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1. If the building will be heated only and will have pinned column bases, use the maximum spacing as specified. 2. If the building will be air-conditioned as well as heated, increase the maximum spacing by 15% provided the environmental control system will run continuously. 3. If the building will be unheated, decrease the maximum spacing by 33%. 4. If the building will have fixed column bases, decrease the maximum spacing by 15%. 5. If the building will have substantially greater stiffness against lateral displacement in one of the plan dimensions, decrease the maximum spacing by 25%. When more than one of these design conditions prevail in a building, the percentile factor to be applied is the algebraic sum of the adjustment factors of all the various applicable conditions. Most building codes include restrictions on location and maximum spacing of fire walls, which often become default locations for expansion joints. The most effective expansion joint is a double line of columns that provides a complete and positive separation. Alternatively, low-friction sliding elements can be used. Such systems, however, are seldom totally friction-free and will induce some level of inherent restraint to movement.

Elevated-Temperature Service For applications involving short-duration loading at elevated temperature, the variations in yield strength, tensile strength, and modulus of elasticity are given in AISC Design Guide 19, Fire Resistance of Structural Steel Framing (Ruddy et al., 2003). For applications involving long-duration loading at elevated temperatures, the effects of creep must also be considered. For further information, see Brockenbrough and Merritt (1999; pp. 1.20–1.22).

FATIGUE AND FRACTURE CONTROL Avoiding Brittle Fracture By definition, brittle fracture occurs by cleavage at a stress level below the yield strength. Generally, a brittle fracture can occur when there is a sufficiently adverse combination of tensile stress, temperature, strain rate and geometrical discontinuity (notch). The exact combination of these conditions and other factors that will cause brittle fracture cannot be readily calculated. Consequently, the best guide in selecting steel material that is appropriate for a given application is experience. The steels listed in AISC Specification Section A3.1a, Section A3.1c and Section A3.1d have been successfully used in a great number of applications, including buildings, bridges, transmission towers and transportation equipment, even at the lowest atmospheric temperatures encountered in the United States. Nonetheless, it is desirable to minimize the conditions that tend to cause brittle fracture: triaxial state-of-stress, increased strain rate, strain aging, stress risers, welding residual stresses, areas of reduced notch toughness, and low-temperature service. 1. Triaxial state-of-stress: While shear stresses are always present in a uniaxial or biaxial state-of-stress, the maximum shear stress approaches zero as the principal stresses approach a common value in a triaxial state-of-stress. A triaxial state-of-stress can also result from uniaxial loading when notches or geometrical discontinuities are present. A triaxial state-of-stress will cause the yield stress of the material to increase above its AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2.

3.

4.

5.

6.

7.

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nominal value, resulting in brittle fracture by cleavage, rather than ductile shear deformations. As a result, in the absence of critical-size notches, the maximum stress is limited by the yield stress of the nearby unaffected material. Triaxial stress conditions should be avoided, when possible. Increased strain rate: Gravity loads, wind loads and seismic loads have essentially similar strain rates. Impact loads, such as those associated with heavy cranes, and blast loads normally have increased strain rates, which tend to increase the possibility of brittle fracture. Note, however, that a rapid strain rate or impact load is not a required condition for the occurrence of brittle fracture. Strain aging: Cold working of steel and the strain aging that normally results generally increases the likelihood of brittle fracture, usually due to a reduction in ductility and notch toughness. The effects of cold work and strain aging can be minimized by selecting a generous forming radius to eliminate or minimize strain hardening. Stress risers: Fabrication operations, such as flame cutting and welding, may induce geometric conditions or discontinuities that are crack-like in nature, creating stress risers. Intersecting welds from multiple directions should be avoided with properly sized weld access holes to minimize the interaction of these various stress fields. Such conditions should be avoided, when possible, or removed or repaired when they occur. Welding residual stresses: In the as-welded condition, residual stresses near the yield strength of the material will be present in any weldment. Residual stresses and the possible accompanying distortions can be minimized through controlled welding procedures and fabrication methods, including the proper positioning of the components of the joint prior to welding, the selection of welding sequences that will minimize distortions, the use of preheat as appropriate, the deposition of a minimum volume of weld metal with a minimum number of passes for the design condition, and proper control of interpass temperatures and cooling rates. In fracture-sensitive applications, notch-toughness should be specified for both the base metal and the filler metal. Areas of reduced notch toughness: Such areas can be found in the core areas of heavy shapes and plates and the k-area of rotary-straightened W-shapes. Accordingly, AISC Specification Sections A3.1c and Section A3.1d include special requirements for material notch toughness. Low-temperature service: While steel yield strength, tensile strength, modulus of elasticity, and fatigue strength increase as temperature decreases, ductility and toughness decrease. Furthermore, there is a temperature below which steel subjected to tensile stress may fracture by cleavage, with little or no plastic deformation, rather than by shear, which is usually preceded by considerable inelastic deformation. Note that cleavage and shear are used in the metallurgical sense to denote different fracture mechanisms.

When notch-toughness is important, Charpy V-notch testing can be specified to ensure a certain level of energy absorption at a given temperature, such as 15 ft-lb at 70 °F. Note that the appropriate test temperature may be higher than the lowest operating temperature depending upon the rate of loading. Although it is primarily intended for bridge-related applications, the information in ASTM A709 Section S83 (including Tables S1.1, S1.2 and S1.3) may be useful in determining the proper level of notch toughness that should be specified. In many cases, weld metal notch toughness exceeds that of the base metal. Filler metals can be selected to meet a desired minimum notch-toughness value. For each welding AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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process, electrodes exist that have no specified notch toughness requirements. Such electrodes should not be assumed to possess any minimum notch-toughness value. When notch toughness is necessary for a given application, the desired value or an appropriate electrode should be specified in the contract documents. For further information, refer to Fisher et al. (1998), Barsom and Rolfe (1999), and Rolfe (1977).

Avoiding Lamellar Tearing Although lamellar tearing is less common today, the restraint against solidified weld deposit contraction inherent in some joint configurations can impose a tensile strain high enough to cause separation or tearing on planes parallel to the rolled surface of the element being joined. The incidence of this phenomenon can be reduced or eliminated through greater understanding by designers, detailers and fabricators of the inherent directionality of rolled steel, the importance of strains associated with solidified weld deposit contraction in the presence of high restraint (rather than externally applied design forces), and the need to adopt appropriate joint and welding details and procedures with proper weld metal for through-thickness connections. Dexter and Melendrez (2000) demonstrate that W-shapes are not susceptible to lamellar tearing or other through-thickness failures when welded tee joints are made to the flanges at locations away from member ends. When needed for other conditions, special production practices can be specified for steel plates to assist in reducing the incidence of lamellar tearing by enhancing through-thickness ductility. For further information, refer to ASTM A770. However, it must be recognized that it is more important and effective to properly design, detail and fabricate to avoid highly restrained joints. AISC (1973) provides guidelines that minimize potential problems.

WIND AND SEISMIC DESIGN In general, nearly all building design and construction can be classified into one of two categories: wind and low-seismic applications, and high-seismic applications. For additional discussion regarding seismic design and the applicability of the AISC Seismic Provisions, see the Scope statement at the front of this manual.

Wind and Low-Seismic Applications Wind and low-seismic applications are those in which the AISC Seismic Provisions are not applicable. Such buildings are designed to meet the provisions in the AISC Specification based upon the code-specified forces distributed throughout the framing assuming a nominally elastic structural response. The resulting systems have normal levels of ductility. It is important to note that the applicable building code includes seismic design requirements even if the AISC Seismic Provisions are not applicable. See the AISC Seismic Design Manual for additional discussion.

High-Seismic Applications High-seismic applications are those in which the building is designed to meet the provisions in both the AISC Seismic Provisions and the AISC Specification. Note that it does not matter if wind or earthquake controls in this case. High-seismic design and construction will AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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generally cost more than wind and low-seismic design and construction, as the resulting systems are designed to have high levels of ductility. High-seismic lateral framing systems are configured to be capable of withstanding strong ground motions as they undergo controlled ductile deformations to dissipate energy. Consider the following three examples: 1. Special Concentrically Braced Frames (SCBF)—SCBF are generally configured so that any inelasticity will occur by tension yielding and/or compression buckling in the braces. The connections of the braces to the columns and beams and between the columns and beams themselves must then be proportioned to remain nominally elastic as they undergo these deformations. 2. Eccentrically Braced Frames (EBF)—EBF are generally configured so that any inelasticity will occur by shear yielding and/or flexural yielding in the link. The beam outside the link, connections, braces and columns must then be proportioned to remain nominally elastic as they undergo these deformations. 3. Special Moment Frames (SMF)—SMF are generally configured so that any inelasticity will occur by flexural yielding in the girders near, but away from, the connection of the girders to the columns. The connections of the girders to the columns and the columns themselves must then be proportioned to remain nominally elastic as they undergo these deformations. Intermediate moment frames (IMF) and ordinary moment frames (OMF) are also configured to provide improved seismic performance, although successively lower than that for SMF. The code-specified base accelerations used to calculate the seismic forces are not necessarily maximums, but rather, they represent the intensity of ground motions that have been selected by the code-writing authorities as reasonable for design purposes. Accordingly, the requirements in both the AISC Seismic Provisions and the AISC Specification must be met so that the resulting frames can then undergo controlled deformations in a ductile, welldistributed manner. The design provisions for high-seismic systems are also intended to result in distributed deformations throughout the frame, rather than the formation of story mechanisms, so as to increase the level of available energy dissipation and corresponding level of ground motion that can be withstood. The member sizes in high-seismic frames will be larger than those in wind and lowseismic frames. The connections will also be much more robust so they can transmit the member-strength-driven force demands. Net sections will often require special attention so as to avoid having fracture limit states control. Special material requirements, design considerations and construction practices must be followed. For further information on the design and construction of high-seismic systems, see the AISC Seismic Provisions, which are available at www.aisc.org.

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PART 2 REFERENCES Much of the material referenced in the Steel Construction Manual may be found at www.aisc.org. ACI (2008), Building Code Requirements for Structural Concrete and Commentary, ACI 318, American Concrete Institute, Farmington Hills, MI. Allison, H. (1991), Low- and Medium-Rise Steel Buildings, Design Guide 5, AISC, Chicago, IL. AISC (1973), “Commentary on Highly Restrained Welded Connections,” Engineering Journal, Vol. 10, No. 3, 3rd Quarter, American Institute of Steel Construction, Chicago, IL. AISC (2005), Specification for Structural Steel Buildings, ANSI/AISC 360-05, American Institute of Steel Construction, Chicago, IL. AISC (2006), Seismic Design Manual, American Institute of Steel Construction, Chicago, IL. AISC (2009), Detailing for Steel Construction, 3rd Ed., American Institute of Steel Construction, Chicago, IL. AISC (2010a), Specification for Structural Steel Buildings, ANSI/AISC 360-10, American Institute of Steel Construction, Chicago, IL. AISC (2010b), Seismic Provisions for Structural Steel Buildings, AISI/AISC 341-10, American Institute of Steel Construction, Chicago, IL. AISC (2010c), Code of Standard Practice for Steel Buildings and Bridges, American Institute of Steel Construction, Chicago, IL. AISC (2011), Design Examples, V. 14.0, American Institute of Steel Construction, Chicago, IL. ASCE (2010), Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 7-10, American Society of Civil Engineers, Reston, VA. AWS (2007), Standard Symbols for Welding, Brazing, and Nondestructive Examination, AWS A2.4, American Welding Society, Miami, FL. AWS (2010), Structural Welding Code—Steel, AWS D1.1:2010, American Welding Society, Miami, FL. Barger, B.L. and West, M.A. (2001), “New OSHA Erection Rules: How They Affect Engineers, Fabricators and Contractors,” Modern Steel Construction, May, AISC, Chicago, IL. Barsom, J.A. and Rolfe, S.T. (1999), Fracture and Fatigue Control in Structures: Applications of Fracture Mechanics, 3rd Edition, ASTM, West Conshohocken, PA. Bjorhovde, R, (2006), “Cold Bending of Wide-Flange Shapes for Construction,” Engineering Journal, AISC, Vol. 43, No. 4, 4th Quarter, Chicago, IL, pp 271-286. Brockenbrough, R.L. and Merritt, F.S. (1999), Structural Steel Designer’s Handbook, 3rd Edition, McGraw-Hill, New York, NY. Brockenbrough, R.L. (2002), AISC Rehabilitation and Retrofit Guide—A Reference for Historic Shapes and Specifications, Design Guide 15, AISC, Chicago, IL. Camp, J.M., Francis, C.B. and McGannon H.E. (1951), The Making, Shaping and Treating of Steel, 6th Edition, U.S. Steel, Pittsburgh, PA. Carter, C.J. (1999), Stiffening of Wide-Flange Columns at Moment Connections: Wind and Seismic Applications, Design Guide 13, AISC, Chicago, IL. CASE (2003), A Guideline Addressing Coordination and Completeness of Structural Construction Documents, Document 962D, Council of American Structural Engineers.

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Churches, C.H., Troup, E.W.J. and Angeloff, C. (2003), Steel-Framed Open-Deck Parking Structures, Design Guide 18, AISC, Chicago, IL. CISC (1989), Roof Framing with Cantilever (Gerber) Girders & Open Web Joists, Canadian Institute of Steel Construction, Willowdale, Ontario, Canada. Darwin, D. (1990), Steel and Composite Beams with Web Openings, Design Guide 2, AISC, Chicago, IL. Dexter, R.J. and Melendrez, M.I. (2000), “Through-Thickness Properties of Column Flanges in Welded Moment Connections,” Journal of Structural Engineering, ASCE, Vol. 126, No. 1, pp. 24–31. DOD (2009), Design of Buildings to Resist Progressive Collapse, UFC 4-023-03, July. Federal Construction Council (1974), Technical Report No. 65 Expansion Joints in Buildings, National Research Council, Washington, DC. Fisher, J.M. and West, M.A. (1997), Erection Bracing of Low-Rise Structural Steel Buildings, Design Guide 10, AISC, Chicago, IL. Fisher, J.M. (2004), Industrial Buildings—Roofs to Anchor Rods, Design Guide 7, 2nd Ed., AISC, Chicago, IL. Fisher, J.M. and Kloiber, L.A. (2006), Base Plate and Anchor Rod Design, Design Guide 1, 2nd Ed., AISC, Chicago, IL. Fisher, J.W., Kulak, G.L. and Smith, I.F.C. (1998), A Fatigue Primer for Structural Engineers, NSBA/AISC, Chicago, IL. Geschwindner, L.F. and Gustafson, K. (2010), “Single-Plate Shear Connection Design to meet Structural Integrity Requirements,” Engineering Journal, AISC, Vol. 47, No. 3, 3rd Quarter, pp. 189–202. Griffis, L.G. (1992), Load and Resistance Factor Design of W-Shapes Encased in Concrete, Design Guide 6, AISC, Chicago, IL. Gross, J.L., Engelhardt, M.D., Uang, C.M., Kasai, K. and Iwankiw, N.R. (1999), Modification of Existing Welded Steel Moment Frame Connections for Seismic Resistance, Design Guide 12, AISC, Chicago, IL. ICC (2009), International Building Code, International Code Council, Falls Church, VA. Kaehler, R.C., White, D.W. and Kim, Y.K. (2010), Web-Tapered Frame Design, Design Guide 25, AISC, Chicago, IL. Kulak, G.L. (2002), High Strength Bolts—A Primer for Structural Engineers, Design Guide 17, AISC, Chicago, IL. Leon, R.T., Hoffman, J.J. and Staeger, T. (1996), Partially Restrained Composite Connections, Design Guide 8, AISC, Chicago, IL. Miller, D.K. (2006), Welded Connections—A Primer for Engineers, Design Guide 21, AISC, Chicago, IL. Murray, T.M. and Sumner, E.A. (2003), Extended End-Plate Moment Connections—Seismic and Wind Applications, Design Guide 4, 2nd Ed., AISC, Chicago, IL. Murray, T.M., Allen, D.E. and Ungar, E.E. (1997), Floor Vibrations Due to Human Activity, Design Guide 11, AISC, Chicago, IL. Murray, T.M. and Shoemaker, W.L. (2002), Flush and Extended Multiple-Row Moment End-Plate Connections, Design Guide 16, AISC, Chicago, IL. OSHA (2001), Safety and Health Standards for the Construction Industry, 29 CFR 1926 Part R Safety Standards for Steel Erection, Occupational Safety and Health Administration, Washington, DC.

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Packer, J., Sherman, D. and Leece, M. (2010), Hollow Structural Section Connections, Design Guide 24, AISC, Chicago, IL. Parker, J.C. (2008), Façade Attachments to Steel-Framed Buildings, Design Guide 22, AISC, Chicago, IL. RCSC (2009), Specification for Structural Joints Using High-Strength Bolts, Research Council on Structural Connections, Chicago, IL. Ricker, D.T. (1988), “Field Welding to Existing Structures,” Engineering Journal, AISC, Vol. 25, No. 1, 1st Quarter, pp. 1–16. Rolfe, S.T. (1977), “Fracture and Fatigue Control in Steel Structures,” Engineering Journal, AISC, Vol. 14, No. 1, 1st Quarter, pp. 2–15. Rongoe, J. (1996), “Design Guidelines for Continuous Beams Supporting Steel Joist Roof Structures,” Proceedings of the AISC National Steel Construction Conference, pp. 23.1–23.44, AISC, Chicago, IL. Ruby, D.I. (2008), Constructability of Structural Steel Buildings, Design Guide 23, AISC, Chicago, IL. Ruddy, J.L. (1986), “Ponding of Concrete Deck Floors,” Engineering Journal, AISC, Vol. 23, No. 3, 3rd Quarter, pp. 107–115. Ruddy, J.L., Marlo, J.P., Ioannides, S.A and Alfawakhiri, F. (2003), Fire Resistance of Structural Steel Framing, Design Guide 19, AISC, Chicago, IL. Sabelli, R. and Bruneau, M. (2006), Steel Plate Shear Walls, Design Guide 20, AISC, Chicago, IL. Seaburg, P.A. and Carter, C.J. (1997), Torsional Analysis of Structural Steel Members, Design Guide 9, AISC, Chicago, IL. SSPC (2000), Systems and Specifications: SSPC Painting Manual, Volume II, 8th Edition, The Society for Protective Coatings, Pittsburgh, PA. Thornton, W.A. (1995), “Connections: Art, Science, and Information in the Quest for Economy and Safety,” Engineering Journal, AISC, Vol 32, No. 4, 4th Quarter, pp. 132–144. Tide, R.H.R. (1990), “Reinforcing Steel Members and the Effects of Welding,” Engineering Journal, AISC, Vol. 27, No. 4, 4th Quarter, pp. 129–131. USGSA (2003), “Progressive Collapse Analysis and Design Guidelines for New Federal Office Buildings and Major Modernization Projects,” U.S. General Services Administration, Washington, DC. West, M.A., Fisher, J.M. and Griffis, L.G. (2003), Serviceability Design Considerations for Steel Buildings, Design Guide 3, 2nd Ed., AISC, Chicago, IL. Wexler, N. and Lin, F.B. (2002), Staggered Truss Framing Systems, Design Guide 14, AISC, Chicago, IL.

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TABLES FOR THE GENERAL DESIGN AND SPECIFICATION OF MATERIALS

Table 2-2

Summary Comparison of Methods for Stability Analysis and Design Direct Analysis Method

Effective Length Method

None

Δ2nd /Δ1st ≤ 1.5

Limitations on Usea

First-Order Analysis Method

Δ2nd /Δ1st ≤ 1.5 α Pr /Py ≤ 0.5

Second-order elasticb

Analysis Type Geometry of Structure

First-order elastic

All three methods use the undeformed geometry in the analysis.

Minimum or Additional Lateral Loads Required in the Analysis

Minimum;c 0.2% of the story gravity load

Minimum; 0.2% of the story gravity load

Additive; at least 0.42% of the story gravity load

Member Stiffnesses Used in the Analysis

Reduced EA and EI

Design of Columns

K = 1 for all frames

K = 1 for braced frames. For moment frames, determine K from sidesway buckling analysisd

K = 1 for all framese

Chapter C

Appendix Section 7.2

Appendix Section 7.3

Specification Reference for Method a

b

c d e

Nominal EA and EI

Δ2nd ⁄Δ1st is the ratio of second-order drift to first-order drift, which can be taken to be equal to B2 calculated per Appendix 8. Δ2nd ⁄Δ1st is determined using LRFD load combinations or a multiple of 1.6 times ASD load combinations. Either a general second-order analysis method or second-order analysis by amplified first-order analysis (the “B1-B2 method” described in Appendix 8) can be used. This notional load is additive if Δ2nd ⁄Δ1st >1.5. K = 1 is permitted for moment frames when Δ2nd ⁄Δ1st ≤1.1. An additional amplification for member curvature effects is required for columns in moment frames.

Table 2-3

AISI Standard Nomenclature for Flat-Rolled Carbon Steel Width, in. 1

Thickness, in.

To 3 1⁄2 incl.

Over 3 ⁄2 To 6

Over 6 To 8

Over 8 To 12

Over 12 To 48

Over 48

0.2300 & thicker

Bar

Bar

Bar

Plate

Plate

Plate

0.2299 to 0.2031

Bar

Bar

Strip

Strip

Sheet

Plate

0.2030 to 0.1800

Strip

Strip

Strip

Strip

Sheet

Plate

0.1799 to 0.0449

Strip

Strip

Strip

Strip

Sheet

Sheet

0.0448 to 0.0344

Strip

Strip

0.0343 to 0.0255

Strip

0.0254 & thinner

Hot-rolled sheet and strip not generally produced in these widths and thicknesses

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Table 2-4

Applicable ASTM Specifications for Various Structural Shapes ASTM Designation A36

36 35

60

42

58

46

58

Gr. B Carbon

Gr. C A501 A529c

A572

HighStrength LowAlloy

A618f

Corrosion Resistant HighStrength Low-Alloy

46

62

50

62 58

Gr. A

36 50

70

Gr. 50

50

65-100

Gr. 55

55

70-100

Gr. 42

42

60

Gr. 50

50

65 d

Gr. 55

55

70

Gr. 60e

60

75

Gr. 65e

65

80

Gr. I & II

50g

70 g

Gr. III

50

65

50

50h

60 h

60

60

75

65

65

80

70

70

90

50

65 i

42j

63 j

46k

67 k

l

50

70 l

A588

50

70

A847

50

70

A992 A242

W

M

S

HP

C

MC

L

Rect.

Pipe

58-80

Gr. B

A913

HSS

b

A53 Gr. B

A500

Applicable Shape Series Round

Steel Type

Fy Min. Fu Yield Tensile Stress Stressa (ksi) (ksi)

= Preferred material specification = Other applicable material specification, the availability of which should be confirmed prior to specification = Material specification does not apply a b c

d e f g h

i j k l

Minimum unless a range is shown. For shapes over 426 lb/ft, only the minimum of 58 ksi applies. For shapes with a flange thickness less than or equal to 11⁄2 in. only. To improve weldability, a maximum carbon equivalent can be specified (per ASTM Supplementary Requirement S78). If desired, maximum tensile stress of 90 ksi can be specified (per ASTM Supplementary Requirement S79). If desired, maximum tensile stress of 70 ksi can be specified (per ASTM Supplementary Requirement S81). For shapes with a flange thickness less than or equal to 2 in. only. ASTM A618 can also be specified as corrosion-resistant; see ASTM A618. Minimum applies for walls nominally 3⁄4-in. thick and under. For wall thicknesses over 3⁄4 in., Fy = 46 ksi and Fu = 67 ksi. If desired, maximum yield stress of 65 ksi and maximum yield-to-tensile strength ratio of 0.85 can be specified (per ASTM Supplementary Requirement S75). A maximum yield-to-tensile strength ratio of 0.85 and carbon equivalent formula are included as mandatory in ASTM A992. For shapes with a flange thickness greater than 2 in. only. For shapes with a flange thickness greater than 11⁄2 in. and less than or equal to 2 in. only. For shapes with a flange thickness less than or equal to 11⁄2 in. only.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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TABLES FOR THE GENERAL DESIGN AND SPECIFICATION OF MATERIALS

2–49

Table 2-5

Applicable ASTM Specifications for Plates and Bars

Steel Type

ASTM Designation A36

Carbon A529

HighStrength LowAlloy

A572

Gr. 50

32

58-80

36

58-80

50

70-100

b

b

b

b

Gr. 55

55

70-100

Gr. 42

42

60

Gr. 50

50

65

Gr. 55

55

70

Gr. 60

60

75

Gr. 65 Corrosion Resistant HighStrength Low-Alloy

Thickness of Plates and Bars, in. Fy Min. Fu over over over over over over over over Yield Tensile to 0.75 1.25 1.5 2 to 2.5 4 to 5 to 6 to Stress Stressa 0.75 to to to 2 2.5 to 4 5 6 8 over (ksi) (ksi) incl. 1.25 1.5 incl. incl. incl. incl. incl. incl. 8

A242

A588

Quenched and Tempered Alloy

A514c

Quenched and Tempered Low-Alloy

A852c

65

80

42

63

46

67

50

70

42

63

46

67

50

70

90

100-130

100

110-130

70

90-110

b

b

= Preferred material specification = Other applicable material specification, the availability of which should be confirmed prior to specification = Material specification does not apply a b c

Minimum unless a range is shown. Applicable to bars only above 1-in. thickness. Available as plates only.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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GENERAL DESIGN CONSIDERATIONS

Table 2-6

Applicable ASTM Specifications for Various Types of Structural Fasteners

A108 d

A325

A490d F1852d F2280d A194 Gr. 2H A563 F436b F959 A36 A193 Gr. B7e A307 Gr. A A354 Gr. BD

A449

A572

Gr. 42 Gr. 50 Gr. 55 Gr. 60 Gr. 65

A588 A687 F1554 Gr. 36 Gr. 55 Gr. 105

— — — — — — — — — — — 36 — — — — — — — — — 42 50 55 60 65 42 46 50 105 36 55 105

65 0.375 to 0.75, incl. 105 over 1 to 1.5, incl. 120 0.5 to 1, incl. 150 0.5 to 1.5 105 1.125 120 0.5 to 1, incl. 150 0.5 to 1.125, incl. — 0.25 to 4 — 0.25 to 4 — 0.25 to 4 — 0.5 to 1.5 58-80 to 10 100 over 4 to 7 115 over 2.5 to 4 125 2.5 and under 60 0.25 to 4 140 2.5 to 4, incl. 150 0.25 to 2.5, incl. 90 1.75 to 3, incl. 105 1.125 to 1.5, incl. 120 0.25 to 1, incl. 60 to 6 65 to 4 70 to 2 75 to 1.25 80 to 1.25 63 Over 5 to 8, incl. 67 Over 4 to 5, incl. 70 4 and under 150 max. 0.625 to 3 58-80 0.25 to 4 75-95 0.25 to 4 125-150 0.25 to 3

Threaded & Nutted

Headed

Hooked

Steel Headed Stud Anchors

Threaded Rods

Direct-TensionIndicator Washers

Washers

Nuts

Anchor Rods Common Bolts

Twist-Off-Type Tension-Control

ASTM Designation

Fy Min. Fu Yield Tensile Stress Stressa Diameter Range (ksi) (ksi) (in.)

Conventional

HighStrength Bolts

c c c

= Preferred material specification = Other applicable material specification, the availability of which should be confirmed prior to specification = Material specification does not apply — Indicates that a value is not specified in the material specification. a Minimum unless a range is shown or maximum (max.) is indicated. b Special washer requirements may apply per RCSC Specification Table 6.1 for some steel-to-steel bolting applications and per Part 14 for anchor-rod applications. c See AISC Specification Section J3.1 for limitations on use of ASTM A449 bolts. d When atmospheric corrosion resistance is desired, Type 3 can be specified. e For anchor rods with temperature and corrosion resistance characteristics.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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TABLES FOR THE GENERAL DESIGN AND SPECIFICATION OF MATERIALS

Table 2-7

Metal Fastener Compatibility to Resist Corrosion Fastener Metal

Base Metal Zinc and Galvanized Steel Aluminum and Aluminum Alloys Steel and Cast Iron

Martensitic Stainless Steel (Type 410)

Austenitic Stainless Steel (Type 302/304, 303, 305)

C

C

C B

Zinc and Galvanized Steel

Aluminum and Aluminum Alloys

Steel and Cast Iron

Brasses, Copper, Bronzes, Monel

A

B

B

A

A

B

C

Not Recommended

A, D

A

A

C

C

B

Terne (Lead-Tin) Plated Steel Sheets

A, D, E

A, E

A, E

C

C

B

Brasses, Copper, Bronzes, Monel

A, D, E

A, E

A, E

A

A

B

Ferritic Stainless Steel (Type 430)

A, D, E

A, E

A, E

A

A

A

Austenitic Stainless Steel (Type 302/304)

A, D, E

A, E

A, E

A, E

A

A

KEY A. B. C. D. E.

The corrosion of the base metal is not increased by the fastener. The corrosion of the base metal is marginally increased by the fastener. The corrosion of the base metal may be markedly increased by the fastener material. The plating on the fastener is rapidly consumed, leaving the bare fastener metal. The corrosion of the fastener is increased by the base metal.

NOTE: Surface treatment and environment can change activity. For a more thorough understanding of metal corrosion in construction materials, please consult a full listing of the galvanic series of metals and alloys. Note: Reprinted from the Specialty Steel Industry of North America Stainless Steel Fasteners Designer’s Handbook.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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GENERAL DESIGN CONSIDERATIONS

Table 2-8

Summary of Surface Preparation Specifications SSPC Specification No.

Title

Description

SP1

Solvent Cleaning

Removal of oil, grease, dirt, soil, salts and contaminants by cleaning with solvent, vapor, alkali, emulson or steam.

SP2

Hand-Tool Cleaning

Removal of all loose rust, loose mill scale and loose paint to degree specified, by hand-chipping, scraping, sanding and wire brushing.

SP3

Power-Tool Cleaning

Removal of all loose rust, loose mill scale and loose paint to degree specified, by power-tool chipping, descaling, sanding, wire brushing, and grinding.

SP5/NACE No.1

Metal Blast Cleaning

Removal of all visible rust, mill scale, paint and foreign matter by blast-cleaning by wheel or nozzle (dry or wet) using sand, grit or shot. (For very corrosive atmospheres where high cost of cleaning is warranted.)

SP6/NACE No.3

Commercial BlastCleaning

SP7/NACE No. 4

Brush-Off BlastCleaning

Blast-cleaning of all except tightly adhering residues of mill scale, rust and coatings, exposing numerous evenly distributed flecks of underlying metal.

SP8

Pickling

Complete removal of rust and mill scale by acid-pickling, duplex-pickling or electrolytic pickling.

SP10/NACE No.2

Near-White Blast-Cleaning

SP11

Power-Tool Cleaning to Bare Metal

Blast-cleaning until at least two-thirds of the surface area is free of all visible residues. (For conditions where thoroughly cleaned surface is required.)

Blast-cleaning to nearly white metal cleanliness, until at least 95% of the surface area is free of all visible residues. (For high humidity, chemical atmosphere, marine or other corrosive environments.) Complete removal of all rust, scale and paint by power tools, with resultant surface profile.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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PART 3 DESIGN OF FLEXURAL MEMBERS

SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–4 SECTION PROPERTIES AND AREAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–4 For Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–4 For Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–4 FLEXURAL STRENGTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–4 Braced, Compact Flexural Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–4 Unbraced Flexural Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–4 Noncompact or Slender Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–4 Available Flexural Strength for Weak-Axis Bending . . . . . . . . . . . . . . . . . . . . . . . . . 3–4 LOCAL BUCKLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–6 Determining the Width-to-Thickness Ratios of the Cross Section . . . . . . . . . . . . . . . 3–6 Classification of Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–6 LATERAL-TORSIONAL BUCKLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–6 Classification of Spans for Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–6 Consideration of Moment Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–6 AVAILABLE SHEAR STRENGTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–7 STEEL W-SHAPE BEAMS WITH COMPOSITE SLABS . . . . . . . . . . . . . . . . . . . . . . 3–7 Concrete Slab Effective Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–7 Steel Anchors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–7 Available Flexural Strength for Positive Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–7 Shored and Unshored Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–8 Available Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–8 OTHER SPECIFICATION REQUIREMENTS AND DESIGN CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–8 Special Requirements for Heavy Shapes and Plates . . . . . . . . . . . . . . . . . . . . . . . . . . 3–8 Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–8 DESIGN TABLE DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–9 Flexural Design Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–9 W-Shape Selection Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–9 Maximum Total Uniform Load Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–10 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF FLEXURAL MEMBERS

Plots of Available Flexural Strength vs. Unbraced Length . . . . . . . . . . . . . . . . . . . . 3–11 Available Flexural Strength of HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–11 Strength of Other Flexural Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–12 Composite Beam Selection Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–12 Beam Diagrams and Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–16 PART 3 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–17 DESIGN TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–18 Flexural Design Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–18 Table 3-1. Values of Cb for Simply Supported Beams . . . . . . . . . . . . . . . . . . . . 3–18 W-Shape Selection Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–19 Table 3-2. W-Shapes—Selection by Zx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–19 Table 3-3. W-Shapes—Selection by Ix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–28 Table 3-4. W-Shapes—Selection by Zy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–30 Table 3-5. W-Shapes—Selection by Iy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–33 Maximum Total Uniform Load Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–35 Table 3-6. W-Shapes—Maximum Total Uniform Load . . . . . . . . . . . . . . . . . . . 3–35 Table 3-7. S-Shapes—Maximum Total Uniform Load . . . . . . . . . . . . . . . . . . . . 3–80 Table 3-8. C-Shapes—Maximum Total Uniform Load . . . . . . . . . . . . . . . . . . . . 3–85 Table 3-9. MC-Shapes—Maximum Total Uniform Load . . . . . . . . . . . . . . . . . . 3–91 Plots of Available Flexural Strength vs. Unbraced Length . . . . . . . . . . . . . . . . . . . 3–99 Table 3-10. W-Shapes—Plots of Available Moment vs. Unbraced Length . . . . 3–99 Table 3-11. C- and MC-Shapes—Plots of Available Moment vs. Unbraced Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–135 Available Flexural Strength of HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–143 Table 3-12. Rectangular HSS—Available Flexural Strength . . . . . . . . . . . . . . 3–143 Table 3-13. Square HSS—Available Flexural Strength . . . . . . . . . . . . . . . . . . . 3–147 Table 3-14. Round HSS—Available Flexural Strength . . . . . . . . . . . . . . . . . . . 3–148 Table 3-15. Pipe—Available Flexural Strength . . . . . . . . . . . . . . . . . . . . . . . . . 3–151 Strength of Other Flexural Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–152 Tables 3-16 and 3-17. Available Shear Stress in Plate Girders . . . . . . . . . . . . . 3–152 Table 3-18. Floor Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–156 Composite Beam Selection Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–158 Table 3-19. Composite W-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–158 Table 3-20. Lower-Bound Elastic Moment of Inertia . . . . . . . . . . . . . . . . . . . . 3–192 Table 3-21. Nominal Horizontal Shear Strength for One Steel Headed Stud Anchor, Qn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–209 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF FLEXURAL MEMBERS

3–3

Beam Diagrams and Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–210 Table 3-22a. Concentrated Load Equivalents . . . . . . . . . . . . . . . . . . . . . . . . . . 3–210 Table 3-22b. Cantilevered Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–211 Table 3-22c. Continuous Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–212 Table 3-23. Shears, Moments and Deflections . . . . . . . . . . . . . . . . . . . . . . . . . 3–213

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF FLEXURAL MEMBERS

SCOPE The specification requirements and other design considerations summarized in this Part apply to the design of flexural members subject to uniaxial flexure without axial forces or torsion. For the design of members subject to biaxial flexure and/or flexure in combination with axial tension or compression and/or torsion, see Part 6.

SECTION PROPERTIES AND AREAS For Flexure Flexural design properties are based upon the full cross section with no reduction for bolt holes when the limitations in AISC Specification Section F13.1(a) are satisfied. Otherwise, the flexural design properties are based upon a flexural rupture check given in AISC Specification Section F13.1(b).

For Shear For shear, the area is determined per AISC Specification Chapter G.

FLEXURAL STRENGTH The nominal flexural strength of W-shapes is illustrated as a function of the unbraced length, Lb, in Figure 3-1. The available strength is determined as φMn or Mn /Ω, which must equal or exceed the required strength (bending moment), Mu or Ma, respectively. The available flexural strength, φMn or Mn /Ω, is determined per AISC Specification Chapter F. Table User Note F1.1 outlines the sections of Chapter F and the corresponding limit states applicable to each member type.

Braced, Compact Flexural Members When flexural members are braced (Lb ≤ Lp) and compact (λ ≤ λp), yielding must be considered in the nominal moment strength of the member, in accordance with the requirements of AISC Specification Chapter F.

Unbraced Flexural Members When flexural members are unbraced (Lb > Lp), have flange width-to-thickness ratios such that λ > λp, or have web width-to-thickness ratios such that λ > λp, lateral-torsional and elastic buckling effects must be considered in the calculation of the nominal moment strength of the member.

Noncompact or Slender Cross Sections For flexural members that have width-to-thickness ratios such that λ > λp, local buckling must be considered in the calculation of the nominal moment strength of the member.

Available Flexural Strength for Weak-Axis Bending The design of flexural members subject to weak-axis bending is similar to that for strongaxis bending, except that lateral-torsional buckling and web local buckling do not apply. See AISC Specification Section F6. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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FLEXURAL STRENGTH

Lp =1.76ry

Lr = 1.95rts

E 0.7Fy

E Fy

(Spec. Eq. F2-5)

2

⎛ 0.7Fy ⎞ ⎛ Jc ⎞ Jc + ⎜ + 6.76 ⎜ ⎟ ⎟ S x ho ⎝ S x ho ⎠ ⎝ E ⎠

2

(Spec. Eq. F2-6) (3-1)

M r = 0.7Fy S x For cross sections with noncompact flanges: ⎛ λ − λ pf ⎞ M p′ = M n = M p − M p − 0.7Fy S x ⎜ ⎟ ⎝ λrf − λ pf ⎠

)

(

(

Lp′ = Lp + Lr − Lp

(from Spec. Eq. F3-1)

M −M′ ) ((Mp − Mp )) p

r

Fig. 3-1. General available flexural strength of beams.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(3-2)

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DESIGN OF FLEXURAL MEMBERS

LOCAL BUCKLING Determining the Width-to-Thickness Ratios of the Cross Section Flexural members are classified for flexure on the basis of the width-to-thickness ratios of the various elements of the cross section. The width-to-thickness ratio, λ, is determined for each element of the cross section per AISC Specification Section B4.1.

Classification of Cross Sections Cross sections are classified as follows: • Flexural members are compact (the plastic moment can be reached without local buckling) when λ is equal to or less than λp and the flange(s) are continuously connected to the web(s). • Flexural members are noncompact (local buckling will occur, but only after initial yielding) when λ exceeds λ p but is equal to or less than λr. • Flexural members are slender-element cross sections (local buckling will occur prior to yielding) when λ exceeds λr. The values of λp and λr are determined per AISC Specification Section B4.1.

LATERAL-TORSIONAL BUCKLING Classification of Spans for Flexure Flexural members bent about their strong axis are classified on the basis of the length, Lb , between braced points. Braced points are points at which support resistance against lateraltorsional buckling is provided per AISC Specification Appendix 6, Section 6.3. Classifications are determined as follows: • If L b ≤ L p , flexural member is not subject to lateral-torsional buckling. • If L p < L b ≤ L r , flexural member is subject to inelastic lateral-torsional buckling. • If L b > Lr , flexural member is subject to elastic lateral-torsional buckling. The values of Lp and Lr are determined per AISC Specification Chapter F. These values are presented in Tables 3-2, 3-6, 3-7, 3-8, 3-9, 3-10 and 3-11. Note that for cross sections with noncompact flanges, the value given for Lp in these tables is L′p as given in Equation 3-2 of Figure 3-1. In Tables 3-10 and 3-11, Lp is defined by • and Lr by °. Lateral-torsional buckling does not apply to flexural members bent about their weak axis or HSS bent about either axis, per AISC Specification Sections F6, F7 and F8.

Consideration of Moment Gradient When Lb > Lp, the moment gradient between braced points can be considered in the determination of the available strength using the lateral-torsional buckling modification factor, Cb, herein referred to as the LTB modification factor. In the case of a uniform moment between braced points causing single-curvature of the member, Cb = 1.0. This represents the worst case and Cb can be conservatively taken equal to 1.0 for use with the maximum moment between braced points in most designs. See AISC Specification Commentary AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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STEEL W-SHAPE BEAMS WITH COMPOSITE SLABS

3–7

Section F1 for further discussion. A nonuniform moment gradient between braced points can be considered using Cb calculated as given in AISC Specification Equation F1-1. Exceptions are provided as follows: 1. As an alternative, when the moment diagram between braced points is a straight line, Cb can be calculated as given in AISC Specification Commentary Equation C-F1-1. 2. For cantilevers or overhangs where the free end is unbraced, Cb = 1.0 per AISC Specification Section F1. 3. For tees with the stem in compression, Cb = 1.0 as recommended in AISC Specification Commentary Section F9.

AVAILABLE SHEAR STRENGTH For flexural members, the available shear strength, φVn or Vn /Ω, which must equal or exceed the required strength, Vu or Va, respectively, is determined in accordance with AISC Specification Chapter G. Values of φVn and Vn /Ω can be found in Tables 3-2, 3-6, 3-7, 3-8 and 3-9.

STEEL W-SHAPE BEAMS WITH COMPOSITE SLABS The following pertains to W-shapes with composite concrete slabs in regions of positive moment. For composite flexural members in regions of negative moment, see AISC Specification Chapter I. For further information on composite design and construction, see Viest et al. (1997).

Concrete Slab Effective Width The effective width of a concrete slab acting compositely with a steel beam is determined per AISC Specification Section I3.1a.

Steel Anchors Material, placement and spacing requirements for steel anchors are given in AISC Specification Chapter I. The nominal shear strength, Qn, of one steel headed stud anchor is determined per AISC Specification Section I8.2a and is tabulated for common design conditions in Table 3-21. The horizontal shear strength, V r′, at the steel-concrete interface will be the least of the concrete crushing strength, steel tensile yield strength, or the shear strength of the steel anchors. Table 3-21 considers only the limit state of shear strength of a steel headed stud anchor.

Available Flexural Strength for Positive Moment The available flexural strength of a composite beam subject to positive moment is determined per AISC Specification Section I3.2a assuming a uniform compressive stress of 0.85fc′ and zero tensile strength in the concrete, and a uniform stress of Fy in the tension area (and compression area, if any) of the steel section. The position of the plastic neutral axis (PNA) can then be determined by static equilibrium. Per AISC Specification Section I3.2d, enough steel anchors must be provided between a point of maximum moment and the nearest point of zero moment to transfer the total horizontal shear force, V r′, between the steel beam and concrete slab, where V r′ is determined per AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF FLEXURAL MEMBERS

AISC Specification Section I3.2d(1). For partial composite design, the horizontal shear strength, V r′, controls the available flexural strength of the composite flexural member.

Shored and Unshored Construction The available flexural strength is identical for both shored and unshored construction. In unshored construction, issues such as lateral support during construction and constructionload deflection may require consideration.

Available Shear Strength Per AISC Specification Section I4, the available shear strength for composite beams is determined as illustrated previously for steel beams.

OTHER SPECIFICATION REQUIREMENTS AND DESIGN CONSIDERATIONS The following other specification requirements and design considerations apply to the design of flexural members.

Special Requirements for Heavy Shapes and Plates For beams with complete-joint-penetration groove welded joints and made from heavy shapes with a flange thickness exceeding 2 in., see AISC Specification Sections A3.1c. For built-up sections consisting of plates with a thickness exceeding 2 in., see Section A3.1d.

Serviceability Serviceability requirements, per AISC Specification Chapter L, should be appropriate for the application. This includes an appropriate limit on the deflection of the flexural member and the vibration characteristics of the system of which the flexural member is a part. See also AISC Design Guide 3, Serviceability Design Considerations for Steel Buildings (West et al., 2003), AISC Design Guide 5, Low- and Medium-Rise Steel Buildings (Allison, 1991) and AISC Design Guide 11, Floor Vibrations Due to Human Activity (Murray et al., 1997). The maximum vertical deflection, Δ, can be calculated using the equations given in Tables 3-22 and 3-23. Alternatively, for common cases of simple-span beams and I-shaped members and channels, the following equation can be used: Δ = ML2 /(C1Ix )

(3-3)

where M = maximum service-load moment, kip-ft L = span length, ft Ix = moment of inertia, in.4 C1 = loading constant (see Figure 3-2) which includes the numerical constants appropriate for the given loading pattern, E (29,000 ksi), and a ft-to-in. conversion factor of 1,728 in.3/ft3.

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DESIGN TABLE DISCUSSION Flexural Design Tables Table 3-1. Values of Cb for Simply Supported Beams Values of the LTB modification factor, Cb, are given for various loading conditions on simple-span beams in Table 3-1.

W-Shape Selection Tables Table 3-2. W-Shapes—Selection by Zx W-shapes are sorted in descending order by strong-axis flexural strength and then grouped in ascending order by weight with the lightest W-shape in each range in bold. Strong-axis available strengths in flexure and shear are given for W-shapes with Fy = 50 ksi (ASTM A992). Cb is taken as unity. For compact W-shapes, when Lb ≤ Lp, the strong-axis available flexural strength, φb Mpx or Mpx /Ωb, can be determined using the tabulated strength values. When L p < L b ≤ Lr , linearly interpolate between the available strength at L p and the available strength at L r as follows: LRFD

ASD

φb Mn = Cb [φb Mpx ⫺ φb BF(Lb − Lp)] ≤ φb Mpx

(3-4a)

Mn BF ⎡ M px ⎤ = Cb ⎢ – (Lb – L p ) ⎥ Ωb Ω Ω b ⎣ b ⎦ (3-4b) M px ≤ Ωb

Fig. 3-2. Loading constants for use in determining simple beam deflections.

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where BF =

( M px − Mrx ) ( Lr − L p )

(3-5)

L p = for compact sections, see Figure 3-1, AISC Specification Equation F2-5 = for noncompact sections, L p = L ′p , see Figure 3-1, Equation 3-2 Lr M px

= see Figure 3-1, AISC Specification Equation F2-6 = Fy Z x for compact sections

(Spec. Eq. F2-1)

= M ′p as given in Figure 3-1, AISC Specification Equation F3-1, for noncompact sectionss Mrx = Mr , see Figure 3-1 φ b = 0.90 Ω b = 1.67 When Lb > Lr, see Table 3-10. The strong-axis available shear strength, φvVnx or Vnx /Ωv , can be determined using the tabulated value.

Table 3-3. W-Shapes—Selection by Ix W-shapes are sorted in descending order by strong-axis moment of inertia, Ix, and then grouped in ascending order by weight with the lightest W-shape in each range in bold.

Table 3-4. W-Shapes—Selection by Zy W-shapes are sorted in descending order by weak-axis flexural strength and then grouped in ascending order by weight with the lightest W-shape in each range in bold. Weak-axis available strengths in flexure are given for W-shapes with Fy = 50 ksi (ASTM A992). Cb is taken as unity. For noncompact W-shapes, the tabulated values of Mny /Ωb and φb Mny have been adjusted to account for the noncompactness. The weak-axis available shear strength must be checked independently.

Table 3-5. W-Shapes—Selection by Iy W-shapes are sorted in descending order by weak-axis moment of inertia, Iy, and then grouped in ascending order by weight with the lightest W-shape in each range in bold.

Maximum Total Uniform Load Tables Table 3-6. W-Shapes—Maximum Total Uniform Load Maximum total uniform loads on braced (Lb ≤ Lp) simple-span beams bent about the strong axis are given for W-shapes with Fy = 50 ksi (ASTM A992). The uniform load constant, φbWc or Wc /Ω b (kip-ft), divided by the span length, L (ft), provides the maximum total uniform load (kips) for a braced simple-span beam bent about the strong axis. This is based on the available flexural strength as discussed for Table 3-2.

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The strong-axis available shear strength, φvVn or Vn /Ωv , can be determined using the tabulated value. Above the heavy horizontal line in the tables, the maximum total uniform load is limited by the strong-axis available shear strength. The tabulated values can also be used for braced simple-span beams with equal concentrated loads spaced as shown in Table 3-22a if the concentrated loads are first converted to an equivalent uniform load.

Table 3-7. S-Shapes—Maximum Total Uniform Load Table 3-7 is similar to Table 3-6, except it covers S-shapes with Fy = 36 ksi (ASTM A36).

Table 3-8. C-Shapes—Maximum Total Uniform Load Table 3-8 is similar to Table 3-6, except it covers C-shapes with Fy = 36 ksi (ASTM A36).

Table 3-9. MC-Shapes—Maximum Total Uniform Load Table 3-9 is similar to Table 3-6, except it covers MC-shapes with Fy = 36 ksi (ASTM A36).

Plots of Available Flexural Strength vs. Unbraced Length Table 3-10. W-Shapes—Plots of Available Moment vs. Unbraced Length The strong-axis available flexural strength, φb Mn or Mn /Ω b, is plotted as a function of the unbraced length, Lb, for W-shapes with Fy = 50 ksi (ASTM A992). The plots show the total available strength for an unbraced length, Lb. The moment demand due to all applicable load combinations on that segment may not exceed the strength shown for Lb. Cb is taken as unity. When the plotted curve is solid, the W-shape for that curve is the lightest cross section for a given combination of available flexural strength and unbraced length. When the plotted curve is dashed, a lighter W-shape than that for the plotted curve exists. The plotted curves are arbitrarily terminated at a span-to-depth ratio of 30 in most cases. Lp is indicated in each curve by a solid dot (•). Lr is indicated in each curve by an open dot (°).

Table 3-11. C- and MC-Shapes—Plots of Available Moment vs. Unbraced Length Table 3-11 is similar to Table 3-10, except it covers C- and MC-shapes with Fy = 36 ksi (ASTM A36).

Available Flexural Strength of HSS Table 3-12. Rectangular HSS—Available Flexural Strength The available flexural strength is tabulated for rectangular HSS with Fy = 46 ksi (ASTM A500 Grade B) as determined by AISC Specification Section F7. For noncompact and slender cross sections, the tabulated values of Mn /Ωb and φb Mn have been adjusted to account for the noncompactness or slenderness.

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Table 3-13. Square HSS—Available Flexural Strength Table 3-13 is similar to Table 3-12, except it covers square HSS with Fy = 46 ksi (ASTM A500 Grade B).

Table 3-14. Round HSS—Available Flexural Strength Table 3-14 is similar to Table 3-12, except it covers round HSS with Fy = 42 ksi (ASTM A500 Grade B) and the available flexural strength is determined from AISC Specification Section F8.

Table 3-15. Pipe—Available Flexural Strength Table 3-15 is similar to Table 3-14, except it covers Pipe with Fy = 35 ksi (ASTM A53 Grade B).

Strength of Other Flexural Members Tables 3-16 and 3-17. Available Shear Stress in Plate Girders The available shear stress for plate girders is plotted as a function of a/h and h/tw in Tables 3-16 (for Fy = 36 ksi) and 3-17 (for Fy = 50 ksi). In part a of each table, tension field action is neglected. In part b of each table, tension field action is considered.

Table 3-18. Floor Plates The recommended maximum uniformly distributed loads are given in Table 3-18 based upon simple-span bending between supports. Table 3-18a is for deflection-controlled applications and should be used with the appropriate serviceability load combinations. The tabulated values correspond to a maximum deflection of L/100. Table 3-18b is for flexural-strength-controlled applications and should be used with LRFD or ASD load combinations. The tabulated values correspond to a maximum bending stress of 24 ksi in LRFD and 16 ksi in ASD.

Composite Beam Selection Tables Table 3-19. Composite W-Shapes The available flexural strength is tabulated for W-shapes with Fy = 50 ksi (ASTM A992). The values tabulated are independent of the specific concrete flange properties allowing the designer to select an appropriate combination of concrete strength and slab geometry. The location of the plastic neutral axis (PNA) is uniquely determined by the horizontal shear force, ΣQn , at the interface between the steel section and the concrete slab. With the knowledge of the location of the PNA and the distance to the centroid of the concrete flange force, ΣQn, the available flexural strength can be computed. Available flexural strengths are tabulated for PNA locations at the seven locations shown. Five of these PNA locations are in the beam flange. The seventh PNA location is computed

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at the point where ΣQn equals 0.25Fy As, and the sixth PNA location is halfway between the location of ΣQn at point five and point seven. Use of beams with a PNA below location seven is discouraged. Table 3-19 can be used to design a composite beam by entering with a required flexural strength and determining the corresponding required ΣQn. Alternatively, Table 3-19 can be used to check the flexural strength of a composite beam by selecting a valid value of ΣQn, using Table 3-21. With the effective width of the concrete flange, b, determined per AISC Specification Section I3.1a, the appropriate value of the distance from concrete flange force to beam top flange, Y2, can be determined as Y 2 = Ycon −

a 2

(3-6)

where Ycon = distance from top of steel beam to top of concrete, in. a

=

ΣQn

(3-7)

0.85 fc′b

and the available flexural strength, φb Mn or Mn /Ωb, can then be determined from Table 3-19. Values for the distance from the PNA to the beam top flange, Y1, are also tabulated for convenience. The parameters Y1 and Y2 are illustrated in Figure 3-3. Note that the model of the steel beam used in the calculation of the available strength assumes that As Af Aw Kdep Karea

= cross-sectional area of the steel section, in.2 = flange area, in.2 = bf tf = web area, in.2 = (d ⫺ 2k)tw = k ⫺ tf , in. = (As ⫺ 2Af ⫺ Aw)/2, in.2

Table 3-20. Lower-Bound Elastic Moment of Inertia The lower-bound elastic moment of inertia of a composite beam can be used to calculate deflection. If calculated deflections using the lower-bound moment of inertia are acceptable, a more complete elastic analysis of the composite section can be avoided. The lowerbound elastic moment of inertia is based upon the area of the beam and an equivalent concrete area equal to ΣQn /Fy as illustrated in Figure 3-4, where Fy = 50 ksi. The analysis includes only the horizontal shear force transferred by the steel anchors supplied. Thus, only the portion of the concrete flange used to balance ΣQn is included in the determination of the lower-bound moment of inertia. The lower bound moment of inertia, therefore, is the moment of inertia of the cross section at the required strength level. This is smaller than the corresponding moment of inertia at the service load where deflection is calculated. The value for the lower bound moment of inertia can be calculated as illustrated in AISC Specification Commentary Section I3.2.

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(a)

(b)

(c) Fig. 3-3. Strength design models for composite beams. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Table 3-21. Nominal Horizontal Shear Strength for One Steel Headed Stud Anchor, Qn The nominal shear strength of steel headed stud anchors is given in Table 3-21, in accordance with AISC Specification Chapter I. Nominal horizontal shear strength values are presented based upon the position of the steel anchor, profile of the deck, and orientation of the deck relative to the steel anchor. See AISC Specification Commentary Figure C-I8.1.

Fig. 3-4. Deflection design model for composite beams.

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Beam Diagrams and Formulas Table 3-22a. Concentrated Load Equivalents Concentrated load equivalents are given in Table 3-22a for beams with various support conditions and loading characteristics.

Table 3-22b. Cantilevered Beams Coefficients are provided in Table 3-22b for cantilevered beams with various support conditions and loading characteristics.

Table 3-22c. Continuous Beams Coefficients are provided in Table 3-22c for continuous beams with various support conditions and loading characteristics.

Table 3-23. Shears, Moments and Deflections Shears, moments and deflections are given in Table 3-23 for beams with various support conditions and loading characteristics.

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PART 3 REFERENCES

3–17

PART 3 REFERENCES Allison, H.R. (1991), Low- and Medium-Rise Steel Buildings, Design Guide 5, American Institute for Steel Construction, Chicago, IL. Murray, T.M., Allen, D.E. and Ungar, E.E. (1997), Floor Vibrations Due to Human Activity, Design Guide 11, American Institute for Steel Construction, Chicago, IL. Viest, I.M., Colaco, J.P., Furlong, R.W., Griffis, L.G., Leon, R.T. and Wyllie, L.A., Jr. (1997), Composite Construction: Design for Buildings, McGraw-Hill, New York, NY. West, M.A., Fisher, J.M. and Griffis, L.G. (2003), Serviceability Design Considerations for Steel Buildings, Design Guide 3, 2nd Ed., American Institute of Steel Construction, Chicago, IL.

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Table 3-1

Values of Cb for Simply Supported Beams

Note: Lateral bracing must always be provided at points of support per AISC Specification Chapter F.

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W-SHAPE SELECTION TABLES

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Table 3-2

Zx

W-Shapes

Fy = 50 ksi

Selection by Zx

Zx

Shape

in.3

Mpx /Ωb φb Mpx Mrx /Ωb φb Mrx BF/ Ωb φb BF kip-ft kip-ft kip-ft kip-ft kips kips ASD LRFD ASD LRFD ASD LRFD

Lp

Lr

Ix

ft

ft

in.4

Vnx /Ωv φvVnx kips kips ASD LRFD

W36×652

h

2910

7260

10900

4300

6460

46.8

70.3

14.5

77.7 50600

1620

2430

W40×593

h

2760

6890

10400

4090

6140

55.4

84.4

13.4

63.9 50400

1540

2310

W36×529h

2330

5810

8740

3480

5220

46.4

70.1

14.1

64.3 39600

1280

1920

W40×503

h

2320

5790

8700

3460

5200

55.3

83.1

13.1

55.2 41600

1300

1950

W36×487

h

2130

5310

7990

3200

4800

46.0

69.5

14.0

59.9 36000

1180

1770

h

W40×431 W36×441h W27×539h

1960 1910 1890

4890 4770 4720

7350 7160 7090

2950 2880 2740

4440 4330 4120

53.6 45.3 26.2

80.4 67.9 39.3

12.9 13.8 12.9

49.1 34800 55.5 32100 88.5 25600

1110 1060 1280

1660 1590 1920

W40×397h

1800

4490

6750

2720

4100

52.4

78.4

12.9

46.7 32000

1000

1500

h

W40×392 W36×395h

1710 1710

4270 4270

6410 6410

2510 2600

3780 3910

60.8 44.9

90.8 67.2

9.33 13.7

38.3 29900 50.9 28500

1180 937

1770 1410

W40×372h W14×730h

1680 1660

4190 4140

6300 6230

2550 2240

3830 3360

51.7 7.35

77.9 11.1

12.7 16.6

44.4 29600 275 14300

942 1380

1410 2060

44.0 28900

W40×362h

1640

4090

6150

2480

3730

51.4

77.3

12.7

909

1360

W44×335 W33×387h W36×361h W14×665h

1620 1560 1550 1480

4040 3890 3870 3690

6080 5850 5810 5550

2460 2360 2360 2010

3700 3540 3540 3020

59.4 38.3 43.6 7.10

89.5 57.8 65.6 10.7

12.3 13.3 13.6 16.3

38.9 53.3 48.2 253

31100 24300 25700 12400

906 907 851 1220

1360 1360 1280 1830

W40×324 W30×391h W40×331h W33×354h

1460 1450 1430 1420

3640 3620 3570 3540

5480 5440 5360 5330

2240 2180 2110 2170

3360 3280 3180 3260

49.0 31.4 59.1 37.4

74.1 47.2 88.2 56.6

12.6 13.0 9.08 13.2

41.2 58.8 33.8 49.8

25600 20700 24700 22000

804 903 996 826

1210 1350 1490 1240

W44×290 W40×327h W36×330 W40×297 W30×357h W14×605h W36×302

1410 1410 1410 1330 1320 1320 1280

3520 3520 3520 3320 3290 3290 3190

5290 5290 5290 4990 4950 4950 4800

2170 2100 2170 2040 1990 1820 1970

3260 3150 3260 3070 2990 2730 2970

54.9 58.0 42.2 47.8 31.3 6.81 40.5

82.5 87.4 63.4 71.6 47.2 10.3 60.8

12.3 9.11 13.5 12.5 12.9 16.1 13.5

36.9 33.6 45.5 39.3 54.4 232 43.6

27000 24500 23300 23200 18700 10800 21100

754 963 769 740 813 1090 705

1130 1440 1150 1110 1220 1630 1060

ASD

LRFD

Ωb = 1.67 Ωv = 1.50

φ b = 0.90 φ v = 1.00

h

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

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Table 3-2 (continued)

Zx

W-Shapes Selection by Zx

W44×262 W40×294 W33×318 W40×277 W27×368h W40×278 W36×282 W30×326h W14×550h W33×291 W40×264 W27×336h W24×370h

in.3 1270 1270 1270 1250 1240 1190 1190 1190 1180 1160 1130 1130 1130

Mpx /Ωb kip-ft ASD 3170 3170 3170 3120 3090 2970 2970 2970 2940 2890 2820 2820 2820

W40×249

Zx

Shape

Fy = 50 ksi

φb Mpx Mrx /Ωb φb Mrx BF/ Ωb φb BF

Lp

Lr

Ix

ft

ft

in.4 24100 21900 19500 21900 16200 20500 19600 16800 9430 17700 19400 14600 13400

kip-ft kip-ft kip-ft LRFD ASD LRFD

kips ASD

kips LRFD

4760 4760 4760 4690 4650 4460 4460 4460 4430 4350 4240 4240 4240

1940 1890 1940 1920 1850 1780 1830 1820 1630 1780 1700 1700 1670

2910 2840 2910 2890 2780 2680 2760 2730 2440 2680 2550 2550 2510

52.6 56.9 36.8 45.8 24.9 55.3 39.6 30.3 6.65 36.0 53.8 25.0 20.0

79.1 85.4 55.4 68.7 37.6 82.8 59.0 45.6 10.1 54.2 81.3 37.7 30.0

12.3 35.7 9.01 31.5 13.1 46.5 12.6 38.8 12.3 62.0 8.90 30.4 13.4 42.2 12.7 50.6 15.9 213 13.0 43.8 8.90 29.7 12.2 57.0 11.6 69.2

1020 1280 1100 989 1260 1240 985 1110 1440 1000 1150 1130 1280

591

887

kips LRFD

1120

2790

4200

1730

2610

42.9

64.4

12.5

v

W44×230 W36×262 W30×292 W14×500h W36×256 W33×263 W36×247 W27×307h W24×335h W40×235

1100 1100 1060 1050 1040 1040 1030 1030 1020 1010

2740 2740 2640 2620 2590 2590 2570 2570 2540 2520

4130 4130 3980 3940 3900 3900 3860 3860 3830 3790

1700 1700 1620 1460 1560 1610 1590 1550 1510 1530

2550 2550 2440 2200 2350 2410 2400 2330 2270 2300

46.8 38.1 29.7 6.43 46.5 34.1 37.4 25.1 19.9 51.0

71.2 57.9 44.9 9.65 70.0 51.9 55.7 37.7 30.2 76.7

12.1 34.3 13.3 40.6 12.6 46.9 15.6 196 9.36 31.5 12.9 41.6 13.2 39.4 12.0 52.6 11.4 63.1 8.97 28.4

20800 17900 14900 8210 16800 15900 16700 13100 11900 17400

547 620 653 858 718 600 587 687 759 659

822 930 979 1290 1080 900 881 1030 1140 989

W40×215 W36×231 W30×261 W33×241 W36×232 W27×281 W14×455h W24×306h

964 963 943 940 936 936 936 922

2410 2400 2350 2350 2340 2340 2340 2300

3620 3610 3540 3530 3510 3510 3510 3460

1500 1490 1450 1450 1410 1420 1320 1380

2250 2240 2180 2180 2120 2140 1980 2070

39.4 35.7 29.1 33.5 44.8 24.8 6.24 19.7

59.3 53.7 44.0 50.2 67.0 36.9 9.36 29.8

12.5 35.6 13.1 38.6 12.5 43.4 12.8 39.7 9.25 30.0 12.0 49.1 15.5 179 11.3 57.9

16700 15600 13100 14200 15000 11900 7190 10700

507 555 588 568 646 621 768 683

761 832 882 852 968 932 1150 1020

W40×211

906

2260

3400

1370

2060

48.6

73.1

27.2 15500

591

887

ASD Ωb = 1.67 Ωv = 1.50

LRFD

h

φ b = 0.90 φ v = 1.00

v

8.87

37.2 19600

φvVnx

Vnx /Ωv kips ASD 680 856 732 659 839 828 657 739 962 668 768 756 851

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67.

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Table 3-2 (continued)

Zx

W-Shapes

Fy = 50 ksi

Selection by Zx

W40×199 W14×426h W33×221 W27×258 W30×235 W24×279h W36×210 W14×398h

in.3 869 869 857 852 847 835 833 801

Mpx /Ωb kip-ft ASD 2170 2170 2140 2130 2110 2080 2080 2000

W40×183 W33×201 W27×235 W36×194 W18×311h W30×211 W24×250 W14×370h

774 773 772 767 754 751 744 736

W36×182 W27×217

Shape

Zx

φb Mpx Mrx /Ωb φb Mrx BF/ Ωb φb BF

Lp

Lr

Ix

ft

ft

φvVnx

Vnx /Ωv kips ASD 503 703 525 568 520 619 609 648

755 1050 788 853 779 929 914 972

kip-ft kip-ft kip-ft LRFD ASD LRFD

kips ASD

kips LRFD

3260 3260 3210 3200 3180 3130 3120 3000

1340 1230 1330 1300 1310 1250 1260 1150

2020 1850 1990 1960 1960 1880 1890 1720

37.6 6.16 31.8 24.4 28.0 19.7 42.3 5.95

56.1 9.23 47.8 36.5 42.7 29.6 63.4 8.96

12.2 34.3 15.3 168 12.7 38.2 11.9 45.9 12.4 41.0 11.2 53.4 9.11 28.5 15.2 158

in.4 14900 6600 12900 10800 11700 9600 13200 6000

1930 1930 1930 1910 1880 1870 1860 1840

2900 2900 2900 2880 2830 2820 2790 2760

1180 1200 1180 1160 1090 1160 1120 1060

1770 1800 1780 1740 1640 1750 1690 1590

44.1 30.3 24.1 40.4 11.2 26.9 19.7 5.87

66.5 45.6 36.0 61.4 16.8 40.5 29.3 8.80

8.80 25.8 12.6 36.7 11.8 42.9 9.04 27.6 10.4 81.1 12.3 38.7 11.1 48.7 15.1 148

13200 11600 9700 12100 6970 10300 8490 5440

507 482 522 558 678 479 547 594

761 723 784 838 1020 718 821 891

718 711

1790 1770

2690 2670

1090 1100

1640 1650

38.9 23.0

58.4 35.1

9.01 11.7

27.0 11300 40.8 8910

526 471

790 707

W40×167 W18×283h W30×191 W24×229 W14×342h W36×170 W27×194 W33×169

693 676 675 675 672 668 631 629

1730 1690 1680 1680 1680 1670 1570 1570

2600 2540 2530 2530 2520 2510 2370 2360

1050 987 1050 1030 975 1010 976 959

1580 1480 1580 1540 1460 1530 1470 1440

41.7 11.1 25.6 19.0 5.73 37.8 22.3 34.2

62.5 16.7 38.6 28.9 8.62 56.1 33.8 51.5

8.48 24.8 11600 10.3 73.6 6170 12.2 36.8 9200 11.0 45.2 7650 15.0 138 4900 8.94 26.4 10500 11.6 38.2 7860 8.83 26.7 9290

502 613 436 499 539 492 422 453

753 920 654 749 809 738 632 679

W36×160 W18×258h W30×173 W24×207 W14×311h W12×336h

624 611 607 606 603 603

1560 1520 1510 1510 1500 1500

2340 2290 2280 2270 2260 2260

947 898 945 927 884 844

1420 1350 1420 1390 1330 1270

36.1 10.9 24.1 18.9 5.59 4.76

54.2 16.5 36.8 28.6 8.44 7.19

8.83 25.8 10.2 67.3 12.1 35.5 10.9 41.7 14.8 125 12.3 150

468 550 398 447 482 598

702 826 597 671 723 897

ASD

LRFD

Ωb = 1.67 Ωv = 1.50

φ b = 0.90 φ v = 1.00

h

9760 5510 8230 6820 4330 4060

kips LRFD

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3A:14th Ed.

2/24/11

8:40 AM

Page 22

3–22

DESIGN OF FLEXURAL MEMBERS

Table 3-2 (continued)

Zx

W-Shapes Selection by Zx

Zx

Shape

in.3 v

Fy = 50 ksi

Mpx /Ωb φb Mpx Mrx /Ωb φb Mrx BF/ Ωb φb BF kip-ft kip-ft kip-ft kip-ft kips kips ASD LRFD ASD LRFD ASD LRFD

Lp

Lr

Ix

ft

ft

in.4

Vnx /Ωv φvVnx kips kips ASD LRFD

W40×149 W36×150 W27×178 W33×152 W24×192 W18×234h W14×283h W12×305h W21×201 W27×161

598 581 570 559 559 549 542 537 530 515

1490 1450 1420 1390 1390 1370 1350 1340 1320 1280

2240 2180 2140 2100 2100 2060 2030 2010 1990 1930

896 880 882 851 858 814 802 760 805 800

1350 1320 1330 1280 1290 1220 1200 1140 1210 1200

38.3 34.4 21.6 31.7 18.4 10.8 5.52 4.64 14.5 20.6

57.4 51.9 32.5 48.3 28.0 16.4 8.36 6.97 22.0 31.3

8.09 23.6 8.72 25.3 11.5 36.4 8.72 25.7 10.8 39.7 10.1 61.4 14.7 114 12.1 137 10.7 46.2 11.4 34.7

9800 9040 7020 8160 6260 4900 3840 3550 5310 6310

432 449 403 425 413 490 431 531 419 364

650 673 605 638 620 734 646 797 628 546

W33×141 W24×176

514 511

1280 1270

1930 1920

782 786

1180 1180

30.3 18.1

45.7 27.7

8.58 10.7

25.0 37.4

7450 5680

403 378

604 567

W36×135v W30×148 W18×211 W14×257 W12×279h W21×182 W24×162

509 500 490 487 481 476 468

1270 1250 1220 1220 1200 1190 1170

1910 1880 1840 1830 1800 1790 1760

767 761 732 725 686 728 723

1150 1140 1100 1090 1030 1090 1090

31.7 29.0 10.7 5.54 4.50 14.4 17.9

47.8 43.9 16.2 8.28 6.75 21.8 26.8

8.41 24.3 8.05 24.9 9.96 55.7 14.6 104 11.9 126 10.6 42.7 10.8 35.8

7800 6680 4330 3400 3110 4730 5170

384 399 439 387 487 377 353

577 599 658 581 730 565 529

W33×130 W27×146 W18×192 W30×132 W14×233 W21×166 W12×252h W24×146

467 464 442 437 436 432 428 418

1170 1160 1100 1090 1090 1080 1070 1040

1750 1740 1660 1640 1640 1620 1610 1570

709 723 664 664 655 664 617 648

1070 1090 998 998 984 998 927 974

29.3 19.9 10.6 26.9 5.40 14.2 4.43 17.0

43.1 29.5 16.1 40.5 8.15 21.2 6.68 25.8

8.44 24.2 11.3 33.3 9.85 51.0 7.95 23.8 14.5 95.0 10.6 39.9 11.8 114 10.6 33.7

6710 5660 3870 5770 3010 4280 2720 4580

384 332 392 373 342 338 431 321

576 497 588 559 514 506 647 482

W33×118v W30×124 W18×175 W27×129 W14×211 W12×230h

415 408 398 395 390 386

1040 1020 993 986 973 963

1560 1530 1490 1480 1460 1450

627 620 601 603 590 561

942 932 903 906 887 843

27.2 26.1 10.6 23.4 5.30 4.31

40.6 8.19 23.4 39.0 7.88 23.2 15.8 9.75 46.9 35.0 7.81 24.2 7.94 14.4 86.6 6.51 11.7 105

5900 5360 3450 4760 2660 2420

325 353 356 337 308 390

489 530 534 505 462 584

ASD Ωb = 1.67 Ωv = 1.50

LRFD

h

φ b = 0.90 φ v = 1.00

v

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3A:14th Ed.

2/24/11

8:40 AM

Page 23

W-SHAPE SELECTION TABLES

3–23

Table 3-2 (continued)

Zx

W-Shapes

Fy = 50 ksi

Selection by Zx

W30×116 W21×147 W24×131 W18×158 W14×193 W12×210

in.3 378 373 370 356 355 348

Mpx /Ωb kip-ft ASD 943 931 923 888 886 868

W30×108 W27×114 W21×132 W24×117 W18×143 W14×176

346 343 333 327 322 320

W30×99 W12×190 W21×122 W27×102 W18×130 W24×104 W14×159

Shape

Zx

φb Mpx Mrx /Ωb φb Mrx BF/ Ωb φb BF

Lp

Lr

Ix

ft

ft

Vnx /Ωv φvVnx kips kips ASD LRFD 339 509 318 477 296 445 319 479 276 414 347 520

kip-ft kip-ft kip-ft LRFD ASD LRFD

kips ASD

kips LRFD

1420 1400 1390 1340 1330 1310

575 575 575 541 541 510

864 864 864 814 814 767

24.8 13.7 16.3 10.5 5.30 4.25

37.4 20.7 24.6 15.9 7.93 6.45

7.74 10.4 10.5 9.68 14.3 11.6

22.6 36.3 31.9 42.8 79.4 95.8

in.4 4930 3630 4020 3060 2400 2140

863 856 831 816 803 798

1300 1290 1250 1230 1210 1200

522 522 515 508 493 491

785 785 774 764 740 738

23.5 21.7 13.2 15.4 10.3 5.20

35.5 7.59 32.8 7.70 19.9 10.3 23.3 10.4 15.7 9.61 7.83 14.2

22.1 23.1 34.2 30.4 39.6 73.2

4470 4080 3220 3540 2750 2140

325 311 283 267 285 252

487 467 425 401 427 378

312 311 307 305 290 289 287

778 776 766 761 724 721 716

1170 1170 1150 1140 1090 1080 1080

470 459 477 466 447 451 444

706 690 717 701 672 677 667

22.2 4.18 12.9 20.1 10.2 14.3 5.17

33.4 6.33 19.3 29.8 15.4 21.3 7.85

7.42 11.5 10.3 7.59 9.54 10.3 14.1

21.3 87.3 32.7 22.3 36.6 29.2 66.7

3990 1890 2960 3620 2460 3100 1900

309 305 260 279 259 241 224

463 458 391 419 388 362 335

W30×90v W24×103 W21×111 W27×94 W12×170 W18×119 W14×145 W24×94 W21×101

283 280 279 278 275 262 260 254 253

706 699 696 694 686 654 649 634 631

1060 1050 1050 1040 1030 983 975 953 949

428 428 435 424 410 403 405 388 396

643 643 654 638 617 606 609 583 596

20.6 18.2 12.4 19.1 4.11 10.1 5.13 17.3 11.8

30.8 27.4 18.9 28.5 6.15 15.2 7.69 26.0 17.7

7.38 7.03 10.2 7.49 11.4 9.50 14.1 6.99 10.2

20.9 21.9 31.2 21.6 78.5 34.3 61.7 21.2 30.1

3610 3000 2670 3270 1650 2190 1710 2700 2420

249 270 237 264 269 249 201 250 214

374 404 355 395 403 373 302 375 321

W27×84 W12×152 W14×132 W18×106

244 243 234 230

609 606 584 574

915 911 878 863

372 365 365 356

559 549 549 536

17.6 4.06 5.15 9.73

26.4 7.31 6.10 11.3 7.74 13.3 14.6 9.40

20.8 70.6 55.8 31.8

2850 1430 1530 1910

246 238 190 221

368 358 284 331

ASD

LRFD

Ωb = 1.67 Ωv = 1.50

φ b = 0.90 φ v = 1.00

v

Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3A:14th Ed.

2/24/11

8:40 AM

Page 24

3–24

DESIGN OF FLEXURAL MEMBERS

Table 3-2 (continued)

Zx

W-Shapes Selection by Zx

W24×84 W21×93 W12×136 W14×120 W18×97

in.3 224 221 214 212 211

Mpx /Ωb kip-ft ASD 559 551 534 529 526

W24×76 W16×100 W21×83 W14×109 W18×86 W12×120

200 198 196 192 186 186

W24×68 W16×89 W14×99f W21×73 W12×106 W18×76

Shape

Fy = 50 ksi

Zx

φb Mpx Mrx /Ωb φb Mrx BF/ Ωb φb BF kip-ft kip-ft kip-ft LRFD ASD LRFD

kips ASD

kips LRFD

Lp

Lr

Ix

ft

ft

Vnx /Ωv φvVnx kips kips ASD LRFD 227 340 251 376 212 318 171 257 199 299

840 829 803 795 791

342 335 325 332 328

515 504 488 499 494

16.2 14.6 4.02 5.09 9.41

24.2 6.89 22.0 6.50 6.06 11.2 7.65 13.2 14.1 9.36

20.3 21.3 63.2 51.9 30.4

in.4 2370 2070 1240 1380 1750

499 494 489 479 464 464

750 743 735 720 698 698

307 306 299 302 290 285

462 459 449 454 436 428

15.1 7.86 13.8 5.01 9.01 3.94

22.6 6.78 11.9 8.87 20.8 6.46 7.54 13.2 13.6 9.29 5.95 11.1

19.5 32.8 20.2 48.5 28.6 56.5

2100 1490 1830 1240 1530 1070

210 199 220 150 177 186

315 298 331 225 265 279

177 175 173 172 164 163

442 437 430 429 409 407

664 656 646 645 615 611

269 271 274 264 253 255

404 407 412 396 381 383

14.1 7.76 4.91 12.9 3.93 8.50

21.2 6.61 11.6 8.80 7.36 13.5 19.4 6.39 5.89 11.0 12.8 9.22

18.9 30.2 45.3 19.2 50.7 27.1

1830 1300 1110 1600 933 1330

197 176 138 193 157 155

295 265 207 289 236 232

W21×68 W14×90f

160 157

399 382

600 574

245 250

368 375

12.5 4.82

18.8 6.36 7.26 15.1

18.7 42.5

1480 999

181 123

272 185

W24x62 W16×77 W12×96 W10×112 W18×71

153 150 147 147 146

382 374 367 367 364

574 563 551 551 548

229 234 229 220 222

344 352 344 331 333

16.1 7.34 3.85 2.69 10.4

24.1 4.87 11.1 8.72 5.78 10.9 4.03 9.47 15.8 6.00

14.4 27.8 46.7 64.1 19.6

1550 1110 833 716 1170

204 150 140 172 183

306 225 210 258 275

W21×62 W14×82

144 139

359 347

540 521

222 215

333 323

11.6 5.40

17.5 8.10

6.25 8.76

18.1 33.2

1330 881

168 146

252 219

W24×55v W18×65 W12×87 W16×67 W10×100 W21×57

134 133 132 130 130 129

334 332 329 324 324 322

503 499 495 488 488 484

199 204 206 204 196 194

299 307 310 307 294 291

14.7 9.98 3.81 6.89 2.64 13.4

22.2 4.73 15.0 5.97 5.73 10.8 10.4 8.69 4.00 9.36 20.3 4.77

13.9 18.8 43.1 26.1 57.9 14.3

1350 1070 740 954 623 1170

167 166 129 129 151 171

252 248 193 193 226 256

ASD

LRFD

Ωb = 1.67 Ωv = 1.50

φ b = 0.90 φ v = 1.00

f v

Shape exceeds compact limit for flexure with Fy = 50 ksi. Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3A_14th Ed._February 25, 2013 14-11-10 10:29 AM Page 25

W-SHAPE SELECTION TABLES

3–25

Table 3-2 (continued)

Zx

W-Shapes

Fy = 50 ksi

Selection by Zx

W21×55 W14×74 W18×60 W12×79 W14×68 W10×88

in.3 126 126 123 119 115 113

Mpx /Ωb kip-ft ASD 314 314 307 297 287 282

W18×55

112

W21×50 W12×72

Shape

Zx

φb Mpx Mrx /Ωb φb Mrx BF/ Ωb φb BF kip-ft kip-ft kip-ft LRFD ASD LRFD

Lp

Lr

Ix

ft

ft

Vnx /Ωv φvVnx kips kips ASD LRFD 156 234 128 192 151 227 117 175 116 174 131 196

kips ASD

kips LRFD

16.3 6.11 8.05 8.76 14.4 5.93 5.67 10.8 7.81 8.69 3.94 9.29

17.4 31.0 18.2 39.9 29.3 51.2

in.4 1140 795 984 662 722 534

13.8

5.90

17.6

890

141

212

473 473 461 446 431 424

192 196 189 187 180 172

289 294 284 281 270 259

10.8 5.31 9.62 3.78 5.19 2.62

279

420

172

258

9.15

110 108

274 269

413 405

165 170

248 256

12.1 3.69

18.3 4.59 5.56 10.7

13.6 37.5

984 597

158 106

237 159

W21×48f W16×57 W14×61 W18×50 W10×77 W12×65f

107 105 102 101 97.6 96.8

265 262 254 252 244 237

398 394 383 379 366 356

162 161 161 155 150 154

244 242 242 233 225 231

9.89 7.98 4.93 8.76 2.60 3.58

14.8 5.86 12.0 5.65 7.48 8.65 13.2 5.83 3.90 9.18 5.39 10.7

16.5 18.3 27.5 16.9 45.3 35.1

959 758 640 800 455 533

144 141 104 128 112 94.4

216 212 156 192 169 142

W21×44 W16×50 W18×46 W14×53 W12×58 W10×68 W16×45

95.4 92.0 90.7 87.1 86.4 85.3 82.3

238 230 226 217 216 213 205

358 345 340 327 324 320 309

143 141 138 136 136 132 127

214 213 207 204 205 199 191

11.1 7.69 9.63 5.22 3.82 2.58 7.12

16.8 11.4 14.6 7.93 5.69 3.85 10.8

4.45 5.62 4.56 6.78 8.87 9.15 5.55

13.0 17.2 13.7 22.3 29.8 40.6 16.5

843 659 712 541 475 394 586

145 124 130 103 87.8 97.8 111

217 186 195 154 132 147 167

W18×40 W14×48 W12×53 W10×60

78.4 78.4 77.9 74.6

196 196 194 186

294 294 292 280

119 123 123 116

180 184 185 175

8.94 5.09 3.65 2.54

13.2 7.67 5.50 3.82

4.49 6.75 8.76 9.08

13.1 21.1 28.2 36.6

612 484 425 341

113 93.8 83.5 85.7

169 141 125 129

W16×40 W12×50 W8×67 W14×43 W10×54

73.0 71.9 70.1 69.6 66.6

182 179 175 174 166

274 270 263 261 250

113 112 105 109 105

170 169 159 164 158

6.67 3.97 1.75 4.88 2.48

10.0 5.98 2.59 7.28 3.75

5.55 6.92 7.49 6.68 9.04

15.9 23.8 47.6 20.0 33.6

518 391 272 428 303

97.6 90.3 103 83.6 74.7

146 135 154 125 112

ASD

LRFD

Ωb = 1.67 Ωv = 1.50

φ b = 0.90 φ v = 1.00

f

Shape exceeds compact limit for flexure with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3A:14th Ed.

2/24/11

8:40 AM

Page 26

3–26

DESIGN OF FLEXURAL MEMBERS

Table 3-2 (continued)

Zx Shape

W-Shapes

Fy = 50 ksi

Selection by Zx

Zx

Mpx /Ωb kip-ft ASD 166 160 160 153 151 149 142 137

φb Mpx Mrx /Ωb φb Mrx BF/ Ωb φb BF

Lp

Lr

Ix

ft

ft

kip-ft kip-ft kip-ft LRFD ASD LRFD

kips ASD

kips LRFD

249 241 240 231 227 224 214 206

101 101 98.7 95.4 95.4 90.8 89.9 85.8

151 151 148 143 143 137 135 129

8.14 3.80 6.24 5.37 2.46 1.70 3.66 2.59

12.3 5.80 9.36 8.20 3.71 2.55 5.54 3.89

4.31 6.89 5.37 5.47 8.97 7.42 6.85 7.10

12.3 22.4 15.2 16.2 31.6 41.6 21.1 26.9

in.4 510 348 448 385 272 228 307 248

φvVnx

Vnx /Ωv kips ASD 106 81.1 93.8 87.4 68.0 89.3 70.2 70.7

159 122 141 131 102 134 105 106

kips LRFD

W18×35 W12×45 W16×36 W14×38 W10×49 W8×58 W12×40 W10×45

in.3 66.5 64.2 64.0 61.5 60.4 59.8 57.0 54.9

W14×34

54.6

136

205

84.9

128

5.01

7.55

5.40

15.6

340

79.8

120

W16×31 W12×35 W8×48

54.0 51.2 49.0

135 128 122

203 192 184

82.4 79.6 75.4

124 120 113

6.86 4.34 1.67

10.3 6.45 2.55

4.13 5.44 7.35

11.8 16.6 35.2

375 285 184

87.5 75.0 68.0

131 113 102

W14×30 W10×39

47.3 46.8

118 117

177 176

73.4 73.5

110 111

4.63 2.53

6.95 3.78

5.26 6.99

14.9 24.2

291 209

74.5 62.5

112 93.7

W16×26v W12×30

44.2 43.1

110 108

166 162

67.1 67.4

101 101

5.93 3.97

8.98 5.96

3.96 5.37

11.2 15.6

301 238

70.5 64.0

106 95.9

W14×26 W8×40 W10×33

40.2 39.8 38.8

100 99.3 96.8

151 149 146

61.7 62.0 61.1

92.7 93.2 91.9

5.33 1.64 2.39

8.11 2.46 3.62

3.81 7.21 6.85

11.0 29.9 21.8

245 146 171

70.9 59.4 56.4

106 89.1 84.7

W12×26 W10×30 W8×35

37.2 36.6 34.7

92.8 91.3 86.6

140 137 130

58.3 56.6 54.5

87.7 85.1 81.9

3.61 3.08 1.62

5.46 4.61 2.43

5.33 4.84 7.17

14.9 16.1 27.0

204 170 127

56.1 63.0 50.3

84.2 94.5 75.5

W14×22 W10×26 W8×31f

33.2 31.3 30.4

82.8 78.1 75.8

125 117 114

50.6 48.7 48.0

76.1 73.2 72.2

4.78 2.91 1.58

7.27 4.34 2.37

3.67 4.80 7.18

10.4 14.9 24.8

199 144 110

63.0 53.6 45.6

94.5 80.3 68.4

W12×22 W8×28

29.3 27.2

73.1 67.9

110 102

44.4 42.4

66.7 63.8

4.68 1.67

7.06 2.50

3.00 5.72

9.13 21.0

156 98.0

64.0 45.9

95.9 68.9

W10×22

26.0

64.9

97.5

40.5

60.9

2.68

4.02

4.70

13.8

118

49.0

73.4

W12×19 W8×24

24.7 23.1

61.6 57.6

92.6 86.6

37.2 36.5

55.9 54.9

4.27 1.60

6.43 2.40

2.90 5.69

8.61 18.9

130 82.7

57.3 38.9

86.0 58.3

W10×19 W8×21

21.6 20.4

53.9 50.9

81.0 76.5

32.8 31.8

49.4 47.8

3.18 1.85

4.76 2.77

3.09 4.45

9.73 14.8

96.3 75.3

51.0 41.4

76.5 62.1

ASD

LRFD

Ωb = 1.67 Ωv = 1.50

φ b = 0.90 φ v = 1.00

f v

Shape exceeds compact limit for flexure with Fy = 50 ksi. Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3A:14th Ed.

2/24/11

8:40 AM

Page 27

W-SHAPE SELECTION TABLES

3–27

Table 3-2 (continued)

Zx

W-Shapes

Fy = 50 ksi

Selection by Zx φb Mpx Mrx /Ωb φb Mrx BF/ Ωb φb BF

W12×16 W10×17

Mpx /Ωb kip-ft ASD in.3 20.1 50.1 18.7 46.7

W12×14v W8×18 W10×15 W8×15

17.4 17.0 16.0 13.6

W10×12f W8×13 W8×10f

Shape

Zx

Lp

Lr

ft

ft

Vnx /Ωv kips ASD in.4 103 52.8 81.9 48.5 Ix

φvVnx

kip-ft kip-ft kip-ft LRFD ASD LRFD

kips ASD

kips LRFD

75.4 70.1

29.9 28.3

44.9 42.5

3.80 2.98

5.73 4.47

2.73 2.98

8.05 9.16

43.4 42.4 39.9 33.9

65.3 63.8 60.0 51.0

26.0 26.5 24.1 20.6

39.1 39.9 36.2 31.0

3.43 1.74 2.75 1.90

5.17 2.61 4.14 2.85

2.66 4.34 2.86 3.09

7.73 13.5 8.61 10.1

88.6 61.9 68.9 48.0

42.8 37.4 46.0 39.7

64.3 56.2 68.9 59.6

12.6 11.4

31.2 28.4

46.9 42.8

19.0 17.3

28.6 26.0

2.36 1.76

3.53 2.67

2.87 2.98

8.05 9.27

53.8 39.6

37.5 36.8

56.3 55.1

8.87

21.9

32.9

13.6

20.5

1.54

2.30

3.14

8.52

30.8

26.8

40.2

ASD

LRFD

Ωb = 1.67 Ωv = 1.50

φ b = 0.90 φ v = 1.00

f v

kips LRFD 79.2 72.7

Shape exceeds compact limit for flexure with Fy = 50 ksi. Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3A:14th Ed.

2/24/11

8:40 AM

Page 28

3–28

DESIGN OF FLEXURAL MEMBERS

Table 3-3

Ix

W-Shapes Selection by Ix Ix

Shape

Shape 4

50600

W40×593h

50400

W40×503h W36×529h

41600 39600

W36×487h

36000

W40×431h W36×441h

34800 32100

W40×397h

W36×652

h

Shape 4

in. h

Ix

32000

20800 20700 20500 19600 19600 19500 19400 18700 17900 17700 17400 16800 16800

W44×335 W40×392h W40×372h W40×362h W36×395h

31100 29900 29600 28900 28500

W40×215 W36×247 W27×368h W33×263 W36×231

16700 16700 16200 15900 15600

W44×290 W36×361h W40×324 W27×539h W40×331h W40×327h W33×387h

27000 25700 25600 25600 24700 24500 24300

W40×211 W36×232

15500 15000

W44×262 W36×330 W40×297 W33×354h W40×277 W40×294 W36×302

24100 23300 23200 22000 21900 21900 21100

W40×199 W30×292 W27×336h W14×730h W33×241 W24×370h

14900 14900 14600 14300 14200 13400

W40×183 W36×210 W30×261 W27×307h W33×221 W14×665h W36×194 W27×281 W24×335h W30×235

13200 13200 13100 13100 12900 12400 12100 11900 11900 11700

Shape 4

in. W44×230 W30×391h W40×278 W40×249 W36×282 W33×318 W40×264 W30×357h W36×262 W33×291 W40×235 W36×256 W30×326h

Ix

in.4

in. W40×167 W33×201 W36×182 W27×258 W14×605h W24×306h W36×170 W30×211

11600 11600 11300 10800 10800 10700 10500 10300

W40×149 W36×160 W27×235 W24×279h W14×550h W33×169 W30×191 W36×150 W27×217 W24×250 W30×173 W14×500h W33×152 W27×194

9800 9760 9700 9600 9430 9290 9200 9040 8910 8490 8230 8210 8160 7860

W36×135 W24×229 W33×141 W14×455h W27×178 W18×311h W24×207

7800 7650 7450 7190 7020 6970 6820

W33×130 W30×148 W14×426h W27×161 W24×192 W18×283h W14×398h

6710 6680 6600 6310 6260 6170 6000

W33×118 W30×132 W24×176 W27×146 W18×258h W14×370h W30×124 W21×201 W24×162

5900 5770 5680 5660 5510 5440 5360 5310 5170

W30×116 W18×234h W14×342h W27×129 W21×182 W24×146

4930 4900 4900 4760 4730 4580

W30×108 W18×211 W14×311h W21×166 W27×114 W12×336h W24×131

4470 4330 4330 4280 4080 4060 4020

W30×99 W18×192 W14×283h W21×147 W27×102

3990 3870 3840 3630 3620

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Ix

AISC_Part 3A:14th Ed.

2/24/11

8:40 AM

Page 29

W-SHAPE SELECTION TABLES

3–29

Table 3-3 (continued)

Ix

W-Shapes Selection by Ix

Shape

Ix

Shape 4

h

3610 3550 3540 3450 3400 3270 3220 3110 3100 3060 3010 3000 2960

W27×84 W18×143 W12×252h W24×94 W21×111 W14×211 W18×130 W21×101 W12×230h W14×193

Shape 4

in. W30×90 W12×305h W24×117 W18×175 W14×257 W27×94 W21×132 W12×279h W24×104 W18×158 W14×233 W24×103 W21×122

Ix

1830 1830 1750 1710 1650 1600

W24×62 W18×86 W14×132 W16×100 W21×68 W12×152 W14×120

1550 1530 1530 1490 1480 1430 1380

2850 2750 2720 2700 2670 2660 2460 2420 2420 2400

W24×55 W21×62 W18×76 W16×89 W14×109 W12×136 W21×57 W18×71

1350 1330 1330 1300 1240 1240 1170 1170

W24×84 W18×119 W14×176 W12×210

2370 2190 2140 2140

W21×55 W16×77 W14×99 W18×65 W12×120 W14×90

1140 1110 1110 1070 1070 999

W24×76 W21×93 W18×106 W14×159 W12×190

2100 2070 1910 1900 1890

W21×50 W18×60

984 984

W21×48 W16×67 W12×106 W18×55 W14×82

959 954 933 890 881

Shape 4

in. W24×68 W21×83 W18×97 W14×145 W12×170 W21×73

Ix

in.4

in. W21×44 W12×96 W18×50 W14×74 W16×57 W12×87 W14×68 W10×112 W18×46 W12×79 W16×50 W14×61 W10×100

843 833 800 795 758 740 722 716 712 662 659 640 623

W18×40 W12×72 W16×45 W14×53 W10×88 W12×65

612 597 586 541 534 533

W16×40

518

W18×35 W14×48 W12×58 W10×77 W16×36 W14×43 W12×53 W10×68 W12×50 W14×38

510 484 475 455 448 428 425 394 391 385

W16×31 W12×45 W10×60 W14×34 W12×40 W10×54

375 348 341 340 307 303

W16×26 W14×30 W12×35 W10×49 W8×67 W10×45

301 291 285 272 272 248

W14×26 W12×30 W8×58 W10×39

245 238 228 209

W12×26

204

W14×22 W8×48 W10×33 W10×30

199 184 171 170

W12×22 W8×40 W10×26

156 146 144

W12×19 W8×35 W10×22 W8×31

130 127 118 110

W12×16 W8×28 W10×19

103 98.0 96.3

W12×14 W8×24 W10×17 W8×21 W10×15 W8×18

88.6 82.7 81.9 75.3 68.9 61.9

W10×12 W8×15 W8×13

53.8 48.0 39.6

W8×10

30.8

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Ix

AISC_Part 3A:14th Ed.

2/24/11

8:41 AM

Page 30

3–30

DESIGN OF FLEXURAL MEMBERS

Table 3-4

Zy

W-Shapes Selection by Zy

Zy

Shape

Mny /Ωb φb Mny

in.3

ASD

kip-ft LRFD

Shape

W14×730h

816

2040

3060

h

W14×665

730

1820

2740

W14×605h

652

1630

2450

h

W14×550 W36×652h

583 581

1450 1450

2190 2180

W14×500h W40×593h

522 481

1300 1200

1960 1800

W14×455h W36×529h W27×539h

468 454 437

1170 1130 1090

1760 1700 1640

W14×426h W36×487h

434 412

1080 1030

1630 1550

W14×398h W40×503h

402 394

1000 983

1510 1480

W14×370h W36×441h

370 368

923 918

1390 1380

h

W14×342 W40×431h W36×395h W33×387h W30×391h

338 328 325 312 310

843 818 811 778 773

1270 1230 1220 1170 1160

W14×311h W40×397h W36×361h W33×354h W30×357h W27×368h W40×372h

304 300 293 282 279 279 277

758 749 731 704 696 696 691

1140 1130 1100 1060 1050 1050 1040

ASD

kip-ft

LRFD

f h

Ωb = 1.67 Ωv = 1.50

Fy = 50 ksi

φ b = 0.90 φ v = 1.00

Zy

Mny /Ωb φb Mny

in.3

ASD

kip-ft LRFD

Shape

W14×283h W12×336h W40×362h W24×370h W36×330 W30×326h W27×336h W33×318

274 274 270 267 265 252 252 250

684 684 674 666 661 629 629 624

1030 1030 1010 1000 994 945 945 938

W14×257 W12×305h W36×302 W40×324 W24×335h W44×335 W27×307h W33×291 W36×282 W30×292

246 244 241 239 238 236 227 226 223 223

614 609 601 596 594 589 566 564 556 556

923 915 904 896 893 885 851 848 836 836

W14×233 W12×279h W40×297 W24×306h W40×392h W18×311h W27×281 W44×290 W40×277 W36×262 W33×263

221 220 215 214 212 207 206 205 204 204 202

551 549 536 534 519 516 514 511 509 509 504

829 825 806 803 780 776 773 769 765 765 758

kip-ft

Zy

Mny /Ωb φb Mny kip-ft

kip-ft LRFD

W14×211 W30×261 W12×252h W24×279h W36×247 W27×258 W18×283h W44×262 W40×249 W33×241

in.3 198 196 196 193 190 187 185 182 182 182

ASD 494 489 489 482 474 467 462 454 454 454

W14×193 W12×230h W36×231 W30×235 W40×331h W24×250 W27×235 W18×258h W33×221

180 177 176 175 172 171 168 166 164

449 442 439 437 423 427 419 414 409

675 664 660 656 636 641 630 623 615

W14×176 W12×210 W44×230f W40×215 W30×211 W27×217 W24×229 W40×294 W18×234h W33×201

163 159 157 156 155 154 154 150 149 147

407 397 392 389 387 384 384 373 372 367

611 596 589 585 581 578 578 561 559 551

743 735 735 724 713 701 694 683 683 683

Shape exceeds compact limit for flexure with Fy = 50 ksi. Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3A:14th Ed.

2/24/11

8:41 AM

Page 31

W-SHAPE SELECTION TABLES

3–31

Table 3-4 (continued)

Zy

W-Shapes

Fy = 50 ksi

Selection by Zy

Shape

Mny /Ωb φb Mny

Zy

kip-ft

kip-ft LRFD

Shape

548 536 523 518 514 514 514 510 499

W14×159 W12×190 W40×278 W30×191 W40×199 W36×256 W24×207 W27×194 W21×201

in.3 146 143 140 138 137 137 137 136 133

ASD 364 357 348 344 342 342 342 339 332

W14×145 W40×264 W18×211 W24×192 W12×170 W30×173 W36×232 W27×178 W21×182 W18×192 W40×235 W24×176

133 132 132 126 126 123 122 122 119 119 118 115

332 329 329 314 314 307 304 304 297 297 294 287

499 495 495 473 473 461 458 458 446 446 443 431

W14×132 W12×152 W27×161 W21×166 W36×210 W18×175 W40×211 W24×162

113 111 109 108 107 106 105 105

282 277 272 269 267 264 262 262

424 416 409 405 401 398 394 394

W14×120 W12×136 W36×194 W27×146 W18×158 W24×146

102 98.0 97.7 97.7 94.8 93.2

254 245 244 244 237 233

383 368 366 366 356 350

ASD

LRFD

Ωb = 1.67 Ωv = 1.50

φ b = 0.90 φ v = 1.00

f

Zy

Mny /Ωb φb Mny kip-ft

kip-ft LRFD

Shape

348 347 340 331 320 320 317 314

W14×109 W21×147 W36×182 W40×183 W18×143 W12×120 W33×169 W36×170

in.3 92.7 92.6 90.7 88.3 85.4 85.4 84.4 83.8

ASD 231 231 226 220 213 213 211 209

W14×99f W21×132 W24×131 W36×160 W18×130 W40×167 W21×122

83.6 82.3 81.5 77.3 76.7 76.0 75.6

207 205 203 193 191 190 189

311 309 306 290 288 285 283

W14×90f W12×106 W33×152 W24×117 W36×150 W10×112 W18×119 W21×111 W30×148 W12×96 W33×141 W24×104 W40×149 W21×101 W10×100 W18×106

75.6 75.1 73.9 71.4 70.9 69.2 69.1 68.2 68.0 67.5 66.9 62.4 62.2 61.7 61.0 60.5

181 187 184 178 177 173 172 170 170 168 167 156 155 154 152 151

273 282 277 268 266 260 259 256 255 253 251 234 233 231 229 227

Zy

Mny /Ωb φb Mny kip-ft

kip-ft LRFD

W12×87 W36×135 W33×130 W30×132 W27×129 W18×97 W16×100

in.3 60.4 59.7 59.5 58.4 57.6 55.3 54.9

ASD 151 149 148 146 144 138 137

W12×79 W30×124 W10×88 W33×118 W27×114 W30×116

54.3 54.0 53.1 51.3 49.3 49.2

135 135 132 128 123 123

204 203 199 192 185 185

W12×72 W18×86 W16×89 W10×77 W14×82

49.2 48.4 48.1 45.9 44.8

123 121 120 115 112

185 182 180 172 168

W12×65f W30×108 W27×102 W18×76 W24×103 W16×77 W14×74 W10×68 W27×94 W30×99 W24×94 W14×68 W16×67

44.1 43.9 43.4 42.2 41.5 41.1 40.5 40.1 38.8 38.6 37.5 36.9 35.5

107 110 108 105 104 103 101 100 96.8 96.3 93.6 92.1 88.6

161 165 163 158 156 154 152 150 146 145 141 138 133

Shape exceeds compact limit for flexure with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

227 224 223 219 216 207 206

AISC_Part 3A:14th Ed.

2/24/11

8:41 AM

Page 32

3–32

DESIGN OF FLEXURAL MEMBERS

Table 3-4 (continued)

Zy Shape

W-Shapes

Fy = 50 ksi

Selection by Zy

Zy

Mny /Ωb φb Mny kip-ft

kip-ft LRFD

W10×60 W30×90 W21×93 W27×84 W14×61 W8×67 W24×84

in.3 35.0 34.7 34.7 33.2 32.8 32.7 32.6

ASD 87.3 86.6 86.6 82.8 81.8 81.6 81.3

131 130 130 125 123 123 122

W12×58

32.5

81.1

122

W10×54 W21×83

31.3 30.5

78.1 76.1

117 114

W12×53 W24×76

29.1 28.6

72.6 71.4

109 107

W10×49 W8×58 W21×73 W18×71 W24×68 W21×68

28.3 27.9 26.6 24.7 24.5 24.4

70.6 69.6 66.4 61.6 61.1 60.9

106 105 99.8 92.6 91.9 91.5

W8×48 W18×65 W14×53 W21×62 W12×50 W18×60

22.9 22.5 22.0 21.7 21.3 20.6

57.1 56.1 54.9 54.1 53.1 51.4

85.9 84.4 82.5 81.4 79.9 77.3

W10×45 W14×48

20.3 19.6

50.6 48.9

76.1 73.5

W12×45 W16×57 W18×55

19.0 18.9 18.5

47.4 47.2 46.2

71.3 70.9 69.4

ASD

LRFD

Ωb = 1.67 Ωv = 1.50

φ b = 0.90 φ v = 1.00

f

Shape

Zy

Mny /Ωb φb Mny kip-ft

kip-ft LRFD

W8×40 W21×55 W14×43

in.3 18.5 18.4 17.3

ASD 46.2 45.9 43.2

W10×39 W12×40 W18×50 W16×50

17.2 16.8 16.6 16.3

42.9 41.9 41.4 40.7

64.5 63.0 62.3 61.1

W8×35 W24×62 W21×48f W21×57 W16×45

16.1 15.7 14.9 14.8 14.5

40.2 39.1 36.7 36.9 36.2

60.4 58.8 55.2 55.5 54.4

W8×31f W10×33 W24×55 W16×40 W21×50 W14×38 W18×46 W12×35 W16×36 W14×34 W21×44

14.1 14.0 13.3 12.7 12.2 12.1 11.7 11.5 10.8 10.6 10.2

35.1 34.9 33.1 31.7 30.4 30.2 29.2 28.7 26.9 26.4 25.4

52.8 52.5 49.8 47.6 45.8 45.4 43.9 43.1 40.5 39.8 38.2

W8×28 W18×40 W12×30 W14×30 W10×30

10.1 10.0 9.56 8.99 8.84

25.2 25.0 23.9 22.4 22.1

37.9 37.5 35.9 33.7 33.2

69.4 69.0 64.9

Shape

Zy

Mny /Ωb φb Mny kip-ft

kip-ft LRFD

W8×24 W12×26 W18×35 W10×26 W16×31

in.3 8.57 8.17 8.06 7.50 7.03

ASD 21.4 20.4 20.1 18.7 17.5

W10×22

6.10

15.2

22.9

W8×21 W14×26 W16×26

5.69 5.54 5.48

14.2 13.8 13.7

21.3 20.8 20.6

W8×18 W14×22 W12×22 W10×19 W12×19

4.66 4.39 3.66 3.35 2.98

11.6 11.0 9.13 8.36 7.44

17.5 16.5 13.7 12.6 11.2

W10×17

2.80

6.99

10.5

W8×15

2.67

6.66

10.0

W10×15 W12×16

2.30 2.26

5.74 5.63

8.63 8.46

W8×13 W12×14

2.15 1.90

5.36 4.74

8.06 7.13

W10×12f

1.74

4.30

6.46

W8×10f

1.66

4.07

6.12

Shape exceeds compact limit for flexure with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

32.1 30.6 30.2 28.1 26.4

AISC_Part 3A:14th Ed.

2/24/11

8:41 AM

Page 33

W-SHAPE SELECTION TABLES

3–33

Table 3-5

Iy

W-Shapes Selection by Iy Iy

Shape

Iy

Shape 4

in.

h

h

W14×730

4720

W14×665h

4170

W14×605h

3680

W14×550h W36×652h

3250 3230

W14×500h

2880

W14×455h W40×593h

2560 2520

W36×529h

2490

W14×426h W36×487h

2360 2250

W14×398h W27×539h W40×503h W36×441h

2170 2110 2040 1990

W14×370h

1990

W14×342h W36×395h W40×431h W33×387h

1810 1750 1690 1620

W14×311h W36×361h W30×391h W40×397h W33×354h

1610 1570 1550 1540 1460

Shape 4

W14×283 W40×372h W36×330 W30×357h W40×362h W27×368h W36×302 W33×318

1440 1420 1420 1390 1380 1310 1300 1290

W14×257 W30×326h W40×324 W44×335 W36×282 W12×336h W27×336h W33×291 W24×370h

1290 1240 1220 1200 1200 1190 1180 1160 1160

W14×233 W30×292 W40×297 W36×262 W27×307h W12×305h W44×290 W40×277 W33×263 W24×335h

1150 1100 1090 1090 1050 1050 1040 1040 1040 1030

W14×211 W36×247 W30×261 W27×281 W36×231 W12×279h W33×241

1030 1010 959 953 940 937 933

Shape 4

in. h

Iy

Iy in.4

in. W14×193 W40×249 W44×262 W24×306h W27×258 W30×235 W33×221

931 926 923 919 859 855 840

W14×132 W21×201 W24×192 W36×256 W40×278 W12×170 W27×161

548 542 530 528 521 517 497

W14×176 W12×252h W24×279h W40×392h W44×230 W40×215 W18×311h W27×235 W30×211 W33×201

838 828 823 803 796 803 795 769 757 749

W14×120 W40×264 W18×211 W21×182 W24×176 W36×232 W12×152

495 493 493 483 479 468 454

W14×159 W12×230h W24×250 W27×217 W18×283h W40×199

748 742 724 704 704 695

W14×109 W40×235 W27×146 W24×162 W18×192 W21×166 W36×210

447 444 443 443 440 435 411

W14×145 W30×191 W12×210 W24×229 W40×331h W40×327h W18×258h W27×194 W30×173 W12×190 W24×207 W40×294 W18×234h W27×178

677 673 664 651 644 640 628 619 598 589 578 562 558 555

W14×99 W12×136 W24×146 W18×175 W40×211 W21×147 W36×194

402 398 391 391 390 376 375

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3A:14th Ed.

2/24/11

8:41 AM

Page 34

3–34

DESIGN OF FLEXURAL MEMBERS

Table 3-5 (continued)

Iy Shape

W-Shapes Selection by Iy Iy

Shape 4

h

362 347 347 345 340 333 331 320 311 310 305 301 297 295 283 278 274 273 270 270 259 253 248 246

W12×87 W10×112 W40×149 W30×148 W36×135 W18×106 W33×130

241 236 229 227 225 220 218

W12×79 W10×100 W18×97 W30×132

216 207 201 196

W12×72 W33×118 W16×100 W27×129 W30×124 W10×88 W18×86

195 187 186 184 181 179 175

Shape 4

in. W14×90 W36×182 W18×158 W12×120 W24×131 W21×132 W40×183 W36×170 W18×143 W33×169 W21×122 W12×106 W24×117 W36×160 W40×167 W18×130 W21×111 W33×152 W36×150 W12×96 W24×104 W18×119 W21×101 W33×141

Iy

174 164 163 159 154 152 148 146 139 138 134 134 128 124 121 119 119

W10×60 W30×90 W24×94 W14×61

116 115 109 107

W12×58 W27×84

107 106

W10×54

103

W12×53 W24×84

95.8 94.4

W10×49 W21×93 W8×67 W24×76 W21×83 W8×58 W21×73 W24×68 W21×68

93.4 92.9 88.6 82.5 81.4 75.1 70.6 70.4 64.7

Shape 4

in. W12×65 W30×116 W16×89 W27×114 W10×77 W18×76 W14×82 W30×108 W27×102 W16×77 W14×74 W10×68 W30×99 W27×94 W14×68 W24×103 W16×67

Iy

in.4

in. W8×48 W18×71 W14×53 W21×62 W12×50 W18×65

60.9 60.3 57.7 57.5 56.3 54.8

W10×45 W14×48 W18×60

53.4 51.4 50.1

W12×45

50.0

W8×40 W21×55 W14×43

49.1 48.4 45.2

W10×39 W18×55 W12×40 W16×57

45.0 44.9 44.1 43.1

W8×35 W18×50 W21×48 W16×50

42.6 40.1 38.7 37.2

W8×31 W10×33 W24×62 W16×45 W21×57 W24×55 W16×40 W14×38 W21×50 W16×36 W12×35 W14×34 W18×46

37.1 36.6 34.5 32.8 30.6 29.1 28.9 26.7 24.9 24.5 24.5 23.3 22.5

W8×28 W21×44 W12×30 W14×30 W18×40

21.7 20.7 20.3 19.6 19.1

W8×24 W12×26 W10×30 W18×35 W10×26 W16×31

18.3 17.3 16.7 15.3 14.1 12.4

W10×22

11.4

W8×21 W16×26 W14×26

9.77 9.59 8.91

W8×18 W14×22 W12×22 W10×19 W12×19

7.97 7.00 4.66 4.29 3.76

W10×17

3.56

W8×15

3.41

W10×15 W12×16

2.89 2.82

W8×13 W12×14

2.73 2.36

W10×12

2.18

W8×10

2.09

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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MAXIMUM TOTAL UNIFORM LOAD TABLES

Table 3-6

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes

W44 W44×

Shape

335

230v

262

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

Span, ft

Design

290

17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

1810 1800 1700 1620 1540 1470 1410 1350 1290 1240 1200 1150 1120 1080 1010 951 898 851 808 770 735 703 674 647 622 599 577 558 539 522 505 490 476 462 449

2720 2700 2560 2430 2310 2210 2110 2030 1940 1870 1800 1740 1680 1620 1520 1430 1350 1280 1220 1160 1100 1060 1010 972 935 900 868 838 810 784 759 736 715 694 675

1510 1480 1410 1340 1280 1220 1170 1130 1080 1040 1010 970 938 879 828 782 741 704 670 640 612 586 563 541 521 503 485 469 454 440 426 414 402 391

2260 2230 2120 2010 1920 1840 1760 1690 1630 1570 1510 1460 1410 1320 1240 1180 1110 1060 1010 961 920 881 846 813 783 755 729 705 682 661 641 622 604 588

1360 1330 1270 1210 1150 1100 1060 1010 975 939 905 874 845 792 746 704 667 634 604 576 551 528 507 487 469 453 437 422 409 396 384 373 362 352

2040 2010 1910 1810 1730 1660 1590 1520 1470 1410 1360 1310 1270 1190 1120 1060 1000 953 907 866 828 794 762 733 706 680 657 635 615 595 577 560 544 529

1090 1050 998 955 915 878 844 813 784 757 732 686 646 610 578 549 523 499 477 457 439 422 407 392 379 366 354 343 333 323 314 305

1640 1570 1500 1430 1380 1320 1270 1220 1180 1140 1100 1030 971 917 868 825 786 750 717 688 660 635 611 589 569 550 532 516 500 485 471 458

Wc /Ωb Mp /Ωb Mr /Ωb BF /Ωb Vn /Ωv

φbWc , kip-ft φb Mp , kip-ft φb Mr , kip-ft φb BF, kips φvVn , kips

32300 4040 2460 59.4 906

48600 6080 3700 89.5 1360

25300 3170 1940 52.6 680

38100 4760 2910 79.1 1020

22000 2740 1700 46.8 547

33000 4130 2550 71.2 822

Beam Properties

Zx , in.3 Lp , ft Lr , ft

1620 12.3 38.9

ASD

LRFD

Ωb = 1.67 Ωv = 1.50

φ b = 0.90 φ v = 1.00

28100 3520 2170 54.9 754 1410 12.3 36.9

42300 5290 3260 82.5 1130

1270 12.3 35.7

v

1100 12.1 34.3

Shape does not meet the h/tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67. Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

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DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W40 Shape Design 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

Span, ft

Fy = 50 ksi

593h ASD LRFD

3080 3060 2900 2750 2620 2500 2400 2300 2200 2120 2040 1970 1900 1840 1720 1620 1530 1450 1380 1310 1250 1200 1150 1100 1060 1020 984 950 918 889 861 835 810 787 765

4620 4600 4360 4140 3940 3760 3600 3450 3310 3180 3070 2960 2860 2760 2590 2440 2300 2180 2070 1970 1880 1800 1730 1660 1590 1530 1480 1430 1380 1340 1290 1250 1220 1180 1150

503 h ASD LRFD

2590 2570 2440 2320 2210 2100 2010 1930 1850 1780 1720 1650 1600 1540 1450 1360 1290 1220 1160 1100 1050 1010 965 926 891 858 827 798 772 747 724 702 681 662 643

3890 3870 3660 3480 3310 3160 3030 2900 2780 2680 2580 2490 2400 2320 2180 2050 1930 1830 1740 1660 1580 1510 1450 1390 1340 1290 1240 1200 1160 1120 1090 1050 1020 994 967

W40× 397 h 431h ASD LRFD ASD LRFD

392 h ASD LRFD

372 h ASD LRFD

2210 2170 2060 1960 1860 1780 1700 1630 1560 1500 1450 1400 1350 1300 1220 1150 1090 1030 978 931 889 850 815 782 752 724 699 675 652 631 611 593 575 559 543

2360 2280 2130 2010 1900 1800 1710 1630 1550 1480 1420 1370 1310 1260 1220 1180 1140 1070 1000 948 898 853 813 776 742 711 683 656 632 609 588 569 551 533 517 502 488 474

1880 1860 1760 1680 1600 1520 1460 1400 1340 1290 1240 1200 1160 1120 1050 986 931 882 838 798 762 729 699 671 645 621 599 578 559 541 524 508 493 479 466

3320 3270 3090 2940 2800 2670 2560 2450 2350 2260 2180 2100 2030 1960 1840 1730 1630 1550 1470 1400 1340 1280 1230 1180 1130 1090 1050 1010 980 948 919 891 865 840 817

2000 1890 1800 1710 1630 1560 1500 1440 1380 1330 1280 1240 1200 1120 1060 998 945 898 855 817 781 749 719 691 665 642 619 599 579 561 544 528 513 499

3000 2840 2700 2570 2450 2350 2250 2160 2080 2000 1930 1860 1800 1690 1590 1500 1420 1350 1290 1230 1170 1130 1080 1040 1000 964 931 900 871 844 818 794 771 750

3540 3420 3210 3020 2850 2700 2570 2440 2330 2230 2140 2050 1970 1900 1830 1770 1710 1600 1510 1430 1350 1280 1220 1170 1120 1070 1030 987 950 916 884 855 827 802 777 754 733 713

2830 2800 2650 2520 2400 2290 2190 2100 2020 1940 1870 1800 1740 1680 1580 1480 1400 1330 1260 1200 1150 1100 1050 1010 969 933 900 869 840 813 788 764 741 720 700

Beam Properties Wc /Ωb φbWc , kip-ft Mp /Ωb φb Mp , kip-ft Mr /Ωb φb Mr , kip-ft BF /Ωb φb BF, kips Vn /Ωv φvVn , kips

55100 82800 46300 69600 39100 58800 35900 54000 34100 51300 33500 50400 6890 10400 5790 8700 4890 7350 4490 6750 4270 6410 4190 6300 4090 6140 3460 5200 2950 4440 2720 4100 2510 3780 2550 3830 55.4 84.4 55.3 83.1 53.6 80.4 52.4 78.4 60.8 90.8 51.7 77.9 1540 2310 1300 1950 1110 1660 1000 1500 1180 1770 942 1410

Zx , in.3 Lp , ft Lr , ft

ASD

2760 13.4 63.9

LRFD

h

2320 13.1 55.2

1960 12.9 49.1

1800 12.9 46.7

1710 9.33 38.3

1680 12.7 44.4

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

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MAXIMUM TOTAL UNIFORM LOAD TABLES

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape Design

Span, ft

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

W40

362h ASD LRFD

331h ASD LRFD

W40× 324 327h ASD LRFD ASD LRFD

1820 1720 1640 1560 1490 1420 1360 1310 1260 1210 1170 1130 1090 1020 963 909 861 818 779 744 712 682 655 630 606 585 564 546 528 511 496 481 468 455

1990 1900 1780 1680 1590 1500 1430 1360 1300 1240 1190 1140 1100 1060 1020 984 951 892 839 793 751 714 680 649 620 595 571 549 529 510 492 476 460 446 432 420 408 396

1930 1880 1760 1660 1560 1480 1410 1340 1280 1220 1170 1130 1080 1040 1010 970 938 879 828 782 741 704 670 640 612 586 563 541 521 503 485 469 454 440 426 414 402 391

2730 2590 2460 2340 2240 2140 2050 1970 1890 1820 1760 1700 1640 1540 1450 1370 1290 1230 1170 1120 1070 1030 984 946 911 879 848 820 794 769 745 724 703 683

2990 2860 2680 2520 2380 2260 2150 2040 1950 1870 1790 1720 1650 1590 1530 1480 1430 1340 1260 1190 1130 1070 1020 975 933 894 858 825 794 766 740 715 692 670 650 631 613 596

2890 2820 2640 2490 2350 2230 2120 2010 1920 1840 1760 1690 1630 1570 1510 1460 1410 1320 1240 1180 1110 1060 1010 961 920 881 846 813 783 755 729 705 682 661 641 622 604 588

1610 1530 1460 1390 1320 1270 1210 1170 1120 1080 1040 1000 971 911 857 809 767 729 694 662 634 607 583 560 540 520 502 486 470 455 442 429 416 405

2410 2310 2190 2090 1990 1900 1830 1750 1680 1620 1560 1510 1460 1370 1290 1220 1150 1100 1040 995 952 913 876 842 811 782 755 730 706 684 664 644 626 608

297 ASD LRFD

294 ASD LRFD

1480 1470 1400 1330 1260 1210 1150 1110 1060 1020 983 948 915 885 830 781 737 699 664 632 603 577 553 531 511 492 474 458 442 428 415 402 390 379 369

1710 1690 1580 1490 1410 1330 1270 1210 1150 1100 1060 1010 975 939 905 874 845 792 746 704 667 634 604 576 551 528 507 487 469 453 437 422 409 396 384 373 362 352

2220 2220 2100 2000 1900 1810 1730 1660 1600 1530 1480 1430 1380 1330 1250 1170 1110 1050 998 950 907 867 831 798 767 739 713 688 665 644 623 605 587 570 554

2570 2540 2380 2240 2120 2010 1910 1810 1730 1660 1590 1520 1470 1410 1360 1310 1270 1190 1120 1060 1000 953 907 866 828 794 762 733 706 680 657 635 615 595 577 560 544 529

Beam Properties Wc /Ωb φbWc , kip-ft 32700 49200 28500 42900 28100 42300 29100 43800 26500 39900.0 25300 38100 Mp /Ωb φb Mp , kip-ft 4090 6150 3570 5360 3520 5290 3640 5480 3320 4990 3170 4760 Mr /Ωb φb Mr , kip-ft 2480 3730 2110 3180 2100 3150 2240 3360 2040 3070 1890 2840 BF /Ωb φb BF, kips 51.4 77.3 59.1 88.2 58.0 87.4 49.0 74.1 47.8 71.6 56.9 85.4 Vn /Ωv φvVn , kips 909 1360 996 1490 963 1440 804 1210 740 1110 856 1280 Zx , in.3 Lp , ft Lr , ft

ASD

1640 12.7 44.0

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

1430 9.08 33.8

1410 9.11 33.6

1460 12.6 41.2

1330 12.5 39.3

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W40 Shape

278 ASD LRFD

Design 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

Span, ft

Fy = 50 ksi

1660 1580 1480 1400 1320 1250 1190 1130 1080 1030 990 950 914 880 848 819 792 742 699 660 625 594 566 540 516 495 475 457 440 424 410 396 383 371 360 349 339 330

2480 2380 2230 2100 1980 1880 1790 1700 1620 1550 1490 1430 1370 1320 1280 1230 1190 1120 1050 992 939 893 850 811 776 744 714 687 661 638 616 595 576 558 541 525 510 496

277 ASD LRFD

W40× 264 249 ASD LRFD ASD LRFD

235 ASD LRFD

215 ASD LRFD

1320 1310 1250 1190 1130 1080 1040 998 960 924 891 860 832 780 734 693 657 624 594 567 542 520 499 480 462 446 430 416 402 390 378 367 356 347

1540 1500 1410 1330 1250 1190 1130 1070 1030 981 940 902 867 835 806 778 752 705 663 627 594 564 537 513 490 470 451 434 418 403 389 376 364 352 342 332 322 313

1320 1260 1190 1120 1060 1010 960 916 877 840 806 775 747 720 695 672 630 593 560 531 504 480 458 438 420 403 388 373 360 348 336 325 315 305 296 288 280

1010 962 916 875 837 802 770 740 713 687 664 641 601 566 534 506 481 458 437 418 401 385 370 356 344 332 321 310 301 292 283 275 267

1980 1970 1880 1790 1700 1630 1560 1500 1440 1390 1340 1290 1250 1170 1100 1040 987 938 893 852 815 781 750 721 694 670 647 625 605 586 568 551 536 521

2300 2260 2120 1990 1880 1780 1700 1610 1540 1470 1410 1360 1300 1260 1210 1170 1130 1060 997 942 892 848 807 770 737 706 678 652 628 605 584 565 547 530 514 499 484 471

1180 1120 1060 1020 972 931 894 860 828 798 771 745 699 658 621 588 559 532 508 486 466 447 430 414 399 385 373 361 349 339 329 319 310

1770 1680 1600 1530 1460 1400 1340 1290 1240 1200 1160 1120 1050 988 933 884 840 800 764 730 700 672 646 622 600 579 560 542 525 509 494 480 467

1980 1890 1780 1680 1590 1520 1440 1380 1320 1260 1210 1170 1120 1080 1040 1010 947 891 842 797 758 721 689 659 631 606 583 561 541 522 505 489 473 459 446 433 421

1520 1450 1380 1310 1260 1210 1160 1110 1070 1030 997 964 904 851 803 761 723 689 657 629 603 578 556 536 516 499 482 466 452 438 425 413 402

Beam Properties Wc /Ωb φbWc , kip-ft 23800 35700 25000 37500 22600 33900 22400 33600 20200 30300 19200 28900 Mp /Ωb φb Mp , kip-ft 2970 4460 3120 4690 2820 4240 2790 4200 2520 3790 2410 3620 Mr /Ωb φb Mr , kip-ft 1780 2680 1920 2890 1700 2550 1730 2610 1530 2300 1500 2250 BF /Ωb φb BF, kips 55.3 82.8 45.8 68.7 53.8 81.3 42.9 64.4 51.0 76.7 39.4 59.3 Vn /Ωv φvVn , kips 828 1240 659 989 768 1150 591 887 659 989 507 761 Zx , in.3 Lp , ft Lr , ft

ASD

1190 8.90 30.4

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

v

1250 12.6 38.8

1130 8.90 29.7

1120 12.5 37.2

1010 8.97 28.4

964 12.5 35.6

Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67.

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MAXIMUM TOTAL UNIFORM LOAD TABLES

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape Design

Span, ft

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

211 ASD 1180 1130 1060 1000 952 904 861 822 786 753 723 696 670 646 624 603 565 532 502 476 452 431 411 393 377 362 348 335 323 312 301 292 283 274 266 258 251

199 LRFD 1770 1700 1600 1510 1430 1360 1290 1240 1180 1130 1090 1050 1010 971 937 906 849 799 755 715 680 647 618 591 566 544 523 503 485 469 453 438 425 412 400 388 378

ASD

1010 964 913 867 826 788 754 723 694 667 642 619 598 578 542 510 482 456 434 413 394 377 361 347 334 321 310 299 289 280 271 263 255 248 241

LRFD

1510 1450 1370 1300 1240 1190 1130 1090 1040 1000 966 931 899 869 815 767 724 686 652 621 593 567 543 521 501 483 466 449 435 420 407 395 383 372 362

W40

W40× 183 ASD LRFD

ASD

LRFD

149v ASD LRFD

1010 966 909 858 813 772 736 702 672 644 618 594 572 552 533 515 483 454 429 407 386 368 351 336 322 309 297 286 276 266 257 249 241 234 227 221 215

1000 988 922 865 814 768 728 692 659 629 601 576 553 532 512 494 477 461 432 407 384 364 346 329 314 301 288 277 266 256 247 238 231 223 216 210 203 198 192

1510 1490 1390 1300 1220 1160 1090 1040 990 945 904 866 832 800 770 743 717 693 650 611 578 547 520 495 473 452 433 416 400 385 371 358 347 335 325 315 306 297 289

865 853 796 746 702 663 628 597 568 543 519 497 477 459 442 426 412 398 373 351 332 314 298 284 271 259 249 239 230 221 213 206 199 193 187 181 176 171 166

1520 1450 1370 1290 1220 1160 1110 1060 1010 968 929 893 860 829 801 774 726 683 645 611 581 553 528 505 484 464 447 430 415 400 387 375 363 352 341 332 323

167

1300 1280 1200 1120 1060 997 944 897 854 815 780 748 718 690 664 641 619 598 561 528 498 472 449 427 408 390 374 359 345 332 320 309 299 289 280 272 264 256 249

Beam Properties Wc /Ωb φbWc , kip-ft 18100 27200 17300 26100 15400 23200 13800 Mp /Ωb φb Mp , kip-ft 2260 3400 2170 3260 1930 2900 1730 Mr /Ωb φb Mr , kip-ft 1370 2060 1340 2020 1180 1770 1050 BF /Ωb φb BF, kips 48.6 73.1 37.6 56.1 44.1 66.5 41.7 Vn /Ωv φvVn , kips 591 887 503 755 507 761 502 Zx , in.3 Lp , ft Lr , ft

ASD

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

20800 11900 2600 1490 1580 896 62.5 38.3 753 432

17900 2240 1350 57.4 650

906 869 774 693 598 8.87 12.2 8.80 8.48 8.09 27.2 34.3 25.8 24.8 23.6 v Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67. Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

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DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W36 Shape Design 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

Span, ft

Fy = 50 ksi

652h ASD LRFD 3240 4860 3230 4850 3060 4590 2900 4370 2770 4160 2640 3970 2530 3800 2420 3640 2320 3490 2230 3360 2150 3230 2070 3120 2000 3010 1940 2910 1820 2730 1710 2570 1610 2430 1530 2300 1450 2180 1380 2080 1320 1980 1260 1900 1210 1820 1160 1750 1120 1680 1080 1620 1040 1560 1000 1510 968 1460 937 1410 908 1360 880 1320 854 1280 830 1250 807 1210

529h ASD LRFD

W36× 441h 487h ASD LRFD ASD LRFD

395h ASD LRFD

361h ASD LRFD

2560 2450 2330 2210 2110 2020 1940 1860 1790 1720 1660 1600 1550 1450 1370 1290 1220 1160 1110 1060 1010 969 930 894 861 830 802 775 750 727 705 684 664 646

2360 2240 2130 2020 1930 1850 1770 1700 1640 1570 1520 1470 1420 1330 1250 1180 1120 1060 1010 966 924 886 850 818 787 759 733 709 686 664 644 625 607 590

1870 1800 1710 1630 1550 1480 1420 1370 1310 1260 1220 1180 1140 1070 1000 948 898 853 813 776 742 711 683 656 632 609 588 569 551 533 517 502 488 474

1700 1630 1550 1470 1410 1350 1290 1240 1190 1150 1100 1070 1030 967 910 859 814 773 737 703 673 645 619 595 573 552 533 516 499 483 469 455 442 430

3840 3680 3500 3330 3180 3040 2910 2800 2690 2590 2500 2410 2330 2180 2060 1940 1840 1750 1660 1590 1520 1460 1400 1340 1290 1250 1210 1170 1130 1090 1060 1030 999 971

3540 3360 3200 3040 2900 2780 2660 2560 2460 2370 2280 2200 2130 2000 1880 1780 1680 1600 1520 1450 1390 1330 1280 1230 1180 1140 1100 1070 1030 998 968 940 913 888

2110 2010 1910 1820 1730 1660 1590 1520 1470 1410 1360 1310 1270 1190 1120 1060 1000 953 908 866 829 794 762 733 706 681 657 635 615 596 578 561 545 529

3170 3020 2870 2730 2600 2490 2390 2290 2200 2120 2050 1980 1910 1790 1690 1590 1510 1430 1360 1300 1250 1190 1150 1100 1060 1020 988 955 924 895 868 843 819 796

2810 2700 2570 2440 2330 2230 2140 2050 1970 1900 1830 1770 1710 1600 1510 1430 1350 1280 1220 1170 1120 1070 1030 987 950 916 884 855 827 802 777 754 733 713

2550 2450 2330 2210 2110 2020 1940 1860 1790 1720 1660 1600 1550 1450 1370 1290 1220 1160 1110 1060 1010 969 930 894 861 830 802 775 750 727 705 684 664 646

Beam Properties Wc /Ωb φbWc , kip-ft Mp /Ωb φb Mp , kip-ft Mr /Ωb φb Mr , kip-ft BF /Ωb φb BF, kips Vn /Ωv φvVn , kips

58100 87300 46500 69900 42500 63900 38100 57300 34100 51300 30900 46500 7260 10900 5810 8740 5310 7990 4770 7160 4270 6410 3870 5810 4300 6460 3480 5220 3200 4800 2880 4330 2600 3910 2360 3540 46.8 70.3 46.4 70.1 46.0 69.5 45.3 67.9 44.9 67.2 43.6 65.6 1620 2430 1280 1920 1180 1770 1060 1590 937 1410 851 1280

Zx , in.3 Lp , ft Lr , ft

ASD

2910 14.5 77.7

LRFD

h

2330 14.1 64.3

2130 14.0 59.9

1910 13.8 55.5

1710 13.7 50.9

1550 13.6 48.2

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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MAXIMUM TOTAL UNIFORM LOAD TABLES

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape Design

Span, ft

17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

330 ASD LRFD

302 ASD LRFD

1540 1480 1410 1340 1280 1220 1170 1130 1080 1040 1010 970 938 879 828 782 741 704 670 640 612 586 563 541 521 503 485 469 454 440 426 414 402 391

1410 1340 1280 1220 1160 1110 1060 1020 983 946 912 881 852 798 751 710 672 639 608 581 555 532 511 491 473 456 440 426 412 399 387 376 365 355

2310 2230 2120 2010 1920 1840 1760 1690 1630 1570 1510 1460 1410 1320 1240 1180 1110 1060 1010 961 920 881 846 813 783 755 729 705 682 661 641 622 604 588

2120 2020 1920 1830 1750 1670 1600 1540 1480 1420 1370 1320 1280 1200 1130 1070 1010 960 914 873 835 800 768 738 711 686 662 640 619 600 582 565 549 533

W36

W36× 282 262 ASD LRFD ASD LRFD 1240 1860 1310 1970 1220 1830 1250 1880 1160 1740 1190 1790 1100 1650 1130 1700 1050 1570 1080 1620 998 1500 1030 1550 955 1430 990 1490 915 1380 950 1430 878 1320 914 1370 844 1270 880 1320 813 1220 848 1280 784 1180 819 1230 757 1140 792 1190 732 1100 742 1120 686 1030 699 1050 646 971 660 992 610 917 625 939 578 868 594 893 549 825 566 850 523 786 540 811 499 750 516 776 477 717 495 744 457 688 475 714 439 660 457 687 422 635 440 661 407 611 424 638 392 589 410 616 379 569 396 595 366 550 383 576 354 532 371 558 343 516 360 541 333 500 349 525 323 485 339 510 314 471 330 496 305 458

247 231 ASD LRFD ASD LRFD 1170 1760 1110 1660 1140 1720 1070 1610 1080 1630 1010 1520 1030 1550 961 1440 979 1470 915 1380 934 1400 874 1310 894 1340 836 1260 857 1290 801 1200 822 1240 769 1160 791 1190 739 1110 761 1140 712 1070 734 1100 686 1030 709 1070 663 996 685 1030 641 963 642 966 601 903 605 909 565 850 571 858 534 803 541 813 506 760 514 773 481 722 489 736 458 688 467 702 437 657 447 672 418 628 428 644 400 602 411 618 384 578 395 594 370 556 381 572 356 535 367 552 343 516 354 533 331 498 343 515 320 482 332 498 310 466 321 483 300 451 311 468 291 438 302 454 283 425 294 441 275 413 286 429 267 401

Beam Properties Wc /Ωb φbWc , kip-ft 28100 42300 25500 38400 23800 35700 22000 33000 20600 30900 19200 28900 Mp /Ωb φb Mp , kip-ft 3520 5290 3190 4800 2970 4460 2740 4130 2570 3860 2400 3610 Mr /Ωb φb Mr , kip-ft 2170 3260 1970 2970 1830 2760 1700 2550 1590 2400 1490 2240 BF /Ωb φb BF, kips 42.2 63.4 40.5 60.8 39.6 59.0 38.1 57.9 37.4 55.7 35.7 53.7 Vn /Ωv φvVn , kips 769 1150 705 1060 657 985 620 930 587 881 555 832 Zx , in.3 Lp , ft Lr , ft

ASD

1410 13.5 45.5

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

1280 13.5 43.6

1190 13.4 42.2

1100 13.3 40.6

1030 13.2 39.4

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

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DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W36 256 ASD LRFD

232 ASD LRFD

W36× 210 194 ASD LRFD ASD LRFD

182 ASD LRFD

170 ASD LRFD

1440 1380 1300 1220 1150 1090 1040 988 944 903 865 830 798 769 741 716 692 649 611 577 546 519 494 472 451 432 415 399 384 371 358 346 335 324 315 305 297 288

1290 1250 1170 1100 1040 983 934 890 849 812 778 747 719 692 667 644 623 584 549 519 492 467 445 425 406 389 374 359 346 334 322 311 301 292 283 275 267 259

1220 1190 1110 1040 978 924 875 831 792 756 723 693 665 639 616 594 573 554 520 489 462 438 416 396 378 361 346 333 320 308 297 287 277 268 260 252 245 238 231

1050 1020 955 896 843 796 754 717 682 651 623 597 573 551 531 512 494 478 448 422 398 377 358 341 326 312 299 287 276 265 256 247 239 231 224 217 211 205 199

985 952 889 833 784 741 702 667 635 606 580 556 533 513 494 476 460 444 417 392 370 351 333 317 303 290 278 267 256 247 238 230 222 215 208 202 196 190 185

Shape Design 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

Span, ft

Fy = 50 ksi

2150 2080 1950 1840 1730 1640 1560 1490 1420 1360 1300 1250 1200 1160 1110 1080 1040 975 918 867 821 780 743 709 678 650 624 600 578 557 538 520 503 488 473 459 446 433

1940 1870 1760 1650 1560 1480 1400 1340 1280 1220 1170 1120 1080 1040 1000 968 936 878 826 780 739 702 669 638 610 585 562 540 520 501 484 468 453 439 425 413 401 390

1830 1790 1670 1560 1470 1390 1320 1250 1190 1140 1090 1040 1000 961 926 893 862 833 781 735 694 658 625 595 568 543 521 500 481 463 446 431 417 403 390 379 368 357 347

1120 1090 1020 957 901 851 806 765 729 696 666 638 612 589 567 547 528 510 478 450 425 403 383 365 348 333 319 306 294 284 273 264 255 247 239 232 225 219 213

1680 1640 1530 1440 1350 1280 1210 1150 1100 1050 1000 959 920 885 852 822 793 767 719 677 639 606 575 548 523 500 479 460 443 426 411 397 384 371 360 349 338 329 320

1580 1540 1440 1350 1270 1200 1130 1080 1030 979 937 898 862 828 798 769 743 718 673 634 598 567 539 513 490 468 449 431 414 399 385 371 359 347 337 326 317 308 299

1480 1430 1340 1250 1180 1110 1050 1000 954 911 871 835 802 771 742 716 691 668 626 589 557 527 501 477 455 436 418 401 385 371 358 346 334 323 313 304 295 286 278

Beam Properties Wc /Ωb φbWc , kip-ft 20800 Mp /Ωb φb Mp , kip-ft 2590 Mr /Ωb φb Mr , kip-ft 1560 BF /Ωb φb BF, kips 46.5 Vn /Ωv φvVn , kips 718 Zx , in.3 Lp , ft Lr , ft

ASD

31200 18700 28100 16600 25000 15300 23000 14300 21500 13300 20000 3900 2340 3510 2080 3120 1910 2880 1790 2690 1670 2510 2350 1410 2120 1260 1890 1160 1740 1090 1640 1010 1530 70.0 44.8 67.0 42.3 63.4 40.4 61.4 38.9 58.4 37.8 56.1 1080 646 968 609 914 558 838 526 790 492 738

1040 9.36 31.5

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

h v

936 9.25 30.0

833 9.11 28.5

767 9.04 27.6

718 9.01 27.0

668 8.94 26.4

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67.

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MAXIMUM TOTAL UNIFORM LOAD TABLES

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes

160 ASD LRFD

W36× 150 ASD LRFD

135v ASD LRFD

387h ASD LRFD

W33× 354h ASD LRFD

318 ASD LRFD

936 890 830 778 733 692 656 623 593 566 542 519 498 479 461 445 429 415 389 366 346 328 311 297 283 271 259 249 240 231 222 215 208 201 195 189 183 178 173

898 892 828 773 725 682 644 610 580 552 527 504 483 464 446 430 414 400 387 362 341 322 305 290 276 264 252 242 232 223 215 207 200 193 187 181 176 171 166 161

767 726 677 635 598 564 535 508 484 462 442 423 406 391 376 363 350 339 317 299 282 267 254 242 231 221 212 203 195 188 181 175 169 164 159 154 149 145 141

1810 1730 1640 1560 1480 1420 1350 1300 1250 1200 1150 1110 1070 1040 973 916 865 819 778 741 708 677 649 623 599 577 556 537 519 502 487 472 458 445 432

1650 1570 1490 1420 1350 1290 1230 1180 1130 1090 1050 1010 977 945 886 834 787 746 709 675 644 616 590 567 545 525 506 489 472 457 443 429 417 405 394

1460 1410 1330 1270 1210 1150 1100 1060 1010 975 939 905 874 845 792 746 704 667 634 604 576 551 528 507 487 469 453 437 422 409 396 384 373 362 352

Shape Design

Span, ft

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

W36-W33

1400 1340 1250 1170 1100 1040 985 936 891 851 814 780 749 720 693 669 646 624 585 551 520 493 468 446 425 407 390 374 360 347 334 323 312 302 293 284 275 267 260

1350 1340 1250 1160 1090 1030 968 917 872 830 792 758 726 697 670 646 623 601 581 545 513 484 459 436 415 396 379 363 349 335 323 311 301 291 281 272 264 256 249 242

1150 1090 1020 954 898 848 804 764 727 694 664 636 611 587 566 545 527 509 477 449 424 402 382 364 347 332 318 305 294 283 273 263 255 246 239 231 225 218 212

2720 2600 2460 2340 2230 2130 2030 1950 1870 1800 1730 1670 1610 1560 1460 1380 1300 1230 1170 1110 1060 1020 975 936 900 867 836 807 780 755 731 709 688 669 650

2480 2370 2240 2130 2030 1940 1850 1780 1700 1640 1580 1520 1470 1420 1330 1250 1180 1120 1070 1010 968 926 888 852 819 789 761 734 710 687 666 645 626 609 592

2200 2120 2010 1910 1810 1730 1660 1590 1520 1470 1410 1360 1310 1270 1190 1120 1060 1000 953 907 866 828 794 762 733 706 680 657 635 615 595 577 560 544 529

Beam Properties Wc /Ωb φbWc , kip-ft 12500 18700 11600 17400 10200 15300 31100 46800 28300 42600 25300 38100 Mp /Ωb φb Mp , kip-ft 1560 2340 1450 2180 1270 1910 3890 5850 3540 5330 3170 4760 Mr /Ωb φb Mr , kip-ft 947 1420 880 1320 767 1150 2360 3540 2170 3260 1940 2910 BF /Ωb φb BF, kips 36.1 54.2 34.4 51.9 31.7 47.8 38.3 57.8 37.4 56.6 36.8 55.4 Vn /Ωv φvVn , kips 468 702 449 673 384 577 907 1360 826 1240 732 1100 Zx , in.3 Lp , ft Lr , ft

ASD

624 8.83 25.8

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

581 8.72 25.3

509 8.41 24.3

1560 13.3 53.3

1420 13.2 49.8

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W33 Shape

291 ASD LRFD

Design 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

Span, ft

Fy = 50 ksi

1340 1290 1220 1160 1100 1050 1010 965 926 891 858 827 798 772 724 681 643 609 579 551 526 503 482 463 445 429 413 399 386 373 362 351 340 331 322

2000 1930 1830 1740 1660 1580 1510 1450 1390 1340 1290 1240 1200 1160 1090 1020 967 916 870 829 791 757 725 696 669 644 621 600 580 561 544 527 512 497 483

263 ASD LRFD

1200 1150 1090 1040 988 944 903 865 830 798 769 741 716 692 649 611 577 546 519 494 472 451 432 415 399 384 371 358 346 335 324 315 305 297 288

1800 1730 1640 1560 1490 1420 1360 1300 1250 1200 1160 1110 1080 1040 975 918 867 821 780 743 709 678 650 624 600 578 557 538 520 503 488 473 459 446 433

W33× 241 221 ASD LRFD ASD LRFD

1140 1100 1040 987 938 893 853 816 782 750 722 695 670 647 625 586 552 521 494 469 447 426 408 391 375 361 347 335 323 313 303 293 284 276 268 261

1700 1660 1570 1480 1410 1340 1280 1230 1180 1130 1080 1040 1010 972 940 881 829 783 742 705 671 641 613 588 564 542 522 504 486 470 455 441 427 415 403 392

1050 1010 950 900 855 815 778 744 713 684 658 634 611 590 570 535 503 475 450 428 407 389 372 356 342 329 317 305 295 285 276 267 259 252 244 238

1580 1510 1430 1350 1290 1220 1170 1120 1070 1030 989 952 918 887 857 803 756 714 677 643 612 584 559 536 514 494 476 459 443 429 415 402 390 378 367 357

201 ASD LRFD

169 ASD LRFD

964 908 857 812 771 735 701 671 643 617 593 571 551 532 514 482 454 429 406 386 367 351 335 321 309 297 286 276 266 257 249 241 234 227 220 214

906 897 837 785 739 697 661 628 598 571 546 523 502 483 465 448 433 418 392 369 349 330 314 299 285 273 262 251 241 232 224 216 209 202 196 190 185 179 174

1450 1360 1290 1220 1160 1100 1050 1010 966 928 892 859 828 800 773 725 682 644 610 580 552 527 504 483 464 446 429 414 400 387 374 362 351 341 331 322

1360 1350 1260 1180 1110 1050 993 944 899 858 820 786 755 726 699 674 651 629 590 555 524 497 472 449 429 410 393 377 363 349 337 325 315 304 295 286 278 270 262

Beam Properties Wc /Ωb φbWc , kip-ft 23200 34800 20800 31200 18800 28200 17100 25700 15400 23200 12600 18900 Mp /Ωb φb Mp , kip-ft 2890 4350 2590 3900 2350 3530 2140 3210 1930 2900 1570 2360 Mr /Ωb φb Mr , kip-ft 1780 2680 1610 2410 1450 2180 1330 1990 1200 1800 959 1440 BF /Ωb φb BF, kips 36.0 54.2 34.1 51.9 33.2 50.2 31.8 47.8 30.3 45.6 34.2 51.5 Vn /Ωv φvVn , kips 668 1000 600 900 568 852 525 788 482 723 453 679 Zx , in.3 Lp , ft Lr , ft

ASD

1160 13.0 43.8

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

h v

1040 12.9 41.6

940 12.8 39.7

857 12.7 38.2

773 12.6 36.7

629 8.83 26.7

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Shape does not meet the h/tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67.

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MAXIMUM TOTAL UNIFORM LOAD TABLES

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes

152 ASD LRFD

141 ASD LRFD

W33× 130 ASD LRFD

118v ASD LRFD

W30× 391h 357h ASD LRFD ASD LRFD

851 797 744 697 656 620 587 558 531 507 485 465 446 429 413 398 385 372 349 328 310 294 279 266 254 243 232 223 215 207 199 192 186 180 174 169 164 159 155

806 789 733 684 641 603 570 540 513 489 466 446 427 410 395 380 366 354 342 321 302 285 270 256 244 233 223 214 205 197 190 183 177 171 165 160 155 151 147 142

768 717 666 621 583 548 518 491 466 444 424 405 388 373 359 345 333 321 311 291 274 259 245 233 222 212 203 194 186 179 173 166 161 155 150 146 141 137 133 129

650 637 592 552 518 487 460 436 414 394 377 360 345 331 319 307 296 286 276 259 244 230 218 207 197 188 180 173 166 159 153 148 143 138 134 129 126 122 118 115

1810 1700 1610 1520 1450 1380 1320 1260 1210 1160 1110 1070 1030 998 965 904 851 804 762 724 689 658 629 603 579 557 536 517 499 482 467 452 439 426 413 402

Shape Design

Span, ft

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

W33-W30

1280 1200 1120 1050 986 932 883 839 799 762 729 699 671 645 621 599 578 559 524 493 466 441 419 399 381 365 349 335 323 311 299 289 280 270 262 254 247 240 233

1210 1190 1100 1030 964 907 857 812 771 734 701 670 643 617 593 571 551 532 514 482 454 428 406 386 367 350 335 321 308 297 286 275 266 257 249 241 234 227 220 214

1150 1080 1000 934 876 824 778 737 701 667 637 609 584 560 539 519 500 483 467 438 412 389 369 350 334 318 305 292 280 269 259 250 242 234 226 219 212 206 200 195

977 958 889 830 778 732 692 655 623 593 566 541 519 498 479 461 445 429 415 389 366 346 328 311 296 283 271 259 249 239 231 222 215 208 201 195 189 183 178 173

2710 2560 2420 2290 2180 2070 1980 1890 1810 1740 1670 1610 1550 1500 1450 1360 1280 1210 1140 1090 1040 989 946 906 870 837 806 777 750 725 702 680 659 640 621 604

1630 1550 1460 1390 1320 1250 1200 1150 1100 1050 1010 976 941 909 878 823 775 732 693 659 627 599 573 549 527 507 488 470 454 439 425 412 399 387 376 366

2440 2330 2200 2080 1980 1890 1800 1720 1650 1580 1520 1470 1410 1370 1320 1240 1160 1100 1040 990 943 900 861 825 792 762 733 707 683 660 639 619 600 582 566 550

Beam Properties Wc /Ωb φbWc , kip-ft 11200 16800 10300 15400 Mp /Ωb φb Mp , kip-ft 1390 2100 1280 1930 Mr /Ωb φb Mr , kip-ft 851 1280 782 1180 BF /Ωb φb BF, kips 31.7 48.3 30.3 45.7 Vn /Ωv φvVn , kips 425 638 403 604 Zx , in.3 Lp , ft Lr , ft

ASD

559 8.72 25.7

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

514 8.58 25.0

9320 14000 1170 1750 709 1070 29.3 43.1 384 576 467 8.44 24.2

8280 12500 28900 43500 26300 39600 1040 1560 3620 5440 3290 4950 627 942 2180 3280 1990 2990 27.2 40.6 31.4 47.2 31.3 47.2 325 489 903 1350 813 1220 415 8.19 23.4

1450 13.0 58.8

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W30 Shape

Span, ft

Fy = 50 ksi

Design 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

W30× 326h ASD LRFD

292 ASD LRFD

261 ASD LRFD

235 ASD LRFD

1480 1400 1320 1250 1190 1130 1080 1030 990 950 914 880 848 819 792 742 699 660 625 594 566 540 516 495 475 457 440 424 410 396 383 371 360 349 339 330

1310 1240 1180 1110 1060 1010 962 920 882 846 814 784 756 730 705 661 622 588 557 529 504 481 460 441 423 407 392 378 365 353 341 331 321 311 302 294

1180 1110 1050 991 941 896 856 818 784 753 724 697 672 649 627 588 554 523 495 471 448 428 409 392 376 362 349 336 325 314 304 294 285 277 269 261

1040 994 939 890 845 805 768 735 704 676 650 626 604 583 564 528 497 470 445 423 403 384 368 352 338 325 313 302 291 282 273 264 256 249 242 235

2220 2100 1980 1880 1790 1700 1620 1550 1490 1430 1370 1320 1280 1230 1190 1120 1050 992 939 893 850 811 776 744 714 687 661 638 616 595 576 558 541 525 510 496

1960 1870 1770 1670 1590 1510 1450 1380 1330 1270 1220 1180 1140 1100 1060 994 935 883 837 795 757 723 691 663 636 612 589 568 548 530 513 497 482 468 454 442

1760 1660 1570 1490 1410 1350 1290 1230 1180 1130 1090 1050 1010 976 943 884 832 786 744 707 674 643 615 589 566 544 524 505 488 472 456 442 429 416 404 393

1560 1490 1410 1340 1270 1210 1160 1100 1060 1020 977 941 908 876 847 794 747 706 669 635 605 578 552 529 508 489 471 454 438 424 410 397 385 374 363 353

211 ASD LRFD 958 1440 937 1410 882 1330 833 1250 789 1190 750 1130 714 1070 681 1020 652 980 625 939 600 901 577 867 555 834 535 805 517 777 500 751 468 704 441 663 416 626 394 593 375 563 357 536 341 512 326 490 312 469 300 451 288 433 278 417 268 402 258 388 250 376 242 363 234 352 227 341 220 331 214 322 208 313

191 ASD LRFD 872 1310 842 1270 793 1190 749 1130 709 1070 674 1010 642 964 612 920 586 880 561 844 539 810 518 779 499 750 481 723 465 698 449 675 421 633 396 596 374 563 355 533 337 506 321 482 306 460 293 440 281 422 269 405 259 389 250 375 241 362 232 349 225 338 217 327 211 316 204 307 198 298 192 289 187 281

Beam Properties Wc /Ωb φbWc , kip-ft 23800 35700 21200 31800 18800 28300 16900 25400 15000 22500 13500 20300 Mp /Ωb φb Mp , kip-ft 2970 4460 2640 3980 2350 3540 2110 3180 1870 2820 1680 2530 Mr /Ωb φb Mr , kip-ft 1820 2730 1620 2440 1450 2180 1310 1960 1160 1750 1050 1580 BF /Ωb φb BF, kips 30.3 45.6 29.7 44.9 29.1 44.0 28.0 42.7 26.9 40.5 25.6 38.6 Vn /Ωv φvVn , kips 739 1110 653 979 588 882 520 779 479 718 436 654 Zx , in.3 Lp , ft Lr , ft

ASD

1190 12.7 50.6

LRFD

h

1060 12.6 46.9

943 12.5 43.4

847 12.4 41.0

751 12.3 38.7

675 12.2 36.8

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

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MAXIMUM TOTAL UNIFORM LOAD TABLES

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape Design

Span, ft

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

173 ASD LRFD

796 757 713 673 638 606 577 551 527 505 485 466 449 433 418 404 379 356 337 319 303 288 275 263 252 242 233 224 216 209 202 195 189 184 178 173 168

1190 1140 1070 1010 958 911 867 828 792 759 728 700 674 650 628 607 569 536 506 479 455 434 414 396 379 364 350 337 325 314 304 294 285 276 268 260 253

W30

148 ASD LRFD

W30× 132 124 ASD LRFD ASD LRFD

116 ASD LRFD

108 ASD LRFD

798 768 713 665 624 587 554 525 499 475 454 434 416 399 384 370 356 344 333 312 294 277 263 250 238 227 217 208 200 192 185 178 172 166 161 156 151 147 143 139

745 727 671 623 582 545 513 485 459 436 415 396 379 363 349 335 323 312 301 291 273 257 242 230 218 208 198 190 182 174 168 162 156 150 145 141 136 132 128 125 121

678 629 580 539 503 472 444 419 397 377 359 343 328 314 302 290 279 269 260 251 236 222 210 199 189 180 171 164 157 151 145 140 135 130 126 122 118 114 111 108 105

650 628 576 531 493 460 432 406 384 363 345 329 314 300 288 276 266 256 247 238 230 216 203 192 182 173 164 157 150 144 138 133 128 123 119 115 111 108 105 102 98.7 95.9

1200 1150 1070 1000 938 882 833 789 750 714 682 652 625 600 577 556 536 517 500 469 441 417 395 375 357 341 326 313 300 288 278 268 259 250 242 234 227 221 214 208

1120 1090 1010 936 874 819 771 728 690 656 624 596 570 546 524 504 486 468 452 437 410 386 364 345 328 312 298 285 273 262 252 243 234 226 219 211 205 199 193 187 182

707 679 626 582 543 509 479 452 429 407 388 370 354 339 326 313 302 291 281 271 254 240 226 214 204 194 185 177 170 163 157 151 145 140 136 131 127 123 120 116 113

1060 1020 942 874 816 765 720 680 644 612 583 556 532 510 490 471 453 437 422 408 383 360 340 322 306 291 278 266 255 245 235 227 219 211 204 197 191 185 180 175 170

1020 945 872 810 756 709 667 630 597 567 540 515 493 473 454 436 420 405 391 378 354 334 315 298 284 270 258 247 236 227 218 210 203 196 189 183 177 172 167 162 158

974 944 865 798 741 692 649 611 577 546 519 494 472 451 433 415 399 384 371 358 346 324 305 288 273 260 247 236 226 216 208 200 192 185 179 173 167 162 157 153 148 144

Beam Properties Wc /Ωb φbWc , kip-ft 12100 18200 Mp /Ωb φb Mp , kip-ft 1510 2280 Mr /Ωb φb Mr , kip-ft 945 1420 BF /Ωb φb BF, kips 24.1 36.8 Vn /Ωv φvVn , kips 398 597 Zx , in.3 Lp , ft Lr , ft

ASD

607 12.1 35.5

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

9980 15000 1250 1880 761 1140 29.0 43.9 399 599 500 8.05 24.9

8720 13100 8140 12200 1090 1640 1020 1530 664 998 620 932 26.9 40.5 26.1 39.0 373 559 353 530 437 7.95 23.8

408 7.88 23.2

7540 11300 943 1420 575 864 24.8 37.4 339 509

6910 10400 863 1300 522 785 23.5 35.5 325 487

378 7.74 22.6

346 7.59 22.1

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

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DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W30-W27 99 ASD LRFD

W30× 90v ASD LRFD

539h ASD LRFD

W27× 368h 336h ASD LRFD ASD LRFD

307h ASD LRFD

618 566 519 479 445 415 389 366 346 328 311 297 283 271 259 249 240 231 222 215 208 195 183 173 164 156 148 142 135 130 125 120 115 111 107 104 100 97.3 94.4 91.6 89.0 86.5

498 471 435 403 377 353 332 314 297 282 269 257 246 235 226 217 209 202 195 188 177 166 157 149 141 134 128 123 118 113 109 105 101 97.4 94.1 91.1 88.3 85.6 83.1 80.7 78.5

2560 2510 2360 2220 2100 1990 1890 1800 1710 1640 1570 1510 1450 1400 1350 1300 1260 1180 1110 1050 993 943 898 857 820 786 754 725 699 674 650 629 608 589 572 555 539 524

1680 1650 1550 1460 1380 1300 1240 1180 1130 1080 1030 990 952 917 884 853 825 773 728 688 651 619 589 563 538 516 495 476 458 442 427 413 399 387 375 364 354 344

1370 1280 1210 1140 1080 1030 979 934 894 857 822 791 761 734 709 685 642 605 571 541 514 489 467 447 428 411 395 381 367 354 343 332 321 311 302 294 286

Shape Design

Span, ft

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

Fy = 50 ksi

927 851 780 720 669 624 585 551 520 493 468 446 425 407 390 374 360 347 334 323 312 293 275 260 246 234 223 213 203 195 187 180 173 167 161 156 151 146 142 138 134 130

749 708 653 606 566 531 499 472 447 425 404 386 369 354 340 327 314 303 293 283 265 250 236 223 212 202 193 185 177 170 163 157 152 146 142 137 133 129 125 121 118

3840 3780 3540 3340 3150 2980 2840 2700 2580 2470 2360 2270 2180 2100 2030 1960 1890 1770 1670 1580 1490 1420 1350 1290 1230 1180 1130 1090 1050 1010 978 945 915 886 859 834 810 788

2520 2480 2330 2190 2070 1960 1860 1770 1690 1620 1550 1490 1430 1380 1330 1280 1240 1160 1090 1030 979 930 886 845 809 775 744 715 689 664 641 620 600 581 564 547 531 517

1510 1500 1410 1330 1250 1190 1130 1070 1030 981 940 902 867 835 806 778 752 705 663 627 594 564 537 513 490 470 451 434 418 403 389 376 364 352 342 332 322 313

2270 2260 2120 1990 1880 1780 1700 1610 1540 1470 1410 1360 1300 1260 1210 1170 1130 1060 997 942 892 848 807 770 737 706 678 652 628 605 584 565 547 530 514 499 484 471

2060 1930 1820 1720 1630 1550 1470 1400 1340 1290 1240 1190 1140 1100 1070 1030 966 909 858 813 773 736 702 672 644 618 594 572 552 533 515 498 483 468 454 441 429

Beam Properties Wc /Ωb φbWc , kip-ft 6230 9360 5650 8490 Mp /Ωb φb Mp , kip-ft 778 1170 706 1060 Mr /Ωb φb Mr , kip-ft 470 706 428 643 BF /Ωb φb BF, kips 22.2 33.4 20.6 30.8 Vn /Ωv φvVn , kips 309 463 249 374 Zx , in.3 Lp , ft Lr , ft

ASD

312 7.42 21.3

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

h v

283 7.38 20.9

37700 56700 24800 37200 22600 33900 20600 30900 4720 7090 3090 4650 2820 4240 2570 3860 2740 4120 1850 2780 1700 2550 1550 2330 26.2 39.3 24.9 37.6 25.0 37.7 25.1 37.7 1280 1920 839 1260 756 1130 687 1030 1890 12.9 88.5

1240 12.3 62.0

1130 12.2 57.0

1030 12.0 52.6

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Shape does not meet the h/tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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MAXIMUM TOTAL UNIFORM LOAD TABLES

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape Design

Span, ft

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

281 ASD LRFD

258 ASD LRFD

1240 1170 1100 1040 983 934 890 849 812 778 747 719 692 667 644 623 584 549 519 492 467 445 425 406 389 374 359 346 334 322 311 301 292 283 275 267 259

1140 1130 1060 1000 945 895 850 810 773 739 709 680 654 630 607 586 567 531 500 472 448 425 405 386 370 354 340 327 315 304 293 283 274 266 258 250 243 236

1860 1760 1650 1560 1480 1400 1340 1280 1220 1170 1120 1080 1040 1000 968 936 878 826 780 739 702 669 638 610 585 562 540 520 501 484 468 453 439 425 413 401 390

1710 1700 1600 1500 1420 1350 1280 1220 1160 1110 1070 1020 983 947 913 881 852 799 752 710 673 639 609 581 556 533 511 492 473 456 441 426 412 399 387 376 365 355

W27

W27× 235 217 ASD LRFD ASD LRFD

194 ASD LRFD

178 ASD LRFD

1040 1030 963 906 856 811 770 734 700 670 642 616 593 571 550 531 514 482 453 428 406 385 367 350 335 321 308 296 285 275 266 257 249 241 233 227 220

843 840 787 741 700 663 630 600 572 548 525 504 484 466 450 434 420 394 370 350 331 315 300 286 274 262 252 242 233 225 217 210 203 197 191 185 180

806 758 711 669 632 599 569 542 517 495 474 455 438 421 406 392 379 356 335 316 299 284 271 259 247 237 228 219 211 203 196 190 184 178 172 167

1570 1540 1450 1360 1290 1220 1160 1100 1050 1010 965 926 891 858 827 799 772 724 681 643 609 579 551 526 503 483 463 445 429 414 399 386 374 362 351 341 331

943 887 835 788 747 710 676 645 617 591 568 546 526 507 489 473 443 417 394 373 355 338 323 309 296 284 273 263 253 245 237 229 222 215 209 203

1410 1330 1250 1190 1120 1070 1020 970 927 889 853 820 790 762 736 711 667 627 593 561 533 508 485 464 444 427 410 395 381 368 356 344 333 323 314 305

1260 1260 1180 1110 1050 996 947 901 860 823 789 757 728 701 676 653 631 592 557 526 498 473 451 430 412 394 379 364 351 338 326 316 305 296 287 278 270

1210 1140 1070 1010 950 900 855 814 777 743 713 684 658 633 611 590 570 534 503 475 450 428 407 389 372 356 342 329 317 305 295 285 276 267 259 251

Beam Properties Wc /Ωb φbWc , kip-ft 18700 28100 17000 25600 15400 23200 14200 21300 12600 18900 11400 17100 Mp /Ωb φb Mp , kip-ft 2340 3510 2130 3200 1930 2900 1770 2670 1570 2370 1420 2140 Mr /Ωb φb Mr , kip-ft 1420 2140 1300 1960 1180 1780 1100 1650 976 1470 882 1330 BF /Ωb φb BF, kips 24.8 36.9 24.4 36.5 24.1 36.0 23.0 35.1 22.3 33.8 21.6 32.5 Vn /Ωv φvVn , kips 621 932 568 853 522 784 471 707 422 632 403 605 Zx , in.3 Lp , ft Lr , ft

ASD

936 12.0 49.1

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

852 11.9 45.9

772 11.8 42.9

711 11.7 40.8

631 11.6 38.2

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

570 11.5 36.4

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DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W27 Shape Design

161 ASD LRFD

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68

Span, ft

Fy = 50 ksi

729 685 642 605 571 541 514 489 467 447 428 411 395 381 367 354 343 321 302 286 271 257 245 234 223 214 206 198 190 184 177 171 166 161 156 151

1090 1030 966 909 858 813 773 736 702 672 644 618 594 572 552 533 515 483 454 429 407 386 368 351 336 322 309 297 286 276 266 258 249 241 234 227

146 ASD LRFD

W27× 129 114 ASD LRFD ASD LRFD

663 662 617 579 545 515 487 463 441 421 403 386 370 356 343 331 319 309 289 272 257 244 232 221 210 201 193 185 178 172 165 160 154 149 145 140 136

673 657 606 563 526 493 464 438 415 394 375 358 343 329 315 303 292 282 272 263 246 232 219 207 197 188 179 171 164 158 152 146 141 136 131 127 123 119 116

995 994 928 870 819 773 733 696 663 633 605 580 557 535 516 497 480 464 435 409 387 366 348 331 316 303 290 278 268 258 249 240 232 225 218 211 205

1010 988 912 846 790 741 697 658 624 593 564 539 515 494 474 456 439 423 409 395 370 349 329 312 296 282 269 258 247 237 228 219 212 204 198 191 185 180 174

622 571 527 489 456 428 403 380 360 342 326 311 298 285 274 263 254 245 236 228 214 201 190 180 171 163 156 149 143 137 132 127 122 118 114 110 107 104 101

934 858 792 735 686 643 605 572 542 515 490 468 447 429 412 396 381 368 355 343 322 303 286 271 257 245 234 224 214 206 198 191 184 177 172 166 161 156 151

102 ASD LRFD

ASD

558 553 507 468 435 406 380 358 338 320 304 290 277 265 254 244 234 225 217 210 203 190 179 169 160 152 145 138 132 127 122 117 113 109 105 101 98.2 95.1 92.2

527 504 462 427 396 370 347 326 308 292 277 264 252 241 231 222 213 206 198 191 185 173 163 154 146 139 132 126 121 116 111 107 103 99.1 95.7 92.5 89.5 86.7 84.1

837 832 763 704 654 610 572 538 508 482 458 436 416 398 381 366 352 339 327 316 305 286 269 254 241 229 218 208 199 191 183 176 169 163 158 153 148 143 139

94 LRFD 791 758 695 642 596 556 521 491 463 439 417 397 379 363 348 334 321 309 298 288 278 261 245 232 219 209 199 190 181 174 167 160 154 149 144 139 135 130 126

Beam Properties Wc /Ωb φbWc , kip-ft 10300 15500 Mp /Ωb φb Mp , kip-ft 1280 1930 Mr /Ωb φb Mr , kip-ft 800 1200 BF /Ωb φb BF, kips 20.6 31.3 Vn /Ωv φvVn , kips 364 546 Zx , in.3 Lp , ft Lr , ft

ASD

515 11.4 34.7

LRFD

h

9260 13900 1160 1740 723 1090 19.9 29.5 332 497 464 11.3 33.3

7880 11900 6850 10300 6090 9150 5550 8340 986 1480 856 1290 761 1140 694 1040 603 906 522 785 466 701 424 638 23.4 35.0 21.7 32.8 20.1 29.8 19.1 28.5 337 505 311 467 279 419 264 395 395 7.81 24.2

343 7.70 23.1

305 7.59 22.3

278 7.49 21.6

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

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MAXIMUM TOTAL UNIFORM LOAD TABLES

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape Design

Span, ft

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70

W27× 84 ASD LRFD 491 487 443 406 375 348 325 304 286 271 256 244 232 221 212 203 195 187 180 174 168 162 152 143 135 128 122 116 111 106 101 97.4 93.7 90.2 87.0 84.0 81.2 78.6 76.1 73.8

737 732 665 610 563 523 488 458 431 407 385 366 349 333 318 305 293 282 271 261 252 244 229 215 203 193 183 174 166 159 153 146 141 136 131 126 122 118 114 111

370h ASD LRFD

335h ASD LRFD

1700 1610 1500 1410 1330 1250 1190 1130 1070 1030 981 940 902 867 835 806 778 752 705 663 627 594 564 537 513 490 470 451 434 418 403 389 376 364 352 342 332 322

1520 1450 1360 1270 1200 1130 1070 1020 969 925 885 848 814 783 754 727 702 679 636 599 566 536 509 485 463 443 424 407 392 377 364 351 339 328 318 308 299

2550 2420 2260 2120 1990 1880 1780 1700 1610 1540 1470 1410 1360 1300 1260 1210 1170 1130 1060 997 942 892 848 807 770 737 706 678 652 628 605 584 565 547 530 514 499 484

2280 2190 2040 1910 1800 1700 1610 1530 1460 1390 1330 1280 1220 1180 1130 1090 1060 1020 956 900 850 805 765 729 695 665 638 612 588 567 546 528 510 494 478 464 450

W27-W24 W24× 306h ASD LRFD

279h ASD LRFD

250 ASD LRFD

1370 1310 1230 1150 1080 1020 969 920 876 837 800 767 736 708 682 657 635 613 575 541 511 484 460 438 418 400 383 368 354 341 329 317 307 297 288 279

1240 1190 1110 1040 980 926 877 833 794 758 725 694 667 641 617 595 575 556 521 490 463 439 417 397 379 362 347 333 321 309 298 287 278 269 260 253

1090 1060 990 928 874 825 782 743 707 675 646 619 594 571 550 530 512 495 464 437 413 391 371 354 338 323 309 297 286 275 265 256 248 240 232

2050 1980 1840 1730 1630 1540 1460 1380 1320 1260 1200 1150 1110 1060 1020 988 954 922 864 814 768 728 692 659 629 601 576 553 532 512 494 477 461 446 432 419

1860 1790 1670 1570 1470 1390 1320 1250 1190 1140 1090 1040 1000 963 928 895 864 835 783 737 696 659 626 596 569 545 522 501 482 464 447 432 418 404 391 380

1640 1590 1490 1400 1310 1240 1170 1120 1060 1010 970 930 893 858 827 797 770 744 698 656 620 587 558 531 507 485 465 446 429 413 399 385 372 360 349

Beam Properties Wc /Ωb φbWc , kip-ft Mp /Ωb φb Mp , kip-ft Mr /Ωb φb Mr , kip-ft BF /Ωb φb BF, kips Vn /Ωv φvVn , kips Zx , in.3 Lp , ft Lr , ft

ASD

4870 7320 22600 33900 20400 30600 18400 27700 16700 25100 14900 22300 609 915 2820 4240 2540 3830 2300 3460 2080 3130 1860 2790 372 559 1670 2510 1510 2270 1380 2070 1250 1880 1120 1690 17.6 26.4 20.0 30.0 19.9 30.2 19.7 29.8 19.7 29.6 19.7 29.3 246 368 851 1280 759 1140 683 1020 619 929 547 821 244 7.31 20.8

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

1130 11.6 69.2

1020 11.4 63.1

922 11.3 57.9

835 11.2 53.4

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

744 11.1 48.7

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DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W24 Shape Design 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64

Span, ft

Fy = 50 ksi

229 ASD LRFD 998 1500 962 1450 898 1350 842 1270 793 1190 749 1130 709 1070 674 1010 642 964 612 920 586 880 561 844 539 810 518 779 499 750 481 723 465 698 449 675 421 633 396 596 374 563 355 533 337 506 321 482 306 460 293 440 281 422 269 405 259 389 250 375 241 362 232 349 225 338 217 327 211 316

207 ASD LRFD 894 1340 864 1300 806 1210 756 1140 712 1070 672 1010 637 957 605 909 576 866 550 826 526 790 504 758 484 727 465 699 448 673 432 649 417 627 403 606 378 568 356 535 336 505 318 478 302 455 288 433 275 413 263 395 252 379 242 364 233 350 224 337 216 325 209 313 202 303 195 293 189 284

W24× 192 176 ASD LRFD ASD LRFD 826 1240 756 1130 797 1200 729 1100 744 1120 680 1020 697 1050 637 958 656 986 600 902 620 932 567 852 587 883 537 807 558 839 510 767 531 799 486 730 507 762 464 697 485 729 443 667 465 699 425 639 446 671 408 613 429 645 392 590 413 621 378 568 398 599 364 548 385 578 352 529 372 559 340 511 349 524 319 479 328 493 300 451 310 466 283 426 294 441 268 403 279 419 255 383 266 399 243 365 254 381 232 348 243 365 222 333 232 349 212 319 223 335 204 307 215 323 196 295 207 311 189 284 199 299 182 274 192 289 176 264 186 280 170 256 180 270 165 247

162 ASD LRFD 705 1060 667 1000 623 936 584 878 549 826 519 780 492 739 467 702 445 669 425 638 406 610 389 585 374 562 359 540 346 520 334 501 322 484 311 468 292 439 275 413 259 390 246 369 234 351 222 334 212 319 203 305 195 293 187 281 180 270 173 260 167 251 161 242 156 234 151 226

146 ASD LRFD 642 963 596 896 556 836 521 784 491 738 464 697 439 660 417 627 397 597 379 570 363 545 348 523 334 502 321 482 309 464 298 448 288 432 278 418 261 392 245 369 232 348 220 330 209 314 199 299 190 285 181 273 174 261 167 251 160 241 155 232 149 224 144 216 139 209

Beam Properties Wc /Ωb φbWc , kip-ft 13500 20300 12100 18200 11200 16800 10200 15300 9340 14000 Mp /Ωb φb Mp , kip-ft 1680 2530 1510 2270 1390 2100 1270 1920 1170 1760 Mr /Ωb φb Mr , kip-ft 1030 1540 927 1390 858 1290 786 1180 723 1090 BF /Ωb φb BF, kips 19.0 28.9 18.9 28.6 18.4 28.0 18.1 27.7 17.9 26.8 Vn /Ωv φvVn , kips 499 749 447 671 413 620 378 567 353 529 Zx , in.3 Lp , ft Lr , ft

ASD

675 11.0 45.2

606 10.9 41.7

559 10.8 39.7

511 10.7 37.4

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

468 10.8 35.8

8340 12500 1040 1570 648 974 17.0 25.8 321 482 418 10.6 33.7

AISC_Part 3A_14th Ed._February 25, 2013 14-11-10 10:38 AM Page 53

MAXIMUM TOTAL UNIFORM LOAD TABLES

3–53

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape Design

Span, ft

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60

131 ASD LRFD

593 568 528 492 462 434 410 389 369 352 336 321 308 295 284 274 264 255 246 231 217 205 194 185 176 168 161 154 148 142 137 132 127 123

889 854 793 740 694 653 617 584 555 529 505 483 463 444 427 411 396 383 370 347 326 308 292 278 264 252 241 231 222 213 206 198 191 185

Wc /Ωb φbWc , kip-ft 7390 11100 Mp /Ωb φb Mp , kip-ft 923 1390 Mr /Ωb φb Mr , kip-ft 575 864 BF /Ωb φb BF, kips 16.3 24.6 Vn /Ωv φvVn , kips 296 445 Zx , in.3 Lp , ft Lr , ft

ASD

370 10.5 31.9

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

117 ASD LRFD

535 502 466 435 408 384 363 344 326 311 297 284 272 261 251 242 233 225 218 204 192 181 172 163 155 148 142 136 131 126 121 117 113 109

W24

W24× 104 103 ASD LRFD ASD LRFD

482 723 802 481 723 755 444 667 701 412 619 654 385 578 613 361 542 577 339 510 545 320 482 516 304 456 491 288 434 467 275 413 446 262 394 427 251 377 409 240 361 392 231 347 377 222 333 363 214 321 350 206 310 338 199 299 327 192 289 307 180 271 289 170 255 273 160 241 258 152 228 245 144 217 234 137 206 223 131 197 213 125 188 204 120 181 196 115 173 189 111 167 182 107 161 175 103 155 169 99.5 149 164 96.1 145 Beam Properties

539 508 466 430 399 373 349 329 310 294 279 266 254 243 233 224 215 207 200 193 186 175 164 155 147 140 133 127 121 116 112 107 103 99.8 96.4 93.1

809 764 700 646 600 560 525 494 467 442 420 400 382 365 350 336 323 311 300 290 280 263 247 233 221 210 200 191 183 175 168 162 156 150 145 140

ASD

94 LRFD

501 461 422 390 362 338 317 298 282 267 253 241 230 220 211 203 195 188 181 175 169 158 149 141 133 127 121 115 110 106 101 97.5 93.9 90.5 87.4 84.5

751 693 635 586 544 508 476 448 423 401 381 363 346 331 318 305 293 282 272 263 254 238 224 212 201 191 181 173 166 159 152 147 141 136 131 127

84 ASD LRFD 453 680 447 672 406 611 373 560 344 517 319 480 298 448 279 420 263 395 248 373 235 354 224 336 213 320 203 305 194 292 186 280 179 269 172 258 166 249 160 240 154 232 149 224 140 210 132 198 124 187 118 177 112 168 106 160 102 153 97.2 146 93.1 140 89.4 134 86.0 129 82.8 124 79.8 120 77.1 116 74.5 112

6530 9810 5770 8670 5590 8400 5070 7620 4470 6720 816 1230 721 1080 699 1050 634 953 559 840 508 764 451 677 428 643 388 583 342 515 15.4 23.3 14.3 21.3 18.2 27.4 17.3 26.0 16.2 24.2 267 401 241 362 270 404 250 375 227 340 327 10.4 30.4

289 10.3 29.2

280 7.03 21.9

254 6.99 21.2

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

224 6.89 20.3

AISC_Part 3A_14th Ed._February 25, 2013 14-11-10 10:41 AM Page 54

3–54

DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W24-W21

W24×

Shape 76 ASD LRFD

68 ASD LRFD

421 399 363 333 307 285 266 250 235 222 210 200 190 181 174 166 160 154 148 143 138 133 125 117 111 105 99.8 95.0 90.7 86.8 83.2 79.8 76.8 73.9 71.3 68.8

393 353 321 294 272 252 236 221 208 196 186 177 168 161 154 147 141 136 131 126 122 118 110 104 98.1 93.0 88.3 84.1 80.3 76.8 73.6 70.7 67.9 65.4 63.1 60.9

Design

Span, ft

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58

Fy = 50 ksi

631 600 545 500 462 429 400 375 353 333 316 300 286 273 261 250 240 231 222 214 207 200 188 176 167 158 150 143 136 130 125 120 115 111 107 103

590 531 483 443 408 379 354 332 312 295 279 266 253 241 231 221 212 204 197 190 183 177 166 156 148 140 133 126 121 115 111 106 102 98.3 94.8 91.6

W21×

62 ASD LRFD 408 611 382 574 339 510 305 459 278 417 254 383 235 353 218 328 204 306 191 287 180 270 170 255 161 242 153 230 145 219 139 209 133 200 127 191 122 184 117 177 113 170 109 164 105 158 102 153 95.4 143 89.8 135 84.8 128 80.4 121 76.3 115 72.7 109 69.4 104 66.4 99.8 63.6 95.6 61.1 91.8 58.7 88.3 56.6 85.0 54.5 82.0 52.7 79.1

55v ASD LRFD 335 503 334 503 297 447 267 402 243 365 223 335 206 309 191 287 178 268 167 251 157 236 149 223 141 212 134 201 127 191 122 183 116 175 111 168 107 161 103 155 99.1 149 95.5 144 92.2 139 89.2 134 83.6 126 78.7 118 74.3 112 70.4 106 66.9 101 63.7 95.7 60.8 91.4 58.1 87.4 55.7 83.8 53.5 80.4 51.4 77.3 49.5 74.4 47.8 71.8 46.1 69.3

201 ASD LRFD

182 ASD LRFD

837 814 756 705 661 622 588 557 529 504 481 460 441 423 407 392 378 365 353 331 311 294 278 264 252 240 230 220 212 203 196 189

754 731 679 633 594 559 528 500 475 452 432 413 396 380 365 352 339 328 317 297 279 264 250 238 226 216 207 198 190 183 176 170

1260 1220 1140 1060 994 935 883 837 795 757 723 691 663 636 612 589 568 548 530 497 468 442 418 398 379 361 346 331 318 306 294 284

1130 1100 1020 952 893 840 793 752 714 680 649 621 595 571 549 529 510 492 476 446 420 397 376 357 340 325 310 298 286 275 264 255

Beam Properties Wc /Ωb φbWc , kip-ft 3990 6000 3530 5310 3050 4590 2670 4020 10600 15900 Mp /Ωb φb Mp , kip-ft 499 750 442 664 382 574 334 503 1320 1990 Mr /Ωb φb Mr , kip-ft 307 462 269 404 229 344 199 299 805 1210 BF /Ωb φb BF, kips 15.1 22.6 14.1 21.2 16.1 24.1 14.7 22.2 14.5 22.0 Vn /Ωv φvVn , kips 210 315 197 295 204 306 167 252 419 628 Zx , in.3 Lp , ft Lr , ft

ASD

200 6.78 19.5

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

v

177 6.61 18.9

153 4.87 14.4

134 4.73 13.9

530 10.7 46.2

9500 14300 1190 1790 728 1090 14.4 21.8 377 565 476 10.6 42.7

Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67.

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MAXIMUM TOTAL UNIFORM LOAD TABLES

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape Design

Span, ft

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56

166 ASD LRFD 675 663 616 575 539 507 479 454 431 411 392 375 359 345 332 319 308 297 287 269 254 240 227 216 205 196 187 180 172 166 160 154

1010 997 926 864 810 762 720 682 648 617 589 563 540 518 498 480 463 447 432 405 381 360 341 324 309 295 282 270 259 249 240 231

147 ASD LRFD 636 955 620 933 573 861 532 799 496 746 465 699 438 658 414 622 392 589 372 560 355 533 338 509 324 487 310 466 298 448 286 430 276 414 266 400 257 386 248 373 233 350 219 329 207 311 196 294 186 280 177 266 169 254 162 243 155 233 149 224 143 215 138 207

W21

W21× 132 122 ASD LRFD ASD LRFD 567 850 521 781 554 833 511 768 511 768 471 708 475 714 438 658 443 666 409 614 415 624 383 576 391 588 360 542 369 555 340 512 350 526 323 485 332 500 306 461 317 476 292 439 302 454 279 419 289 434 266 400 277 416 255 384 266 400 245 368 256 384 236 354 246 370 227 341 237 357 219 329 229 344 211 318 222 333 204 307 208 312 191 288 195 294 180 271 185 278 170 256 175 263 161 242 166 250 153 230 158 238 146 219 151 227 139 209 144 217 133 200 138 208 128 192 133 200 123 184 128 192 118 177 123 185 113 171

111 ASD LRFD 473 710 464 698 428 644 398 598 371 558 348 523 328 492 309 465 293 441 278 419 265 399 253 380 242 364 232 349 223 335 214 322 206 310 199 299 192 289 186 279 174 262 164 246 155 233 147 220 139 209 133 199 127 190 121 182 116 174 111 167 107 161

101 ASD LRFD 428 642 421 633 388 584 361 542 337 506 316 474 297 446 281 422 266 399 252 380 240 361 230 345 220 330 210 316 202 304 194 292 187 281 180 271 174 262 168 253 158 237 149 223 140 211 133 200 126 190 120 181 115 173 110 165 105 158 101 152 97.1 146

Beam Properties Wc /Ωb φbWc , kip-ft 8620 13000 Mp /Ωb φb Mp , kip-ft 1080 1620 Mr /Ωb φb Mr , kip-ft 664 998 BF /Ωb φb BF, kips 14.2 21.2 Vn /Ωv φvVn , kips 338 506 Zx , in.3 Lp , ft Lr , ft

ASD

432 10.6 39.9

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

7450 11200 931 1400 575 864 13.7 20.7 318 477 373 10.4 36.3

6650 9990 6130 9210 5570 8370 5050 7590 831 1250 766 1150 696 1050 631 949 515 774 477 717 435 654 396 596 13.2 19.9 12.9 19.3 12.4 18.9 11.8 17.7 283 425 260 391 237 355 214 321 333 10.3 34.2

307 10.3 32.7

279 10.2 31.2

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

253 10.2 30.1

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DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W21 Shape

93

Design

83

ASD 501 490 441 401 368 339 315 294 276 259 245 232 221 210 201 192 184 176 170 163 158 152 147 138 130 123 116 110 105 100 95.9 91.9 88.2 84.8 81.7

LRFD 752 737 663 603 553 510 474 442 414 390 368 349 332 316 301 288 276 265 255 246 237 229 221 207 195 184 174 166 158 151 144 138 133 128 123

ASD 441 435 391 356 326 301 279 261 245 230 217 206 196 186 178 170 163 156 150 145 140 135 130 122 115 109 103 97.8 93.1 88.9 85.0 81.5 78.2 75.2

Wc /Ωb φbWc , kip-ft 4410 Mp /Ωb φb Mp , kip-ft 551 Mr /Ωb φb Mr , kip-ft 335 BF /Ωb φb BF, kips 14.6 Vn /Ωv φvVn , kips 251

6630 829 504 22.0 376

3910 489 299 13.8 220

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54

Span, ft

Fy = 50 ksi

LRFD 661 653 588 535 490 452 420 392 368 346 327 309 294 280 267 256 245 235 226 218 210 203 196 184 173 163 155 147 140 134 128 122 118 113

W21× 73 ASD LRFD 386 579 381 573 343 516 312 469 286 430 264 397 245 369 229 344 215 323 202 304 191 287 181 272 172 258 163 246 156 235 149 224 143 215 137 206 132 198 127 191 123 184 118 178 114 172 107 161 101 152 95.4 143 90.3 136 85.8 129 81.7 123 78.0 117 74.6 112 71.5 108 68.7 103 66.0 99.2

68

62

ASD 363 355 319 290 266 246 228 213 200 188 177 168 160 152 145 139 133 128 123 118 114 110 106 99.8 93.9 88.7 84.0 79.8 76.0 72.6 69.4 66.5 63.9 61.4

LRFD 544 533 480 436 400 369 343 320 300 282 267 253 240 229 218 209 200 192 185 178 171 166 160 150 141 133 126 120 114 109 104 100 96.0 92.3

ASD 336 319 287 261 240 221 205 192 180 169 160 151 144 137 131 125 120 115 111 106 103 99.1 95.8 89.8 84.5 79.8 75.6 71.9 68.4 65.3 62.5 59.9 57.5 55.3

LRFD 504 480 432 393 360 332 309 288 270 254 240 227 216 206 196 188 180 173 166 160 154 149 144 135 127 120 114 108 103 98.2 93.9 90.0 86.4 83.1

3190 399 245 12.5 181

4800 600 368 18.8 272

2870 359 222 11.6 168

4320 540 333 17.5 252

Beam Properties

Zx , in.3 Lp , ft Lr , ft

ASD

221 6.50 21.3

LRFD

f

5880 735 449 20.8 331

196 6.46 20.2

3430 429 264 12.9 193

5160 645 396 19.4 289

172 6.39 19.2

Shape does not meet compact limit for flexure with Fy = 50 ksi.

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

160 6.36 18.7

144 6.25 18.1

AISC_Part 3A_14th Ed._February 25, 2013 14-11-10 10:43 AM Page 57

MAXIMUM TOTAL UNIFORM LOAD TABLES

3–57

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape Design

57

55

ASD

LRFD

ASD

LRFD

342 322 286 257 234 215 198 184 172 161 151 143 136 129 123 117 112 107 103 99.0 95.4 92.0 88.8 85.8 80.5 75.7 71.5 67.8 64.4 61.3 58.5 56.0 53.6 51.5 49.5

513 484 430 387 352 323 298 276 258 242 228 215 204 194 184 176 168 161 155 149 143 138 133 129 121 114 108 102 96.8 92.1 88.0 84.1 80.6 77.4 74.4

312 279 251 229 210 193 180 168 157 148 140 132 126 120 114 109 105 101 96.7 93.1 89.8 86.7 83.8 78.6 74.0 69.9 66.2 62.9 59.9 57.2 54.7 52.4 50.3 48.4

468 420 378 344 315 291 270 252 236 222 210 199 189 180 172 164 158 151 145 140 135 130 126 118 111 105 99.5 94.5 90.0 85.9 82.2 78.8 75.6 72.7

Wc /Ωb φbWc , kip-ft 2570 Mp /Ωb φb Mp , kip-ft 322 Mr /Ωb φb Mr , kip-ft 194 BF /Ωb φb BF, kips 13.4 Vn /Ωv φvVn , kips 171

3870 484 291 20.3 256

2510 314 192 10.8 156

Span, ft

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52

W21

W21× 50 ASD LRFD 316 474 314 471 274 413 244 367 220 330 200 300 183 275 169 254 157 236 146 220 137 206 129 194 122 183 116 174 110 165 105 157 99.8 150 95.5 143 91.5 138 87.8 132 84.4 127 81.3 122 78.4 118 75.7 114 73.2 110 68.6 103 64.6 97.1 61.0 91.7 57.8 86.8 54.9 82.5 52.3 78.6 49.9 75.0 47.7 71.7 45.7 68.8 43.9 66.0 42.2 63.5

44

48f

433 398 354 318 289 265 245 227 212 199 187 177 168 159 152 145 138 133 127 122 118 114 110 106 99.5 93.6 88.4 83.8 79.6 75.8 72.3 69.2 66.3 63.7

ASD 290 272 238 212 190 173 159 146 136 127 119 112 106 100 95.2 90.7 86.6 82.8 79.3 76.2 73.2 70.5 68.0 65.7 63.5 59.5 56.0 52.9 50.1 47.6 45.3 43.3 41.4 39.7 38.1

LRFD 435 409 358 318 286 260 239 220 204 191 179 168 159 151 143 136 130 124 119 114 110 106 102 98.7 95.4 89.4 84.2 79.5 75.3 71.6 68.1 65.0 62.2 59.6 57.2

3180 398 244 14.8 216

1900 238 143 11.1 145

2860 358 214 16.8 217

ASD

LRFD

288 265 235 212 193 176 163 151 141 132 125 118 111 106 101 96.3 92.1 88.2 84.7 81.5 78.4 75.6 73.0 70.6 66.2 62.3 58.8 55.7 52.9 50.4 48.1 46.0 44.1 42.4

2120 265 162 9.89 144

Beam Properties

Zx , in.3 Lp , ft Lr , ft

ASD

129 4.77 14.3

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

3780 473 289 16.3 234

126 6.11 17.4

2200 274 165 12.1 158

3300 413 248 18.3 237

110 4.59 13.6

107 5.86 16.5

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

95.4 4.45 13.0

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DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W18 Shape

Span, ft

Fy = 50 ksi

Design 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 44 46 48 50 52 54

W18× 234h 283h 258h 311h ASD LRFD ASD LRFD ASD LRFD ASD LRFD 1360 2030 1230 1840 1100 1650 979 1470 1250 1890 1120 1690 1020 1530 913 1370 1160 1740 1040 1560 938 1410 843 1270 1070 1620 964 1450 871 1310 783 1180 1000 1510 900 1350 813 1220 731 1100 941 1410 843 1270 762 1150 685 1030 885 1330 794 1190 717 1080 645 969 836 1260 750 1130 678 1020 609 915 792 1190 710 1070 642 965 577 867 752 1130 675 1010 610 917 548 824 717 1080 643 966 581 873 522 784 684 1030 613 922 554 833 498 749 654 983 587 882 530 797 476 716 627 943 562 845 508 764 457 686 602 905 540 811 488 733 438 659 579 870 519 780 469 705 421 633 557 838 500 751 452 679 406 610 537 808 482 724 436 655 391 588 519 780 465 699 421 632 378 568 502 754 450 676 407 611 365 549 485 730 435 654 393 591 353 531 470 707 422 634 381 573 342 515 456 685 409 615 370 555 332 499 443 665 397 596 359 539 322 484 430 646 386 579 348 524 313 471 418 628 375 563 339 509 304 458 407 611 365 548 330 495 296 445 396 595 355 534 321 482 288 433 386 580 346 520 313 470 281 422 376 566 337 507 305 458 274 412 358 539 321 483 290 436 261 392 342 514 307 461 277 417 249 374 327 492 293 441 265 398 238 358 314 471 281 423 254 382 228 343 301 452 270 406 244 367 219 329 289 435 259 390 235 353 211 317 279 419 250 376

211 ASD LRFD 878 1320 815 1230 752 1130 699 1050 652 980 611 919 575 865 543 817 515 774 489 735 466 700 445 668 425 639 408 613 391 588 376 565 362 544 349 525 337 507 326 490 315 474 306 459 296 445 288 432 279 420 272 408 264 397 257 387 251 377 245 368 233 350 222 334 213 320 204 306 196 294

192 ASD LRFD 783 1180 735 1110 679 1020 630 947 588 884 551 829 519 780 490 737 464 698 441 663 420 631 401 603 384 577 368 553 353 530 339 510 327 491 315 474 304 457 294 442 285 428 276 414 267 402 259 390 252 379 245 368 238 358 232 349 226 340 221 332 210 316 201 301 192 288 184 276 176 265

9780 14700 1220 1840 732 1100 10.7 16.2 439 658

8820 13300 1100 1660 664 998 10.6 16.1 392 588

490 9.96 55.7

442 9.85 51.0

Beam Properties Wc /Ωb φbWc , kip-ft 15000 22600 13500 20300 12200 18300 11000 16500 Mp /Ωb φb Mp , kip-ft 1880 2830 1690 2540 1520 2290 1370 2060 Mr /Ωb φb Mr , kip-ft 1090 1640 987 1480 898 1350 814 1220 BF /Ωb φb BF, kips 11.2 16.8 11.1 16.7 10.9 16.5 10.8 16.4 Vn /Ωv φvVn , kips 678 1020 613 920 550 826 490 734 Zx , in.3 Lp , ft Lr , ft

ASD

754 10.4 81.1

LRFD

h

676 10.3 73.6

611 10.2 67.3

549 10.1 61.4

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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MAXIMUM TOTAL UNIFORM LOAD TABLES

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape Design

Span, ft

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 44 46 48 50

W18

175 ASD LRFD

158 ASD LRFD

W18× 143 130 ASD LRFD ASD LRFD

712 662 611 567 530 497 467 441 418 397 378 361 345 331 318 306 294 284 274 265 256 248 241 234 227 221 215 209 204 199 189 181 173 166 159

638 592 547 508 474 444 418 395 374 355 338 323 309 296 284 273 263 254 245 237 229 222 215 209 203 197 192 187 182 178 169 161 154 148

569 536 494 459 428 402 378 357 338 321 306 292 279 268 257 247 238 230 222 214 207 201 195 189 184 179 174 169 165 161 153 146 140 134

1070 995 918 853 796 746 702 663 628 597 569 543 519 498 478 459 442 426 412 398 385 373 362 351 341 332 323 314 306 299 284 271 260 249 239

957 890 822 763 712 668 628 593 562 534 509 485 464 445 427 411 396 381 368 356 345 334 324 314 305 297 289 281 274 267 254 243 232 223

854 805 743 690 644 604 568 537 508 483 460 439 420 403 386 372 358 345 333 322 312 302 293 284 276 268 261 254 248 242 230 220 210 201

517 482 445 413 386 362 340 322 305 289 276 263 252 241 232 223 214 207 200 193 187 181 175 170 165 161 156 152 148 145 138 132 126 121

776 725 669 621 580 544 512 483 458 435 414 395 378 363 348 335 322 311 300 290 281 272 264 256 249 242 235 229 223 218 207 198 189 181

119 ASD LRFD 498 747 475 715 436 655 402 605 374 561 349 524 327 491 308 462 291 437 275 414 261 393 249 374 238 357 227 342 218 328 209 314 201 302 194 291 187 281 180 271 174 262 169 254 163 246 158 238 154 231 149 225 145 218 141 212 138 207 134 202 131 197 125 187 119 179 114 171

106 ASD LRFD 441 662 417 627 383 575 353 531 328 493 306 460 287 431 270 406 255 383 242 363 230 345 219 329 209 314 200 300 191 288 184 276 177 265 170 256 164 246 158 238 153 230 148 223 143 216 139 209 135 203 131 197 128 192 124 186 121 182 118 177 115 173 109 164 104 157 99.8 150

Beam Properties Wc /Ωb φbWc , kip-ft 7940 11900 Mp /Ωb φb Mp , kip-ft 993 1490 Mr /Ωb φb Mr , kip-ft 601 903 BF /Ωb φb BF, kips 10.6 15.8 Vn /Ωv φvVn , kips 356 534 Zx , in.3 Lp , ft Lr , ft

ASD

398 9.75 46.9

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

7110 10700 888 1340 541 814 10.5 15.9 319 479 356 9.68 42.8

6430 9660 5790 8700 5230 7860 803 1210 724 1090 654 983 493 740 447 672 403 606 10.3 15.7 10.2 15.4 10.1 15.2 285 427 259 388 249 373 322 9.61 39.6

290 9.54 36.6

262 9.50 34.3

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4590 574 356 9.73 221

6900 863 536 14.6 331

230 9.40 31.8

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DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W18 Shape Design 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 44 46

Span, ft

Fy = 50 ksi

97 ASD LRFD

86 ASD LRFD

398 383 351 324 301 281 263 248 234 222 211 201 191 183 175 168 162 156 150 145 140 136 132 128 124 120 117 114 111 108 105 100 95.7 91.6

597 575 528 487 452 422 396 372 352 333 317 301 288 275 264 253 243 234 226 218 211 204 198 192 186 181 176 171 167 162 158 151 144 138

353 338 309 286 265 248 232 218 206 195 186 177 169 161 155 149 143 138 133 128 124 120 116 113 109 106 103 100 97.7 95.2 92.8 88.4 84.4 80.7

530 507 465 429 399 372 349 328 310 294 279 266 254 243 233 223 215 207 199 192 186 180 174 169 164 159 155 151 147 143 140 133 127 121

4210 526 328 9.41 199

6330 791 494 14.1 299

3710 464 290 9.01 177

5580 698 436 13.6 265

W18× 76 71 ASD LRFD ASD LRFD 366 549 364 548 324 487 309 464 291 438 296 445 265 398 271 408 243 365 250 376 224 337 232 349 208 313 217 326 194 292 203 306 182 274 191 288 171 258 181 272 162 243 171 257 153 231 163 245 146 219 155 233 139 209 148 222 132 199 141 213 127 190 136 204 121 183 130 196 117 175 125 188 112 168 120 181 108 162 116 175 104 156 112 169 100 151 108 163 97.1 146 105 158 94.0 141 102 153 91.1 137 98.6 148 88.3 133 95.7 144 85.7 129 93.0 140 83.3 125 90.4 136 80.9 122 87.9 132 78.8 118 85.6 129 76.7 115 83.4 125 74.7 112 81.3 122 72.9 110 77.5 116 69.4 104 73.9 111 66.2 99.5 63.4 95.2

ASD

65 LRFD

ASD

60 LRFD

331 295 265 241 221 204 190 177 166 156 147 140 133 126 121 115 111 106 102 98.3 94.8 91.5 88.5 85.6 83.0 80.4 78.1 75.8 73.7 71.7 69.9 68.1 66.4 63.2 60.3 57.7

497 443 399 363 333 307 285 266 249 235 222 210 200 190 181 173 166 160 153 148 143 138 133 129 125 121 117 114 111 108 105 102 99.8 95.0 90.7 86.7

302 273 246.0 223 205 189 175 164 153 144 136 129 123 117 112 107 102 98.2 94.4 90.9 87.7 84.7 81.8 79.2 76.7 74.4 72.2 70.1 68.2 66.4 64.6 63.0 61.4 58.5 55.8

453 410 369 335 308 284 264 246 231 217 205 194 185 176 168 160 154 148 142 137 132 127 123 119 115 112 109 105 103 99.7 97.1 94.6 92.3 87.9 83.9

2650 332 204 9.98 166

3990 499 307 15.0 248

2460 307 189 9.62 151

3690 461 284 14.4 227

Beam Properties Wc /Ωb φbWc , kip-ft Mp /Ωb φb Mp , kip-ft Mr /Ωb φb Mr , kip-ft BF /Ωb φb BF, kips Vn /Ωv φvVn , kips Zx , in.3 Lp , ft Lr , ft

ASD

211 9.36 30.4

186 9.29 28.6

3250 407 255 8.50 155

4890 2910 4380 611 364 548 383 222 333 12.8 10.4 15.8 232 183 275

163 9.22 27.1

146 6.00 19.6

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

133 5.97 18.8

123 5.93 18.2

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MAXIMUM TOTAL UNIFORM LOAD TABLES

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape Design

Span, ft

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 44

55 ASD LRFD

50 ASD LRFD

282 279 248 224 203 186 172 160 149 140 132 124 118 112 106 102 97.2 93.1 89.4 86.0 82.8 79.8 77.1 74.5 72.1 69.9 67.7 65.8 63.9 62.1 60.4 58.8 57.3 55.9 53.2 50.8

424 420 373 336 305 280 258 240 224 210 198 187 177 168 160 153 146 140 134 129 124 120 116 112 108 105 102 98.8 96.0 93.3 90.8 88.4 86.2 84.0 80.0 76.4

256 252 224 202 183 168 155 144 134 126 119 112 106 101 96.0 91.6 87.7 84.0 80.6 77.5 74.7 72.0 69.5 67.2 65.0 63.0 61.1 59.3 57.6 56.0 54.5 53.1 51.7 50.4 48.0 45.8

383 379 337 303 275 253 233 216 202 189 178 168 159 152 144 138 132 126 121 117 112 108 104 101 97.7 94.7 91.8 89.1 86.6 84.2 81.9 79.7 77.7 75.8 72.1 68.9

3360 420 258 13.8 212

2020 252 155 8.76 128

3030 379 233 13.2 192

W18-W16

W18× 46 40 ASD LRFD ASD LRFD 261 391 226 338 259 389 224 336 226 340 196 294 201 302 174 261 181 272 156 235 165 247 142 214 151 227 130 196 139 209 120 181 129 194 112 168 121 181 104 157 113 170 97.8 147 106 160 92.1 138 101 151 86.9 131 95.3 143 82.4 124 90.5 136 78.2 118 86.2 130 74.5 112 82.3 124 71.1 107 78.7 118 68.0 102 75.4 113 65.2 98.0 72.4 109 62.6 94.1 69.6 105 60.2 90.5 67.1 101 58.0 87.1 64.7 97.2 55.9 84.0 62.4 93.8 54.0 81.1 60.3 90.7 52.2 78.4 58.4 87.8 50.5 75.9 56.6 85.0 48.9 73.5 54.9 82.5 47.4 71.3 53.2 80.0 46.0 69.2 51.7 77.7 44.7 67.2 50.3 75.6 43.5 65.3 48.9 73.5 42.3 63.6 47.6 71.6 41.2 61.9 46.4 69.8 40.1 60.3 45.3 68.0 39.1 58.8 43.1 64.8 37.3 56.0 41.1 61.8 35.6 53.5

W16× 35 ASD LRFD 212 319 190 285 166 249 147 222 133 200 121 181 111 166 102 153 94.8 143 88.5 133 83.0 125 78.1 117 73.7 111 69.9 105 66.4 99.8 63.2 95.0 60.3 90.7 57.7 86.7 55.3 83.1 53.1 79.8 51.1 76.7 49.2 73.9 47.4 71.3 45.8 68.8 44.2 66.5 42.8 64.4 41.5 62.3 40.2 60.5 39.0 58.7 37.9 57.0 36.9 55.4 35.9 53.9 34.9 52.5 34.0 51.2 33.2 49.9 31.6 47.5 30.2 45.3

100 ASD LRFD

398 395 359 329 304 282 263 247 232 220 208 198 188 180 172 165 158 152 146 141 136 132 127 124 120 116 113 110 107 104 101 98.8 94.1

597 594 540 495 457 424 396 371 349 330 313 297 283 270 258 248 238 228 220 212 205 198 192 186 180 175 170 165 161 156 152 149 141

3950 494 306 7.86 199

5940 743 459 11.9 298

Beam Properties Wc /Ωb φbWc , kip-ft 2240 Mp /Ωb φb Mp , kip-ft 279 Mr /Ωb φb Mr , kip-ft 172 BF /Ωb φb BF, kips 9.15 Vn /Ωv φvVn , kips 141 Zx , in.3 Lp , ft Lr , ft

ASD

112 5.90 17.6

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

101 5.83 16.9

1810 2720 226 340 138 207 9.63 14.6 130 195 90.7 4.56 13.7

1560 196 119 8.94 113

2350 294 180 13.2 169

78.4 4.49 13.1

1330 166 101 8.14 106

2000 249 151 12.3 159

66.5 4.31 12.3

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

198 8.87 32.8

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DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W16 Shape

89

Design 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42

Span, ft

Fy = 50 ksi

77

ASD

LRFD

ASD

LRFD

353 349 318 291 269 250 233 218 205 194 184 175 166 159 152 146 140 134 129 125 120 116 113 109 106 103 99.8 97.0 94.4 91.9 89.6 87.3 83.2

529 525 477 438 404 375 350 328 309 292 276 263 250 239 228 219 210 202 194 188 181 175 169 164 159 154 150 146 142 138 135 131 125

300 299 272 250 230 214 200 187 176 166 158 150 143 136 130 125 120 115 111 107 103 99.8 96.6 93.6 90.7 88.1 85.5 83.2 80.9 78.8 76.8 74.9

450 450 409 375 346 321 300 281 265 250 237 225 214 205 196 188 180 173 167 161 155 150 145 141 136 132 129 125 122 118 115 113

5250 656 407 11.6 265

2990 374 234 7.34 150

W16× 67 ASD LRFD

258 236 216 200 185 173 162 153 144 137 130 124 118 113 108 104 99.8 96.1 92.7 89.5 86.5 83.7 81.1 78.6 76.3 74.1 72.1 70.1 68.3 66.5 64.9

57

50

386 355 325 300 279 260 244 229 217 205 195 186 177 170 163 156 150 144 139 134 130 126 122 118 115 111 108 105 103 100 97.5

ASD 282 262 233 210 191 175 161 150 140 131 123 116 110 105 99.8 95.3 91.1 87.3 83.8 80.6 77.6 74.9 72.3 69.9 67.6 65.5 63.5 61.6 59.9 58.2 56.6 55.2 53.7 52.4

LRFD 423 394 350 315 286 263 242 225 210 197 185 175 166 158 150 143 137 131 126 121 117 113 109 105 102 98.4 95.5 92.6 90.0 87.5 85.1 82.9 80.8 78.8

ASD 248 230 204 184 167 153 141 131 122 115 108 102 96.6 91.8 87.4 83.5 79.8 76.5 73.5 70.6 68.0 65.6 63.3 61.2 59.2 57.4 55.6 54.0 52.5 51.0 49.6 48.3 47.1 45.9

LRFD 372 345 307 276 251 230 212 197 184 173 162 153 145 138 131 125 120 115 110 106 102 98.6 95.2 92.0 89.0 86.3 83.6 81.2 78.9 76.7 74.6 72.6 70.8 69.0

3900 488 307 10.4 193

2100 262 161 7.98 141

3150 394 242 12.0 212

1840 230 141 7.69 124

2760 345 213 11.4 186

Beam Properties Wc /Ωb φbWc , kip-ft 3490 Mp /Ωb φb Mp , kip-ft 437 Mr /Ωb φb Mr , kip-ft 271 BF /Ωb φb BF, kips 7.76 Vn /Ωv φvVn , kips 176 Zx , in.3 Lp , ft Lr , ft

ASD

175 8.80 30.2

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

v

4500 563 352 11.1 225

150 8.72 27.8

2590 324 204 6.89 129

130 8.69 26.1

105 5.65 18.3

92.0 5.62 17.2

Shape does not meet the h/tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 63

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MAXIMUM TOTAL UNIFORM LOAD TABLES

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes W16×

Shape 45 Design

Span, ft

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

W16

40

36

ASD

LRFD

ASD

LRFD

223 205 183 164.0 149 137 126 117 110 103 96.6 91.3 86.5 82.1 78.2 74.7 71.4 68.4 65.7 63.2 60.8 58.7 56.6 54.8 53.0 51.3 49.8 48.3 46.9 45.6 44.4 43.2 42.1 41.1

333 309 274 247 224 206 190 176 165 154 145 137 130 123 118 112 107 103 98.8 95.0 91.4 88.2 85.1 82.3 79.6 77.2 74.8 72.6 70.5 68.6 66.7 65.0 63.3 61.7

195 182 162 146 132 121 112 104 97.1 91.1 85.7 80.9 76.7 72.9 69.4 66.2 63.4 60.7 58.3 56.0 54.0 52.0 50.2 48.6 47.0 45.5 44.2 42.9 41.6 40.5 39.4 38.3 37.4 36.4

293 274 243 219 199 183 168 156 146 137 129 122 115 110 104 99.5 95.2 91.3 87.6 84.2 81.1 78.2 75.5 73.0 70.6 68.4 66.4 64.4 62.6 60.8 59.2 57.6 56.2 54.8

2470 309 191 10.8 167

1460 182 113 6.67 97.6

ASD 188 182 160 142 128 116 106 98.3 91.2 85.2 79.8 75.1 71.0 67.2 63.9 60.8 58.1 55.5 53.2 51.1 49.1 47.3 45.6 44.0 42.6 41.2 39.9 38.7 37.6 36.5 35.5 34.5 33.6 32.8

26v

31 LRFD 281 274 240 213 192 175 160 148 137 128 120 113 107 101 96.0 91.4 87.3 83.5 80.0 76.8 73.8 71.1 68.6 66.2 64.0 61.9 60.0 58.2 56.5 54.9 53.3 51.9 50.5 49.2

ASD 175 154 135 120 108 98.0 89.8 82.9 77.0 71.9 67.4 63.4 59.9 56.7 53.9 51.3 49.0 46.9 44.9 43.1 41.5 39.9 38.5 37.2 35.9 34.8 33.7 32.7 31.7 30.8 29.9 29.1 28.4 27.6

LRFD 262 231 203 180 162 147 135 125 116 108 101 95.3 90.0 85.3 81.0 77.1 73.6 70.4 67.5 64.8 62.3 60.0 57.9 55.9 54.0 52.3 50.6 49.1 47.6 46.3 45.0 43.8 42.6 41.5

ASD 141 126 110 98.0 88.2 80.2 73.5 67.9 63.0 58.8 55.1 51.9 49.0 46.4 44.1 42.0 40.1 38.4 36.8 35.3 33.9 32.7 31.5 30.4 29.4 28.5 27.6 26.7 25.9 25.2 24.5 23.8 23.2 22.6

LRFD 212 189 166 147 133 121 111 102 94.7 88.4 82.9 78.0 73.7 69.8 66.3 63.1 60.3 57.7 55.3 53.0 51.0 49.1 47.4 45.7 44.2 42.8 41.4 40.2 39.0 37.9 36.8 35.8 34.9 34.0

1620 203 124 10.3 131

882 110 67.1 5.93 70.5

1330 166 101 8.98 106

Beam Properties Wc /Ωb φbWc , kip-ft 1640 Mp /Ωb φb Mp , kip-ft 205 Mr /Ωb φb Mr , kip-ft 127 BF /Ωb φb BF, kips 7.12 Vn /Ωv φvVn , kips 111 Zx , in.3 Lp , ft Lr , ft

ASD

82.3 5.55 16.5

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

2190 274 170 10.0 146

73.0 5.55 15.9

1280 1920 1080 160 240 135 98.7 148 82.4 6.24 9.36 6.86 93.8 141 87.5 64.0 5.37 15.2

54.0 4.13 11.8

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

44.2 3.96 11.2

AISC_Part 3B_14th Ed._Nov. 19, 2012 14-11-10 10:48 AM Page 64

3–64

DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W14 Shape

W14× 730h ASD LRFD

665h ASD LRFD

605h ASD LRFD

550h ASD LRFD

500h ASD LRFD

455h ASD LRFD

12 13 14 15

2750 2550 2370 2210

4130 3830 3560 3320

2450 2270 2110 1970

3670 3420 3170 2960

2170 2030 1880 1760

3260 3050 2830 2640

1920 1810 1680 1570

2880 2720 2530 2360

1720 1610 1500 1400

2580 2420 2250 2100

1540 1440 1330 1250

2300 2160 2010 1870

16 17 18 19 20

2070 1950 1840 1740 1660

3110 2930 2770 2620 2490

1850 1740 1640 1550 1480

2780 2610 2470 2340 2220

1650 1550 1460 1390 1320

2480 2330 2200 2080 1980

1470 1390 1310 1240 1180

2210 2080 1970 1860 1770

1310 1230 1160 1100 1050

1970 1850 1750 1660 1580

1170 1100 1040 983 934

1760 1650 1560 1480 1400

21 22 23 24 25

1580 1510 1440 1380 1330

2370 2260 2170 2080 1990

1410 1340 1280 1230 1180

2110 2020 1930 1850 1780

1250 1200 1150 1100 1050

1890 1800 1720 1650 1580

1120 1070 1020 981 942

1690 1610 1540 1480 1420

998 953 911 873 838

1500 1430 1370 1310 1260

890 849 812 778 747

1340 1280 1220 1170 1120

26 27 28 29 30

1270 1230 1180 1140 1100

1920 1840 1780 1720 1660

1140 1090 1060 1020 985

1710 1640 1590 1530 1480

1010 976 941 909 878

1520 1470 1410 1370 1320

906 872 841 812 785

1360 1310 1260 1220 1180

806 776 749 723 699

1210 1170 1130 1090 1050

719 692 667 644 623

1080 1040 1000 968 936

31 32 33 34 35

1070 1040 1000 975 947

1610 1560 1510 1460 1420

953 923 895 869 844

1430 1390 1350 1310 1270

850 823 798 775 753

1280 1240 1200 1160 1130

760 736 714 693 673

1140 1110 1070 1040 1010

676 655 635 616 599

1020 984 955 926 900

603 584 566 549 534

906 878 851 826 802

36 37 38 39 40

920 896 872 850 828

1380 1350 1310 1280 1250

821 798 777 757 739

1230 1200 1170 1140 1110

732 712 693 676 659

1100 1070 1040 1020 990

654 637 620 604 589

983 957 932 908 885

582 566 552 537 524

875 851 829 808 788

519 505 492 479 467

780 759 739 720 702

42 44 46 48 50

789 753 720 690 663

1190 1130 1080 1040 996

703 671 642 615 591

1060 1010 965 925 888

627 599 573 549 527

943 900 861 825 792

561 535 512 491 471

843 805 770 738 708

499 476 456 437

750 716 685 656

445 425 406

669 638 610

52 54 56

667 614 592

958 922 889

568 547

854 822

507

762

Design

Span, ft

Fy = 50 ksi

Beam Properties Wc /Ωb φbWc , kip-ft Mp /Ωb φb Mp , kip-ft Mr /Ωb φb Mr , kip-ft BF /Ωb φb BF, kips Vn /Ωv φvVn , kips

33100 49800 29500 4140 6230 3690 2240 3360 2010 7.35 11.1 7.10 1380 2060 1220

Zx , in.3 Lp , ft Lr , ft

ASD

1660 16.6 275

LRFD

h

44400 26300 39600 23600 35400 21000 31500 18700 28100 5550 3290 4950 2940 4430 2620 3940 2340 3510 3020 1820 2730 1630 2440 1460 2200 1320 1980 10.7 6.81 10.3 6.65 10.1 6.43 9.65 6.24 9.36 1830 1090 1630 962 1440 858 1290 768 1150

1480 16.3 253

1320 16.1 232

1180 15.9 213

1050 15.6 196

936 15.5 179

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3B:14th Ed.

2/24/11

8:49 AM

Page 65

MAXIMUM TOTAL UNIFORM LOAD TABLES

3–65

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape

W14×

12 13 14 15

426h ASD LRFD 1410 2110 1330 2010 1240 1860 1160 1740

16 17 18 19 20

1080 1020 964 913 867

1630 1530 1450 1370 1300

999 940 888 841 799

1500 1410 1340 1260 1200

918 864 816 773 735

1380 1300 1230 1160 1100

838 789 745 706 671

1260 1190 1120 1060 1010

752 708 669 633 602

1130 1060 1010 952 905

676 636 601 569 541

1020 956 903 856 813

21 22 23 24 25

826 788 754 723 694

1240 1190 1130 1090 1040

761 727 695 666 640

1140 1090 1040 1000 961

700 668 639 612 588

1050 1000 960 920 883

639 610 583 559 537

960 916 877 840 806

573 547 523 501 481

861 822 787 754 724

515 492 470 451 433

774 739 707 678 650

26 27 28 29 30

667 642 619 598 578

1000 966 931 899 869

615 592 571 551 533

924 890 858 829 801

565 544 525 507 490

849 818 789 761 736

516 497 479 463 447

775 747 720 695 672

463 446 430 415 401

696 670 646 624 603

416 401 386 373 361

625 602 581 561 542

31 32 33 34 35

560 542 526 510 496

841 815 790 767 745

516 500 484 470 457

775 751 728 707 687

474 459 445 432 420

712 690 669 649 631

433 419 406 395 383

650 630 611 593 576

388 376 365 354 344

584 565 548 532 517

349 338 328 318 309

525 508 493 478 465

36 37 38 39 40

482 469 456 445 434

724 705 686 668 652

444 432 421 410 400

668 649 632 616 601

408 397 387 377 367

613 597 581 566 552

373 363 353 344 335

560 545 531 517 504

334 325 317 309 301

503 489 476 464 452

301 292 285 277 270

452 439 428 417 407

42 44 46

413 394 377

621 593 567

381 363

572 546

350 334

526 502

319

480

287

431

Design

Span, ft

W14

342h 398h 370h ASD LRFD ASD LRFD ASD LRFD 1300 1940 1190 1780 1080 1620 1230 1850 1130 1700 1030 1550 1140 1720 1050 1580 958 1440 1070 1600 979 1470 894 1340

311h ASD LRFD 964 1450 926 1390 860 1290 802 1210

283h ASD LRFD 862 1290 832 1250 773 1160 721 1080

Beam Properties Wc /Ωb φbWc , kip-ft Mp /Ωb φb Mp , kip-ft Mr /Ωb φb Mr , kip-ft BF /Ωb φb BF, kips Vn /Ωv φvVn , kips Zx , in.3 Lp , ft Lr , ft

ASD

17300 26100 16000 2170 3260 2000 1230 1850 1150 6.16 9.23 5.95 703 1050 648 869 15.3 168

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

24000 14700 22100 13400 20200 12000 18100 10800 16300 3000 1840 2760 1680 2520 1500 2260 1350 2030 1720 1060 1590 975 1460 884 1330 802 1200 8.96 5.87 8.80 5.73 8.62 5.59 8.44 5.52 8.36 972 594 891 539 809 482 723 431 646

801 15.2 158

736 15.1 148

672 15.0 138

603 14.8 125

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

542 14.7 114

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Page 66

3–66

DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes

W14

12 13 14 15

257 ASD LRFD 774 1160 748 1120 694 1040 648 974

233 ASD LRFD 685 1030 669 1010 622 934 580 872

W14× 211 193 ASD LRFD ASD LRFD 615 923 552 828 599 900 545 819 556 836 506 761 519 780 472 710

176 ASD LRFD 505 757 491 738 456 686 426 640

159 ASD LRFD 447 671 441 662 409 615 382 574

16 17 18 19 20

608 572 540 512 486

913 859 812 769 731

544 512 483 458 435

818 769 727 688 654

487 458 432 410 389

731 688 650 616 585

443 417 394 373 354

666 626 592 561 533

399 376 355 336 319

600 565 533 505 480

358 337 318 302 286

538 506 478 453 431

21 22 23 24 25

463 442 423 405 389

696 664 635 609 584

414 396 378 363 348

623 595 569 545 523

371 354 338 324 311

557 532 509 488 468

337 322 308 295 283

507 484 463 444 426

304 290 278 266 255

457 436 417 400 384

273 260 249 239 229

410 391 374 359 344

26 27 28 29 30

374 360 347 335 324

562 541 522 504 487

335 322 311 300 290

503 484 467 451 436

299 288 278 268 259

450 433 418 403 390

273 262 253 244 236

410 394 380 367 355

246 237 228 220 213

369 356 343 331 320

220 212 205 198 191

331 319 308 297 287

31 32 33 34 35

314 304 295 286 278

471 457 443 430 417

281 272 264 256 249

422 409 396 385 374

251 243 236 229 222

377 366 355 344 334

229 221 215 208 202

344 333 323 313 304

206 200 194 188 182

310 300 291 282 274

185 179 174 168 164

278 269 261 253 246

36 37 38 39 40

270 263 256 249 243

406 395 384 375 365

242 235 229 223 218

363 354 344 335 327

216 210 205 200

325 316 308 300

197 192 186

296 288 280

177 173 168

267 259 253

159 155

239 233

Wc /Ωb φbWc , kip-ft 9720 Mp /Ωb φb Mp , kip-ft 1220 Mr /Ωb φb Mr , kip-ft 725 BF /Ωb φb BF, kips 5.54 Vn /Ωv φvVn , kips 387

14600 1830 1090 8.28 581

8700 1090 655 5.40 342

13100 1640 984 8.15 514

7090 886 541 5.30 276

10700 1330 814 7.93 414

6390 798 491 5.20 252

9600 1200 738 7.83 378

5730 716 444 5.17 224

8610 1080 667 7.85 335

Shape

Span, ft

Design

Beam Properties

Zx , in.3 Lp , ft Lr , ft

ASD

487 14.6 104

LRFD

f

436 14.5 95.0

7780 973 590 5.30 308

11700 1460 887 7.94 462

390 14.4 86.6

355 14.3 79.4

Shape does not meet compact limit for flexure with Fy = 50 ksi.

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

320 14.2 73.2

287 14.1 66.7

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Page 67

MAXIMUM TOTAL UNIFORM LOAD TABLES

3–67

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape

W14

W14×

12 13 14 15

145 ASD LRFD 403 604 399 600 371 557 346 520

132 ASD LRFD 379 569 359 540 334 501 311 468

120 ASD LRFD 342 513 326 489 302 454 282 424

109 ASD LRFD 300 450 295 443 274 411 255 384

99f ASD LRFD 275 413 264 397 246 369 229 344

90f ASD LRFD 246 370 235 353 218 328 204 306

16 17 18 19 20

324 305 288 273 259

488 459 433 411 390

292 275 259 246 234

439 413 390 369 351

264 249 235 223 212

398 374 353 335 318

240 225 213 202 192

360 339 320 303 288

215 202 191 181 172

323 304 287 272 258

191 180 170 161 153

287 270 255 242 230

21 22 23 24 25

247 236 226 216 208

371 355 339 325 312

222 212 203 195 187

334 319 305 293 281

202 192 184 176 169

303 289 277 265 254

182 174 167 160 153

274 262 250 240 230

164 156 149 143 137

246 235 225 215 207

145 139 133 127 122

219 209 200 191 184

26 27 28 29 30

200 192 185 179 173

300 289 279 269 260

180 173 167 161 156

270 260 251 242 234

163 157 151 146 141

245 236 227 219 212

147 142 137 132 128

222 213 206 199 192

132 127 123 119 115

199 191 185 178 172

117 113 109 105 102

177 170 164 158 153

31 32 33 34 35

167 162 157 153 148

252 244 236 229 223

151 146 142 137 133

226 219 213 206 201

137 132 128 124 121

205 199 193 187 182

124 120 116 113 109

186 180 175 169 165

111 107 104 101 98.2

167 161 157 152 148

98.5 95.4 92.5 89.8 87.3

148 143 139 135 131

36 37

144 140

217 211

130

195

118

177

Wc /Ωb φbWc , kip-ft 5190 Mp /Ωb φb Mp , kip-ft 649 Mr /Ωb φb Mr , kip-ft 405 BF /Ωb φb BF, kips 5.13 Vn /Ωv φvVn , kips 201

7800 975 609 7.69 302

4670 584 365 5.15 190

7020 878 549 7.74 284

3830 479 302 5.01 150

5760 720 454 7.54 225

3440 430 274 4.91 138

5170 646 412 7.36 207

3050 382 250 4.82 123

4590 574 375 7.26 185

Span, ft

Design

Beam Properties

Zx , in.3 Lp , ft Lr , ft

ASD

260 14.1 61.7

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

234 13.3 55.8

4230 529 332 5.09 171 212 13.2 51.9

6360 795 499 7.65 257

192 13.2 48.5

173 13.5 45.3

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

157 15.1 42.5

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Page 68

3–68

DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes

W14 Shape

74 ASD LRFD

W14× 68 61 ASD LRFD ASD LRFD

8 9 10

292 277

438 417

256 251

383 378

232 230

349 345

209 204

313 306

53 48 ASD LRFD ASD LRFD 206 309 188 282 193 290 174 261 174 261 156 235

11 12 13 14 15

252 231 213 198 185

379 348 321 298 278

229 210 193 180 168

344 315 291 270 252

209 191 177 164 153

314 288 265 246 230

185 170 157 145 136

278 255 235 219 204

158 145 134 124 116

238 218 201 187 174

16 17 18 19 20

173 163 154 146 139

261 245 232 219 209

157 148 140 132 126

236 222 210 199 189

143 135 128 121 115

216 203 192 182 173

127 120 113 107 102

191 180 170 161 153

109 102 96.6 91.5 86.9

163 154 145 138 131

97.8 92.1 86.9 82.4 78.2

21 22 23 24 25

132 126 121 116 111

199 190 181 174 167

120 114 109 105 101

180 172 164 158 151

109 104 99.8 95.6 91.8

164 157 150 144 138

96.9 92.5 88.5 84.8 81.4

146 139 133 128 122

82.8 79.0 75.6 72.4 69.5

124 119 114 109 105

74.5 112 71.1 107 68.0 102 65.2 98.0 62.6 94.1

26 27 28 29 30

107 103 99.1 95.7 92.5

160 154 149 144 139

96.7 93.1 89.8 86.7 83.8

145 140 135 130 126

88.3 85.0 82.0 79.2 76.5

133 128 123 119 115

78.3 75.4 72.7 70.2 67.9

118 113 109 106 102

66.9 101 64.4 96.8 62.1 93.3 59.9 90.1 58.0 87.1

60.2 58.0 55.9 54.0 52.2

90.5 87.1 84.0 81.1 78.4

31 32 33 34 35

89.5 86.7 84.1 81.6 79.3

135 130 126 123 119

81.1 78.6 76.2 74.0 71.9

122 118 115 111 108

74.0 71.7 69.6 67.5 65.6

111 108 105 101 98.6

65.7 63.6 61.7 59.9

98.7 95.6 92.7 90.0

56.1 54.3 52.7 51.1

84.3 81.7 79.2 76.9

50.5 48.9 47.4 46.0

75.9 73.5 71.3 69.2

Wc /Ωb φbWc , kip-ft 2770 Mp /Ωb φb Mp , kip-ft 347 Mr /Ωb φb Mr , kip-ft 215 BF /Ωb φb BF, kips 5.40 Vn /Ωv φvVn , kips 146

4170 521 323 8.10 219

2510 314 196 5.31 128

3780 473 294 8.05 192

2040 254 161 4.93 104

3060 383 242 7.48 156

1740 217 136 5.22 103

2610 327 204 7.93 154

1560 196 123 5.09 93.8

2350 294 184 7.67 141

Span, ft

Design

82 ASD LRFD

142 130 120 112 104

214 196 181 168 157 147 138 131 124 118

Beam Properties

Zx , in.3 Lp , ft Lr , ft

ASD

139 8.76 33.2

126 8.76 31.0

2300 287 180 5.19 116

3450 431 270 7.81 174

115 8.69 29.3

102 8.65 27.5

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

87.1 6.78 22.3

78.4 6.75 21.1

AISC_Part 3B:14th Ed.

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Page 69

MAXIMUM TOTAL UNIFORM LOAD TABLES

3–69

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape

43 ASD LRFD

Design

38 ASD LRFD

W14

W14× 34 30 ASD LRFD ASD LRFD

Span, ft

5 6 7 8 9 10

167 154 139

11 12 13 14 15

251 232 209

175 153 136 123

262 231 205 185

126 116 107 99.2 92.6

190 174 161 149 139

112 102 94.4 87.7 81.8

168 154 142 132 123

16 17 18 19 20

86.8 81.7 77.2 73.1 69.5

131 123 116 110 104

21 22 23 24 25

66.2 63.1 60.4 57.9 55.6

26 27 28 29 30 31 32 33 34 35

160 156 136 121 109 99.1 90.8 83.8 77.8 72.7

239 234 205 182 164

149 135 118 105 94.4

224 203 177 158 142

149 137 126 117 109

85.8 78.7 72.6 67.4 62.9

129 118 109 101 94.6

26 22 ASD LRFD ASD LRFD 142 213 126 189 134 115 100 89.2 80.2

201 172 151 134 121

110 94.7 82.8 73.6 66.3

166 142 125 111 99.6

72.9 110 66.9 101 61.7 92.8 57.3 86.1 53.5 80.4

60.2 55.2 51.0 47.3 44.2

90.5 83.0 76.6 71.1 66.4

76.7 115 72.2 109 68.2 103 64.6 97.1 61.4 92.3

68.1 102 64.1 96.4 60.5 91.0 57.4 86.2 54.5 81.9

59.0 55.5 52.5 49.7 47.2

88.7 83.5 78.8 74.7 71.0

50.1 47.2 44.6 42.2 40.1

75.4 70.9 67.0 63.5 60.3

41.4 39.0 36.8 34.9 33.1

62.3 58.6 55.3 52.4 49.8

99.4 94.9 90.8 87.0 83.5

58.5 55.8 53.4 51.1 49.1

87.9 83.9 80.2 76.9 73.8

51.9 49.5 47.4 45.4 43.6

78.0 74.5 71.2 68.3 65.5

45.0 42.9 41.0 39.3 37.8

67.6 64.5 61.7 59.1 56.8

38.2 36.5 34.9 33.4 32.1

57.4 54.8 52.4 50.3 48.2

31.6 30.1 28.8 27.6 26.5

47.4 45.3 43.3 41.5 39.8

53.4 51.5 49.6 47.9 46.3

80.3 77.3 74.6 72.0 69.6

47.2 45.5 43.8 42.3 40.9

71.0 68.3 65.9 63.6 61.5

41.9 40.4 38.9 37.6 36.3

63.0 60.7 58.5 56.5 54.6

36.3 35.0 33.7 32.6 31.5

54.6 52.6 50.7 48.9 47.3

30.9 29.7 28.7 27.7 26.7

46.4 44.7 43.1 41.6 40.2

25.5 24.5 23.7 22.9 22.1

38.3 36.9 35.6 34.3 33.2

44.8 43.4 42.1 40.9

67.4 65.3 63.3 61.4

39.6 38.4 37.2 36.1 35.1

59.5 57.7 55.9 54.3 52.7

35.2 34.1 33.0 32.1 31.1

52.8 51.2 49.6 48.2 46.8

30.5 29.5 28.6 27.8

45.8 44.3 43.0 41.7

25.9 25.1 24.3 23.6

38.9 37.7 36.5 35.5

21.4 20.7 20.1 19.5

32.1 31.1 30.2 29.3

1230 153 95.4 5.37 87.4

1850 231 143 8.20 131

944 118 73.4 4.63 74.5

1420 177 110 6.95 112

802 100 61.7 5.33 70.9

1210 151 92.7 8.11 106

663 82.8 50.6 4.78 63.0

996 125 76.1 7.27 94.5

Beam Properties Wc /Ωb φbWc , kip-ft 1390 Mp /Ωb φb Mp , kip-ft 174 Mr /Ωb φb Mr , kip-ft 109 BF /Ωb φb BF, kips 4.88 Vn /Ωv φvVn , kips 83.6 Zx , in.3 Lp , ft Lr , ft

ASD

2090 261 164 7.28 125

69.6 6.68 20.0

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

61.5 5.47 16.2

1090 136 84.9 5.01 79.8

1640 205 128 7.55 120

54.6 5.40 15.6

47.3 5.26 14.9

40.2 3.81 11.0

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

33.2 3.67 10.4

AISC_Part 3B:14th Ed.

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Page 70

3–70

DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes

W12 Shape

W12× 336h ASD LRFD

305h ASD LRFD

252h ASD LRFD 862 1290 854 1280

230h ASD LRFD 779 1170 770 1160

210 ASD LRFD

1590

279h ASD LRFD 973 1460 960 1440

9 10

1200

1790

1060

11 12 13 14 15

1090 1000 926 860 802

1640 1510 1390 1290 1210

974 893 825 766 715

694

1040

1460 1340 1240 1150 1070

873 800 739 686 640

1310 1200 1110 1030 962

777 712 657 610 570

1170 1070 988 917 856

700 642 593 550 514

1050 965 891 827 772

631 579 534 496 463

949 870 803 746 696

16 17 18 19 20

752 708 669 633 602

1130 1060 1010 952 905

670 631 595 564 536

1010 948 895 848 806

600 565 533 505 480

902 849 802 759 722

534 503 475 450 427

803 755 713 676 642

482 453 428 406 385

724 681 643 609 579

434 409 386 366 347

653 614 580 549 522

21 22 23 24 25

573 547 523 501 481

861 822 787 754 724

510 487 466 447 429

767 732 700 671 644

457 436 417 400 384

687 656 627 601 577

407 388 371 356 342

611 584 558 535 514

367 350 335 321 308

551 526 503 483 463

331 316 302 289 278

497 475 454 435 418

26 27 28 29 30

463 446 430 415 401

696 670 646 624 603

412 397 383 370 357

620 597 575 556 537

369 356 343 331 320

555 534 515 498 481

329 316 305 295 285

494 476 459 443 428

296 285 275 266 257

445 429 414 399 386

267 257 248 240 232

402 387 373 360 348

31 32 33 34 35

388 376 365 354 344

584 565 548 532 517

346 335 325 315 306

520 503 488 474 460

310 300 291 282 274

465 451 437 424 412

276 267 259 251 244

414 401 389 378 367

249 241 233 227 220

374 362 351 341 331

224 217 210 204 198

337 326 316 307 298

36 37 38 39 40

334 325 317 309 301

503 489 476 464 452

298 290 282 275 268

448 435 424 413 403

267 259 253 246

401 390 380 370

237 231 225

357 347 338

214 208

322 313

193

290

41 42

294 287

441 431

Wc /Ωb φbWc , kip-ft 12000 18100 10700 Mp /Ωb φb Mp , kip-ft 1500 2260 1340 Mr /Ωb φb Mr , kip-ft 844 1270 760 BF /Ωb φb BF, kips 4.76 7.19 4.64 Vn /Ωv φvVn , kips 598 897 531

16100 2010 1140 6.97 797

8540 1070 617 4.43 431

12800 1610 927 6.68 647

7700 963 561 4.31 390

11600 1450 843 6.51 584

6950 868 510 4.25 347

10400 1310 767 6.45 520

Span, ft

Design

Beam Properties

Zx , in.3 Lp , ft Lr , ft

ASD

603 12.3 150

LRFD

h

537 12.1 137

9600 1200 686 4.50 487

14400 1800 1030 6.75 730

481 11.9 126

428 11.8 114

386 11.7 105

348 11.6 95.8

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3B_14th Ed._Nov. 19, 2012 14-11-10 10:49 AM Page 71

MAXIMUM TOTAL UNIFORM LOAD TABLES

3–71

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes

W12

190 ASD LRFD

170 ASD LRFD

W12× 152 136 ASD LRFD ASD LRFD

9 10

611

916

538

806

477

715

423

11 12 13 14 15

564 517 478 443 414

848 778 718 666 622

499 457 422 392 366

750 688 635 589 550

441 404 373 346 323

663 608 561 521 486

16 17 18 19 20

388 365 345 327 310

583 549 518 491 467

343 323 305 289 274

516 485 458 434 413

303 285 269 255 243

21 22 23 24 25

296 282 270 259 248

444 424 406 389 373

261 250 239 229 220

393 375 359 344 330

26 27 28 29 30

239 230 222 214 207

359 346 333 322 311

211 203 196 189 183

31 32 33 34 35

200 194 188 183 177

301 292 283 274 267

36

172

259

Wc /Ωb φbWc , kip-ft 6210 Mp /Ωb φb Mp , kip-ft 776 Mr /Ωb φb Mr , kip-ft 459 BF /Ωb φb BF, kips 4.18 Vn /Ωv φvVn , kips 305

9330 1170 690 6.33 458

Shape

Span, ft

Design

106 ASD LRFD

635

120 ASD LRFD 372 558 371 558

315

472

388 356 329 305 285

584 535 494 459 428

338 309 286 265 248

507 465 429 399 372

298 273 252 234 218

447 410 378 351 328

456 429 405 384 365

267 251 237 225 214

401 378 357 338 321

232 218 206 195 186

349 328 310 294 279

205 193 182 172 164

308 289 273 259 246

231 220 211 202 194

347 331 317 304 292

203 194 186 178 171

306 292 279 268 257

177 169 161 155 149

266 254 243 233 223

156 149 142 136 131

234 224 214 205 197

317 306 295 284 275

187 180 173 167 162

280 270 260 251 243

164 158 153 147 142

247 238 229 221 214

143 138 133 128 124

215 207 199 192 186

126 121 117 113 109

189 182 176 170 164

177 172 166 161 157

266 258 250 243 236

156 152 147 143

235 228 221 214

138 133 129

207 201 195

120 116

180 174

106 102

159 154

5490 686 410 4.11 269

8250 1030 617 6.15 403

4270 534 325 4.02 212

6420 803 488 6.06 318

3710 464 285 3.94 186

5580 698 428 5.95 279

3270 409 253 3.93 157

4920 615 381 5.89 236

Beam Properties

Zx , in.3 Lp , ft Lr , ft

ASD

311 11.5 87.3

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

275 11.4 78.5

4850 606 365 4.06 238 243 11.3 70.6

7290 911 549 6.10 358

214 11.2 63.2

186 11.1 56.5

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

164 11.0 50.7

AISC_Part 3B_14th Ed._Nov. 19, 2012 14-11-10 10:53 AM Page 72

3–72

DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W12

W12×

Shape

96 ASD LRFD

87 ASD LRFD

79 ASD LRFD

72 ASD LRFD

65f ASD LRFD

9 10

279

419

258

386

233

350

212

317

189

11 12 13 14 15

267 245 226 210 196

401 368 339 315 294

240 220 203 188 176

360 330 305 283 264

216 198 183 170 158

325 298 275 255 238

196 180 166 154 144

295 270 249 231 216

16 17 18 19 20

183 173 163 154 147

276 259 245 232 221

165 155 146 139 132

248 233 220 208 198

148 140 132 125 119

223 210 198 188 179

135 127 120 113 108

21 22 23 24 25

140 133 128 122 117

210 200 192 184 176

125 120 115 110 105

189 180 172 165 158

113 108 103 99.0 95.0

170 162 155 149 143

26 27 28 29 30

113 109 105 101 97.8

170 163 158 152 147

101 97.6 94.1 90.9 87.8

152 147 141 137 132

91.4 88.0 84.8 81.9 79.2

137 132 128 123 119

31

94.6

142

85.0

128

76.6

115

Design

Span, ft

Fy = 50 ksi

283

ASD 176 172

58 LRFD 264 259

172 158 146 135 126

259 237 219 204 190

157 144 133 123 115

236 216 199 185 173

203 191 180 171 162

118 112 105 99.8 94.8

178 168 158 150 142

108 101 95.8 90.8 86.2

162 152 144 136 130

103 98.0 93.7 89.8 86.2

154 147 141 135 130

90.3 86.2 82.4 79.0 75.8

136 130 124 119 114

82.1 78.4 75.0 71.9 69.0

123 118 113 108 104

82.9 79.8 77.0 74.3 71.9

125 120 116 112 108

72.9 110 70.2 106 67.7 102 65.4 98.3 63.2 95.0

66.3 63.9 61.6 59.5 57.5

99.7 96.0 92.6 89.4 86.4

2160 269 170 3.69 106

3240 405 256 5.56 159

1900 237 154 3.58 94.4

1720 216 136 3.82 87.8

2590 324 205 5.69 132

Beam Properties Wc /Ωb φbWc , kip-ft 2930 Mp /Ωb φb Mp , kip-ft 367 Mr /Ωb φb Mr , kip-ft 229 BF /Ωb φb BF, kips 3.85 Vn /Ωv φvVn , kips 140 Zx , in.3 Lp , ft Lr , ft

ASD

4410 551 344 5.78 210

147 10.9 46.7

LRFD

f

2630 329 206 3.81 129 132 10.8 43.1

3960 495 310 5.73 193

2380 297 187 3.78 117 119 10.8 39.9

3570 446 281 5.67 175

108 10.7 37.5

Shape does not meet compact limit for flexure with Fy = 50 ksi.

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

96.8 10.7 35.1

2850 356 231 5.39 142

86.4 8.87 29.8

AISC_Part 3B:14th Ed.

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8:50 AM

Page 73

MAXIMUM TOTAL UNIFORM LOAD TABLES

3–73

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape

Span, ft

Design

53 ASD LRFD

50 ASD LRFD

W12× 45 40 ASD LRFD ASD LRFD

271 270 240 216

162 160 142 128

243 241 214 193

140 126 114

211 190 171

ASD 150 146 128 114 102

175 161 148 138 128

103 94.8 87.5 81.3 75.8

155 143 132 122 114

92.9 85.2 78.6 73.0 68.1

6 7 8 9 10

167 155

250 234

181 179 159 144

11 12 13 14 15

141 130 120 111 104

212 195 180 167 156

130 120 110 103 95.7

196 180 166 154 144

116 107 98.6 91.5 85.4

146 137 130 123 117

89.7 84.4 79.7 75.5 71.8

135 127 120 114 108

80.1 75.4 71.2 67.4 64.1

120 113 107 101 96.3

16 17 18 19 20

97.2 91.5 86.4 81.8 77.7

21 22 23 24 25

74.0 111 70.7 106 67.6 102 64.8 97.4 62.2 93.5

68.3 103 65.2 98.0 62.4 93.8 59.8 89.9 57.4 86.3

61.0 58.2 55.7 53.4 51.3

26 27 28 29 30

59.8 57.6 55.5 53.6 51.8

55.2 53.2 51.3 49.5 47.8

49.3 47.5 45.8 44.2 42.7

89.9 86.6 83.5 80.6 77.9

W12

83.0 79.9 77.0 74.4 71.9

35 30 LRFD ASD LRFD 225 128 192 219 123 185 192 108 162 171 95.6 144 154 86.0 129 140 128 118 110 102

78.2 118 71.7 108 66.2 99.5 61.4 92.4 57.4 86.2

71.1 107 66.9 101 63.2 95.0 59.9 90.0 56.9 85.5

63.9 60.1 56.8 53.8 51.1

96.0 90.4 85.3 80.8 76.8

53.8 50.6 47.8 45.3 43.0

80.8 76.1 71.8 68.1 64.7

91.7 87.5 83.7 80.3 77.0

54.2 51.7 49.5 47.4 45.5

81.4 77.7 74.3 71.3 68.4

48.7 46.5 44.4 42.6 40.9

73.1 69.8 66.8 64.0 61.4

41.0 39.1 37.4 35.8 34.4

61.6 58.8 56.2 53.9 51.7

74.1 71.3 68.8 66.4 64.2

43.8 42.1 40.6 39.2

65.8 63.3 61.1 59.0

39.3 37.9 36.5 35.2 34.1

59.1 56.9 54.9 53.0 51.2

33.1 31.9 30.7 29.7 28.7

49.7 47.9 46.2 44.6 43.1

33.0

49.5

1020 128 79.6 4.34 75.0

1540 192 120 6.45 113

860 108 67.4 3.97 64.0

1290 162 101 5.96 95.9

31

Beam Properties Wc /Ωb φbWc , kip-ft 1550 Mp /Ωb φb Mp , kip-ft 194 Mr /Ωb φb Mr , kip-ft 123 BF /Ωb φb BF, kips 3.65 Vn /Ωv φvVn , kips 83.5 Zx , in.3 Lp , ft Lr , ft

ASD

2340 292 185 5.50 125

77.9 8.76 28.2

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

1440 179 112 3.97 90.3

2160 270 169 5.98 135

71.9 6.92 23.8

1280 160 101 3.80 81.1

1930 241 151 5.80 122

64.2 6.89 22.4

1140 142 89.9 3.66 70.2

1710 214 135 5.54 105

57.0 6.85 21.1

51.2 5.44 16.6

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

43.1 5.37 15.6

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8:51 AM

Page 74

3–74

DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W12

W12×

Shape

26 ASD LRFD

Design 3 4 5 6 7 8 9 10

Span, ft

Fy = 50 ksi

112 106 92.8 82.5 74.3

168 159 140 124 112

22 ASD LRFD

19 ASD LRFD

128 117

115 172 98.6 148

192 176

W10× 16 ASD LRFD 106 158 100 151 80.2 121

14v ASD LRFD

112 ASD LRFD

85.5 129 69.5 104

97.5 147 83.5 126 73.1 110 65.0 97.7 58.5 87.9

82.2 124 70.4 106 61.6 92.6 54.8 82.3 49.3 74.1

66.9 101 57.3 86.1 50.1 75.4 44.6 67.0 40.1 60.3

57.9 49.6 43.4 38.6 34.7

87.0 74.6 65.3 58.0 52.2

344 326 293

516 490 441

11 12 13 14 15

67.5 101 61.9 93.0 57.1 85.8 53.0 79.7 49.5 74.4

53.2 48.7 45.0 41.8 39.0

79.9 73.3 67.6 62.8 58.6

44.8 41.1 37.9 35.2 32.9

67.4 61.8 57.0 52.9 49.4

36.5 33.4 30.9 28.7 26.7

54.8 50.3 46.4 43.1 40.2

31.6 28.9 26.7 24.8 23.2

47.5 43.5 40.2 37.3 34.8

267 245 226 210 196

401 368 339 315 294

16 17 18 19 20

46.4 43.7 41.3 39.1 37.1

69.8 65.6 62.0 58.7 55.8

36.6 34.4 32.5 30.8 29.2

54.9 51.7 48.8 46.3 44.0

30.8 29.0 27.4 25.9 24.7

46.3 43.6 41.2 39.0 37.1

25.1 23.6 22.3 21.1 20.1

37.7 35.5 33.5 31.7 30.2

21.7 20.4 19.3 18.3 17.4

32.6 30.7 29.0 27.5 26.1

183 173 163 154 147

276 259 245 232 221

21 22 23 24 25

35.4 33.8 32.3 30.9 29.7

53.1 50.7 48.5 46.5 44.6

27.8 26.6 25.4 24.4 23.4

41.9 40.0 38.2 36.6 35.2

23.5 22.4 21.4 20.5 19.7

35.3 33.7 32.2 30.9 29.6

19.1 18.2 17.4 16.7 16.0

28.7 27.4 26.2 25.1 24.1

16.5 15.8 15.1 14.5 13.9

24.9 23.7 22.7 21.8 20.9

140 133 128 122 117

210 200 192 184 176

26 27 28 29 30

28.6 27.5 26.5 25.6 24.8

42.9 41.3 39.9 38.5 37.2

22.5 21.7 20.9 20.2 19.5

33.8 32.6 31.4 30.3 29.3

19.0 18.3 17.6 17.0 16.4

28.5 27.4 26.5 25.6 24.7

15.4 14.9 14.3 13.8 13.4

23.2 22.3 21.5 20.8 20.1

13.4 12.9 12.4 12.0

20.1 19.3 18.6 18.0

113 109 105

170 163 158

743 92.8 58.3 3.61 56.1

1120 140 87.7 5.46 84.2

585 73.1 44.4 4.68 64.0

879 110 66.7 7.06 95.9

401 50.1 29.9 3.80 52.8

603 75.4 44.9 5.73 79.2

347 43.4 26.0 3.43 42.8

522 65.3 39.1 5.17 64.3

2930 367 220 2.69 172

4410 551 331 4.03 258

Beam Properties Wc /Ωb φbWc , kip-ft Mp /Ωb φb Mp , kip-ft Mr /Ωb φb Mr , kip-ft BF /Ωb φb BF, kips Vn /Ωv φvVn , kips Zx , in.3 Lp , ft Lr , ft

ASD

37.2 5.33 14.9

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

v

29.3 3.00 9.13

493 61.6 37.2 4.27 57.3

741 92.6 55.9 6.43 86.0

24.7 2.90 8.61

20.1 2.73 8.05

17.4 2.66 7.73

147 9.47 64.1

Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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8:51 AM

Page 75

MAXIMUM TOTAL UNIFORM LOAD TABLES

3–75

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape

W10×

8 9 10

88 77 68 60 54 100 ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 302 453 261 392 225 337 196 293 171 257 149 224 288 433 251 377 216 325 189 284 165 249 148 222 259 390 226 339 195 293 170 256 149 224 133 200

11 12 13 14 15

236 216 200 185 173

355 325 300 279 260

205 188 173 161 150

308 283 261 242 226

177 162 150 139 130

266 244 225 209 195

155 142 131 122 114

233 213 197 183 171

135 124 115 106 99.3

203 187 172 160 149

121 111 102 95.0 88.6

16 17 18 19 20

162 153 144 137 130

244 229 217 205 195

141 133 125 119 113

212 199 188 178 170

122 115 108 103 97.4

183 172 163 154 146

106 100 94.6 89.6 85.1

160 151 142 135 128

93.1 87.6 82.7 78.4 74.5

140 132 124 118 112

83.1 78.2 73.9 70.0 66.5

125 118 111 105 99.9

21 22 23 24 25

124 118 113 108 104

186 177 170 163 156

107 103 98.1 94.0 90.2

161 154 147 141 136

92.8 88.6 84.7 81.2 77.9

139 133 127 122 117

81.1 77.4 74.0 70.9 68.1

122 116 111 107 102

70.9 107 67.7 102 64.7 97.3 62.0 93.3 59.6 89.5

63.3 60.4 57.8 55.4 53.2

95.1 90.8 86.9 83.3 79.9

150 144

86.7 83.5

130 126

74.9

113

65.5

Design

Span, ft

W10

26 27

99.8 96.1

182 167 154 143 133

98.4

Beam Properties Wc /Ωb φbWc , kip-ft 2590 3900 2260 3390 1950 2930 1700 2560 1490 2240 1330 2000 Mp /Ωb φb Mp , kip-ft 324 488 282 424 244 366 213 320 186 280 166 250 Mr /Ωb φb Mr , kip-ft 196 294 172 259 150 225 132 199 116 175 105 158 BF /Ωb φb BF, kips 2.64 4.00 2.62 3.94 2.60 3.90 2.58 3.85 2.54 3.82 2.48 3.75 Vn /Ωv φvVn , kips 151 226 131 196 112 169 97.8 147 85.7 129 74.7 112 Zx , in.3 Lp , ft Lr , ft

ASD

130 9.36 57.9

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

113 9.29 51.2

97.6 9.18 45.3

85.3 9.15 40.6

74.6 9.08 36.6

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

66.6 9.04 33.6

AISC_Part 3B:14th Ed.

2/24/11

8:51 AM

Page 76

3–76

DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips W-Shapes

W10 Shape

49 ASD LRFD

Design

45 ASD LRFD

W10× 39 33 ASD LRFD ASD LRFD

141 137 122 110

212 206 183 165

125 117 104 93.4

150 137 127 118 110

84.9 77.8 71.9 66.7 62.3

128 117 108 100 93.6

5

Span, ft

Fy = 50 ksi

6 7 8 9 10

136 134 121

204 201 181

11 12 13 14 15

110 100 92.7 86.1 80.4

165 151 139 129 121

99.6 91.3 84.3 78.3 73.1

187 176 156 140

113 111 96.8 86.1 77.4

169 166 146 129 116

30 26 ASD LRFD ASD LRFD 126 189 107 161 122 104 91.3 81.2 73.1

183 157 137 122 110

104 89.3 78.1 69.4 62.5

157 134 117 104 93.9

70.4 106 64.5 97.0 59.6 89.5 55.3 83.1 51.6 77.6

66.4 60.9 56.2 52.2 48.7

99.8 91.5 84.5 78.4 73.2

56.8 52.1 48.1 44.6 41.7

85.4 78.3 72.2 67.1 62.6

16 17 18 19 20

75.3 113 70.9 107 67.0 101 63.5 95.4 60.3 90.6

68.5 103 64.5 96.9 60.9 91.5 57.7 86.7 54.8 82.4

58.4 54.9 51.9 49.2 46.7

87.8 82.6 78.0 73.9 70.2

48.4 45.6 43.0 40.8 38.7

72.8 68.5 64.7 61.3 58.2

45.7 43.0 40.6 38.4 36.5

68.6 64.6 61.0 57.8 54.9

39.0 36.8 34.7 32.9 31.2

58.7 55.2 52.2 49.4 47.0

21 22 23 24 25

57.4 54.8 52.4 50.2 48.2

52.2 49.8 47.6 45.7 43.8

44.5 42.5 40.6 38.9

66.9 63.8 61.0 58.5

36.9 35.2 33.7 32.3

55.4 52.9 50.6 48.5

34.8 33.2 31.8 30.4 29.2

52.3 49.9 47.7 45.8 43.9

29.8 28.4 27.2 26.0 25.0

44.7 42.7 40.8 39.1 37.6

28.1

42.2

86.3 82.4 78.8 75.5 72.5

78.4 74.9 71.6 68.6 65.9

26

Beam Properties Wc /Ωb φbWc , kip-ft 1210 1810 1100 1650 Mp /Ωb φb Mp , kip-ft 151 227 137 206 Mr /Ωb φb Mr , kip-ft 95.4 143 85.8 129 BF /Ωb φb BF, kips 2.46 3.71 2.59 3.89 Vn /Ωv φvVn , kips 68.0 102 70.7 106 Zx , in.3 Lp , ft Lr , ft

ASD

60.4 8.97 31.6

LRFD

f

54.9 7.10 26.9

934 1400 774 1160 731 1100 117 176 96.8 146 91.3 137 73.5 111 61.1 91.9 56.6 85.1 2.53 3.78 2.39 3.62 3.08 4.61 62.5 93.7 56.4 84.7 63.0 94.5 46.8 6.99 24.2

38.8 6.85 21.8

Shape does not meet compact limit for flexure with Fy = 50 ksi.

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

36.6 4.84 16.1

625 939 78.1 117 48.7 73.2 2.91 4.34 53.6 80.3 31.3 4.80 14.9

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MAXIMUM TOTAL UNIFORM LOAD TABLES

3–77

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes W10×

Shape

22 ASD LRFD

Design

Span, ft

W10-W8 W8×

17 ASD LRFD 97.0 145 93.3 140 74.7 112

15 ASD LRFD 91.9 138 79.8 120 63.9 96.0

12f ASD LRFD 75.0 113 62.4 93.8 49.9 75.0

71.9 108 61.6 92.6 53.9 81.0 47.9 72.0 43.1 64.8

62.2 53.3 46.7 41.5 37.3

93.5 80.1 70.1 62.3 56.1

53.2 45.6 39.9 35.5 31.9

80.0 68.6 60.0 53.3 48.0

41.6 35.7 31.2 27.7 25.0

62.5 53.6 46.9 41.7 37.5

19 ASD LRFD

ASD

67 LRFD

3 4 5

97.9

147

6 7 8 9 10

86.5 74.1 64.9 57.7 51.9

130 111 97.5 86.7 78.0

11 12 13 14 15

47.2 43.2 39.9 37.1 34.6

70.9 65.0 60.0 55.7 52.0

39.2 35.9 33.2 30.8 28.7

58.9 54.0 49.8 46.3 43.2

33.9 31.1 28.7 26.7 24.9

51.0 46.8 43.2 40.1 37.4

29.0 26.6 24.6 22.8 21.3

43.6 40.0 36.9 34.3 32.0

22.7 20.8 19.2 17.8 16.6

34.1 127 31.3 117 28.9 108 26.8 99.9 25.0 93.3

191 175 162 150 140

16 17 18 19 20

32.4 30.5 28.8 27.3 25.9

48.8 45.9 43.3 41.1 39.0

26.9 25.4 24.0 22.7 21.6

40.5 38.1 36.0 34.1 32.4

23.3 22.0 20.7 19.6 18.7

35.1 33.0 31.2 29.5 28.1

20.0 18.8 17.7 16.8 16.0

30.0 28.2 26.7 25.3 24.0

15.6 14.7 13.9 13.1 12.5

23.5 22.1 20.8 19.7 18.8

87.5 82.3 77.7 73.6 70.0

131 124 117 111 105

21 22 23 24 25

24.7 23.6 22.6 21.6 20.8

37.1 35.5 33.9 32.5 31.2

20.5 19.6 18.7 18.0 17.2

30.9 29.5 28.2 27.0 25.9

17.8 17.0 16.2 15.6 14.9

26.7 25.5 24.4 23.4 22.4

15.2 14.5 13.9 13.3

22.9 21.8 20.9 20.0

11.9 11.3 10.9 10.4

17.9 17.1 16.3 15.6

66.6 100 63.6 95.6

102 153 86.2 130

205 200 175 155 140

308 300 263 234 210

Beam Properties Wc /Ωb φbWc , kip-ft 519 780 431 648 373 561 319 480 250 375 Mp /Ωb φb Mp , kip-ft 64.9 97.5 53.9 81.0 46.7 70.1 39.9 60.0 31.2 46.9 Mr /Ωb φb Mr , kip-ft 40.5 60.9 32.8 49.4 28.3 42.5 24.1 36.2 19.0 28.6 BF /Ωb φb BF, kips 2.68 4.02 3.18 4.76 2.98 4.47 2.75 4.14 2.36 3.53 Vn /Ωv φvVn , kips 49.0 73.4 51.0 76.5 48.5 72.7 46.0 68.9 37.5 56.3 Zx , in.3 Lp , ft Lr , ft

ASD

26.0 4.70 13.8

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

21.6 3.09 9.73

18.7 2.98 9.16

16.0 2.86 8.61

12.6 2.87 8.05

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1400 2100 175 263 105 159 1.75 2.59 103 154 70.1 7.49 47.6

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3–78

DESIGN OF FLEXURAL MEMBERS

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes

W8

W8×

Shape

58 ASD LRFD

Design

48 ASD LRFD

40 ASD LRFD

35 ASD LRFD

31f ASD LRFD

28 ASD LRFD 91.9 138

119 113 99.3 88.3 79.4

101 98.9 86.6 77.0 69.3

151.0 149 130 116 104

91.2 86.6 75.8 67.4 60.6

137 130 114 101 91.1

90.5 136 77.6 117 67.9 102 60.3 90.7 54.3 81.6

72.2 109 66.2 99.5 61.1 91.8 56.7 85.3 53.0 79.6

63.0 57.7 53.3 49.5 46.2

94.6 86.8 80.1 74.4 69.4

55.1 50.5 46.6 43.3 40.4

82.8 75.9 70.1 65.1 60.7

49.4 45.2 41.8 38.8 36.2

74.2 68.0 62.8 58.3 54.4

49.7 46.7 44.1 41.8 39.7

43.3 40.7 38.5 36.5 34.6

65.1 61.2 57.8 54.8 52.1

37.9 35.7 33.7 31.9 30.3

56.9 53.6 50.6 48.0 45.6

33.9 31.9 30.2 28.6 27.1

51.0 48.0 45.3 42.9 40.8

Span, ft

5 6 7 8 9 10

179 171 149 133 119

268 256 224 199 179

136 122 109 97.8

11 12 13 14 15

109 99.5 91.8 85.3 79.6

163 150 138 128 120

88.9 81.5 75.2 69.9 65.2

134 123 113 105 98.0

204 184 163 147

16 17 18 19 20

74.6 112 70.2 106 66.3 99.7 62.8 94.4 59.7 89.7

61.1 57.5 54.3 51.5 48.9

91.9 86.5 81.7 77.4 73.5

21

56.8

46.6

70.0

85.4

178 171 149 133 119

74.6 70.2 66.3 62.8 59.7

Beam Properties Wc /Ωb φbWc , kip-ft 1190 1790 Mp /Ωb φb Mp , kip-ft 149 224 Mr /Ωb φb Mr , kip-ft 90.8 137 BF /Ωb φb BF, kips 1.70 2.55 Vn /Ωv φvVn , kips 89.3 134 Zx , in.3 Lp , ft Lr , ft

ASD

59.8 7.42 41.6

LRFD

f

978 122 75.4 1.67 68.0

1470 794 1190 693 1040 606 911 543 816 184 99.3 149 86.6 130 75.8 114 67.9 102 113 62.0 93.2 54.5 81.9 48.0 72.2 42.4 63.8 2.55 1.64 2.46 1.62 2.43 1.58 2.37 1.67 2.50 102 59.4 89.1 50.3 75.5 45.6 68.4 45.9 68.9

49.0 7.35 35.2

39.8 7.21 29.9

34.7 7.17 27.0

Shape does not meet compact limit for flexure with Fy = 50 ksi.

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

30.4 7.18 24.8

27.2 5.72 21.0

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MAXIMUM TOTAL UNIFORM LOAD TABLES

3–79

Table 3-6 (continued)

Maximum Total Uniform Load, kips

Fy = 50 ksi

W-Shapes Shape

Span, ft

124 122

W8× 18 15 ASD LRFD ASD LRFD 79.5 119 74.9 112 67.9 102 67.9 102 54.3 81.6

13 ASD LRFD 73.5 110 56.9 85.5 45.5 68.4

10f ASD LRFD 53.7 80.5 43.7 65.7 35.0 52.6

67.9 58.2 50.9 45.2 40.7

102 87.4 76.5 68.0 61.2

56.6 48.5 42.4 37.7 33.9

85.0 72.9 63.8 56.7 51.0

45.2 38.8 33.9 30.2 27.1

68.0 58.3 51.0 45.3 40.8

37.9 32.5 28.4 25.3 22.8

57.0 48.9 42.8 38.0 34.2

29.2 25.0 21.9 19.4 17.5

43.8 37.6 32.9 29.2 26.3

63.0 57.8 53.3 49.5 46.2

37.0 33.9 31.3 29.1 27.1

55.6 51.0 47.1 43.7 40.8

30.8 28.3 26.1 24.2 22.6

46.4 42.5 39.2 36.4 34.0

24.7 22.6 20.9 19.4 18.1

37.1 34.0 31.4 29.1 27.2

20.7 19.0 17.5 16.3 15.2

31.1 28.5 26.3 24.4 22.8

15.9 14.6 13.5 12.5 11.7

23.9 21.9 20.2 18.8 17.5

43.3 40.8 38.5 36.5

25.4 24.0 22.6 21.4 20.4

38.3 36.0 34.0 32.2 30.6

21.2 20.0 18.9 17.9 17.0

31.9 30.0 28.3 26.8 25.5

17.0 16.0 15.1 14.3 13.6

25.5 24.0 22.7 21.5 20.4

14.2 13.4 12.6 12.0

21.4 20.1 19.0 18.0

10.9 10.3 9.72 9.21

16.4 15.5 14.6 13.8

24 ASD LRFD

21 ASD LRFD

3 4 5

77.7

117

82.8 81.4

6 7 8 9 10

76.8 65.9 57.6 51.2 46.1

115 99.0 86.6 77.0 69.3

11 12 13 14 15

41.9 38.4 35.5 32.9 30.7

16 17 18 19 20

28.8 27.1 25.6 24.3

Design

W8

Beam Properties Wc /Ωb φbWc , kip-ft 461 693 407 612 339 510 271 408 228 342 175 263 Mp /Ωb φb Mp , kip-ft 57.6 86.6 50.9 76.5 42.4 63.8 33.9 51.0 28.4 42.8 21.9 32.9 Mr /Ωb φb Mr , kip-ft 36.5 54.9 31.8 47.8 26.5 39.9 20.6 31.0 17.3 26.0 13.6 20.5 BF /Ωb φb BF, kips 1.60 2.40 1.85 2.77 1.74 2.61 1.90 2.85 1.76 2.67 1.54 2.30 Vn /Ωv φvVn , kips 38.9 58.3 41.4 62.1 37.4 56.2 39.7 59.6 36.8 55.1 26.8 40.2 Zx , in.3 Lp , ft Lr , ft

ASD

23.1 5.69 18.9

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

20.4 4.45 14.8

17.0 4.34 13.5

13.6 3.09 10.1

11.4 2.98 9.27

Note: For beams laterally unsupported, see Table 3-10. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.87 3.14 8.52

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Page 80

3–80

DESIGN OF FLEXURAL MEMBERS

Table 3-7

Maximum Total Uniform Load, kips S-Shapes

S24-S20 Shape Design

Span, ft

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60

Fy = 36 ksi

121 ASD LRFD 564 550 489 440 400 366 338 314 293 275 259 244 231 220 209 200 191 183 176 169 163 157 152 147 137 129 122 116 110 105 99.9 95.6 91.6 88.0 84.6 81.4 78.5 75.8 73.3

847 826 734 661 601 551 508 472 441 413 389 367 348 330 315 300 287 275 264 254 245 236 228 220 207 194 184 174 165 157 150 144 138 132 127 122 118 114 110

106 ASD LRFD

S24× 100 ASD LRFD

90 ASD LRFD

437 401 365 334 308 286 267 251 236 223 211 200 191 182 174 167 160 154 149 143 138 134 125 118 111 106 100 95.5 91.1 87.2 83.5 80.2 77.1 74.3 71.6 69.1 66.8

515 491 429 382 343 312 286 264 245 229 215 202 191 181 172 164 156 149 143 137 132 127 123 118 114 107 101 95.4 90.4 85.9 81.8 78.1 74.7 71.6 68.7 66.1 63.6 61.3 59.2 57.2

432 399 354 319 290 266 245 228 213 199 188 177 168 160 152 145 139 133 128 123 118 114 110 106 99.7 93.8 88.6 84.0 79.8 76.0 72.5 69.4 66.5 63.8 61.4 59.1 57.0 55.0 53.2

656 603 548 502 464 430 402 377 354 335 317 301 287 274 262 251 241 232 223 215 208 201 188 177 167 159 151 143 137 131 126 121 116 112 108 104 100

772 737 645 574 516 469 430 397 369 344 323 304 287 272 258 246 235 224 215 206 199 191 184 178 172 161 152 143 136 129 123 117 112 108 103 99.3 95.6 92.2 89.0 86.0

S20×

648 599 533 480 436 400 369 343 320 300 282 266 252 240 228 218 208 200 192 184 178 171 165 160 150 141 133 126 120 114 109 104 99.9 95.9 92.2 88.8 85.6 82.7 79.9

80 ASD LRFD 346 326 293 267 244 226 209 195 183 172 163 154 147 140 133 127 122 117 113 109 105 101 97.7 91.6 86.2 81.4 77.2 73.3 69.8 66.6 63.7 61.1 58.6 56.4 54.3 52.4 50.5 48.9

518 490 441 401 367 339 315 294 275 259 245 232 220 210 200 192 184 176 169 163 157 152 147 138 130 122 116 110 105 100 95.8 91.8 88.1 84.7 81.6 78.7 76.0 73.4

ASD

96 LRFD

468 407 356 316 285 259 237 219 203 190 178 167 158 150 142 136 129 124 119 114 109 105 102 98.1 94.9 88.9 83.7 79.0 74.9 71.1 67.8 64.7 61.9 59.3 56.9

702 611 535 475 428 389 356 329 305 285 267 252 238 225 214 204 194 186 178 171 164 158 153 147 143 134 126 119 113 107 102 97.2 93.0 89.1 85.5

2850 356 207 7.63 234

4280 535 312 11.5 351

Beam Properties Wc /Ωb φbWc , kip-ft 4400 6610 4010 6030 3430 5160 3190 4800 2930 4410 Mp /Ωb φb Mp , kip-ft 550 826 501 753 429 645 399 599 366 551 Mr /Ωb φb Mr , kip-ft 324 488 302 454 250 376 235 353 220 331 BF /Ωb φb BF, kips 11.4 17.1 11.0 16.5 11.6 17.5 11.4 17.1 10.8 16.2 Vn /Ωv φvVn , kips 282 423 219 328 257 386 216 324 173 259 Zx , in.3 Lp , ft Lr , ft

ASD

306 6.37 26.2

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

279 6.54 24.7

239 5.29 20.7

222 5.41 19.8

204 5.58 19.2

Note: Beams must be laterally supported if Table 3-7 is used. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

198 5.54 24.9

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Page 81

MAXIMUM TOTAL UNIFORM LOAD TABLES

3–81

Table 3-7 (continued)

Maximum Total Uniform Load, kips

Fy = 36 ksi

S-Shapes Shape Design

Span, ft

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 46 48 50

86 ASD LRFD

S20× 75 ASD LRFD

66 ASD LRFD

386 376 329 292 263 239 219 202 188 175 164 155 146 138 131 125 120 114 110 105 101 97.4 93.9 90.7 87.7 82.2 77.4 73.1 69.2 65.7 62.6 59.8 57.2 54.8 52.6

579 565 494 439 395 359 329 304 282 264 247 233 220 208 198 188 180 172 165 158 152 146 141 136 132 124 116 110 104 98.8 94.1 89.8 85.9 82.4 79.1

366 364 312 273 243 218 199 182 168 156 146 137 128 121 115 109 104 99.3 95.0 91.0 87.4 84.0 80.9 78.0 75.3 72.8 68.3 64.2 60.7 57.5 54.6 52.0 49.6 47.5 45.5 43.7

549 547 469 410 365 328 298 274 253 235 219 205 193 182 173 164 156 149 143 137 131 126 122 117 113 109 103 96.6 91.2 86.4 82.1 78.2 74.6 71.4 68.4 65.7

291 285 250 222 200 182 166 154 143 133 125 118 111 105 99.9 95.1 90.8 86.9 83.2 79.9 76.8 74.0 71.3 68.9 66.6 62.4 58.8 55.5 52.6 49.9 47.6 45.4 43.4 41.6 40.0

3950 494 293 11.3 289

2180 273 161 7.74 183

3280 410 242 11.6 274

S20-S15 S18×

436 429 375 334 300 273 250 231 214 200 188 177 167 158 150 143 136 131 125 120 115 111 107 104 100 93.8 88.3 83.4 79.0 75.1 71.5 68.2 65.3 62.6 60.0

70 ASD LRFD 369 553 356 536 297 446 255 383 223 335 198 298 178 268 162 243 149 223 137 206 127 191 119 179 111 167 105 158 99.0 149 93.8 141 89.1 134 84.9 128 81.0 122 77.5 116 74.3 112 71.3 107 68.5 103 66.0 99.2 63.6 95.7 61.4 92.4 59.4 89.3 55.7 83.7 52.4 78.8 49.5 74.4 46.9 70.5 44.6 67.0 42.4 63.8 40.5 60.9

S15×

54.7 ASD LRFD

239 214 187 166 149 136 125 115 107 99.6 93.4 87.9 83.0 78.7 74.7 71.2 67.9 65.0 62.3 59.8 57.5 55.4 53.4 51.5 49.8 46.7 44.0 41.5 39.3 37.4 35.6 34.0

358 321 281 250 225 204 187 173 160 150 140 132 125 118 112 107 102 97.7 93.6 89.9 86.4 83.2 80.2 77.5 74.9 70.2 66.1 62.4 59.1 56.2 53.5 51.1

50 ASD LRFD 238 356 221 333 184 277 158 238 138 208 123 185 111 166 101 151 92.2 139 85.1 128 79.0 119 73.8 111 69.2 104 65.1 97.8 61.5 92.4 58.2 87.5 55.3 83.2 52.7 79.2 50.3 75.6 48.1 72.3 46.1 69.3 44.3 66.5 42.6 64.0 41.0 61.6 39.5 59.4 38.2 57.4 36.9 34.6 52.0 32.5 48.9 30.7 46.2

Beam Properties Wc /Ωb φbWc , kip-ft 2630 Mp /Ωb φb Mp , kip-ft 329 Mr /Ωb φb Mr , kip-ft 195 BF /Ωb φb BF, kips 7.53 Vn /Ωv φvVn , kips 193 Zx , in.3 Lp , ft Lr , ft

ASD

183 5.66 23.4

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

152 4.83 19.3

2000 250 150 7.49 145

3000 375 225 11.3 218

139 4.95 18.3

1780 2680 1490 2250 1110 1660 223 335 187 281 138 208 130 195 112 168 81.4 122 6.12 9.19 5.98 8.99 4.07 6.12 184 276 119 179 119 178 124 4.50 19.7

104 4.75 17.3

Note: Beams must be laterally supported if Table 3-7 is used. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

77.0 4.29 18.3

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3–82

DESIGN OF FLEXURAL MEMBERS

Table 3-7 (continued)

Maximum Total Uniform Load, kips S-Shapes

S15-S10 Shape Design

Span, ft

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36

Fy = 36 ksi

S15× 42.9 ASD LRFD

178 166 142 124 110 99.4 90.4 82.9 76.5 71.0 66.3 62.2 58.5 55.2 52.3 49.7 47.4 45.2 43.2 41.4 39.8 38.2 36.8 35.5 34.3 33.1 31.1 29.2 27.6

266 249 214 187 166 149 136 125 115 107 99.6 93.4 87.9 83.0 78.7 74.7 71.2 67.9 65.0 62.3 59.8 57.5 55.4 53.4 51.5 49.8 46.7 44.0 41.5

50 ASD LRFD

S12× 40.8 35 ASD LRFD ASD LRFD

237 219 175 146 125 109 97.2 87.5 79.6 72.9 67.3 62.5 58.3 54.7 51.5 48.6 46.1 43.8 41.7 39.8 38.1 36.5 35.0 33.7 32.4 31.3 30.2 29.2

160 151 126 108 94.7 84.2 75.7 68.9 63.1 58.3 54.1 50.5 47.3 44.6 42.1 39.9 37.9 36.1 34.4 32.9 31.6 30.3 29.1 28.1 27.0 26.1 25.2

356 329 263 219 188 164 146 132 120 110 101 94.0 87.7 82.2 77.4 73.1 69.2 65.8 62.6 59.8 57.2 54.8 52.6 50.6 48.7 47.0 45.4 43.8

240 148 228 128 190 107 163 91.6 142 80.1 126 71.2 114 64.1 103 58.3 94.9 53.4 87.6 49.3 81.3 45.8 75.9 42.7 71.1 40.1 67.0 37.7 63.2 35.6 59.9 33.7 56.9 32.0 54.2 30.5 51.7 29.1 49.5 27.9 47.4 26.7 45.5 25.6 43.8 24.7 42.2 23.7 40.7 22.9 39.3 22.1 37.9 21.4

S10× 31.8 ASD LRFD

222 121 193 120 161 100 138 85.8 120 75.1 107 66.7 96.3 60.1 87.6 54.6 80.3 50.1 74.1 46.2 68.8 42.9 64.2 40.0 60.2 37.5 56.7 35.3 53.5 33.4 50.7 31.6 48.2 30.0 45.9 28.6 43.8 27.3 41.9 26.1 40.1 25.0 38.5 24.0 37.1 23.1 35.7 22.2 34.4 21.5 33.2 20.7 32.1 20.0

181 150 129 113 100 90.3 82.1 75.2 69.5 64.5 60.2 56.4 53.1 50.2 47.5 45.1 43.0 41.0 39.3 37.6 36.1 34.7 33.4 32.2 31.1 30.1

35 ASD LRFD 171 257 170 255 127 191 102 153 84.8 127 72.7 109 63.6 95.6 56.5 85.0 50.9 76.5 46.2 69.5 42.4 63.7 39.1 58.8 36.3 54.6 33.9 51.0 31.8 47.8 29.9 45.0 28.3 42.5 26.8 40.2 25.4 38.2 24.2 36.4 23.1 34.8 22.1 33.2 21.2 31.9 20.3 30.6

Beam Properties Wc /Ωb φbWc , kip-ft 994 Mp /Ωb φb Mp , kip-ft 124 Mr /Ωb φb Mr , kip-ft 74.7 BF /Ωb φb BF, kips 4.01 Vn /Ωv φvVn , kips 88.8 Zx , in.3 Lp , ft Lr , ft

ASD

1490 875 1320 757 1140 641 963 601 903 509 765 187 109 164 94.7 142 80.1 120 75.1 113 63.6 95.6 112 63.6 95.6 56.7 85.2 47.9 72.0 45.5 68.4 37.0 55.6 6.03 2.22 3.33 2.31 3.48 2.45 3.69 2.43 3.66 1.51 2.26 133 119 178 79.8 120 74.0 111 60.5 90.7 85.5 128

69.2 4.41 16.8

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

60.9 4.29 24.9

52.7 4.41 20.8

44.6 4.08 17.2

41.8 4.16 16.3

Note: Beams must be laterally supported if Table 3-7 is used. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

35.4 3.74 21.4

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MAXIMUM TOTAL UNIFORM LOAD TABLES

3–83

Table 3-7 (continued)

Maximum Total Uniform Load, kips

Fy = 36 ksi

S-Shapes S10×

Shape

25.4 ASD LRFD

Span, ft

Design

S8× 23 18.4 ASD LRFD ASD LRFD 102 152 92.0 138 62.4 93.7 69.0 104 59.3 89.1 55.2 82.9 47.4 71.3

S10-S5 S6×

S5×

17.25 ASD LRFD 75.4 113 50.3 75.6 37.7 56.7 30.2 45.4

12.5 ASD LRFD 40.1 30.4 24.3

60.1 45.6 36.5

ASD 30.8 27.1 20.3 16.3

10 LRFD 46.2 40.8 30.6 24.5

2 3 4 5

89.6 81.3

134 122

6 7 8 9 10

67.8 58.1 50.8 45.2 40.7

102 87.3 76.4 67.9 61.1

46.0 39.4 34.5 30.7 27.6

69.1 59.2 51.8 46.1 41.5

39.5 33.9 29.6 26.3 23.7

59.4 50.9 44.6 39.6 35.6

25.1 21.6 18.9 16.8 15.1

37.8 32.4 28.4 25.2 22.7

20.2 17.3 15.2 13.5 12.1

30.4 26.1 22.8 20.3 18.3

13.6 11.6 10.2 9.04 8.13

20.4 17.5 15.3 13.6 12.2

11 12 13 14 15

37.0 33.9 31.3 29.1 27.1

55.6 50.9 47.0 43.7 40.8

25.1 23.0 21.2 19.7 18.4

37.7 34.6 31.9 29.6 27.6

21.6 19.8 18.2 16.9 15.8

32.4 29.7 27.4 25.5 23.8

13.7 12.6 11.6 10.8 10.1

20.6 18.9 17.4 16.2 15.1

11.0 10.1 9.34 8.67 8.10

16.6 15.2 14.0 13.0 12.2

7.39 6.78

11.1 10.2

16 17 18 19 20

25.4 23.9 22.6 21.4 20.3

38.2 36.0 34.0 32.2 30.6

17.2 16.2 15.3 14.5 13.8

25.9 24.4 23.0 21.8 20.7

14.8 13.9 13.2 12.5 11.9

22.3 21.0 19.8 18.8 17.8

21 22 23 24 25

19.4 18.5 17.7 16.9 16.3

29.1 27.8 26.6 25.5 24.5

276 34.5 20.4 0.948 50.8

415 51.8 30.6 1.42 76.2

Beam Properties Wc /Ωb φbWc , kip-ft 407 611 Mp /Ωb φb Mp , kip-ft 50.8 76.4 Mr /Ωb φb Mr , kip-ft 30.9 46.5 BF /Ωb φb BF, kips 1.58 2.38 Vn /Ωv φvVn , kips 44.8 67.2 Zx , in.3 Lp , ft Lr , ft

ASD

28.3 3.95 16.5

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.50 φ v = 1.00

19.2 3.31 18.2

237 29.6 18.1 0.974 31.2

356 44.6 27.2 1.46 46.8

16.5 3.44 15.3

151 227 121 183 81.3 122 18.9 28.4 15.2 22.8 10.2 15.3 11.0 16.5 9.23 13.9 6.16 9.26 0.460 0.691 0.516 0.775 0.341 0.512 40.2 60.3 20.0 30.1 15.4 23.1 10.5 2.80 19.9

8.45 2.92 14.5

Note: Beams must be laterally supported if Table 3-7 is used. Available strength tabulated above heavy line is limited by available shear strength.

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DESIGN OF FLEXURAL MEMBERS

Table 3-7 (continued)

Maximum Total Uniform Load, kips

Fy = 36 ksi

S-Shapes

S4-S3

S4×

Shape

S3× 7.7

9.5

Design 2 3 4 5

5.7

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

29.0 19.4 14.5 11.6

43.6 29.1 21.8 17.5

22.2 16.8 12.6 10.1

33.4 25.2 18.9 15.1

16.9 11.3 8.44 6.75

25.4 16.9 12.7 10.2

13.9 9.29 6.97 5.58

21.0 14.0 10.5 8.38

12.6 10.8 9.45 8.40 7.56

5.63 4.82

8.46 7.25

4.65 3.98

6.98 5.99

33.8 4.22 2.44 0.0899 15.1

50.8 6.35 3.67 0.135 22.6

27.9 3.49 2.10 0.102 7.34

41.9 5.24 3.16 0.154 11.0

9.68 8.29 7.26 6.45 5.81

14.5 12.5 10.9 9.70 8.73

58.1 7.26 4.25 0.190 18.8

87.3 10.9 6.39 0.285 28.2

8.38 7.19 6.29 5.59 5.03

Span, ft

6 7 8 9 10

7.5

Beam Properties φbWc , kip-ft φb Mp , kip-ft φb Mr , kip-ft φb BF, kips φvVn , kips

Wc /Ωb Mp /Ωb Mr /Ωb BF /Ωb Vn /Ωv

Zx , in.3 Lp , ft Lr , ft

4.04 2.35 18.2

ASD

LRFD

Ωb = 1.67 Ωv = 1.50

φ b = 0.90 φ v = 1.00

50.3 6.29 3.81 0.202 11.1

75.6 9.45 5.73 0.304 16.7 3.50 2.40 14.6

2.35 2.14 22.0

Note: Beams must be laterally supported if Table 3-7 is used. Available strength tabulated above heavy line is limited by available shear strength.

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MAXIMUM TOTAL UNIFORM LOAD TABLES

3–85

Table 3-8

Maximum Total Uniform Load, kips

Fy = 36 ksi

C-Shapes Shape Design

Span, ft

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

50 ASD LRFD 278 418 246 370 197 296 164 247 141 211 123 185 109 164 98.4 148 89.5 135 82.0 123 75.7 114 70.3 106 65.6 98.6 61.5 92.5 57.9 87.0 54.7 82.2 51.8 77.9 49.2 74.0 46.9 70.5 44.7 67.3 42.8 64.3 41.0 61.7 39.4 59.2 37.9 56.9 36.5 54.8 35.2 52.8 33.9 51.0 32.8 49.3 31.8 47.7 30.8 46.2 29.8 44.8 29.0 43.5 28.1 42.3 27.3 41.1 26.6 40.0

C15× 40 ASD LRFD

33.9 ASD LRFD

202 165 138 118 103 91.8 82.6 75.1 68.9 63.6 59.0 55.1 51.6 48.6 45.9 43.5 41.3 39.3 37.6 35.9 34.4 33.1 31.8 30.6 29.5 28.5 27.5 26.7 25.8 25.0 24.3 23.6 23.0 22.3

155 146 122 104 91.3 81.1 73.0 66.4 60.8 56.2 52.1 48.7 45.6 42.9 40.6 38.4 36.5 34.8 33.2 31.7 30.4 29.2 28.1 27.0 26.1 25.2 24.3 23.6 22.8 22.1 21.5 20.9 20.3 19.7

303 248 207 177 155 138 124 113 104 95.5 88.7 82.8 77.6 73.1 69.0 65.4 62.1 59.1 56.5 54.0 51.8 49.7 47.8 46.0 44.4 42.8 41.4 40.1 38.8 37.6 36.5 35.5 34.5 33.6

C15-C12 C12×

233 219 183 157 137 122 110 99.8 91.4 84.4 78.4 73.2 68.6 64.5 61.0 57.8 54.9 52.3 49.9 47.7 45.7 43.9 42.2 40.6 39.2 37.8 36.6 35.4 34.3 33.3 32.3 31.4 30.5 29.7

30 25 ASD LRFD ASD LRFD 158 238 120 181 121 183 106 159 97.1 146 84.5 127 81.0 122 70.4 106 69.4 104 60.4 90.7 60.7 91.3 52.8 79.4 54.0 81.1 46.9 70.6 48.6 73.0 42.3 63.5 44.2 66.4 38.4 57.7 40.5 60.8 35.2 52.9 37.4 56.2 32.5 48.8 34.7 52.1 30.2 45.4 32.4 48.7 28.2 42.3 30.4 45.6 26.4 39.7 28.6 42.9 24.9 37.4 27.0 40.6 23.5 35.3 25.6 38.4 22.2 33.4 24.3 36.5 21.1 31.8 23.1 34.8 20.1 30.2 22.1 33.2 19.2 28.9 21.1 31.7 18.4 27.6 20.2 30.4 17.6 26.5 19.4 29.2 16.9 25.4 18.7 28.1 16.3 24.4 18.0 27.0 15.6 23.5 17.3 26.1 15.1 22.7 16.7 25.2 14.6 21.9 16.2 24.3 14.1 21.2

20.7 ASD LRFD 87.5 132 73.6 111 61.3 92.2 52.6 79.0 46.0 69.1 40.9 61.4 36.8 55.3 33.4 50.3 30.7 46.1 28.3 42.5 26.3 39.5 24.5 36.9 23.0 34.6 21.6 32.5 20.4 30.7 19.4 29.1 18.4 27.6 17.5 26.3 16.7 25.1 16.0 24.0 15.3 23.0 14.7 22.1 14.2 21.3 13.6 20.5 13.1 19.7 12.7 19.1 12.3 18.4

Beam Properties Wc /Ωb φbWc , kip-ft 984 Mp /Ωb φb Mp , kip-ft 123 Mr /Ωb φb Mr , kip-ft 67.7 BF /Ωb φb BF, kips 3.46 Vn /Ωv φvVn , kips 139 Zx , in.3 Lp , ft Lr , ft

ASD

1480 185 102 5.19 209

68.5 3.60 19.6

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.67 φ v = 0.90

826 1240 103 155 58.5 87.9 3.58 5.40 101 152

730 1100 91.3 137 52.8 79.4 3.58 5.36 77.6 117

57.5 3.68 16.1

50.8 3.75 14.5

486 730 423 635 368 553 60.7 91.3 52.8 79.4 46.0 69.1 34.0 51.0 30.2 45.4 27.0 40.6 2.18 3.30 2.22 3.35 2.16 3.25 79.2 119 60.1 90.3 43.8 65.8 33.8 3.17 15.4

29.4 3.24 13.4

Note: For beams laterally unsupported, see Table 3-11. Available strength tabulated above heavy line is limited by available shear strength.

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DESIGN OF FLEXURAL MEMBERS

Table 3-8 (continued)

Maximum Total Uniform Load, kips C-Shapes

C10-C9

C10×

Shape

30

Design

C9× 20

25

15.3 ASD LRFD

20

93.3 85.9 68.7

ASD 104 81.0 60.7 48.6

LRFD 157 122 91.3 73.0

38.1 32.6 28.6 25.4 22.9

57.2 49.1 42.9 38.2 34.3

40.5 34.7 30.4 27.0 24.3

60.8 52.1 45.6 40.6 36.5

38.1 34.9 32.2 29.9 27.9

20.8 19.0 17.6 16.3 15.2

31.2 28.6 26.4 24.5 22.9

22.1 20.2 18.7 17.3 16.2

33.2 30.4 28.1 26.1 24.3

17.4 16.4 15.5 14.7 13.9

26.2 24.6 23.3 22.1 21.0

14.3 13.4 12.7 12.0 11.4

21.5 20.2 19.1 18.1 17.2

15.2 14.3 13.5 12.8 12.1

22.8 21.5 20.3 19.2 18.3

13.3 12.7 12.1 11.6 11.2

20.0 19.0 18.2 17.5 16.8

10.9 10.4 9.93 9.52 9.14

16.4 15.6 14.9 14.3 13.7

11.6 11.0

17.4 16.6

419 52.4 29.9 2.22 73.7

229 28.6 17.0 1.44 31.0

343 42.9 25.5 2.16 46.7

243 30.4 17.0 1.12 52.2

365 45.6 25.5 1.68 78.4

2 3 4 5

ASD 174 128 95.9 76.7

LRFD 262 192 144 115

ASD 136 111 83.0 66.4

LRFD 205 166 125 99.8

ASD 98.0 92.9 69.7 55.8

LRFD 147 140 105 83.8

62.1 57.1 45.7

6 7 8 9 10

64.0 54.8 48.0 42.6 38.4

96.1 82.4 72.1 64.1 57.7

55.3 47.4 41.5 36.9 33.2

83.2 71.3 62.4 55.4 49.9

46.5 39.8 34.9 31.0 27.9

69.8 59.9 52.4 46.6 41.9

11 12 13 14 15

34.9 32.0 29.5 27.4 25.6

52.4 48.1 44.4 41.2 38.4

30.2 27.7 25.5 23.7 22.1

45.4 41.6 38.4 35.6 33.3

25.3 23.2 21.4 19.9 18.6

16 17 18 19 20

24.0 22.6 21.3 20.2 19.2

36.0 33.9 32.0 30.4 28.8

20.7 19.5 18.4 17.5 16.6

31.2 29.4 27.7 26.3 24.9

21 22 23 24 25

18.3 17.4 16.7 16.0 15.3

27.5 26.2 25.1 24.0 23.1

15.8 15.1 14.4 13.8 13.3

23.8 22.7 21.7 20.8 20.0

Wc /Ωb φbWc , kip-ft 384 Mp /Ωb φb Mp , kip-ft 48.0 Mr /Ωb φb Mr , kip-ft 26.0 BF /Ωb φb BF, kips 1.27 Vn /Ωv φvVn , kips 87.0

577 72.1 39.1 1.91 131

332 41.5 22.9 1.40 68.0

Span, ft

Fy = 36 ksi

Beam Properties

Zx , in.3 Lp , ft Lr , ft

ASD

26.7 2.78 20.1

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.67 φ v = 0.90

499 62.4 34.4 2.11 102

23.1 2.81 16.1

279 34.9 19.9 1.48 49.0

19.4 2.87 13.0

15.9 2.96 11.0

Note: For beams laterally unsupported, see Table 3-11. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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MAXIMUM TOTAL UNIFORM LOAD TABLES

3–87

Table 3-8 (continued)

Maximum Total Uniform Load, kips

Fy = 36 ksi

C-Shapes C9×

Shape

C8× 13.7 ASD LRFD 62.7 94.2 52.7 79.2 39.5 59.4 31.6 47.5

ASD

11.5 LRFD

45.5 34.6 27.7

68.4 52.0 41.6

2 3 4 5

ASD 66.4 65.1 48.9 39.1

LRFD 99.7 97.9 73.4 58.8

54.2 45.3 36.2

81.5 68.0 54.4

18.75 ASD LRFD 99.9 150 66.6 100 49.9 75.1 40.0 60.0

6 7 8 9 10

32.6 27.9 24.4 21.7 19.5

49.0 42.0 36.7 32.6 29.4

30.2 25.9 22.6 20.1 18.1

45.4 38.9 34.0 30.2 27.2

33.3 28.5 25.0 22.2 20.0

50.0 42.9 37.5 33.4 30.0

26.3 22.6 19.8 17.6 15.8

39.6 33.9 29.7 26.4 23.8

23.1 19.8 17.3 15.4 13.8

34.7 29.7 26.0 23.1 20.8

11 12 13 14 15

17.8 16.3 15.0 14.0 13.0

26.7 24.5 22.6 21.0 19.6

16.5 15.1 13.9 12.9 12.1

24.7 22.7 20.9 19.4 18.1

18.2 16.6 15.4 14.3 13.3

27.3 25.0 23.1 21.4 20.0

14.4 13.2 12.2 11.3 10.5

21.6 19.8 18.3 17.0 15.8

12.6 11.5 10.6 9.89 9.23

18.9 17.3 16.0 14.9 13.9

16 17 18 19 20

12.2 11.5 10.9 10.3 9.77

18.4 17.3 16.3 15.5 14.7

11.3 10.7 10.1 9.53 9.05

17.0 16.0 15.1 14.3 13.6

12.5 11.8 11.1 10.5 9.99

18.8 17.7 16.7 15.8 15.0

9.88 9.30 8.78 8.32 7.90

14.9 14.0 13.2 12.5 11.9

8.65 8.14 7.69 7.28 6.92

13.0 12.2 11.6 10.9 10.4

21 22

9.31 8.88

14.0 13.4

8.62 8.23

13.0 12.4

294 36.7 21.4 1.77 49.9

181 22.6 13.3 1.17 27.1

300 37.5 20.8 1.24 75.7

158 19.8 11.3 0.929 31.4

238 29.7 17.0 1.39 47.1

138 17.3 10.2 0.909 22.8

208 26.0 15.4 1.36 34.2

15

Design

Span, ft

C9-C8

13.4 ASD LRFD

Beam Properties Wc /Ωb φbWc , kip-ft 195 Mp /Ωb φb Mp , kip-ft 24.4 Mr /Ωb φb Mr , kip-ft 14.2 BF /Ωb φb BF, kips 1.18 Vn /Ωv φvVn , kips 33.2 Zx , in.3 Lp , ft Lr , ft

ASD

13.6 2.74 11.4

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.67 φ v = 0.90

272 34.0 20.0 1.77 40.8

12.6 2.77 10.7

200 25.0 13.8 0.829 50.4

13.9 2.49 16.0

11.0 2.55 11.7

Note: For beams laterally unsupported, see Table 3-11. Available strength tabulated above heavy line is limited by available shear strength.

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DESIGN OF FLEXURAL MEMBERS

Table 3-8 (continued)

Maximum Total Uniform Load, kips C-Shapes

C7-C6

C7×

Shape

C6× 9.8

13

10.5 LRFD 66.7 44.5 33.4 26.7

14.75 ASD LRFD 70.1 105 46.7 70.2 35.0 52.7 28.0 42.1

12.25 ASD LRFD 56.9 85.5 40.5 60.9 30.4 45.7 24.3 36.5

ASD 38.0 34.4 25.8 20.7

LRFD 57.2 51.8 38.8 31.1

ASD 52.4 34.9 26.2 21.0

LRFD 78.7 52.5 39.4 31.5

ASD 44.4 29.6 22.2 17.8

6 7 8 9 10

23.4 20.0 17.5 15.6 14.0

35.1 30.1 26.3 23.4 21.1

20.3 17.4 15.2 13.5 12.2

30.5 26.1 22.8 20.3 18.3

17.2 14.8 12.9 11.5 10.3

25.9 22.2 19.4 17.3 15.5

17.5 15.0 13.1 11.6 10.5

26.2 22.5 19.7 17.5 15.7

14.8 12.7 11.1 9.87 8.88

22.2 19.1 16.7 14.8 13.3

11 12 13 14 15

12.7 11.7 10.8 10.0 9.34

19.1 17.6 16.2 15.0 14.0

11.1 10.1 9.35 8.68 8.11

16.6 15.2 14.1 13.1 12.2

9.39 8.61 7.95 7.38 6.89

14.3 13.1 12.1 11.2 10.5

8.07 7.40 6.83 6.34 5.92

12.1 11.1 10.3 9.53 8.90

16 17

8.76 8.24

13.2 12.4

7.60 7.15

11.4 10.7

6.46 6.08

88.8 11.1 6.34 0.458 24.4

133 16.7 9.53 0.689 36.6

Design 2 3 4 5

Span, ft

Fy = 36 ksi

14.1 12.9 11.9 11.1 10.4

9.52 8.73 8.06 7.48 6.98

9.72 9.14

Beam Properties Wc /Ωb φbWc , kip-ft 140 211 122 183 103 Mp /Ωb φb Mp , kip-ft 17.5 26.3 15.2 22.8 12.9 Mr /Ωb φb Mr , kip-ft 9.78 14.7 8.70 13.1 7.63 BF /Ωb φb BF, kips 0.620 0.931 0.661 0.986 0.677 Vn /Ωv φvVn , kips 37.9 57.0 28.4 42.7 19.0 Zx , in.3 Lp , ft Lr , ft

ASD

9.75 2.34 14.8

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.67 φ v = 0.90

8.46 2.36 12.2

155 19.4 11.5 1.01 28.6

105 157 13.1 19.7 7.27 10.9 0.413 0.623 33.9 51.0

7.19 2.41 10.2

7.29 2.18 16.3

Note: For beams laterally unsupported, see Table 3-11. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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MAXIMUM TOTAL UNIFORM LOAD TABLES

3–89

Table 3-8 (continued)

Maximum Total Uniform Load, kips

Fy = 36 ksi

C-Shapes C6×

Shape Design 2 3 4 5 6 7 8 9 10

Span, ft

11 12 13 14 15

C6-C4

8.2 ASD LRFD 31.0 46.7 24.7 37.2 18.5 27.9 14.8 22.3

ASD 31.5 21.0 15.8 12.6

C4× 5.4 6.7 7.25 6.25 LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 47.4 24.6 36.9 20.4 30.7 17.5 26.2 16.5 24.7 31.6 17.0 25.6 13.6 20.4 11.6 17.5 11.0 16.5 23.7 12.8 19.2 10.2 15.3 8.73 13.1 8.23 12.4 19.0 10.2 15.3 8.16 12.3 6.98 10.5 6.58 9.89

12.4 10.6 9.27 8.24 7.42

10.5 9.01 7.89 7.01 6.31

15.8 13.5 11.9 10.5 9.48

5.74 5.26

8.62 7.90

18.6 15.9 13.9 12.4 11.1

6.74 10.1 6.18 9.29 5.70 8.57 5.30 7.96 4.94 7.43

C5×

9

8.50 12.8 7.29 11.0 6.38 9.59 5.67 8.52 5.10 7.67 4.64 4.25

6.80 10.2 5.83 8.76 5.10 7.67 4.53 6.82 4.08 6.13

5.82 4.99 4.37 3.88 3.49

8.75 7.50 6.56 5.83 5.25

5.49 4.70 4.11 3.66 3.29

8.24 7.07 6.18 5.50 4.95

6.97 6.39

Beam Properties Wc /Ωb φbWc , kip-ft 74.2 111 Mp /Ωb φb Mp , kip-ft 9.27 13.9 Mr /Ωb φb Mr , kip-ft 5.47 8.22 BF /Ωb φb BF, kips 0.477 0.713 Vn /Ωv φvVn , kips 15.5 23.3 Zx , in.3 Lp , ft Lr , ft

ASD

5.16 2.23 10.2

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.67 φ v = 0.90

63.1 94.8 51.0 76.7 40.8 61.3 34.9 52.5 32.9 49.5 7.89 11.9 6.38 9.59 5.10 7.67 4.37 6.56 4.11 6.18 4.48 6.73 3.76 5.65 2.88 4.33 2.51 3.78 2.41 3.63 0.287 0.435 0.313 0.471 0.165 0.249 0.178 0.266 0.186 0.279 21.0 31.6 12.3 18.5 16.6 25.0 12.8 19.2 9.52 14.3 4.39 2.02 13.9

3.55 2.04 10.4

2.84 1.86 15.3

2.43 1.84 12.3

Note: For beams laterally unsupported, see Table 3-11. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF FLEXURAL MEMBERS

Table 3-8 (continued)

Maximum Total Uniform Load, kips C-Shapes

C4-C3 C4×

Shape

C3×

4.5

Design

Fy = 36 ksi

5

6

4.1

3.5

LRFD 19.4 15.3 11.4 9.16

ASD 12.5 8.34 6.25 5.00

LRFD 18.8 12.5 9.40 7.52

ASD 10.9 7.28 5.46 4.37

LRFD 16.4 10.9 8.21 6.57

ASD 9.49 6.32 4.74 3.79

LRFD 14.3 9.50 7.13 5.70

ASD 8.91 5.94 4.46 3.56

LRFD 13.4 8.93 6.70 5.36

6 7 8 9 10

5.08 4.35 3.81 3.39 3.05

7.63 6.54 5.72 5.09 4.58

4.17 3.57

6.26 5.37

3.64 3.12

5.47 4.69

3.16 2.71

4.75 4.07

2.97 2.55

4.46 3.83

Wc /Ωb φbWc , kip-ft 30.5 Mp /Ωb φb Mp , kip-ft 3.81 Mr /Ωb φb Mr , kip-ft 2.30 BF /Ωb φb BF, kips 0.184 Vn /Ωv φvVn , kips 6.47

45.8 5.72 3.46 0.276 9.72

25.0 3.13 1.74 0.0760 13.8

32.8 4.10 2.32 0.130 15.0

19.0 2.37 1.38 0.0930 6.60

28.5 3.56 2.08 0.139 9.91

17.8 2.23 1.31 0.0962 5.12

26.8 3.35 1.97 0.144 7.70

Span, ft

2 3 4 5

ASD 12.9 10.2 7.62 6.09

Beam Properties

Zx , in.3 Lp , ft Lr , ft

ASD

2.12 1.90 10.1

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.67 φ v = 0.90

37.6 4.70 2.61 0.114 20.8

1.74 1.72 20.0

21.8 2.73 1.55 0.0861 10.0

1.52 1.69 15.4

1.32 1.66 12.3

Note: For beams laterally unsupported, see Table 3-11. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.24 1.64 11.2

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MAXIMUM TOTAL UNIFORM LOAD TABLES

3–91

Table 3-9

Maximum Total Uniform Load, kips

Fy = 36 ksi

MC-Shapes Shape Design

Span, ft

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44

58 ASD LRFD 326 274 229 196 171 152 137 125 114 105 97.9 91.4 85.7 80.6 76.2 72.2 68.6 65.3 62.3 59.6 57.1 54.8 52.7 50.8 49.0 47.3 45.7 42.8 40.3 38.1 36.1 34.3 32.6 31.2

490 412 343 294 258 229 206 187 172 159 147 137 129 121 114 108 103 98.1 93.7 89.6 85.9 82.4 79.3 76.3 73.6 71.1 68.7 64.4 60.6 57.2 54.2 51.5 49.1 46.8

MC18× 51.9 45.8 ASD LRFD ASD LRFD 279 251 209 179 157 139 125 114 105 96.5 89.6 83.6 78.4 73.8 69.7 66.0 62.7 59.7 57.0 54.5 52.3 50.2 48.3 46.5 44.8 43.3 41.8 39.2 36.9 34.9 33.0 31.4 29.9 28.5

420 377 314 269 236 210 189 171 157 145 135 126 118 111 105 99.2 94.3 89.8 85.7 82.0 78.6 75.4 72.5 69.8 67.3 65.0 62.9 58.9 55.5 52.4 49.6 47.1 44.9 42.9

233 228 190 163 142 126 114 103 94.9 87.6 81.3 75.9 71.1 67.0 63.2 59.9 56.9 54.2 51.7 49.5 47.4 45.5 43.8 42.2 40.7 39.2 37.9 35.6 33.5 31.6 30.0 28.5 27.1 25.9

350 342 285 244 214 190 171 156 143 132 122 114 107 101 95.0 90.0 85.5 81.5 77.8 74.4 71.3 68.4 65.8 63.4 61.1 59.0 57.0 53.5 50.3 47.5 45.0 42.8 40.7 38.9

MC18-MC13 MC13× 42.7 ASD LRFD

210 180 154 135 120 108 98.1 89.9 83.0 77.1 72.0 67.5 63.5 60.0 56.8 54.0 51.4 49.1 46.9 45.0 43.2 41.5 40.0 38.5 37.2 36.0 33.7 31.7 30.0 28.4 27.0 25.7 24.5

315 270 232 203 180 162 147 135 125 116 108 101 95.4 90.1 85.4 81.1 77.2 73.7 70.5 67.6 64.9 62.4 60.1 57.9 55.9 54.1 50.7 47.7 45.1 42.7 40.6 38.6 36.9

50 ASD LRFD 265 398 218 328 175 263 146 219 125 188 109 164 97.1 146 87.4 131 79.4 119 72.8 109 67.2 101 62.4 93.8 58.3 87.6 54.6 82.1 51.4 77.3 48.5 73.0 46.0 69.1 43.7 65.7 41.6 62.5 39.7 59.7 38.0 57.1 36.4 54.7 35.0 52.5 33.6 50.5 32.4 48.6 31.2 46.9 30.1 45.3 29.1 43.8 27.3 41.0

40 ASD LRFD 188 283 184 276 147 221 123 184 105 158 92.0 138 81.8 123 73.6 111 66.9 101 61.3 92.2 56.6 85.1 52.6 79.0 49.1 73.7 46.0 69.1 43.3 65.1 40.9 61.4 38.7 58.2 36.8 55.3 35.0 52.7 33.4 50.3 32.0 48.1 30.7 46.1 29.4 44.2 28.3 42.5 27.3 41.0 26.3 39.5 25.4 38.1 24.5 36.9 23.0 34.6

Beam Properties Wc /Ωb φbWc , kip-ft 1370 Mp /Ωb φb Mp , kip-ft 171 Mr /Ωb φb Mr , kip-ft 94.3 BF /Ωb φb BF, kips 5.16 Vn /Ωv φvVn , kips 163 Zx , in.3 Lp , ft Lr , ft

ASD

2060 1250 1890 1140 1710 1080 1620 874 1310 258 157 236 142 214 135 203 109 164 142 87.5 132 80.7 121 77.3 116 60.7 91.3 7.81 5.26 7.87 5.23 7.93 5.17 7.80 2.08 3.13 245 140 210 116 175 105 157 132 199

95.4 4.25 19.1

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.67 φ v = 0.90

87.3 4.29 17.5

79.2 4.37 16.1

75.1 4.45 15.6

60.8 4.41 27.6

Note: For beams laterally unsupported, see Table 3-11. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

736 1110 92.0 138 52.7 79.2 2.28 3.42 94.2 142 51.2 4.50 21.7

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3–92

DESIGN OF FLEXURAL MEMBERS

Table 3-9 (continued)

Maximum Total Uniform Load, kips MC-Shapes

MC13-MC12 MC13×

Shape

35 ASD LRFD

Design

Span, ft

3 4 5

Fy = 36 ksi

31.8 ASD LRFD

MC12× 50 45 40 35 ASD LRFD ASD LRFD ASD LRFD ASD LRFD 259 390 220 331 183 275 203 305 187 281 171 258 144 217 162 244 149 225 137 206 124 187

150 134

226 201

126 125

190 187

6 7 8 9 10

111 95.5 83.5 74.3 66.8

167 143 126 112 100

104 89.1 78.0 69.3 62.4

156 135 134 116 117 101 104 90.2 93.7 81.2

11 12 13 14 15

60.8 55.7 51.4 47.7 44.6

91.3 83.7 77.3 71.7 67.0

56.7 52.0 48.0 44.6 41.6

85.2 78.1 72.1 67.0 62.5

73.8 111 67.7 102 62.5 93.9 58.0 87.2 54.1 81.4

67.9 102 62.3 93.6 57.5 86.4 53.4 80.2 49.8 74.9

62.3 57.1 52.7 49.0 45.7

16 17 18 19 20

41.8 39.3 37.1 35.2 33.4

62.8 59.1 55.8 52.9 50.2

39.0 36.7 34.7 32.8 31.2

58.6 55.1 52.1 49.3 46.9

50.7 47.8 45.1 42.7 40.6

76.3 71.8 67.8 64.2 61.0

46.7 44.0 41.5 39.3 37.4

70.2 66.1 62.4 59.1 56.2

21 22 23 24 25

31.8 30.4 29.1 27.8 26.7

47.8 45.7 43.7 41.9 40.2

29.7 28.4 27.1 26.0 24.9

44.6 42.6 40.8 39.1 37.5

38.7 36.9 35.3 33.8 32.5

58.1 55.5 53.1 50.9 48.8

35.6 34.0 32.5 31.1 29.9

26 27 28 29 30

25.7 24.8 23.9 23.0 22.3

38.6 37.2 35.9 34.6 33.5

24.0 23.1 22.3 21.5 20.8

36.1 34.7 33.5 32.3 31.2

31.2 30.1 29.0 28.0 27.1

46.9 45.2 43.6 42.1 40.7

28.7 27.7 26.7 25.8 24.9

32

20.9

31.4

19.5

29.3

203 174 153 136 122

125 107 93.4 83.0 74.7

187 160 140 125 112

114 97.9 85.7 76.2 68.6

172 147 129 114 103

103 88.7 77.6 69.0 62.1

156 133 117 104 93.3

93.7 85.9 79.3 73.6 68.7

56.4 51.7 47.8 44.3 41.4

84.8 77.8 71.8 66.7 62.2

42.8 40.3 38.1 36.1 34.3

64.4 60.6 57.2 54.2 51.5

38.8 36.5 34.5 32.7 31.0

58.3 54.9 51.8 49.1 46.7

53.5 51.1 48.8 46.8 44.9

32.6 31.2 29.8 28.6 27.4

49.1 46.8 44.8 42.9 41.2

29.6 28.2 27.0 25.9 24.8

44.4 42.4 40.6 38.9 37.3

43.2 41.6 40.1 38.7 37.4

26.4 25.4 24.5 23.6 22.9

39.6 38.2 36.8 35.5 34.3

23.9 23.0 22.2 21.4 20.7

35.9 34.6 33.3 32.2 31.1

Beam Properties Wc /Ωb φbWc , kip-ft 668 1000 624 937 812 1220 Mp /Ωb φb Mp , kip-ft 83.5 126 78.0 117 101 153 Mr /Ωb φb Mr , kip-ft 48.8 73.3 46.1 69.4 56.5 84.9 BF /Ωb φb BF, kips 2.34 3.55 2.31 3.44 1.65 2.53 Vn /Ωv φvVn , kips 75.2 113 63.1 94.8 130 195 Zx , in.3 Lp , ft Lr , ft

ASD

46.5 4.54 19.4

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.67 φ v = 0.90

43.4 4.58 18.4

56.5 4.54 31.5

747 1120 686 1030 621 933 93.4 140 85.7 129 77.6 117 52.7 79.2 49.0 73.7 45.3 68.0 1.77 2.65 1.87 2.82 1.92 2.92 110 166 91.6 138 72.2 108 52.0 4.54 27.5

47.7 4.58 24.2

Note: For beams laterally unsupported, see Table 3-11. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

43.2 4.62 21.4

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MAXIMUM TOTAL UNIFORM LOAD TABLES

3–93

Table 3-9 (continued)

Maximum Total Uniform Load, kips

Fy = 36 ksi

MC-Shapes Shape

31 ASD LRFD

Design

Span, ft

2 3 4 5

115 114

173 172

MC12× 14.3 ASD LRFD 77.6 117 76.2 114 57.1 85.9 45.7 68.7

10.6 ASD LRFD 59.0 88.6 55.6 83.5 41.7 62.6 33.3 50.1

MC12-MC10 MC10× 41.1 33.6 28.5 ASD LRFD ASD LRFD ASD LRFD 206 309 188 283 149 224 110 165 141 212 121 182 108 162 113 170 96.9 146 86.2 130

6 7 8 9 10

95.1 143 81.5 123 71.3 107 63.4 95.3 57.1 85.8

38.1 32.6 28.6 25.4 22.9

57.2 49.1 42.9 38.2 34.3

27.8 23.8 20.8 18.5 16.7

41.8 35.8 31.3 27.8 25.1

94.1 141 80.7 121 70.6 106 62.8 94.3 56.5 84.9

80.7 121 69.2 104 60.5 91.0 53.8 80.9 48.4 72.8

71.9 108 61.6 92.6 53.9 81.0 47.9 72.0 43.1 64.8

11 12 13 14 15

51.9 47.5 43.9 40.8 38.0

78.0 71.5 66.0 61.3 57.2

20.8 19.0 17.6 16.3 15.2

31.2 28.6 26.4 24.5 22.9

15.2 13.9 12.8 11.9 11.1

22.8 20.9 19.3 17.9 16.7

51.3 47.1 43.4 40.3 37.7

77.2 70.7 65.3 60.6 56.6

44.0 40.4 37.3 34.6 32.3

66.2 60.7 56.0 52.0 48.5

39.2 35.9 33.2 30.8 28.7

58.9 54.0 49.8 46.3 43.2

16 17 18 19 20

35.7 33.6 31.7 30.0 28.5

53.6 50.4 47.6 45.1 42.9

14.3 13.4 12.7 12.0 11.4

21.5 10.4 20.2 9.81 19.1 9.26 18.1 8.77 17.2 8.34

15.7 14.7 13.9 13.2 12.5

35.3 33.2 31.4 29.7 28.2

53.1 49.9 47.2 44.7 42.4

30.3 28.5 26.9 25.5 24.2

45.5 42.8 40.4 38.3 36.4

26.9 25.4 24.0 22.7 21.6

40.5 38.1 36.0 34.1 32.4

21 22 23 24 25

27.2 25.9 24.8 23.8 22.8

40.8 10.9 39.0 10.4 37.3 9.93 35.7 9.52 34.3 9.14

16.4 15.6 14.9 14.3 13.7

7.94 7.58 7.25 6.95 6.67

11.9 11.4 10.9 10.4 10.0

26.9 25.7 24.6 23.5 22.6

40.4 38.6 36.9 35.4 34.0

23.1 22.0 21.1 20.2 19.4

34.7 33.1 31.6 30.3 29.1

20.5 19.6 18.7 18.0 17.2

30.9 29.5 28.2 27.0 25.9

26 27 28 29 30

21.9 21.1 20.4 19.7 19.0

33.0 31.8 30.6 29.6 28.6

13.2 12.7 12.3 11.8 11.4

6.41 6.17 5.95 5.75 5.56

8.79 8.46 8.16 7.88 7.62

9.64 9.28 8.95 8.64 8.35

Beam Properties Wc /Ωb φbWc , kip-ft 571 858 229 343 167 251 565 849 484 728 431 648 Mp /Ωb φb Mp , kip-ft 71.3 107 28.6 42.9 20.8 31.3 70.6 106 60.5 91.0 53.9 81.0 Mr /Ωb φb Mr , kip-ft 42.4 63.7 16.0 24.0 11.6 17.4 39.6 59.5 35.0 52.5 31.8 47.8 BF /Ωb φb BF, kips 1.90 2.85 2.49 3.73 2.72 4.11 1.00 1.50 1.13 1.71 1.22 1.83 Vn /Ωv φvVn , kips 57.4 86.3 38.8 58.3 29.5 44.3 103 155 74.4 112 55.0 82.6 Zx , in.3 Lp , ft Lr , ft

ASD

39.7 4.62 19.8

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.67 φ v = 0.90

15.9 2.04 7.11

11.6 1.45 4.83

39.3 4.75 35.7

33.7 4.79 27.3

Note: For beams laterally unsupported, see Table 3-11. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

30.0 4.83 23.0

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3–94

DESIGN OF FLEXURAL MEMBERS

Table 3-9 (continued)

Maximum Total Uniform Load, kips MC-Shapes

MC10-MC9 Shape

25 ASD LRFD

Span, ft

Design

Fy = 36 ksi

MC10× 22 8.4 ASD LRFD ASD LRFD 44.0 66.1 37.9 57.0 75.0 113 28.5 42.8 68.7 103 22.8 34.2

6.5 25.4 ASD LRFD ASD LRFD 39.3 59.1 28.3 42.5 105 157 21.2 31.9 84.4 127 17.0 25.5 67.5 102

23.9 ASD LRFD 93.1 80.8 64.7

140 121 97.2

14.1 12.1 10.6 9.42 8.48

2 3 4 5

98.3 94.1 75.3

6 7 8 9 10

62.8 53.8 47.1 41.8 37.7

94.3 80.8 70.7 62.9 56.6

57.2 49.1 42.9 38.2 34.3

86.0 73.7 64.5 57.4 51.6

11 12 13 14 15

34.2 31.4 29.0 26.9 25.1

51.4 47.2 43.5 40.4 37.7

31.2 28.6 26.4 24.5 22.9

46.9 10.3 43.0 9.49 39.7 8.76 36.9 8.13 34.4 7.59

16 17 18 19 20

23.5 22.1 20.9 19.8 18.8

35.4 33.3 31.4 29.8 28.3

21.5 20.2 19.1 18.1 17.2

32.3 30.4 28.7 27.2 25.8

21 22 23 24 25

17.9 17.1 16.4 15.7 15.1

26.9 25.7 24.6 23.6 22.6

16.4 15.6 14.9 14.3 13.7

24.6 23.5 22.4 21.5 20.6

148 141 113

19.0 16.3 14.2 12.6 11.4

28.5 24.4 21.4 19.0 17.1

MC9×

56.3 48.2 42.2 37.5 33.8

84.6 72.5 63.5 56.4 50.8

53.9 46.2 40.4 35.9 32.3

81.0 69.4 60.8 54.0 48.6

7.71 11.6 7.07 10.6 6.52 9.80 6.06 9.10 5.65 8.50

30.7 28.1 26.0 24.1 22.5

46.1 42.3 39.0 36.3 33.8

29.4 26.9 24.9 23.1 21.6

44.2 40.5 37.4 34.7 32.4

7.11 10.7 6.70 10.1 6.32 9.50 5.99 9.00 5.69 8.55

5.30 4.99 4.71 4.46 4.24

7.97 7.50 7.08 6.71 6.37

21.1 19.9 18.8 17.8 16.9

31.7 29.9 28.2 26.7 25.4

20.2 19.0 18.0 17.0 16.2

30.4 28.6 27.0 25.6 24.3

5.42 5.17 4.95 4.74 4.55

4.04 3.85 3.69 3.53 3.39

6.07 5.79 5.54 5.31 5.10

16.1 15.4

24.2 23.1

15.4 14.7

23.1 22.1

338 42.2 24.5 0.967 52.4

508 63.5 36.9 1.45 78.7

323 40.4 23.8 0.982 46.6

15.6 14.3 13.2 12.2 11.4

8.15 7.78 7.44 7.13 6.84

21.2 18.2 15.9 14.2 12.7

Beam Properties Wc /Ωb φbWc , kip-ft 377 566 344 516 114 171 84.8 127 Mp /Ωb φb Mp , kip-ft 47.1 70.7 42.9 64.5 14.2 21.4 10.6 15.9 Mr /Ωb φb Mr , kip-ft 27.7 41.6 25.8 38.7 8.04 12.1 5.77 8.68 BF /Ωb φb BF, kips 1.29 1.93 1.28 1.93 1.75 2.65 1.95 2.91 Vn /Ωv φvVn , kips 49.1 73.9 37.5 56.4 22.0 33.0 19.7 29.5 Zx , in.3 Lp , ft Lr , ft

ASD

26.2 4.13 19.2

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.67 φ v = 0.90

23.9 4.15 17.5

7.92 1.52 5.03

5.90 1.09 3.57

23.5 4.20 22.5

Note: For beams laterally unsupported, see Table 3-11. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

486 60.8 35.7 1.49 70.0

22.5 4.20 21.1

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MAXIMUM TOTAL UNIFORM LOAD TABLES

3–95

Table 3-9 (continued)

Maximum Total Uniform Load, kips

Fy = 36 ksi

MC-Shapes Shape

21.4 ASD LRFD

2 3 4 5

88.4 68.6 54.9

133 103 82.5

77.6 65.4 52.3

117 98.3 78.6

6 7 8 9 10

45.7 39.2 34.3 30.5 27.4

68.8 58.9 51.6 45.8 41.3

43.6 37.4 32.7 29.1 26.2

65.5 56.2 49.1 43.7 39.3

39.3 33.7 29.5 26.2 23.6

11 12 13 14 15

25.0 22.9 21.1 19.6 18.3

37.5 34.4 31.7 29.5 27.5

23.8 21.8 20.1 18.7 17.4

35.7 32.8 30.2 28.1 26.2

16 17 18 19 20

17.2 16.1 15.2 14.4 13.7

25.8 24.3 22.9 21.7 20.6

16.3 15.4 14.5 13.8 13.1

24.6 23.1 21.8 20.7 19.7

274 34.3 20.0 0.724 44.2

413 51.6 30.1 1.09 66.4

262 32.7 19.4 0.733 38.8

393 49.1 29.1 1.10 58.3

Design

Span, ft

MC8× 20 ASD LRFD 82.8 124 78.6 118 58.9 88.6 47.1 70.8

22.8 ASD LRFD

MC8-MC7 MC7× 18.7 ASD LRFD

8.5 ASD LRFD 37.0 55.7 73.1 110 33.3 50.0 56.0 84.2 25.0 37.5 44.8 67.4 20.0 30.0

22.7 ASD LRFD 91.1 137 78.6 118 58.9 88.6 47.1 70.8

59.0 50.6 44.3 39.4 35.4

37.4 32.0 28.0 24.9 22.4

56.2 48.1 42.1 37.4 33.7

16.6 14.3 12.5 11.1 9.99

25.0 21.4 18.8 16.7 15.0

39.3 33.7 29.5 26.2 23.6

59.0 50.6 44.3 39.4 35.4

21.4 19.6 18.1 16.8 15.7

32.2 29.5 27.2 25.3 23.6

20.4 18.7 17.2 16.0 14.9

30.6 28.1 25.9 24.1 22.5

9.08 8.32 7.68 7.13 6.66

13.6 12.5 11.5 10.7 10.0

21.4 19.6 18.1 16.8 15.7

32.2 29.5 27.2 25.3 23.6

14.7 13.9 13.1 12.4 11.8

22.1 20.8 19.7 18.6 17.7

14.0 13.2 12.5 11.8 11.2

21.1 19.8 18.7 17.7 16.8

6.24 5.88 5.55 5.26 4.99

14.7 13.9

22.1 20.8

9.38 8.83 8.34 7.90 7.51

Beam Properties Wc /Ωb φbWc , kip-ft Mp /Ωb φb Mp , kip-ft Mr /Ωb φb Mr , kip-ft BF /Ωb φb BF, kips Vn /Ωv φvVn , kips Zx , in.3 Lp , ft Lr , ft

ASD

19.1 4.25 24.0

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.67 φ v = 0.90

18.2 4.25 22.4

236 29.5 17.1 0.775 41.4

354 44.3 25.7 1.16 62.2

16.4 3.61 19.6

224 28.0 16.5 0.778 36.5

337 99.9 150 236 354 42.1 12.5 18.8 29.5 44.3 24.8 7.32 11.0 17.0 25.5 1.17 0.970 1.46 0.493 0.741 54.9 18.5 27.8 45.5 68.4

15.6 3.61 18.4

6.95 2.08 7.42

Note: For beams laterally unsupported, see Table 3-11. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

16.4 4.33 29.7

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DESIGN OF FLEXURAL MEMBERS

Table 3-9 (continued)

Maximum Total Uniform Load, kips MC-Shapes

MC7-MC6 MC7×

Shape

19.1 ASD LRFD

Span, ft

Design

Fy = 36 ksi

LRFD 88.4 84.2 63.2 50.5

MC6× 15.3 16.3 ASD ASD LRFD LRFD 52.8 79.3 58.2 87.5 47.5 71.4 49.8 74.9 35.6 53.5 37.4 56.2 28.5 42.8 29.9 44.9

18

ASD 49.0 47.1 35.3 28.3

15.1 LRFD 73.7 70.8 53.1 42.5

2 3 4 5

63.7 52.1 41.7

95.8 78.3 62.6

ASD 58.8 56.0 42.0 33.6

6 7 8 9 10

34.7 29.8 26.0 23.2 20.8

52.2 44.7 39.2 34.8 31.3

28.0 24.0 21.0 18.7 16.8

42.1 36.1 31.6 28.1 25.3

23.7 20.3 17.8 15.8 14.2

35.7 30.6 26.8 23.8 21.4

24.9 21.4 18.7 16.6 14.9

37.4 32.1 28.1 25.0 22.5

23.5 20.2 17.7 15.7 14.1

35.4 30.3 26.5 23.6 21.2

11 12 13 14 15

18.9 17.4 16.0 14.9 13.9

28.5 26.1 24.1 22.4 20.9

15.3 14.0 12.9 12.0 11.2

23.0 21.1 19.4 18.1 16.8

12.9 11.9 11.0 10.2 9.49

19.5 17.8 16.5 15.3 14.3

13.6 12.5 11.5 10.7 9.96

20.4 18.7 17.3 16.0 15.0

12.8 11.8 10.9 10.1 9.42

19.3 17.7 16.3 15.2 14.2

16 17

13.0 12.3

19.6 18.4

Beam Properties Wc /Ωb φbWc , kip-ft 208 313 168 253 142 214 149 225 141 212 Mp /Ωb φb Mp , kip-ft 26.0 39.2 21.0 31.6 17.8 26.8 18.7 28.1 17.7 26.5 Mr /Ωb φb Mr , kip-ft 15.5 23.2 12.4 18.7 10.6 16.0 10.9 16.4 10.4 15.7 BF /Ωb φb BF, kips 0.523 0.797 0.356 0.535 0.372 0.559 0.373 0.560 0.384 0.568 Vn /Ωv φvVn , kips 31.9 47.9 29.4 44.2 26.4 39.7 29.1 43.7 24.5 36.9 Zx , in.3 Lp , ft Lr , ft

ASD

14.5 4.33 24.4

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.67 φ v = 0.90

11.7 4.37 28.5

9.91 4.37 23.7

10.4 3.69 24.6

Note: For beams laterally unsupported, see Table 3-11. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.83 3.68 22.7

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 97

MAXIMUM TOTAL UNIFORM LOAD TABLES

3–97

Table 3-9 (continued)

Maximum Total Uniform Load, kips

Fy = 36 ksi

MC-Shapes MC6×

2 3 4 5

ASD 48.1 35.8 26.8 21.5

LRFD 72.3 53.8 40.3 32.3

ASD 27.8 21.6 16.2 12.9

LRFD 41.8 32.4 24.3 19.4

ASD 24.1 20.5 15.4 12.3

LRFD 36.2 30.8 23.1 18.5

MC4× 13.8 ASD LRFD 39.7 59.7 26.5 39.8 19.9 29.9 15.9 23.9

6 7 8 9 10

17.9 15.3 13.4 11.9 10.7

26.9 23.1 20.2 17.9 16.1

10.8 9.24 8.08 7.19 6.47

16.2 13.9 12.2 10.8 9.72

10.3 8.79 7.69 6.83 6.15

15.4 13.2 11.6 10.3 9.24

13.2 11.4 9.93 8.83 7.95

14.7 13.4 12.4 11.5 10.8

5.88 5.39 4.97 4.62 4.31

8.84 8.10 7.48 6.94 6.48

5.59 5.13 4.73 4.39 4.10

8.40 7.70 7.11 6.60 6.16

79.5 9.93 5.57 0.126 25.9

Shape

12

Design

11 12 13 14 15

Span, ft

MC6-MC3

9.76 8.95 8.26 7.67 7.16

6.5

7

MC3× 7.1 ASD 16.1 10.7 8.05 6.44

LRFD 24.2 16.1 12.1 9.68

19.9 17.1 14.9 13.3 11.9

5.37 4.60

8.06 6.91

119 14.9 8.37 0.189 38.9

32.2 4.02 2.28 0.0745 12.1

48.4 6.05 3.42 0.113 18.2

Beam Properties Wc /Ωb φbWc , kip-ft 107 161 Mp /Ωb φb Mp , kip-ft 13.4 20.2 Mr /Ωb φb Mr , kip-ft 7.85 11.8 BF /Ωb φb BF, kips 0.414 0.627 Vn /Ωv φvVn , kips 24.1 36.2 Zx , in.3 Lp , ft Lr , ft

ASD

7.47 3.01 16.4

LRFD

Ωb = 1.67 φ b = 0.90 Ωv = 1.67 φ v = 0.90

64.7 8.08 4.79 0.490 13.9

97.2 12.2 7.20 0.744 20.9 4.50 2.24 8.96

61.5 7.69 4.60 0.485 12.0

92.4 11.6 6.92 0.735 18.1 4.28 2.24 8.61

5.53 3.03 37.6

Note: For beams laterally unsupported, see Table 3-11. Available strength tabulated above heavy line is limited by available shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.24 2.34 25.7

AISC_Part 3B:14th Ed.

3–98

2/24/11

8:54 AM

Page 98

DESIGN OF FLEXURAL MEMBERS

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 99

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

12000

7700

11550

7400

11100

7100

10650

6800

10200

6500

9750

6200

9300

5900

8850

5600

8400

5300

7950

5000

7500

W-Shapes Available Moment vs. Unbraced Length

52

6X6

W3

8000

Table 3-10

93

0x5

W4

503

29

6X5

0x W4

W3

Available Moment, Mn /Ωb (60 kip-ft increments) and φb Mn (90 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

3–99

52

6X6

W3

3

9 0x5

16

W4

87

6X4

W3

4

28 40 52 Unbraced Length (3-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

64

76

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

3–100

DESIGN OF FLEXURAL MEMBERS

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

Available Moment, Mn /Ωb (40 kip-ft increments) and φb Mn (60 kip-ft increments)

Page 100

5000

7500

4800

7200

4600

6900

4400

6600

4200

6300

4000

6000

3800

5700

3600

5400

3400

5100

3200

4800

3000

4500

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

6

10

14 18 22 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

26

30

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 101

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (40 kip-ft increments) and φb Mn (60 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 5000

7500

4800

7200

4600

6900

4400

6600

4200

6300

4000

6000

3800

5700

3600

5400

3400

5100

3200

4800

3000

4500

3–101

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

30

34

38 42 46 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

50

54

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

3–102

DESIGN OF FLEXURAL MEMBERS

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

Available Moment, Mn /Ωb (20 kip-ft increments) and φb Mn (30 kip-ft increments)

Page 102

3000

4500

2900

4350

2800

4200

2700

4050

2600

3900

2500

3750

2400

3600

2300

3450

2200

3300

2100

3150

2000

3000

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

6

10

14 18 22 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

26

30

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 103

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (20 kip-ft increments) and φb Mn (30 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 3000

4500

2900

4350

2800

4200

2700

4050

2600

3900

2500

3750

2400

3600

2300

3450

2200

3300

2100

3150

2000

3000

3–103

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

30

34

38 42 46 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

50

54

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

3–104

DESIGN OF FLEXURAL MEMBERS

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

Available Moment, Mn /Ωb (8 kip-ft increments) and φb Mn (12 kip-ft increments)

Page 104

2000

3000

1960

2940

1920

2880

1880

2820

1840

2760

1800

2700

1760

2640

1720

2580

1680

2520

1640

2460

1600

2400

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

6

10

14 18 22 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

26

30

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 105

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (8 kip-ft increments) and φb Mn (12 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 2000

3000

1960

2940

1920

2880

1880

2820

1840

2760

1800

2700

1760

2640

1720

2580

1680

2520

1640

2460

1600

2400

3–105

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

30

34

38 42 46 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

50

54

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

3–106

DESIGN OF FLEXURAL MEMBERS

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

Available Moment, Mn /Ωb (8 kip-ft increments) and φb Mn (12 kip-ft increments)

Page 106

1600

2400

1560

2340

1520

2280

1480

2220

1440

2160

1400

2100

1360

2040

1320

1980

1280

1920

1240

1860

1200

1800

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

6

10

14 18 22 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

26

30

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 107

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (8 kip-ft increments) and φb Mn (12 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 1600

2400

1560

2340

1520

2280

1480

2220

1440

2160

1400

2100

1360

2040

1320

1980

1280

1920

1240

1860

1200

1800

3–107

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

30

34

38 42 46 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

50

54

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

3–108

DESIGN OF FLEXURAL MEMBERS

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

Available Moment, Mn /Ωb (4 kip-ft increments) and φb Mn (6 kip-ft increments)

Page 108

1200

1800

1180

1770

1160

1740

1140

1710

1120

1680

1100

1650

1080

1620

1060

1590

1040

1560

1020

1530

1000

1500

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

6

10

14 18 22 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

26

30

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 109

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (4 kip-ft increments) and φb Mn (6 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 1200

1800

1180

1770

1160

1740

1140

1710

1120

1680

1100

1650

1080

1620

1060

1590

1040

1560

1020

1530

1000

1500

3–109

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

30

34

38 42 46 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

50

54

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

3–110

DESIGN OF FLEXURAL MEMBERS

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Page 110

1000

1500

990

1485

980

1470

970

1455

960

1440

950

1425

940

1410

930

1395

920

1380

910

1365

900

1350

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

6

10

14 18 22 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

26

30

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 111

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 1000

1500

990

1485

980

1470

970

1455

960

1440

950

1425

940

1410

930

1395

920

1380

910

1365

900

1350

3–111

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

30

34

38 42 46 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

50

54

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

3–112

DESIGN OF FLEXURAL MEMBERS

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Page 112

900

1350

890

1335

880

1320

870

1305

860

1290

850

1275

840

1260

830

1245

820

1230

810

1215

800

1200

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

6

10

14 18 22 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

26

30

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 113

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 900

1350

890

1335

880

1320

870

1305

860

1290

850

1275

840

1260

830

1245

820

1230

810

1215

800

1200

3–113

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

30

34

38 42 46 Unbraced Length (1-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

50

54

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 114

3–114

DESIGN OF FLEXURAL MEMBERS

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 800

1200

790

1185

780

1170

770

1155

760

1140

750

1125

740

1110

730

1095

720

1080

710

1065

700

1050

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

6

8

10

12 14 16 18 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

20

22

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 115

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 800

1200

790

1185

780

1170

770

1155

760

1140

750

1125

740

1110

730

1095

720

1080

710

1065

700

1050

3–115

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

22

24

26

28 30 32 34 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

36

38

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 116

3–116

DESIGN OF FLEXURAL MEMBERS

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 700

1050

690

1035

680

1020

670

1005

660

990

650

975

640

960

630

945

620

930

610

915

600

900

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

6

8

10

12 14 16 18 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

20

22

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 117

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 700

1050

690

1035

680

1020

670

1005

660

990

650

975

640

960

630

945

620

930

610

915

600

900

3–117

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

22

24

26

28 30 32 34 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

36

38

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 118

3–118

DESIGN OF FLEXURAL MEMBERS

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 600

900

590

885

580

870

570

855

560

840

550

825

540

810

530

795

520

780

510

765

500

750

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

6

8

10

12 14 16 18 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

20

22

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 119

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 600

900

590

885

580

870

570

855

560

840

550

825

540

810

530

795

520

780

510

765

500

750

3–119

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

22

24

26

28 30 32 34 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

36

38

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 120

3–120

DESIGN OF FLEXURAL MEMBERS

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 500

750

490

735

480

720

470

705

460

690

450

675

440

660

430

645

420

630

410

615

400

600

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

6

8

10

12 14 16 18 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

20

22

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 121

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 500

750

490

735

480

720

470

705

460

690

450

675

440

660

430

645

420

630

410

615

400

600

3–121

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

22

24

26

28 30 32 34 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

36

38

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 122

3–122

DESIGN OF FLEXURAL MEMBERS

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

9 x9 14 W

93 W21x 6 8x8 W1

4 W27x8

x73 W21

06 9 x1 6x8 12 W1 W 76 W24x

585

83 W21x

390

Available Moment vs. Unbraced Length 6 8x7 W1 68 W24x

600

W-Shapes

x68 W21

400

Table 3-10 (continued)

W24x62 W14x90

570

W12x96

W10x112

0

x9

555

14

W

370

W18x71

9 6x8 W1

x68 W21

68 W24x

7 6x7 W1

W 10 x1 12

x73 W21

x62 W21

6

x9

12

W

495

82 4x W1

330

x71 W18

510

62 W24x

340

W14x82

83 W21x

6

525

x9

350

W21x62

12

540

W

360

W12x87

83 W21x W24x76

10 12 14 16 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

6 8x7 W1

7 x8 12 W

8

7 6x7 W1

6

x68 W21

4

x62 W21

450

4 x7 62 W24x 14

W

300

W18x60

x55 W21

465

x57 W21

310

x71 W18

W21x55

68 W24x

7 6x6 W1

480

x65 W18

320

W 10 x1 00

82 4x W1

W16x67 W21x57

55 W24x

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

W16x77

06 x86 x1 W18 12 93 W W21x

84 W24x

380

18

20

AISC_Part 3B:14th Ed.

2/24/11

8:54 AM

Page 123

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

00

111 W21x

W30x99

02 W27x1

W24x94

93 W21x

03 W24x1

00 6x1

W1

6 x9 12 W 6 8x8 W1 9 6x8 W1 4 W24x9

W27x84

83 W21x

24

26 28 30 32 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

34

x101 W21

W 10 x1 12

3 W21x9

6 8x7 W1

22

104 W24x

0 x9

W24x84

14 W

W27x94

9 6x8 W1

06 x1 12 W

W30x90

W27x84

9 x9 14 W

6 8x8 W1

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

W27x94 W30x90

0

x9

14

W

20

7

450

11 W24x

300

x106 W18

465

119 W18x

310

09 x1 14 W

480

111 W21x

320

x97 W18

495

106 W18x

330

04 W24x1

510

01 W21x1

340

6 x10 W18

525

20 x1 12 W

350

9 x9 14 W

540

4 W27x11

360

W30x108

555

6x1

370

W1

570

W27x102

380

7 8x9 W1 3 W24x10

585

Available Moment vs. Unbraced Length W30x99

390

W-Shapes W27x94 W30x90

600

Table 3-10 (continued)

84 W27x

400

3–123

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3–124

DESIGN OF FLEXURAL MEMBERS

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

2

x62 W21

68 W21x 5

x6

12

W

x65 W18

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8 W24x6

x7

12

8

x6

10 12 14 16 Unbraced Length (0.5-ft increments)

3 W21x7

7 6x6 W1 1x68 W2

W

14

8

x60 W18 x55 W21 W24x62

6

1 x6

4

14

300

W 10 x7 7

W

200

5 8x5 W1

W16x45

8 x5 12 W 8x50 W1

53 x50 x W21 14 W 0 6x5 W1 x44 W21

315

57 W21x

7 6x5 W1 x48 W21

W14x53 W12x58 W10x68

210

x71 W18 x65 W18

x6

14 5 8x5 W1

330

0 8x5 W1 x50 W21

220

W12x65

0 6x5 W1

345

W21x44

8

W

1

W 10 x7 7

W

55 W24x

62 W24x

W10x77

x8

x55 W21

375

x46 W18

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

10

x48 7 W21 6x5 W1

W18x50

230

82 4x W1

W14x61

W

x60 W18

57 W21x

390

360

7 6x7 W1

55 W24x

5 8x5 W1

W16x57

240

9 x7 x74 4 12 W W1

W12x72

405

W21x48

250

7 x8 12 W

x71 W18

W18x55 W21x50

260

68 W24x x73 W21

W10x88

270

x68 W21

420

W14x68

W 10 x1 00

x62 W21

280

7 6x6 W1

435

W12x79

62 W24x x65 W18

290

Available Moment vs. Unbraced Length

x55 W21

450

W-Shapes

57 W21x

300

Table 3-10 (continued)

18

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PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

6 x9

W 0 0 x9 x10 14 W16 x97 W18

375

12

250

W

390

7 x8 12 W

260

6 8x7 W1 93 W21x

405

84 W24x

270

3 W21x8 W24x76

420

W 10 x1 00

4 W24x8 7 2 6x7 4x8 W1 W1

280

6 8x8 W1 9 6x8 W1

435

4 W24x9

290

Available Moment vs. Unbraced Length W27x84

450

W-Shapes 3 W21x9

300

Table 3-10 (continued)

315

200

300

14

W

4

W 12 2 x7

22

x7 14

x73 W21 68 W24x 5 x6

12

W

20

W

7 6x6 W1

8 x6

68 W21x

71 W18x

W 10 x7 7

6 8x8 W1

210

9 x7 2 12 W 4x8 W1

330

9 6x8 W1

220

8

x76 W18 7 6x7 W1

345

x8

4 x7 14 W x83 W21

230

76 W24x

360

2 x7 12 W

240

x86 W18

10

7 6x7 W1

9 x7 12 W W

7 6x6 W1

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

3–125

24

26 28 30 32 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

34

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3–126

DESIGN OF FLEXURAL MEMBERS

Available Moment, Mn /Ωb (1 kip-ft increments) and φb Mn (1.5 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 200

300

196

294

192

288

188

282

184

276

180

270

176

264

172

258

168

252

164

246

160

240

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

2

4

6

8 10 12 14 Unbraced Length (0.5-ft increments)

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PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (1 kip-ft increments) and φb Mn (1.5 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 200

300

196

294

192

288

188

282

184

276

180

270

176

264

172

258

168

252

164

246

160

240

3–127

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

18

20

22

24 26 28 30 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

32

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3–128

DESIGN OF FLEXURAL MEMBERS

Available Moment, Mn /Ωb (1 kip-ft increments) and φb Mn (1.5 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 160

240

156

234

152

228

148

222

144

216

140

210

136

204

132

198

128

192

124

186

120

180

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

2

4

6

8 10 12 14 Unbraced Length (0.5-ft increments)

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PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (1 kip-ft increments) and φb Mn (1.5 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 160

240

156

234

152

228

148

222

144

216

140

210

136

204

132

198

128

192

124

186

120

180

3–129

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

18

20

22

24 26 28 30 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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3–130

DESIGN OF FLEXURAL MEMBERS

Available Moment, Mn /Ωb (1 kip-ft increments) and φb Mn (1.5 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 120

180

116

174

112

168

108

162

104

156

100

150

96

144

92

138

88

132

84

126

80

120

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

2

4

6

8 10 12 14 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 131

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (1 kip-ft increments) and φb Mn (1.5 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 120

180

116

174

112

168

108

162

104

156

100

150

96

144

92

138

88

132

84

126

80

120

3–131

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

18

20

22

24 26 28 30 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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3–132

DESIGN OF FLEXURAL MEMBERS

Available Moment, Mn /Ωb (1 kip-ft increments) and φb Mn (1.5 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 80

120

76

114

72

108

68

102

64

96

60

90

56

84

52

78

48

72

44

66

40

60

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

2

4

6

8 10 12 14 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 133

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (1 kip-ft increments) and φb Mn (1.5 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 80

120

76

114

72

108

68

102

64

96

60

90

56

84

52

78

48

72

44

66

40

60

3–133

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

18

20

22

24 26 28 30 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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3–134

DESIGN OF FLEXURAL MEMBERS

Available Moment, Mn /Ωb (1 kip-ft increments) and φb Mn (1.5 kip-ft increments)

Fy = 50 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 40

60

36

54

32

48

28

42

24

36

20

30

16

24

12

18

8

12

4

6

0

0

Table 3-10 (continued)

W-Shapes Available Moment vs. Unbraced Length

2

4

6

8 10 12 14 Unbraced Length (0.5-ft increments)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 135

PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (2 kip-ft increments) and φb Mn (3 kip-ft increments)

Fy = 36 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 180

270

172

258

164

246

156

234

148

222

140

210

132

198

124

186

116

174

108

162

100

150

3–135

Table 3-11

Channels Available Moment vs. Unbraced Length

0

2

4

6 8 10 12 Unbraced Length (0.5-ft increments)

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3–136

DESIGN OF FLEXURAL MEMBERS

Available Moment, Mn /Ωb (1 kip-ft increments) and φb Mn (1.5 kip-ft increments)

Fy = 36 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 100

150

96

144

92

138

88

132

84

126

80

120

76

114

72

108

68

102

64

96

60

90

Table 3-11 (continued)

Channels Available Moment vs. Unbraced Length

0

2

4

6 8 10 12 Unbraced Length (0.5-ft increments)

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PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (1 kip-ft increments) and φb Mn (1.5 kip-ft increments)

Fy = 36 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 100

150

96

144

92

138

88

132

84

126

80

120

76

114

72

108

68

102

64

96

60

90

3–137

Table 3-11 (continued)

Channels Available Moment vs. Unbraced Length

16

18

20

22 24 26 28 Unbraced Length (0.5-ft increments)

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3–138

DESIGN OF FLEXURAL MEMBERS

Available Moment, Mn /Ωb (0.5 kip-ft increments) and φb Mn (0.75 kip-ft increments)

Fy = 36 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 60

90

58

87

56

84

54

81

52

78

50

75

48

72

46

69

44

66

42

63

40

60

Table 3-11 (continued)

Channels Available Moment vs. Unbraced Length

0

2

4

6 8 10 12 Unbraced Length (0.5-ft increments)

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PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (0.5 kip-ft increments) and φb Mn (0.75 kip-ft increments)

Fy = 36 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD 60

90

58

87

56

84

54

81

52

78

50

75

48

72

46

69

44

66

42

63

40

60

3–139

Table 3-11 (continued)

Channels Available Moment vs. Unbraced Length

16

18

20

22 24 26 28 Unbraced Length (0.5-ft increments)

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3–140

DESIGN OF FLEXURAL MEMBERS

Fy = 36 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

36

54

x30 C12

7 x20. C12

x25 10 .4 MC 25 9x 0 0x3 MC C1

51 MC8x21.4

32

48

C9x20

45

MC

MC8x20

C9x15

36

5 0x2 C1

7 x20. C12

24

x22 10 MC

0 0x2 C1

C8x18.75

25 C12x 8 2. x2 5 C8 0x2 C1 M

4

39

1.

26

MC8x18.7

x2

42

C8

28

M

C10x15.3 MC12x14.3

.9

23

9x

30

.3 2x14 MC1

Available Moment, Mn /Ωb (0.5 kip-ft increments) and φb Mn (0.75 kip-ft increments)

x22 10 MC

x25 C12

5 0x2 C1

.4 25 9x MC

.9

C10x20 MC8x22.8

34

x30 C12

57

x25 10 MC

38

Available Moment vs. Unbraced Length

3 x2

60

Channels 9 MC

40

Table 3-11 (continued)

x C8

M 20

x C8

C9x13.4

5

33

20

30

7

8.

x1

C8

M

0 x2 C9

3

5 x1 C9

MC12x10.6

5. 0x1 C1

.7

18

22

C8x13.75

0

2

4

6 8 10 12 Unbraced Length (0.5-ft increments)

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PLOTS OF AVAILABLE FLEXURAL STRENGTH VS. UNBRACED LENGTH

Available Moment, Mn /Ωb (0.5 kip-ft increments) and φb Mn (0.75 kip-ft increments)

Fy = 36 ksi Cb = 1 φb Mn Mn /Ωb kip-ft kip-ft LRFD ASD 40

60

38

57

36

54

34

51

32

48

30

45

28

42

26

39

24

36

22

33

20

30

3–141

Table 3-11 (continued)

Channels Available Moment vs. Unbraced Length

16

18

20

22 24 26 28 Unbraced Length (0.5-ft increments)

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3–142

DESIGN OF FLEXURAL MEMBERS

Fy = 36 ksi Cb = 1 Mn /Ωb φb Mn kip-ft kip-ft LRFD ASD

.3 2x14 MC1

8.4

10x

MC

MC8x8.5

3.4 3. x1

C8

12

x1

8

5 x1 C9

15

C9

10

x10.6 MC12

18

6.5

75

10x

12

MC

Available Moment, Mn /Ωb (0.5 kip-ft increments) and φb Mn (0.75 kip-ft increments)

0.7 2x2 C1 .7

8 x1

C8

21

0 0x2 C1

14

5.3 0x1 C1

24

20

C8x11.5

16

M

x C9

75 8. x1 C8

27

C8x13.75 5 x1 C9

18

Available Moment vs. Unbraced Length

3.4 x1 C9

30

Channels

.6 2x10 MC1

20

Table 3-11 (continued)

C8

x1 1.

5

6

9

4

6

MC 8x8 .5

MC 10x 8.4

2

3 MC10x

6.5

0

0 0

2

4

6 8 10 12 Unbraced Length (0.5-ft increments)

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AVAILABLE FLEXURAL STRENGTH OF HSS

3–143

Table 3-12

Available Flexural Strength, kip-ft

Fy = 46 ksi

Rectangular HSS Shape HSS20×12×

5/8 1/2 3/8 5/16

HSS20×8×

5/8 1/2 3/8 5/16

HSS20×4×

1/2 3/8 5/16 1/4

HSS18×6×

5/8 1/2 3/8 5/16 1/4

HSS16×12×

5/8 1/2 3/8 5/16

HSS16×8×

5/8 1/2 3/8 5/16 1/4

HSS16×4×

5/8 1/2 3/8 5/16 1/4 3/16

HSS14×10×

5/8 1/2 3/8 5/16 1/4

ASD

LRFD

Ωb = 1.67

φ b = 0.90

X-Axis Mn /Ωb φb Mn ASD LRFD 528 794 432 649 305 459 226 339

Y-Axis Mn /Ωb φb Mn ASD LRFD 350 527 254 382 169 255 130 196

425 349 269 223

638 524 404 336

209 152 101 76.8

264 205 171 131

397 308 257 198

62.7 42.2 32.1 22.8

310 257 198 168 132

466 386 298 252 198

140 210 102 153 68.0 102 52.2 78.5 37.3 56.1

379 310 221 166

569 466 333 249

310 240 159 123

466 360 238 185

296 243 188 159 119

445 366 283 240 178

182 142 94.3 73.0 52.6

273 213 142 110 79.1

213 177 138 117 94.3 66.9

321 267 208 176 142 100

275 227 175 137 97.3

414 341 263 207 146

314 229 152 115

218 180 120 93.2 68.2

Shape HSS14×6×

328 271 180 140 103

5/8 1/2 3/8 5/16 1/4 3/16

HSS14×4×

5/8

252 211 165 140 115 83.2

181 140 111 78.9

272 211 166 119

188 156 122 103 77.8 50.0

283 142 214 235 118 178 183 86.8 130 155 66.3 99.7 117 48.8 73.4 75.2 32.1 48.3

158 132 103 87.5 71.4 49.6

237 198 155 132 107 74.6

96.6 145 80.9 122 59.9 90.1 46.1 69.4 33.8 50.8 22.0 33.1

1/4 3/16

127 107 84.2 71.9 58.8 44.3

192 161 127 108 88.4 66.6

56.3 47.9 35.8 27.7 20.3 13.1

84.6 71.9 53.8 41.6 30.5 19.7

3/8 5/16

79.6 67.9

120 102

30.2 23.4

45.4 35.1

3/8 5/16 1/4 3/16

HSS12×10×

1/2 3/8 5/16 1/4

HSS12×8×

5/8 1/2 3/8 5/16 1/4 3/16

HSS12×6×

5/8 1/2 3/8 5/16 1/4 3/16

HSS12×4×

5/8 1/2 3/8 5/16

HSS12×31/2×

X-Axis Y-Axis Mn /Ωb φb Mn Mn /Ωb φb Mn ASD LRFD ASD LRFD 204 306 111 167 169 254 92.7 139 131 198 62.6 94.2 112 168 48.7 73.2 90.9 137 35.2 53.0 62.7 94.3 22.8 34.2 168 140 110 93.3 76.2 55.4

1/2

94.3 63.4 48.3 34.3

74.6 112 58.8 88.3 39.4 59.2 30.4 45.7 21.8 32.8 13.9 20.9

HSS20-HSS12

65.4 55.4 37.5 29.2 21.1 13.6

98.3 83.3 56.3 43.9 31.8 20.4

160 240 116 175 88.7 133 65.5 98.5

Note: Values are reduced for compactness criteria, when appropriate. See Table 1-12A for limiting dimensions for compactness.

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Page 144

3–144

DESIGN OF FLEXURAL MEMBERS

Table 3-12 (continued)

Available Flexural Strength, kip-ft Rectangular HSS

HSS12-HSS8 Shape HSS12×3×

5/16 1/4 3/16

HSS12×2×

5/16 1/4 3/16

HSS10×8×

5/8 1/2 3/8 5/16 1/4 3/16

HSS10×6×

5/8 1/2 3/8 5/16 1/4 3/16

HSS10×5×

3/8 5/16 1/4 3/16

HSS10×4×

5/8 1/2 3/8 5/16 1/4 3/16 1/8

HSS10×31/2

1/2 3/8 5/16 1/4 3/16 1/8

ASD

LRFD

Ωb = 1.67

φ b = 0.90

Fy = 46 ksi

X-Axis Y-Axis Mn /Ωb φb Mn Mn /Ωb φb Mn ASD LRFD ASD LRFD 64.0 96.2 19.2 28.8 52.5 79.0 14.1 21.2 39.6 59.5 9.15 13.7 56.2 46.3 34.9 143 119 93.0 79.0 60.0 39.0

84.5 69.5 52.4

11.2 16.8 8.37 12.6 5.48 8.24

215 122 184 179 102 153 140 79.8 120 119 63.8 95.9 90.2 46.1 69.2 58.6 30.7 46.2

118 177 98.7 148 77.5 116 66.1 99.3 54.1 81.3 37.9 57.0

82.1 123 69.1 104 54.4 81.8 43.9 65.9 31.8 47.9 21.1 31.7

69.8 105 59.6 89.5 48.8 73.4 37.3 56.1

42.9 34.7 25.3 16.7

64.5 52.2 38.0 25.1

92.6 139 78.3 118 62.0 93.2 53.1 79.8 43.6 65.5 33.4 50.2 20.7 31.1

47.2 40.3 32.2 26.1 19.1 12.6 6.84

70.9 60.6 48.4 39.3 28.7 18.9 10.3

73.2 110 58.2 87.4 49.8 74.9 41.0 61.6 31.5 47.3 20.3 30.5

33.8 27.2 22.1 16.1 10.6 5.75

50.8 40.8 33.2 24.3 16.0 8.65

Shape HSS10×3×

3/8 5/16 1/4 3/16 1/8

HSS10×2×

3/8 5/16 1/4 3/16 1/8

HSS9×7×

5/8 1/2 3/8 5/16 1/4 3/16

HSS9×5×

5/8 1/2 3/8 5/16 1/4 3/16

HSS9×3×

1/2 3/8 5/16 1/4 3/16

HSS8×6×

5/8 1/2 3/8 5/16 1/4 3/16

X-Axis Mn /Ωb φb Mn ASD LRFD 54.3 81.6 46.6 70.0 38.4 57.7 29.5 44.3 19.0 28.5 46.6 40.1 33.2 25.6 16.3

70.0 60.3 49.8 38.4 24.6

Y-Axis Mn /Ωb φb Mn ASD LRFD 22.3 33.6 18.1 27.3 13.3 20.0 8.75 13.2 4.72 7.10 13.2 10.8 7.86 5.25 2.83

19.9 16.2 11.8 7.89 4.25

111 167 92.9 140 72.9 110 62.2 93.4 50.9 76.5 32.3 48.6

93.0 78.1 61.4 52.4 37.3 25.0

140 117 92.3 78.7 56.0 37.6

88.3 133 74.7 112 59.1 88.8 50.5 75.9 41.5 62.4 31.8 47.8

58.1 49.3 39.2 33.6 24.3 16.2

87.3 74.1 58.9 50.5 36.5 24.3

56.4 45.2 38.9 32.1 24.7

24.8 20.2 17.5 12.7 8.50

37.3 30.4 26.3 19.1 12.8

67.7 57.3 45.4 38.8 30.1 19.7

102 86.1 68.2 58.4 45.2 29.7

84.8 67.9 58.5 48.3 37.2

82.8 124 69.9 105 55.3 83.1 47.3 71.1 38.8 58.4 27.5 41.4

Note: Values are reduced for compactness criteria, when appropriate. See Table 1-12A for limiting dimensions for compactness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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AVAILABLE FLEXURAL STRENGTH OF HSS

3–145

Table 3-12 (continued)

Available Flexural Strength, kip-ft

Fy = 46 ksi

Rectangular HSS Shape HSS8×4×

5/8 1/2 3/8 5/16 1/4 3/16 1/8

HSS8×3×

1/2 3/8 5/16 1/4 3/16 1/8

HSS8×2×

3/8 5/16 1/4 3/16 1/8

HSS7×5×

1/2 3/8 5/16 1/4 3/16 1/8

HSS7×4×

1/2 3/8 5/16 1/4 3/16 1/8

HSS7×3×

1/2 3/8 5/16 1/4 3/16 1/8

ASD

LRFD

Ωb = 1.67

φ b = 0.90

X-Axis Y-Axis Mn /Ωb φb Mn Mn /Ωb φb Mn ASD LRFD ASD LRFD 63.0 94.7 38.1 57.2 53.8 80.9 32.8 49.3 43.0 64.7 26.4 39.6 37.0 55.6 22.7 34.2 30.5 45.9 17.8 26.7 23.5 35.3 11.8 17.7 14.7 22.1 6.53 9.82 45.8 36.9 31.9 26.4 20.4 13.8

68.8 55.5 47.9 39.6 30.6 20.8

22.1 18.1 15.7 12.3 8.19 4.52

33.3 27.2 23.6 18.6 12.3 6.79

30.8 26.7 22.2 17.2 11.7

46.3 40.1 33.4 25.9 17.6

10.6 15.9 9.33 14.0 7.37 11.1 4.90 7.37 2.71 4.07

50.2 40.1 34.4 28.4 21.8 12.1

75.4 60.2 51.8 42.7 32.8 18.2

39.6 31.7 27.3 22.6 14.9 8.47

59.6 47.7 41.1 33.9 22.4 12.7

43.2 34.7 30.0 24.8 19.1 12.1

64.9 52.2 45.0 37.3 28.7 18.1

29.0 23.4 20.3 16.8 11.2 6.33

43.6 35.2 30.5 25.3 16.8 9.51

36.2 29.4 25.5 21.2 16.4 11.3

54.4 44.2 38.3 31.8 24.6 17.0

19.4 16.0 13.9 11.6 7.80 4.38

29.2 24.0 20.9 17.4 11.7 6.58

HSS8-HSS5

Shape HSS7×2×

1/4 3/16 1/8

HSS6×5×

1/2 3/8 5/16 1/4 3/16 1/8

HSS6×4×

1/2 3/8 5/16 1/4 3/16 1/8

HSS6×3×

1/2 3/8 5/16 1/4 3/16 1/8

HSS6×2×

3/8 5/16 1/4 3/16 1/8

HSS5×4×

1/2 3/8 5/16 1/4 3/16 1/8

X-Axis Y-Axis Mn /Ωb φb Mn Mn /Ωb φb Mn ASD LRFD ASD LRFD 17.5 26.4 6.94 10.4 13.7 20.5 4.67 7.01 9.49 14.3 2.63 3.95 39.5 31.8 27.4 22.7 17.5 9.80

59.4 47.8 41.2 34.1 26.3 14.7

34.8 28.0 24.2 20.0 14.5 8.12

52.3 42.1 36.3 30.1 21.8 12.2

33.6 27.3 23.6 19.6 15.2 9.65

50.5 41.0 35.4 29.4 22.8 14.5

25.2 20.5 17.8 14.8 10.8 6.07

37.9 30.8 26.7 22.2 16.2 9.12

27.7 22.7 19.8 16.5 12.8 8.89

41.7 34.2 29.7 24.8 19.3 13.4

16.7 13.8 12.1 10.1 7.46 4.20

25.1 20.8 18.2 15.2 11.2 6.31

18.2 16.0 13.4 10.5 7.33

27.4 24.0 20.2 15.8 11.0

25.1 20.6 17.9 14.9 11.6 7.45

37.8 30.9 26.9 22.4 17.4 11.2

7.94 11.9 7.05 10.6 5.99 9.01 4.46 6.70 2.52 3.79 21.5 17.6 15.3 12.8 9.95 5.72

32.2 26.5 23.0 19.2 15.0 8.60

Note: Values are reduced for compactness criteria, when appropriate. See Table 1-12A for limiting dimensions for compactness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 146

3–146

DESIGN OF FLEXURAL MEMBERS

Table 3-12 (continued)

Available Flexural Strength, kip-ft Rectangular HSS

HSS5-HSS2 Shape HSS5×3×

1/2 3/8 5/16 1/4 3/16 1/8

HSS5×21/2×

1/4 3/16 1/8

HSS5×2×

3/8 5/16 1/4 3/16 1/8

HSS4×3×

3/8 5/16 1/4 3/16 1/8

HSS4×21/2×

3/8 5/16 1/4 3/16 1/8

HSS4×2×

3/8 5/16 1/4 3/16 1/8

HSS31/2×21/2×

3/8 5/16 1/4 3/16 1/8

ASD

LRFD

Ωb = 1.67

φ b = 0.90

Fy = 46 ksi

X-Axis Mn /Ωb φb Mn ASD LRFD 20.3 30.5 16.8 25.3 14.7 22.1 12.4 18.6 9.66 14.5 6.73 10.1

Y-Axis Shape Mn /Ωb φb Mn ASD LRFD 14.0 21.1 HSS31/2×2× 11.7 17.6 10.3 15.4 8.65 13.0 HSS31/2×11/2× 6.79 10.2 3.96 5.95

11.1 16.7 8.70 13.1 6.08 9.14

6.78 10.2 5.35 8.04 3.14 4.72

13.1 11.6 9.81 7.74 5.43

19.7 17.4 14.7 11.6 8.16

6.62 5.91 5.05 4.02 2.37

11.7 10.4 8.76 6.90 4.84

17.7 15.6 13.2 10.4 7.27

9.58 14.4 8.47 12.7 7.17 10.8 5.66 8.50 3.73 5.61

10.3 15.5 9.12 13.7 7.75 11.6 6.13 9.22 4.32 6.49

9.95 8.88 7.59 6.04 3.57

HSS3×21/2×

5.30 4.76 4.10 3.29 2.21

7.96 7.16 6.17 4.94 3.32

8.24 12.4 7.35 11.1 6.28 9.44 5.00 7.51 3.54 5.32

6.48 5.79 4.96 3.96 2.81

9.74 8.71 7.46 5.95 4.22

1/8 1/4 3/16 1/8 5/16 1/4 3/16 1/8

HSS3×2×

5/16 1/4 3/16 1/8

HSS3×11/2×

1/4 3/16

HSS3×1×

3/16

1/8

7.34 11.0 HSS21/2×2× 6.53 9.82 5.57 8.37 4.42 6.65 2.94 4.42 HSS21/2×11/2×

8.82 13.3 7.88 11.8 6.74 10.1 5.37 8.07 3.80 5.71

1/4 3/16

1/8 1/4 3/16 1/8 1/4 3/16 1/8

HSS21/2×1×

3/16 1/8

HSS21/4×2×

3/16 1/8

HSS2×11/2×

3/16 1/8

HSS2×1×

3/16 1/8

X-Axis Y-Axis Mn /Ωb φb Mn Mn /Ωb φb Mn ASD LRFD ASD LRFD 5.41 8.13 3.63 5.46 4.33 6.51 2.92 4.40 3.09 4.64 2.09 3.15 4.53 3.67 2.64

6.82 5.51 3.96

2.43 1.99 1.45

3.65 2.99 2.17

5.75 4.95 3.96 2.82

8.65 7.44 5.96 4.24

5.06 4.36 3.49 2.49

7.60 6.55 5.25 3.74

4.85 4.21 3.40 2.44

7.29 6.33 5.11 3.66

3.62 3.16 2.56 1.84

5.45 4.75 3.85 2.77

3.47 2.83 2.05

5.21 4.26 3.09

2.09 1.73 1.26

3.14 2.59 1.90

2.27 1.67

3.41 2.51

0.991 1.49 0.747 1.12

3.14 2.56 1.86

4.73 3.86 2.79

2.69 2.20 1.59

4.04 3.30 2.39

2.54 2.10 1.54

3.81 3.16 2.31

1.75 1.46 1.08

2.64 2.20 1.62

1.64 1.22

2.46 1.84

0.826 1.24 0.629 0.945

2.19 1.59

3.28 2.39

2.01 1.47

1.47 1.09

2.20 1.64

1.20 1.80 0.893 1.34

1.10 0.840

1.66 1.26

0.661 0.994 0.511 0.768

3.03 2.20

Note: Values are reduced for compactness criteria, when appropriate. See Table 1-12A for limiting dimensions for compactness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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AVAILABLE FLEXURAL STRENGTH OF HSS

3–147

Table 3-13

Available Flexural Strength, kip-ft

Fy = 46 ksi

Square HSS Shape HSS16×16×

5/8 1/2 3/8 5/16

HSS14×14×

5/8 1/2 3/8 5/16

HSS12×12×

5/8 1/2 3/8 5/16 1/4 3/16

HSS10×10×

5/8 1/2 3/8 5/16 1/4 3/16

HSS9×9×

5/8 1/2 3/8 5/16 1/4 3/16 1/8

HSS8×8×

5/8 1/2 3/8 5/16 1/4 3/16 1/8

HSS7×7×

5/8 1/2 3/8 5/16 1/4 3/16 1/8

HSS6×6×

5/8 1/2 3/8 5/16 1/4 3/16 1/8

ASD

LRFD

Ωb = 1.67

φ b = 0.90

Mn /Ωb

φb Mn

ASD

LRFD

459 352 232 181 347 285 185 145 250 206 149 113 83.3 55.7 168 139 108 86.1 61.6 41.4 133 111 86.8 73.8 51.7 35.0 20.0 103 86.0 67.6 57.6 44.1 28.8 16.5 75.9 64.1 50.7 43.4 35.6 23.1 13.3 53.2 45.4 36.3 31.2 25.7 18.5 10.4

690 529 348 272 521 428 278 219 376 309 223 169 125 83.8 252 210 163 129 92.5 62.3 200 167 130 111 77.8 52.5 30.1 154 129 102 86.6 66.3 43.3 24.8 114 96.4 76.2 65.2 53.6 34.7 20.0 80.0 68.3 54.6 46.9 38.7 27.8 15.6

HSS16-HSS2

Shape HSS51/2×51/2×

3/8 5/16 1/4 3/16 1/8

HSS5×5×

1/2 3/8 5/16 1/4 3/16 1/8

HSS41/2×41/2×

1/2 3/8 5/16 1/4 3/16 1/8

HSS4×4×

1/2 3/8 5/16 1/4 3/16 1/8

HSS31/2×31/2×

3/8 5/16 1/4 3/16 1/8

HSS3×3×

3/8 5/16 1/4 3/16 1/8

HSS21/2×21/2×

5/16 1/4 3/16 1/8

HSS21/4×21/4×

1/4 3/16 1/8

HSS2×2×

1/4 3/16 1/8

Mn /Ωb

φb Mn

ASD

LRFD

30.0 25.9 21.4 16.4 8.98 30.0 24.3 21.0 17.5 13.5 7.67 23.4 19.2 16.7 13.9 10.8 6.43 17.7 14.7 12.8 10.8 8.42 5.48 10.8 9.50 8.03 6.33 4.44 7.46 6.66 5.69 4.53 3.21 4.32 3.75 3.03 2.17 2.93 2.39 1.73 2.21 1.83 1.34

45.1 38.9 32.2 24.6 13.5 45.0 36.5 31.6 26.2 20.3 11.5 35.2 28.8 25.1 20.9 16.3 9.66 26.6 22.1 19.3 16.2 12.7 8.23 16.2 14.3 12.1 9.51 6.67 11.2 10.0 8.55 6.81 4.82 6.49 5.64 4.55 3.27 4.41 3.60 2.60 3.33 2.75 2.02

Note: Values are reduced for compactness criteria, when appropriate. See Table 1-12A for limiting dimensions for compactness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

8:57 AM

Page 148

3–148

DESIGN OF FLEXURAL MEMBERS

Table 3-14

Available Flexural Strength, kip-ft HSS20HSS6.625

Round HSS

Shape

Mn /Ωb

φb Mn

ASD

LRFD

HSS20×

0.500 0.375f

371 273

558 410

HSS18×

0.500 0.375f

300 225

450 338

HSS16×

0.625 0.500 0.438 0.375 0.312f 0.250f

289 235 207 179 147 114

435 353 312 269 221 171

0.625 0.500 0.375 0.312 0.250f

220 179 136 115 88.8

331 268 205 172 133

HSS12.750×

0.500 0.375 0.250f

147 113 74.6

221 169 112

HSS10.750×

0.500 0.375 0.250

103 79.2 54.0

155 119 81.2

HSS10×

0.625 0.500 0.375 0.312 0.250 0.188f

108 88.7 68.2 57.5 46.6 34.0

163 133 102 86.4 70.0 51.2

0.500 0.375 0.312 0.250 0.188f

81.8 63.0 53.2 43.1 31.7

123 94.6 79.9 64.8 47.7

HSS14×

HSS9.625×

ASD

LRFD

Ωb = 1.67

φ b = 0.90

Fy = 42 ksi

f

Mn /Ωb

Shape

φb Mn

ASD

LRFD

HSS8.625×

0.625 0.500 0.375 0.322 0.250 0.188f

78.9 65.0 50.1 43.6 34.4 25.9

119 97.6 75.3 65.5 51.7 39.0

HSS7.625×

0.375 0.328

38.8 34.3

58.2 51.5

HSS7.500×

0.500 0.375 0.312 0.250 0.188

48.3 37.4 31.7 25.8 19.6

72.6 56.3 47.7 38.8 29.4

HSS7×

0.500 0.375 0.312 0.250 0.188 0.125f

41.7 32.4 27.5 22.4 17.0 11.0

62.7 48.7 41.3 33.6 25.5 16.6

HSS6.875×

0.500 0.375 0.312 0.250 0.188

40.1 31.2 26.5 21.6 16.4

60.3 46.9 39.8 32.4 24.6

HSS6.625×

0.500 0.432 0.375 0.312 0.280 0.250 0.188 0.125f

37.1 32.7 28.8 24.5 22.1 20.0 15.2 9.97

55.7 49.1 43.3 36.8 33.2 30.0 22.8 15.0

Shape exceeds compact limit for flexure with Fy = 42 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

8:57 AM

Page 149

AVAILABLE FLEXURAL STRENGTH OF HSS

3–149

Table 3-14 (continued)

Available Flexural Strength, kip-ft

Fy = 42 ksi

HSS6HSS1.66

Round HSS Shape

Mn /Ωb

φb Mn

ASD

LRFD

Mn /Ωb

Shape

φb Mn

ASD

LRFD

HSS6×

0.500 0.375 0.312 0.280 0.250 0.188 0.125f

29.9 23.4 19.9 18.0 16.2 12.4 8.30

45.0 35.2 29.9 27.0 24.4 18.6 12.5

HSS3.500×

0.313 0.300 0.250 0.216 0.203 0.188 0.125

6.30 6.08 5.22 4.59 4.35 4.04 2.79

9.47 9.14 7.85 6.90 6.53 6.07 4.19

HSS5.563×

0.500 0.375 0.258 0.188 0.134

25.4 19.9 14.3 10.6 7.69

38.2 29.9 21.4 15.9 11.6

HSS3×

HSS5.500×

0.500 0.375 0.258

24.8 19.4 13.9

37.2 29.2 20.9

0.250 0.216 0.203 0.188 0.152 0.134 0.125

3.75 3.31 3.13 2.92 2.42 2.15 2.02

5.63 4.97 4.71 4.38 3.63 3.23 3.04

HSS2.875×

0.500 0.375 0.312 0.258 0.250 0.188 0.125

20.1 15.9 13.5 11.4 11.1 8.50 5.80

30.2 23.8 20.4 17.1 16.7 12.8 8.72

0.250 0.203 0.188 0.125

3.42 2.86 2.66 1.85

5.14 4.30 4.00 2.78

HSS2.500×

0.250 0.188 0.125

2.52 1.98 1.38

3.79 2.97 2.08

HSS2.375× HSS4.500×

0.375 0.337 0.237 0.188 0.125

12.6 11.5 8.45 6.83 4.67

19.0 17.3 12.7 10.3 7.02

0.250 0.218 0.188 0.154 0.125

2.25 2.01 1.77 1.50 1.24

3.38 3.03 2.66 2.25 1.87

HSS1.900× HSS4×

0.313 0.250 0.237 0.226 0.220 0.188 0.125

8.41 6.94 6.60 6.33 6.19 5.34 3.67

12.6 10.4 9.91 9.51 9.31 8.03 5.51

0.188 0.145 0.120

1.09 0.883 0.746

1.64 1.33 1.12

HSS1.660×

0.140

0.639

0.961

HSS5×

ASD

LRFD

Ωb = 1.67

φ b = 0.90

f

Shape exceeds compact limit for flexure with Fy = 42 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3C:14th Ed.

3–150

2/24/11

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Page 150

DESIGN OF FLEXURAL MEMBERS

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

8:57 AM

Page 151

AVAILABLE FLEXURAL STRENGTH OF HSS

3–151

Table 3-15 Fy = 35 ksi

Pipe Available Flexural Strength, kip-ft Mn /Ωb ASD

φb Mn

Pipe 12 x-Strong Pipe 12 Std.

123 93.8

184 141

Pipe 10 x-Strong Pipe 10 Std.

86.0 64.4

129 96.8

Pipe 8 xx-Strong Pipe 8 x-Strong Pipe 8 Std.

87.2 54.1 36.3

131 81.4 54.6

Pipe 6 xx-Strong Pipe 6 x-Strong Pipe 6 Std.

47.9 27.3 18.5

72.0 41.0 27.8

Pipe 5 xx-Strong Pipe 5 x-Strong Pipe 5 Std.

29.1 16.6 11.9

43.7 24.9 17.9

Pipe 4 xx-Strong Pipe 4 x-Strong Pipe 4 Std.

16.6 9.65 7.07

24.9 14.5 10.6

Pipe 31/2 x-Strong Pipe 31/2 Std.

7.11 5.30

10.7 7.96

Pipe 3 xx-Strong Pipe 3 x-Strong Pipe 3 Std.

8.55 5.08 3.83

12.8 7.64 5.75

Shape

ASD

LRFD

Ωb = 1.67

φ b = 0.90

LRFD

Mn /Ωb ASD

φb Mn

Pipe 21/2 xx-Strong Pipe 21/2 x-Strong Pipe 21/2 Std.

5.08 3.09 2.39

7.64 4.64 3.59

Pipe 2 xx-Strong Pipe 2 x-Strong Pipe 2 Std.

2.79 1.68 1.25

4.19 2.53 1.87

Pipe 11/2 x-Strong Pipe 11/2 Std.

0.958 0.736

1.44 1.11

Pipe 11/4 x-Strong Pipe 11/4 Std.

0.686 0.533

1.03 0.801

Pipe 1 x-Strong Pipe 1 Std.

0.385 0.308

0.579 0.463

Pipe 3/4 x-Strong Pipe 3/4 Std.

0.207 0.164

0.311 0.247

Pipe 1/2 x-Strong Pipe 1/2 Std.

0.120 0.0969

0.180 0.146

Shape

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

LRFD

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2/24/11

8:57 AM

Page 152

3–152

DESIGN OF FLEXURAL MEMBERS

Table 3-16a

Available Shear Stress, ksi

Fy = 36 ksi

Tension Field Action NOT Included

Vn Ωv Aw

φvVn Aw

ASD

LRFD

12.9 12.0

19.4 18.0

10.0

15.0

8.00

12.0

7.00

10.5

6.00

9.00

5.00

7.50

4.00

6.00

3.00

4.50

2.00

3.00

ASD

LRFD

60

80

100

120

140

160

180 h ᎏᎏ tw

200

220

240

260

280

300

320 0.00 0.25

Ωv = 1.67 φ v = 0.90

0.50 0.75 1.00

1.25 1.50 1.75

2.00 2.25 2.50 2.75 3.00

a ᎏᎏ h

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

8:57 AM

Page 153

STRENGTH OF OTHER FLEXURAL MEMBERS

3–153

Table 3-16b

Available Shear Stress, ksi

Fy = 36 ksi

Tension Field Action Included

Vn Ωv Aw

φvVn Aw

ASD

LRFD

60 12.9

19.4

80

12.0

18.0

100

10.0

15.0

120

8.00

12.0

7.00

10.5

6.00

9.00

ASD

LRFD

140

160

180 h ᎏᎏ tw

200

220

240

260

280

300

320 0.00 0.25

Ωv = 1.67 φ v = 0.90

0.50 0.75 1.00

1.25 1.50 1.75

2.00 2.25 2.50 2.75 3.00

a ᎏᎏ h

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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8:57 AM

Page 154

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DESIGN OF FLEXURAL MEMBERS

Table 3-17a

Available Shear Stress, ksi

Fy = 50 ksi

Tension Field Action NOT Included

Vn Ωv Aw

φvVn Aw

ASD

LRFD

60

18.0 16.0

27.0 24.0

80

14.0 12.0

21.0 18.0

10.0

15.0

8.00 7.00

12.0 10.5

6.00

9.00

5.00

7.50

4.00

6.00

3.00

4.50

2.00

3.00

ASD

LRFD

100

120

140

160

180 h ᎏᎏ tw

200

220

240

260

280

300

320 0.00 0.25

Ωv = 1.67 φ v = 0.90

0.50 0.75 1.00

1.25 1.50 1.75

2.00 2.25 2.50 2.75 3.00

a ᎏᎏ h

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3C:14th Ed.

2/24/11

8:57 AM

Page 155

STRENGTH OF OTHER FLEXURAL MEMBERS

3–155

Table 3-17b

Available Shear Stress, ksi

Fy = 50 ksi

Tension Field Action Included 60

80

Vn Ωv Aw

φvVn Aw

ASD

LRFD

18.0

27.0

16.0

24.0

14.0

21.0

12.0

18.0

10.0

15.0

8.00

12.0

7.00

10.5

ASD

LRFD

100

120

140

160

180 h ᎏᎏ tw

200

220

240

260

280

300

320 0.00 0.25

Ωv = 1.67 φ v = 0.90

0.50 0.75 1.00

1.25 1.50 1.75

2.00 2.25 2.50 2.75 3.00

a ᎏᎏ h

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

8:57 AM

Page 156

3–156

DESIGN OF FLEXURAL MEMBERS

Table 3-18a

Raised Pattern Floor Plate Deflection-Controlled Applications Recommended Maximum Uniformly Distributed Service Load, lb/ft2 Plate thickness t, in.

Theoretical weight, lb/ft2

1/8

6.15

3/16

8.70

Span, ft 1.5 89.5

2 37.8

302

127

2.5

3

3.5

19.3

11.2

65.3

37.8

23.8

7.05

89.5

56.4

Moment of inertia per ft of width, in.4/ft 0.00195 0.00659

1/4

11.3

716

302

155

5/16

13.8

1400

590

302

175

110

0.0305

3/8

16.4

2420

1020

522

302

190

0.0527

1/2

21.5

5730

2420

1240

716

451

0.125

5/8

26.6

11200

4720

2420

1400

881

0.244

3/4

31.7

19300

8160

4180

2420

1520

0.422

7/8

36.8

30700

13000

6630

3840

2420

0.670

1

41.9

45800

19300

9900

5730

3610

1.00

11/4

52.1

89500

37800

19300

11200

7050

1.95

11/2

62.3

155000

65300

33400

19300

12200

3.38

13/4

72.5

246000

104000

53100

30700

19300

5.36

2

82.7

367000

155000

79200

45800

28900

Plate thickness t, in.

Theoretical weight, lb/ft2

3/16

8.70

Span, ft 4

4.5

5 8.16

0.0156

8.00 Moment of inertia per ft of width, in.4/ft

6

7

4.72

2.97

0.00659

7.05

0.0156

15.9

11.2

1/4

11.3

37.8

26.5

19.3

11.2

5/16

13.8

73.8

51.8

37.8

21.9

13.8

0.0305

3/8

16.4

127

89.5

65.3

37.8

23.8

0.0527

56.4

0.125

1/2

21.5

302

212

155

5/8

26.6

590

414

302

175

110

0.244

3/4

31.7

1020

716

522

302

190

0.422

7/8

36.8

1620

1140

829

480

302

0.670

1

41.9

2420

1700

1240

716

451

1.00

11/4

52.1

4720

3320

2420

1400

881

1.95

11/2

62.3

8160

5730

4180

2420

1520

3.38

13/4

72.5

13000

9100

6630

3840

2420

5.36

2

82.7

19300

13600

9900

5730

3610

8.00

89.5

Note: Material conforms to ASTM A786.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

8:57 AM

Page 157

STRENGTH OF OTHER FLEXURAL MEMBERS

3–157

Table 3-18b

Raised Pattern Floor Plate Flexural-Strength-Controlled Applications Recommended Maximum Uniformly Distributed Load, lb/ft2 Plate Theoretical thickness t , weight, in. lb/ft2 Design 1/8

6.15 8.70 11.3 13.8 16.4 21.5 26.6 31.7 36.8 41.9 52.1 62.3 72.5 82.7

3/16 1/4 5/16 3/8 1/2 5/8 3/4 7/8

1 11/4 11/2 13/4 2

Plate Theoretical thickness t , weight, in. lb/ft2 Design 3/16 1/4 5/16 3/8 1/2 5/8 3/4 7/8

1 11/4 11/2 13/4 2

8.70 11.3 13.8 16.4 21.5 26.6 31.7 36.8 41.9 52.1 62.3 72.5 82.7

Plastic section modulus 1.5 2.5 3.5 2 3 per ft of ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD width, in.3/ft Span, ft

222 499 887 1390 2000 3550 5540 7980 10900 14200 22200 31900 43500 56800

333 750 1330 2080 3000 5330 8330 12000 16300 21300 33300 48000 65300 85300

125 281 499 780 1120 2000 3120 4490 6110 7980 12500 18000 24500 31900

188 422 750 1170 1690 3000 4690 6750 9190 12000 18800 27000 36800 48000

79.8 180 319 499 719 1280 2000 2870 3910 5110 7980 11500 15600 20400

120 270 480 750 1080 1920 3000 4320 5880 7680 12000 17300 23500 30700

55.4 125 222 347 499 887 1390 2000 2720 3550 5540 7980 10900 14200

83.3 188 333 521 750 1330 2080 3000 4080 5330 8330 12000 16300 21300

40.7 91.7 163 255 367 652 1020 1470 2000 2610 4070 5870 7980 10400

61.2 138 245 383 551 980 1530 2200 3000 3920 6120 8820 12000 15700

0.0469 0.105 0.188 0.293 0.422 0.750 1.17 1.69 2.30 3.00 4.69 6.75 9.19 12.0

Plastic section modulus 4 5 7 4.5 6 per ft of ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD width, in.3/ft Span, ft

70.2 125 195 281 499 780 1120 1530 2000 3120 4490 6110 7980

105 188 293 422 750 1170 1690 2300 3000 4690 6750 9190 12000

55.4 98.6 154 222 394 616 887 1210 1580 2460 3550 4830 6310

83.3 148 231 333 593 926 1330 1810 2370 3700 5330 7260 9480

44.9 79.8 125 180 319 499 719 978 1280 2000 2870 3910 5110

67.5 120 188 270 480 750 1080 1470 1920 3000 4320 5880 7680

31.2 55.4 86.6 125 222 347 499 679 887 1390 2000 2720 3550

46.9 83.3 130 188 333 521 750 1020 1330 2080 3000 4080 5330

Note: Material conforms to ASTM A786.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

22.9 40.7 63.6 91.7 163 255 367 499 652 1020 1470 2000 2610

34.4 61.2 95.7 138 245 383 551 750 980 1530 2200 3000 3920

0.105 0.188 0.293 0.422 0.750 1.17 1.69 2.30 3.00 4.69 6.75 9.19 12.0

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DESIGN OF FLEXURAL MEMBERS

Table 3-19

Composite W-Shapes W40

Shape W40×297

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp kip-ft PNAc ASD LRFD 3320 4990 TFL 2 3 4 BFL 6 7

Y 2 b, in.

Y 1a

∑Qn

in.

kip

ASD

LRFD

ASD

0 0.413 0.825 1.24 1.65 4.58 8.17

4370 3710 3060 2410 1760 1420 1090

4770 4700 4610 4510 4400 4320 4180

7170 7060 6930 6790 6620 6490 6280

4880 4790 4690 4570 4450 4360 4210

2

2.5 LRFD

3

3.5 LRFD

ASD

LRFD

ASD

7330 7200 7050 6880 6680 6550 6320

4990 4880 4770 4630 4490 4390 4240

7500 7340 7160 6970 6750 6600 6370

5100 4980 4840 4700 4530 4430 4260

7660 7480 7280 7060 6820 6650 6410

W40×294

3170

4760

TFL 0 2 0.483 3 0.965 4 1.45 BFL 1.93 6 5.71 7 10.0

4310 3730 3150 2570 1990 1540 1080

4770 4710 4630 4540 4430 4300 4080

7180 7080 6960 6820 6660 6470 6130

4880 4800 4710 4600 4480 4340 4110

7340 7220 7080 6920 6740 6520 6170

4990 4900 4790 4670 4530 4380 4130

7500 7360 7200 7010 6810 6580 6210

5100 4990 4870 4730 4580 4420 4160

7660 7500 7320 7110 6880 6640 6250

W40×278

2970

4460

TFL 0 2 0.453 3 0.905 4 1.36 BFL 1.81 6 5.67 7 10.1

4120 3570 3030 2490 1940 1490 1030

4540 4480 4410 4320 4220 4100 3870

6820 6730 6620 6490 6350 6160 5820

4640 4570 4480 4380 4270 4130 3900

6970 6860 6730 6590 6420 6210 5860

4740 4660 4560 4440 4320 4170 3920

7130 7000 6850 6680 6490 6270 5900

4850 4750 4630 4510 4370 4210 3950

7280 7130 6960 6770 6570 6320 5930

W40×277

3120

4690

TFL 2 3 4 BFL 6 7

0 0.395 0.790 1.19 1.58 4.20 7.58

4080 3450 2830 2200 1580 1300 1020

4440 4370 4290 4200 4100 4030 3920

6680 6580 6450 6310 6160 6060 5890

4540 4460 4360 4260 4130 4060 3940

6830 6700 6560 6400 6210 6110 5930

4650 4550 4440 4310 4170 4090 3970

6980 6830 6670 6480 6270 6150 5970

4750 4630 4510 4370 4210 4130 4000

7140 6960 6770 6560 6330 6200 6010

W40×264

2820

4240

TFL 2 3 4 BFL 6 7

0 0.433 0.865 1.30 1.73 5.53 9.92

3870 3360 2840 2330 1810 1390 968

4250 4190 4120 4040 3950 3840 3630

6390 6300 6200 6080 5940 5770 5460

4350 4280 4190 4100 4000 3870 3660

6530 6430 6300 6170 6010 5820 5500

4440 4360 4270 4160 4040 3910 3680

6680 6550 6410 6250 6080 5870 5540

4540 4440 4340 4220 4090 3940 3710

6820 6680 6520 6340 6150 5930 5570

ASD

LRFD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67 φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 159

COMPOSITE BEAM SELECTION TABLES

3–159

Table 3-19 (continued) Fy = 50 ksi

Composite W-Shapes Available Strength in Flexure, kip-ft

W40

W40×297

5210 5070 4920 4760 4580 4460 4290

7820 7620 7390 7150 6880 6710 6450

5310 5160 5000 4820 4620 4500 4320

7990 7760 7510 7240 6950 6760 6490

5420 5250 5070 4880 4670 4530 4340

8150 7900 7620 7330 7010 6810 6530

Y 2 b, in. 5.5 ASD LRFD 5530 8320 5350 8040 5150 7740 4940 7420 4710 7080 4570 6870 4370 6570

W40×294

5200 5080 4950 4800 4630 4460 4190

7820 7640 7430 7210 6960 6700 6290

5310 5180 5020 4860 4680 4490 4210

7980 7780 7550 7300 7030 6760 6330

5420 5270 5100 4920 4730 4530 4240

8150 7920 7670 7400 7110 6810 6370

5530 5360 5180 4990 4780 4570 4270

8310 8060 7790 7500 7180 6870 6410

5630 5450 5260 5050 4830 4610 4290

8470 8200 7910 7590 7260 6930 6450

5740 5550 5340 5120 4880 4650 4320

8630 8340 8020 7690 7330 6990 6500

5850 5640 5420 5180 4930 4690 4350

8790 8480 8140 7790 7410 7040 6540

W40×278

4950 4830 4710 4570 4420 4250 3970

7440 7270 7080 6870 6640 6380 5970

5050 4920 4780 4630 4470 4280 4000

7590 7400 7190 6960 6710 6440 6010

5150 5010 4860 4690 4510 4320 4030

7750 7530 7300 7050 6780 6490 6050

5260 5100 4930 4750 4560 4360 4050

7900 7670 7420 7150 6860 6550 6090

5360 5190 5010 4820 4610 4390 4080

8060 7800 7530 7240 6930 6600 6130

5460 5280 5090 4880 4660 4430 4100

8210 7940 7640 7330 7000 6660 6170

5560 5370 5160 4940 4710 4470 4130

8360 8070 7760 7430 7080 6720 6200

W40×277

4850 4720 4580 4420 4250 4160 4020

7290 7090 6880 6640 6390 6250 6040

4950 4810 4650 4480 4290 4190 4050

7440 7220 6980 6730 6450 6300 6080

5050 4890 4720 4530 4330 4220 4070

7590 7350 7090 6810 6510 6350 6120

5150 4980 4790 4590 4370 4260 4100

7750 7480 7200 6890 6570 6400 6160

5260 5060 4860 4640 4410 4290 4120

7900 7610 7300 6970 6630 6450 6200

5360 5150 4930 4700 4450 4320 4150

8050 7740 7410 7060 6690 6500 6230

5460 5240 5000 4750 4490 4350 4170

8210 7870 7510 7140 6750 6540 6270

W40×264

4630 4530 4410 4280 4130 3980 3730

6970 6800 6620 6430 6210 5980 5610

4730 4610 4480 4330 4180 4010 3760

7110 6930 6730 6520 6280 6030 5640

4830 4690 4550 4390 4230 4050 3780

7260 7060 6840 6600 6350 6080 5680

4920 4780 4620 4450 4270 4080 3800

7400 7180 6940 6690 6420 6140 5720

5020 4860 4690 4510 4320 4120 3830

7550 7310 7050 6780 6490 6190 5750

5120 4950 4760 4570 4360 4150 3850

7690 7430 7160 6860 6550 6240 5790

5210 5030 4830 4630 4410 4190 3880

7840 7560 7260 6950 6620 6290 5830

Shape

4 4.5 5 ASD LRFD ASD LRFD ASD LRFD

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 5640 5440 5220 5000 4750 4600 4400

8480 8180 7850 7510 7140 6920 6610

5750 5530 5300 5060 4800 4640 4430

8640 8310 7970 7600 7210 6970 6650

5860 5620 5380 5120 4840 4670 4450

8810 8450 8080 7690 7280 7030 6690

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 160

3–160

DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W40

Shape W40×249

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp kip-ft PNAc ASD LRFD 2790 4200 TFL 2 3 4 BFL 6 7

Y 2 b, in.

Y 1a

∑Qn

in.

kip

ASD

LRFD

ASD

0 0.355 0.710 1.07 1.42 4.03 7.45

3680 3110 2550 1990 1430 1180 919

3980 3920 3850 3770 3680 3620 3520

5980 5890 5780 5660 5520 5440 5290

4070 4000 3910 3820 3710 3650 3540

2

2.5 LRFD

3

3.5 LRFD

ASD

LRFD

ASD

6120 6010 5880 5740 5580 5480 5320

4160 4070 3970 3870 3750 3680 3560

6260 6120 5970 5810 5630 5530 5360

4250 4150 4040 3920 3780 3710 3590

6390 6240 6070 5890 5690 5570 5390

W40×235

2520

3790

TFL 2 3 4 BFL 6 7

0 0.395 0.790 1.19 1.58 5.16 9.44

3460 2980 2510 2040 1570 1220 864

3770 3720 3650 3580 3510 3410 3250

5660 5580 5490 5390 5270 5130 4880

3850 3790 3720 3640 3540 3440 3270

5790 5700 5590 5460 5330 5180 4920

3940 3860 3780 3690 3580 3470 3290

5920 5810 5680 5540 5390 5220 4950

4030 3940 3840 3740 3620 3500 3310

6050 5920 5780 5620 5450 5270 4980

W40×215

2410

3620

TFL 2 3 4 BFL 6 7

0 0.305 0.610 0.915 1.22 3.80 7.29

3180 2690 2210 1730 1250 1020 794

3410 3350 3300 3230 3160 3110 3020

5120 5040 4950 4850 4740 4670 4540

3490 3420 3350 3270 3190 3130 3040

5240 5140 5040 4920 4790 4710 4570

3560 3490 3410 3320 3220 3160 3060

5360 5240 5120 4980 4840 4750 4600

3640 3560 3460 3360 3250 3180 3080

5480 5340 5200 5050 4880 4780 4630

W40×211

2260

3400

TFL 2 3 4 BFL 6 7

0 0.355 0.710 1.07 1.42 5.00 9.35

3110 2690 2270 1850 1430 1100 776

3360 3320 3260 3200 3140 3050 2900

5050 4990 4910 4810 4710 4590 4370

3440 3380 3320 3250 3170 3080 2920

5170 5090 4990 4880 4770 4630 4390

3520 3450 3380 3300 3210 3110 2940

5290 5190 5080 4950 4820 4670 4420

3590 3520 3430 3340 3240 3140 2960

5400 5290 5160 5020 4870 4710 4450

W40×199

2170

3260

TFL 2 3 4 BFL 6 7

0 0.268 0.535 0.803 1.07 4.09 8.04

2940 2520 2090 1670 1250 992 735

3130 3090 3040 2980 2920 2860 2760

4710 4640 4560 4480 4390 4300 4150

3210 3150 3090 3020 2950 2890 2780

4820 4730 4640 4540 4430 4340 4170

3280 3210 3140 3060 2980 2910 2800

4930 4830 4720 4600 4480 4380 4200

3350 3280 3190 3110 3010 2940 2810

5040 4920 4800 4670 4530 4410 4230

ASD

LRFD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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8:58 AM

Page 161

COMPOSITE BEAM SELECTION TABLES

3–161

Table 3-19 (continued) Fy = 50 ksi

Composite W-Shapes Available Strength in Flexure, kip-ft

W40

W40×249

4350 4230 4100 3970 3820 3740 3610

6530 6360 6170 5960 5740 5610 5430

4440 4310 4170 4020 3850 3770 3630

6670 6470 6260 6030 5790 5660 5460

4530 4380 4230 4060 3890 3790 3660

6810 6590 6360 6110 5850 5700 5500

Y 2 b, in. 5.5 ASD LRFD 4620 6950 4460 6710 4290 6450 4110 6180 3930 5900 3820 5750 3680 5530

W40×235

4110 4010 3910 3790 3660 3540 3330

6180 6030 5870 5690 5500 5310 5010

4200 4090 3970 3840 3700 3570 3360

6310 6140 5960 5770 5560 5360 5040

4280 4160 4030 3890 3740 3600 3380

6440 6260 6060 5850 5620 5410 5080

4370 4240 4090 3940 3780 3630 3400

6570 6370 6150 5920 5680 5450 5110

4460 4310 4160 3990 3820 3660 3420

6700 6480 6250 6000 5740 5500 5140

4540 4390 4220 4040 3860 3690 3440

6830 6590 6340 6080 5800 5540 5170

4630 4460 4280 4090 3900 3720 3460

6960 6700 6440 6150 5860 5590 5210

W40×215

3720 3620 3520 3400 3280 3210 3100

5600 5450 5280 5110 4930 4820 4660

3800 3690 3570 3440 3310 3230 3120

5720 5550 5370 5180 4980 4860 4690

3880 3760 3630 3490 3340 3260 3140

5830 5650 5450 5240 5020 4900 4720

3960 3820 3680 3530 3370 3280 3160

5950 5750 5530 5310 5070 4940 4750

4040 3890 3740 3570 3400 3310 3180

6070 5850 5620 5370 5120 4970 4780

4120 3960 3790 3620 3440 3340 3200

6190 5950 5700 5440 5160 5010 4810

4200 4030 3850 3660 3470 3360 3220

6310 6050 5780 5500 5210 5050 4840

W40×211

3670 3580 3490 3390 3280 3160 2980

5520 5390 5250 5090 4930 4760 4480

3750 3650 3550 3430 3310 3190 3000

5640 5490 5330 5160 4980 4800 4510

3830 3720 3600 3480 3350 3220 3020

5750 5590 5420 5230 5030 4840 4540

3900 3790 3660 3530 3390 3250 3040

5870 5690 5500 5300 5090 4880 4570

3980 3850 3720 3570 3420 3270 3060

5980 5790 5590 5370 5140 4920 4600

4060 3920 3770 3620 3460 3300 3080

6100 5890 5670 5440 5200 4960 4630

4140 3990 3830 3660 3490 3330 3100

6220 5990 5760 5510 5250 5000 4660

W40×199

3430 3340 3250 3150 3040 2960 2830

5150 5020 4880 4730 4570 4450 4260

3500 3400 3300 3190 3070 2990 2850

5260 5110 4960 4790 4620 4490 4280

3570 3460 3350 3230 3110 3010 2870

5370 5210 5030 4860 4670 4530 4310

3650 3530 3400 3270 3140 3040 2890

5480 5300 5110 4920 4710 4560 4340

3720 3590 3450 3310 3170 3060 2910

5590 5400 5190 4980 4760 4600 4370

3790 3650 3510 3360 3200 3090 2920

5700 5490 5270 5040 4810 4640 4390

3870 3720 3560 3400 3230 3110 2940

5810 5580 5350 5110 4850 4670 4420

Shape

4 4.5 5 ASD LRFD ASD LRFD ASD LRFD

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 4710 4540 4360 4160 3960 3850 3700

7080 6820 6550 6260 5950 5790 5560

4800 4620 4420 4210 4000 3880 3730

7220 6940 6640 6330 6010 5840 5600

4900 4700 4480 4260 4030 3910 3750

7360 7060 6740 6410 6060 5880 5630

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

8:58 AM

Page 162

3–162

DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W40-W36

Shape W40×183

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp kip-ft PNAc ASD LRFD 1930 2900 TFL 2 3 4 BFL 6 7

Y 2 b, in.

Y 1a

∑Qn

in.

kip

ASD

LRFD

ASD

0 0.300 0.600 0.900 1.20 4.77 9.25

2670 2310 1960 1600 1250 958 666

2860 2820 2780 2730 2680 2610 2480

4300 4240 4180 4100 4020 3920 3720

2930 2880 2830 2770 2710 2630 2490

2

2.5 LRFD

3

3.5 LRFD

ASD

LRFD

ASD

4400 4330 4250 4160 4070 3950 3750

2990 2940 2880 2810 2740 2650 2510

4500 4410 4320 4220 4110 3990 3770

3060 2990 2920 2850 2770 2680 2530

4600 4500 4400 4280 4160 4030 3800

W40×167

1730

2600

TFL 2 3 4 BFL 6 7

0 0.258 0.515 0.773 1.03 4.95 9.82

2470 2160 1860 1550 1250 933 616

2620 2590 2550 2510 2470 2390 2240

3940 3890 3840 3770 3710 3600 3370

2680 2640 2600 2550 2490 2420 2260

4030 3970 3900 3830 3760 3630 3400

2740 2700 2640 2590 2530 2440 2280

4120 4050 3970 3890 3800 3670 3420

2800 2750 2690 2630 2560 2460 2290

4220 4130 4040 3950 3850 3700 3440

W40×149

1490

2240

TFL 0 2 0.208 3 0.415 4 0.623 BFL 0.830 6 5.15 7 10.4

2190 1950 1700 1460 1210 879 548

2310 2280 2250 2220 2190 2110 1950

3470 3430 3380 3340 3290 3170 2930

2360 2330 2290 2260 2220 2130 1960

3550 3500 3450 3390 3330 3200 2950

2420 2380 2340 2290 2250 2150 1980

3630 3570 3510 3450 3380 3240 2970

2470 2430 2380 2330 2280 2180 1990

3710 3650 3580 3500 3420 3270 2990

W36×302

3190

4800

TFL 2 3 4 BFL 6 7

0 0.420 0.840 1.26 1.68 4.06 6.88

4450 3750 3050 2350 1640 1380 1110

4590 4510 4420 4310 4190 4120 4030

6890 6780 6640 6480 6290 6200 6050

4700 4600 4490 4370 4230 4160 4050

7060 6920 6750 6570 6360 6250 6090

4810 4700 4570 4430 4270 4190 4080

7230 7060 6870 6650 6420 6300 6130

4920 4790 4640 4490 4310 4230 4110

7390 7200 6980 6740 6480 6350 6170

W36×282

2970

4460

TFL 2 3 4 BFL 6 7

0 0.393 0.785 1.18 1.57 4.00 6.84

4150 3490 2840 2190 1540 1290 1040

4250 4180 4090 4000 3890 3830 3740

6390 6280 6150 6010 5840 5760 5620

4350 4270 4170 4050 3930 3860 3760

6540 6410 6260 6090 5900 5800 5660

4460 4350 4240 4110 3970 3890 3790

6700 6540 6370 6170 5960 5850 5690

4560 4440 4310 4160 4000 3930 3810

6850 6670 6470 6260 6020 5900 5730

ASD

LRFD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COMPOSITE BEAM SELECTION TABLES

3–163

Table 3-19 (continued) Fy = 50 ksi

Composite W-Shapes Available Strength in Flexure, kip-ft

W40-W36

W40×183

3130 3050 2970 2890 2800 2700 2540

4700 4590 4470 4340 4210 4060 3820

3190 3110 3020 2930 2830 2730 2560

4800 4670 4540 4400 4260 4100 3850

3260 3170 3070 2970 2860 2750 2580

4900 4760 4620 4460 4300 4130 3870

Y 2 b, in. 5.5 ASD LRFD 3320 5000 3220 4850 3120 4690 3010 4520 2890 4350 2770 4170 2590 3900

W40×167

2870 2800 2740 2670 2590 2490 2310

4310 4210 4110 4010 3900 3740 3470

2930 2860 2780 2710 2620 2510 2320

4400 4290 4180 4070 3940 3770 3490

2990 2910 2830 2740 2650 2530 2340

4490 4380 4250 4120 3990 3810 3510

3050 2970 2880 2780 2690 2560 2350

4580 4460 4320 4180 4040 3840 3540

3110 3020 2920 2820 2720 2580 2370

4680 4540 4390 4240 4080 3880 3560

3170 3070 2970 2860 2750 2600 2380

4770 4620 4460 4300 4130 3910 3580

3240 3130 3020 2900 2780 2630 2400

4860 4700 4530 4360 4180 3950 3600

W40×149

2520 2470 2420 2370 2310 2200 2000

3790 3720 3640 3560 3470 3300 3010

2580 2520 2460 2400 2340 2220 2020

3880 3790 3700 3610 3520 3340 3030

2630 2570 2510 2440 2370 2240 2030

3960 3860 3770 3670 3560 3370 3050

2690 2620 2550 2480 2400 2260 2040

4040 3940 3830 3720 3610 3400 3070

2740 2670 2590 2510 2430 2290 2060

4120 4010 3890 3780 3650 3430 3090

2800 2720 2630 2550 2460 2310 2070

4200 4080 3960 3830 3700 3470 3110

2850 2770 2680 2580 2490 2330 2090

4290 4160 4020 3880 3740 3500 3130

W36×302

5030 4880 4720 4540 4350 4260 4140

7560 7340 7090 6830 6540 6410 6220

5140 4980 4800 4600 4390 4300 4160

7730 7480 7210 6920 6600 6460 6260

5250 5070 4870 4660 4430 4330 4190

7890 7620 7320 7010 6660 6510 6300

5360 5160 4950 4720 4470 4370 4220

8060 7760 7440 7090 6730 6560 6340

5470 5260 5020 4780 4520 4400 4250

8230 7900 7550 7180 6790 6610 6380

5580 5350 5100 4840 4560 4430 4270

8390 8040 7670 7270 6850 6670 6420

5700 5440 5180 4900 4600 4470 4300

8560 8180 7780 7360 6910 6720 6470

W36×282

4660 4530 4380 4220 4040 3960 3840

7010 6810 6580 6340 6080 5950 5770

4770 4610 4450 4270 4080 3990 3870

7170 6940 6690 6420 6130 6000 5810

4870 4700 4520 4330 4120 4020 3890

7320 7070 6790 6500 6190 6050 5850

4970 4790 4590 4380 4160 4050 3920

7480 7200 6900 6580 6250 6090 5890

5080 4880 4660 4440 4200 4090 3940

7630 7330 7010 6670 6310 6140 5930

5180 4960 4730 4490 4230 4120 3970

7790 7460 7110 6750 6360 6190 5970

5280 5050 4800 4540 4270 4150 4000

7940 7590 7220 6830 6420 6240 6010

Shape

4 4.5 5 ASD LRFD ASD LRFD ASD LRFD

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 3390 3280 3170 3050 2920 2800 2610

5100 4930 4760 4580 4400 4200 3920

3460 3340 3220 3090 2960 2820 2630

5200 5020 4840 4640 4440 4240 3950

3520 3400 3270 3130 2990 2850 2640

5300 5110 4910 4700 4490 4280 3970

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W36

Shape W36×262

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp kip-ft PNAc ASD LRFD 2740 4130 TFL 2 3 4 BFL 6 7

Y2b, in.

Y 1a

∑Qn

in.

kip

ASD

LRFD

ASD

0 0.360 0.720 1.08 1.44 3.96 6.96

3860 3260 2660 2070 1470 1220 965

3940 3870 3800 3710 3610 3560 3460

5920 5820 5710 5580 5430 5350 5210

4040 3960 3860 3760 3650 3590 3490

2

2.5 LRFD

3

3.5 LRFD

ASD

LRFD

ASD

6070 5940 5810 5660 5490 5390 5240

4130 4040 3930 3820 3690 3620 3510

6210 6070 5910 5730 5540 5440 5280

4230 4120 4000 3870 3720 3650 3540

6350 6190 6010 5810 5600 5480 5310

W36×256

2590

3900

TFL 2 3 4 BFL 6 7

0 0.433 0.865 1.30 1.73 5.18 8.90

3770 3240 2710 2180 1650 1300 941

3890 3830 3760 3680 3590 3490 3330

5850 5760 5650 5530 5390 5250 5010

3980 3910 3830 3730 3630 3520 3350

5990 5880 5750 5610 5450 5300 5040

4080 3990 3900 3790 3670 3560 3380

6130 6000 5860 5690 5520 5350 5080

4170 4070 3960 3840 3710 3590 3400

6270 6120 5960 5780 5580 5390 5110

W36×247

2570

3860

TFL 2 3 4 BFL 6 7

0 0.338 0.675 1.01 1.35 3.95 7.02

3630 3070 2510 1950 1400 1150 906

3680 3620 3550 3470 3380 3330 3240

5530 5440 5340 5220 5090 5000 4860

3770 3700 3610 3520 3420 3360 3260

5670 5560 5430 5290 5140 5050 4900

3860 3770 3680 3570 3450 3390 3280

5800 5670 5530 5360 5190 5090 4930

3950 3850 3740 3620 3490 3410 3300

5940 5790 5620 5440 5240 5130 4970

W36×232

2340

3510

TFL 2 3 4 BFL 6 7

0 0.393 0.785 1.18 1.57 5.04 8.78

3400 2930 2450 1980 1500 1180 850

3490 3430 3370 3300 3220 3140 2990

5240 5160 5070 4960 4840 4720 4500

3570 3510 3430 3350 3260 3170 3010

5370 5270 5160 5040 4900 4760 4530

3660 3580 3500 3400 3300 3200 3040

5500 5380 5250 5110 4960 4810 4560

3740 3650 3560 3450 3330 3230 3060

5620 5490 5350 5190 5010 4850 4590

W36×231

2400

3610

TFL 2 3 4 BFL 6 7

0 0.315 0.630 0.945 1.26 3.88 7.03

3410 2890 2370 1850 1330 1090 853

3450 3390 3330 3250 3170 3120 3030

5180 5090 5000 4890 4770 4690 4560

3530 3460 3380 3300 3210 3150 3050

5310 5200 5090 4960 4820 4730 4590

3620 3530 3440 3350 3240 3170 3070

5430 5310 5180 5030 4870 4770 4620

3700 3610 3500 3390 3270 3200 3090

5560 5420 5270 5100 4920 4810 4650

ASD

LRFD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COMPOSITE BEAM SELECTION TABLES

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Table 3-19 (continued) Fy = 50 ksi

Composite W-Shapes Available Strength in Flexure, kip-ft

W36

W36×262

4320 4200 4060 3920 3760 3680 3560

6500 6310 6110 5890 5650 5530 5350

4420 4280 4130 3970 3800 3710 3580

6640 6430 6210 5970 5710 5570 5390

4520 4360 4200 4020 3830 3740 3610

6790 6560 6310 6040 5760 5620 5420

Y 2 b, in. 5.5 ASD LRFD 4610 6930 4440 6680 4260 6410 4070 6120 3870 5820 3770 5670 3630 5460

W36×256

4260 4150 4030 3900 3750 3620 3420

6410 6240 6060 5860 5640 5440 5150

4360 4230 4100 3950 3790 3650 3450

6550 6360 6160 5940 5700 5490 5180

4450 4320 4170 4010 3830 3690 3470

6690 6490 6260 6020 5760 5540 5220

4550 4400 4230 4060 3880 3720 3500

6830 6610 6360 6100 5830 5590 5250

4640 4480 4300 4120 3920 3750 3520

6970 6730 6470 6190 5890 5640 5290

4730 4560 4370 4170 3960 3780 3540

7120 6850 6570 6270 5950 5690 5320

4830 4640 4440 4220 4000 3820 3570

7260 6970 6670 6350 6010 5740 5360

W36×247

4040 3930 3800 3670 3520 3440 3330

6080 5900 5710 5510 5300 5170 5000

4130 4000 3860 3720 3560 3470 3350

6210 6020 5810 5580 5350 5220 5030

4220 4080 3930 3760 3590 3500 3370

6350 6130 5900 5660 5400 5260 5070

4310 4160 3990 3810 3630 3530 3390

6480 6250 6000 5730 5450 5300 5100

4400 4230 4050 3860 3660 3560 3420

6620 6360 6090 5800 5510 5350 5140

4500 4310 4110 3910 3700 3590 3440

6760 6480 6180 5880 5560 5390 5170

4590 4390 4180 3960 3730 3620 3460

6890 6590 6280 5950 5610 5430 5200

W36×232

3830 3730 3620 3500 3370 3260 3080

5750 5600 5440 5260 5070 4890 4630

3910 3800 3680 3550 3410 3290 3100

5880 5710 5530 5330 5120 4940 4660

4000 3870 3740 3600 3450 3310 3120

6010 5820 5620 5410 5180 4980 4690

4080 3950 3800 3650 3480 3340 3140

6130 5930 5710 5480 5240 5030 4720

4170 4020 3860 3700 3520 3370 3160

6260 6040 5800 5560 5290 5070 4750

4250 4090 3920 3750 3560 3400 3180

6390 6150 5900 5630 5350 5110 4790

4330 4160 3980 3800 3600 3430 3210

6520 6260 5990 5710 5410 5160 4820

W36×231

3790 3680 3560 3440 3310 3230 3120

5690 5530 5350 5170 4970 4850 4680

3870 3750 3620 3480 3340 3260 3140

5820 5640 5440 5240 5020 4890 4720

3960 3820 3680 3530 3370 3280 3160

5950 5750 5530 5310 5070 4930 4750

4040 3890 3740 3580 3410 3310 3180

6070 5850 5620 5380 5120 4980 4780

4130 3970 3800 3620 3440 3340 3200

6200 5960 5710 5440 5170 5020 4810

4210 4040 3860 3670 3470 3360 3220

6330 6070 5800 5510 5220 5060 4840

4300 4110 3920 3720 3500 3390 3240

6460 6180 5890 5580 5270 5100 4880

Shape

4 4.5 5 ASD LRFD ASD LRFD ASD LRFD

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 4710 4530 4330 4120 3910 3800 3660

7080 6800 6510 6200 5870 5710 5490

4810 4610 4400 4180 3940 3830 3680

7220 6920 6610 6280 5930 5760 5530

4900 4690 4460 4230 3980 3860 3700

7370 7050 6710 6350 5980 5800 5570

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W36

Shape W36×210

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp kip-ft PNAc ASD LRFD 2080 3120 TFL 2 3 4 BFL 6 7

Y 2 b, in.

Y 1a

∑Qn

in.

kip

ASD

LRFD

ASD

0 0.340 0.680 1.02 1.36 5.04 9.03

3100 2680 2270 1850 1440 1100 774

3140 3100 3050 2990 2920 2840 2690

4720 4660 4580 4490 4390 4260 4040

3220 3160 3100 3030 2960 2860 2710

2

2.5 LRFD

3

3.5 LRFD

ASD

LRFD

ASD

4840 4760 4660 4560 4440 4300 4070

3300 3230 3160 3080 2990 2890 2730

4960 4860 4750 4630 4500 4350 4100

3370 3300 3220 3130 3030 2920 2750

5070 4960 4830 4700 4550 4390 4130

W36×194

1910

2880

TFL 2 3 4 BFL 6 7

0 0.315 0.630 0.945 1.26 4.93 8.94

2850 2470 2090 1710 1330 1020 713

2880 2840 2790 2740 2680 2600 2470

4330 4270 4200 4120 4030 3910 3710

2950 2900 2840 2780 2710 2630 2480

4440 4360 4270 4180 4080 3950 3730

3020 2960 2900 2820 2750 2650 2500

4540 4450 4350 4240 4130 3990 3760

3090 3020 2950 2870 2780 2680 2520

4650 4540 4430 4310 4180 4030 3790

W36×182

1790

2690

TFL 2 3 4 BFL 6 7

0 0.295 0.590 0.885 1.18 4.89 8.91

2680 2320 1970 1610 1250 961 670

2690 2660 2610 2560 2510 2440 2310

4050 3990 3930 3850 3770 3670 3470

2760 2710 2660 2600 2540 2460 2330

4150 4080 4000 3910 3820 3700 3500

2830 2770 2710 2640 2570 2490 2340

4250 4170 4070 3970 3870 3740 3520

2900 2830 2760 2680 2600 2510 2360

4350 4250 4150 4040 3910 3770 3550

W36×170

1670

2510

TFL 2 3 4 BFL 6 7

0 0.275 0.550 0.825 1.10 4.83 8.91

2500 2170 1840 1510 1180 903 625

2510 2470 2430 2390 2340 2270 2150

3770 3720 3660 3590 3520 3420 3230

2570 2530 2480 2430 2370 2300 2170

3860 3800 3730 3650 3560 3450 3250

2630 2580 2520 2460 2400 2320 2180

3960 3880 3790 3700 3600 3480 3280

2690 2630 2570 2500 2430 2340 2200

4050 3960 3860 3760 3650 3520 3300

W36×160

1560

2340

TFL 2 3 4 BFL 6 7

0 0.255 0.510 0.765 1.02 4.82 8.96

2350 2040 1740 1430 1130 857 588

2350 2310 2280 2240 2190 2130 2010

3530 3480 3420 3360 3290 3200 3020

2400 2360 2320 2270 2220 2150 2020

3610 3550 3490 3410 3340 3230 3040

2460 2410 2360 2310 2250 2170 2040

3700 3630 3550 3470 3380 3260 3060

2520 2470 2410 2340 2280 2190 2050

3790 3710 3620 3520 3420 3290 3080

ASD

LRFD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COMPOSITE BEAM SELECTION TABLES

3–167

Table 3-19 (continued) Fy = 50 ksi

Composite W-Shapes Available Strength in Flexure, kip-ft

W36

W36×210

3450 3370 3270 3170 3060 2950 2760

5190 5060 4920 4770 4610 4430 4160

3530 3430 3330 3220 3100 2970 2780

5300 5160 5000 4840 4660 4470 4180

3610 3500 3390 3260 3140 3000 2800

5420 5260 5090 4910 4710 4510 4210

Y 2 b, in. 5.5 ASD LRFD 3680 5540 3570 5360 3440 5170 3310 4980 3170 4770 3030 4550 2820 4240

W36×194

3160 3090 3000 2910 2810 2710 2540

4760 4640 4510 4370 4230 4070 3810

3240 3150 3050 2950 2840 2730 2560

4860 4730 4590 4440 4280 4100 3840

3310 3210 3100 2990 2880 2760 2570

4970 4820 4670 4500 4330 4140 3870

3380 3270 3160 3040 2910 2780 2590

5080 4910 4740 4560 4380 4180 3900

3450 3330 3210 3080 2940 2810 2610

5180 5010 4820 4630 4430 4220 3920

3520 3390 3260 3120 2980 2830 2630

5290 5100 4900 4690 4480 4260 3950

3590 3450 3310 3160 3010 2860 2640

5400 5190 4980 4760 4530 4300 3980

W36×182

2960 2890 2810 2720 2630 2530 2380

4450 4340 4220 4100 3960 3810 3570

3030 2950 2860 2760 2670 2560 2390

4550 4430 4300 4160 4010 3850 3600

3100 3000 2910 2810 2700 2580 2410

4650 4520 4370 4220 4050 3880 3620

3160 3060 2960 2850 2730 2610 2430

4750 4600 4440 4280 4100 3920 3650

3230 3120 3010 2890 2760 2630 2440

4850 4690 4520 4340 4150 3950 3670

3300 3180 3050 2930 2790 2650 2460

4950 4780 4590 4400 4190 3990 3700

3360 3240 3110 2970 2820 2680 2480

5060 4860 4660 4460 4240 4030 3720

W36×170

2760 2690 2620 2540 2460 2360 2210

4140 4040 3930 3820 3690 3550 3320

2820 2740 2660 2580 2490 2390 2230

4240 4120 4000 3870 3740 3580 3350

2880 2800 2710 2610 2520 2410 2240

4330 4200 4070 3930 3780 3620 3370

2940 2850 2750 2650 2550 2430 2260

4430 4290 4140 3990 3830 3650 3400

3010 2910 2800 2690 2580 2450 2270

4520 4370 4210 4040 3870 3690 3420

3070 2960 2850 2730 2600 2480 2290

4610 4450 4280 4100 3910 3720 3440

3130 3010 2890 2770 2630 2500 2310

4710 4530 4350 4160 3960 3750 3470

W36×160

2580 2520 2450 2380 2300 2210 2070

3880 3780 3680 3580 3460 3330 3110

2640 2570 2490 2410 2330 2230 2080

3970 3860 3750 3630 3510 3360 3130

2700 2620 2540 2450 2360 2260 2100

4050 3940 3810 3680 3550 3390 3150

2760 2670 2580 2490 2390 2280 2110

4140 4010 3880 3740 3590 3420 3170

2810 2720 2620 2520 2420 2300 2130

4230 4090 3940 3790 3630 3450 3190

2870 2770 2670 2560 2450 2320 2140

4320 4170 4010 3840 3680 3490 3220

2930 2820 2710 2590 2470 2340 2150

4410 4240 4070 3900 3720 3520 3240

Shape

4 4.5 5 ASD LRFD ASD LRFD ASD LRFD

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 3760 3630 3500 3360 3210 3060 2840

5650 5460 5260 5040 4820 4590 4270

3840 3700 3550 3400 3240 3080 2860

5770 5560 5340 5110 4880 4640 4300

3920 3770 3610 3450 3280 3110 2880

5880 5660 5430 5180 4930 4680 4330

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 168

3–168

DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W36-W33

Shape W36×150

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp kip-ft PNAc ASD LRFD 1450 2180 TFL 2 3 4 BFL 6 7

Y2b, in.

Y1a

∑Qn

in.

kip

ASD

LRFD

ASD

0 0.235 0.470 0.705 0.940 4.82 9.09

2220 1930 1650 1370 1090 820 554

2210 2180 2140 2110 2070 2000 1880

3310 3270 3220 3160 3110 3010 2830

2260 2220 2180 2140 2090 2020 1900

2

2.5 LRFD

3

3.5 LRFD

ASD

LRFD

ASD

3400 3340 3280 3220 3150 3040 2850

2320 2270 2220 2170 2120 2040 1910

3480 3410 3340 3270 3190 3070 2870

2370 2320 2270 2210 2150 2060 1930

3560 3490 3410 3320 3230 3100 2890

W36×135

1270

1910

TFL 2 3 4 BFL 6 7

0 0.198 0.395 0.593 0.790 4.92 9.49

2000 1760 1520 1280 1050 773 499

1970 1950 1920 1890 1860 1790 1670

2960 2930 2880 2840 2790 2700 2510

2020 1990 1960 1920 1880 1810 1680

3040 2990 2940 2890 2830 2720 2530

2070 2030 2000 1950 1910 1830 1690

3110 3060 3000 2940 2870 2750 2540

2120 2080 2030 1990 1940 1850 1710

3190 3120 3060 2980 2910 2780 2560

W33×221

2140

3210

TFL 2 3 4 BFL 6 7

0 0.320 0.640 0.960 1.28 3.67 6.42

3270 2760 2250 1750 1240 1030 816

3090 3030 2970 2900 2820 2770 2700

4640 4560 4460 4360 4240 4170 4060

3170 3100 3030 2940 2850 2800 2720

4760 4660 4550 4420 4290 4210 4090

3250 3170 3080 2990 2880 2830 2740

4890 4770 4630 4490 4330 4250 4120

3330 3240 3140 3030 2910 2850 2760

5010 4870 4720 4560 4380 4290 4150

W33×201

1930

2900

TFL 2 3 4 BFL 6 7

0 0.288 0.575 0.863 1.15 3.65 6.52

2960 2500 2050 1600 1150 944 739

2780 2730 2680 2620 2550 2500 2430

4180 4110 4020 3930 3830 3760 3650

2850 2790 2730 2660 2580 2530 2450

4290 4200 4100 3990 3870 3800 3680

2930 2860 2780 2700 2600 2550 2470

4400 4290 4180 4050 3920 3830 3710

3000 2920 2830 2740 2630 2570 2490

4510 4390 4250 4110 3960 3870 3740

W33×169

1570

2360

TFL 2 3 4 BFL 6 7

0 0.305 0.610 0.915 1.22 4.28 7.66

2480 2120 1770 1420 1070 845 619

2330 2300 2250 2210 2150 2100 2010

3510 3450 3390 3310 3230 3150 3020

2400 2350 2300 2240 2180 2120 2020

3600 3530 3450 3370 3270 3190 3040

2460 2400 2340 2280 2200 2140 2040

3690 3610 3520 3420 3310 3220 3070

2520 2460 2390 2310 2230 2160 2060

3790 3690 3590 3470 3350 3250 3090

ASD

LRFD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COMPOSITE BEAM SELECTION TABLES

3–169

Table 3-19 (continued) Fy = 50 ksi

Composite W-Shapes Available Strength in Flexure, kip-ft

W36-W33

W36×150

2430 2370 2310 2240 2170 2080 1940

3650 3560 3470 3370 3270 3130 2910

2480 2420 2350 2280 2200 2100 1950

3730 3630 3530 3420 3310 3160 2940

2540 2460 2390 2310 2230 2130 1970

3810 3700 3590 3470 3350 3200 2960

Y 2 b, in. 5.5 ASD LRFD 2590 3900 2510 3780 2430 3650 2340 3520 2260 3390 2150 3230 1980 2980

W36×135

2170 2120 2070 2020 1960 1870 1720

3260 3190 3110 3030 2950 2810 2580

2220 2170 2110 2050 1990 1890 1730

3340 3250 3170 3080 2990 2840 2600

2270 2210 2150 2080 2010 1910 1740

3410 3320 3230 3130 3030 2870 2620

2320 2250 2180 2110 2040 1930 1750

3490 3390 3280 3180 3070 2900 2640

2370 2300 2220 2150 2070 1950 1770

3560 3450 3340 3220 3110 2930 2660

2420 2340 2260 2180 2090 1970 1780

3640 3520 3400 3270 3150 2960 2670

2470 2380 2300 2210 2120 1990 1790

3710 3580 3450 3320 3190 2990 2690

W33×221 3410 3310 3200 3070 2940 2880 2780

5130 4970 4800 4620 4430 4320 4180

3490 3380 3250 3120 2980 2900 2800

5250 5080 4890 4690 4470 4360 4210

3580 3450 3310 3160 3010 2930 2820

5380 5180 4970 4750 4520 4400 4240

3660 3510 3360 3210 3040 2950 2840

5500 5280 5060 4820 4570 4440 4270

3740 3580 3420 3250 3070 2980 2860

5620 5390 5140 4880 4610 4480 4300

3820 3650 3480 3290 3100 3010 2880

5740 5490 5220 4950 4660 4520 4330

3900 3720 3530 3340 3130 3030 2900

5860 5590 5310 5010 4710 4560 4360

W33×201 3070 2980 2880 2770 2660 2600 2500

4620 4480 4330 4170 4000 3900 3760

3150 3040 2930 2810 2690 2620 2520

4730 4570 4410 4230 4040 3940 3790

3220 3110 2980 2850 2720 2640 2540

4840 4670 4480 4290 4090 3980 3820

3300 3170 3030 2890 2750 2670 2560

4950 4760 4560 4350 4130 4010 3850

3370 3230 3090 2930 2780 2690 2580

5060 4860 4640 4410 4170 4050 3880

3440 3290 3140 2970 2810 2720 2600

5170 4950 4720 4470 4220 4080 3900

3520 3360 3190 3010 2830 2740 2620

5290 5040 4790 4530 4260 4120 3930

W33×169 2580 2510 2430 2350 2260 2180 2070

3880 3770 3650 3530 3390 3280 3110

2640 2560 2470 2380 2290 2200 2090

3970 3850 3720 3580 3430 3310 3140

2700 2610 2520 2420 2310 2230 2100

4070 3930 3790 3630 3470 3350 3160

2770 2670 2560 2450 2340 2250 2120

4160 4010 3850 3690 3510 3380 3180

2830 2720 2610 2490 2370 2270 2130

4250 4090 3920 3740 3550 3410 3210

2890 2770 2650 2520 2390 2290 2150

4340 4170 3990 3790 3600 3440 3230

2950 2830 2700 2560 2420 2310 2160

4440 4250 4050 3850 3640 3470 3250

Shape

4 4.5 5 ASD LRFD ASD LRFD ASD LRFD

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 2650 2560 2470 2380 2280 2170 1990

3980 3850 3710 3580 3430 3260 3000

2700 2610 2510 2410 2310 2190 2010

4060 3920 3780 3630 3470 3290 3020

2760 2660 2550 2450 2340 2210 2020

4140 3990 3840 3680 3510 3320 3040

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W33-W30

Shape W33×152

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp kip-ft PNAc ASD LRFD 1390 2100 TFL 2 3 4 BFL 6 7

Y 2 b, in.

Y 1a

∑Qn

in.

kip

ASD

LRFD

ASD

0 0.265 0.530 0.795 1.06 4.34 7.91

2250 1940 1630 1320 1020 788 561

2100 2070 2030 1990 1950 1890 1800

3160 3110 3050 2990 2920 2850 2710

2160 2120 2070 2020 1970 1910 1820

2

2.5 LRFD

3

3.5 LRFD

ASD

LRFD

ASD

3240 3180 3110 3040 2960 2870 2730

2210 2160 2110 2060 2000 1930 1830

3330 3250 3170 3090 3000 2900 2750

2270 2210 2150 2090 2020 1950 1840

3410 3330 3240 3140 3040 2930 2770

W33×141

1280

1930

TFL 2 3 4 BFL 6 7

0 0.240 0.480 0.720 0.960 4.34 8.08

2080 1800 1520 1250 971 745 519

1930 1900 1870 1830 1790 1740 1650

2900 2860 2810 2760 2700 2620 2480

1980 1950 1910 1860 1820 1760 1660

2980 2930 2870 2800 2730 2650 2500

2030 1990 1950 1900 1840 1780 1680

3060 2990 2920 2850 2770 2680 2520

2090 2040 1980 1930 1870 1800 1690

3140 3060 2980 2900 2810 2700 2540

W33×130

1170

1750

TFL 2 3 4 BFL 6 7

0 0.214 0.428 0.641 0.855 4.39 8.30

1920 1670 1420 1180 932 705 479

1770 1750 1720 1690 1650 1600 1510

2660 2630 2580 2540 2490 2410 2270

1820 1790 1750 1720 1680 1620 1520

2740 2690 2640 2580 2520 2440 2290

1870 1830 1790 1750 1700 1640 1530

2810 2750 2690 2620 2560 2460 2300

1920 1870 1820 1780 1720 1660 1540

2880 2810 2740 2670 2590 2490 2320

W33×118

1040

1560

TFL 2 3 4 BFL 6 7

0 0.185 0.370 0.555 0.740 4.47 8.56

1740 1520 1310 1100 884 659 434

1600 1580 1550 1520 1500 1450 1350

2400 2370 2330 2290 2250 2170 2030

1640 1610 1580 1550 1520 1460 1360

2470 2420 2380 2330 2280 2200 2050

1680 1650 1620 1580 1540 1480 1370

2530 2480 2430 2370 2320 2220 2060

1730 1690 1650 1610 1560 1500 1380

2600 2540 2480 2420 2350 2250 2080

W30×116

943

1420

TFL 2 3 4 BFL 6 7

0 0.213 0.425 0.638 0.850 3.98 7.43

1710 1490 1260 1040 818 623 428

1450 1430 1400 1370 1340 1300 1230

2180 2150 2110 2060 2020 1960 1840

1490 1460 1430 1400 1360 1320 1240

2240 2200 2150 2100 2050 1980 1860

1540 1500 1460 1430 1380 1330 1250

2310 2260 2200 2140 2080 2000 1870

1580 1540 1500 1450 1400 1350 1260

2370 2310 2250 2180 2110 2030 1890

ASD

LRFD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COMPOSITE BEAM SELECTION TABLES

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Table 3-19 (continued) Fy = 50 ksi

Composite W-Shapes Available Strength in Flexure, kip-ft

W33-W30

W33×152 2320 2260 2190 2120 2050 1970 1860

3490 3400 3300 3190 3080 2960 2790

2380 2310 2230 2160 2070 1990 1870

3580 3470 3360 3240 3110 2990 2810

2440 2360 2280 2190 2100 2010 1890

3660 3540 3420 3290 3150 3020 2830

Y 2 b, in. 5.5 ASD LRFD 2490 3750 2410 3620 2320 3480 2220 3340 2120 3190 2030 3050 1900 2850

W33×141 2140 2080 2020 1960 1890 1820 1700

3210 3130 3040 2940 2840 2730 2560

2190 2130 2060 1990 1920 1840 1720

3290 3200 3100 2990 2880 2760 2580

2240 2170 2100 2020 1940 1850 1730

3370 3260 3150 3040 2920 2790 2600

2290 2220 2140 2050 1960 1870 1740

3450 3330 3210 3080 2950 2820 2620

2350 2260 2170 2080 1990 1890 1750

3520 3400 3270 3130 2990 2840 2640

2400 2310 2210 2110 2010 1910 1770

3600 3470 3320 3180 3020 2870 2660

2450 2350 2250 2140 2040 1930 1780

3680 3530 3380 3220 3060 2900 2680

W33×130 1960 1910 1860 1800 1750 1670 1560

2950 2880 2800 2710 2630 2510 2340

2010 1960 1900 1830 1770 1690 1570

3020 2940 2850 2760 2660 2540 2360

2060 2000 1930 1860 1790 1710 1580

3100 3000 2900 2800 2690 2570 2370

2110 2040 1970 1890 1820 1730 1590

3170 3060 2960 2850 2730 2590 2390

2150 2080 2000 1920 1840 1740 1600

3240 3130 3010 2890 2760 2620 2410

2200 2120 2040 1950 1860 1760 1620

3310 3190 3060 2930 2800 2650 2430

2250 2160 2070 1980 1890 1780 1630

3380 3250 3120 2980 2830 2670 2450

W33×118 1770 1730 1680 1630 1580 1510 1390

2660 2600 2530 2460 2380 2270 2100

1810 1760 1710 1660 1610 1530 1410

2730 2650 2580 2500 2420 2300 2110

1860 1800 1750 1690 1630 1550 1420

2790 2710 2630 2540 2450 2320 2130

1900 1840 1780 1720 1650 1560 1430

2860 2770 2670 2580 2480 2350 2140

1940 1880 1810 1740 1670 1580 1440

2920 2820 2720 2620 2510 2370 2160

1990 1920 1850 1770 1700 1590 1450

2990 2880 2770 2660 2550 2400 2180

2030 1950 1880 1800 1720 1610 1460

3050 2940 2820 2700 2580 2420 2190

W30×116 1620 1580 1530 1480 1420 1360 1270

2440 2370 2300 2220 2140 2050 1910

1660 1610 1560 1500 1440 1380 1280

2500 2420 2340 2260 2170 2070 1920

1710 1650 1590 1530 1470 1390 1290

2570 2480 2390 2300 2200 2100 1940

1750 1690 1620 1550 1490 1410 1300

2630 2540 2440 2340 2230 2120 1950

1790 1720 1650 1580 1510 1430 1310

2690 2590 2490 2380 2260 2140 1970

1830 1760 1680 1610 1530 1440 1320

2760 2650 2530 2410 2290 2170 1990

1880 1800 1720 1630 1550 1460 1330

2820 2700 2580 2450 2320 2190 2000

Shape

4 4.5 5 ASD LRFD ASD LRFD ASD LRFD

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 2550 2450 2360 2250 2150 2050 1910

3830 3690 3540 3390 3230 3080 2880

2600 2500 2400 2290 2170 2070 1930

3910 3760 3600 3440 3270 3110 2900

2660 2550 2440 2320 2200 2090 1940

4000 3830 3660 3490 3310 3140 2920

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W30-W27

Shape W30×108

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp kip-ft PNAc ASD LRFD 863 1300 TFL 2 3 4 BFL 6 7

Y 1a

∑Qn

in.

kip

Y 2 b, in. 2

2.5 LRFD

ASD

LRFD

ASD

0 1590 0.190 1390 0.380 1190 0.570 987 0.760 787 4.04 592 7.63 396

1340 1320 1290 1270 1240 1200 1120

2010 1980 1940 1910 1870 1800 1690

1380 1350 1320 1290 1260 1210 1130

3

3.5 LRFD

ASD

LRFD

ASD

2070 2030 1990 1940 1900 1830 1700

1420 1380 1350 1320 1280 1230 1140

2130 2080 2030 1980 1930 1850 1720

1460 1420 1380 1340 1300 1240 1150

2190 2130 2080 2020 1960 1870 1730

W30×99

778

1170

TFL 2 3 4 BFL 6 7

0 1450 0.168 1270 0.335 1100 0.503 922 0.670 747 4.19 555 7.88 363

1220 1200 1180 1160 1140 1100 1020

1830 1800 1780 1740 1710 1650 1530

1260 1230 1210 1180 1160 1110 1030

1890 1850 1820 1780 1740 1670 1540

1290 1260 1240 1210 1170 1120 1040

1940 1900 1860 1810 1770 1690 1560

1330 1300 1260 1230 1190 1140 1050

2000 1950 1900 1850 1790 1710 1570

W30×90

706

1060

TFL 2 3 4 BFL 6 7

0 1320 0.153 1160 0.305 998 0.458 839 0.610 681 4.01 505 7.76 329

1100 1080 1070 1050 1030 989 920

1650 1630 1600 1570 1540 1490 1380

1130 1110 1090 1070 1040 1000 928

1700 1670 1640 1600 1570 1510 1400

1160 1140 1110 1090 1060 1010 937

1750 1710 1680 1640 1590 1530 1410

1200 1170 1140 1110 1080 1030 945

1800 1760 1710 1670 1620 1540 1420

W27×102

761

1140

TFL 2 3 4 BFL 6 7

0 1500 0.208 1290 0.415 1090 0.623 878 0.830 670 3.40 523 6.27 375

1160 1140 1120 1090 1060 1030 984

1750 1720 1680 1640 1600 1550 1480

1200 1170 1150 1110 1080 1050 993

1810 1770 1720 1670 1620 1570 1490

1240 1210 1170 1140 1100 1060 1000

1860 1810 1760 1710 1650 1590 1510

1280 1240 1200 1160 1110 1070 1010

1920 1860 1800 1740 1670 1610 1520

W27×94

694

1040

TFL 2 3 4 BFL 6 7

0 1380 0.186 1190 0.373 1010 0.559 821 0.745 635 3.45 490 6.41 345

1060 1040 1020 1000 976 947 897

1600 1570 1540 1500 1470 1420 1350

1100 1070 1050 1020 992 959 905

1650 1610 1580 1530 1490 1440 1360

1130 1100 1070 1040 1010 971 914

1700 1660 1610 1570 1510 1460 1370

1170 1130 1100 1060 1020 983 922

1750 1700 1650 1600 1540 1480 1390

ASD

LRFD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

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COMPOSITE BEAM SELECTION TABLES

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Table 3-19 (continued) Fy = 50 ksi

Composite W-Shapes Available Strength in Flexure, kip-ft

W30-W27

W30×108 1490 1450 1410 1370 1320 1260 1160

2250 2190 2120 2050 1980 1890 1750

1530 1490 1440 1390 1340 1270 1170

2310 2240 2170 2090 2010 1910 1760

1570 1520 1470 1420 1360 1290 1180

2370 2290 2210 2130 2040 1940 1780

Y 2 b, in. 5.5 ASD LRFD 1610 2430 1560 2340 1500 2260 1440 2170 1380 2070 1300 1960 1190 1790

W30×99

1360 1330 1290 1250 1210 1150 1050

2050 2000 1940 1880 1820 1730 1590

1400 1360 1320 1270 1230 1160 1060

2100 2040 1980 1920 1850 1750 1600

1440 1390 1350 1300 1250 1180 1070

2160 2090 2020 1950 1880 1770 1610

1470 1420 1370 1320 1270 1190 1080

2210 2140 2060 1990 1910 1790 1630

1510 1460 1400 1340 1290 1210 1090

2270 2190 2100 2020 1930 1810 1640

1540 1490 1430 1370 1300 1220 1100

2320 2230 2150 2050 1960 1830 1650

1580 1520 1460 1390 1320 1230 1110

2380 2280 2190 2090 1990 1850 1670

W30×90

1230 1200 1160 1130 1090 1040 953

1850 1800 1750 1700 1640 1560 1430

1260 1230 1190 1150 1110 1050 961

1900 1840 1790 1730 1670 1580 1440

1300 1260 1210 1170 1130 1070 969

1950 1890 1830 1760 1700 1600 1460

1330 1280 1240 1190 1150 1080 978

2000 1930 1860 1790 1720 1620 1470

1360 1310 1260 1210 1160 1090 986

2050 1970 1900 1820 1750 1640 1480

1390 1340 1290 1230 1180 1100 994

2100 2020 1940 1860 1770 1660 1490

1430 1370 1310 1260 1200 1120 1000

2150 2060 1970 1890 1800 1680 1510

W27×102 1310 1270 1230 1180 1130 1090 1020

1970 1910 1840 1770 1700 1630 1540

1350 1300 1250 1200 1150 1100 1030

2030 1960 1880 1810 1720 1650 1550

1390 1340 1280 1220 1160 1110 1040

2090 2010 1930 1840 1750 1670 1560

1430 1370 1310 1250 1180 1130 1050

2140 2060 1970 1870 1770 1690 1580

1460 1400 1340 1270 1200 1140 1060

2200 2100 2010 1900 1800 1710 1590

1500 1430 1360 1290 1210 1150 1070

2260 2150 2050 1940 1830 1730 1610

1540 1460 1390 1310 1230 1160 1080

2310 2200 2090 1970 1850 1750 1620

W27×94

1810 1750 1690 1630 1560 1500 1400

1240 1190 1150 1110 1050 1010 940

1860 1790 1730 1660 1590 1510 1410

1270 1220 1170 1120 1070 1020 948

1910 1840 1760 1690 1610 1530 1430

1300 1250 1200 1140 1090 1030 957

1960 1880 1800 1720 1630 1550 1440

1340 1280 1220 1160 1100 1040 965

2010 1930 1840 1750 1660 1570 1450

1370 1310 1250 1180 1120 1060 974

2060 1970 1880 1780 1680 1590 1460

1410 1340 1270 1210 1130 1070 983

2120 2020 1920 1810 1700 1610 1480

Shape

4 4.5 5 ASD LRFD ASD LRFD ASD LRFD

1200 1160 1120 1080 1040 996 931

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 1650 1590 1530 1470 1400 1320 1200

2480 2390 2300 2200 2100 1980 1810

1690 1630 1560 1490 1420 1330 1210

2540 2450 2340 2240 2130 2000 1820

1730 1660 1590 1510 1440 1350 1220

2600 2500 2390 2280 2160 2030 1840

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W27-W24

Shape W27×84

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp kip-ft PNAc ASD LRFD 609 915 TFL 2 3 4 BFL 6 7

Y 1a

∑Qn

in.

kip

Y 2 b, in. 2

2.5 LRFD

ASD

LRFD

ASD

0 1240 0.160 1080 0.320 915 0.480 755 0.640 595 3.53 452 6.64 309

946 929 911 892 872 843 793

1420 1400 1370 1340 1310 1270 1190

977 956 934 911 887 855 800

3

3.5 LRFD

ASD

LRFD

ASD

1470 1440 1400 1370 1330 1280 1200

1010 983 957 930 902 866 808

1510 1480 1440 1400 1360 1300 1210

1040 1010 980 949 916 877 816

1560 1520 1470 1430 1380 1320 1230

W24×94

634

953

TFL 2 3 4 BFL 6 7

0 1390 0.219 1190 0.438 988 0.656 790 0.875 591 3.05 469 5.43 346

978 957 934 909 881 858 819

1470 1010 1440 987 1400 959 1370 928 1320 896 1290 869 1230 828

1520 1480 1440 1400 1350 1310 1240

1050 1020 983 948 911 881 837

1570 1530 1480 1430 1370 1320 1260

1080 1050 1010 968 926 893 845

1630 1570 1510 1450 1390 1340 1270

W24×84

559

840

TFL 2 3 4 BFL 6 7

0 1240 0.193 1060 0.385 888 0.578 714 0.770 540 3.02 425 5.48 309

866 848 828 806 783 761 725

1300 1270 1240 1210 1180 1140 1090

897 874 850 824 797 772 733

1350 1310 1280 1240 1200 1160 1100

927 901 872 842 810 782 740

1390 1350 1310 1270 1220 1180 1110

958 927 894 860 824 793 748

1440 1390 1340 1290 1240 1190 1120

W24×76

499

750

TFL 2 3 4 BFL 6 7

0 1120 0.170 967 0.340 814 0.510 662 0.680 509 2.99 394 5.59 280

780 764 747 728 708 687 651

1170 1150 1120 1090 1060 1030 979

808 788 767 745 721 697 658

1210 1180 1150 1120 1080 1050 989

836 812 787 761 734 707 665

1260 1220 1180 1140 1100 1060 1000

863 836 807 778 746 716 672

1300 1260 1210 1170 1120 1080 1010

W24×68

442

664

TFL 2 3 4 BFL 6 7

0 1010 0.146 874 0.293 743 0.439 611 0.585 480 3.04 366 5.80 251

695 681 666 651 635 613 577

1040 1020 1000 978 954 922 867

720 703 685 666 647 623 583

1080 1060 1030 1000 972 936 876

745 725 704 681 658 632 589

1120 1090 1060 1020 990 949 886

770 746 722 697 670 641 595

1160 1120 1090 1050 1010 963 895

ASD

LRFD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COMPOSITE BEAM SELECTION TABLES

3–175

Table 3-19 (continued) Fy = 50 ksi

Composite W-Shapes Available Strength in Flexure, kip-ft

W27-W24

W27×84

1070 1040 1000 968 931 888 824

1610 1100 1650 1130 1700 1560 1060 1600 1090 1640 1510 1030 1540 1050 1580 1450 987 1480 1010 1510 1400 946 1420 961 1440 1340 900 1350 911 1370 1240 831 1250 839 1260

Y 2 b, in. 5.5 ASD LRFD 1160 1750 1120 1680 1070 1610 1020 1540 976 1470 922 1390 847 1270

W24×94

1120 1080 1030 988 940 904 854

1680 1620 1550 1480 1410 1360 1280

1220 1160 1110 1050 985 939 880

W24×84

989 954 916 878 837 804 756

1490 1020 1530 1050 1580 1080 1630 1110 1670 1140 1720 1170 1760 1430 980 1470 1010 1510 1030 1550 1060 1590 1090 1630 1110 1670 1380 939 1410 961 1440 983 1480 1010 1510 1030 1540 1050 1580 1320 895 1350 913 1370 931 1400 949 1430 967 1450 985 1480 1260 851 1280 864 1300 878 1320 891 1340 904 1360 918 1380 1210 814 1220 825 1240 835 1260 846 1270 856 1290 867 1300 1140 764 1150 771 1160 779 1170 787 1180 794 1190 802 1210

W24×76

891 860 828 794 759 726 679

1340 1290 1240 1190 1140 1090 1020

919 884 848 811 772 736 686

1380 1330 1270 1220 1160 1110 1030

947 909 868 827 784 746 693

1420 1370 1310 1240 1180 1120 1040

975 933 889 844 797 756 700

1470 1000 1510 1030 1550 1060 1590 1400 957 1440 981 1470 1010 1510 1340 909 1370 929 1400 950 1430 1270 860 1290 877 1320 893 1340 1200 810 1220 823 1240 835 1260 1140 766 1150 775 1170 785 1180 1050 707 1060 714 1070 721 1080

W24×68

795 768 741 712 682 650 602

1190 1150 1110 1070 1030 977 904

820 790 759 727 694 659 608

1230 1190 1140 1090 1040 990 914

845 812 778 742 706 668 614

1270 1220 1170 1120 1060 1000 923

870 834 796 758 718 677 620

1310 1250 1200 1140 1080 1020 933

Shape

4 4.5 5 ASD LRFD ASD LRFD ASD LRFD

1150 1110 1060 1010 955 916 863

1730 1660 1590 1510 1440 1380 1300

1190 1130 1080 1030 970 928 871

1780 1710 1630 1540 1460 1390 1310

1830 1750 1660 1570 1480 1410 1320

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 1190 1140 1090 1040 991 933 854

1790 1720 1640 1570 1490 1400 1280

1220 1170 1120 1060 1010 945 862

1840 1760 1680 1600 1510 1420 1300

1250 1200 1140 1080 1020 956 870

1880 1800 1710 1620 1530 1440 1310

1250 1190 1130 1070 999 951 888

1890 1790 1700 1600 1500 1430 1340

1290 1220 1160 1090 1010 963 897

1940 1840 1740 1630 1520 1450 1350

1320 1250 1180 1110 1030 975 906

1990 1880 1770 1660 1550 1460 1360

895 855 815 773 730 686 627

1350 1290 1220 1160 1100 1030 942

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

920 877 833 788 742 696 633

1380 1320 1250 1180 1120 1050 951

945 899 852 804 754 705 639

1420 1350 1280 1210 1130 1060 961

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Page 176

3–176

DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W24-W21

Shape W24×62

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp kip-ft PNAc ASD LRFD 382 574 TFL 2 3 4 BFL 6 7

Y 2 b, in.

Y 1a

∑Qn

in.

kip

ASD

LRFD

ASD

2.5 LRFD

ASD

LRFD

ASD

3.5 LRFD

0 0.148 0.295 0.443 0.590 3.45 6.56

910 806 702 598 495 361 228

629 618 607 594 581 555 509

945 929 912 893 874 834 764

652 638 624 609 594 564 514

979 959 938 916 892 848 773

674 658 642 624 606 573 520

1010 990 964 938 911 862 781

697 679 659 639 618 582 526

1050 1020 991 961 929 875 790

2

3

W24×55

334

503

TFL 2 3 4 BFL 6 7

0 0.126 0.253 0.379 0.505 3.46 6.67

810 721 633 544 456 329 203

558 549 539 529 518 493 449

838 825 810 795 779 742 675

578 567 555 542 529 502 454

869 852 834 815 796 754 682

598 585 571 556 541 510 459

899 879 858 836 813 766 690

618 603 586 570 552 518 464

929 906 881 856 830 779 697

W21×73

429

645

TFL 2 3 4 BFL 6 7

0 1080 0.185 921 0.370 768 0.555 614 0.740 461 2.58 365 4.69 269

676 660 642 624 603 586 559

1020 992 966 937 907 881 840

703 683 662 639 615 595 566

1060 1030 994 960 924 895 851

730 706 681 654 626 604 573

1100 1060 1020 983 941 908 861

756 729 700 670 638 613 579

1140 1100 1050 1010 959 922 871

W21×68

399

600

TFL 2 3 4 BFL 6 7

0 1000 0.171 858 0.343 717 0.514 575 0.685 434 2.60 342 4.74 250

626 612 596 578 560 544 518

941 919 895 869 842 817 778

651 633 613 593 571 552 524

979 951 922 891 858 830 787

676 654 631 607 582 561 530

1020 983 949 912 874 843 797

701 676 649 621 593 569 536

1050 1020 976 934 891 856 806

W21×62

359

540

TFL 2 3 4 BFL 6 7

0 0.154 0.308 0.461 0.615 2.54 4.78

571 558 544 528 512 497 472

858 838 817 794 770 747 709

594 577 560 542 523 505 477

892 868 842 814 785 759 717

616 597 577 555 533 513 483

926 897 867 834 801 771 726

639 617 593 568 543 521 489

961 927 891 854 816 782 734

ASD

LRFD

915 788 662 535 408 318 229

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 177

COMPOSITE BEAM SELECTION TABLES

3–177

Table 3-19 (continued)

Composite W-Shapes

Fy = 50 ksi

Available Strength in Flexure, kip-ft

W24×62

720 1080 699 1050 677 1020 654 983 631 948 591 889 531 798

742 719 694 669 643 600 537

1120 1080 1040 1010 967 902 807

765 739 712 684 655 609 543

1150 1110 1070 1030 985 916 816

Y 2 b, in. 5.5 ASD LRFD 788 1180 759 1140 729 1100 699 1050 668 1000 618 929 548 824

W24×55

639 621 602 583 564 526 469

960 933 905 876 847 791 705

659 639 618 597 575 534 474

990 960 929 897 864 803 713

679 657 634 610 586 543 479

1020 987 953 917 881 816 720

699 675 650 624 598 551 484

W21×73

783 752 719 685 649 623 586

1180 1130 1080 1030 976 936 881

810 775 738 700 661 632 593

1220 1160 1110 1050 993 949 891

837 798 757 715 672 641 599

1260 1200 1140 1080 1010 963 901

W21×68

726 1090 697 1050 667 1000 636 956 603 907 578 868 543 816

751 719 685 650 614 586 549

1130 1080 1030 977 923 881 825

776 740 703 664 625 595 555

W21×62

662 636 610 582 553 529 494

685 656 626 595 563 536 500

1030 986 941 895 847 806 752

708 676 643 609 573 544 506

Shape

4 4.5 5 ASD LRFD ASD LRFD ASD LRFD

995 956 916 874 831 794 743

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 811 779 747 714 680 627 554

1220 1170 1120 1070 1020 943 833

833 799 764 729 692 636 560

1250 1200 1150 1100 1040 956 841

856 819 782 744 705 645 565

1290 1230 1180 1120 1060 970 850

1050 1010 976 938 898 828 728

719 693 665 637 609 559 489

1080 1040 1000 958 915 840 735

740 711 681 651 620 567 494

1110 1070 1020 978 932 853 743

760 729 697 665 632 576 499

1140 1100 1050 999 950 865 751

864 821 777 731 684 650 606

1300 1230 1170 1100 1030 977 911

890 844 796 746 695 659 613

1340 1270 1200 1120 1040 990 921

917 867 815 761 707 668 620

1380 1300 1220 1140 1060 1000 931

944 890 834 777 718 677 626

1420 1340 1250 1170 1080 1020 941

1170 1110 1060 999 939 894 834

801 761 721 679 636 603 561

1200 1140 1080 1020 956 907 844

826 783 739 693 647 612 568

1240 1180 1110 1040 972 920 853

851 804 757 708 657 620 574

1280 1210 1140 1060 988 933 862

876 826 774 722 668 629 580

1320 1240 1160 1080 1000 945 872

1060 1020 966 915 862 818 760

731 695 659 622 584 552 511

1100 1050 991 935 877 830 769

753 715 676 635 594 560 517

1130 1070 1020 955 893 842 777

776 735 692 649 604 568 523

1170 1100 1040 975 908 854 786

799 754 709 662 614 576 529

1200 1130 1070 995 923 866 795

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

W24-W21

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3C:14th Ed.

2/24/11

9:00 AM

Page 178

3–178

DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W21

Shape W21×57

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp kip-ft PNAc ASD LRFD 322 484 TFL 2 3 4 BFL 6 7

Y 2 b, in.

Y 1a

∑Qn

in.

kip

ASD

LRFD

ASD

2.5 LRFD

ASD

LRFD

ASD

3.5 LRFD

0 0.163 0.325 0.488 0.650 2.93 5.40

835 728 622 515 409 309 209

523 512 500 487 473 455 424

786 769 751 732 712 684 637

544 530 515 500 484 463 429

817 797 775 751 727 695 645

565 548 531 513 494 470 435

849 824 798 771 742 707 653

585 566 546 526 504 478 440

880 851 821 790 758 718 661

2

3

W21×55

314

473

TFL 2 3 4 BFL 6 7

0 0.131 0.261 0.392 0.522 2.62 5.00

810 703 595 488 381 292 203

501 490 478 466 453 437 411

753 737 719 700 681 657 618

521 508 493 478 462 445 417

784 763 741 719 695 668 626

542 525 508 490 472 452 422

814 789 764 737 709 679 634

562 543 523 502 481 459 427

844 816 786 755 723 690 641

W21×50

274

413

TFL 2 3 4 BFL 6 7

0 0.134 0.268 0.401 0.535 2.91 5.56

735 648 560 473 386 285 184

455 446 436 426 415 397 366

684 670 656 640 624 597 550

473 462 450 438 425 404 370

711 694 677 658 639 607 557

491 478 464 450 435 411 375

739 719 698 676 653 618 563

510 494 478 461 444 418 379

766 743 719 694 668 629 570

W21×48

265

398

TFL 2 3 4 BFL 6 7

0 0.108 0.215 0.323 0.430 2.71 5.26

705 617 530 442 355 266 176

433 424 414 404 394 379 352

650 637 623 608 592 569 529

450 439 428 415 403 385 356

677 660 643 624 606 579 535

468 455 441 426 412 392 361

703 683 662 641 619 589 542

485 470 454 437 421 398 365

730 706 682 658 632 599 549

W21×44

238

358

TFL 2 3 4 BFL 6 7

0 0.113 0.225 0.338 0.450 2.92 5.71

650 577 504 431 358 260 163

401 393 385 377 368 351 320

602 591 579 566 553 527 481

417 407 398 388 377 357 324

626 612 598 583 567 537 487

433 422 410 398 386 364 328

651 634 617 599 580 547 493

449 436 423 409 395 370 332

675 656 636 615 594 556 499

ASD

LRFD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3C:14th Ed.

2/24/11

9:00 AM

Page 179

COMPOSITE BEAM SELECTION TABLES

3–179

Table 3-19 (continued)

Composite W-Shapes

Fy = 50 ksi

Shape W21×57

Available Strength in Flexure, kip-ft

Y 2 b, in. 4 4.5 5 5.5 ASD LRFD ASD LRFD ASD LRFD ASD LRFD 606 911 627 943 648 974 669 1010 585 879 603 906 621 933 639 960 562 845 577 868 593 891 609 915 539 809 551 829 564 848 577 867 514 773 524 788 535 804 545 819 486 730 493 742 501 753 509 765 445 669 450 677 455 684 461 692

W21

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 690 657 624 590 555 517 466

1040 988 938 887 834 776 700

710 675 640 603 565 524 471

1070 1020 961 906 850 788 708

731 694 655 616 575 532 476

1100 1040 985 925 865 800 716

W21×55

582 560 538 515 491 466 432

875 842 808 774 738 701 649

602 578 553 527 500 474 437

905 868 831 792 752 712 656

622 595 568 539 510 481 442

936 895 853 810 766 723 664

643 613 582 551 519 488 447

966 921 875 828 781 734 672

663 630 597 563 529 496 452

996 948 898 847 795 745 679

683 648 612 576 538 503 457

1030 974 920 865 809 756 687

703 665 627 588 548 510 462

1060 1000 942 883 823 767 695

W21×50

528 510 492 473 454 425 384

794 767 740 711 682 639 577

546 527 506 485 463 433 389

821 791 761 729 696 650 584

565 543 520 497 473 440 393

849 816 782 747 711 661 591

583 559 534 509 483 447 398

876 840 803 764 725 671 598

601 575 548 520 492 454 402

904 864 824 782 740 682 605

620 591 562 532 502 461 407

932 889 845 800 754 693 612

638 607 576 544 512 468 412

959 913 866 818 769 704 619

W21×48

503 485 467 449 429 405 369

756 729 702 674 645 609 555

521 501 480 460 438 412 374

783 753 722 691 659 619 562

538 516 494 471 447 418 378

809 776 742 707 672 629 568

556 532 507 482 456 425 383

835 799 762 724 685 639 575

573 547 520 493 465 432 387

862 822 782 741 699 649 582

591 562 533 504 474 438 391

888 845 802 757 712 659 588

609 578 547 515 483 445 396

915 868 821 774 725 669 595

W21×44

465 451 435 420 404 377 336

700 677 654 631 607 566 505

482 465 448 431 413 383 340

724 699 673 647 620 576 511

498 479 461 441 422 390 344

748 721 692 663 634 586 518

514 494 473 452 431 396 348

773 742 711 679 647 595 524

530 508 486 463 440 403 352

797 764 730 696 661 605 530

547 523 498 474 448 409 357

821 785 749 712 674 615 536

563 537 511 484 457 416 361

846 807 768 728 687 625 542

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

9:01 AM

Page 180

3–180

DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W18

Shape W18×60

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp kip-ft PNAc ASD LRFD 307 461 TFL 2 3 4 BFL 6 7

Y 2 b, in.

Y 1a

∑Qn

in.

kip

ASD

LRFD

ASD

2.5 LRFD

ASD

LRFD

ASD

3.5 LRFD

0 0.174 0.348 0.521 0.695 2.18 3.80

880 749 617 486 355 287 220

487 474 459 443 426 414 398

733 712 690 666 640 623 598

509 492 474 455 435 422 403

766 740 713 684 653 634 606

531 511 490 467 444 429 409

799 768 736 702 667 644 614

553 530 505 479 452 436 414

832 796 759 720 680 655 623

2

3

W18×55

279

420

TFL 2 3 4 BFL 6 7

0 0.158 0.315 0.473 0.630 2.15 3.86

810 691 573 454 336 269 203

447 434 421 407 392 381 364

671 653 633 612 589 572 547

467 452 435 418 400 387 369

702 679 654 629 602 582 555

487 469 450 430 409 394 374

732 705 676 646 614 592 563

507 486 464 441 417 401 379

762 731 697 663 627 603 570

W18×50

252

379

TFL 2 3 4 BFL 6 7

0 0.143 0.285 0.428 0.570 2.08 3.82

735 628 521 414 308 246 184

403 392 381 368 355 345 329

606 590 572 553 533 518 495

422 408 394 378 362 351 334

634 613 592 569 545 527 502

440 424 407 389 370 357 339

662 637 611 584 556 537 509

458 439 420 399 378 363 343

689 660 631 600 568 546 516

W18×46

226

340

TFL 2 3 4 BFL 6 7

0 0.151 0.303 0.454 0.605 2.42 4.36

675 583 492 400 308 239 169

372 363 353 342 330 318 299

559 545 530 513 496 478 450

389 377 365 352 338 324 303

585 567 548 528 508 487 456

406 392 377 362 345 330 308

610 589 567 543 519 496 462

423 406 389 372 353 336 312

635 611 585 558 531 505 469

W18×40

196

294

TFL 2 3 4 BFL 6 7

0 0.131 0.263 0.394 0.525 2.26 4.27

590 511 432 353 274 211 148

322 314 306 296 287 276 260

485 472 459 445 431 415 390

337 327 316 305 294 282 263

507 491 475 459 441 423 396

352 340 327 314 300 287 267

529 511 492 472 451 431 401

367 352 338 323 307 292 271

551 530 508 485 462 439 407

ASD

LRFD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3C:14th Ed.

2/24/11

9:01 AM

Page 181

COMPOSITE BEAM SELECTION TABLES

3–181

Table 3-19 (continued)

Composite W-Shapes

Fy = 50 ksi

Shape W18×60

Available Strength in Flexure, kip-ft

Y 2 b, in. 4 4.5 5 5.5 ASD LRFD ASD LRFD ASD LRFD ASD LRFD 575 865 597 898 619 931 641 964 548 824 567 852 586 880 605 909 521 782 536 805 551 829 567 852 491 739 504 757 516 775 528 793 461 693 470 707 479 720 488 733 443 666 450 677 457 688 465 698 420 631 425 639 431 647 436 656

W18

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 663 623 582 540 497 472 442

997 937 875 812 747 709 664

685 642 598 552 506 479 447

1030 965 898 830 760 720 672

707 661 613 564 514 486 453

1060 993 921 848 773 731 680

W18×55

527 503 478 452 425 408 384

793 756 719 680 639 613 578

548 521 493 464 434 414 389

823 782 740 697 652 623 585

568 538 507 475 442 421 395

854 808 762 714 664 633 593

588 555 521 486 450 428 400

884 834 783 731 677 643 601

608 572 535 498 459 434 405

914 860 805 748 690 653 608

629 590 550 509 467 441 410

945 886 826 765 702 663 616

649 607 564 520 476 448 415

975 912 848 782 715 673 623

W18×50

477 455 433 409 385 369 348

717 684 650 615 579 555 523

495 471 446 420 393 375 352

744 708 670 631 591 564 530

513 486 459 430 401 381 357

772 731 689 646 602 573 537

532 502 472 440 408 388 362

799 755 709 662 614 583 543

550 518 485 451 416 394 366

827 778 728 677 625 592 550

568 533 498 461 424 400 371

854 802 748 693 637 601 557

587 549 511 471 431 406 375

882 825 767 708 649 610 564

W18×46

440 421 402 382 361 342 316

661 633 604 573 542 514 475

456 435 414 392 369 348 320

686 655 622 588 554 523 481

473 450 426 402 376 354 325

711 676 640 603 565 532 488

490 465 438 412 384 360 329

737 698 659 618 577 541 494

507 479 451 421 392 366 333

762 720 677 633 589 550 500

524 494 463 431 399 372 337

787 742 696 648 600 559 507

541 508 475 441 407 378 341

813 764 714 663 612 568 513

W18×40

381 365 349 332 314 297 274

573 549 524 498 472 447 412

396 378 359 340 321 303 278

595 568 540 512 482 455 418

411 391 370 349 328 308 282

617 587 556 525 493 463 424

425 403 381 358 335 313 286

639 606 573 538 503 471 429

440 416 392 367 341 318 289

662 626 589 551 513 479 435

455 429 403 376 348 324 293

684 645 605 565 523 486 440

470 442 413 384 355 329 297

706 664 621 578 534 494 446

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

9:01 AM

Page 182

3–182

DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W18-W16

Shape W18×35

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp kip-ft PNAc ASD LRFD 166 249 TFL 2 3 4 BFL 6 7

Y 2 b, in.

Y 1a

∑Qn

in.

kip

ASD

LRFD

ASD

2.5 LRFD

ASD

LRFD

ASD

3.5 LRFD

0 0.106 0.213 0.319 0.425 2.37 4.56

515 451 388 324 260 194 129

279 272 265 258 251 240 222

419 409 399 388 377 360 334

292 284 275 266 257 245 225

438 426 413 400 387 368 338

305 295 285 274 264 250 228

458 443 428 412 396 375 343

317 306 294 282 270 254 232

477 460 443 425 406 382 348

2

3

W16×45

205

309

TFL 2 3 4 BFL 6 7

0 0.141 0.283 0.424 0.565 1.77 3.23

665 566 466 367 267 217 166

333 323 312 301 288 280 269

501 486 469 452 433 421 404

350 337 324 310 295 286 273

526 507 487 466 443 430 411

367 351 336 319 302 291 277

551 528 504 479 453 438 417

383 366 347 328 308 297 281

576 549 522 493 463 446 423

W16×40

182

274

TFL 2 3 4 BFL 6 7

0 0.126 0.253 0.379 0.505 1.70 3.16

590 502 413 325 237 192 148

294 285 276 265 255 248 238

443 429 414 399 383 373 358

309 298 286 274 261 253 242

465 448 430 411 392 380 363

324 310 296 282 267 258 246

487 466 445 423 401 387 369

339 323 307 290 272 262 249

509 485 461 436 409 394 375

W16×36

160

240

TFL 2 3 4 BFL 6 7

0 0.108 0.215 0.323 0.430 1.82 3.46

530 455 380 305 229 181 133

263 255 247 239 230 223 211

396 384 372 359 346 334 318

276 267 257 246 236 227 215

415 401 386 370 354 341 323

290 278 266 254 241 232 218

435 418 400 382 363 348 328

303 289 276 262 247 236 221

455 435 414 393 371 355 333

W16×31

135

203

TFL 2 3 4 BFL 6 7

0 0.110 0.220 0.330 0.440 2.00 3.80

457 396 335 274 213 164 114

227 220 214 207 200 192 180

341 331 321 311 300 289 270

238 230 222 214 205 196 183

358 346 334 321 308 295 275

249 240 231 221 210 200 186

375 361 347 332 316 301 279

261 250 239 227 216 204 188

392 376 359 342 324 307 283

ASD

LRFD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3C:14th Ed.

2/24/11

9:01 AM

Page 183

COMPOSITE BEAM SELECTION TABLES

3–183

Table 3-19 (continued)

Composite W-Shapes

Fy = 50 ksi

Shape W18×35

Available Strength in Flexure, kip-ft

Y 2 b, in. 4 4.5 5 5.5 ASD LRFD ASD LRFD ASD LRFD ASD LRFD 330 496 343 516 356 535 369 554 317 477 329 494 340 511 351 528 304 457 314 472 323 486 333 501 291 437 299 449 307 461 315 473 277 416 283 426 290 435 296 445 259 390 264 397 269 404 274 411 235 353 238 358 241 363 244 367

W18-W16

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 382 362 343 323 303 279 248

574 545 515 485 455 419 372

394 374 352 331 309 283 251

593 562 530 497 465 426 377

407 385 362 339 316 288 254

612 578 544 510 474 433 382

W16×45

400 380 359 337 315 302 286

601 571 539 507 473 454 429

416 394 370 346 322 307 290

626 592 557 521 483 462 436

433 408 382 355 328 313 294

651 613 574 534 493 470 442

450 422 394 365 335 318 298

676 634 592 548 503 478 448

466 436 405 374 342 324 302

701 655 609 562 513 486 454

483 450 417 383 348 329 306

726 677 627 576 523 495 460

499 464 429 392 355 334 310

751 698 644 589 533 503 467

W16×40

353 335 317 298 278 267 253

531 504 476 448 418 401 380

368 348 327 306 284 272 257

553 523 492 460 427 409 386

383 360 338 314 290 277 260

575 542 507 472 436 416 391

397 373 348 322 296 282 264

597 561 523 484 445 423 397

412 385 358 330 302 286 268

620 579 538 496 454 430 402

427 398 368 338 308 291 271

642 598 554 509 463 438 408

442 410 379 347 314 296 275

664 617 569 521 472 445 413

W16×36

316 301 285 269 253 241 225

475 452 429 405 380 362 338

329 312 295 277 259 245 228

495 469 443 416 389 368 343

342 324 304 284 264 250 231

515 486 457 428 397 375 348

356 335 314 292 270 254 235

535 503 471 439 406 382 353

369 346 323 300 276 259 238

555 520 486 450 414 389 358

382 358 333 307 281 263 241

574 537 500 462 423 396 363

395 369 342 315 287 268 245

594 555 514 473 432 402 367

W16×31

272 260 247 234 221 208 191

409 391 372 352 332 313 287

284 270 256 241 226 212 194

426 405 384 362 340 319 292

295 280 264 248 232 216 197

443 420 397 373 348 325 296

306 290 272 255 237 221 200

460 435 409 383 356 332 300

318 299 281 262 242 225 203

478 450 422 393 364 338 304

329 309 289 268 248 229 205

495 465 434 404 372 344 309

341 319 297 275 253 233 208

512 480 447 414 380 350 313

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

9:01 AM

Page 184

3–184

DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W16-W14

Shape W16×26

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp Y 1a kip-ft PNAc in. ASD LRFD 110 166 TFL 0 2 0.0863 3 0.173 4 0.259 BFL 0.345 6 2.05 7 4.01

Y 2 b, in.

∑Qn kip

ASD

2 LRFD

ASD

2.5 LRFD

ASD

3 LRFD

ASD

3.5 LRFD

384 337 289 242 194 145 96.0

189 184 179 174 168 161 148

284 276 269 261 253 241 223

198 192 186 180 173 164 151

298 289 280 270 260 247 226

208 201 193 186 178 168 153

312 302 291 279 267 252 230

217 209 201 192 183 171 155

327 314 301 288 275 258 234

W14×38

153

231

TFL 2 3 4 BFL 6 7

0 0.129 0.258 0.386 0.515 1.38 2.53

560 473 386 299 211 176 140

253 244 234 224 214 209 201

380 367 352 337 321 313 303

267 256 244 232 219 213 205

401 384 367 348 329 320 308

281 268 254 239 224 217 208

422 402 381 360 337 327 313

295 279 263 247 229 222 212

443 420 396 371 345 333 319

W14×34

136

205

TFL 2 3 4 BFL 6 7

0 0.114 0.228 0.341 0.455 1.42 2.61

500 423 346 270 193 159 125

225 217 208 200 190 186 179

338 326 313 300 286 279 269

237 227 217 206 195 190 182

356 342 326 310 293 285 273

250 238 226 213 200 193 185

375 357 339 320 301 291 278

262 248 234 220 205 197 188

394 373 352 330 308 297 283

W14×30

118

177

TFL 2 3 4 BFL 6 7

0 0.0963 0.193 0.289 0.385 1.46 2.80

443 378 313 248 183 147 111

197 190 183 176 168 163 156

295 285 275 264 253 245 234

208 199 191 182 173 167 158

312 300 287 273 260 250 238

219 209 199 188 177 170 161

329 314 298 283 266 256 242

230 218 206 194 182 174 164

345 328 310 292 273 261 246

W14×26

100

151

TFL 2 3 4 BFL 6 7

0 0.105 0.210 0.315 0.420 1.67 3.18

385 332 279 226 173 135 96.1

172 166 161 155 148 143 134

258 250 241 232 223 215 202

181 175 168 160 153 146 137

273 262 252 241 230 220 205

191 183 175 166 157 149 139

287 275 262 249 236 225 209

201 191 182 172 161 153 141

301 287 273 258 243 230 213

ASD

LRFD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

9:01 AM

Page 185

COMPOSITE BEAM SELECTION TABLES

3–185

Table 3-19 (continued)

Composite W-Shapes

Fy = 50 ksi

Shape W16×26

Available Strength in Flexure, kip-ft

Y 2 b, in. 4 4.5 5 5.5 ASD LRFD ASD LRFD ASD LRFD ASD LRFD 227 341 237 356 246 370 256 384 218 327 226 340 234 352 243 365 208 312 215 323 222 334 229 345 198 297 204 306 210 315 216 324 188 282 192 289 197 296 202 304 175 263 179 268 182 274 186 279 158 237 160 241 163 244 165 248

W16-W14

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 265 251 237 222 207 189 167

399 377 356 333 311 285 252

275 259 244 228 212 193 170

413 390 366 343 318 290 255

285 268 251 234 217 197 172

428 403 377 352 326 296 259

W14×38

309 291 273 254 235 226 215

464 438 410 382 353 340 324

323 303 283 262 240 230 219

485 455 425 393 361 346 329

337 315 292 269 245 235 222

506 473 439 404 369 353 334

351 327 302 276 250 239 226

527 491 454 416 376 360 340

365 338 311 284 256 244 229

548 508 468 427 384 366 345

379 350 321 291 261 248 233

569 526 482 438 392 373 350

393 362 331 299 266 252 236

590 544 497 449 400 379 355

W14×34

274 259 243 227 210 201 191

413 389 365 340 315 303 287

287 269 252 233 214 205 194

431 405 378 351 322 309 292

299 280 260 240 219 209 197

450 421 391 361 330 315 297

312 291 269 247 224 213 201

469 437 404 371 337 321 301

324 301 277 253 229 217 204

488 453 417 381 344 327 306

337 312 286 260 234 221 207

506 468 430 391 351 333 311

349 322 295 267 239 225 210

525 484 443 401 359 338 316

W14×30

241 228 214 201 186 178 167

362 342 322 301 280 267 250

252 237 222 207 191 181 169

378 356 334 311 287 273 255

263 246 230 213 196 185 172

395 370 345 320 294 278 259

274 256 238 219 200 189 175

412 385 357 329 301 284 263

285 265 245 225 205 192 178

428 399 369 339 308 289 267

296 275 253 231 209 196 180

445 413 381 348 315 295 271

307 284 261 238 214 200 183

461 427 392 357 321 300 275

W14×26

210 199 188 177 166 156 144

316 300 283 266 249 235 216

220 208 195 183 170 160 146

330 312 294 275 256 240 220

229 216 202 188 174 163 149

345 325 304 283 262 245 223

239 224 209 194 179 166 151

359 337 315 292 269 250 227

248 233 216 200 183 170 153

373 349 325 300 275 255 231

258 241 223 205 187 173 156

388 362 336 309 282 260 234

268 249 230 211 192 176 158

402 374 346 317 288 265 238

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3C:14th Ed.

2/24/11

9:01 AM

Page 186

3–186

DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W14-W12

Shape W14×22

Fy = 50 ksi

Available Strength in Flexure, kip-ft

Mp /Ωb φb Mp Y 1a kip-ft PNAc in. ASD LRFD 82.8 125 TFL 0 2 0.0838 3 0.168 4 0.251 BFL 0.335 6 1.67 7 3.32

Y 2 b, in.

∑Qn kip

2 ASD

LRFD

ASD

2.5 LRFD

3 ASD

LRFD

ASD

3.5 LRFD

325 283 241 199 157 119 81.1

143 139 135 130 125 120 111

215 209 202 195 188 180 167

151 146 141 135 129 123 113

228 220 211 203 194 184 170

159 153 147 140 133 126 115

240 230 220 210 200 189 173

168 160 153 145 137 129 117

252 241 229 218 206 193 176

W12×30

108

162

TFL 2 3 4 BFL 6 7

0 0.110 0.220 0.330 0.440 1.10 1.92

440 368 296 224 153 131 110

179 171 164 155 147 144 140

269 258 246 234 221 216 211

190 181 171 161 151 147 143

285 271 257 242 227 221 215

201 190 178 167 155 151 146

302 285 268 251 232 226 219

212 199 186 172 158 154 149

318 299 279 259 238 231 223

W12×26

92.8

140

TFL 2 3 4 BFL 6 7

0 0.0950 0.190 0.285 0.380 1.07 1.94

383 321 259 198 136 116 95.6

155 148 142 135 128 125 121

232 223 213 203 192 188 183

164 156 148 140 131 128 124

247 235 223 210 197 192 186

174 164 155 145 134 131 126

261 247 232 217 202 197 190

183 172 161 150 138 134 129

275 259 242 225 207 201 193

W12×22

73.1

110

TFL 2 3 4 BFL 6 7

0 0.106 0.213 0.319 0.425 1.66 3.03

324 281 238 196 153 117 81.0

132 127 123 118 113 107 99.8

198 191 185 177 170 162 150

140 134 129 123 117 110 102

210 202 193 185 175 166 153

148 141 135 128 120 113 104

222 213 202 192 181 170 156

156 148 141 133 124 116 106

234 223 211 199 187 175 159

W12×19

61.6

92.6

TFL 2 3 4 BFL 6 7

0 0.0875 0.175 0.263 0.350 1.68 3.14

279 243 208 173 138 104 69.6

113 109 105 101 97.3 92.3 84.7

169 164 158 152 146 139 127

120 115 110 106 101 94.9 86.4

180 173 166 159 151 143 130

126 121 116 110 104 97.4 88.2

190 182 174 165 157 146 133

133 127 121 114 108 100 89.9

201 191 182 172 162 150 135

ASD

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force φ b = 0.90 c See Figure 3-3c for PNA locations.

LRFD

a

b

Ωb = 1.67

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3C:14th Ed.

2/24/11

9:01 AM

Page 187

COMPOSITE BEAM SELECTION TABLES

3–187

Table 3-19 (continued)

Composite W-Shapes

Fy = 50 ksi

Available Strength in Flexure, kip-ft

W14-W12

W14×22

176 167 159 150 141 132 119

264 251 238 225 212 198 179

184 174 165 155 145 135 121

276 262 247 233 218 202 182

192 181 171 160 149 138 123

288 273 256 240 223 207 185

Y 2 b, in. 5.5 ASD LRFD 200 301 188 283 177 266 165 248 153 229 140 211 125 188

W12×30

223 208 193 178 162 157 151

335 313 290 267 244 236 227

234 217 201 183 166 160 154

351 327 301 276 250 241 232

245 226 208 189 170 164 157

368 340 313 284 255 246 236

255 236 215 195 174 167 160

384 354 324 293 261 251 240

266 245 223 200 177 170 162

400 368 335 301 267 256 244

277 254 230 206 181 173 165

417 382 346 309 272 261 248

288 263 237 211 185 177 168

433 396 357 318 278 266 252

W12×26

193 180 168 155 141 137 131

290 271 252 232 212 205 197

202 188 174 160 145 139 133

304 283 262 240 217 210 200

212 196 181 164 148 142 136

318 295 271 247 222 214 204

221 204 187 169 151 145 138

333 307 281 255 228 218 208

231 212 193 174 155 148 141

347 319 291 262 233 223 211

240 220 200 179 158 151 143

361 331 300 269 238 227 215

250 228 206 184 162 154 145

376 343 310 277 243 231 218

W12×22

164 155 147 137 128 119 108

247 234 220 207 193 179 162

172 162 152 142 132 122 110

259 244 229 214 198 183 165

180 169 158 147 136 125 112

271 255 238 221 204 188 168

188 176 164 152 140 128 114

283 265 247 229 210 192 171

196 183 170 157 143 131 116

295 276 256 236 215 197 174

205 191 176 162 147 134 118

307 286 265 243 221 201 177

213 198 182 167 151 137 120

320 297 274 251 227 205 180

W12×19

140 133 126 119 111 103 91.7

211 200 189 178 167 154 138

147 139 131 123 115 105 93.4

221 209 197 185 172 158 140

154 145 136 127 118 108 95.1

232 219 205 191 177 162 143

161 151 142 132 121 110 96.9

242 228 213 198 183 166 146

168 158 147 136 125 113 98.6

253 237 221 204 188 170 148

175 164 152 140 128 116 100

263 246 228 211 193 174 151

182 170 157 145 132 118 102

274 255 236 217 198 178 153

Shape

4 4.5 5 ASD LRFD ASD LRFD ASD LRFD

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 208 195 183 170 157 143 127

313 294 275 255 235 216 191

216 203 189 175 160 146 129

325 304 284 262 241 220 194

224 210 195 180 164 149 131

337 315 293 270 247 225 198

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3C:14th Ed.

2/24/11

9:02 AM

Page 188

3–188

DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W12-W10

Shape W12×16

Mp /Ωb φb Mp Y 1a kip-ft PNAc in. ASD LRFD 50.1 75.4 TFL 0 2 0.0663 3 0.133 4 0.199 BFL 0.265 6 1.71 7 3.32

2

2.5 LRFD

kip

ASD

LRFD

ASD

236 209 183 156 130 94.3 58.9

94.0 91.3 88.6 85.7 82.8 77.6 69.6

141 137 133 129 124 117 105

99.9 96.5 93.1 89.6 86.0 79.9 71.1

150 145 140 135 129 120 107

82.5 80.3 77.9 75.5 73.1 68.3 60.8

124 121 117 114 110 103 91.4

87.7 84.9 82.0 79.1 76.1 70.4 62.1

132 128 123 119 114 106 93.3

43.4

65.3

TFL 2 3 4 BFL 6 7

0 0.0563 0.113 0.169 0.225 1.68 3.35

208 186 163 141 119 85.3 52.0

W10×26

78.1

117

TFL 2 3 4 BFL 6 7

0 0.110 0.220 0.330 0.440 0.886 1.49

381 317 254 190 127 111 95.1

W10×22

64.9

97.5

TFL 2 3 4 BFL 6 7

0 0.0900 0.180 0.270 0.360 0.962 1.72

W10×19

53.9

81.0

TFL 2 3 4 BFL 6 7

0 0.0988 0.198 0.296 0.395 1.25 2.29

LRFD

Y 2 b, in.

∑Qn

W12×14

ASD

136 129 122 115 108 106 103

φ b = 0.90

3 ASD 106 102 97.7 93.5 89.2 82.3 72.5 92.9 89.5 86.1 82.6 79.0 72.6 63.4

3.5 LRFD ASD LRFD 159 112 168 153 107 161 147 102 154 141 97.4 146 134 92.5 139 124 84.6 127 109 74.0 111 140 135 129 124 119 109 95.3

98.1 94.2 90.2 86.1 82.0 74.7 64.7

147 142 135 129 123 112 97.2

204 194 184 173 162 159 155

145 137 129 120 111 108 105

218 206 193 180 167 163 158

155 145 135 125 114 111 108

233 218 203 187 171 167 162

164 153 141 129 117 114 110

247 230 213 195 176 171 166

325 115 273 110 221 104 169 98.4 118 92.5 99.3 90.1 81.1 87.0

173 165 157 148 139 135 131

123 116 110 103 95.4 92.5 89.1

185 175 165 154 143 139 134

131 123 115 107 98.3 95.0 91.1

197 185 173 161 148 143 137

139 130 121 111 101 97.5 93.1

209 196 181 167 152 147 140

281 241 202 162 122 96.2 70.3

150 144 137 130 123 118 111

107 102 96.3 90.8 85.2 80.9 75.4

160 153 145 137 128 122 113

114 108 101 94.9 88.2 83.3 77.2

171 162 152 143 133 125 116

121 114 106 98.9 91.3 85.8 78.9

181 171 160 149 137 129 119

99.6 95.5 91.2 86.8 82.1 78.5 73.7

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

Fy = 50 ksi

Available Strength in Flexure, kip-ft

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3C:14th Ed.

2/24/11

9:02 AM

Page 189

COMPOSITE BEAM SELECTION TABLES

3–189

Table 3-19 (continued) Fy = 50 ksi

Composite W-Shapes Available Strength in Flexure, kip-ft

W12-W10

129.0 123 116 109 102 91.7 78.4

194 184 174 164 154 138 118

Y 2 b, in. 5.5 ASD LRFD 135.0 203 128 192 120 181 113 170 105 158 94.1 141 79.9 120

155 108 148 103 142 98.3 135 93.1 128 87.9 115 79.0 99.2 67.3

163 114 155 108 148 102 140 96.7 132 90.9 119 81.1 101 68.6

171 162 154 145 137 122 103

119 113 106 100 93.9 83.2 69.9

179 169 160 151 141 125 105

124 117 111 104 96.8 85.3 71.2

186 176 166 156 146 128 107

129 122 115 107 99.8 87.5 72.5

194 183 172 161 150 131 109

134 127 119 111 103 89.6 73.8

202 190 178 166 154 135 111

174 161 148 134 120 117 113

261 242 222 202 181 175 169

183 169 154 139 123 119 115

275 254 232 209 186 179 173

193 177 160 144 127 122 117

290 266 241 216 190 184 176

202 185 167 148 130 125 120

304 277 251 223 195 188 180

212 193 173 153 133 128 122

318 289 260 230 200 192 183

221 200 179 158 136 130 124

332 301 270 237 205 196 187

231 208 186 163 139 133 127

347 313 279 244 209 200 191

W10×22

147 137 126 115 104 100 95.1

221 206 190 173 157 150 143

155 144 132 120 107 102 97.1

234 216 198 180 161 154 146

164 151 137 124 110 105 99.2

246 226 206 186 165 158 149

172 157 143 128 113 107 101

258 236 215 192 170 161 152

180 164 148 132 116 110 103

270 247 223 199 174 165 155

188 171 154 136 119 112 105

282 257 231 205 179 169 158

196 178 159 141 122 115 107

294 267 239 211 183 173 161

W10×19

128 120 111 103 94.3 88.2 80.7

192 180 167 155 142 132 121

135 126 116 107 97.4 90.6 82.4

202 189 175 161 146 136 124

142 132 121 111 100 93.0 84.2

213 198 183 167 151 140 127

149 138 126 115 103 95.4 85.9

223 207 190 173 156 143 129

156 144 132 119 107 97.8 87.7

234 216 198 179 160 147 132

163 150 137 123 110 100 89.4

244 225 205 185 165 151 134

170 156 142 127 113 103 91.2

255 234 213 191 169 154 137

Shape

4 4.5 5 ASD LRFD ASD LRFD ASD LRFD

W12×16

118.0 112 107 101 95.7 87.0 75.5

177 169 161 152 144 131 113

W12×14

103 98.8 94.2 89.6 85.0 76.8 66.0

W10×26

123.0 117 111 105 99.0 89.4 77.0

185 176 167 158 149 134 116

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 141.0 133 125 117 109 96.4 81.4

212 200 188 176 163 145 122

147.0 138 130 121 112 98.8 82.8

221 208 195 182 168 148 125

153.0 143 134 125 115 101 84.3

230 216 202 187 173 152 127

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

9:02 AM

Page 190

3–190

DESIGN OF FLEXURAL MEMBERS

Table 3-19 (continued)

Composite W-Shapes W10

Shape W10×17

Mp /Ωb φb Mp Y 1a kip-ft PNAc in. ASD LRFD 46.7 70.1 TFL 0 2 0.0825 3 0.165 4 0.248 BFL 0.330 6 1.31 7 2.45

Y 2 b, in.

∑Qn

2

kip

ASD

LRFD

ASD

250 216 183 150 117 89.8 62.4

87.8 84.4 80.9 77.2 73.5 69.7 64.4

132 127 122 116 110 105 96.8

94.0 89.8 85.5 81.0 76.4 71.9 65.9

2.5 LRFD

141 100 135 95.2 128 90.0 122 84.7 115 79.3 108 74.2 99.1 67.5

151 143 135 127 119 111 101

106 101 94.6 88.5 82.2 76.4 69.1

132 126 120 113 107 98.7 88.0

60.0

TFL 2 3 4 BFL 6 7

0 0.0675 0.135 0.203 0.270 1.35 2.60

221 194 167 140 113 83.8 55.1

77.0 74.2 71.4 68.5 65.5 61.5 55.8

116 112 107 103 98.4 92.5 83.9

82.5 79.1 75.6 72.0 68.3 63.6 57.2

124 119 114 108 103 95.6 86.0

W10×12

31.2

46.9

TFL 2 3 4 BFL 6 7

0 0.0525 0.105 0.158 0.210 1.30 2.61

177 156 135 115 93.8 69.0 44.3

61.3 59.1 57.0 54.8 52.5 49.2 44.3

92.1 88.9 85.7 82.4 78.9 73.9 66.6

65.7 63.0 60.4 57.7 54.9 50.9 45.4

98.7 94.8 90.7 86.7 82.4 76.5 68.2

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. a

b

Ωb = 1.67

φ b = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ASD

3.5 LRFD

ASD

39.9

LRFD

3 LRFD

W10×15

ASD

Fy = 50 ksi

Available Strength in Flexure, kip-ft

88.0 83.9 79.7 75.5 71.1 65.7 58.6

70.1 105 66.9 100 63.7 95.8 60.5 91.0 57.2 86.0 52.6 79.1 46.5 69.9

93.5 88.7 83.9 78.9 73.9 67.8 59.9

160 151 142 133 124 115 104 140 133 126 119 111 102 90.1

74.5 112 70.8 106 67.1 101 63.4 95.3 59.5 89.5 54.4 81.7 47.6 71.5

AISC_Part 3C:14th Ed.

2/24/11

9:02 AM

Page 191

COMPOSITE BEAM SELECTION TABLES

3–191

Table 3-19 (continued) Fy = 50 ksi

Shape W10×17

Composite W-Shapes Available Strength in Flexure, kip-ft

Y 2 b, in. 4 4.5 5 5.5 ASD LRFD ASD LRFD ASD LRFD ASD LRFD 113.0 169.0 119.0 179.0 125.0 188.0 131.0 197.0 106 159 111 167 117 176 122 184 99.2 149 104 156 108 163 113 170 92.2 139 96.0 144 99.7 150 103 156 85.2 128 88.1 132 91.0 137 93.9 141 78.6 118 80.9 122 83.1 125 85.4 128 70.6 106 72.2 108 73.7 111 75.3 113

W10×15

99.0 93.5 88.0 82.4 76.7 69.9 61.3

149 104 141 98.4 132 92.2 124 85.9 115 79.5 105 72.0 92.2 62.7

W10×12

78.9 119 74.7 112 70.5 106 66.2 99.6 61.9 93.0 56.1 84.3 48.7 73.2

83.3 78.6 73.9 69.1 64.2 57.8 49.8

6 6.5 7 ASD LRFD ASD LRFD ASD LRFD 138.0 128 117 107 96.8 87.6 76.8

207.0 192 177 161 146 132 115

144.0 133 122 111 99.8 89.8 78.4

216.0 200 183 167 150 135 118

150.0 138 127 115 103 92.1 80.0

225.0 208 190 172 154 138 120

126 118 109 99.8 90.8 80.3 68.2

190 177 164 150 136 121 102

132 123 113 103 93.6 82.4 69.6

198 184 170 155 141 124 105

157 110 148 103 139 96.3 129 89.4 120 82.3 108 74.1 94.2 64.1

165 115 155 108 145 100 134 92.9 124 85.2 111 76.2 96.3 65.4

174 121 162 113 151 105 140 96.4 128 88.0 114 78.2 98.3 66.8

182 170 157 145 132 118 100

125 118 111 104 96.5 86.9 74.9

132 124 116 108 100 89.5 76.5

139 130 121 112 104 92.1 78.2

145 101 136 94.2 126 87.4 117 80.5 107 73.6 94.6 64.7 79.8 54.2

87.7 82.5 77.3 72.0 66.6 59.5 50.9

92.2 86.4 80.6 74.8 68.9 61.2 52.0

96.6 90.3 84.0 77.7 71.2 63.0 53.1

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force Ωb = 1.67 φ b = 0.90 c See Figure 3-3c for PNA locations.

ASD

LRFD

W10

a

b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

152 105 142 98.1 131 90.8 121 83.4 111 75.9 97.2 66.4 81.5 55.3

158 147 136 125 114 99.8 83.2

AISC_Part 3D:14th Ed.

2/24/11

9:03 AM

Page 192

DESIGN OF FLEXURAL MEMBERS

3–192

Table 3-20

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

W40

Fy = 50 ksi

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W40×297 (23200)

TFL 2 3 4 BFL 6 7

0 0.413 0.825 1.24 1.65 4.58 8.17

4370 3710 3060 2410 1760 1420 1090

44100 42400 40500 38100 35200 33500 31600

45100 43300 41300 38800 35800 34000 32000

46100 44200 42100 39500 36400 34400 32300

47100 45200 42900 40200 36900 34900 32800

48100 46100 43800 40900 37500 35400 33200

49200 47100 44600 41700 38100 36000 33600

50300 48100 45500 42500 38800 36500 34000

51400 49100 46400 43200 39400 37000 34500

52500 50100 47300 44000 40000 37600 34900

53600 51200 48300 44800 40700 38100 35400

54800 52200 49200 45700 41400 38700 35800

W40×294 (21900)

TFL 0 2 0.483 3 0.965 4 1.45 BFL 1.93 6 5.71 7 10.0

4310 3730 3150 2570 1990 1540 1080

43100 41600 39800 37800 35300 33100 30400

44100 42500 40700 38500 35900 33600 30800

45100 43400 41500 39200 36600 34100 31200

46100 44400 42300 40000 37200 34600 31600

47100 45300 43200 40800 37800 35200 32000

48200 46300 44100 41500 38500 35700 32400

49300 47300 45000 42300 39200 36300 32900

50400 48300 45900 43200 39900 36900 33300

51500 49400 46900 44000 40600 37500 33800

52600 50400 47800 44900 41300 38100 34200

53800 51500 48800 45700 42000 38700 34700

W40×278 (20500)

TFL 0 2 0.453 3 0.905 4 1.36 BFL 1.81 6 5.67 7 10.1

4120 3570 3030 2490 1940 1490 1030

40600 39200 37500 35700 33400 31200 28500

41500 40000 38300 36300 34000 31700 28900

42500 40900 39100 37100 34600 32200 29300

43400 41800 39900 37800 35200 32700 29700

44400 42700 40800 38500 35800 33200 30100

45400 43600 41600 39300 36500 33700 30500

46400 44600 42500 40000 37100 34300 30900

47500 45600 43400 40800 37800 34800 31300

48500 46500 44300 41600 38500 35400 31700

49600 47600 45200 42500 39200 36000 32200

50700 48600 46100 43300 39900 36600 32600

W40×277 (21900)

TFL 2 3 4 BFL 6 7

0 0.395 0.790 1.19 1.58 4.20 7.58

4080 3450 2830 2200 1580 1300 1020

41400 39700 37800 35500 32800 31300 29700

42300 40600 38600 36200 33300 31700 30100

43200 41400 39300 36800 33800 32200 30400

44100 42300 40100 37500 34300 32600 30800

45100 43200 40900 38200 34900 33100 31200

46100 44100 41700 38800 35400 33600 31600

47100 45000 42500 39500 36000 34100 32000

48100 45900 43400 40300 36500 34600 32400

49100 46900 44200 41000 37100 35100 32800

50200 47800 45100 41700 37700 35600 33200

51300 48800 46000 42500 38300 36100 33700

W40×264 (19400)

TFL 2 3 4 BFL 6 7

0 0.433 0.865 1.30 1.73 5.53 9.92

3870 3360 2840 2330 1810 1390 968

38100 36800 35300 33500 31300 29300 26900

39000 37600 36000 34100 31900 29800 27200

39900 38400 36700 34800 32400 30200 27600

40800 39300 37500 35500 33000 30700 28000

41700 40100 38300 36200 33600 31200 28300

42600 41000 39100 36900 34200 31700 28700

43600 41900 39900 37600 34800 32200 29100

44600 42800 40700 38300 35400 32700 29500

45600 43700 41500 39100 36100 33200 29900

46600 44700 42400 39800 36700 33800 30300

47600 45600 43300 40600 37400 34300 30700

Y 2 b, in. 4.5 5

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:03 AM

Page 193

COMPOSITE BEAM SELECTION TABLES

3–193

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

Fy = 50 ksi

W40

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W40×249 (19600)

TFL 2 3 4 BFL 6 7

0 0.355 0.710 1.07 1.42 4.03 7.45

3680 3110 2550 1990 1430 1180 919

36900 35500 33800 31800 29300 28000 26500

37700 36200 34400 32300 29700 28400 26800

38500 37000 35100 32900 30200 28800 27200

39400 37700 35800 33500 30700 29200 27500

40300 38500 36500 34100 31200 29600 27900

41100 39300 37200 34700 31700 30100 28200

42000 40200 38000 35400 32200 30500 28600

43000 41000 38700 36000 32700 30900 28900

43900 41900 39500 36700 33200 31400 29300

44800 42700 40300 37300 33700 31900 29700

45800 43600 41100 38000 34300 32300 30100

W40×235 (17400)

TFL 2 3 4 BFL 6 7

0 0.395 0.790 1.19 1.58 5.16 9.44

3460 2980 2510 2040 1570 1220 864

33900 32700 31300 29600 27700 26000 24000

34700 33400 31900 30200 28200 26400 24300

35500 34100 32600 30800 28700 26800 24600

36300 34800 33300 31400 29200 27200 24900

37100 35600 33900 32000 29700 27700 25300

37900 36400 34600 32600 30200 28100 25600

38800 37200 35400 33200 30700 28500 25900

39600 38000 36100 33900 31300 29000 26300

40500 38800 36800 34500 31800 29400 26600

41400 39600 37600 35200 32400 29900 27000

42300 40500 38400 35900 33000 30400 27400

W40×215 (16700)

TFL 2 3 4 BFL 6 7

0 0.305 0.610 0.915 1.22 3.80 7.29

3180 2690 2210 1730 1250 1020 794

31400 30200 28700 27100 25000 23800 22600

32100 30800 29300 27500 25400 24200 22800

32800 31400 29900 28000 25800 24500 23100

33500 32100 30500 28500 26200 24900 23400

34200 32800 31100 29100 26600 25200 23700

35000 33500 31700 29600 27000 25600 24000

35800 34200 32300 30100 27500 26000 24300

36600 34900 33000 30700 27900 26300 24600

37400 35600 33600 31300 28400 26700 25000

38200 36400 34300 31800 28800 27100 25300

39000 37200 35000 32400 29300 27500 25600

W40×211 (15500)

TFL 2 3 4 BFL 6 7

0 0.355 0.710 1.07 1.42 5.00 9.35

3110 2690 2270 1850 1430 1100 776

30100 29100 27800 26400 24700 23100 21300

30800 29700 28400 26900 25200 23500 21600

31500 30400 29000 27400 25600 23900 21900

32200 31000 29600 28000 26000 24200 22200

33000 31700 30200 28500 26500 24600 22500

33700 32400 30900 29100 27000 25000 22800

34500 33100 31500 29600 27400 25400 23100

35200 33800 32200 30200 27900 25800 23400

36000 34500 32800 30800 28400 26200 23700

36800 35300 33500 31400 28900 26700 24000

37700 36100 34200 32000 29500 27100 24400

W40×199 (14900)

TFL 2 3 4 BFL 6 7

0 0.268 0.535 0.803 1.07 4.09 8.04

2940 2520 2090 1670 1250 992 735

28300 27300 26000 24600 22900 21700 20300

28900 27900 26600 25100 23300 22000 20500

29600 28500 27100 25500 23700 22300 20800

30300 29100 27700 26000 24100 22600 21000

30900 29700 28200 26500 24500 23000 21300

31600 30300 28800 27000 24900 23300 21600

32300 31000 29400 27500 25300 23700 21900

33100 31700 30000 28100 25700 24100 22200

33800 32300 30600 28600 26200 24400 22500

34500 33000 31200 29100 26600 24800 22800

35300 33700 31900 29700 27100 25200 23100

Y 2 b, in. 4.5 5

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:03 AM

Page 194

DESIGN OF FLEXURAL MEMBERS

3–194

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

W40-W36

Fy = 50 ksi

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W40×183 (13200)

TFL 2 3 4 BFL 6 7

0 0.300 0.600 0.900 1.20 4.77 9.25

2670 2310 1960 1600 1250 958 666

25500 24600 23600 22400 21100 19700 18100

26100 25200 24100 22900 21400 20000 18400

26700 25700 24600 23300 21800 20300 18600

27300 26300 25100 23800 22200 20700 18800

27900 26900 25700 24200 22600 21000 19100

28600 27500 26200 24700 23000 21300 19300

29200 28100 26800 25200 23400 21700 19600

29900 28700 27300 25700 23800 22000 19900

30500 29300 27900 26200 24300 22400 20100

31200 29900 28500 26700 24700 22700 20400

31900 30600 29100 27200 25200 23100 20700

W40×167 (11600)

TFL 2 3 4 BFL 6 7

0 0.258 0.515 0.773 1.03 4.95 9.82

2470 2160 1860 1550 1250 933 616

22800 22000 21200 20200 19100 17700 16100

23300 22500 21700 20600 19500 18000 16300

23900 23000 22100 21100 19800 18300 16500

24400 23600 22600 21500 20200 18600 16700

25000 24100 23100 21900 20600 18900 17000

25600 24600 23600 22400 21000 19300 17200

26200 25200 24100 22800 21400 19600 17400

26800 25800 24600 23300 21800 19900 17700

27400 26300 25200 23800 22200 20300 17900

28000 26900 25700 24300 22600 20600 18200

28700 27500 26300 24800 23100 21000 18400

W40×149 (9800)

TFL 0 2 0.208 3 0.415 4 0.623 BFL 0.830 6 5.15 7 10.4

2190 1950 1700 1460 1210 879 548

19600 19000 18300 17600 16700 15400 13700

20000 19400 18700 18000 17100 15700 13900

20500 19900 19100 18400 17400 15900 14100

21000 20300 19600 18700 17800 16200 14300

21500 20800 20000 19100 18100 16500 14500

22000 21300 20500 19600 18500 16800 14700

22500 21800 20900 20000 18900 17100 14900

23100 22300 21400 20400 19200 17400 15100

23600 22800 21900 20800 19600 17700 15300

24200 23300 22300 21300 20000 18000 15500

24700 23900 22800 21700 20400 18300 15800

W36×302 (21100)

TFL 2 3 4 BFL 6 7

0 0.420 0.840 1.26 1.68 4.06 6.88

4450 3750 3050 2350 1640 1380 1110

40100 38500 36500 34200 31300 30100 28700

41000 39300 37300 34900 31800 30500 29000

42000 40200 38100 35500 32300 31000 29400

42900 41100 38900 36200 32900 31400 29800

43900 42000 39700 36900 33400 31900 30200

44900 42900 40500 37600 33900 32400 30600

46000 43900 41300 38300 34500 32900 31000

47100 44800 42200 39000 35100 33400 31500

48100 45800 43100 39800 35700 33900 31900

49200 46800 44000 40600 36300 34400 32300

50400 47900 44900 41300 36900 35000 32800

W36×282 (19600)

TFL 2 3 4 BFL 6 7

0 0.393 0.785 1.18 1.57 4.00 6.84

4150 3490 2840 2190 1540 1290 1040

37100 35600 33800 31700 29100 27900 26600

38000 36400 34500 32300 29600 28300 27000

38900 37200 35300 32900 30000 28700 27300

39800 38000 36000 33500 30500 29200 27700

40700 38900 36700 34200 31000 29600 28100

41600 39700 37500 34800 31500 30100 28400

42600 40600 38300 35500 32100 30500 28800

43600 41500 39100 36200 32600 31000 29200

44600 42400 39900 36900 33100 31500 29600

45600 43400 40800 37600 33700 31900 30000

46700 44300 41600 38300 34300 32400 30500

Y 2 b, in. 4.5 5

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:03 AM

Page 195

COMPOSITE BEAM SELECTION TABLES

3–195

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

Fy = 50 ksi

W36

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W36×262 (17900)

TFL 2 3 4 BFL 6 7

0 0.360 0.720 1.08 1.44 3.96 6.96

3860 3260 2660 2070 1470 1220 965

34000 32700 31100 29200 26800 25700 24400

34800 33400 31700 29700 27200 26000 24700

35700 34200 32400 30300 27700 26400 25000

36500 34900 33100 30900 28200 26800 25300

37400 35700 33800 31500 28600 27200 25700

38200 36500 34500 32100 29100 27700 26000

39100 37300 35200 32700 29600 28100 26400

40000 38200 36000 33400 30100 28500 26800

41000 39000 36700 34000 30600 29000 27100

41900 39900 37500 34700 31200 29400 27500

42900 40800 38300 35400 31700 29900 27900

W36×256 (16800)

TFL 2 3 4 BFL 6 7

0 0.433 0.865 1.30 1.73 5.18 8.90

3770 3240 2710 2180 1650 1300 941

32900 31700 30300 28600 26600 25100 23300

33700 32500 31000 29200 27100 25500 23600

34500 33200 31600 29800 27600 25900 23900

35400 34000 32300 30400 28100 26300 24200

36200 34700 33000 31000 28600 26800 24600

37100 35500 33800 31700 29100 27200 24900

38000 36400 34500 32300 29700 27700 25300

38900 37200 35300 33000 30200 28100 25600

39800 38000 36000 33600 30800 28600 26000

40700 38900 36800 34300 31400 29100 26400

41700 39800 37600 35000 32000 29600 26700

W36×247 (16700)

TFL 2 3 4 BFL 6 7

0 0.338 0.675 1.01 1.35 3.95 7.02

3630 3070 2510 1950 1400 1150 906

31700 30500 29000 27200 25100 23900 22700

32500 31200 29600 27700 25500 24300 23000

33200 31900 30200 28300 25900 24700 23300

34000 32600 30900 28800 26300 25000 23600

34800 33300 31500 29400 26800 25400 23900

35600 34100 32200 29900 27200 25800 24300

36500 34800 32900 30500 27700 26200 24600

37300 35600 33600 31100 28200 26600 24900

38200 36400 34300 31700 28700 27100 25300

39100 37200 35000 32400 29200 27500 25700

40000 38100 35800 33000 29700 27900 26000

W36×232 (15000)

TFL 2 3 4 BFL 6 7

0 0.393 0.785 1.18 1.57 5.04 8.78

3400 2930 2450 1980 1500 1180 850

29400 28300 27000 25600 23800 22400 20700

30100 28900 27600 26100 24200 22800 21000

30800 29600 28200 26600 24700 23100 21300

31500 30300 28800 27200 25100 23500 21600

32300 31000 29500 27700 25600 23900 21900

33100 31700 30100 28300 26100 24300 22200

33900 32500 30800 28900 26500 24700 22500

34700 33200 31500 29500 27000 25100 22900

35500 34000 32200 30100 27500 25600 23200

36300 34800 32900 30700 28100 26000 23500

37200 35500 33600 31300 28600 26400 23900

W36×231 (15600)

TFL 2 3 4 BFL 6 7

0 0.315 0.630 0.945 1.26 3.88 7.03

3410 2890 2370 1850 1330 1090 853

29600 28400 27100 25400 23400 22400 21200

30300 29100 27600 25900 23800 22700 21500

31000 29700 28200 26400 24200 23100 21800

31700 30400 28800 26900 24700 23400 22100

32500 31100 29400 27500 25100 23800 22400

33200 31800 30100 28000 25500 24100 22700

34000 32500 30700 28600 25900 24500 23000

34800 33200 31400 29100 26400 24900 23300

35700 34000 32000 29700 26900 25300 23600

36500 34800 32700 30300 27300 25700 24000

37300 35500 33400 30900 27800 26100 24300

Y 2 b, in. 4.5 5

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:03 AM

Page 196

DESIGN OF FLEXURAL MEMBERS

3–196

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

W36

Fy = 50 ksi

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W36×210 (13200)

TFL 2 3 4 BFL 6 7

0 0.340 0.680 1.02 1.36 5.04 9.03

3100 2680 2270 1850 1440 1100 774

26000 25100 24000 22800 21300 19900 18300

26700 25700 24600 23300 21700 20300 18600

27300 26300 25100 23800 22200 20600 18800

28000 26900 25700 24300 22600 20900 19100

28700 27500 26300 24800 23000 21300 19400

29400 28200 26900 25300 23500 21700 19700

30100 28900 27500 25800 23900 22000 20000

30800 29500 28100 26400 24400 22400 20200

31600 30200 28700 26900 24900 22800 20500

32300 30900 29400 27500 25300 23200 20800

33100 31700 30000 28100 25800 23600 21200

W36×194 (12100)

TFL 2 3 4 BFL 6 7

0 0.315 0.630 0.945 1.26 4.93 8.94

2850 2470 2090 1710 1330 1020 713

23800 23000 22000 20900 19500 18300 16800

24400 23500 22500 21300 19900 18600 17000

25000 24100 23000 21800 20300 18900 17300

25600 24600 23500 22200 20700 19200 17500

26200 25200 24000 22700 21100 19500 17700

26900 25800 24600 23200 21500 19900 18000

27500 26400 25100 23700 21900 20200 18300

28200 27000 25700 24200 22300 20600 18500

28900 27700 26300 24700 22800 20900 18800

29600 28300 26900 25200 23200 21300 19100

30300 29000 27500 25700 23700 21700 19400

W36×182 (11300)

TFL 2 3 4 BFL 6 7

0 0.295 0.590 0.885 1.18 4.89 8.91

2680 2320 1970 1610 1250 961 670

22200 21400 20500 19500 18200 17000 15700

22700 21900 21000 19900 18600 17300 15900

23300 22400 21500 20300 18900 17600 16100

23900 23000 21900 20700 19300 17900 16300

24400 23500 22400 21200 19700 18200 16600

25000 24100 22900 21600 20000 18600 16800

25700 24600 23500 22100 20400 18900 17000

26300 25200 24000 22600 20800 19200 17300

26900 25800 24500 23000 21200 19600 17600

27600 26400 25100 23500 21700 19900 17800

28300 27000 25700 24000 22100 20200 18100

W36×170 (10500)

TFL 2 3 4 BFL 6 7

0 0.275 0.550 0.825 1.10 4.83 8.91

2500 2170 1840 1510 1180 903 625

20600 19900 19100 18100 17000 15900 14500

21100 20400 19500 18500 17300 16100 14700

21600 20800 19900 18900 17600 16400 15000

22200 21300 20400 19300 18000 16700 15200

22700 21800 20900 19700 18300 17000 15400

23300 22400 21300 20100 18700 17300 15600

23800 22900 21800 20500 19100 17600 15800

24400 23400 22300 21000 19400 17900 16100

25000 24000 22800 21400 19800 18200 16300

25600 24600 23300 21900 20200 18500 16600

26300 25100 23900 22400 20600 18900 16800

W36×160 (9760)

TFL 2 3 4 BFL 6 7

0 0.255 0.510 0.765 1.02 4.82 8.96

2350 2040 1740 1430 1130 857 588

19200 18500 17800 16900 15900 14800 13500

19600 18900 18200 17200 16200 15000 13700

20100 19400 18600 17600 16500 15300 13900

20600 19900 19000 18000 16800 15600 14100

21100 20300 19400 18400 17100 15800 14300

21700 20800 19900 18800 17500 16100 14500

22200 21300 20300 19200 17800 16400 14700

22700 21800 20800 19600 18200 16700 15000

23300 22300 21300 20000 18600 17000 15200

23900 22900 21800 20400 18900 17300 15400

24400 23400 22300 20900 19300 17600 15600

Y 2 b, in. 4.5 5

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:04 AM

Page 197

COMPOSITE BEAM SELECTION TABLES

3–197

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

Fy = 50 ksi

W36-W33

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W36×150 (9040)

TFL 2 3 4 BFL 6 7

0 0.235 0.470 0.705 0.940 4.82 9.09

2220 1930 1650 1370 1090 820 554

17900 17200 16600 15800 14900 13800 12600

18300 17700 16900 16100 15200 14000 12700

18800 18100 17300 16500 15500 14300 12900

19200 18500 17700 16800 15800 14500 13100

19700 19000 18200 17200 16100 14800 13300

20200 19400 18600 17600 16400 15100 13500

20700 19900 19000 18000 16700 15300 13700

21200 20400 19400 18300 17100 15600 13900

21800 20900 19900 18800 17400 15900 14100

22300 21400 20300 19200 17800 16200 14300

22800 21900 20800 19600 18100 16500 14600

W36×135 (7800)

TFL 2 3 4 BFL 6 7

0 0.198 0.395 0.593 0.790 4.92 9.49

2000 1760 1520 1280 1050 773 499

15600 15100 14600 13900 13200 12200 10900

16000 15500 14900 14200 13500 12400 11100

16400 15900 15300 14500 13800 12600 11300

16900 16300 15600 14900 14000 12900 11400

17300 16700 16000 15200 14300 13100 11600

17700 17100 16400 15600 14600 13300 11800

18200 17500 16800 15900 15000 13600 11900

18600 18000 17200 16300 15300 13800 12100

19100 18400 17600 16600 15600 14100 12300

19600 18800 18000 17000 15900 14400 12500

20100 19300 18400 17400 16300 14700 12700

W33×221 (12900)

TFL 2 3 4 BFL 6 7

0 0.320 0.640 0.960 1.28 3.67 6.42

3270 2760 2250 1750 1240 1030 816

24600 23600 22500 21100 19400 18500 17600

25300 24200 23000 21500 19700 18800 17800

25900 24800 23500 22000 20100 19100 18100

26600 25400 24000 22400 20400 19400 18400

27200 26000 24600 22900 20800 19800 18600

27900 26700 25200 23400 21200 20100 18900

28600 27300 25700 23900 21600 20400 19200

29400 28000 26300 24400 22000 20800 19500

30100 28700 26900 24900 22400 21100 19800

30900 29300 27500 25400 22800 21500 20100

31600 30100 28200 26000 23200 21900 20400

W33×201 (11600)

TFL 2 3 4 BFL 6 7

0 0.288 0.575 0.863 1.15 3.65 6.52

2960 2500 2050 1600 1150 944 739

22100 21200 20200 19000 17500 16700 15800

22700 21700 20700 19400 17800 17000 16000

23300 22300 21100 19800 18100 17200 16300

23800 22800 21600 20200 18500 17500 16500

24500 23400 22100 20600 18800 17800 16700

25100 23900 22600 21100 19100 18100 17000

25700 24500 23200 21500 19500 18400 17200

26400 25100 23700 22000 19900 18700 17500

27000 25700 24200 22400 20200 19100 17800

27700 26400 24800 22900 20600 19400 18000

28400 27000 25400 23400 21000 19700 18300

W33×169 (9290)

TFL 2 3 4 BFL 6 7

0 0.305 0.610 0.915 1.22 4.28 7.66

2480 2120 1770 1420 1070 845 619

18100 17400 16700 15700 14600 13800 12800

18600 17900 17100 16100 14900 14000 13000

19100 18300 17500 16400 15200 14300 13200

19600 18800 17900 16800 15500 14500 13400

20100 19300 18300 17200 15800 14800 13600

20600 19700 18700 17600 16100 15100 13800

21200 20200 19200 17900 16500 15300 14000

21700 20700 19600 18300 16800 15600 14300

22300 21300 20100 18800 17100 15900 14500

22900 21800 20600 19200 17500 16200 14700

23400 22300 21100 19600 17800 16500 14900

Y 2 b, in. 4.5 5

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:04 AM

Page 198

DESIGN OF FLEXURAL MEMBERS

3–198

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

W33-W30

Fy = 50 ksi

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W33×152 (8160)

TFL 2 3 4 BFL 6 7

0 0.265 0.530 0.795 1.06 4.34 7.91

2250 1940 1630 1320 1020 788 561

16100 15500 14800 14000 13100 12300 11300

16500 15900 15200 14300 13400 12500 11500

16900 16300 15500 14600 13600 12700 11700

17400 16700 15900 15000 13900 12900 11800

17800 17100 16300 15300 14200 13200 12000

18300 17600 16700 15700 14500 13400 12200

18800 18000 17100 16000 14800 13700 12400

19300 18500 17500 16400 15100 13900 12600

19800 18900 17900 16800 15400 14200 12800

20300 19400 18400 17100 15700 14500 13000

20800 19900 18800 17500 16100 14700 13200

W33×141 (7450)

TFL 2 3 4 BFL 6 7

0 0.240 0.480 0.720 0.960 4.34 8.08

2080 1800 1520 1250 971 745 519

14700 14200 13600 12900 12100 11300 10300

15100 14500 13900 13200 12300 11500 10500

15500 14900 14200 13500 12600 11700 10700

15900 15300 14600 13800 12800 11900 10800

16300 15700 14900 14100 13100 12100 11000

16700 16100 15300 14400 13400 12400 11200

17200 16500 15700 14800 13700 12600 11300

17600 16900 16100 15100 13900 12800 11500

18100 17300 16500 15500 14200 13100 11700

18600 17800 16900 15800 14500 13300 11900

19100 18200 17300 16200 14800 13600 12100

W33×130 (6710)

TFL 2 3 4 BFL 6 7

0 0.214 0.428 0.641 0.855 4.39 8.30

1920 1670 1420 1180 932 705 479

13300 12800 12300 11700 11000 10300 9350

13700 13200 12600 12000 11300 10500 9490

14000 13500 12900 12300 11500 10600 9640

14400 13900 13300 12600 11800 10900 9790

14800 14200 13600 12900 12000 11100 9950

15200 14600 13900 13200 12300 11300 10100

15600 15000 14300 13500 12500 11500 10300

16000 15400 14600 13800 12800 11700 10400

16500 15800 15000 14100 13100 12000 10600

16900 16200 15400 14500 13400 12200 10800

17300 16600 15800 14800 13700 12400 11000

W33×118 (5900)

TFL 2 3 4 BFL 6 7

0 0.185 0.370 0.555 0.740 4.47 8.56

1740 1520 1310 1100 884 659 434

11800 11400 11000 10500 9890 9150 8260

12100 11700 11300 10700 10100 9330 8390

12500 12000 11500 11000 10300 9510 8530

12800 12300 11800 11300 10600 9700 8660

13200 12700 12100 11500 10800 9890 8800

13500 13000 12500 11800 11000 10100 8950

13900 13400 12800 12100 11300 10300 9090

14300 13700 13100 12400 11500 10500 9250

14700 14100 13400 12700 11800 10700 9400

15100 14400 13800 13000 12100 10900 9560

15500 14800 14100 13300 12300 11200 9720

W30×116 (4930)

TFL 2 3 4 BFL 6 7

0 0.213 0.425 0.638 0.850 3.98 7.43

1710 1490 1260 1040 818 623 428

9870 9530 9120 8670 8130 7570 6910

10200 9810 9370 8890 8320 7730 7030

10500 10100 9630 9120 8520 7890 7150

10800 10400 9900 9360 8720 8060 7270

11100 10700 10200 9600 8920 8230 7400

11400 11000 10400 9850 9140 8400 7530

11800 11300 10700 10100 9360 8580 7670

12100 11600 11000 10400 9580 8770 7810

12500 12000 11300 10600 9810 8960 7950

12800 12300 11600 10900 10000 9150 8090

13200 12600 12000 11200 10300 9350 8240

Y 2 b, in. 4.5 5

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:04 AM

Page 199

COMPOSITE BEAM SELECTION TABLES

3–199

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

Fy = 50 ksi

Y 1a in.

∑Qn kip

Y 2 b, in. 4.5 5

W30-W27

Shaped

PNAc

W30×108 (4470)

TFL 2 3 4 BFL 6 7

0 1590 9000 9280 9560 9840 10100 10400 10800 11100 11400 11700 12100 0.190 1390 8700 8950 9220 9480 9760 10000 10300 10600 10900 11300 11600 0.380 1190 8350 8590 8830 9070 9330 9590 9850 10100 10400 10700 11000 0.570 987 7940 8150 8370 8590 8820 9050 9290 9530 9780 10000 10300 0.760 787 7470 7650 7840 8030 8230 8430 8640 8850 9060 9290 9510 4.04 592 6930 7080 7230 7390 7550 7710 7880 8060 8240 8420 8600 7.63 396 6280 6390 6500 6620 6730 6850 6980 7110 7240 7370 7510

W30×99 (3990)

TFL 2 3 4 BFL 6 7

0 1450 8110 8350 8610 8870 0.168 1270 7830 8070 8300 8550 0.335 1100 7540 7760 7980 8200 0.503 922 7190 7380 7580 7790 0.670 747 6790 6960 7130 7310 4.19 555 6270 6410 6550 6690 7.88 363 5640 5740 5840 5950

9140 8800 8440 8000 7490 6840 6050

9420 9060 8670 8210 7680 7000 6160

9700 9330 8920 8430 7880 7150 6280

9990 9600 9170 8660 8070 7310 6390

10300 9880 9430 8890 8280 7480 6510

10600 10200 9690 9130 8480 7650 6640

10900 10500 9960 9370 8700 7820 6760

W30×90 (3610)

TFL 2 3 4 BFL 6 7

0 1320 7310 7530 7760 8000 0.153 1160 7070 7280 7490 7720 0.305 998 6790 6990 7190 7390 0.458 839 6480 6660 6840 7020 0.610 681 6130 6280 6440 6600 4.01 505 5660 5780 5910 6040 7.76 329 5090 5180 5270 5360

8240 7940 7600 7210 6760 6180 5460

8490 8180 7820 7410 6940 6310 5560

8750 8420 8040 7610 7110 6460 5660

9010 8660 8260 7810 7290 6600 5770

9280 8920 8500 8020 7470 6750 5880

9560 9180 8730 8240 7660 6910 5990

9840 9440 8980 8460 7850 7060 6100

W27×102 (3620)

TFL 2 3 4 BFL 6 7

0 1500 7250 7480 7730 7980 0.208 1290 6970 7190 7420 7650 0.415 1090 6670 6870 7080 7290 0.623 878 6300 6470 6650 6840 0.830 670 5860 6010 6160 6310 3.40 523 5500 5620 5740 5870 6.27 375 5070 5170 5260 5360

8240 7890 7510 7030 6470 6010 5470

8510 8140 7730 7230 6640 6150 5570

8780 8390 7960 7430 6810 6290 5680

9060 8650 8200 7640 6980 6430 5800

9350 8920 8450 7850 7160 6580 5910

9650 9200 8700 8070 7340 6740 6030

9950 9480 8950 8300 7530 6900 6150

W27×94 (3270)

TFL 2 3 4 BFL 6 7

0 1380 6560 6780 7000 7230 0.186 1190 6320 6520 6730 6940 0.373 1010 6050 6240 6430 6620 0.559 821 5730 5890 6060 6230 0.745 635 5350 5480 5620 5770 3.45 490 5000 5110 5230 5350 6.41 345 4590 4670 4760 4860

7470 7160 6820 6400 5920 5470 4950

7720 7390 7030 6590 6070 5600 5050

7970 7620 7240 6770 6230 5730 5150

8230 7860 7460 6970 6390 5870 5250

8490 8100 7680 7160 6560 6010 5360

8760 8360 7910 7370 6730 6150 5470

9040 8610 8150 7580 6910 6290 5580

2

2.5

3

3.5

4

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5.5

6

6.5

7

AISC_Part 3D:14th Ed.

2/24/11

9:04 AM

Page 200

DESIGN OF FLEXURAL MEMBERS

3–200

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

W27-W24 Y 1a in.

∑Qn kip

Y 2 b, in. 4.5 5

Fy = 50 ksi

Shaped

PNAc

5.5

6

6.5

7

W27×84 (2850)

TFL 2 3 4 BFL 6 7

0 1240 5770 5960 6160 6360 6580 6790 0.160 1080 5570 5740 5930 6120 6320 6520 0.320 915 5330 5490 5660 5830 6010 6200 0.480 755 5060 5200 5360 5510 5670 5840 0.640 595 4740 4870 5000 5130 5270 5410 3.53 452 4410 4510 4620 4730 4840 4960 6.64 309 4010 4090 4170 4250 4340 4430

7020 6730 6390 6010 5550 5080 4510

7250 6940 6590 6180 5700 5200 4610

7480 7160 6790 6360 5860 5330 4700

7730 7390 6990 6540 6010 5460 4800

7970 7620 7200 6730 6180 5590 4900

W24×94 (2700)

TFL 2 3 4 BFL 6 7

0 1390 5480 5680 5880 6100 6320 6550 0.219 1190 5260 5450 5640 5840 6040 6250 0.438 988 5010 5180 5350 5520 5710 5900 0.656 790 4710 4860 5010 5160 5320 5490 0.875 591 4360 4480 4600 4730 4860 5000 3.05 469 4100 4200 4310 4420 4530 4640 5.43 346 3810 3890 3970 4060 4140 4230

6780 6470 6090 5660 5140 4760 4330

7020 6690 6290 5830 5280 4880 4420

7270 6920 6500 6010 5430 5010 4520

7530 7150 6710 6200 5580 5140 4630

7790 7390 6930 6390 5740 5270 4730

W24×84 (2370)

TFL 2 3 4 BFL 6 7

0 1240 4810 4990 5170 5360 5560 5760 0.193 1060 4620 4790 4950 5130 5310 5490 0.385 888 4410 4560 4710 4870 5030 5200 0.578 714 4160 4290 4420 4560 4700 4850 0.770 540 3850 3960 4070 4190 4310 4430 3.02 425 3620 3710 3800 3900 4000 4100 5.48 309 3350 3420 3490 3570 3640 3720

5970 5690 5370 5000 4550 4210 3810

6180 5880 5550 5160 4680 4320 3890

6400 6090 5740 5320 4820 4430 3980

6630 6300 5930 5480 4960 4550 4070

6860 6510 6120 5650 5100 4660 4160

W24×76 (2100)

TFL 2 3 4 BFL 6 7

0 1120 4280 4440 4600 4770 4950 5130 0.170 967 4120 4270 4420 4580 4740 4910 0.340 814 3930 4070 4210 4350 4500 4650 0.510 662 3720 3840 3960 4090 4220 4350 0.680 509 3460 3560 3660 3770 3880 3990 2.99 394 3230 3320 3400 3490 3580 3680 5.59 280 2970 3040 3100 3170 3240 3310

5320 5080 4810 4490 4110 3770 3390

5510 5260 4970 4630 4230 3880 3460

5710 5440 5140 4780 4360 3980 3540

5910 5630 5310 4930 4480 4080 3630

6120 5830 5490 5090 4610 4190 3710

W24×68 (1830)

TFL 2 3 4 BFL 6 7

0 1010 3760 3900 4050 4200 4360 4520 0.146 874 3620 3760 3890 4030 4180 4330 0.293 743 3470 3590 3710 3840 3980 4110 0.439 611 3290 3390 3510 3620 3740 3860 0.585 480 3080 3170 3260 3360 3460 3570 3.04 366 2860 2930 3010 3090 3180 3260 5.80 251 2600 2660 2720 2780 2840 2900

4690 4480 4260 3990 3670 3350 2970

4860 4640 4400 4120 3790 3450 3040

5040 4810 4550 4250 3900 3540 3110

5220 4980 4710 4390 4020 3640 3180

5410 5150 4870 4530 4140 3740 3260

2

2.5

3

3.5

4

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:04 AM

Page 201

COMPOSITE BEAM SELECTION TABLES

3–201

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

Fy = 50 ksi

W24-W21

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W24×62 (1550)

TFL 2 3 4 BFL 6 7

0 0.148 0.295 0.443 0.590 3.45 6.56

910 806 702 598 495 361 228

3300 3190 3070 2930 2780 2540 2250

3420 3310 3180 3040 2870 2610 2300

3560 3440 3300 3140 2960 2690 2350

3690 3560 3420 3250 3060 2770 2410

3840 3700 3540 3360 3160 2850 2470

3980 3840 3670 3480 3260 2930 2520

4130 3980 3800 3600 3370 3020 2590

4290 4120 3940 3720 3480 3110 2650

4450 4270 4080 3850 3590 3200 2710

4610 4430 4220 3980 3710 3290 2780

4780 4590 4370 4110 3830 3390 2850

W24×55 (1350)

TFL 2 3 4 BFL 6 7

0 0.126 0.253 0.379 0.505 3.46 6.67

810 721 633 544 456 329 203

2890 2800 2700 2590 2460 2240 1970

3010 2910 2800 2680 2540 2310 2010

3120 3020 2910 2780 2630 2370 2060

3250 3140 3010 2870 2720 2450 2110

3370 3250 3120 2970 2810 2520 2160

3500 3380 3240 3080 2900 2590 2210

3640 3500 3360 3190 3000 2670 2270

3770 3630 3480 3300 3100 2750 2320

3920 3770 3600 3410 3200 2830 2380

4060 3900 3730 3530 3300 2920 2440

4210 4050 3860 3650 3410 3000 2500

W21×73 (1600)

TFL 2 3 4 BFL 6 7

0 1080 3310 3450 3590 3740 3900 4060 0.185 921 3170 3300 3430 3570 3710 3860 0.370 768 3020 3140 3260 3380 3510 3640 0.555 614 2840 2940 3050 3150 3270 3380 0.740 461 2620 2710 2790 2880 2980 3070 2.58 365 2470 2540 2610 2680 2760 2840 4.69 269 2280 2340 2400 2460 2520 2580

4220 4010 3780 3500 3170 2930 2650

4390 4170 3920 3630 3270 3010 2720

4570 4330 4070 3750 3380 3100 2790

4750 4500 4220 3890 3490 3190 2860

4940 4670 4380 4020 3600 3290 2930

W21×68 (1480)

TFL 2 3 4 BFL 6 7

0 1000 3060 3180 3320 3450 3600 3750 0.171 858 2930 3050 3180 3300 3440 3570 0.343 717 2800 2900 3010 3130 3250 3370 0.514 575 2630 2720 2820 2920 3030 3130 0.685 434 2430 2510 2590 2670 2760 2850 2.60 342 2280 2350 2420 2490 2560 2630 4.74 250 2110 2160 2210 2270 2330 2390

3900 3710 3500 3250 2940 2710 2450

4060 3860 3630 3360 3040 2790 2510

4220 4010 3770 3480 3140 2880 2580

4390 4160 3910 3600 3240 2960 2640

4560 4320 4050 3730 3340 3050 2710

W21×62 (1330)

TFL 2 3 4 BFL 6 7

0 0.154 0.308 0.461 0.615 2.54 4.78

3530 3360 3180 2950 2690 2460 2210

3670 3500 3300 3060 2770 2540 2270

3820 3640 3420 3170 2870 2610 2330

3970 3780 3550 3280 2960 2690 2390

4130 3920 3680 3400 3060 2780 2450

915 788 662 535 408 318 229

2760 2650 2530 2390 2210 2070 1900

2880 2760 2630 2470 2280 2130 1950

3000 2870 2730 2560 2360 2190 2000

3120 2990 2840 2650 2440 2260 2050

3250 3110 2950 2750 2520 2320 2100

Y 2 b, in. 4.5 5

3390 3240 3060 2850 2600 2390 2150

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:04 AM

Page 202

DESIGN OF FLEXURAL MEMBERS

3–202

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

W21

Fy = 50 ksi

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W21×57 (1170)

TFL 2 3 4 BFL 6 7

0 0.163 0.325 0.488 0.650 2.93 5.40

835 728 622 515 409 309 209

2490 2400 2290 2170 2030 1880 1700

2590 2490 2380 2250 2110 1940 1740

2700 2600 2480 2340 2180 2000 1780

2820 2710 2580 2430 2250 2060 1830

2940 2820 2680 2520 2330 2120 1880

3060 2930 2780 2610 2410 2190 1930

3190 3050 2890 2710 2500 2260 1980

3320 3170 3010 2810 2580 2330 2030

3460 3300 3120 2910 2670 2410 2090

3600 3430 3240 3020 2770 2480 2140

3740 3570 3370 3130 2860 2560 2200

W21×55 (1140)

TFL 2 3 4 BFL 6 7

0 0.131 0.261 0.392 0.522 2.62 5.00

810 703 595 488 381 292 203

2390 2300 2190 2080 1940 1800 1640

2490 2390 2280 2150 2000 1850 1680

2590 2490 2370 2230 2070 1910 1720

2710 2590 2470 2320 2140 1970 1770

2820 2700 2560 2400 2210 2030 1810

2940 2810 2660 2490 2290 2090 1860

3060 2930 2770 2580 2370 2160 1910

3190 3040 2870 2680 2450 2230 1960

3320 3160 2990 2780 2530 2290 2010

3450 3290 3100 2880 2620 2370 2070

3590 3420 3220 2980 2710 2440 2120

W21×50 (984)

TFL 2 3 4 BFL 6 7

0 0.134 0.268 0.401 0.535 2.91 5.56

735 648 560 473 386 285 184

2110 2040 1960 1870 1760 1620 1440

2210 2130 2040 1940 1830 1670 1470

2300 2220 2130 2020 1890 1720 1510

2400 2310 2210 2100 1960 1780 1550

2510 2410 2300 2180 2030 1840 1590

2620 2510 2400 2260 2110 1900 1640

2730 2620 2490 2350 2180 1960 1680

2840 2730 2590 2440 2260 2020 1730

2960 2840 2690 2530 2350 2090 1780

3080 2950 2800 2630 2430 2160 1820

3210 3070 2910 2730 2520 2230 1880

W21×48 (959)

TFL 2 3 4 BFL 6 7

0 0.108 0.215 0.323 0.430 2.71 5.26

705 617 530 442 355 266 176

2030 1950 1870 1780 1670 1540 1390

2110 2040 1950 1850 1730 1590 1420

2210 2120 2030 1920 1790 1640 1460

2300 2210 2110 1990 1860 1690 1500

2400 2300 2200 2070 1920 1750 1540

2500 2400 2280 2150 1990 1810 1580

2610 2500 2380 2230 2060 1860 1620

2720 2600 2470 2320 2140 1920 1660

2830 2710 2570 2400 2210 1990 1710

2950 2820 2670 2490 2290 2050 1750

3070 2930 2770 2590 2370 2120 1800

W21×44 (843)

TFL 2 3 4 BFL 6 7

0 0.113 0.225 0.338 0.450 2.92 5.71

650 577 504 431 358 260 163

1830 1780 1710 1630 1550 1410 1240

1920 1850 1780 1700 1610 1460 1270

2000 1930 1850 1770 1670 1500 1310

2090 2020 1930 1840 1730 1560 1340

2180 2100 2010 1910 1790 1610 1380

2280 2190 2100 1990 1860 1660 1420

2370 2280 2180 2060 1930 1720 1460

2480 2380 2270 2150 2000 1780 1500

2580 2480 2360 2230 2080 1840 1540

2690 2580 2460 2310 2150 1900 1580

2800 2680 2550 2400 2230 1960 1630

Y 2 b, in. 4.5 5

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:04 AM

Page 203

COMPOSITE BEAM SELECTION TABLES

3–203

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

Fy = 50 ksi

W18

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W18×60 (984)

TFL 2 3 4 BFL 6 7

0 0.174 0.348 0.521 0.695 2.18 3.80

880 749 617 486 355 287 220

2070 1980 1880 1760 1610 1520 1420

2170 2070 1960 1830 1660 1570 1460

2270 2170 2050 1900 1720 1620 1500

2380 2270 2140 1980 1790 1670 1540

2490 2370 2230 2060 1850 1730 1590

2610 2480 2330 2140 1920 1780 1640

2730 2590 2430 2230 1990 1840 1680

2860 2710 2530 2320 2060 1910 1730

2990 2830 2640 2410 2140 1970 1790

3130 2950 2750 2510 2220 2040 1840

3270 3080 2860 2610 2300 2110 1900

W18×55 (890)

TFL 2 3 4 BFL 6 7

0 0.158 0.315 0.473 0.630 2.15 3.86

810 691 573 454 336 269 203

1880 1800 1710 1600 1470 1380 1290

1970 1880 1790 1670 1520 1430 1320

2070 1970 1860 1730 1580 1480 1360

2170 2060 1950 1810 1640 1530 1400

2270 2160 2030 1880 1700 1580 1440

2380 2260 2120 1960 1760 1630 1490

2490 2360 2210 2040 1830 1690 1530

2600 2470 2310 2120 1900 1750 1580

2720 2580 2410 2210 1970 1800 1630

2850 2690 2510 2300 2040 1870 1670

2980 2810 2620 2390 2110 1930 1730

W18×50 (800)

TFL 2 3 4 BFL 6 7

0 0.143 0.285 0.428 0.570 2.08 3.82

735 628 521 414 308 246 184

1690 1620 1540 1440 1330 1250 1160

1770 1700 1610 1500 1370 1290 1190

1860 1780 1680 1560 1430 1330 1220

1950 1860 1750 1630 1480 1380 1260

2040 1940 1830 1700 1530 1420 1300

2140 2030 1910 1770 1590 1470 1340

2240 2130 2000 1840 1650 1520 1380

2350 2220 2080 1910 1710 1580 1420

2450 2320 2170 1990 1780 1630 1460

2570 2430 2260 2070 1840 1690 1510

2680 2530 2360 2160 1910 1740 1550

W18×46 (712)

TFL 2 3 4 BFL 6 7

0 0.151 0.303 0.454 0.605 2.42 4.36

675 583 492 400 308 239 169

1540 1480 1410 1330 1230 1140 1040

1610 1550 1470 1380 1280 1180 1070

1690 1620 1540 1440 1330 1220 1100

1780 1700 1610 1500 1380 1270 1140

1860 1780 1680 1570 1430 1310 1170

1950 1860 1760 1630 1490 1360 1210

2040 1950 1840 1700 1550 1410 1250

2140 2040 1920 1780 1610 1460 1280

2240 2130 2000 1850 1670 1510 1320

2340 2220 2090 1930 1730 1570 1370

2450 2320 2180 2010 1800 1620 1410

W18×40 (612)

TFL 2 3 4 BFL 6 7

0 0.131 0.263 0.394 0.525 2.26 4.27

590 511 432 353 274 211 148

1320 1270 1210 1140 1060 985 896

1390 1330 1270 1190 1100 1020 922

1450 1390 1320 1240 1150 1060 950

1530 1460 1390 1300 1190 1090 979

1600 1530 1450 1350 1240 1130 1010

1680 1600 1510 1410 1290 1170 1040

1760 1680 1580 1470 1340 1220 1070

1840 1760 1650 1530 1390 1260 1110

1930 1840 1730 1600 1450 1310 1140

2020 1920 1800 1670 1510 1350 1180

2110 2010 1880 1740 1560 1400 1210

Y 2 b, in. 4.5 5

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

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DESIGN OF FLEXURAL MEMBERS

3–204

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

W18-W16

Fy = 50 ksi

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W18×35 (510)

TFL 2 3 4 BFL 6 7

0 0.106 0.213 0.319 0.425 2.37 4.56

515 451 388 324 260 194 129

1120 1080 1030 978 917 842 753

1170 1130 1080 1020 955 873 776

1230 1190 1130 1070 995 906 800

1300 1240 1190 1120 1040 940 825

1360 1300 1240 1170 1080 975 851

1430 1370 1300 1220 1130 1010 878

1500 1430 1360 1270 1170 1050 906

1570 1500 1420 1330 1220 1090 935

1650 1570 1490 1390 1270 1130 965

1720 1640 1550 1450 1320 1170 996

1800 1720 1620 1510 1380 1220 1030

W16×45 (586)

TFL 2 3 4 BFL 6 7

0 0.141 0.283 0.424 0.565 1.77 3.23

665 566 466 367 267 217 166

1260 1200 1140 1060 971 917 854

1330 1270 1200 1110 1010 950 882

1400 1330 1260 1160 1050 986 910

1470 1400 1320 1220 1090 1020 940

1550 1470 1380 1270 1140 1060 972

1630 1550 1450 1330 1190 1100 1000

1720 1630 1520 1390 1230 1140 1040

1810 1710 1590 1450 1290 1190 1070

1900 1790 1670 1520 1340 1230 1110

1990 1880 1750 1590 1390 1280 1150

2090 1970 1830 1660 1450 1330 1190

W16×40 (518)

TFL 2 3 4 BFL 6 7

0 0.126 0.253 0.379 0.505 1.70 3.16

590 502 413 325 237 192 148

1110 1170 1230 1300 1370 1440 1520 1060 1120 1170 1240 1300 1370 1430 1000 1050 1110 1160 1220 1280 1340 937 980 1030 1070 1120 1170 1230 856 891 927 965 1000 1050 1090 808 837 869 901 935 971 1010 755 779 804 831 859 888 918

1590 1510 1400 1280 1130 1050 949

1670 1580 1470 1340 1180 1090 982

1760 1660 1540 1400 1230 1130 1020

1850 1740 1610 1460 1280 1170 1050

W16×36 (448)

TFL 2 3 4 BFL 6 7

0 0.108 0.215 0.323 0.430 1.82 3.46

530 455 380 305 229 181 133

973 1030 1080 1140 1200 933 983 1040 1090 1150 886 931 979 1030 1080 831 871 912 956 1000 765 797 831 867 905 715 743 772 802 833 659 680 703 727 752

1410 1330 1250 1150 1030 936 833

1480 1400 1310 1200 1070 973 862

1550 1470 1370 1260 1120 1010 892

1630 1540 1440 1310 1160 1050 923

W16×31 (375)

TFL 2 3 4 BFL 6 7

0 0.110 0.220 0.330 0.440 2.00 3.80

457 396 335 274 213 164 114

827 795 758 714 663 614 556

874 838 797 749 692 639 574

923 884 838 786 723 664 594

Y 2 b, in. 4.5 5

1270 1210 1130 1050 944 866 778

1340 1270 1190 1100 984 901 805

974 1030 1080 1140 1200 1260 1330 1400 931 981 1030 1090 1140 1200 1260 1320 882 927 974 1020 1070 1130 1180 1240 824 864 906 949 995 1040 1090 1140 756 790 825 862 900 940 982 1020 691 720 749 780 812 845 879 914 614 636 658 681 705 730 756 783

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 205

COMPOSITE BEAM SELECTION TABLES

3–205

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

Fy = 50 ksi

W16-W14

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

4.5

5

5.5

W16×26 (301)

TFL 2 3 4 BFL 6 7

0 0.0863 0.173 0.259 0.345 2.05 4.01

384 337 289 242 194 145 96.0

674 649 621 589 551 505 450

712 686 654 619 577 527 466

753 724 689 651 604 549 482

796 763 726 683 633 572 499

840 805 764 718 663 597 517

887 849 804 754 694 622 535

935 894 846 791 727 649 555

985 1040 1090 1150 941 990 1040 1090 889 934 980 1030 830 871 912 956 760 795 832 869 676 705 734 765 575 596 617 640

W14×38 (385)

TFL 2 3 4 BFL 6 7

0 0.129 0.258 0.386 0.515 1.38 2.53

560 473 386 299 211 176 140

844 805 759 704 636 604 568

896 853 802 741 665 629 589

951 903 847 779 695 656 611

W14×34 (340)

TFL 2 3 4 BFL 6 7

0 0.114 0.228 0.341 0.455 1.42 2.61

500 423 346 270 193 159 125

745 711 671 624 566 535 502

791 754 709 656 591 558 521

840 798 749 691 618 581 540

891 845 791 727 647 606 561

945 1000 1060 1120 1190 1250 1320 895 946 1000 1060 1110 1180 1240 835 881 929 979 1030 1090 1140 764 804 845 888 933 979 1030 677 708 741 775 811 848 886 632 659 687 717 748 780 813 582 605 628 653 678 705 732

W14×30 (291)

TFL 2 3 4 BFL 6 7

0 0.0963 0.193 0.289 0.385 1.46 2.80

443 378 313 248 183 147 111

642 614 581 543 496 466 432

682 651 615 572 520 486 448

725 691 650 603 545 507 465

770 732 688 635 571 530 483

817 775 727 669 599 553 502

866 821 767 704 627 578 522

918 868 810 741 658 604 542

972 1030 1090 1150 918 969 1020 1080 855 901 949 999 780 820 862 905 689 722 756 791 630 658 687 717 564 586 610 634

W14×26 (245)

TFL 2 3 4 BFL 6 7

0 0.105 0.210 0.315 0.420 1.67 3.18

385 332 279 226 173 135 96.1

553 530 504 473 436 405 368

589 563 534 499 458 423 382

626 598 565 527 481 443 397

665 634 598 556 506 463 413

706 672 633 586 531 485 429

749 712 669 618 558 507 447

794 754 707 652 586 530 465

841 797 746 686 615 555 483

Y 2 b, in. 6

6.5

7

1010 1070 1130 1200 1270 1340 1410 1490 956 1010 1070 1130 1190 1260 1330 1400 894 943 995 1050 1100 1160 1220 1290 819 861 905 951 999 1050 1100 1150 726 759 794 830 868 907 948 990 683 712 742 774 807 841 877 914 634 659 684 710 738 766 796 827

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

890 843 787 722 645 580 503

941 890 830 760 677 607 523

994 938 874 799 709 634 544

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9:04 AM

Page 206

DESIGN OF FLEXURAL MEMBERS

3–206

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

W14-W12

Fy = 50 ksi

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W14×22 (199)

TFL 2 3 4 BFL 6 7

0 0.0838 0.168 0.251 0.335 1.67 3.32

325 283 241 199 157 119 81.1

453 436 416 392 365 335 301

483 463 441 415 384 351 312

514 492 467 438 404 368 325

547 523 495 463 426 386 338

581 555 525 489 448 404 352

617 588 555 517 472 423 366

655 624 587 545 496 444 381

694 660 621 575 522 465 397

735 698 656 606 548 487 413

778 738 692 639 576 509 430

822 779 730 672 605 533 448

W12×30 (238)

TFL 2 3 4 BFL 6 7

0 0.110 0.220 0.330 0.440 1.10 1.92

440 368 296 224 153 131 110

530 504 473 435 389 372 355

567 538 503 460 408 389 370

606 573 534 486 428 407 385

648 611 567 514 449 426 402

691 651 602 544 472 446 419

737 692 639 575 495 467 438

785 736 678 607 520 489 457

835 782 718 641 546 512 477

887 829 760 676 573 536 498

942 879 804 713 601 561 520

998 931 850 751 631 587 542

W12×26 (204)

TFL 2 3 4 BFL 6 7

0 0.0950 0.190 0.285 0.380 1.07 1.94

383 321 259 198 136 116 95.6

455 433 407 375 336 321 304

487 462 432 397 352 336 317

521 493 460 420 370 351 331

557 526 489 444 389 368 345

594 560 519 470 409 386 360

634 596 551 497 429 404 376

676 634 585 525 451 423 392

719 674 620 555 474 444 410

764 715 656 586 498 465 428

812 758 694 618 523 487 447

861 803 734 652 548 509 467

W12×22 (156)

TFL 2 3 4 BFL 6 7

0 0.106 0.213 0.319 0.425 1.66 3.03

324 281 238 196 153 117 81.0

371 356 338 318 294 270 242

398 381 361 339 312 285 253

427 408 386 360 330 300 265

458 436 412 383 350 316 277

490 466 439 408 370 333 290

523 497 467 433 392 351 303

559 530 497 460 414 370 317

596 564 528 487 438 389 332

634 600 561 517 463 410 347

674 638 595 547 489 431 363

716 676 631 578 515 453 380

W12×19 (130)

TFL 2 3 4 BFL 6 7

0 0.0875 0.175 0.263 0.350 1.68 3.14

279 243 208 173 138 104 69.6

313 300 286 270 251 229 203

336 322 306 288 266 242 212

361 345 327 307 283 255 222

387 369 349 327 300 270 233

414 395 373 348 318 284 244

443 422 398 370 337 300 255

473 450 423 393 357 317 267

505 479 450 417 378 334 280

538 510 479 442 400 352 293

573 542 508 469 423 370 307

608 575 539 496 447 390 321

Y 2 b, in. 4.5 5

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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9:04 AM

Page 207

COMPOSITE BEAM SELECTION TABLES

3–207

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

Fy = 50 ksi

W12-W10

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W12×16 (103)

TFL 2 3 4 BFL 6 7

0 0.0663 0.133 0.199 0.265 1.71 3.32

236 209 183 156 130 94.3 58.9

254 245 235 223 210 189 163

273 263 252 239 224 200 171

294 282 270 255 239 212 179

316 303 289 272 254 225 188

339 324 309 291 271 238 197

363 347 330 310 288 251 207

388 371 352 330 306 266 217

415 396 375 351 325 281 228

442 422 400 373 344 297 239

471 449 425 396 365 313 250

501 477 451 420 386 331 262

W12×14 (88.6)

TFL 2 3 4 BFL 6 7

0 0.0563 0.113 0.169 0.225 1.68 3.35

208 186 163 141 119 85.3 52.0

220 213 204 195 184 165 141

237 229 219 209 197 175 148

255 246 235 223 210 186 155

274 264 252 239 224 197 163

295 283 270 255 238 208 171

316 303 288 272 254 221 179

338 324 308 290 270 234 188

361 346 328 309 287 247 198

386 369 350 329 305 261 207

411 393 372 349 323 276 218

437 418 395 370 342 291 228

W10×26 (144)

TFL 2 3 4 BFL 6 7

0 0.110 0.220 0.330 0.440 0.886 1.49

381 317 254 190 127 111 95.1

339 321 300 274 241 232 222

367 346 322 292 255 245 233

397 374 346 312 270 258 245

429 403 372 334 286 273 258

463 434 399 356 303 288 271

499 466 428 380 321 304 286

536 500 458 405 340 321 301

576 536 490 431 360 339 317

617 574 523 459 381 358 333

661 613 557 488 402 377 351

706 655 594 518 425 398 369

W10×22 (118)

TFL 2 3 4 BFL 6 7

0 0.0900 0.180 0.270 0.360 0.962 1.72

325 273 221 169 118 99.3 81.1

282 267 251 230 205 195 183

306 289 270 246 218 206 193

331 313 291 264 232 218 203

358 337 312 282 246 230 214

387 364 336 302 261 244 225

417 391 360 323 277 258 238

449 420 386 345 295 273 250

483 451 413 368 312 289 264

518 483 442 392 331 305 278

555 517 472 417 351 323 293

593 552 503 443 371 341 308

W10×19 (96.3)

TFL 2 3 4 BFL 6 7

0 0.0988 0.198 0.296 0.395 1.25 2.29

281 241 202 162 122 96.2 70.3

238 227 215 200 182 169 153

259 246 232 215 195 179 161

281 267 251 231 208 190 170

304 288 270 248 222 202 179

329 311 291 266 237 215 189

355 335 313 286 253 228 200

383 361 336 306 270 243 211

412 388 360 327 287 257 223

443 416 386 350 306 273 235

474 445 413 373 325 289 248

508 476 440 397 345 306 261

Y 2 b, in. 4.5 5

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:04 AM

Page 208

DESIGN OF FLEXURAL MEMBERS

3–208

Table 3-20 (continued)

ILB

Lower-Bound Elastic Moment of Inertia, ILB, for Plastic Composite Sections

W10

Fy = 50 ksi

Shaped

PNAc

Y 1a in.

∑Qn kip

2

2.5

3

3.5

4

5.5

6

6.5

7

W10×17 (81.9)

TFL 2 3 4 BFL 6 7

0 0.0825 0.165 0.248 0.330 1.31 2.45

250 216 183 150 117 89.8 62.4

206 197 187 175 161 148 132

224 214 202 189 173 157 139

244 232 219 203 185 167 147

264 251 236 219 198 178 155

286 272 255 235 212 190 164

310 293 274 253 227 202 173

334 316 295 271 243 215 183

360 340 317 290 259 229 193

387 365 340 311 276 243 204

415 391 364 332 294 258 215

445 418 388 354 313 274 227

W10×15 (68.9)

TFL 2 3 4 BFL 6 7

0 0.0675 0.135 0.203 0.270 1.35 2.60

221 194 167 140 113 83.8 55.1

177 170 162 153 142 128 112

193 185 176 165 153 137 118

210 201 190 178 164 147 125

228 218 206 192 177 157 133

248 236 223 207 190 167 140

268 255 240 223 204 178 148

289 275 259 240 218 190 157

312 296 278 258 233 203 166

336 318 299 276 250 216 175

361 342 320 295 266 229 185

387 366 342 315 284 244 196

W10×12 (53.8)

TFL 2 3 4 BFL 6 7

0 0.0525 0.105 0.158 0.210 1.30 2.61

177 156 135 115 93.8 69.0 44.3

139 134 127 121 113 102 87.9

152 145 138 131 122 109 93.0

165 158 150 142 131 116 98.4

180 172 163 153 141 124 104

195 186 176 165 152 133 110

211 201 190 178 163 142 117

229 217 205 191 175 152 124

247 234 221 206 187 162 131

265 252 237 221 200 173 139

285 271 254 236 214 184 146

306 290 272 252 228 195 155

Y 2 b, in. 4.5 5

a

Y 1 = distance from top of the steel beam to plastic neutral axis Y 2 = distance from top of the steel beam to concrete flange force c See Figure 3-3c for PNA locations. d Value in parentheses is I (in.4) of noncomposite steel shape. x b

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/17/12

8:35 AM

Page 209

COMPOSITE BEAM SELECTION TABLES

3–209

Table 3-21

Shear Stud Anchor

Fu = 65 ksi

n

Nominal Horizontal Shear Strength for One Steel Headed Stud Anchor, Qn, kips Stud anchor diameter, in.

Deck condition

3/8 1/2

No deck

5/8 3/4

Deck Parallel

3/8

wr ≥ 1.5 hr

1/2 5/8 3/4 3/8

wr < 1.5 hr

1/2 5/8 3/4

Weak studs per rib (Rp = 0.60)

1

1/2 5/8 3/4 3/8

2

1/2 5/8 3/4 3/8

3

1/2 5/8 3/4 3/8

Strong studs per rib (Rp = 0.75)

Deck Perpendicular

3/8

1

1/2 5/8 3/4 3/8

2

1/2 5/8 3/4 3/8

3

1/2 5/8 3/4

Normal weight concrete

wc = 145 pcf

Lightweight concrete

wc = 110 pcf

fc′ = 3 ksi

fc′ = 4 ksi

fc′ = 3 ksi

fc′ = 4 ksi

5.26 9.35 14.6 21.0 5.26 9.35 14.6 21.0 4.58 8.14 12.7 18.3 4.31 7.66 12.0 17.2 3.66 6.51 10.2 14.6 3.02 5.36 8.38 12.1 5.26 9.35 14.6 21.0 4.58 8.14 12.7 18.3 3.77 6.70 10.5 15.1

5.38 9.57 15.0 21.5 5.38 9.57 15.0 21.5 4.58 8.14 12.7 18.3 4.31 7.66 12.0 17.2 3.66 6.51 10.2 14.6 3.02 5.36 8.38 12.1 5.38 9.57 15.0 21.5 4.58 8.14 12.7 18.3 3.77 6.70 10.5 15.1

4.28 7.60 11.9 17.1 4.28 7.60 11.9 17.1 4.28 7.60 11.9 17.1 4.28 7.60 11.9 17.1 3.66 6.51 10.2 14.6 3.02 5.36 8.38 12.1 4.28 7.60 11.9 17.1 4.28 7.60 11.9 17.1 3.77 6.70 10.5 15.1

5.31 9.43 14.7 21.2 5.31 9.43 14.7 21.2 4.58 8.14 12.7 18.3 4.31 7.66 12.0 17.2 3.66 6.51 10.2 14.6 3.02 5.36 8.38 12.1 5.31 9.43 14.7 21.2 4.58 8.14 12.7 18.3 3.77 6.70 10.5 15.1

Note: Tabulated values are applicable only to concrete made with ASTM C33 aggregates for normal weight concrete and ASTM C330 aggregates for lightweight concrete. After-weld steel headed stud anchor lengths assumed to be ≥ Deck height + 1.5 in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:04 AM

Page 210

DESIGN OF FLEXURAL MEMBERS

3–210

Table 3-22a

Concentrated Load Equivalents

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:04 AM

Page 211

BEAM DIAGRAMS AND FORMULAS

3–211

Table 3-22b

Cantilevered Beams Beam Diagrams and Formulas— Equal Loads, Equally Spaced

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

9:04 AM

Page 212

DESIGN OF FLEXURAL MEMBERS

3–212

Table 3-22c

Continuous Beams Moments and Shear Coefficients— Equal Spans, Equally Loaded

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

9:04 AM

Page 213

BEAM DIAGRAMS AND FORMULAS

3–213

Table 3-23

Shears, Moments and Deflections

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

3–214

2/24/11

9:04 AM

Page 214

DESIGN OF FLEXURAL MEMBERS

Table 3-23 (continued)

Shears, Moments and Deflections

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D_14th Ed._February 25, 2012 14-11-24 9:34 AM Page 215

(Black plate)

BEAM DIAGRAMS AND FORMULAS

Table 3-23 (continued)

Shears, Moments and Deflections

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3–215

AISC_Part 3D:14th Ed.

3–216

2/24/11

9:04 AM

Page 216

DESIGN OF FLEXURAL MEMBERS

Table 3-23 (continued)

Shears, Moments and Deflections

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

4/12/11

2:02 PM

Page 217

BEAM DIAGRAMS AND FORMULAS

Table 3-23 (continued)

Shears, Moments and Deflections

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3–217

AISC_Part 3D:14th Ed.

4/12/11

2:54 PM

Page 218

3–218

DESIGN OF FLEXURAL MEMBERS

Table 3-23 (continued)

Shears, Moments and Deflections

load

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D_14th Ed._Nov. 19, 2012 12/02/13 11:28 AM Page 219

BEAM DIAGRAMS AND FORMULAS

Table 3-23 (continued)

Shears, Moments and Deflections

M1

R

V

M1 M max

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3–219

AISC_Part 3D:14th Ed.

3–220

4/12/11

3:05 PM

Page 220

DESIGN OF FLEXURAL MEMBERS

Table 3-23 (continued)

Shears, Moments and Deflections

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

2/24/11

9:04 AM

Page 221

BEAM DIAGRAMS AND FORMULAS

Table 3-23 (continued)

Shears, Moments and Deflections

NOTE: For a negative value of

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3–221

AISC_Part 3D:14th Ed.

3–222

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9:04 AM

Page 222

DESIGN OF FLEXURAL MEMBERS

Table 3-23 (continued)

Shears, Moments and Deflections

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

9:04 AM

Page 223

BEAM DIAGRAMS AND FORMULAS

3–223

Table 3-23 (continued)

Shears, Moments and Deflections 29. CONTINUOUS BEAM — TWO EQUAL SPANS — UNIFORM LOAD ON ONE SPAN

l from R1 ) 31. CONTINUOUS BEAM — TWO EQUAL SPANS — CONCENTRATED LOAD AT ANY POINT

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

3–224

2/24/11

9:04 AM

Page 224

DESIGN OF FLEXURAL MEMBERS

Table 3-23 (continued)

Shears, Moments and Deflections

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D_14th Ed._ 01/03/12 10:12 AM Page 225

BEAM DIAGRAMS AND FORMULAS

3–225

Table 3-23 (continued)

Shears, Moments and Deflections

a

R (l – x)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D:14th Ed.

3–226

2/24/11

9:04 AM

Page 226

DESIGN OF FLEXURAL MEMBERS

Table 3-23 (continued)

Shears, Moments and Deflections 37. CONTINUOUS BEAM — THREE EQUAL SPANS — ONE END SPAN UNLOADED

38. CONTINUOUS BEAM — THREE EQUAL SPANS — END SPANS LOADED

39. CONTINUOUS BEAM — THREE EQUAL SPANS — ALL SPANS LOADED

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 3D_14th Ed._February 25, 2012 25/02/13 3:18 PM Page 227

BEAM DIAGRAMS AND FORMULAS

Table 3-23 (continued)

Shears, Moments and Deflections 40. CONTINUOUS BEAM — FOUR EQUAL SPANS — THIRD SPAN UNLOADED

41. CONTINUOUS BEAM — FOUR EQUAL SPANS — LOAD FIRT AND THIRD SPANS

42. CONTINUOUS BEAM — FOUR EQUAL SPANS — ALL SPANS LOADED

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3–227

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9:04 AM

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DESIGN OF FLEXURAL MEMBERS

3–228

Table 3-23 (continued)

Shears, Moments and Deflections 43. SIMPLE BEAM — ONE CONCENTRATED MOVING LOAD

44. SIMPLE BEAM — TWO EQUAL CONCENTRATED MOVING LOADS

45. SIMPLE BEAM — TWO UNEQUAL CONCENTRATED MOVING LOADS

GENERAL RULES FOR SIMPLE BEAMS CARRYING MOVING CONCENTRATED LOADS

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 4A:14th Ed.

4/1/11

8:47 AM

Page 1

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PART 4 DESIGN OF COMPRESSION MEMBERS

SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–3 AVAILABLE COMPRESSIVE STRENGTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–3 LOCAL BUCKLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–3 Determining the Width-to-Thickness Ratios of the Cross Section . . . . . . . . . . . . . . . 4–3 Determining the Slenderness of the Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–3 EFFECTIVE LENGTH AND COLUMN SLENDERNESS . . . . . . . . . . . . . . . . . . . . . . 4–3 COMPOSITE COMPRESSION MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–4 DESIGN TABLE DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–4 Steel Compression—Member Selection Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–4 Composite Compression—Member Selection Tables . . . . . . . . . . . . . . . . . . . . . . . . 4–9 PART 4 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–11 STEEL COMPRESSION—MEMBER SELECTION TABLES . . . . . . . . . . . . . . . . . . 4–12 Table 4-1. W-Shapes in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–12 Table 4-2. HP-Shapes in Axial Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–24 Table 4-3. Rectangular HSS in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . 4–28 Table 4-4. Square HSS in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–52 Table 4-5. Round HSS in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–68 Table 4-6. Pipe in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–85 Table 4-7. WT-Shapes in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–89 Table 4-8. Equal-Leg Double Angles in Axial Compression . . . . . . . . . . . . . . . . . 4–122 Table 4-9. LLBB Double Angles in Axial Compression . . . . . . . . . . . . . . . . . . . . 4–131 Table 4-10. SLBB Double Angles in Axial Compression . . . . . . . . . . . . . . . . . . . 4–146 Table 4-11. Concentrically Loaded Single Angles in Axial Compression . . . . . . . 4–161 Table 4-12. Eccentrically Loaded Single Angles in Axial Compression . . . . . . . . 4–183 COMPOSITE COMPRESSION—MEMBER SELECTION TABLES . . . . . . . . . . . 4–205 Table 4-13. Rectangular HSS Filled with 4-ksi Normal Weight Concrete in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–205 Table 4-14. Rectangular HSS Filled with 5-ksi Normal Weight Concrete in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–226 Table 4-15. Square HSS Filled with 4-ksi Normal Weight Concrete in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–247 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Table 4-16. Square HSS Filled with 5-ksi Normal Weight Concrete in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–263 Table 4-17. Round HSS Filled with 4-ksi Normal Weight Concrete in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–279 Table 4-18. Round HSS Filled with 5-ksi Normal Weight Concrete in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–296 Table 4-19. Pipe Filled with 4-ksi Normal Weight Concrete in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–313 Table 4-20. Pipe Filled with 5-ksi Normal Weight Concrete in Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–317 Table 4-21. Stiffness Reduction Factor τb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–321 Table 4-22. Available Critical Stress for Compression Members . . . . . . . . . . . . . . 4–322

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SCOPE The specification requirements and other design considerations summarized in this Part apply to the design of members subject to axial compression. For the design of members subject to eccentric compression or combined axial compression and flexure, see Part 6.

AVAILABLE COMPRESSIVE STRENGTH The available strength of compression members, φPn or Pn/Ω, which must equal or exceed the required strength, Pu or Pa, respectively, is determined according to AISC Specification Chapter E.

LOCAL BUCKLING Determining the Width-to-Thickness Ratios of the Cross Section Steel compression members are classified on the basis of the width-to-thickness ratios of the various elements of the cross section. The width-to-thickness ratio is calculated for each element of the cross section per AISC Specification Section B4.

Determining the Slenderness of the Cross Section When the width-to-thickness ratios of all compression elements are less than or equal to λr, the cross section is nonslender, and Q, the reduction factor for slender compression elements (elastic local buckling effects), equals 1.0. When the width-to-thickness ratio of a compression element is greater than λr, the cross section is a slender-element cross section and Q must be included in the calculation of the available compressive strength. Q is determined per AISC Specification Section E7, and λr is determined per AISC Specification Section B4 and Table B4.1a.

EFFECTIVE LENGTH AND COLUMN SLENDERNESS Columns are designed for their slenderness, KL/r, per AISC Specification Section E2. The effective length, KL, is equal to the effective length factor, K, multiplied by L, the physical length between braced points (see AISC Specification Appendix 6). When a stability analysis is performed using the direct analysis method per AISC Specification Chapter C, K = 1. When a stability analysis is performed using the first-order analysis method in AISC Specification Appendix Section 7.3, K = 1. When a stability analysis is performed using the effective length method in AISC Specification Appendix Section 7.2, the following applies: K = 1 for columns braced at each end and whose flexural stiffnesses are not considered to contribute to lateral stability and resistance to lateral loads. K = 1 for all columns when the ratio of maximum second-order drift to first-order drift in all stories is less than 1.1. K shall be determined from a sidesway buckling analysis for all columns whose flexural stiffnesses are considered to contribute to lateral stability and resistance to lateral AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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loads. Guidance on the proper determination of the value of K is given in AISC Specification Commentary to Appendix Section 7.2. As indicated in the User Note in AISC Specification Section E2, compression member slenderness, KL/r, should preferably be limited to a maximum of 200. Note that this recommendation does not apply to members that are primarily tension members, but subject to incidental compression under other load combinations. Additional information is available in the SSRC Guide to Stability Design Criteria for Metal Structures (Ziemian, 2010).

COMPOSITE COMPRESSION MEMBERS For the design of encased composite and filled composite compression members, see AISC Specification Section I2. See also AISC Design Guide 6, Load and Resistance Factor Design of W-Shapes Encased in Concrete (Griffis, 1992). For further information on composite design and construction, see also Viest et al. (1997).

DESIGN TABLE DISCUSSION Steel Compression—Member Selection Tables Table 4-1. W-Shapes in Axial Compression Available strengths in axial compression are given for W-shapes with Fy = 50 ksi (ASTM A992). The tabulated values are given for the effective length with respect to the y-axis (KL)y. However, the effective length with respect to the x-axis (KL)x must also be investigated. To determine the available strength in axial compression, the table should be entered at the larger of (KL)y and (KL)y eq, where

( KL ) y eq =

( KL )x

(4-1)

rx ry

Values of the ratio rx /ry and other properties useful in the design of W-shape compression members are listed at the bottom of Table 4-1. Variables Pwo , Pwi, Pwb and Pfb shown in Table 4-1 can be used to determine the strength of W-shapes without stiffeners to resist concentrated forces applied normal to the face(s) of the flange(s). In these tables it is assumed that the concentrated forces act far enough away from the member ends that end effects are not considered (end effects are addressed in Chapter 9). When Pr ≤ φRn or Rn /Ω, column web stiffeners are not required. Figures 4-1, 4-2 and 4-3 illustrate the limit states and the applicable variables for each. Web Local Yielding: The variables Pwo and Pwi can be used in the calculation of the available web local yielding strength for the column as follows: LRFD

ASD

φRn = Pwo + Pwi lb

(4-2a)

Rn /Ω = Pwo + Pwi lb

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where Rn = Fywtw (5k + lb ) = 5Fyw tw k + Fyw tw lb, kips (AISC Specification Equation J10-2 ) Pwo = φ5Fyw twk for LRFD and 5Fyw tw k/Ω for ASD, kips Pwi = φFyw tw for LRFD and Fyw tw /Ω for ASD, kips/in. k = distance from outer face of flange to the web toe of fillet, in. lb = length of bearing, in. tw = thickness of web, in. φ = 1.00 Ω = 1.50 Web Compression Buckling: The variable Pwb is the available web compression buckling strength for the column as follows: LRFD

ASD

φRn = Pwb

(4-3a)

Rn /Ω = Pwb

(4-3b)

where Rn = Pwb =

24 t w3 EFyw h φ24 t w3 EFyw

(AISC Specification Equation J10-8 ) for LRFD and

24 t w3 EFyw

for ASD, kips Ωh h Fyw = specified minimum yield stress of the web, ksi h = clear distance between flanges less the fillet or corner radius for rolled shapes, in. φ = 0.90 Ω = 1.67

Fig. 4-1. Illustration of web local yielding limit state (AISC Specification Section J10.2).

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Flange Local Bending: The variable Pfb is the available flange local bending strength for the column as follows: LRFD

ASD

φRn = Pfb

(4-4a)

Rn /Ω = Pfb

where Rn = 6.25 Fyf t 2f , kips (AISC Specification Equation J10-1 ) Pfb = φ6.25 Fyf t 2f for LRFD and 6.25 Fyf t 2f /Ω for ASD, kips φ = 0.90 Ω = 1.67

Fig. 4-2. Illustration of web compression buckling limit state (AISC Specification Section J10.5).

Fig. 4-3. Illustration of flange local bending limit state (AISC Specification Section J10.1).

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Table 4-2. HP-Shapes in Axial Compression Table 4-2 is similar to Table 4-1, except it covers HP-shapes with Fy = 50 ksi (ASTM A572 Grade 50).

Table 4-3. Rectangular HSS in Axial Compression Available strengths in axial compression are given for rectangular HSS with Fy = 46 ksi (ASTM A500 Grade B). The tabulated values are given for the effective length with respect to the y-axis, (KL)y. However, the effective length with respect to the x-axis (KL)x must also be investigated. To determine the available strength in axial compression, the table should be entered at the larger of (KL)y and (KL)y eq, where

( KL ) y eq =

( KL )x rx ry

(4-1)

Values of the ratio rx /ry and other properties useful in the design of rectangular HSS compression members are listed at the bottom of Table 4-3.

Table 4-4. Square HSS in Axial Compression Table 4-4 is similar to Table 4-3, except that it covers square HSS.

Table 4-5. Round HSS in Axial Compression Available strengths in axial compression are given for round HSS with Fy = 42 ksi (ASTM A500 Grade B). To determine the available strength in axial compression, the table should be entered at KL. Other properties useful in the design of compression members are listed at the bottom of the available column strength tables.

Table 4-6. Pipe in Axial Compression Table 4-6 is similar to Table 4-5, except it covers pipe with Fy = 35 ksi (ASTM A53 Grade B).

Table 4-7. WT-Shapes in Axial Compression Available strengths in axial compression, including the limit state of flexural-torsional buckling, are given for WT-shapes with Fy = 50 ksi (ASTM A992). Separate tabulated values are given for the effective lengths with respect to the x- and y-axes, (KL)x and (KL)y, respectively. Other properties useful in the design of WT-shape compression members are listed at the bottom of Table 4-7.

Table 4-8. Equal-Leg Double Angles in Axial Compression Available strengths in axial compression, including the limit state of flexural-torsional buckling, are given for equal-leg double angles with Fy = 36 ksi (ASTM A36), assuming 3/ 8-in. separation between the angles. These values can be used conservatively when a larger separation is provided. Alternatively, the value of (KL)y can be multiplied by the ratio of (ry for a 3/ 8-in. separation) to (ry for the actual separation). Separate tabulated values are given for the effective lengths with respect to the x- and y-axes, (KL)x and (KL)y, respectively. For buckling about the x-axis, the available strength AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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is not affected by the number of intermediate connectors. However, for buckling about the y-axis, the effects of shear deformations of the intermediate connectors must be considered. The tabulated values for (KL)y have been adjusted for the shear deformations in accordance with AISC Specification Equations E6-2a and E6-2b, which is applicable to welded and pretensioned bolted intermediate shear connectors. The number of intermediate connectors, n, is given in the table and the line of demarcation between the required connector values is dashed. Intermediate connectors are selected such that the available compression buckling strength about the y-axis is equal to or greater than 90% of that for compression buckling of the two angles as a unit. If fewer connectors or snug-tightened bolted intermediate connectors are used, the available strength must be recalculated per AISC Specification Section E6. Per AISC Specification Section E6.2, the slenderness of the individual components of the built-up member based upon the distance between intermediate connectors, a, must not exceed three-quarters of the controlling slenderness of the overall built-up compression member. Other properties useful in the design of double-angle compression members are listed at the bottom of Table 4-8.

Table 4-9. LLBB Double Angles in Axial Compression Table 4-9 is the same as Table 4-8, except that it provides available strengths in axial compression for double angles with long legs back-to-back.

Table 4-10. SLBB Double Angles in Axial Compression Table 4-10 is the same as Table 4-8, except that it provides available strengths in axial compression for double angles with short legs back-to-back.

Table 4-11. Concentrically Loaded Single Angles in Axial Compression Available strengths in axial compression are given for single angles, loaded through the centroid of the cross section, with Fy = 36 ksi (ASTM A36) based upon the effective length with respect to the z-axis, (KL)z. Single angles may be assumed to be loaded through the centroid when the requirements of AISC Specification Section E5 are met, as in these cases the eccentricity is accounted for and the slenderness is reduced by the restraining effects of the support at both ends of the member.

Table 4-12. Eccentrically Loaded Single Angles in Axial Compression Available strengths in axial compression are given for eccentrically loaded single angles with Fy = 36 ksi (ASTM A36). The long leg of the angle is assumed to be attached to a gusset plate with a thickness of 1.5t. The tabulated values assume a load placed at the mid-width of the long leg of the angle at a distance of 0.75t from the face of this leg. Effective length, KL, is assumed to be the same on all axes (rx, ry, rz and rw). Table 4-12 considers the combined bending stresses at the heel and the tips of the angle (points A, B and C in Figure 4-4) produced by axial compression plus biaxial bending moments about

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the principal w- and z-axes using AISC Specification Equation H2-1. Points A and C are assumed at the angle mid-thickness at distances b and d (respectively) from the heel. Note that for some sections, such as L31/2 ×3× 5/16, the calculated available strength can increase slightly as the unbraced length increases from zero, and then decrease as the unbraced length further increases.

Composite Compression—Member Selection Tables Table 4-13. Rectangular HSS Filled with 4-ksi Normal Weight Concrete in Axial Compression Available strengths in axial compression are given for rectangular HSS with Fy = 46 ksi (ASTM A500 Grade B) filled with 4-ksi normal weight concrete. The tabulated values are given for the effective length with respect to the y-axis (KL)y. However, the effective length with respect to the x-axis (KL)x must also be investigated. To determine the available strength in axial compression, the table should be entered at the larger of (KL)y and (KL)y eq, where

( KL ) y eq =

( KL )x rmx rmy

(4-5)

Values of the ratio rmx /rmy and other properties useful in the design of composite HSS compression members are listed at the bottom of Table 4-13. The variables rmx and rmy are the radii of gyration for the composite cross section. The ratio rmx /rmy is determined as rmx = rmy

Pex ( K x Lx )2 Pey ( K y L y )2

Fig. 4-4. Eccentrically loaded single angle.

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For compact composite sections, the values of φMn and Mn/Ω were calculated using the nominal moment strength equations for point B of the interaction diagram in Table C of the Discussion of Limit State Response of Composite Columns and Beam-Columns Part II: Application of Design Provisions for the 2005 AISC Specification (Geschwindner, 2010). For noncompact sections, the values of φMn and Mn /Ω were calculated using the closed formed equations presented in the Commentary Figure C-I3-7. The available strengths tabulated in Tables 4-13 through 4-20 are given for the indicated shape with the associated concrete fill. AISC Specification Section I2.2b stipulates that the available compressive strength of a filled composite member need not be less than that specified for a bare steel member. In these tables, available strengths controlled by the bare steel acting alone are identified. Additionally, there is no longitudinal reinforcement provided, because there is no requirement for minimum reinforcement in the AISC Specification. The use of filled shapes without longitudinal reinforcement is a common industry practice.

Table 4-14. Square HSS Filled with 4-ksi Normal Weight Concrete in Axial Compression Table 4-14 is the same as Table 4-13, except that it provides available strengths in axial compression for square HSS filled with 4-ksi normal weight concrete.

Table 4-15. Rectangular HSS Filled with 5-ksi Normal Weight Concrete in Axial Compression Table 4-15 is the same as Table 4-13, except that it provides available strengths in axial compression for rectangular HSS filled with 5-ksi normal weight concrete.

Table 4-16. Square HSS Filled with 5-ksi Normal Weight Concrete in Axial Compression Table 4-16 is the same as Table 4-13, except that it provides available strengths in axial compression for square HSS filled with 5-ksi normal weight concrete.

Table 4-17. Round HSS Filled with 4-ksi Normal Weight Concrete in Axial Compression Available strengths in axial compression are given for round HSS with Fy = 42 ksi (ASTM A500 Grade B) filled with 4-ksi normal weight concrete. To determine the available strength in axial compression, the table should be entered at the largest effective length, KL. Other properties useful in the design of compression members are listed at the bottom of Table 4-5. The values of φMn and Mn/Ω were calculated using the nominal moment strength equations for point B of the interaction diagram in Table D of the Discussion of Limit State Response of Composite Columns and Beam-Columns Part II: Application of Design Provisions for the 2005 AISC Specification (Geschwindner, 2010).

Table 4-18. Round HSS Filled with 5-ksi Normal Weight Concrete in Axial Compression Table 4-18 is the same as Table 4-17, except that it provides available strengths in axial compression for round HSS filled with 5-ksi normal weight concrete. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Table 4-19. Pipe Filled with 4-ksi Normal Weight Concrete in Axial Compression Available strengths in axial compression are given for pipe with Fy = 35 ksi (ASTM A53 Grade B) filled with 4-ksi normal weight concrete. To determine the available strength in axial compression, the table should be entered at the largest effective length, KL. Other properties useful in the design of compression members are listed at the bottom of Table 4-6.

Table 4-20. Pipe Filled with 5-ksi Normal Weight Concrete in Axial Compression Table 4-20 is the same as Table 4-19, except that it provides available strengths in axial compression for pipe filled with 5-ksi normal weight concrete.

Table 4-21. Stiffness Reduction Factor

τb

When an analysis is performed using the effective length method in AISC Specification Appendix Section 7.2, that procedure requires determination of the effective length factor, K. A common method of determining K is through the use of alignment charts provided in the AISC Specification Commentary. When column buckling occurs in the inelastic range, the alignment charts usually give conservative results. For more accurate solutions, inelastic K-factors can be determined from the alignment chart by using τb times the elastic modulus of the columns in the equation for G. The stiffness reduction factor, τb, is the ratio of the tangent modulus, ET , to the elastic modulus, E. Values are tabulated for steels with Fy = 35 ksi, 36 ksi, 42 ksi, 46 ksi and 50 ksi.

Table 4-22. Available Critical Stress for Compression Members Table 4-22 provides the available critical stress for various ratios of Kl/r, for materials with a minimum specified yield strength of 35 ksi, 36 ksi, 42 ksi, 46 ksi and 50 ksi.

PART 4 REFERENCES Geschwindner, L.F. (2010), “Discussion of Limit State Responses of Composite Columns and Beam-Columns Part II: Application of Design Provisions for the 2005 AISC Specification,” Engineering Journal, AISC, Vol. 47, No. 2, 2nd Quarter, pp. 131–139, Chicago, IL. Griffis, L.G. (1992), Load and Resistance Factor Design of W-Shapes Encased in Concrete, Design Guide 6, AISC, Chicago, IL. Sakla, S. (2001), “Tables for the Design Strength of Eccentrically-Loaded Single Angle Struts,” Engineering Journal, AISC, Vol. 38, No. 3, 3rd Quarter, pp. 127–136, Chicago, IL. Viest, I.M., Colaco, J.P., Furlong, R.W., Griffis, L.G., Leon, R.T. and Wyllie, L.A. (1997), Composite Construction Design for Buildings, ASCE, New York, NY. Ziemian, R.D. (ed.) (2010), Guide to Stability Design Criteria for Metal Structures, 6th Ed., John Wiley and Sons, Hoboken, NJ.

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Table 4-1

Available Strength in Axial Compression, kips W-Shapes

W14 Shape

W14×

lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 50 ksi

0 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

730h 665h Pn /Ωc φc Pn Pn /Ωc φc Pn

605h Pn /Ωc φc Pn

550h Pn /Ωc φc Pn

500h 455h Pn /Ωc φc Pn Pn /Ωc φc Pn

ASD LRFD ASD 6440 9670 5870 6070 9130 5530 6010 9030 5470 5940 8920 5400 5860 8810 5330 5780 8690 5250 5690 8560 5170 5610 8430 5090 5510 8290 5000 5420 8140 4910 5320 7990 4820 5110 7670 4620 4890 7340 4420 4660 7000 4200 4420 6650 3990 4180 6290 3760 3940 5930 3540 3700 5560 3320 3460 5200 3100 3220 4850 2880 2990 4500 2670 2770 4160 2460 2550 3830 2260 2330 3510 2060 2140 3220 1900 1970 2970 1750

ASD 5330 5010 4950 4890 4820 4750 4680 4600 4520 4440 4350 4170 3980 3780 3580 3370 3170 2960 2760 2560 2360 2170 1990 1820 1670 1540

ASD 4850 4550 4500 4440 4380 4310 4240 4170 4100 4020 3940 3770 3590 3410 3220 3030 2840 2650 2460 2280 2100 1930 1760 1610 1480 1360

ASD 4400 4120 4070 4020 3960 3900 3840 3770 3700 3630 3550 3390 3230 3060 2890 2720 2540 2370 2200 2030 1870 1710 1560 1420 1310 1200

LRFD 8820 8310 8220 8110 8010 7890 7770 7650 7520 7380 7240 6950 6640 6320 5990 5660 5320 4990 4650 4330 4010 3690 3390 3100 2850 2630

LRFD 8010 7530 7440 7350 7250 7140 7030 6920 6790 6670 6540 6260 5980 5680 5380 5070 4760 4450 4140 3840 3550 3270 2990 2730 2510 2310

LRFD 7290 6840 6760 6670 6580 6480 6380 6270 6160 6040 5920 5660 5400 5120 4840 4560 4270 3990 3700 3430 3160 2900 2650 2420 2220 2050

LRFD 6610 6200 6120 6040 5950 5860 5770 5660 5560 5450 5340 5100 4860 4600 4340 4080 3820 3560 3300 3050 2800 2570 2340 2140 1960 1810

ASD 4010 3750 3710 3660 3600 3550 3490 3420 3360 3290 3220 3080 2920 2770 2610 2450 2290 2130 1970 1820 1670 1520 1390 1270 1160 1070

LRFD 6030 5640 5570 5500 5420 5330 5240 5150 5050 4950 4840 4620 4400 4160 3920 3680 3440 3200 2960 2730 2510 2290 2080 1910 1750 1610

Properties

Pwo , kips 2820 4230 2410 3620 2060 3090 1750 2630 1500 2240 1280 1920 Pwi , kips/in. 102 154 94.3 142 86.7 130 79.3 119 73.0 110 67.3 101 Pwb , kips 44000 66100 34400 51700 26600 40100 20500 30800 15900 23900 12500 18800 Pfb , kips 4510 6780 3820 5750 3240 4870 2730 4100 2290 3450 1930 2900 Lp , ft 16.6 16.3 16.1 15.9 15.6 15.5 Lr , ft 275 253 232 213 196 179 Ag , in.2 215 196 178 162 147 134 Ix , in.4 14300 12400 10800 9430 8210 7190 Iy , in.4 4720 4170 3680 3250 2880 2560 ry , in. 4.69 4.62 4.55 4.49 4.43 4.38 rx /ry 1.74 1.73 1.71 1.70 1.69 1.67 Pex (KL) 2/104, k-in.2 409000 355000 309000 270000 235000 206000 Pey (KL) 2/104, k-in.2 135000 119000 105000 93000 82400 73300 h ASD LRFD Flange thickness is greater than 2 in. Special requirements may apply per AISC Ωc = 1.67

φc = 0.90

Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-1 (continued) Fy = 50 ksi

Available Strength in Axial Compression, kips W-Shapes

Shape

W14×

lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, ry

W14

0 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

426h 398h Pn /Ωc φc Pn Pn /Ωc φc Pn

370h Pn /Ωc φc Pn

342h Pn /Ωc φc Pn

311h 283h Pn /Ωc φc Pn Pn /Ωc φc Pn

ASD LRFD ASD 3740 5620 3500 3500 5260 3270 3450 5190 3230 3410 5120 3180 3350 5040 3130 3300 4960 3080 3240 4870 3030 3180 4790 2970 3120 4690 2920 3060 4600 2850 2990 4500 2790 2860 4290 2660 2710 4080 2530 2560 3850 2390 2410 3630 2250 2260 3400 2100 2110 3170 1960 1960 2950 1820 1810 2730 1680 1670 2510 1550 1530 2300 1410 1390 2090 1290 1270 1910 1170 1160 1750 1070 1070 1600 985 983 1480 907

ASD 3260 3040 3000 2960 2910 2870 2810 2760 2710 2650 2590 2470 2340 2210 2080 1940 1810 1670 1540 1420 1300 1180 1070 980 900 830

ASD 3020 2820 2780 2740 2700 2650 2600 2550 2500 2450 2390 2280 2160 2040 1910 1790 1660 1540 1420 1300 1180 1070 979 896 823 758

ASD 2740 2550 2510 2470 2430 2390 2350 2300 2260 2210 2160 2050 1940 1830 1710 1600 1490 1370 1260 1160 1050 954 869 795 730 673

LRFD 5260 4920 4850 4780 4710 4630 4550 4470 4380 4290 4200 4000 3800 3590 3380 3160 2950 2730 2530 2320 2130 1930 1760 1610 1480 1360

LRFD 4900 4570 4510 4450 4380 4310 4230 4150 4070 3980 3890 3710 3520 3320 3120 2920 2720 2520 2320 2130 1950 1770 1610 1470 1350 1250

LRFD 4540 4230 4180 4120 4050 3980 3910 3840 3760 3680 3600 3420 3240 3060 2870 2680 2500 2310 2130 1950 1780 1610 1470 1350 1240 1140

LRFD 4110 3830 3770 3720 3660 3600 3530 3460 3390 3320 3240 3080 2920 2750 2580 2400 2230 2060 1900 1740 1580 1430 1310 1200 1100 1010

ASD 2490 2320 2290 2250 2210 2180 2140 2090 2050 2000 1960 1860 1760 1660 1550 1450 1340 1240 1140 1040 945 857 781 715 656 605

LRFD 3750 3480 3440 3380 3330 3270 3210 3150 3080 3010 2940 2800 2640 2490 2330 2170 2020 1860 1710 1560 1420 1290 1170 1070 986 909

Properties

Pwo , kips 1140 1710 1010 1520 902 1350 788 1180 672 1010 574 861 Pwi , kips/in. 62.7 94.0 59.0 88.5 55.3 83.0 51.3 77.0 47.0 70.5 43.0 64.5 Pwb , kips 10100 15100 8420 12700 6920 10400 5540 8320 4250 6390 3260 4900 Pfb , kips 1730 2600 1520 2280 1320 1990 1140 1720 956 1440 802 1210 Lp , ft 15.3 15.2 15.1 15.0 14.8 14.7 Lr , ft 168 158 148 138 125 114 Ag , in.2 125 117 109 101 91.4 83.3 Ix , in.4 6600 6000 5440 4900 4330 3840 Iy , in.4 2360 2170 1990 1810 1610 1440 ry , in. 4.34 4.31 4.27 4.24 4.20 4.17 rx /ry 1.67 1.66 1.66 1.65 1.64 1.63 Pex (KL) 2/104, k-in.2 189000 172000 156000 140000 124000 110000 Pey (KL) 2/104, k-in.2 67500 62100 57000 51800 46100 41200 h ASD LRFD Flange thickness is greater than 2 in. Special requirements may apply per AISC Ωc = 1.67

φc = 0.90

Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF COMPRESSION MEMBERS

Table 4-1 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

W-Shapes

W14 Shape

W14×

lb/ft

257 233 Pn /Ωc φc Pn Pn /Ωc φc Pn

211 Pn /Ωc φc Pn

193 Pn /Ωc φc Pn

176 159 Pn /Ωc φc Pn Pn /Ωc φc Pn

ASD LRFD ASD 2260 3400 2050 2210 3330 2010 2200 3300 1990 2180 3270 1970 2150 3240 1950 2130 3200 1930 2100 3160 1900 2070 3110 1870 2040 3060 1840 2010 3010 1810 1970 2960 1780 1930 2900 1750 1890 2850 1710 1850 2790 1670 1810 2720 1640 1770 2660 1600 1680 2520 1510 1590 2380 1430 1490 2240 1340 1400 2100 1260 1300 1950 1170 1200 1810 1080 1110 1670 994 1020 1530 911 928 1400 830 841 1260 751

ASD 1860 1810 1800 1780 1760 1740 1720 1690 1670 1640 1610 1580 1540 1510 1480 1440 1360 1290 1210 1130 1050 968 890 815 741 670

ASD 1700 1660 1650 1630 1610 1590 1570 1550 1530 1500 1470 1440 1410 1380 1350 1320 1250 1170 1100 1030 954 881 810 740 673 608

LRFD 2560 2500 2480 2450 2430 2400 2360 2330 2290 2250 2210 2170 2120 2080 2030 1980 1870 1770 1660 1550 1430 1320 1220 1110 1010 914

ASD 1550 1510 1500 1490 1470 1450 1430 1410 1390 1360 1340 1310 1280 1260 1230 1200 1130 1070 998 931 863 796 730 667 605 546

Pwo , kips 490 735 414 621 353 529 303 454 Pwi , kips/in. 39.3 59.0 35.7 53.5 32.7 49.0 29.7 44.5 Pwb , kips 2480 3730 1850 2780 1430 2150 1070 1610 Pfb , kips 668 1000 554 832 455 684 388 583 Lp , ft 14.6 14.5 14.4 14.3 Lr , ft 104 95.0 86.6 79.4 Ag , in.2 75.6 68.5 62.0 56.8 Ix , in.4 3400 3010 2660 2400 Iy , in.4 1290 1150 1030 931 ry , in. 4.13 4.10 4.07 4.05 rx /ry 1.62 1.62 1.61 1.60 Pex (KL) 2/104, k-in.2 97300 86200 76100 68700 Pey (KL) 2/104, k-in.2 36900 32900 29500 26600 ASD LRFD

264 27.7 870 321

Effective length, KL (ft), with respect to least radius of gyration, ry

Design 0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40

LRFD 3080 3010 2990 2960 2930 2900 2860 2820 2770 2730 2680 2630 2570 2520 2460 2400 2280 2150 2020 1890 1750 1620 1490 1370 1250 1130

LRFD 2790 2730 2700 2680 2650 2620 2580 2550 2510 2460 2420 2370 2320 2270 2220 2160 2050 1930 1820 1700 1570 1460 1340 1220 1110 1010

LRFD 2330 2280 2260 2240 2210 2180 2150 2120 2090 2050 2010 1970 1930 1890 1840 1800 1700 1600 1500 1400 1300 1200 1100 1000 909 821

ASD 1400 1370 1350 1340 1330 1310 1290 1270 1250 1230 1210 1180 1160 1130 1100 1070 1020 957 896 835 773 713 653 596 540 487

396 41.5 1310 483 14.2 73.2 51.8 2140 838 4.02 1.60 61300 24000

222 24.8 628 265

LRFD 2100 2050 2030 2010 1990 1970 1940 1910 1880 1850 1810 1780 1740 1700 1660 1620 1530 1440 1350 1250 1160 1070 982 896 812 733

Properties

Ωc = 1.67

φc = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

333 37.3 944 398 14.1 66.7 46.7 1900 748 4.00 1.60 54400 21400

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STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-1 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

W-Shapes Shape

W14×

lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, ry

W14

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40

145 132 Pn /Ωc φc Pn Pn /Ωc φc Pn

120 Pn /Ωc φc Pn

ASD LRFD ASD 1280 1920 1160 1250 1880 1130 1240 1860 1120 1230 1840 1110 1210 1820 1090 1200 1800 1080 1180 1770 1060 1160 1750 1040 1140 1720 1020 1120 1690 1000 1100 1650 982 1080 1620 960 1060 1590 937 1030 1550 913 1010 1510 888 980 1470 862 927 1390 810 872 1310 756 816 1230 702 759 1140 648 703 1060 594 647 973 542 593 891 491 540 812 442 489 735 397 441 663 358

ASD 1060 1030 1020 1010 994 980 965 948 931 912 892 872 850 828 805 782 734 685 635 586 537 489 443 398 357 322

LRFD 1750 1700 1680 1660 1640 1620 1600 1570 1540 1510 1480 1440 1410 1370 1330 1300 1220 1140 1060 974 893 814 738 664 596 538

LRFD 1590 1550 1530 1510 1490 1470 1450 1430 1400 1370 1340 1310 1280 1240 1210 1180 1100 1030 955 880 807 735 665 598 536 484

109 Pn /Ωc φc Pn ASD 958 932 923 913 901 888 874 859 843 826 808 789 770 750 729 708 664 620 574 529 485 441 399 359 322 290

99 90 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD 1440 1400 1390 1370 1350 1340 1310 1290 1270 1240 1210 1190 1160 1130 1100 1060 998 931 863 796 729 663 600 539 484 437

ASD 871 848 839 830 819 807 794 780 766 750 733 716 698 680 661 642 602 561 519 478 438 398 360 323 290 261

LRFD 1310 1270 1260 1250 1230 1210 1190 1170 1150 1130 1100 1080 1050 1020 994 964 904 843 781 719 658 598 541 485 435 393

ASD 793 772 764 755 745 735 723 710 697 682 667 652 635 618 601 583 547 509 472 434 397 361 326 292 262 237

192 26.3 330 208 13.2 48.5 32.0 1240 447 3.73 1.67 35500 12800

112 16.2 173 114

167 24.3 260 171 13.5 45.3 29.1 1110 402 3.71 1.66 31800 11500

96.1 14.7 129 94.3

LRFD 1190 1160 1150 1140 1120 1100 1090 1070 1050 1030 1000 979 955 929 903 877 822 766 709 653 597 543 490 439 394 356

Properties

Pwo , kips Pwi , kips/in. Pwb , kips Pfb , kips Lp , ft Lr , ft Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry Pex (KL) 2/104, k-in.2 Pey (KL) 2/104, k-in.2 ASD Ωc = 1.67

192 22.7 476 222

287 34.0 716 334 14.1 61.7 42.7 1710 677 3.98 1.59 48900 19400 LRFD

175 21.5 407 199

263 32.3 611 298 13.3 55.8 38.8 1530 548 3.76 1.67 43800 15700

151 19.7 312 165

227 29.5 469 249 13.2 51.9 35.3 1380 495 3.74 1.67 39500 14200

128 17.5 220 138

φc = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

144 22.0 194 142 15.1 42.5 26.5 999 362 3.70 1.66 28600 10400

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DESIGN OF COMPRESSION MEMBERS

Table 4-1 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

W-Shapes

W14 Shape

W14×

lb/ft

82 74 68 61 53 48 43c Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn

Effective length, KL (ft), with respect to least radius of gyration, ry

Design 0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40

ASD 719 676 661 644 626 606 584 562 538 514 489 464 438 413 387 362 314 267 228 197 171 150 133 119 107 96.3

LRFD 1080 1020 993 968 940 910 878 844 809 772 735 697 659 620 582 545 472 402 343 295 257 226 200 179 160 145

ASD 653 614 600 585 568 550 531 510 489 467 444 421 398 375 352 329 285 243 207 179 156 137 121 108 96.9 87.5

LRFD 981 922 902 879 854 827 797 767 735 701 667 633 598 563 529 495 428 365 311 268 234 205 182 162 146 131

ASD 599 562 550 536 520 503 485 466 446 426 405 384 362 341 320 299 258 219 187 161 140 123 109 97.5 87.5 79.0

LRFD 900 845 826 805 782 756 729 701 671 640 608 577 544 512 480 449 388 330 281 242 211 185 164 147 131 119

ASD 536 503 492 479 465 450 433 416 398 380 361 342 323 304 285 266 229 195 166 143 125 110 97.0 86.5 77.7 70.1

LRFD 805 756 739 720 699 676 651 626 599 571 543 514 485 456 428 399 345 293 249 215 187 165 146 130 117 105

ASD 467 421 406 389 371 351 331 310 288 267 246 225 205 185 166 150 124 104 88.8 76.6 66.7 58.6

LRFD 702 633 610 585 557 528 497 465 433 401 369 338 308 278 250 226 186 157 133 115 100 88.1

ASD 422 380 366 351 334 316 298 279 259 240 221 202 183 166 149 134 111 93.2 79.4 68.5 59.7

LRFD 634 572 551 527 502 475 447 419 390 360 331 303 276 249 224 202 167 140 119 103 89.7

ASD 374 339 327 312 297 281 264 247 229 212 194 177 161 145 130 117 97.1 81.6 69.5 59.9 52.2

123 185 104 155 90.6 136 77.5 116 77.1 116 17.0 25.5 15.0 22.5 13.8 20.8 12.5 18.8 12.3 18.5 201 302 138 207 108 163 80.1 120 76.7 115 137 206 115 173 97.0 146 77.8 117 81.5 123 8.76 8.76 8.69 8.65 6.78 33.2 31.0 29.3 27.5 22.3 24.0 21.8 20.0 17.9 15.6 881 795 722 640 541 148 134 121 107 57.7 2.48 2.48 2.46 2.45 1.92 2.44 2.44 2.44 2.44 3.07 25200 22800 20700 18300 15500 4240 3840 3460 3060 1650 c LRFD Shape is slender for compression with Fy = 50 ksi.

67.4 11.3 59.5 66.2

101 17.0 89.5 99.6 6.75 21.1 14.1 484 51.4 1.91 3.06 13900 1470

56.9 10.2 43.0 52.6

LRFD 562 510 491 470 447 422 397 371 345 318 292 267 242 218 196 177 146 123 104 90.1 78.5

Properties

Pwo , kips Pwi , kips/in. Pwb , kips Pfb , kips Lp , ft Lr , ft Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry Pex (KL) 2/104, k-in.2 Pey (KL) 2/104, k-in.2 ASD Ωc = 1.67

φc = 0.90

Note: Heavy line indicates KL /ry equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

85.4 15.3 64.7 79.0 6.68 20.0 12.6 428 45.2 1.89 3.08 12300 1290

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STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-1 (continued) Fy = 50 ksi

Available Strength in Axial Compression, kips W-Shapes

Shape

W12× h

lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, ry

W12

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40

h

h

336 305 Pn /Ωc φc Pn Pn /Ωc φc Pn

279 252h Pn /Ωc φc Pn Pn /Ωc φc Pn

230h 210 Pn /Ωc φc Pn Pn /Ωc φc Pn

ASD LRFD ASD 2960 4450 2680 2870 4310 2590 2840 4260 2560 2800 4210 2530 2760 4150 2490 2710 4080 2450 2660 4000 2400 2610 3920 2350 2550 3840 2300 2490 3750 2250 2430 3660 2190 2370 3560 2130 2300 3460 2070 2230 3350 2000 2160 3250 1940 2090 3140 1870 1940 2910 1730 1790 2690 1600 1640 2460 1460 1490 2240 1320 1350 2030 1190 1210 1820 1070 1080 1620 945 959 1440 843 861 1290 757 777 1170 683

LRFD 4030 3900 3850 3800 3740 3680 3610 3540 3460 3380 3290 3200 3100 3010 2910 2810 2610 2400 2190 1990 1790 1600 1420 1270 1140 1030

ASD 2450 2370 2340 2310 2280 2240 2190 2150 2100 2050 1990 1940 1880 1820 1760 1700 1570 1440 1320 1190 1070 954 845 754 676 610

ASD 2030 1960 1930 1910 1880 1840 1800 1760 1720 1680 1630 1580 1540 1480 1430 1380 1270 1170 1060 954 854 756 670 597 536 484

LRFD 3690 3570 3520 3470 3420 3360 3300 3230 3150 3080 3000 2910 2820 2730 2640 2550 2360 2170 1980 1790 1610 1430 1270 1130 1020 917

ASD 2220 2140 2120 2090 2060 2020 1980 1940 1890 1840 1790 1740 1690 1630 1580 1520 1410 1290 1170 1060 949 843 746 666 598 539

LRFD 3330 3220 3180 3140 3090 3030 2970 2910 2840 2770 2700 2620 2540 2460 2370 2290 2110 1940 1760 1590 1430 1270 1120 1000 898 811

LRFD 3050 2940 2910 2860 2820 2770 2710 2650 2590 2520 2450 2380 2310 2230 2150 2070 1910 1750 1590 1430 1280 1140 1010 898 806 727

ASD 1850 1790 1760 1740 1710 1680 1640 1610 1570 1530 1480 1440 1390 1350 1300 1250 1150 1050 955 859 767 678 600 535 481 434

LRFD 2780 2680 2650 2610 2570 2520 2470 2420 2360 2300 2230 2160 2100 2030 1950 1880 1730 1580 1440 1290 1150 1020 902 805 722 652

Properties

Pwo , kips 1050 1580 897 1340 783 1170 665 998 574 861 492 738 Pwi , kips/in. 59.3 89.0 54.3 81.5 51.0 76.5 46.7 70.0 43.0 64.5 39.3 59.0 Pwb , kips 10000 15100 7690 11600 6380 9590 4870 7320 3810 5730 2930 4400 Pfb , kips 1640 2460 1370 2070 1140 1720 947 1420 802 1210 676 1020 Lp , ft 12.3 12.1 11.9 11.8 11.7 11.6 Lr , ft 150 137 126 114 105 95.8 Ag , in.2 98.9 89.5 81.9 74.1 67.7 61.8 Ix , in.4 4060 3550 3110 2720 2420 2140 Iy , in.4 1190 1050 937 828 742 664 ry , in. 3.47 3.42 3.38 3.34 3.31 3.28 rx /ry 1.85 1.84 1.82 1.81 1.80 1.80 Pex (KL) 2/104, k-in.2 116000 102000 89000 77900 69300 61300 Pey (KL) 2/104, k-in.2 34100 30100 26800 23700 21200 19000 h ASD LRFD Flange thickness is greater than 2 in. Special requirements may apply per AISC Ωc = 1.67

φc = 0.90

Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF COMPRESSION MEMBERS

Table 4-1 (continued)

Available Strength in Axial Compression, kips W-Shapes

W12 Shape

W12×

lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 50 ksi

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40

190 170 Pn /Ωc φc Pn Pn /Ωc φc Pn

152 Pn /Ωc φc Pn

136 Pn /Ωc φc Pn

ASD LRFD ASD 1680 2520 1500 1620 2430 1440 1600 2400 1420 1570 2360 1400 1550 2320 1380 1520 2280 1350 1490 2230 1320 1450 2180 1290 1420 2130 1260 1380 2070 1230 1340 2010 1190 1300 1950 1150 1260 1890 1120 1210 1820 1080 1170 1760 1040 1130 1690 997 1030 1560 916 944 1420 834 855 1280 754 767 1150 675 684 1030 600 603 906 528 534 803 468 476 716 418 428 643 375 386 580 338

ASD 1340 1290 1270 1250 1230 1210 1180 1150 1120 1090 1060 1030 992 957 921 885 811 737 665 595 527 464 411 366 329 297

ASD 1190 1150 1130 1120 1100 1080 1050 1030 1000 972 942 912 881 849 816 784 717 651 586 523 462 406 360 321 288 260

LRFD ASD 1800 1050 1730 1010 1710 1000 1680 984 1650 966 1620 947 1580 925 1540 903 1500 879 1460 854 1420 828 1370 800 1320 773 1280 744 1230 715 1180 686 1080 626 978 567 880 510 786 454 695 400 610 352 541 311 482 278 433 249 391 225

244 26.3 878 292

201 23.7 637 231

LRFD 2250 2170 2140 2110 2070 2030 1990 1940 1900 1840 1790 1730 1680 1620 1560 1500 1380 1250 1130 1010 902 794 704 628 563 508

LRFD 2010 1940 1910 1880 1850 1810 1770 1730 1690 1640 1590 1540 1490 1440 1380 1330 1220 1110 999 894 793 697 617 551 494 446

120 106 Pn /Ωc φc Pn Pn /Ωc φc Pn LRFD 1580 1520 1500 1480 1450 1420 1390 1360 1320 1280 1240 1200 1160 1120 1070 1030 942 853 766 682 601 528 468 417 375 338

ASD 934 898 886 871 855 838 819 799 777 755 731 707 682 656 631 604 552 499 448 398 350 308 272 243 218 197

302 35.5 957 347 11.1 56.5 35.2 1070 345 3.13 1.76 30600 9870

162 20.3 405 183

LRFD 1400 1350 1330 1310 1290 1260 1230 1200 1170 1130 1100 1060 1030 987 948 908 829 750 673 598 526 462 410 365 328 296

Properties

Pwo , kips 412 617 346 518 290 435 Pwi , kips/in. 35.3 53.0 32.0 48.0 29.0 43.5 Pwb , kips 2120 3190 1580 2370 1170 1760 Pfb , kips 567 852 455 684 367 551 Lp , ft 11.5 11.4 11.3 Lr , ft 87.3 78.5 70.6 Ag , in.2 56.0 50.0 44.7 Ix , in.4 1890 1650 1430 Iy , in.4 589 517 454 ry , in. 3.25 3.22 3.19 rx /ry 1.79 1.78 1.77 Pex (KL) 2/104, k-in.2 54100 47200 40900 Pey (KL) 2/104, k-in.2 16900 14800 13000 ASD LRFD Ωc = 1.67

365 39.5 1320 439 11.2 63.2 39.9 1240 398 3.16 1.77 35500 11400

φc = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

242 30.5 609 276 11.0 50.7 31.2 933 301 3.11 1.76 26700 8620

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STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-1 (continued) Fy = 50 ksi

Available Strength in Axial Compression, kips W-Shapes

Shape

W12×

lb/ft

96

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

W12

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40

87

79

72

65

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD 844 811 800 787 772 756 739 720 701 680 659 637 614 591 567 543 495 447 401 356 312 274 243 217 195 176

LRFD 1270 1220 1200 1180 1160 1140 1110 1080 1050 1020 990 957 923 888 852 816 744 672 602 535 469 413 365 326 293 264

ASD 766 736 726 714 700 685 670 653 635 616 596 576 555 534 512 490 446 403 360 319 280 246 218 194 174 157

LRFD 1150 1110 1090 1070 1050 1030 1010 981 954 925 896 865 834 802 770 737 671 605 541 480 421 370 327 292 262 237

ASD 695 667 657 646 634 620 606 590 574 556 538 520 501 481 462 442 402 362 323 286 250 220 195 174 156 141

LRFD 1040 1000 988 971 953 932 910 887 862 836 809 781 753 723 694 664 604 544 486 430 376 331 293 261 234 212

ASD 632 606 597 587 576 564 550 536 521 505 489 472 455 437 419 401 364 328 292 259 226 199 176 157 141 127

LRFD 949 911 898 883 866 847 827 806 783 759 735 709 683 656 629 602 547 493 440 389 340 299 265 236 212 191

ASD 572 549 540 531 521 510 497 484 470 456 441 426 410 393 377 360 327 294 262 231 202 178 157 140 126 114

LRFD 859 825 812 798 783 766 747 728 707 685 663 640 616 591 567 542 492 442 394 348 304 267 236 211 189 171

156 23.5 278 152 10.8 39.9 23.2 662 216 3.05 1.75 18900 6180

91.0 14.3 142 84.0

137 21.5 213 126 10.7 37.5 21.1 597 195 3.04 1.75 17100 5580

78.0 13.0 106 68.5

Properties

Pwo , kips Pwi , kips/in. Pwb , kips Pfb , kips Lp , ft Lr , ft Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry Pex (KL) 2/104, k-in.2 Pey (KL) 2/104, k-in.2 ASD Ωc = 1.67

138 18.3 296 152

206 27.5 445 228 10.9 46.7 28.2 833 270 3.09 1.76 23800 7730 LRFD

121 17.2 243 123

182 25.8 365 185 10.8 43.1 25.6 740 241 3.07 1.75 21200 6900

104 15.7 185 101

φc = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

117 19.5 159 103 11.9 35.1 19.1 533 174 3.02 1.75 15300 4980

AISC_Part 4A:14th Ed.

2/23/11

10:03 AM

Page 20

4–20

DESIGN OF COMPRESSION MEMBERS

Table 4-1 (continued)

Available Strength in Axial Compression, kips W-Shapes

W12 Shape

W12×

lb/ft

58

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 50 ksi

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40

53

50

45

40

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD 509 479 469 457 445 431 416 400 384 367 349 332 314 296 278 261 227 194 165 143 124 109 96.7 86.3 77.4 69.9

LRFD 765 720 705 687 668 647 625 601 577 551 525 499 472 445 418 392 341 292 249 214 187 164 145 130 116 105

ASD 467 439 429 419 407 394 380 365 350 334 318 301 285 268 252 235 204 174 148 128 111 97.8 86.6 77.3 69.4 62.6

LRFD 702 660 646 629 611 592 571 549 526 502 478 453 428 403 378 354 307 261 223 192 167 147 130 116 104 94.1

ASD 437 396 382 367 350 332 314 295 275 255 236 217 198 180 162 146 121 102 86.6 74.7 65.0 57.2

LRFD 657 595 574 551 526 500 472 443 413 384 355 326 298 270 244 220 182 153 130 112 97.8 85.9

ASD 392 355 342 329 313 297 281 263 246 228 210 193 176 160 144 130 107 90.3 76.9 66.3 57.8 50.8

LRFD 589 534 515 494 471 447 422 396 369 343 316 290 265 240 216 195 161 136 116 99.7 86.8 76.3

ASD 350 317 305 293 279 265 250 234 218 202 187 171 156 142 127 115 95.0 79.8 68.0 58.6 51.1 44.9

LRFD 526 476 459 440 420 398 375 352 328 304 281 257 235 213 191 173 143 120 102 88.1 76.8 67.5

105 18.5 133 115 6.92 23.8 14.6 391 56.3 1.96 2.64 11200 1610

60.3 11.2 65.6 61.9

90.5 16.8 98.6 93.0 6.89 22.4 13.1 348 50.0 1.95 2.64 9960 1430

50.2 9.83 44.8 49.6

Properties

Pwo , kips Pwi , kips/in. Pwb , kips Pfb , kips Lp , ft Lr , ft Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry Pex (KL) 2/104, k-in.2 Pey (KL) 2/104, k-in.2 ASD Ωc = 1.67

74.4 12.0 83.1 76.6

112 18.0 125 115 8.87 29.8 17.0 475 107 2.51 2.10 13600 3060 LRFD

67.9 11.5 73.3 61.9

102 17.3 110 93.0 8.76 28.2 15.6 425 95.8 2.48 2.11 12200 2740

70.3 12.3 88.4 76.6

Note: Heavy line indicates KL /ry equal to or greater than 200.

φc = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

75.2 14.8 67.4 74.6 6.85 21.1 11.7 307 44.1 1.94 2.64 8790 1260

AISC_Part 4A:14th Ed.

2/23/11

10:03 AM

Page 21

4–21

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-1 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

W-Shapes Shape

W10×

lb/ft

112 100 Pn /Ωc φc Pn Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

W10

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40

ASD 985 934 917 897 875 851 825 798 769 739 708 677 645 613 580 548 485 423 365 315 274 241 213 190 171 154

LRFD 1480 1400 1380 1350 1310 1280 1240 1200 1160 1110 1060 1020 969 921 872 824 728 636 548 473 412 362 321 286 257 232

ASD 877 831 815 797 777 755 732 707 681 654 626 598 569 540 511 482 425 370 318 274 239 210 186 166 149 134

LRFD 1320 1250 1230 1200 1170 1130 1100 1060 1020 983 941 898 855 811 767 724 638 556 478 412 359 315 279 249 224 202

88

77 Pn /Ωc φc Pn Pn /Ωc φc Pn ASD 778 737 722 706 688 669 647 625 602 578 553 527 501 475 449 423 373 324 278 239 209 183 162 145 130 117

LRFD 1170 1110 1090 1060 1030 1000 973 940 905 868 831 792 754 714 675 636 560 487 417 360 313 276 244 218 195 176

ASD 680 643 630 615 599 582 563 543 522 501 479 456 433 410 387 365 320 277 237 204 178 156 139 124 111 100

68 60 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD 1020 966 946 925 900 874 846 816 785 753 720 686 651 617 582 548 481 417 356 307 267 235 208 186 167 150

ASD 596 563 552 539 525 509 493 475 457 438 419 399 379 358 338 318 279 241 206 178 155 136 121 108 96.5 87.1

LRFD 895 846 829 810 789 765 741 714 687 658 629 599 569 539 508 478 419 363 310 267 233 205 181 162 145 131

ASD 530 500 490 479 466 452 437 421 405 388 370 352 334 316 298 280 245 212 181 156 136 119 106 94.2 84.5 76.3

182 26.5 494 213 9.18 45.3 22.7 455 154 2.60 1.73 13000 4410

99.5 15.7 229 111

149 23.5 344 167 9.15 40.6 19.9 394 134 2.59 1.71 11300 3840

82.6 14.0 163 86.5

LRFD 796 752 737 719 700 679 657 633 608 583 556 530 502 475 448 421 368 318 271 234 204 179 159 142 127 115

Properties

Pwo , kips Pwi , kips/in. Pwb , kips Pfb , kips Lp , ft Lr , ft Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry Pex (KL) 2/104, k-in.2 Pey (KL) 2/104, k-in.2 ASD Ωc = 1.67

220 25.2 949 292

330 37.8 1430 439 9.47 64.1 32.9 716 236 2.68 1.74 20500 6750 LRFD

184 22.7 690 235

275 34.0 1040 353 9.36 57.9 29.3 623 207 2.65 1.74 17800 5920

150 20.2 487 183

225 30.3 732 276 9.29 51.2 26.0 534 179 2.63 1.73 15300 5120

121 17.7 328 142

φc = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

124 21.0 245 130 9.08 36.6 17.7 341 116 2.57 1.71 9760 3320

AISC_Part 4A:14th Ed.

2/23/11

10:03 AM

Page 22

4–22

DESIGN OF COMPRESSION MEMBERS

Table 4-1 (continued)

Available Strength in Axial Compression, kips W-Shapes

W10 Shape

W10×

lb/ft

54

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 50 ksi

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40

49

45

39

33

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD 473 446 437 427 415 403 389 375 361 345 330 314 297 281 265 249 217 188 160 138 120 106 93.5 83.4 74.8 67.6

LRFD 711 671 657 642 624 605 585 564 542 519 495 471 447 422 398 374 327 282 240 207 180 159 141 125 112 102

ASD 431 407 398 388 378 366 354 341 327 313 299 284 269 254 239 224 196 168 143 124 108 94.7 83.9 74.8 67.2 60.6

LRFD 648 611 598 584 568 550 532 512 492 471 449 427 404 382 360 337 294 253 216 186 162 142 126 112 101 91.1

ASD 398 363 350 337 322 307 291 274 256 239 222 204 188 171 155 140 116 97.4 83.0 71.5 62.3 54.8

LRFD 598 545 527 507 485 461 437 411 385 359 333 307 282 257 234 211 174 146 125 108 93.7 82.3

ASD 344 313 302 290 277 263 249 234 219 203 188 173 158 144 130 118 97.2 81.7 69.6 60.0 52.3 46.0

LRFD 517 470 454 436 416 396 374 352 329 306 283 260 238 217 196 177 146 123 105 90.2 78.6 69.1

ASD 291 263 253 243 232 220 207 194 181 168 155 142 130 117 106 95.4 78.8 66.2 56.4 48.7 42.4 37.3

LRFD 437 395 381 365 348 330 311 292 272 253 233 214 195 177 159 143 118 99.5 84.8 73.1 63.7 56.0

98.0 17.5 142 108 7.10 26.9 13.3 248 53.4 2.01 2.15 7100 1530

54.1 10.5 68.7 52.6

81.1 15.8 103 79.0 6.99 24.2 11.5 209 45.0 1.98 2.16 5980 1290

45.2 9.67 53.7 35.4

Properties

Pwo , kips Pwi , kips/in. Pwb , kips Pfb , kips Lp , ft Lr , ft Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry Pex (KL) 2/104, k-in.2 Pey (KL) 2/104, k-in.2 ASD Ωc = 1.67

69.1 12.3 112 70.8

104 18.5 168 106 9.04 33.6 15.8 303 103 2.56 1.71 8670 2950 LRFD

60.1 11.3 86.6 58.7

90.1 17.0 130 88.2 8.97 31.6 14.4 272 93.4 2.54 1.71 7790 2670

65.3 11.7 94.2 71.9

Note: Heavy line indicates KL /ry equal to or greater than 200.

φc = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

67.8 14.5 80.7 53.2 6.85 21.8 9.71 171 36.6 1.94 2.16 4890 1050

AISC_Part 4A:14th Ed.

2/23/11

10:03 AM

Page 23

4–23

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-1 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

W-Shapes Shape

W8×

lb/ft

67

58

48

Pn /Ωc φc Pn Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

W8

40 Pn /Ωc φc Pn Pn /Ωc φc Pn

35 31 Pn /Ωc φc Pn Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

590

886

512

769

422

634

350

526

308

463

273

411

6 7 8 9 10

542 526 508 488 467

815 790 763 733 701

470 455 439 422 403

706 685 660 634 606

387 375 361 347 331

581 563 543 521 497

320 309 298 285 272

481 465 448 429 409

281 272 262 251 239

423 409 394 377 359

249 241 232 222 211

374 362 348 333 317

11 12 13 14 15

444 421 397 373 348

668 633 597 560 523

384 363 342 321 299

576 546 514 482 450

314 297 280 262 244

473 447 421 394 367

258 243 228 213 198

388 366 343 321 298

226 213 200 187 174

340 321 301 281 261

200 189 177 165 153

301 283 266 248 230

16 17 18 19 20

324 300 276 253 231

487 450 415 381 347

278 257 236 216 197

418 386 355 325 296

226 209 192 175 159

340 314 288 264 239

183 169 154 141 127

275 253 232 211 191

160 147 135 123 111

241 221 203 184 166

141 130 118 108 97.2

212 195 178 162 146

22 24 26 28 30

191 160 137 118 103

287 241 205 177 154

163 137 116 100 87.5

244 205 175 151 131

132 111 94.2 81.2 70.7

198 166 142 122 106

105 88.2 75.2 64.8 56.5

158 133 113 97.4 84.9

91.5 76.9 65.5 56.5 49.2

138 116 98.5 84.9 74.0

80.3 67.5 57.5 49.6 43.2

121 101 86.5 74.5 64.9

32 34

90.3 79.9

136 120

76.9 68.1

116 102

62.2 55.1

93.5 82.8

49.6 44.0

74.6 66.1

43.3

65.0

38.0

57.1

190 28.5 761 246 7.49 47.6 19.7 272 88.6 2.12 1.75 7790 2540 LRFD

102 17.0 363 123

85.9 18.0 192 88.2 7.21 29.9 11.7 146 49.1 2.04 1.73 4180 1410

45.9 10.3 81.1 45.9

68.9 15.5 122 68.9 7.17 27.0 10.3 127 42.6 2.03 1.73 3630 1220

39.4 9.50 63.0 35.4

Properties

Pwo , kips Pwi , kips/in. Pwb , kips Pfb , kips Lp , ft Lr , ft Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry Pex (KL) 2/104, k-in.2 Pey (KL) 2/104, k-in.2 ASD Ωc = 1.67

126 19.0 507 164

153 25.5 546 185 7.42 41.6 17.1 228 75.1 2.10 1.74 6530 2150

72.0 13.3 174 87.8

108 20.0 262 132 7.35 35.2 14.1 184 60.9 2.08 1.74 5270 1740

57.2 12.0 127 58.7

Note: Heavy line indicates KL /ry equal to or greater than 200.

φc = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

59.1 14.3 94.7 53.2 7.18 24.8 9.13 110 37.1 2.02 1.72 3150 1060

AISC_Part 4A:14th Ed.

2/23/11

10:03 AM

Page 24

4–24

DESIGN OF COMPRESSION MEMBERS

Table 4-2

Available Strength in Axial Compression, kips HP18

HP-Shapes

Shape

HP18×

lb/ft

204

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 50 ksi

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40

181

157

135

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD 1800 1770 1750 1740 1720 1700 1680 1660 1640 1610 1590 1560 1530 1500 1470 1440 1370 1300 1230 1160 1080 1010 936 865 795 728

LRFD 2710 2650 2630 2610 2590 2560 2530 2500 2460 2420 2380 2340 2300 2250 2210 2160 2060 1950 1850 1740 1630 1520 1410 1300 1190 1090

ASD 1590 1560 1550 1540 1520 1500 1490 1470 1450 1420 1400 1370 1350 1320 1290 1270 1210 1140 1080 1010 950 884 820 756 695 635

LRFD 2390 2340 2330 2310 2290 2260 2230 2200 2170 2140 2100 2070 2030 1990 1950 1900 1810 1720 1620 1530 1430 1330 1230 1140 1040 954

ASD 1380 1350 1340 1330 1320 1300 1290 1270 1250 1230 1210 1190 1170 1150 1120 1100 1040 989 933 876 819 761 705 650 596 544

LRFD 2080 2040 2020 2000 1980 1960 1940 1910 1880 1850 1820 1790 1760 1720 1680 1650 1570 1490 1400 1320 1230 1140 1060 977 896 818

ASD 1190 1170 1160 1150 1140 1130 1110 1100 1080 1060 1050 1030 1010 985 964 942 896 848 800 750 700 650 601 553 507 461

LRFD 1800 1760 1740 1730 1710 1690 1670 1650 1620 1600 1570 1540 1510 1480 1450 1420 1350 1280 1200 1130 1050 977 904 831 761 693

Properties

Pwo , kips Pwi , kips/in. Pwb , kips Pfb , kips Lp , ft Lr , ft Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry Pex (KL) 2/104, k-in.2 Pey (KL) 2/104, k-in.2 ASD Ωc = 1.67

435 653 37.7 56.5 1830 2740 239 359 15.2 67.8 60.2 3480 1120 4.31 1.76 99600 32100 LRFD

363 545 33.3 50.0 1270 1910 187 281 15.1 61.3 53.2 3020 974 4.28 1.76 86400 27900

297 446 29.0 43.5 840 1260 142 213 18.1 55.8 46.2 2570 833 4.25 1.75 73600 23800

φc = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

241 25.0 535 105 21.4 50.5 39.9 2200 706 4.21 1.76 63000 20200

362 37.5 804 158

AISC_Part 4A:14th Ed._

2/17/12

8:54 AM

Page 25

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–25

Table 4-2 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

HP16

HP-Shapes Shape

HP16×

lb/ft

Effective length, KL (ft), with respect to least radius of gyration, ry

Design 0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40

183 162 Pn /Ωc φc Pn Pn /Ωc φc Pn

141 Pn /Ωc φc Pn

121 Pn /Ωc φc Pn

101 88c Pn /Ωc φc Pn Pn /Ωc φc Pn

ASD 1610 1570 1560 1540 1520 1500 1480 1460 1430 1410 1380 1350 1320 1280 1250 1220 1150 1070 1000 927 854 783 713 646 581 524

ASD 1250 1220 1200 1190 1180 1160 1140 1120 1100 1080 1060 1030 1010 985 958 931 876 819 761 703 645 589 535 482 433 391

ASD 1070 1040 1030 1020 1010 995 979 962 944 926 906 885 863 841 818 794 746 696 646 596 546 498 451 405 364 328

ASD 895 871 862 852 841 829 816 802 787 771 754 736 718 699 679 659 618 576 534 491 450 409 370 331 297 268

LRFD 2430 2360 2340 2320 2290 2260 2230 2190 2150 2110 2070 2020 1980 1930 1880 1830 1720 1610 1500 1390 1280 1180 1070 971 873 787

ASD 1430 1390 1380 1360 1350 1330 1310 1290 1260 1240 1210 1190 1160 1130 1100 1070 1010 942 877 811 746 682 620 561 503 454

LRFD 2150 2090 2070 2050 2020 2000 1970 1930 1900 1860 1820 1780 1740 1700 1650 1610 1510 1420 1320 1220 1120 1030 932 843 756 682

LRFD 1880 1830 1810 1790 1770 1740 1720 1690 1660 1630 1590 1560 1520 1480 1440 1400 1320 1230 1140 1060 970 886 804 725 651 587

LRFD 1610 1570 1550 1540 1520 1490 1470 1450 1420 1390 1360 1330 1300 1260 1230 1190 1120 1050 971 896 821 748 678 609 547 494

LRFD 1350 1310 1300 1280 1260 1250 1230 1210 1180 1160 1130 1110 1080 1050 1020 991 929 866 802 739 676 615 556 498 447 404

ASD 749 729 722 714 705 694 684 672 659 646 632 617 602 587 570 554 520 485 450 415 380 346 313 281 253 228

LRFD 1130 1100 1080 1070 1060 1040 1030 1010 991 971 950 928 905 882 857 833 782 729 676 623 571 520 471 423 380 343

Properties

Pwo , kips 435 653 363 545 300 451 241 362 189 283 155 232 Pwi , kips/in. 37.7 56.5 33.3 50.0 29.2 43.8 25.0 37.5 20.8 31.3 18.0 27.0 Pwb , kips 2100 3160 1450 2190 974 1460 612 920 356 535 229 345 Pfb , kips 239 359 187 281 143 215 105 158 73.1 110 54.6 82.0 Lp , ft 13.6 13.5 13.4 16.7 20.2 22.9 Lr , ft 67.6 60.2 54.5 48.6 43.6 40.6 Ag , in.2 53.9 47.7 41.7 35.8 29.9 25.8 Ix , in.4 2490 2190 1870 1590 1300 1110 Iy , in.4 803 697 599 504 412 349 ry , in. 3.86 3.82 3.79 3.75 3.71 3.68 rx /ry 1.76 1.77 1.77 1.78 1.78 1.78 Pex (KL) 2/104, k-in.2 71300 62700 53500 45500 37200 31800 Pey (KL) 2/104, k-in.2 23000 19900 17100 14400 11800 9990 c ASD LRFD Shape is slender for compression with Fy = 50 ksi. Ωc = 1.67

φc = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 4A_14th Ed._ 22/02/12 2:45 PM Page 26

4–26

DESIGN OF COMPRESSION MEMBERS

Table 4-2 (continued)

Available Strength in Axial Compression, kips HP14-HP12

HP-Shapes

Shape

HP14×

lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 50 ksi

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40

117 102 Pn /Ωc φc Pn Pn /Ωc φc Pn ASD 1030 1000 990 977 964 949 933 916 897 878 857 836 813 790 767 743 694 643 593 543 494 446 400 357 320 289

LRFD 1550 1500 1490 1470 1450 1430 1400 1380 1350 1320 1290 1260 1220 1190 1150 1120 1040 967 891 816 742 671 602 537 482 435

ASD 901 875 865 855 843 829 815 800 783 766 748 729 709 689 668 646 603 558 514 470 427 385 344 307 276 249

LRFD 1350 1310 1300 1280 1270 1250 1220 1200 1180 1150 1120 1100 1070 1030 1000 972 906 839 772 706 641 579 518 462 414 374

HP12×

Pn /Ωc φc Pn

73c Pn /Ωc φc Pn

74 Pn /Ωc φc Pn Pn /Ωc φc Pn

ASD 781 758 750 740 730 718 705 692 677 662 646 629 612 594 576 557 519 480 441 403 365 329 294 262 235 212

ASD 623 605 598 590 582 573 563 552 541 528 516 502 489 475 460 445 415 384 353 322 292 263 235 210 188 170

ASD 737 705 694 681 667 652 636 618 599 580 560 539 518 496 474 452 408 365 323 283 247 217 192 171 154 139

89 LRFD 1170 1140 1130 1110 1100 1080 1060 1040 1020 995 971 946 920 893 866 838 780 722 663 606 549 494 441 394 353 319

LRFD 937 909 899 887 875 861 846 830 813 794 775 755 735 713 691 669 623 577 531 484 439 396 354 316 283 256

84

LRFD 1110 1060 1040 1020 1000 980 955 929 901 872 842 810 779 746 713 680 614 549 486 425 371 326 289 257 231 208

ASD 653 624 614 603 591 577 562 546 530 512 494 476 457 437 418 398 359 320 283 247 216 189 168 150 134 121

LRFD 981 938 923 906 888 867 845 821 796 770 743 715 687 658 628 599 540 482 426 372 324 285 252 225 202 182

Properties

Pwo , kips Pwi , kips/in. Pwb , kips Pfb , kips Lp , ft Lr , ft Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry Pex (KL) 2/104, k-in.2 Pey (KL) 2/104, k-in.2 ASD Ωc = 1.67

201 302 162 243 134 201 100 150 158 236 132 198 26.8 40.3 23.5 35.3 20.5 30.8 16.8 25.3 22.8 34.3 20.2 30.3 790 1190 531 798 354 532 195 294 572 859 393 591 121 182 93.0 140 70.8 106 47.7 71.7 87.8 132 69.6 105 12.9 15.6 17.8 21.2 10.4 11.9 50.5 45.7 41.7 37.6 41.3 37.9 34.4 30.1 26.1 21.4 24.6 21.8 1220 1050 904 729 650 569 443 380 326 261 213 186 3.59 3.56 3.53 3.49 2.94 2.92 1.66 1.66 1.67 1.67 1.75 1.75 34900 30100 25900 20900 18600 16300 12700 10900 9330 7470 6100 5320 c LRFD Shape is slender for compression with Fy = 50 ksi. φc = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 4A:14th Ed._

2/17/12

9:17 AM

Page 27

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–27

Table 4-2 (continued) Fy = 50 ksi

Available Strength in Axial Compression, kips HP12-HP8

HP-Shapes HP12 ×

Shape lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HP10× 53c

63

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40

HP8×

57

42

36

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD 551 526 518 508 497 485 472 459 445 430 414 398 382 365 348 332 298 265 234 203 177 156 138 123 110 99.6

LRFD 828 791 778 763 747 729 710 690 668 646 622 598 574 549 524 498 448 399 351 305 266 234 207 185 166 150

ASD 460 439 432 424 415 405 394 383 371 358 345 332 318 304 290 276 248 221 194 169 147 129 114 102 91.6 82.7

LRFD 691 660 649 637 623 608 592 575 557 538 519 499 478 457 436 415 373 332 292 254 221 194 172 153 138 124

ASD 500 469 459 447 434 420 404 388 372 355 337 319 301 283 265 248 214 182 155 133 116 102 90.5 80.7 72.5 65.4

LRFD 751 706 690 672 652 631 608 584 559 533 506 480 453 426 399 373 322 273 233 201 175 154 136 121 109 98.3

ASD 371 348 340 331 321 310 298 286 273 260 247 233 220 206 193 180 154 131 111 95.9 83.5 73.4 65.0 58.0 52.1 47.0

LRFD 558 523 511 497 482 465 448 430 411 391 371 351 330 310 290 270 232 196 167 144 126 110 97.7 87.2 78.2 70.6

ASD 317 287 277 266 254 241 227 213 199 184 170 156 143 129 117 105 86.9 73.0 62.2 53.7 46.7 41.1

LRFD 477 432 416 400 381 362 341 320 299 277 256 235 214 194 175 158 131 110 93.5 80.7 70.3 61.8

177 28.3 597 89.8 8.65 34.8 16.7 294 101 2.45 1.71 8410 2890

78.2 13.8 158 33.0

117 20.8 237 49.6 12.3 28.3 12.4 210 71.7 2.41 1.71 6010 2050

83.8 14.8 241 37.1

Properties

Pwo , kips Pwi , kips/in. Pwb , kips Pfb , kips Lp , ft Lr , ft Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry Pex (KL) 2/104, k-in.2 Pey (KL) 2/104, k-in.2 ASD Ωc = 1.67

107 17.2 243 49.6

161 25.8 365 74.6 14.4 34.0 18.4 472 153 2.88 1.76 13500 4380 LRFD

φc = 0.90

81.9 14.5 147 35.4

123 21.8 221 53.2 16.6 31.1 15.5 393 127 2.86 1.76 11200 3630

118 18.8 397 59.7

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

126 22.3 363 55.7 6.90 27.3 10.6 119 40.3 1.95 1.72 3410 1150

AISC_Part 4A:14th Ed.

2/23/11

10:03 AM

Page 28

4–28

DESIGN OF COMPRESSION MEMBERS

Table 4-3

Available Strength in Axial Compression, kips Rectangular HSS

HSS20-HSS16

HSS20× 12×

Shape

t design, in. lb/ft

HSS16× 12×

5/8

1/2 c

3/8 c

5/16c

5/8

0.581 127

0.465 103

0.349 78.5

0.291 65.9

0.581 110

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

Pn /Ωc φc Pn Pn /Ωc

φc Pn

1/2 0.465 89.7

Pn /Ωc φc Pn

0

ASD 964

LRFD 1450

ASD 740

LRFD 1110

ASD 495

LRFD 743

ASD 375

LRFD 563

ASD 835

LRFD 1250

ASD 678

LRFD 1020

6 7 8 9 10

950 945 940 933 926

1430 1420 1410 1400 1390

732 730 726 723 719

1100 1100 1090 1090 1080

490 488 487 484 482

737 734 731 728 725

372 372 370 369 368

560 558 557 555 553

822 818 812 807 800

1240 1230 1220 1210 1200

668 664 660 655 650

1000 998 992 985 978

11 12 13 14 15

919 910 901 892 881

1380 1370 1350 1340 1320

714 709 704 698 692

1070 1070 1060 1050 1040

480 477 474 470 467

721 717 712 707 702

367 365 363 361 360

551 549 546 543 540

793 786 777 769 759

1190 1180 1170 1160 1140

645 639 632 625 618

969 960 950 940 929

16 17 18 19 20

871 859 847 835 822

1310 1290 1270 1250 1240

685 678 671 663 655

1030 1020 1010 997 985

463 459 455 451 446

696 690 684 677 670

357 355 353 350 347

537 534 530 526 522

749 739 728 717 705

1130 1110 1090 1080 1060

610 602 593 584 575

917 905 892 878 864

21 22 23 24 25

809 795 781 766 752

1220 1190 1170 1150 1130

647 638 629 619 610

972 959 945 931 916

441 436 431 425 420

663 656 648 639 631

345 342 338 335 331

518 513 509 504 497

693 681 668 655 642

1040 1020 1000 985 965

565 556 545 535 524

850 835 820 804 788

26 27 28 29 30 32 34 36 38 40

736 721 705 690 673 641 608 575 542 510

1110 1080 1060 1040 1010 963 914 864 815 766

599 587 575 562 549 523 497 471 444 418

901 882 864 845 826 787 747 708 668 629

414 408 402 395 389 375 361 346 330 314

622 613 604 594 584 563 542 519 496 472

327 322 318 313 309 299 289 278 267 255

491 485 478 471 464 449 434 418 401 384

628 614 600 586 572 543 513 484 455 426

944 923 902 881 859 816 772 727 684 640

514 503 491 480 468 445 422 398 375 352

772 755 738 721 704 669 634 599 563 528

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

35.0 1880 851 4.93 1.49 LRFD

28.3 1550 705 4.99 1.48 c

21.5 1200 547 5.04 1.48

18.1 1010 464 5.07 1.48

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

30.3 1090 700 4.80 1.25

24.6 904 581 4.86 1.25

AISC_Part 4A:14th Ed.

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10:04 AM

Page 29

4–29

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-3 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

Rectangular HSS HSS16× 12×

Shape

t design, in. lb/ft

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS16× 8×

3/8 c

5/16c

5/8

1/2

3/8 c

5/16c

0.349 68.3

0.291 57.4

0.581 93.3

0.465 76.1

0.349 58.1

0.291 48.9

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Design

HSS16

Pn /Ωc φc Pn Pn /Ωc

φc Pn

0

ASD 479

LRFD 720

ASD 364

LRFD 547

ASD 708

LRFD 1060

ASD 576

LRFD 865

ASD 405

LRFD 609

ASD 310

LRFD 466

6 7 8 9 10

474 472 470 468 465

712 710 706 703 699

361 360 359 358 356

543 541 540 537 535

685 677 668 658 647

1030 1020 1000 989 972

558 551 544 536 527

838 829 818 806 792

396 393 389 385 380

595 590 585 579 572

304 302 299 297 294

457 454 450 446 441

11 12 13 14 15

462 459 455 451 447

694 689 684 678 672

354 353 351 348 346

533 530 527 524 520

634 621 607 593 577

954 934 913 891 868

518 507 496 485 472

778 762 746 728 710

375 370 364 358 351

564 556 547 537 527

290 286 282 278 273

436 430 424 418 411

16 17 18 19 20

443 438 433 428 423

665 658 651 644 635

344 341 338 335 332

516 512 508 504 499

561 545 528 510 493

844 819 793 767 741

460 447 433 419 405

691 671 651 630 609

344 336 328 320 311

516 505 493 480 467

268 263 258 252 246

403 395 387 378 369

21 22 23 24 25

417 411 405 399 393

627 618 609 600 590

329 325 321 316 312

494 489 482 475 468

475 457 438 420 402

714 686 659 631 604

391 376 362 347 332

587 565 544 522 500

302 292 281 270 259

453 438 422 405 389

239 233 226 219 212

360 350 340 329 319

26 27 28 29 30 32 34 36 38 40

386 379 372 365 357 341 324 306 288 271

580 570 559 548 537 513 487 460 433 407

307 302 297 292 286 275 264 252 239 227

461 454 446 438 430 414 396 378 360 341

384 366 348 330 313 280 248 221 199 179

577 550 523 497 471 421 373 333 299 269

318 303 289 275 261 234 208 186 167 150

478 456 434 413 392 352 313 279 250 226

248 237 226 215 205 184 164 146 131 119

372 356 339 323 307 277 247 220 197 178

205 197 189 181 173 156 140 125 112 101

307 296 284 273 260 235 210 188 168 152

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

18.7 702 452 4.91 1.25 LRFD

15.7 595 384 4.94 1.24 c

25.7 815 274 3.27 1.72

20.9 679 230 3.32 1.72

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

16.0 531 181 3.37 1.71

13.4 451 155 3.40 1.71

AISC_Part 4A:14th Ed.

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10:04 AM

Page 30

4–30

DESIGN OF COMPRESSION MEMBERS

Table 4-3 (continued)

Available Strength in Axial Compression, kips Rectangular HSS

HSS16-HSS14 HSS16× 8×

Shape

t design, in. lb/ft

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS14× 10×

1/4c

5/8

1/2

3/8 c

5/16c

1/4c

0.233 39.4

0.581 93.3

0.465 76.1

0.349 58.1

0.291 48.9

0.233 39.4

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Design

Fy = 46 ksi

ASD

Pn /Ωc φc Pn Pn /Ωc

φc Pn

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

224

337

708

1060

576

865

432

649

336

505

237

356

6 7 8 9 10

220 219 217 216 214

331 329 327 324 321

692 687 681 674 666

1040 1030 1020 1010 1000

564 559 554 549 543

847 840 833 825 815

425 422 419 416 412

639 635 630 625 620

331 329 327 325 322

497 495 492 488 484

235 234 233 232 230

353 351 350 348 346

11 12 13 14 15

211 209 206 203 200

318 314 310 306 301

657 648 638 628 617

988 974 960 944 927

536 529 521 512 504

805 794 783 770 757

408 404 399 393 387

613 607 599 591 581

319 316 313 309 305

480 475 470 464 459

229 227 226 224 222

344 342 339 336 333

16 17 18 19 20

197 194 190 187 183

297 291 286 281 275

605 593 581 568 554

910 892 873 853 833

495 485 475 465 454

743 729 714 698 682

380 373 365 358 350

571 560 549 537 525

301 297 292 287 282

452 446 439 431 424

219 217 215 212 209

330 326 323 319 315

21 22 23 24 25

179 175 170 166 161

269 262 256 249 242

541 527 512 498 483

812 791 770 748 726

443 432 421 409 397

666 649 632 615 597

341 333 324 316 307

513 500 488 475 461

277 271 266 260 254

416 408 399 390 381

206 203 200 196 192

310 306 301 295 289

26 27 28 29 30 32 34 36 38 40

156 151 146 141 136 125 113 102 91.3 82.4

235 227 220 212 204 187 171 153 137 124

468 453 438 423 408 378 349 320 293 266

704 681 659 636 614 569 525 482 440 399

385 374 362 349 337 314 290 267 244 223

579 561 543 525 507 471 436 401 367 334

298 289 280 271 262 244 226 208 191 174

448 434 421 407 393 366 339 313 287 262

248 241 235 228 221 206 191 176 162 148

372 362 353 343 332 309 287 265 243 223

188 184 179 175 170 161 151 141 131 120

282 276 269 263 256 242 227 212 196 181

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

10.8 368 127 3.42 1.70 LRFD

25.7 687 407 3.98 1.30 c

20.9 573 341 4.04 1.29

16.0 447 267 4.09 1.29

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

13.4 380 227 4.12 1.29

10.8 310 186 4.14 1.29

AISC_Part 4A:14th Ed.

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10:04 AM

Page 31

4–31

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-3 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

Rectangular HSS HSS12× 10×

Shape

t design, in. lb/ft

HSS12× 8×

1/2

3/8

5/16c

1/4c

5/8

0.465 69.3

0.349 53.0

0.291 44.6

0.233 36.0

0.581 76.3

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS12

Pn /Ωc φc Pn Pn /Ωc

φc Pn

1/2 0.465 62.5

Pn /Ωc φc Pn

0

ASD 523

LRFD 787

ASD 402

LRFD 604

ASD 327

LRFD 491

ASD 234

LRFD 351

ASD 578

LRFD 869

ASD 474

LRFD 712

6 7 8 9 10

512 508 503 498 492

769 763 756 748 739

394 390 387 383 379

591 587 582 576 569

321 319 317 314 311

482 479 476 472 468

231 230 229 228 226

347 346 344 342 340

559 552 544 535 525

840 829 817 804 789

458 452 446 439 431

688 680 671 660 648

11 12 13 14 15

486 479 471 464 455

730 720 709 697 685

374 369 363 357 351

562 554 546 537 528

308 305 301 297 293

463 458 452 446 440

225 223 221 219 216

337 335 332 329 325

514 503 491 478 465

773 756 738 719 699

423 414 404 394 383

636 622 607 592 576

16 17 18 19 20

447 438 428 419 409

672 658 644 629 614

345 338 331 324 316

518 508 497 486 475

288 283 277 271 265

433 425 417 408 398

214 211 209 206 203

322 318 314 309 305

451 437 422 408 392

678 657 635 613 590

372 361 349 337 325

560 543 525 507 489

21 22 23 24 25

399 388 377 367 356

599 583 567 551 535

308 300 292 284 276

463 452 439 427 415

259 252 246 239 232

389 379 369 359 349

199 196 192 187 183

300 294 288 282 275

377 362 346 331 315

567 544 520 497 474

313 301 288 276 263

470 452 433 414 396

26 27 28 29 30 32 34 36 38 40

345 334 322 311 300 278 256 235 214 194

518 501 485 468 451 418 385 353 322 292

268 259 251 242 234 217 200 184 169 153

402 390 377 364 351 326 301 277 253 230

225 218 211 204 197 183 169 156 143 130

338 328 317 307 296 275 254 234 214 195

179 174 169 164 159 149 139 128 117 107

268 261 254 247 240 224 208 192 176 161

300 285 270 256 242 214 189 169 152 137

451 429 406 385 363 321 285 254 228 206

251 239 227 215 203 181 160 143 128 116

377 359 341 323 306 272 241 215 193 174

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

19.0 395 298 3.96 1.15 LRFD

14.6 310 234 4.01 1.15 c

12.2 264 200 4.04 1.15

9.90 216 164 4.07 1.15

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

21.0 397 210 3.16 1.37

17.2 333 178 3.21 1.37

AISC_Part 4A:14th Ed.

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10:04 AM

Page 32

4–32

DESIGN OF COMPRESSION MEMBERS

Table 4-3 (continued)

Available Strength in Axial Compression, kips Rectangular HSS

HSS12

HSS12× 8×

Shape

t design, in. lb/ft

HSS12× 6×

3/8

5 /16c

1/4c

3/16c

5/8

0.349 47.9

0.291 40.4

0.233 32.6

0.174 24.7

0.581 67.8

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

Pn /Ωc φc Pn Pn /Ωc

φc Pn

1/2 0.465 55.7

Pn /Ωc φc Pn

0

ASD 364

LRFD ASD 546 296

LRFD ASD 445 218

LRFD ASD LRFD ASD 327 136 204 515

LRFD ASD LRFD 774 421 633

6 7 8 9 10

352 348 343 338 332

529 523 516 508 499

289 286 283 280 276

434 430 425 420 415

213 211 209 207 204

320 317 314 311 307

134 133 132 131 130

201 200 199 197 196

485 474 462 449 435

728 712 695 675 653

397 389 380 369 358

597 585 571 555 538

11 12 13 14 15

326 319 312 304 297

490 480 469 458 446

272 267 262 257 250

408 401 394 386 376

202 199 195 192 188

303 298 294 288 283

129 128 127 125 124

194 192 190 188 186

420 403 387 369 352

631 606 581 555 529

346 333 320 306 292

520 501 481 460 439

16 17 18 19 20

288 280 271 262 253

433 421 407 394 380

243 236 229 221 214

365 355 344 333 321

184 180 176 172 167

277 271 265 258 251

122 120 118 116 114

183 180 177 174 171

334 316 297 279 261

502 474 447 420 393

278 263 249 234 220

418 396 374 352 330

21 22 23 24 25

244 235 225 216 206

367 352 338 324 310

206 198 190 183 175

310 298 286 274 263

162 157 152 147 141

244 236 228 220 212

111 109 106 103 100

167 164 160 156 151

244 227 210 194 178

366 341 316 291 268

206 192 178 165 152

309 288 268 248 229

26 27 28 29 30 32 34 36 38 40

197 188 179 170 161 144 127 114 102 92.1

296 282 269 255 242 216 192 171 153 138

167 159 152 144 137 122 108 96.8 86.8 78.4

251 239 228 217 205 184 163 145 131 118

136 130 124 118 112 100 89.2 79.5 71.4 64.4

204 195 186 177 168 151 134 120 107 96.8

146 141 136 130 125 114 103 91.8 82.4 74.4

165 153 142 133 124 109 96.4 86.0 77.2

248 230 214 199 186 164 145 129 116

141 130 121 113 106 92.9 82.2 73.4 65.8 59.4

211 196 182 170 159 140 124 110 99.0 89.3

97.0 93.6 90.2 86.7 83.2 75.9 68.5 61.1 54.8 49.5

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

13.2 262 140 3.27 1.37 LRFD φc = 0.90

11.1 224 120 3.29 1.37

8.96 184 98.8 3.32 1.36

6.76 140 75.7 3.35 1.36

18.7 321 107 2.39 1.73

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

15.3 271 91.1 2.44 1.73

AISC_Part 4A:14th Ed.

2/23/11

10:04 AM

Page 33

4–33

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-3 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

Rectangular HSS HSS12× 6×

Shape

t design, in. lb/ft

HSS10× 8×

3/8

5/16c

1/4c

3/16c

5/8

0.349 42.8

0.291 36.1

0.233 29.2

0.174 22.2

0.581 67.8

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS12-HSS10

Pn /Ωc φc Pn Pn /Ωc

φc Pn

1/2 0.465 55.7

Pn /Ωc φc Pn

0

ASD 325

LRFD ASD 489 264

LRFD ASD 396 192

LRFD ASD LRFD 288 126 189

ASD 515

LRFD ASD 774 421

LRFD 633

6 7 8 9 10

307 301 294 286 278

462 453 442 430 418

253 249 244 239 234

380 374 367 360 352

185 183 180 177 173

278 274 270 265 260

122 120 119 117 115

183 181 179 176 173

497 490 483 474 465

746 737 726 713 699

407 402 396 389 382

611 604 595 585 574

11 12 13 14 15

269 260 250 239 229

404 390 375 360 344

227 219 211 203 194

341 330 317 305 291

169 165 160 156 150

254 248 241 234 226

113 111 108 105 103

170 166 162 158 154

456 445 434 422 410

685 669 652 635 616

374 366 357 348 338

562 550 537 522 508

16 17 18 19 20

218 207 196 185 174

327 311 294 278 262

185 176 167 158 148

278 264 251 237 223

145 139 133 127 121

218 209 200 191 182

99.5 96.3 92.9 89.4 85.8

150 145 140 134 129

397 384 371 357 343

597 577 557 537 516

328 317 307 296 284

493 477 461 444 428

21 22 23 24 25

163 153 142 132 122

245 229 214 199 184

139 131 122 113 105

210 196 183 171 158

114 107 100 93.1 86.5

171 161 150 140 130

82.1 78.2 74.2 70.1 66.0

123 118 112 105 99.2

329 315 301 287 273

495 474 453 432 411

273 262 251 239 228

411 394 377 360 343

26 27 28 29 30 32 34 36 38 40

113 105 97.4 90.8 84.9 74.6 66.1 58.9 52.9 47.7

170 157 146 136 128 112 99.3 88.6 79.5 71.7

61.7 57.3 53.3 49.7 46.4 40.8 36.1 32.2 28.9 26.1

92.8 86.1 80.1 74.7 69.8 61.3 54.3 48.5 43.5 39.2

259 246 233 219 207 182 161 144 129 116

390 370 349 330 311 274 242 216 194 175

217 206 195 184 174 154 136 121 109 98.4

326 309 293 277 262 231 205 183 164 148

97.3 90.2 83.9 78.2 73.1 64.2 56.9 50.7 45.5 41.1

146 136 126 118 110 96.5 85.5 76.3 68.4 61.8

80.0 120 74.2 111 69.0 104 64.3 96.6 60.1 90.3 52.8 79.4 46.8 70.3 41.7 62.7 37.4 56.3 33.8 50.8 Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

11.8 215 72.9 2.49 1.72 LRFD

9.92 184 62.8 2.52 1.71 c

8.03 151 51.9 2.54 1.71

6.06 116 40.0 2.57 1.70

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

18.7 253 178 3.09 1.19

15.3 214 151 3.14 1.19

AISC_Part 4A:14th Ed.

2/23/11

10:04 AM

Page 34

4–34

DESIGN OF COMPRESSION MEMBERS

Table 4-3 (continued)

Available Strength in Axial Compression, kips Rectangular HSS

HSS10

HSS10× 8×

Shape

t design, in. lb/ft

HSS10× 6×

3/8

5/16

1/4c

3/16c

0.349 42.8

0.291 36.1

0.233 29.2

0.174 22.2

5/8 0.581 59.3

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 325

LRFD 489

ASD 273

LRFD 411

ASD 212

LRFD 318

ASD 133

LRFD 200

ASD 452

LRFD 679

6 7 8 9 10

314 310 306 301 296

472 466 460 452 444

264 261 257 253 249

397 392 387 381 374

206 204 202 199 197

310 307 303 300 295

131 130 129 128 127

197 196 194 193 191

424 414 403 391 378

637 623 606 588 569

11 12 13 14 15

290 283 277 270 262

435 426 416 405 394

244 239 233 228 221

367 359 351 342 333

194 190 187 183 179

291 286 280 275 269

126 124 123 121 119

189 187 185 182 179

365 350 335 319 303

548 526 504 480 456

16 17 18 19 20

255 247 239 231 222

383 371 359 346 334

215 209 202 195 188

323 314 303 293 283

174 170 164 159 153

262 255 247 239 230

117 115 113 111 108

176 173 170 166 162

287 271 255 239 223

432 407 383 359 335

21 22 23 24 25

214 205 196 188 179

321 308 295 282 269

181 174 167 160 152

272 261 251 240 229

148 142 136 130 125

222 213 205 196 187

105 103 99.4 95.9 92.4

158 154 149 144 139

207 192 177 163 150

311 288 266 245 225

26 27 28 29 30 32 34 36 38 40

171 162 154 146 138 122 108 96.7 86.8 78.3

257 244 232 219 207 184 163 145 130 118

145 138 131 125 118 105 92.9 82.8 74.3 67.1

218 208 197 187 177 158 140 125 112 101

119 113 108 102 96.9 86.5 76.6 68.3 61.3 55.3

179 170 162 154 146 130 115 103 92.1 83.2

134 128 123 117 111 99.8 88.5 78.9 70.8 63.9

139 129 120 111 104 91.5 81.1 72.3 64.9

208 193 180 168 157 138 122 109 97.6

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

88.9 85.2 81.5 77.8 74.0 66.4 58.9 52.5 47.1 42.5

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

11.8 169 120 3.19 1.19 LRFD

9.92 145 103 3.22 1.19

8.03 119 84.7 3.25 1.18

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

φc = 0.90

6.06 91.4 65.1 3.28 1.18

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

16.4 201 89.4 2.34 1.50

AISC_Part 4A:14th Ed.

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10:04 AM

Page 35

4–35

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-3 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

Rectangular HSS HSS10× 6×

Shape

t design, in. lb/ft

1/2

3/8

5/16

1/4c

3/16c

0.465 48.9

0.349 37.7

0.291 31.8

0.233 25.8

0.174 19.6

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 372

LRFD 559

ASD 286

LRFD 431

ASD 241

LRFD 363

ASD 186

LRFD 279

ASD 123

LRFD 185

6 7 8 9 10

350 342 334 324 314

526 514 501 487 472

270 265 258 251 243

406 398 388 377 366

228 223 218 212 206

343 336 328 319 309

178 175 172 168 164

268 263 259 253 247

119 117 116 114 111

179 176 174 171 167

11 12 13 14 15

303 291 279 267 254

455 438 420 401 382

235 227 218 208 199

354 341 327 313 299

199 192 185 177 169

299 289 277 266 254

160 155 150 144 138

241 234 226 216 207

109 106 103 100 97.0

164 160 155 151 146

16 17 18 19 20

241 228 215 202 189

362 342 323 303 284

189 179 169 159 149

284 269 254 239 225

161 152 144 136 128

242 229 217 204 192

131 125 118 111 105

197 187 177 167 157

93.5 90.0 86.2 82.4 78.4

141 135 130 124 118

21 22 23 24 25

176 164 152 140 129

265 246 228 210 194

140 130 121 112 103

210 196 182 169 155

120 112 104 96.7 89.3

180 168 157 145 134

98.2 91.8 85.6 79.5 73.5

148 138 129 120 110

74.3 70.1 65.8 61.4 57.0

112 105 98.9 92.3 85.6

26 27 28 29 30 32 34 36 38 40

119 110 103 95.7 89.4 78.6 69.6 62.1 55.7

179 166 154 144 134 118 105 93.3 83.8

124 115 107 99.7 93.2 81.9 72.5 64.7 58.1 52.4

68.0 63.0 58.6 54.6 51.1 44.9 39.7 35.5 31.8 28.7

102 94.7 88.1 82.1 76.7 67.4 59.7 53.3 47.8 43.2

52.7 48.8 45.4 42.3 39.6 34.8 30.8 27.5 24.7 22.2

79.1 73.4 68.2 63.6 59.4 52.2 46.3 41.3 37.0 33.4

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS10

95.6 88.7 82.4 76.8 71.8 63.1 55.9 49.9 44.8 40.4

144 133 124 116 108 94.9 84.0 75.0 67.3 60.7

82.5 76.5 71.2 66.3 62.0 54.5 48.3 43.0 38.6 34.9

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

13.5 171 76.8 2.39 1.49 LRFD

10.4 137 61.8 2.44 1.49

8.76 118 53.3 2.47 1.48

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

φc = 0.90

7.10 96.9 44.1 2.49 1.48

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5.37 74.6 34.1 2.52 1.48

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Page 36

4–36

DESIGN OF COMPRESSION MEMBERS

Table 4-3 (continued)

Available Strength in Axial Compression, kips Rectangular HSS

HSS10-HSS9

HSS10× 5×

Shape

t design, in. lb/ft

HSS9× 7×

3/8

5/16

1/4c

3/16c

0.349 35.1

0.291 29.7

0.233 24.1

0.174 18.4

5/8 0.581 59.3

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

266

400

225

338

173

260

114

171

452

679

6 7 8 9 10

245 238 230 221 212

368 358 345 332 318

207 201 195 187 180

312 303 293 282 270

163 159 155 151 146

245 240 233 227 219

108 106 104 102 98.7

163 160 156 153 148

430 423 414 405 395

647 636 623 609 593

11 12 13 14 15

202 191 180 170 159

303 287 271 255 238

171 163 154 144 135

257 244 231 217 203

140 133 126 119 111

210 200 189 178 167

95.7 92.4 88.9 85.1 81.2

144 139 134 128 122

384 372 360 347 334

577 559 541 521 501

16 17 18 19 20

148 137 126 116 106

222 206 190 174 159

126 117 108 99.5 91.1

190 176 163 150 137

104 96.8 89.6 82.6 75.9

156 145 135 124 114

77.0 72.7 68.2 63.6 58.8

116 109 103 95.5 88.4

320 306 292 278 263

481 460 439 417 396

145 132 121 111 102

82.9 75.5 69.1 63.4 58.5

125 113 104 95.3 87.9

69.2 63.1 57.7 53.0 48.8

104 94.8 86.7 79.6 73.4

53.9 49.1 44.9 41.3 38.0

81.0 73.8 67.5 62.0 57.2

249 235 221 208 194

375 353 333 312 292

54.1 50.1 46.6 43.4 40.6 35.7 31.6

81.2 75.3 70.1 65.3 61.0 53.6 47.5

45.1 41.9 38.9 36.3 33.9 29.8 26.4

67.9 62.9 58.5 54.5 51.0 44.8 39.7

35.2 32.6 30.3 28.3 26.4 23.2 20.6

52.9 49.0 45.6 42.5 39.7 34.9 30.9

182 169 157 146 137 120 106 94.9 85.1 76.8

273 253 236 220 205 180 160 143 128 115

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

21 22 23 24 25

96.2 87.6 80.2 73.6 67.9

26 27 28 29 30 32 34 36 38 40

62.7 58.2 54.1 50.4 47.1 41.4 36.7

94.3 87.5 81.3 75.8 70.8 62.3 55.2

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

9.67 120 40.6 2.05 1.72 LRFD

8.17 104 35.2 2.07 1.72

6.63 85.8 29.3 2.10 1.71

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

φc = 0.90

5.02 66.2 22.7 2.13 1.70

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

16.4 174 117 2.68 1.22

AISC_Part 4A:14th Ed.

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Page 37

4–37

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-3 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

Rectangular HSS HSS9× 7×

Shape

t design, in. lb/ft

1/2

3/8

5/16

1/4 c

3/16c

0.465 48.9

0.349 37.7

0.291 31.8

0.233 25.8

0.174 19.6

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 372

LRFD 559

ASD 286

LRFD 431

ASD 241

LRFD 363

ASD 195

LRFD 293

ASD 129

LRFD 194

6 7 8 9 10

355 349 342 335 327

533 524 514 503 491

274 269 264 259 253

412 405 397 389 380

231 227 223 218 213

347 342 335 328 321

187 184 181 177 173

282 277 272 267 261

126 125 123 122 120

189 188 186 183 181

11 12 13 14 15

318 308 299 288 278

478 464 449 433 417

246 239 232 224 216

370 359 348 337 325

208 202 196 190 183

313 304 295 285 275

169 165 160 155 149

254 247 240 232 224

118 116 113 110 108

178 174 170 166 162

16 17 18 19 20

267 255 244 233 221

401 384 367 350 332

208 199 191 182 174

312 300 287 274 261

176 169 162 155 148

265 254 244 233 222

144 138 133 127 121

216 208 199 191 182

104 101 97.8 94.3 90.7

157 152 147 142 136

21 22 23 24 25

210 198 187 176 165

315 298 281 264 248

165 156 148 139 131

248 235 222 209 197

140 133 126 119 112

211 200 190 179 168

115 109 104 97.9 92.3

173 164 156 147 139

86.9 83.1 79.2 75.1 70.9

131 125 119 113 107

26 27 28 29 30 32 34 36 38 40

154 144 134 125 117 103 90.8 81.0 72.7 65.6

232 217 201 188 175 154 137 122 109 98.7

123 115 107 99.8 93.2 81.9 72.6 64.7 58.1 52.4

185 173 161 150 140 123 109 97.3 87.3 78.8

105 98.7 92.1 85.8 80.2 70.5 62.5 55.7 50.0 45.1

158 148 138 129 121 106 93.9 83.7 75.1 67.8

131 122 115 107 99.8 87.7 77.7 69.3 62.2 56.2

66.8 62.8 58.8 54.9 51.3 45.1 39.9 35.6 32.0 28.9

100 94.3 88.4 82.5 77.1 67.8 60.0 53.5 48.1 43.4

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS9

86.8 81.5 76.2 71.1 66.4 58.4 51.7 46.1 41.4 37.4

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

13.5 149 100 2.73 1.22 LRFD

10.4 119 80.4 2.78 1.22 c

8.76 102 69.2 2.81 1.21

7.10 84.1 57.2 2.84 1.21

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5.37 64.7 44.1 2.87 1.21

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4–38

DESIGN OF COMPRESSION MEMBERS

Table 4-3 (continued)

Available Strength in Axial Compression, kips Rectangular HSS

HSS9

HSS9× 5×

Shape

t design, in. lb/ft

5/8

1/2

3/8

5/16

1/4c

3/16c

0.581 50.8

0.465 42.1

0.349 32.6

0.291 27.6

0.233 22.4

0.174 17.1

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

ASD

Pn /Ωc φc Pn Pn /Ωc

LRFD

ASD

LRFD

ASD

φc Pn LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

386

580

320

480

247

371

209

314

169

254

112

168

6 7 8 9 10

351 339 326 312 297

527 510 490 468 446

292 283 272 261 249

439 425 409 392 374

227 220 213 204 195

341 331 319 307 294

192 187 180 173 166

289 281 271 261 250

157 152 147 142 136

236 229 221 213 204

106 104 102 98.8 95.8

159 156 153 149 144

11 12 13 14 15

281 264 247 230 214

422 397 372 346 321

236 223 210 196 182

355 335 315 294 274

186 176 166 156 146

279 265 250 234 219

158 150 142 133 124

238 225 213 200 187

130 123 116 110 103

195 185 175 165 154

92.6 89.0 85.2 81.2 77.0

139 134 128 122 116

16 17 18 19 20

197 180 165 149 135

296 271 247 224 202

169 155 142 130 117

253 233 214 195 177

135 125 115 106 96.5

203 188 173 159 145

116 107 99.1 91.0 83.2

174 161 149 137 125

144 134 124 114 104

72.6 109 68.1 102 63.1 94.9 58.2 87.5 53.4 80.3

21 22 23 24 25

122 111 102 93.5 86.2

184 167 153 141 130

107 97.1 88.8 81.6 75.2

160 146 134 123 113

87.5 79.7 72.9 67.0 61.7

131 120 110 101 92.8

95.8 89.0 82.3 75.7 69.4

75.5 113 68.8 103 62.9 94.6 57.8 86.9 53.3 80.1

63.2 57.6 52.7 48.4 44.6

95.0 86.5 79.2 72.7 67.0

48.7 44.4 40.6 37.3 34.4

73.3 66.8 61.1 56.1 51.7

26 27 28 29 30

79.7 120 73.9 111 68.7 103 64.1 96.3 59.9 90.0

69.5 104 64.5 96.9 59.9 90.1 55.9 84.0 52.2 78.5

57.1 52.9 49.2 45.9 42.9

85.8 79.5 74.0 69.0 64.4

49.3 45.7 42.5 39.6 37.0

74.0 68.6 63.8 59.5 55.6

41.2 38.2 35.5 33.1 31.0

62.0 57.4 53.4 49.8 46.5

31.8 29.5 27.4 25.6 23.9

47.8 44.3 41.2 38.4 35.9

32 34

52.6

45.9

37.7

56.6

32.5 28.8

48.9 43.3

27.2 24.1

40.9 36.2

21.0 18.6

31.6 27.9

79.1

69.0

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

14.0 133 52.0 1.92 1.60 LRFD φc = 0.90

11.6 115 45.2 1.97 1.59

8.97 92.5 36.8 2.03 1.58

7.59 79.8 32.0 2.05 1.58

6.17 66.1 26.6 2.08 1.57

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.67 51.1 20.7 2.10 1.58

AISC_Part 4A:14th Ed.

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Page 39

4–39

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-3 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

Rectangular HSS HSS8× 6×

Shape

t design, in. lb/ft

5/8

1/2

0.581 50.8

0.465 42.1

3/8 0.349 32.6

5/16 0.291 27.6

1/4 0.233 22.4

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 386

LRFD 580

ASD 320

LRFD 480

ASD 247

LRFD 371

ASD 209

LRFD 314

ASD 170

LRFD 255

6 7 8 9 10

360 352 342 331 320

542 529 514 498 480

299 293 285 276 267

450 440 428 415 401

232 227 221 215 208

349 342 333 323 313

197 193 188 182 177

296 289 282 274 266

160 157 153 149 144

241 236 230 224 217

11 12 13 14 15

307 294 281 267 253

462 442 422 401 380

257 247 236 225 213

386 371 354 337 320

201 193 185 177 168

302 290 278 266 253

171 164 157 150 143

256 247 236 226 215

139 134 129 123 117

209 202 194 185 177

16 17 18 19 20

238 224 210 196 182

358 337 315 294 273

202 190 178 167 156

303 285 268 251 234

159 151 142 133 125

240 227 213 200 187

136 129 121 114 107

204 193 182 171 160

112 106 99.9 94.0 88.2

168 159 150 141 133

21 22 23 24 25

168 155 142 131 120

253 233 214 196 181

144 134 123 113 104

217 201 185 170 157

116 108 100 92.1 84.9

175 162 150 138 128

99.6 92.6 85.9 79.2 73.0

150 139 129 119 110

82.4 76.8 71.4 66.0 60.8

124 115 107 99.2 91.5

26 27 28 29 30 32 34 36 38 40

111 103 96.0 89.5 83.7 73.5 65.1 58.1

167 155 144 135 126 111 97.9 87.3

118 109 102 94.8 88.6 77.8 69.0 61.5 55.2

67.5 62.6 58.2 54.3 50.7 44.6 39.5 35.2 31.6 28.5

101 94.1 87.5 81.6 76.2 67.0 59.3 52.9 47.5 42.9

56.3 52.2 48.5 45.2 42.3 37.1 32.9 29.3 26.3 23.8

84.6 78.4 72.9 68.0 63.5 55.8 49.4 44.1 39.6 35.7

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS8

96.4 89.4 83.1 77.5 72.4 63.6 56.4 50.3 45.1

145 134 125 116 109 95.7 84.7 75.6 67.8

78.5 72.8 67.6 63.1 58.9 51.8 45.9 40.9 36.7

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

14.0 114 72.3 2.27 1.26 LRFD

11.6 98.2 62.5 2.32 1.25

8.97 79.1 50.6 2.38 1.25

7.59 68.3 43.8 2.40 1.25

Note: Heavy line indicates KL /ry equal to or greater than 200.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

6.17 56.6 36.4 2.43 1.25

AISC_Part 4A:14th Ed.

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10:05 AM

Page 40

4–40

DESIGN OF COMPRESSION MEMBERS

Table 4-3 (continued)

Available Strength in Axial Compression, kips Rectangular HSS

HSS8 HSS8× 6×

Shape

t design, in. lb/ft

HSS8× 4×

3/16c

5/8

1/2

0.174 17.1

0.581 42.3

0.465 35.2

3/8 0.349 27.5

5/16 0.291 23.3

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 119

LRFD 180

ASD 322

LRFD 484

ASD 268

LRFD 403

ASD 209

LRFD 314

ASD 177

LRFD 266

6 7 8 9 10

114 113 110 108 105

172 169 166 162 159

277 262 246 228 211

416 393 369 343 317

232 221 208 194 180

349 332 313 292 271

183 174 164 154 144

274 261 247 232 216

155 148 140 132 123

233 223 211 198 185

11 12 13 14 15

103 99.6 96.3 92.9 89.2

154 150 145 140 134

193 175 157 140 124

290 263 236 211 186

166 151 137 123 110

249 227 206 185 165

133 122 111 100 90.1

200 183 167 151 135

114 105 95.6 86.7 78.0

171 157 144 130 117

16 17 18 19 20

85.4 81.0 76.6 72.2 67.8

128 122 115 108 102

109 96.4 85.9 77.1 69.6

163 145 129 116 105

21 22 23 24 25

63.5 59.3 55.2 51.2 47.2

95.4 89.1 82.9 76.9 70.9

26 27 28 29 30 32 34 36 38 40

43.6 40.5 37.6 35.1 32.8 28.8 25.5 22.8 20.4 18.4

65.6 60.8 56.6 52.7 49.3 43.3 38.4 34.2 30.7 27.7

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

63.1 57.5 52.6 48.3 44.6

94.9 86.5 79.1 72.7 67.0

96.6 85.6 76.4 68.5 61.9

145 129 115 103 93.0

80.1 71.0 63.3 56.8 51.3

120 107 95.1 85.4 77.1

69.6 61.7 55.0 49.4 44.6

105 92.7 82.7 74.2 67.0

56.1 51.1 46.8 43.0 39.6

84.3 76.8 70.3 64.6 59.5

46.5 42.4 38.8 35.6 32.8

69.9 63.7 58.3 53.5 49.3

40.4 36.8 33.7 31.0 28.5

60.8 55.4 50.7 46.5 42.9

36.6

55.0

30.3

45.6

26.4 24.5

39.6 36.8

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

4.67 43.7 28.2 2.46 1.24 LRFD

11.7 82.0 26.6 1.51 1.75

9.74 71.8 23.6 1.56 1.74

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

φc = 0.90

7.58 58.7 19.6 1.61 1.73

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

6.43 51.0 17.2 1.63 1.73

AISC_Part 4A:14th Ed.

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10:05 AM

Page 41

4–41

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-3 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

Rectangular HSS HSS8× 4×

Shape

t design, in. lb/ft

HSS7× 5×

1/4

3/16c

1/8 c

1/2

0.233 19.0

0.174 14.5

0.116 9.86

0.465 35.2

3/8 0.349 27.5

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

144

217

100

151

56.0

84.2

268

403

209

314

6 7 8 9 10

127 121 115 109 102

191 183 173 163 153

91.9 88.8 85.4 81.6 77.3

138 134 128 123 116

52.2 50.8 49.3 47.6 45.7

78.4 76.4 74.1 71.5 68.6

244 236 226 216 206

366 354 340 325 309

191 185 178 171 163

287 278 267 256 244

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS8-HSS7

11 12 13 14 15

94.3 87.0 79.7 72.5 65.4

142 131 120 109 98.4

72.7 67.3 61.8 56.4 51.1

109 101 92.9 84.8 76.8

43.6 41.4 39.0 36.5 33.9

65.5 62.2 58.6 54.9 50.9

195 183 171 159 148

292 275 257 240 222

154 146 137 128 119

232 219 206 192 179

16 17 18 19 20

58.7 52.2 46.5 41.8 37.7

88.2 78.4 69.9 62.8 56.6

46.0 41.1 36.6 32.9 29.7

69.2 61.7 55.0 49.4 44.6

31.2 28.4 25.4 22.8 20.6

46.8 42.6 38.2 34.3 31.0

136 125 113 103 92.7

204 187 171 154 139

110 101 93.0 84.8 76.8

166 153 140 127 115

21 22 23 24 25

34.2 31.1 28.5 26.2 24.1

51.4 46.8 42.8 39.3 36.2

26.9 24.5 22.4 20.6 19.0

40.4 36.8 33.7 31.0 28.5

18.7 17.0 15.6 14.3 13.2

28.1 25.6 23.4 21.5 19.8

84.1 76.6 70.1 64.4 59.3

126 115 105 96.8 89.2

69.6 63.4 58.0 53.3 49.1

105 95.4 87.2 80.1 73.8

26 27 28 29 30

22.3 20.7

33.5 31.1

17.6 16.3 15.1

26.4 24.5 22.7

12.2 11.3 10.5

18.3 17.0 15.8

54.9 50.9 47.3 44.1 41.2

82.5 76.5 71.1 66.3 61.9

45.4 42.1 39.2 36.5 34.1

68.3 63.3 58.9 54.9 51.3

30.0

45.1

32 Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

5.24 42.5 14.4 1.66 1.72 LRFD

3.98 33.1 11.3 1.69 1.70

2.70 22.9 7.90 1.71 1.71

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

φc = 0.90

9.74 60.6 35.6 1.91 1.31

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7.58 49.5 29.3 1.97 1.30

AISC_Part 4A:14th Ed.

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Page 42

4–42

DESIGN OF COMPRESSION MEMBERS

Table 4-3 (continued)

Available Strength in Axial Compression, kips Rectangular HSS

HSS7

HSS7× 5×

Shape

t design, in. lb/ft

HSS7× 4×

5/16

1/4

3/16 c

1/8c

0.291 23.3

0.233 19.0

0.174 14.5

0.116 9.86

1/2 0.465 31.8

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

177

266

144

217

107

161

59.2

89.0

243

365

6 7 8 9 10

162 157 151 145 139

244 236 228 218 208

133 128 124 119 114

199 193 186 179 171

100 97.9 94.6 91.0 87.1

151 147 142 137 131

56.7 55.8 54.8 53.6 52.2

85.2 83.9 82.3 80.5 78.5

209 198 186 174 160

314 298 280 261 241

11 12 13 14 15

132 125 117 110 102

198 187 176 165 154

108 103 96.6 90.6 84.6

163 154 145 136 127

82.9 78.7 74.3 69.8 65.3

125 118 112 105 98.1

50.8 49.0 47.0 44.8 42.5

76.3 73.7 70.6 67.3 63.9

147 134 121 108 95.6

221 201 181 162 144

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

16 17 18 19 20

94.7 87.3 80.2 73.2 66.4

142 131 121 110 99.9

78.6 72.7 66.9 61.3 55.8

118 109 101 92.1 83.9

60.8 56.3 52.0 47.7 43.6

91.3 84.6 78.1 71.7 65.5

40.2 37.7 35.2 32.7 30.1

60.4 56.7 52.9 49.1 45.2

84.1 74.5 66.4 59.6 53.8

126 112 99.9 89.6 80.9

21 22 23 24 25

60.3 54.9 50.2 46.1 42.5

90.6 82.5 75.5 69.4 63.9

50.6 46.1 42.2 38.7 35.7

76.1 69.3 63.4 58.2 53.7

39.6 36.1 33.0 30.3 27.9

59.5 54.2 49.6 45.6 42.0

27.4 25.0 22.8 21.0 19.3

41.2 37.5 34.3 31.5 29.0

48.8 44.5 40.7 37.4 34.4

73.4 66.8 61.2 56.2 51.8

26 27 28 29 30

39.3 36.5 33.9 31.6 29.5

59.1 54.8 51.0 47.5 44.4

33.0 30.6 28.5 26.5 24.8

49.6 46.0 42.8 39.9 37.3

25.8 23.9 22.3 20.8 19.4

38.8 36.0 33.5 31.2 29.2

17.9 16.6 15.4 14.4 13.4

26.8 24.9 23.2 21.6 20.2

32 34

26.0

39.0

21.8

32.8

17.0 15.1

25.6 22.7

11.8 10.4

17.7 15.7

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

6.43 43.0 25.5 1.99 1.30 LRFD

5.24 35.9 21.3 2.02 1.30

3.98 27.9 16.6 2.05 1.29

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

φc = 0.90

2.70 19.3 11.6 2.07 1.29

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.81 50.7 20.7 1.53 1.57

AISC_Part 4A:14th Ed.

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10:05 AM

Page 43

4–43

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-3 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

Rectangular HSS HSS7× 4×

Shape

t design, in. lb/ft

3/8

5/16

1/4

3/16c

1/8c

0.349 24.9

0.291 21.2

0.233 17.3

0.174 13.3

0.116 9.01

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

190

285

161

242

131

197

97.7

147

55.1

82.8

6 7 8 9 10

165 157 148 138 129

248 236 222 208 193

141 134 127 119 111

212 202 191 179 167

115 110 104 98.1 91.7

173 166 157 148 138

88.1 84.2 79.8 75.2 70.4

132 127 120 113 106

50.9 49.4 47.7 45.8 43.8

76.4 74.2 71.7 68.9 65.8

11 12 13 14 15

119 108 98.4 88.6 79.2

178 163 148 133 119

103 94.1 85.7 77.5 69.5

154 141 129 116 104

85.0 78.2 71.5 64.9 58.4

128 118 107 97.5 87.8

65.3 60.3 55.2 50.2 45.3

98.2 90.6 83.0 75.5 68.1

41.5 39.1 36.6 33.9 31.2

62.4 58.8 55.0 51.0 46.9

16 17 18 19 20

70.0 62.0 55.3 49.7 44.8

105 93.2 83.2 74.6 67.4

61.8 54.8 48.9 43.8 39.6

92.9 82.3 73.4 65.9 59.5

52.3 46.3 41.3 37.1 33.5

78.5 69.6 62.1 55.8 50.3

40.7 36.1 32.2 28.9 26.1

61.1 54.3 48.4 43.5 39.2

28.3 25.4 22.6 20.3 18.3

42.6 38.1 34.0 30.5 27.6

21 22 23 24 25

40.7 37.0 33.9 31.1 28.7

61.1 55.7 50.9 46.8 43.1

35.9 32.7 29.9 27.5 25.3

53.9 49.2 45.0 41.3 38.1

30.4 27.7 25.3 23.2 21.4

45.6 41.6 38.0 34.9 32.2

23.7 21.6 19.7 18.1 16.7

35.6 32.4 29.7 27.2 25.1

16.6 15.2 13.9 12.7 11.7

25.0 22.8 20.8 19.1 17.6

26 27 28

26.5

39.9

23.4

35.2

19.8 18.4

29.8 27.6

15.4 14.3

23.2 21.5

10.8 10.1 9.35

16.3 15.1 14.1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS7

Properties 2

Ag , in. Ix , in.4 Iy , in.4 ry , in. rx /ry

ASD

6.88 41.8 17.3 1.58 1.56 LRFD

5.85 36.5 15.2 1.61 1.55

Ωc = 1.67

φc = 0.90

4.77 30.5 12.8 1.64 1.54

3.63 23.8 10.0 1.66 1.54

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.46 16.6 7.03 1.69 1.53

AISC_Part 4A:14th Ed.

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10:05 AM

Page 44

4–44

DESIGN OF COMPRESSION MEMBERS

Table 4-3 (continued)

Available Strength in Axial Compression, kips Rectangular HSS

HSS6

HSS6× 5×

Shape

t design, in. lb/ft

1/2

3/8

5/16

1/4

3/16

1/8 c

0.465 31.8

0.349 24.9

0.291 21.2

0.233 17.3

0.174 13.3

0.116 9.01

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

Pn /Ωc φc Pn Pn /Ωc

φc Pn

0

ASD 243

LRFD ASD 365 190

LRFD ASD 285 161

LRFD ASD 242 131

LRFD ASD 197 100

LRFD 150

ASD 57.9

LRFD 87.0

1 2 3 4 5

242 240 237 232 226

364 361 356 349 340

189 188 185 182 177

284 282 278 273 267

161 160 157 155 151

242 240 237 233 227

131 130 128 126 124

197 196 193 190 186

99.7 99.0 97.9 96.2 94.2

150 149 147 145 142

57.8 57.6 57.2 56.7 56.0

86.9 86.6 86.0 85.2 84.2

6 7 8 9 10

220 212 203 194 184

330 318 305 291 276

172 167 160 153 146

259 250 241 230 219

147 142 137 131 125

221 214 206 197 188

120 116 112 108 103

181 175 169 162 154

91.7 88.9 85.8 82.3 78.7

138 134 129 124 118

55.2 54.2 53.0 51.7 50.2

82.9 81.4 79.7 77.7 75.5

11 12 13 14 15

174 163 152 141 130

261 245 228 212 196

138 130 122 113 105

207 195 183 170 158

118 112 105 97.8 90.8

178 168 157 147 137

146 138 130 122 113

74.8 112 70.8 106 66.7 100 62.5 93.9 58.3 87.6

48.6 46.5 44.2 41.9 39.5

73.0 69.8 66.5 63.0 59.3

16 17 18 19 20

119 109 98.9 89.1 80.4

179 164 149 134 121

21 22 23 24 25 26 27 28 29 30

72.9 110 66.4 99.9 60.8 91.4 55.8 83.9 51.5 77.3 47.6 71.5 44.1 66.3 41.0 61.6 38.2 57.5 35.7 53.7

96.7 88.7 80.9 73.3 66.2

145 133 122 110 99.5

60.0 54.7 50.0 46.0 42.4 39.2 36.3 33.8 31.5 29.4

90.2 82.2 75.2 69.1 63.7 58.9 54.6 50.8 47.3 44.2

97.4 92.1 86.5 81.0 75.4

83.9 126 77.2 116 70.6 106 64.2 96.6 58.0 87.2

69.8 105 64.3 96.7 59.0 88.7 53.8 80.9 48.8 73.3

54.1 50.0 46.0 42.1 38.3

81.3 75.2 69.1 63.2 57.5

37.0 34.4 31.6 29.0 26.5

55.6 51.6 47.6 43.6 39.8

52.7 48.0 43.9 40.3 37.2 34.3 31.9 29.6 27.6 25.8

44.3 40.3 36.9 33.9 31.2 28.9 26.8 24.9 23.2 21.7

34.7 31.6 28.9 26.6 24.5 22.6 21.0 19.5 18.2 17.0

52.2 47.5 43.5 39.9 36.8 34.0 31.6 29.3 27.4 25.6

24.0 21.9 20.0 18.4 16.9 15.7 14.5 13.5 12.6 11.8

36.1 32.9 30.1 27.6 25.4 23.5 21.8 20.3 18.9 17.7

79.1 72.1 66.0 60.6 55.8 51.6 47.9 44.5 41.5 38.8

66.5 60.6 55.5 50.9 46.9 43.4 40.2 37.4 34.9 32.6

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

8.81 41.1 30.8 1.87 1.16 LRFD

6.88 33.9 25.5 1.92 1.16 c

5.85 29.6 22.3 1.95 1.15

4.77 24.7 18.7 1.98 1.15

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.63 19.3 14.6 2.01 1.15

2.46 13.4 10.2 2.03 1.15

AISC_Part 4A:14th Ed.

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10:05 AM

Page 45

4–45

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-3 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

Rectangular HSS HSS6× 4×

Shape

t design, in. lb/ft

1/2

3/8

5/16

1/4

3/16

1/8 c

0.465 28.4

0.349 22.4

0.291 19.1

0.233 15.6

0.174 12.0

0.116 8.16

φc Pn Pn /Ωc

φc Pn Pn /Ωc

φc Pn Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

217

326

170

256

145

218

118

178

90.3

136

54.1

81.3

1 2 3 4 5

216 213 209 203 195

325 321 314 305 293

170 168 164 160 154

255 252 247 240 231

144 143 140 136 131

217 214 210 205 198

118 117 115 112 108

177 175 172 168 162

90.0 89.0 87.4 85.2 82.5

135 134 131 128 124

53.9 53.5 52.9 51.9 50.8

81.0 80.4 79.5 78.1 76.3

6 7 8 9 10

186 176 165 153 141

279 264 248 230 212

147 140 132 123 114

221 210 198 185 171

126 120 113 106 98.3

189 180 170 159 148

104 98.6 93.2 87.5 81.5

156 148 140 132 123

79.2 75.6 71.5 67.2 62.7

119 114 108 101 94.3

49.4 47.7 45.8 43.8 41.5

74.2 71.7 68.9 65.8 62.4

11 12 13 14 15

129 117 105 93.3 82.3

194 176 158 140 124

105 95.3 86.1 77.2 68.7

157 143 129 116 103

90.6 82.9 75.2 67.7 60.5

136 125 113 102 91.0

75.4 113 69.2 104 63.0 94.7 56.9 85.6 51.1 76.8

58.1 53.4 48.8 44.2 39.8

87.4 80.3 73.3 66.5 59.8

39.1 36.5 33.7 30.8 27.9

58.7 54.8 50.7 46.4 41.9

Pn /Ωc

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS6

16 17 18 19 20

72.3 109 64.0 96.2 57.1 85.9 51.3 77.1 46.3 69.5

60.5 53.6 47.8 42.9 38.7

91.0 80.6 71.9 64.5 58.2

53.5 47.4 42.3 38.0 34.3

80.5 71.3 63.6 57.1 51.5

45.4 40.3 35.9 32.2 29.1

68.3 60.5 54.0 48.4 43.7

35.5 31.5 28.1 25.2 22.7

53.4 47.3 42.2 37.9 34.2

25.0 22.2 19.8 17.8 16.0

37.5 33.4 29.8 26.7 24.1

21 22 23 24 25

42.0 38.2 35.0 32.1 29.6

35.1 32.0 29.3 26.9 24.8

52.8 48.1 44.0 40.4 37.3

31.1 28.3 25.9 23.8 21.9

46.7 42.6 38.9 35.8 33.0

26.4 24.0 22.0 20.2 18.6

39.7 36.1 33.1 30.4 28.0

20.6 18.8 17.2 15.8 14.6

31.0 28.2 25.8 23.7 21.9

14.5 13.3 12.1 11.1 10.3

21.9 19.9 18.2 16.7 15.4

20.3

30.5

17.2

25.9

13.5 12.5

20.2 18.8

63.1 57.5 52.6 48.3 44.5

26 27

9.49 8.80

14.3 13.2

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

7.88 34.0 17.8 1.50 1.39 LRFD φc = 0.90

6.18 28.3 14.9 1.55 1.38

5.26 24.8 13.2 1.58 1.37

4.30 20.9 11.1 1.61 1.37

3.28 16.4 8.76 1.63 1.37

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.23 11.4 6.15 1.66 1.36

AISC_Part 4A:14th Ed.

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10:05 AM

Page 46

4–46

DESIGN OF COMPRESSION MEMBERS

Table 4-3 (continued)

Available Strength in Axial Compression, kips Rectangular HSS

HSS6

HSS6× 3×

Shape

t design, in. lb/ft

1/2

3/8

5/16

1/4

3/16

1/8 c

0.465 25.0

0.349 19.8

0.291 17.0

0.233 13.9

0.174 10.7

0.116 7.31

φc Pn Pn /Ωc

φc Pn Pn /Ωc

φc Pn Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

191

288

151

227

129

194

106

159

80.7

121

47.7

71.7

1 2 3 4 5

190 186 179 169 158

286 279 268 254 237

150 147 142 135 126

225 221 213 203 190

128 125 121 116 109

192 189 182 174 163

105 103 99.8 95.3 89.9

158 155 150 143 135

80.2 78.7 76.3 73.1 69.1

121 118 115 110 104

47.5 47.0 46.0 44.7 43.0

71.4 70.6 69.2 67.2 64.7

145 131 117 102 88.4

218 197 176 154 133

117 107 96.0 85.1 74.4

176 160 144 128 112

101 92.2 83.2 74.1 65.0

151 139 125 111 97.8

Pn /Ωc

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

6 7 8 9 10

83.7 126 76.9 116 69.7 105 62.4 93.8 55.2 82.9

64.6 59.6 54.3 48.8 43.4

97.0 89.5 81.6 73.4 65.3

41.0 38.7 36.1 33.2 30.1

61.6 58.1 54.2 49.9 45.2

26.6 23.2 19.9 17.2 15.0

40.0 34.9 29.9 25.8 22.5

11 12 13 14 15

75.2 113 63.2 95.0 53.8 80.9 46.4 69.8 40.4 60.8

64.1 54.4 46.3 39.9 34.8

96.4 81.7 69.6 60.0 52.3

56.3 48.0 40.9 35.3 30.7

84.7 72.2 61.5 53.0 46.2

48.1 41.4 35.3 30.4 26.5

72.3 62.3 53.1 45.7 39.9

38.1 33.1 28.3 24.4 21.2

57.3 49.7 42.5 36.6 31.9

16 17 18 19 20

35.5 31.5 28.1

30.6 27.1 24.2 21.7

46.0 40.7 36.3 32.6

27.0 23.9 21.4 19.2

40.6 36.0 32.1 28.8

23.3 20.6 18.4 16.5 14.9

35.0 31.0 27.7 24.8 22.4

18.7 16.5 14.7 13.2 11.9

28.1 13.2 24.9 11.7 22.2 10.4 19.9 9.33 18.0 8.42

19.8 17.5 15.6 14.0 12.7

7.64

11.5

53.4 47.3 42.2

21

Properties 2

Ag , in. Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

6.95 26.8 8.69 1.12 1.76 LRFD φc = 0.90

5.48 22.7 7.48 1.17 1.74

4.68 20.1 6.67 1.19 1.74

3.84 17.0 5.70 1.22 1.72

2.93 13.4 4.55 1.25 1.71

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.00 9.43 3.23 1.27 1.71

AISC_Part 4A:14th Ed.

2/23/11

10:05 AM

Page 47

4–47

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-3 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

Rectangular HSS HSS5× 4×

Shape

t design, in. lb/ft

1/2

3/8

5/16

1/4

3/16

1/8 c

0.465 25.0

0.349 19.8

0.291 17.0

0.233 13.9

0.174 10.7

0.116 7.31

φc Pn Pn /Ωc

φc Pn Pn /Ωc

φc Pn Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

191

288

151

227

129

194

106

159

80.7

121

52.6

79.1

1 2 3 4 5

191 188 184 178 171

286 283 276 268 257

150 148 145 141 136

226 223 218 212 204

128 127 124 121 116

193 191 187 181 175

105 104 102 99.3 95.9

158 156 153 149 144

80.4 79.5 78.0 76.0 73.4

121 119 117 114 110

52.4 52.0 51.2 50.2 48.9

78.8 78.1 77.0 75.4 73.4

6 7 8 9 10

163 153 143 132 122

244 230 215 199 183

130 123 115 107 99.3

195 185 173 162 149

111 106 99.3 92.6 85.7

167 159 149 139 129

91.8 87.2 82.3 76.9 71.4

138 131 124 116 107

70.4 67.0 63.3 59.4 55.3

106 101 95.2 89.3 83.1

47.3 45.4 43.3 40.9 38.1

71.0 68.3 65.1 61.4 57.2

11 12 13 14 15

110 99.5 88.8 78.6 68.7

166 150 133 118 103

16 17 18 19 20

60.4 53.5 47.7 42.8 38.7

21 22 23 24 25

35.1 31.9 29.2 26.8

Pn /Ωc

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS5

90.9 137 82.5 124 74.3 112 66.4 99.7 58.7 88.3

78.6 118 71.6 108 64.6 97.2 57.9 87.0 51.4 77.3

65.7 60.1 54.4 49.0 43.7

98.8 90.3 81.8 73.6 65.7

51.1 46.8 42.6 38.4 34.4

76.7 70.3 64.0 57.8 51.8

35.2 32.4 29.5 26.7 24.0

53.0 48.7 44.4 40.2 36.1

90.8 80.4 71.7 64.4 58.1

51.6 45.7 40.8 36.6 33.0

77.6 68.7 61.3 55.0 49.7

45.3 40.1 35.8 32.1 29.0

68.0 60.3 53.7 48.2 43.5

38.6 34.2 30.5 27.4 24.7

58.0 51.4 45.8 41.1 37.1

30.6 27.1 24.2 21.7 19.6

46.0 40.7 36.3 32.6 29.4

21.4 19.0 16.9 15.2 13.7

32.2 28.5 25.4 22.8 20.6

52.7 48.0 43.9 40.4

30.0 27.3 25.0 22.9 21.1

45.0 41.0 37.5 34.5 31.8

26.3 23.9 21.9 20.1 18.5

39.5 36.0 32.9 30.2 27.9

22.4 20.4 18.7 17.2 15.8

33.7 30.7 28.1 25.8 23.8

17.8 16.2 14.8 13.6 12.5

26.7 12.4 24.3 11.3 22.2 10.4 20.4 9.51 18.8 8.77

18.7 17.0 15.6 14.3 13.2

14.6

22.0

11.6

17.4

12.2 11.3

26 27

8.10 7.52

Properties

Ag , in.2 Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

6.95 21.2 14.9 1.46 1.20 LRFD φc = 0.90

5.48 17.9 12.6 1.52 1.19

4.68 15.8 11.1 1.54 1.19

3.84 13.4 9.46 1.57 1.19

2.93 10.6 7.48 1.60 1.19

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.00 7.42 5.27 1.62 1.19

AISC_Part 4A:14th Ed.

2/23/11

10:05 AM

Page 48

4–48

DESIGN OF COMPRESSION MEMBERS

Table 4-3 (continued)

Available Strength in Axial Compression, kips Rectangular HSS

HSS5

HSS5× 3×

Shape

t design, in. lb/ft

1/2

3/8

5/16

1/4

3/16

1/8 c

0.465 21.6

0.349 17.3

0.291 14.8

0.233 12.2

0.174 9.42

0.116 6.46

Pn /Ωc φc Pn

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

166

249

132

198

113

170

92.8

140

71.1

107

46.3

69.5

1 2 3 4 5

164 160 154 146 135

247 241 232 219 203

131 128 123 117 109

196 192 185 176 164

112 110 106 101 94.6

169 165 159 152 142

92.2 90.3 87.3 83.2 78.2

139 136 131 125 118

70.6 69.2 67.0 64.0 60.4

106 104 101 96.2 90.8

46.0 45.4 44.3 42.8 41.0

69.2 68.2 66.6 64.4 61.6

6 7 8 9 10

124 111 98.4 85.7 73.4

186 167 148 129 110

101 91.4 81.7 72.0 62.5

151 137 123 108 93.9

87.5 132 79.8 120 71.8 108 63.7 95.7 55.7 83.7

72.6 66.4 59.9 53.3 46.8

109 99.8 90.1 80.2 70.4

56.2 51.7 46.9 41.9 37.1

84.5 77.6 70.4 63.0 55.7

38.7 36.0 32.8 29.5 26.2

58.2 54.1 49.3 44.3 39.4

11 12 13 14 15

61.7 51.8 44.2 38.1 33.2

92.7 77.9 66.4 57.2 49.9

53.4 45.0 38.4 33.1 28.8

80.3 67.7 57.7 49.7 43.3

48.0 40.7 34.7 29.9 26.0

72.1 61.1 52.1 44.9 39.1

40.6 34.6 29.5 25.4 22.1

61.0 52.0 44.3 38.2 33.3

32.3 27.8 23.7 20.5 17.8

48.6 41.8 35.6 30.7 26.8

23.0 20.0 17.1 14.7 12.8

34.6 30.0 25.7 22.1 19.3

16 17 18 19 20

29.2 25.8 23.0

43.8 38.8 34.6

25.3 22.4 20.0 18.0

38.1 33.7 30.1 27.0

22.9 20.3 18.1 16.2

34.4 30.5 27.2 24.4

19.5 17.2 15.4 13.8

29.2 25.9 23.1 20.7

15.7 13.9 12.4 11.1 10.0

23.5 11.3 20.8 9.99 18.6 8.91 16.7 8.00 15.1 7.22

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

Pn /Ωc φc Pn Pn /Ωc

16.9 15.0 13.4 12.0 10.8

Properties 2

Ag , in. Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

6.02 16.4 7.18 1.09 1.51 LRFD φc = 0.90

4.78 14.1 6.25 1.14 1.51

4.10 12.6 5.60 1.17 1.50

3.37 10.7 4.81 1.19 1.50

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.58 8.53 3.85 1.22 1.49

1.77 6.03 2.75 1.25 1.48

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4–49

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-3 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

Rectangular HSS HSS5× 2 1/2 ×

Shape

t design, in. lb/ft

HSS4× 3×

1/4

3/16

1/8 c

3/8

0.233 11.4

0.174 8.78

0.116 6.03

0.349 14.7

5/16 0.291 12.7

Pn /Ωc φc Pn

Pn /Ωc φc Pn Pn /Ωc

1/4 0.233 10.5

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

86.5

130

66.4

99.8

43.0

64.6

113

169

97.0

146

80.2

120

1 2 3 4 5

85.7 83.2 79.3 74.0 67.8

129 125 119 111 102

65.8 64.0 61.0 57.2 52.6

98.8 96.1 91.7 86.0 79.0

42.7 41.8 40.5 38.6 36.2

64.1 62.9 60.8 58.0 54.4

112 109 105 99.3 92.5

168 164 158 149 139

96.2 94.1 90.6 85.9 80.2

145 141 136 129 121

79.6 77.9 75.1 71.4 66.9

120 117 113 107 101

6 7 8 9 10

61.0 53.8 46.5 39.4 32.7

91.7 80.8 69.8 59.2 49.2

47.5 42.1 36.6 31.2 26.2

71.4 63.2 55.0 46.9 39.3

33.1 29.5 25.9 22.3 18.9

49.8 44.4 38.9 33.5 28.4

84.9 128 76.6 115 68.1 102 59.6 89.6 51.3 77.1

73.8 66.9 59.7 52.4 45.4

111 100 89.7 78.8 68.2

61.9 56.3 50.6 44.7 39.0

93.0 84.7 76.0 67.2 58.6

11 12 13 14 15

27.0 22.7 19.4 16.7 14.5

40.6 34.1 29.1 25.1 21.9

21.6 18.2 15.5 13.4 11.6

32.5 27.3 23.3 20.1 17.5

15.7 13.2 11.2 9.69 8.44

23.6 19.8 16.9 14.6 12.7

43.5 36.5 31.1 26.8 23.4

65.3 54.9 46.8 40.3 35.1

38.7 32.6 27.8 23.9 20.9

58.2 49.0 41.7 36.0 31.3

33.5 28.4 24.2 20.9 18.2

50.4 42.7 36.3 31.3 27.3

16 17 18 19

12.8

19.2 10.2 9.06

20.5 18.2 16.2

30.9 27.4 24.4

18.3 16.2 14.5

27.5 24.4 21.8

16.0 14.1 12.6 11.3

24.0 21.3 19.0 17.0

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS5-HSS4

15.4 13.6

7.42 11.1 6.57 9.88

Pn /Ωc φc Pn

Properties 2

Ag , in. Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

3.14 9.40 3.13 0.999 1.73 LRFD φc = 0.90

2.41 7.51 2.53 1.02 1.74

1.65 5.34 1.82 1.05 1.71

4.09 7.93 5.01 1.11 1.25

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.52 7.14 4.52 1.13 1.26

2.91 6.15 3.91 1.16 1.25

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Page 50

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DESIGN OF COMPRESSION MEMBERS

Table 4-3 (continued)

Available Strength in Axial Compression, kips Rectangular HSS

HSS4

HSS4× 2 1/2 ×

HSS4× 3×

Shape

t design, in. lb/ft

3/16

1/8

3/8

5/16

0.174 8.15

0.116 5.61

0.349 13.4

0.291 11.6

1/4 0.233 9.66

Pn /Ωc φc Pn

Pn /Ωc φc Pn Pn /Ωc

3/16 0.174 7.51

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

61.7

92.7

42.4

63.8

103

155

89.0

134

73.5

111

56.7

85.3

1 2 3 4 5

61.3 60.0 58.0 55.3 52.0

92.1 90.2 87.2 83.1 78.2

42.1 41.3 40.0 38.2 36.0

63.3 62.1 60.1 57.3 54.0

102 98.4 93.0 85.8 77.5

153 148 140 129 116

88.0 85.2 80.7 74.8 67.9

132 128 121 112 102

72.8 70.6 67.1 62.4 56.9

109 106 101 93.8 85.6

56.2 54.6 52.0 48.6 44.5

84.5 82.0 78.1 73.0 66.9

6 7 8 9 10

48.2 44.1 39.8 35.5 31.1

72.5 66.3 59.9 53.3 46.8

33.4 30.7 27.8 24.8 21.9

50.2 46.1 41.7 37.3 32.9

68.4 103 58.9 88.6 49.7 74.7 40.9 61.5 33.2 49.9

60.3 52.4 44.6 37.1 30.2

90.6 78.8 67.0 55.7 45.4

50.9 44.5 38.2 32.1 26.4

76.5 67.0 57.4 48.3 39.7

40.0 35.3 30.5 25.9 21.5

60.1 53.0 45.8 38.9 32.3

11 12 13 14 15

27.0 23.0 19.6 16.9 14.7

40.5 34.6 29.4 25.4 22.1

19.0 16.3 13.9 12.0 10.5

28.6 24.6 20.9 18.0 15.7

27.4 23.0 19.6 16.9 14.7

25.0 21.0 17.9 15.4 13.4

37.6 31.6 26.9 23.2 20.2

21.8 18.3 15.6 13.5 11.7

32.8 27.5 23.5 20.2 17.6

17.7 14.9 12.7 10.9 9.54

26.7 22.4 19.1 16.5 14.3

16 17 18 19 20

12.9 11.5 10.2 9.17

19.4 17.2 15.4 13.8

10.3

15.5

8.38

12.6

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

41.2 34.6 29.5 25.4 22.2

9.19 13.8 8.14 12.2 7.26 10.9 6.52 9.80 5.88 8.84

Pn /Ωc φc Pn

Properties 2

Ag , in. Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

2.24 4.93 3.16 1.19 1.25 LRFD

1.54 3.52 2.27 1.21 1.26

3.74 6.77 3.17 0.922 1.46

3.23 6.13 2.89 0.947 1.46

Note: Heavy line indicates KL /ry equal to or greater than 200.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.67 5.32 2.53 0.973 1.45

2.06 4.30 2.06 0.999 1.44

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Page 51

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STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-3 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

Rectangular HSS HSS4× 2 1/2 ×

Shape

t design, in. lb/ft

3/8

5/16

0.116 5.18

0.349 12.2

0.291 10.6

Pn /Ωc φc Pn Pn /Ωc

1/4 0.233 8.81

3/16 0.174 6.87

1/8 0.116 4.75

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

39.1

58.8

93.4

140

81.0

122

67.2

101

52.1

78.2

35.8

53.8

1 2 3 4 5

38.8 37.7 36.0 33.8 31.1

58.3 56.7 54.1 50.8 46.8

91.7 86.8 79.2 69.7 59.2

138 130 119 105 89.0

79.6 75.6 69.5 61.7 52.9

120 114 104 92.7 79.5

66.1 63.0 58.2 52.1 45.1

99.4 94.8 87.5 78.2 67.8

51.3 49.0 45.5 41.0 35.8

77.1 73.7 68.4 61.6 53.8

35.3 33.8 31.5 28.6 25.2

53.1 50.9 47.4 43.0 37.9

6 7 8 9 10

28.2 25.0 21.8 18.7 15.7

42.3 37.6 32.8 28.1 23.6

48.4 38.2 29.4 23.2 18.8

72.8 57.5 44.2 34.9 28.3

43.9 35.1 27.3 21.5 17.4

65.9 52.8 41.0 32.4 26.2

37.8 30.7 24.1 19.1 15.5

56.9 46.2 36.3 28.7 23.2

30.4 25.0 19.9 15.7 12.8

45.6 37.5 29.9 23.7 19.2

21.6 18.0 14.6 11.5 9.35

32.4 27.0 21.9 17.3 14.1

11 12 13 14 15

13.0 10.9 9.30 8.02 6.99

19.5 16.4 14.0 12.1 10.5

15.5 13.1

23.4 19.6

14.4 12.1

21.7 18.2

12.8 10.7

19.2 10.5 16.1 8.86 7.55

16 17

6.14 5.44

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS4× 2×

1/8

Pn /Ωc φc Pn

HSS4

15.8 13.3 11.3

Pn /Ωc φc Pn

7.73 11.6 6.49 9.76 5.53 8.31

9.23 8.18

Properties 2

Ag , in. Ix , in.4 Iy , in.4 ry , in. rx /ry ASD Ωc = 1.67

1.42 3.09 1.49 1.03 1.43 LRFD

3.39 5.60 1.80 0.729 1.77

2.94 5.13 1.67 0.754 1.75

2.44 4.49 1.48 0.779 1.75

Note: Heavy line indicates KL /ry equal to or greater than 200.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.89 3.66 1.22 0.804 1.73

1.30 2.65 0.898 0.830 1.72

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DESIGN OF COMPRESSION MEMBERS

Table 4-4

Available Strength in Axial Compression, kips HSS16-HSS14

t design, in. lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Square HSS HSS16× 16×

Shape

Fy = 46 ksi

HSS14× 14×

1/2

3/8 c

5/16c

5/8

1/2

3/8 c

0.465 103 Pn /Ωc φc Pn

0.349 78.5 Pn /Ωc φc Pn

0.291 65.9 Pn /Ωc φc Pn

0.581 110 Pn /Ωc φc Pn

0.465 89.7 Pn /Ωc φc Pn

0.349 68.3 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

780

1170

521

782

381

572

835

1250

678

1020

498

748

6 7 8 9 10

773 770 767 764 761

1160 1160 1150 1150 1140

518 517 516 515 513

779 777 776 774 772

379 379 378 377 376

570 569 568 567 566

825 821 817 813 808

1240 1230 1230 1220 1210

670 667 664 660 656

1010 1000 998 992 986

494 493 491 489 487

743 741 738 736 733

11 12 13 14 15

757 753 748 743 738

1140 1130 1120 1120 1110

512 510 508 506 504

769 767 764 761 758

375 374 373 372 371

564 563 561 559 557

802 796 790 783 775

1210 1200 1190 1180 1170

652 647 642 636 630

980 972 965 956 947

485 483 480 477 474

729 726 722 718 713

16 17 18 19 20

732 727 720 714 707

1100 1090 1080 1070 1060

502 500 497 495 492

755 751 747 743 739

370 368 367 365 363

555 553 551 549 546

768 759 751 742 732

1150 1140 1130 1110 1100

624 618 611 603 596

938 928 918 907 896

471 468 464 460 454

708 703 697 691 683

21 22 23 24 25

700 693 685 678 670

1050 1040 1030 1020 1010

489 486 482 479 475

735 730 725 720 714

361 360 358 356 353

543 540 537 534 531

722 712 702 691 680

1090 1070 1050 1040 1020

588 580 572 563 554

884 872 859 846 833

448 442 436 430 423

674 665 656 646 636

26 27 28 29 30

661 653 644 635 626

994 981 968 955 941

472 468 464 459 455

709 703 697 691 684

351 349 346 344 341

528 524 520 517 513

669 657 646 634 622

1010 988 970 953 934

545 536 527 517 507

820 806 792 777 763

416 410 403 395 388

626 616 605 594 583

32 34 36 38 40

608 588 569 549 528

913 884 855 825 794

446 436 426 415 403

670 656 640 623 606

336 330 323 316 309

504 495 486 476 465

597 572 546 520 494

897 859 821 782 743

488 467 447 426 405

733 702 671 640 609

373 358 343 327 311

561 538 515 492 468

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in. ASD Ωc = 1.67

28.3 1130 6.31 LRFD

21.5 873 6.37 c

18.1 739 6.39

30.3 897 5.44

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

24.6 743 5.49

18.7 577 5.55

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10:06 AM

Page 53

4–53

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-4 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

HSS14-HSS12

Square HSS HSS14× 14×

Shape

t design, in. lb/ft

5/8

1/2

3/8

5/16c

1/4c

0.291 57.4

0.581 93.3

0.465 76.1

0.349 58.1

0.291 48.9

0.233 39.4

Pn /Ωc φc Pn

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

366

551

708

1060

576

865

441

662

350

526

239

359

6 7 8 9 10

364 363 362 361 360

547 546 545 543 541

696 692 688 682 676

1050 1040 1030 1030 1020

567 563 560 555 551

852 847 841 835 828

434 431 429 426 422

652 648 644 640 634

347 345 344 342 340

521 519 517 515 512

237 236 236 235 234

356 355 354 353 351

11 12 13 14 15

359 357 356 354 352

539 537 535 532 529

670 663 656 648 639

1010 997 985 973 961

546 540 534 528 521

820 812 803 793 783

418 414 410 405 400

629 622 616 609 601

338 336 334 331 328

509 505 502 498 494

233 232 230 229 227

350 348 346 344 342

16 17 18 19 20

350 348 346 344 341

526 523 520 516 513

630 621 611 601 590

947 933 918 903 887

514 507 499 491 482

773 761 750 738 725

394 389 383 377 371

593 584 576 567 557

325 322 319 315 311

489 484 479 474 468

226 224 222 220 218

339 337 334 331 328

21 22 23 24 25

339 336 333 330 327

509 505 500 496 491

580 568 557 545 533

871 854 837 819 801

474 465 456 446 437

712 699 685 671 656

364 357 351 343 336

547 537 527 516 505

306 300 294 289 283

459 451 442 434 425

216 214 211 209 206

325 321 318 314 310

26 27 28 29 30

323 320 316 313 309

486 481 476 470 464

521 509 496 483 471

783 764 745 726 707

427 417 407 397 387

642 627 612 597 581

329 321 314 306 298

494 483 472 460 449

276 270 264 258 251

416 406 397 387 378

203 201 198 194 191

306 301 297 292 287

32 34 36 38 40

301 292 283 273 263

452 439 425 411 395

445 419 393 368 342

669 630 591 552 515

366 345 325 304 284

550 519 488 457 426

283 267 251 236 220

425 402 378 354 331

238 225 212 199 186

358 338 319 299 280

184 177 169 161 151

277 266 254 242 228

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS12× 12×

5/16c

Pn /Ωc φc Pn Pn /Ωc

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in. ASD Ωc = 1.67

15.7 490 5.58 LRFD

25.7 548 4.62 c

20.9 457 4.68

16.0 357 4.73

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

13.4 304 4.76

10.8 248 4.79

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Page 54

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DESIGN OF COMPRESSION MEMBERS

Table 4-4 (continued)

Available Strength in Axial Compression, kips HSS12-HSS10

t design, in. lb/ft

HSS10× 10×

3/16c

5/8

1/2

3/8

5/16

1/4c

0.174 29.8

0.581 76.3

0.465 62.5

0.349 47.9

0.291 40.4

0.233 32.6

Pn /Ωc φc Pn

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

142

213

578

869

474

712

364

546

306

6 7 8 9 10

141 141 140 140 140

212 212 211 211 210

565 560 554 548 541

849 841 833 823 813

463 459 454 449 444

696 690 683 676 667

355 353 349 345 341

534 530 525 519 513

299 297 294 291 287

11 12 13 14 15

139 139 138 137 137

209 208 208 207 206

533 525 516 507 497

802 789 776 762 748

438 431 424 417 409

658 648 638 627 615

337 332 327 321 316

506 499 491 483 474

16 17 18 19 20

136 135 135 134 133

205 203 202 201 200

487 477 465 454 442

732 716 700 682 665

401 393 384 375 365

603 590 577 563 549

309 303 296 290 283

21 22 23 24 25

132 131 130 129 128

198 197 195 193 192

430 418 406 393 380

647 628 610 591 572

356 346 336 326 316

535 520 505 490 474

26 27 28 29 30

126 125 124 122 121

190 188 186 184 182

368 355 342 329 316

552 533 514 495 475

305 295 285 274 264

32 34 36 38 40

118 115 111 108 104

177 173 167 162 156

291 266 242 219 198

437 400 364 329 297

243 223 204 185 167

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Square HSS

HSS12× 12×

Shape

Fy = 46 ksi

Pn /Ωc φc Pn Pn /Ωc

ASD

LRFD

460

228

342

449 446 442 437 432

224 223 222 221 219

337 336 334 331 329

284 279 275 271 266

426 420 414 407 399

217 215 213 211 208

326 323 320 316 313

465 455 446 435 425

261 255 250 244 238

392 384 375 367 358

205 202 199 196 193

308 304 299 295 289

275 268 260 253 245

414 403 392 380 369

232 226 220 213 207

349 340 330 321 311

188 183 178 173 168

283 275 268 260 253

459 443 428 412 397

237 230 222 214 206

357 345 333 322 310

201 194 187 181 174

301 292 282 272 262

163 158 152 147 142

245 237 229 221 213

366 336 307 278 251

191 175 161 146 132

287 264 241 220 199

161 149 136 124 112

243 223 205 187 169

132 121 111 102 92.1

198 182 167 153 138

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in. ASD Ωc = 1.67

8.15 189 4.82 LRFD

21.0 304 3.80 c

17.2 256 3.86

13.2 202 3.92

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11.1 172 3.94

8.96 141 3.97

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STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-4 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

HSS10-HSS9

Square HSS HSS10× 10×

Shape

t design, in. lb/ft

5/8

1/2

3/8

5/16

1/4c

0.174 24.7

0.581 67.8

0.465 55.7

0.349 42.8

0.291 36.1

0.233 29.2

Pn /Ωc φc Pn

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

0

137

206

515

774

421

633

325

489

273

6 7 8 9 10

136 135 135 134 133

204 203 202 201 200

500 494 488 481 474

751 743 734 723 712

409 405 400 395 388

615 609 601 593 584

316 313 309 305 300

475 470 465 458 452

266 263 260 257 253

11 12 13 14 15

132 132 131 130 128

199 198 196 195 193

465 457 447 437 427

700 686 672 657 641

382 375 367 359 351

574 563 552 540 527

296 290 285 279 272

444 436 428 419 409

16 17 18 19 20

127 126 125 123 122

191 189 187 185 183

416 404 393 381 368

625 608 590 572 554

342 333 324 314 304

514 501 487 472 457

266 259 252 245 237

21 22 23 24 25

120 118 116 115 113

180 178 175 172 169

356 343 331 318 305

535 516 497 478 459

294 284 274 264 253

442 427 412 396 381

26 27 28 29 30

111 108 106 104 101

166 163 159 156 152

292 280 267 255 242

439 420 401 383 364

243 233 223 213 203

144 136 127 117 106

218 195 174 156 141

328 293 262 235 212

183 164 147 132 119

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS9× 9×

3/16c

32 34 36 38 40

96.0 90.3 84.2 77.7 70.6

Pn /Ωc φc Pn Pn /Ωc

LRFD

ASD

LRFD

411

219

330

399 395 391 386 380

215 213 211 208 205

323 320 317 312 308

249 244 240 235 230

374 367 360 353 345

202 198 194 190 186

303 298 292 286 280

399 389 379 368 357

224 219 213 207 201

337 328 320 311 301

182 177 173 168 163

273 267 260 252 245

230 222 214 207 199

345 334 322 311 299

194 188 182 175 169

292 283 273 263 253

158 153 148 142 137

237 230 222 214 206

365 350 335 319 305

191 183 175 168 160

287 275 264 252 241

162 156 149 143 136

244 234 224 214 205

132 127 121 116 111

198 190 183 175 167

275 247 220 198 179

145 131 117 105 94.8

218 197 176 158 143

124 112 100 89.9 81.1

186 168 150 135 122

101 91.4 82.0 73.6 66.4

152 137 123 111 99.8

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in. ASD Ωc = 1.67

6.76 108 4.00 LRFD

18.7 216 3.40 c

15.3 183 3.45

11.8 145 3.51

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.92 124 3.54

8.03 102 3.56

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DESIGN OF COMPRESSION MEMBERS

Table 4-4 (continued)

Available Strength in Axial Compression, kips HSS9-HSS8

Square HSS HSS9× 9×

Shape

t design, in. lb/ft

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS8× 8×

3/16c

1/8 c

5/8

1/2

0.174 22.2

0.116 15.0

0.581 59.3

0.465 48.9

3/8 0.349 37.7

Pn /Ωc φc Pn

Design

Fy = 46 ksi

Pn /Ωc φc Pn Pn /Ωc

5/16 0.291 31.8

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

452

679

372

559

286

431

241

363

434 428 421 414 405

653 644 633 622 609

358 353 348 342 335

538 531 523 513 503

276 273 269 264 259

415 410 404 397 389

233 230 226 223 219

350 346 340 335 329

93.9 93.3 92.7 92.0 91.3

396 386 376 365 354

596 581 565 549 532

328 320 311 303 294

492 481 468 455 441

254 248 242 235 228

381 372 363 353 343

214 209 204 199 193

322 315 307 299 290

60.2 59.7 59.1 58.5 57.8

90.5 89.7 88.8 87.9 86.9

342 330 318 306 293

514 496 478 459 440

284 275 265 255 245

427 413 398 383 367

221 214 207 199 191

333 322 311 299 288

187 181 175 169 162

282 273 263 254 244

166 163 159 155 151

57.1 56.4 55.6 54.8 54.0

85.9 84.8 83.6 82.4 81.1

280 267 255 242 230

421 402 383 364 345

234 224 214 203 193

352 337 321 306 290

184 176 168 160 153

276 264 253 241 229

156 150 143 137 130

234 225 215 205 195

147 142 138 133 128

53.1 52.1 51.1 50.1 49.0

79.8 78.3 76.9 75.3 73.7

217 205 193 182 170

326 308 290 273 256

183 173 163 154 145

275 260 246 231 217

145 137 130 123 116

218 206 195 184 174

124 117 111 105 99.1

186 176 167 158 149

46.7 44.2 41.4 38.4 35.0

70.2 66.4 62.2 57.7 52.6

149 132 118 106 95.6

225 199 177 159 144

127 113 100 90.2 81.4

191 169 151 136 122

102 90.2 80.5 72.2 65.2

153 136 121 109 98.0

ASD

LRFD

ASD

LRFD

ASD

0

134

201

64.4

96.8

6 7 8 9 10

132 131 130 130 129

198 197 196 195 193

63.8 63.6 63.4 63.1 62.8

95.9 95.6 95.2 94.8 94.4

11 12 13 14 15

128 126 125 124 122

192 190 188 186 184

62.4 62.1 61.7 61.2 60.7

16 17 18 19 20

120 119 117 115 113

181 178 176 173 170

21 22 23 24 25

111 108 106 103 101

26 27 28 29 30

97.7 94.7 91.6 88.4 84.9

32 34 36 38 40

77.3 116 70.0 105 62.9 94.5 56.5 84.9 51.0 76.6

Pn /Ωc φc Pn

87.5 131 77.5 116 69.1 104 62.0 93.2 56.0 84.1

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in. ASD Ωc = 1.67

6.06 78.2 3.59 LRFD

4.09 53.5 3.62 c

16.4 146 2.99

13.5 125 3.04

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

10.4 100 3.10

8.76 85.6 3.13

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STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-4 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

HSS8-HSS7

Square HSS HSS8× 8×

Shape

t design, in. lb/ft

3/16c

1/8c

5/8

0.233 25.8

0.174 19.6

0.116 13.3

0.581 50.8

1/2 0.465 42.1

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

196

294

130

195

63.0

94.7

386

580

320

480

247

371

6 7 8 9 10

189 186 184 181 177

284 280 276 272 267

127 126 125 124 122

191 190 188 186 184

62.2 61.9 61.6 61.2 60.8

93.5 93.0 92.5 92.0 91.3

366 359 351 343 333

550 540 528 515 501

304 298 292 285 278

457 448 439 429 417

235 231 227 222 216

354 348 341 333 325

11 12 13 14 15

174 170 166 162 157

261 255 249 243 236

121 119 117 115 113

182 179 176 174 170

60.3 59.7 59.2 58.5 57.9

90.6 89.8 88.9 88.0 87.0

323 313 302 290 278

486 470 453 436 418

270 261 252 243 233

405 393 379 365 350

210 204 197 190 183

316 306 296 286 275

16 17 18 19 20

152 147 143 137 132

229 222 214 207 199

111 109 106 103 100

167 163 159 155 151

57.2 56.4 55.6 54.7 53.7

85.9 84.7 83.5 82.2 80.8

266 253 241 228 215

399 381 362 343 324

223 213 203 193 182

336 320 305 290 274

175 168 160 152 145

264 252 241 229 217

21 22 23 24 25

127 122 117 111 106

191 183 175 168 160

97.0 93.0 89.1 85.2 81.3

146 140 134 128 122

52.7 51.7 50.6 49.4 48.2

79.3 77.7 76.0 74.3 72.4

203 191 179 167 155

305 287 268 251 233

172 162 152 143 133

259 244 229 214 200

137 129 122 114 107

206 194 183 172 161

26 27 28 29 30

101 96.0 91.0 86.0 81.2

152 144 137 129 122

77.4 116 73.6 111 69.8 105 66.1 99.3 62.5 93.9

46.9 45.5 44.1 42.6 41.0

70.5 68.4 66.2 64.0 61.6

144 133 124 116 108

216 201 186 174 162

124 115 107 99.6 93.1

186 173 161 150 140

100 92.9 86.4 80.6 75.3

150 140 130 121 113

55.4 49.0 43.7 39.3 35.4

37.5 33.7 30.0 27.0 24.3

56.4 50.6 45.2 40.5 36.6

32 34 36 38 40

Pn /Ωc φc Pn Pn /Ωc

3/8 0.349 32.6

ASD

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS7× 7×

1/4

71.8 108 63.6 95.6 56.7 85.3 50.9 76.5 46.0 69.1

83.2 73.7 65.7 59.0 53.2

95.0 84.1 75.1 67.4 60.8

143 126 113 101 91.4

81.8 123 72.4 109 64.6 97.1 58.0 87.2 52.3 78.7

Pn /Ωc φc Pn ASD

66.2 58.6 52.3 46.9 42.3

LRFD

99.4 88.1 78.6 70.5 63.6

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in. ASD Ωc = 1.67

7.10 70.7 3.15 LRFD

5.37 54.4 3.18 c

3.62 37.4 3.21

14.0 93.4 2.58

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11.6 80.5 2.63

8.97 65.0 2.69

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DESIGN OF COMPRESSION MEMBERS

Table 4-4 (continued)

Available Strength in Axial Compression, kips HSS7-HSS6

Square HSS HSS7× 7×

Shape

t design, in. lb/ft

HSS6× 6×

5/16

1/4

3/16c

1/8 c

5/8

0.291 27.6

0.233 22.4

0.174 17.1

0.116 11.6

0.581 42.3

Pn /Ωc φc Pn

Pn /Ωc φc Pn Pn /Ωc

1/2 0.465 35.2

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

209

314

170

255

124

187

61.7

92.7

322

484

268

403

6 7 8 9 10

199 196 192 188 183

300 295 289 283 276

162 160 157 153 150

244 240 235 230 225

120 119 117 116 113

181 179 177 174 170

60.5 60.0 59.5 59.0 58.3

90.9 90.2 89.5 88.6 87.6

299 291 283 273 262

450 438 425 410 394

250 244 237 229 221

376 367 356 344 332

11 12 13 14 15

178 173 168 162 156

268 260 252 243 234

146 141 137 132 127

219 212 206 199 191

110 107 104 100 96.8

166 161 156 151 146

57.6 56.8 56.0 55.0 54.0

86.6 85.4 84.1 82.7 81.2

251 240 228 215 203

378 360 342 324 305

212 203 193 183 173

319 305 290 275 260

16 17 18 19 20

150 143 137 130 124

225 215 206 196 186

122 117 112 107 102

184 176 169 161 153

93.1 89.3 85.5 81.6 77.6

140 134 128 123 117

52.9 51.8 50.5 49.2 47.8

79.6 77.8 75.9 73.9 71.8

190 178 165 153 142

286 267 249 231 213

163 153 143 133 123

245 230 215 200 185

21 22 23 24 25

117 111 105 98.3 92.2

176 167 157 148 139

96.6 91.4 86.3 81.3 76.3

145 137 130 122 115

73.7 111 69.8 105 66.0 99.1 62.2 93.4 58.4 87.8

46.3 44.7 43.0 41.2 39.3

69.5 67.1 64.6 61.9 59.1

130 119 109 99.8 92.0

196 179 163 150 138

114 104 95.6 87.8 80.9

171 157 144 132 122

26 27 28 29 30

86.3 80.4 74.8 69.7 65.1

130 121 112 105 97.9

71.5 107 66.8 100 62.1 93.4 57.9 87.0 54.1 81.3

54.8 51.2 47.7 44.5 41.6

82.4 77.0 71.7 66.8 62.5

37.3 35.2 33.0 30.7 28.7

56.1 52.9 49.6 46.2 43.2

85.1 78.9 73.4 68.4 63.9

128 119 110 103 96.0

32 34 36 38 40

57.2 50.7 45.2 40.6 36.6

86.0 76.2 68.0 61.0 55.1

47.6 42.1 37.6 33.7 30.4

36.5 32.4 28.9 25.9 23.4

54.9 48.6 43.4 38.9 35.1

25.3 22.4 20.0 17.9 16.2

38.0 33.6 30.0 26.9 24.3

56.2 49.7 44.4

84.4 74.8 66.7

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

71.5 63.3 56.5 50.7 45.8

Pn /Ωc φc Pn

74.8 112 69.4 104 64.5 96.9 60.1 90.4 56.2 84.4 49.4 43.7 39.0

74.2 65.7 58.6

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in. ASD Ωc = 1.67

7.59 56.1 2.72 LRFD φc = 0.90

6.17 46.5 2.75

4.67 36.0 2.77

3.16 24.8 2.80

11.7 55.2 2.17

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.74 48.3 2.23

AISC_Part 4A:14th Ed.

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Page 59

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STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-4 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

HSS6

Square HSS HSS6× 6×

Shape

t design, in. lb/ft

5/16

0.349 27.5

0.291 23.3

Pn /Ωc

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

3/8

φc Pn

Pn /Ωc

1/4 0.233 19.0

φc Pn

1/8 c 0.116 9.86

3/16 0.174 14.5

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

209

314

177

266

144

217

110

165

59.6

89.6

6 7 8 9 10

195 191 185 180 173

293 286 279 270 260

166 162 158 153 148

249 244 237 230 222

135 132 129 125 121

204 199 194 188 182

103 101 98.2 95.3 92.3

155 151 148 143 139

57.8 57.1 56.3 55.4 54.4

86.8 85.8 84.6 83.3 81.8

11 12 13 14 15

167 160 152 145 137

250 240 229 218 206

142 136 130 124 118

214 205 196 187 177

117 112 107 102 96.9

175 168 161 153 146

89.0 85.5 81.9 78.2 74.4

134 129 123 118 112

53.3 52.1 50.7 49.3 47.7

80.1 78.3 76.2 74.0 71.6

16 17 18 19 20

130 122 114 107 99.1

195 183 172 160 149

111 105 98.4 92.0 85.7

167 158 148 138 129

91.8 86.6 81.4 76.2 71.1

138 130 122 115 107

70.5 66.6 62.7 58.8 55.0

106 100 94.2 88.4 82.7

46.0 44.1 42.2 40.1 37.7

69.1 66.3 63.4 60.2 56.7

21 22 23 24 25

91.8 84.7 77.8 71.4 65.8

138 127 117 107 98.9

79.5 73.6 67.7 62.2 57.3

120 111 102 93.5 86.1

66.2 61.3 56.6 52.0 47.9

99.4 92.1 85.1 78.1 72.0

51.2 47.6 44.0 40.5 37.3

77.0 71.5 66.2 60.9 56.1

35.2 32.7 30.3 27.9 25.8

52.9 49.2 45.6 42.0 38.7

26 27 28 29 30

60.8 56.4 52.5 48.9 45.7

91.4 84.8 78.8 73.5 68.7

53.0 49.1 45.7 42.6 39.8

79.6 73.8 68.7 64.0 59.8

44.3 41.1 38.2 35.6 33.3

66.6 61.7 57.4 53.5 50.0

34.5 32.0 29.8 27.7 25.9

51.9 48.1 44.7 41.7 39.0

23.8 22.1 20.5 19.1 17.9

35.8 33.2 30.9 28.8 26.9

32 34 36 38

40.2 35.6 31.7 28.5

60.4 53.5 47.7 42.8

35.0 31.0 27.6 24.8

52.6 46.6 41.5 37.3

29.2 25.9 23.1 20.7

44.0 38.9 34.7 31.2

22.8 20.2 18.0 16.2

34.2 30.3 27.1 24.3

15.7 13.9 12.4 11.1

23.6 20.9 18.7 16.8

Properties

Ag , in.2 Ix = Iy , in.4 rx = ry , in. ASD Ωc = 1.67

7.58 39.5 2.28 LRFD

6.43 34.3 2.31 c

5.24 28.6 2.34

3.98 22.3 2.37

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.70 15.5 2.39

AISC_Part 4A:14th Ed.

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Page 60

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DESIGN OF COMPRESSION MEMBERS

Table 4-4 (continued)

Available Strength in Axial Compression, kips HSS51⁄ 2 -HSS5

Square HSS HSS5 1/2 × 5 1/2 ×

Shape

t design, in. lb/ft

HSS5× 5×

3/8

5/16

1/4

3/16

1/8 c

0.349 24.9

0.291 21.2

0.233 17.3

0.174 13.3

0.116 9.01

Pn /Ωc φc Pn

Pn /Ωc φc Pn Pn /Ωc

1/2 0.465 28.4

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

190

285

161

242

131

197

100

150

58.0

87.2

217

326

1 2 3 4 5

189 188 186 183 179

284 282 279 275 269

161 160 158 156 153

242 240 237 234 229

131 130 129 127 125

197 196 194 191 187

99.8 99.2 98.1 96.7 94.9

150 149 147 145 143

58.0 57.8 57.5 57.0 56.4

87.1 86.9 86.4 85.7 84.8

216 215 211 207 202

325 322 318 311 303

6 7 8 9 10

175 170 164 158 151

263 255 247 238 228

149 145 140 135 130

224 218 211 203 195

122 118 115 111 106

183 178 172 166 160

92.8 90.3 87.5 84.5 81.2

139 136 132 127 122

55.7 54.8 53.8 52.7 51.4

83.7 82.4 80.9 79.2 77.3

195 188 180 171 162

294 283 271 257 244

11 12 13 14 15

145 137 130 122 115

217 206 195 184 172

124 118 112 105 98.8

186 177 168 158 148

101 96.6 91.6 86.5 81.3

153 145 138 130 122

77.8 74.1 70.4 66.6 62.7

117 111 106 100 94.2

50.0 48.5 46.7 44.9 42.9

75.2 72.8 70.3 67.5 64.5

152 142 132 122 112

229 214 199 184 169

16 17 18 19 20

107 99.2 91.7 84.5 77.4

161 149 138 127 116

92.3 85.9 79.6 73.5 67.5

139 129 120 110 101

76.1 114 70.9 107 65.8 98.9 60.8 91.4 55.9 84.1

58.8 54.9 51.0 47.3 43.6

88.3 82.5 76.7 71.0 65.5

40.4 37.8 35.2 32.7 30.2

60.7 56.8 52.9 49.1 45.4

103 93.2 84.1 75.5 68.1

154 140 126 113 102

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

Pn /Ωc φc Pn ASD

LRFD

21 22 23 24 25

70.5 106 64.2 96.5 58.7 88.3 53.9 81.1 49.7 74.7

61.6 56.2 51.4 47.2 43.5

92.7 84.4 77.2 70.9 65.4

51.2 46.7 42.7 39.2 36.1

77.0 70.1 64.2 58.9 54.3

40.0 36.5 33.4 30.7 28.3

60.2 54.9 50.2 46.1 42.5

27.8 25.4 23.3 21.4 19.7

41.8 38.2 35.0 32.1 29.6

61.8 56.3 51.5 47.3 43.6

92.9 84.6 77.4 71.1 65.5

26 27 28 29 30

46.0 42.6 39.6 36.9 34.5

40.2 37.3 34.7 32.3 30.2

60.4 56.0 52.1 48.6 45.4

33.4 31.0 28.8 26.9 25.1

50.2 46.6 43.3 40.4 37.7

26.2 24.2 22.5 21.0 19.6

39.3 36.4 33.9 31.6 29.5

18.2 16.9 15.7 14.6 13.7

27.4 25.4 23.6 22.0 20.6

40.3 37.4 34.8 32.4 30.3

60.6 56.2 52.2 48.7 45.5

69.1 64.1 59.6 55.5 51.9

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in. ASD Ωc = 1.67

6.88 29.7 2.08 LRFD

5.85 25.9 2.11 c

4.77 21.7 2.13

3.63 17.0 2.16

Shape is slender for compression with Fy = 46 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.46 11.8 2.19

7.88 26.0 1.82

AISC_Part 4A:14th Ed.

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10:07 AM

Page 61

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STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-4 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

HSS5-HSS4 1⁄ 2

Square HSS

t design, in. lb/ft

3/8

5/16

1/4

3/16

1/8 c

0.349 22.4

0.291 19.1

0.233 15.6

0.174 12.0

0.116 8.16

Pn /Ωc φc Pn

Pn /Ωc φc Pn Pn /Ωc

1/2 0.465 25.0

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

170

256

145

218

118

178

90.3

136

56.4

84.8

191

288

1 2 3 4 5

170 168 166 163 159

255 253 250 245 239

144 143 141 139 135

217 215 213 209 204

118 117 116 114 111

178 176 174 171 167

90.1 89.4 88.3 86.8 84.8

135 134 133 130 127

56.4 56.1 55.7 55.1 54.3

84.7 84.3 83.7 82.8 81.6

191 189 185 180 174

287 283 278 271 262

6 7 8 9 10

154 149 143 136 129

232 223 214 204 194

132 127 122 117 111

198 191 183 175 167

108 104 100 95.9 91.3

162 157 151 144 137

82.5 79.8 76.9 73.7 70.2

124 120 116 111 106

53.4 52.3 51.0 49.5 47.8

80.2 78.5 76.6 74.4 71.9

167 159 151 141 132

252 240 227 213 198

11 12 13 14 15

122 114 107 98.9 91.3

183 172 160 149 137

105 98.5 92.1 85.6 79.2

157 148 138 129 119

86.5 81.4 76.3 71.1 66.0

130 122 115 107 99.2

66.6 62.8 59.0 55.1 51.2

100 94.4 88.7 82.8 77.0

45.7 43.2 40.6 38.0 35.4

68.7 64.9 61.1 57.2 53.2

122 112 102 92.0 82.6

183 168 153 138 124

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

HSS41/2 × 41/2 ×

HSS5× 5×

Shape

Pn /Ωc φc Pn ASD

LRFD

16 17 18 19 20

83.8 126 76.4 115 69.4 104 62.5 93.9 56.4 84.8

72.9 110 66.7 100 60.7 91.3 54.9 82.5 49.6 74.5

60.9 55.9 51.0 46.3 41.8

91.5 84.0 76.7 69.6 62.8

47.4 43.6 39.9 36.4 32.9

71.2 65.5 60.0 54.6 49.4

32.8 30.3 27.8 25.4 23.0

49.4 45.5 41.8 38.2 34.6

73.5 110 65.1 97.8 58.0 87.2 52.1 78.3 47.0 70.7

21 22 23 24 25

51.2 46.6 42.6 39.2 36.1

76.9 70.0 64.1 58.9 54.2

44.9 41.0 37.5 34.4 31.7

67.6 61.5 56.3 51.7 47.7

37.9 34.5 31.6 29.0 26.7

57.0 51.9 47.5 43.6 40.2

29.8 27.2 24.9 22.8 21.0

44.8 40.8 37.4 34.3 31.6

20.9 19.0 17.4 16.0 14.7

31.4 28.6 26.2 24.1 22.2

42.6 38.9 35.5 32.6 30.1

64.1 58.4 53.4 49.1 45.2

26 27 28 29

33.4 30.9 28.8 26.8

50.2 46.5 43.2 40.3

29.3 27.2 25.3 23.6

44.1 40.9 38.0 35.4

24.7 22.9 21.3 19.9

37.2 34.5 32.1 29.9

19.5 18.0 16.8 15.6

29.2 27.1 25.2 23.5

13.6 12.6 11.8 11.0

20.5 19.0 17.7 16.5

27.8

41.8

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in. ASD Ωc = 1.67

6.18 21.7 1.87 LRFD φc = 0.90

5.26 19.0 1.90

4.30 16.0 1.93

3.28 12.6 1.96

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.23 8.80 1.99

6.95 18.1 1.61

AISC_Part 4A:14th Ed.

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Page 62

4–62

DESIGN OF COMPRESSION MEMBERS

Table 4-4 (continued)

Available Strength in Axial Compression, kips HSS41⁄ 2 -HSS4

Square HSS HSS4 1/2 × 4 1/2 ×

Shape

t design, in. lb/ft

HSS4× 4×

3/8

5/16

1/4

3/16

1/8 c

0.349 19.8

0.291 17.0

0.233 13.9

0.174 10.7

0.116 7.31

Pn /Ωc φc Pn

Pn /Ωc φc Pn Pn /Ωc

1/2 0.465 21.6

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

151

227

129

194

106

159

80.7

121

54.4

81.8

166

249

1 2 3 4 5

150 149 146 143 138

226 224 220 215 208

128 127 125 122 119

193 191 188 184 178

105 104 103 100 97.5

158 157 154 151 147

80.5 79.7 78.4 76.7 74.6

121 120 118 115 112

54.3 54.0 53.4 52.5 51.0

81.6 81.1 80.3 78.8 76.7

165 163 159 153 147

248 244 239 231 221

6 7 8 9 10

133 127 121 114 107

200 191 182 171 160

114 109 104 98.3 92.2

172 164 156 148 139

94.1 90.3 86.0 81.4 76.5

141 136 129 122 115

72.0 69.1 65.9 62.5 58.8

108 104 99.1 93.9 88.4

49.3 47.4 45.3 43.0 40.6

74.2 71.3 68.1 64.6 61.0

139 131 121 112 102

209 196 182 168 153

149 138 126 115 104

85.9 79.6 73.2 66.8 60.6

129 120 110 100 91.1

71.5 107 66.4 99.8 61.2 92.0 56.1 84.3 51.1 76.7

55.0 51.2 47.3 43.4 39.6

82.7 76.9 71.1 65.3 59.5

38.1 35.5 32.9 30.3 27.7

57.2 53.3 49.4 45.5 41.6

92.0 138 82.2 124 72.8 109 63.7 95.8 55.5 83.5

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

Pn /Ωc φc Pn ASD

LRFD

11 12 13 14 15

99.2 91.5 83.9 76.4 69.1

16 17 18 19 20

62.0 55.2 49.2 44.2 39.9

93.2 83.0 74.0 66.4 59.9

54.7 48.8 43.6 39.1 35.3

82.1 73.4 65.5 58.8 53.0

46.2 41.5 37.0 33.2 30.0

69.4 62.4 55.6 49.9 45.1

35.9 32.4 28.9 25.9 23.4

54.0 48.6 43.4 39.0 35.2

25.2 22.8 20.4 18.3 16.5

37.9 34.2 30.7 27.5 24.9

48.8 43.2 38.6 34.6 31.2

73.3 65.0 58.0 52.0 46.9

21 22 23 24 25

36.2 33.0 30.2 27.7 25.5

54.4 49.5 45.3 41.6 38.4

32.0 29.2 26.7 24.5 22.6

48.1 43.8 40.1 36.8 34.0

27.2 24.8 22.7 20.8 19.2

40.9 37.3 34.1 31.3 28.8

21.2 19.4 17.7 16.3 15.0

31.9 29.1 26.6 24.4 22.5

15.0 13.7 12.5 11.5 10.6

22.5 20.5 18.8 17.3 15.9

28.3 25.8 23.6

42.6 38.8 35.5

26 27 28 29

23.6 21.9

35.5 32.9

20.9 19.4 18.0

31.4 29.1 27.1

17.7 16.5 15.3

26.7 24.7 23.0

13.9 12.8 11.9 11.1

20.8 19.3 18.0 16.7

9.78 9.07 8.44 7.86

14.7 13.6 12.7 11.8

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in. ASD Ωc = 1.67

5.48 15.3 1.67 LRFD φc = 0.90

4.68 13.5 1.70

3.84 11.4 1.73

2.93 9.02 1.75

Shape is slender for compression with Fy = 46 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.00 6.35 1.78

6.02 11.9 1.41

AISC_Part 4A:14th Ed.

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10:07 AM

Page 63

4–63

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-4 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

HSS4

Square HSS HSS4× 4×

Shape

t design, in. lb/ft

5/16

0.349 17.3

0.291 14.8

Pn /Ωc

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

3/8

φc Pn

1/4 0.233 12.2

Pn /Ωc

φc Pn

Pn /Ωc

3/16 0.174 9.42

φc Pn

Pn /Ωc

1/8 0.116 6.46

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

132

198

113

170

92.8

140

71.1

107

48.8

73.3

1 2 3 4 5

131 129 126 123 118

197 194 190 184 177

112 111 109 105 101

169 167 163 158 152

92.4 91.3 89.4 86.8 83.6

139 137 134 130 126

70.8 69.9 68.5 66.6 64.2

106 105 103 100 96.6

48.6 48.0 47.1 45.8 44.2

73.0 72.1 70.8 68.9 66.5

6 7 8 9 10

112 106 98.8 91.6 84.1

168 159 149 138 126

96.5 91.2 85.4 79.3 73.0

145 137 128 119 110

79.8 75.6 71.0 66.1 61.0

120 114 107 99.3 91.7

61.5 58.3 54.9 51.3 47.5

92.4 87.7 82.5 77.1 71.4

42.4 40.3 38.0 35.6 33.1

63.7 60.6 57.2 53.5 49.7

11 12 13 14 15

76.5 69.0 61.7 54.7 47.9

115 104 92.8 82.2 72.0

66.6 60.3 54.0 48.0 42.2

100 90.6 81.2 72.2 63.5

55.9 50.8 45.7 40.8 36.1

84.0 76.3 68.7 61.3 54.3

43.6 39.8 36.0 32.2 28.7

65.6 59.8 54.0 48.5 43.1

30.5 27.9 25.3 22.8 20.4

45.8 41.9 38.0 34.3 30.6

16 17 18 19 20

42.1 37.3 33.3 29.9 27.0

63.3 56.1 50.0 44.9 40.5

37.1 32.9 29.3 26.3 23.8

55.8 49.4 44.1 39.6 35.7

31.7 28.1 25.1 22.5 20.3

47.7 42.3 37.7 33.8 30.5

25.3 22.4 20.0 17.9 16.2

38.0 33.6 30.0 26.9 24.3

18.0 16.0 14.2 12.8 11.5

27.1 24.0 21.4 19.2 17.3

21 22 23 24 25

24.4 22.3 20.4 18.7

36.7 33.5 30.6 28.1

21.5 19.6 18.0 16.5

32.4 29.5 27.0 24.8

18.4 16.8 15.4 14.1 13.0

27.7 25.2 23.1 21.2 19.5

14.7 13.4 12.2 11.2 10.4

22.1 20.1 18.4 16.9 15.6

10.5 9.53 8.72 8.01 7.38

15.7 14.3 13.1 12.0 11.1

6.82

10.3

26

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in.

4.78 10.3 1.47

ASD

LRFD

Ωc = 1.67

φc = 0.90

4.10 9.14 1.49

3.37 7.80 1.52

2.58 6.21 1.55

Note: Heavy line indicates KL /ry equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.77 4.40 1.58

AISC_Part 4A:14th Ed.

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10:07 AM

Page 64

4–64

DESIGN OF COMPRESSION MEMBERS

Table 4-4 (continued)

Available Strength in Axial Compression, kips HSS31⁄ 2

Square HSS HSS3 1/2 × 3 1/2 ×

Shape

t design, in. lb/ft

3/8

5/16

0.349 14.7

0.291 12.7

Pn /Ωc

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

φc Pn

Pn /Ωc

1/4 0.233 10.5

φc Pn

Pn /Ωc

3/16 0.174 8.15

φc Pn

Pn /Ωc

φc Pn

1/8 0.116 5.61

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

113

169

97.0

146

80.2

120

61.7

92.7

42.4

63.8

1 2 3 4 5

112 110 107 102 96.7

168 165 160 154 145

96.4 94.7 92.0 88.3 83.8

145 142 138 133 126

79.7 78.4 76.2 73.3 69.8

120 118 115 110 105

61.4 60.4 58.8 56.7 54.0

92.2 90.8 88.4 85.2 81.2

42.2 41.6 40.5 39.1 37.3

63.4 62.5 60.9 58.7 56.0

6 7 8 9 10

90.4 83.5 76.2 68.7 61.2

136 126 115 103 92.0

78.6 72.9 66.8 60.5 54.2

118 110 100 90.9 81.4

65.6 61.0 56.2 51.1 46.0

98.6 91.7 84.4 76.8 69.1

51.0 47.6 43.9 40.1 36.3

76.6 71.5 66.0 60.3 54.5

35.2 32.9 30.5 27.9 25.3

52.9 49.5 45.8 42.0 38.1

11 12 13 14 15

53.8 46.8 40.1 34.6 30.1

80.9 70.3 60.3 52.0 45.3

47.9 41.9 36.2 31.2 27.2

72.1 63.0 54.4 46.9 40.8

40.9 36.0 31.3 27.0 23.5

61.5 54.1 47.1 40.6 35.4

32.4 28.7 25.1 21.7 18.9

48.7 43.1 37.8 32.7 28.5

22.7 20.2 17.7 15.4 13.4

34.1 30.3 26.7 23.1 20.2

16 17 18 19 20

26.5 23.5 20.9 18.8 16.9

39.8 35.2 31.4 28.2 25.5

23.9 21.2 18.9 16.9 15.3

35.9 31.8 28.4 25.5 23.0

20.7 18.3 16.3 14.7 13.2

31.1 27.5 24.6 22.0 19.9

16.6 14.7 13.2 11.8 10.7

25.0 22.2 19.8 17.7 16.0

11.8 10.4 9.31 8.36 7.54

17.7 15.7 14.0 12.6 11.3

21 22

15.4

23.1

13.9

20.8

12.0 10.9

18.0 16.4

14.5 13.2

6.84 6.23

10.3 9.37

9.66 8.80

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in.

4.09 6.49 1.26

ASD

LRFD

Ωc = 1.67

φc = 0.90

3.52 5.84 1.29

2.91 5.04 1.32

2.24 4.05 1.35

Note: Heavy line indicates KL /ry equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.54 2.90 1.37

AISC_Part 4A:14th Ed.

2/23/11

10:07 AM

Page 65

4–65

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-4 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

HSS3

Square HSS HSS3× 3×

Shape

t design, in. lb/ft

5/16

0.349 12.2

0.291 10.6

Pn /Ωc

Design

Effective length, KL (ft), with respect to least radius of gyration, ry

3/8

φc Pn

Pn /Ωc

1/4 0.233 8.81

φc Pn

Pn /Ωc

3/16 0.174 6.87

φc Pn

Pn /Ωc

φc Pn

1/8 0.116 4.75

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

93.4

140

81.0

122

67.2

101

52.1

78.2

35.8

53.8

1 2 3 4 5

92.6 90.2 86.4 81.3 75.3

139 136 130 122 113

80.3 78.3 75.1 70.9 65.8

121 118 113 107 98.9

66.7 65.1 62.6 59.3 55.2

100 97.9 94.1 89.1 83.0

51.7 50.5 48.7 46.2 43.2

77.7 75.9 73.2 69.4 64.9

35.6 34.8 33.6 32.0 30.0

53.4 52.3 50.5 48.1 45.1

6 7 8 9 10

68.5 61.2 53.8 46.4 39.4

103 92.0 80.8 69.8 59.3

60.1 53.9 47.6 41.3 35.3

90.3 81.0 71.5 62.1 53.0

50.6 45.7 40.6 35.6 30.6

76.1 68.7 61.1 53.4 46.0

39.8 36.1 32.3 28.5 24.7

59.8 54.3 48.6 42.8 37.1

27.8 25.3 22.8 20.2 17.6

41.7 38.1 34.2 30.3 26.5

11 12 13 14 15

32.9 27.6 23.5 20.3 17.7

49.4 41.5 35.4 30.5 26.6

29.6 24.9 21.2 18.3 15.9

44.5 37.4 31.8 27.4 23.9

25.9 21.8 18.6 16.0 13.9

39.0 32.8 27.9 24.1 21.0

21.1 17.8 15.2 13.1 11.4

31.8 26.8 22.8 19.7 17.1

15.2 12.9 11.0 9.48 8.26

22.9 19.4 16.5 14.2 12.4

16 17 18 19

15.5 13.8

23.3 20.7

14.0 12.4 11.0

21.0 18.6 16.6

12.3 10.9 9.69

18.4 16.3 14.6

10.0 8.87 7.91 7.10

15.1 13.3 11.9 10.7

7.26 6.43 5.73 5.15

10.9 9.66 8.62 7.73

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in.

3.39 3.78 1.06

ASD

LRFD

Ωc = 1.67

φc = 0.90

2.94 3.45 1.08

2.44 3.02 1.11

1.89 2.46 1.14

Note: Heavy line indicates KL /ry equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.30 1.78 1.17

AISC_Part 4A:14th Ed.

2/23/11

10:07 AM

Page 66

4–66

DESIGN OF COMPRESSION MEMBERS

Table 4-4 (continued)

Available Strength in Axial Compression, kips HSS21⁄ 2 -HSS21⁄4

Square HSS HSS2 1/2 × 2 1/2 ×

Shape

t design, in. lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, ry

Fy = 46 ksi

HSS2 1/4× 2 1/4×

5/16

1/4

3/16

1/8

0.291 8.45

0.233 7.11

0.174 5.59

0.116 3.90

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

1/4 0.233 6.26

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

64.7

97.3

54.3

81.6

42.4

63.8

29.5

44.3

47.9

72.0

1 2 3 4 5

63.9 61.6 57.8 53.0 47.3

96.1 92.5 86.9 79.6 71.2

53.6 51.8 48.8 45.0 40.4

80.6 77.8 73.4 67.6 60.8

42.0 40.6 38.4 35.6 32.2

63.1 61.0 57.7 53.4 48.4

29.2 28.3 26.8 25.0 22.7

43.8 42.5 40.3 37.5 34.2

47.2 45.2 41.9 37.8 33.0

71.0 67.9 63.0 56.7 49.6

6 7 8 9 10

41.3 35.1 29.1 23.5 19.0

62.0 52.7 43.7 35.2 28.6

35.5 30.5 25.6 20.9 17.0

53.4 45.9 38.5 31.5 25.5

28.5 24.7 20.9 17.4 14.1

42.9 37.1 31.5 26.1 21.2

20.3 17.7 15.1 12.7 10.4

30.5 26.6 22.8 19.1 15.6

28.0 23.1 18.4 14.6 11.8

42.1 34.7 27.7 21.9 17.7

11 12 13 14 15

15.7 13.2 11.2 9.69

23.6 19.8 16.9 14.6

14.0 11.8 10.0 8.65 7.53

21.1 17.7 15.1 13.0 11.3

11.7 9.80 8.35 7.20 6.27

17.5 14.7 12.6 10.8 9.43

16

8.60 7.22 6.15 5.31 4.62

12.9 10.9 9.25 7.98 6.95

4.06

6.11

9.75 8.19 6.98

14.7 12.3 10.5

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in.

2.35 1.82 0.880

1.97 1.63 0.908

1.54 1.35 0.937

1.07 0.998 0.965

Note: Heavy line indicates KL /ry equal to or greater than 200.

ASD

LRFD

Ωc = 1.67

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.74 1.13 0.806

AISC_Part 4A:14th Ed.

2/23/11

10:07 AM

Page 67

4–67

STEEL COMPRESSION—MEMBER SELECTION TABLES

Table 4-4 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi

HSS21⁄4 -HSS2

Square HSS HSS2 1/4 × 2 1/4 ×

Shape

t design, in. lb/ft

Effective length, KL (ft), with respect to least radius of gyration, ry

Design

HSS2× 2×

3/16

1/8

1/4

0.174 4.96

0.116 3.48

0.233 5.41

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

3/16 0.174 4.32

Pn /Ωc

φc Pn

1/8 0.116 3.05

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

37.7

56.7

26.3

39.6

41.6

62.5

32.8

49.3

23.1

34.8

1 2 3 4 5

37.2 35.7 33.3 30.2 26.7

55.9 53.6 50.0 45.4 40.1

26.0 25.0 23.4 21.4 19.0

39.1 37.6 35.2 32.1 28.6

40.8 38.5 34.9 30.4 25.5

61.3 57.8 52.4 45.7 38.3

32.2 30.5 27.9 24.6 20.9

48.4 45.8 41.9 36.9 31.4

22.8 21.6 19.9 17.7 15.2

34.2 32.5 29.9 26.6 22.9

6 7 8 9 10

22.9 19.1 15.5 12.3 9.97

34.4 28.7 23.3 18.5 15.0

16.5 13.9 11.5 9.18 7.43

24.8 20.9 17.2 13.8 11.2

20.6 15.9 12.2 9.64 7.81

30.9 24.0 18.3 14.5 11.7

17.1 13.5 10.4 8.24 6.67

25.7 20.4 15.7 12.4 10.0

12.7 10.2 7.93 6.27 5.08

19.0 15.3 11.9 9.42 7.63

11 12 13 14

8.24 6.92 5.90

12.4 10.4 8.87

6.14 5.16 4.40 3.79

4.20 3.53

6.31 5.30

9.23 7.76 6.61 5.70

6.46

9.70

5.52 4.63

8.29 6.97

Properties 2

Ag , in. Ix = Iy , in.4 rx = ry , in.

1.37 0.953 0.835

0.956 0.712 0.863

1.51 0.747 0.704

1.19 0.641 0.733

Note: Heavy line indicates KL /ry equal to or greater than 200.

ASD

LRFD

Ωc = 1.67

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

0.840 0.486 0.761

AISC_Part 4B:14th Ed.

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Page 68

4–68

DESIGN OF COMPRESSION MEMBERS

Table 4-5

Available Strength in Axial Compression, kips Round HSS

HSS20-HSS16 HSS20×

Shape

t design, in. lb/ft

0.500 0.465 104

HSS18× 0.375 0.349 78.7

Pn /Ωc φc Pn

0.500 0.465 93.5

Pn /Ωc φc Pn Pn /Ωc

HSS16× 0.375 0.349 70.7

0.625 0.581 103

0.500 0.465 82.9

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

717

1080

541

813

644

968

488

733

707

1060

571

858

6 7 8 9 10

712 710 708 706 704

1070 1070 1060 1060 1060

537 536 534 533 531

807 805 803 801 798

639 637 634 632 629

960 957 954 950 946

484 483 481 479 477

727 725 723 720 717

699 697 693 690 686

1050 1050 1040 1040 1030

565 563 560 557 554

849 846 842 838 833

11 12 13 14 15

701 698 695 691 688

1050 1050 1040 1040 1030

529 527 524 522 519

795 792 788 784 780

626 623 619 615 611

941 936 931 925 919

475 472 470 467 464

713 710 706 701 697

682 677 672 667 661

1020 1020 1010 1000 994

551 547 543 539 534

828 823 817 810 803

16 17 18 19 20

684 679 675 670 666

1030 1020 1010 1010 1000

516 513 510 506 503

775 771 766 761 755

607 602 598 593 587

912 905 898 891 883

460 457 453 449 446

692 687 681 676 670

655 649 642 635 628

984 975 965 954 943

530 524 519 514 508

796 788 780 772 763

21 22 23 24 25

661 655 650 644 638

993 985 977 968 960

499 495 491 487 482

750 744 738 731 725

582 576 570 564 558

874 866 857 848 838

441 437 433 428 423

663 657 650 643 636

620 612 604 596 587

932 920 908 895 882

502 495 489 482 475

754 744 735 725 714

26 27 28 29 30

632 626 620 613 607

951 941 932 922 912

478 473 468 464 459

718 711 704 697 689

551 544 538 531 523

828 818 808 797 787

418 413 408 403 398

629 621 614 606 598

578 569 560 551 541

869 856 842 828 813

468 461 454 446 438

704 693 682 670 659

32 34 36 38 40

593 579 564 549 533

891 870 847 824 801

448 438 426 415 403

674 658 641 624 606

509 493 478 462 446

765 742 718 694 670

387 375 363 351 339

581 564 546 528 510

522 502 481 460 440

784 754 723 692 661

423 407 390 374 357

635 611 587 562 537

Design

Effective length, KL (ft), with respect to least radius of gyration, r

Fy = 42 ksi

Properties 2

Ag , in. I , in.4 r , in. ASD Ωc = 1.67

28.5 1360 6.91 LRFD

21.5 1040 6.95

25.6 985 6.20

19.4 754 6.24

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

28.1 838 5.46

22.7 685 5.49

AISC_Part 4B:14th Ed.

2/23/11

10:09 AM

Page 69

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–69

Table 4-5 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi

Round HSS HSS16×

Shape

t design, in. lb/ft

0.438 0.407 72.9

0.375 0.349 62.6

Pn /Ωc φc Pn

HSS14× 0.312 0.291 52.3

Pn /Ωc φc Pn Pn /Ωc

0.250 0.233 42.1

0.625 0.581 89.4

0.500 0.465 72.2

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

500

752

433

650

362

544

289

435

616

926

498

748

6 7 8 9 10

495 493 491 489 486

744 742 738 735 731

428 426 425 423 420

643 641 638 635 632

358 357 356 354 352

539 537 534 532 529

286 285 284 283 281

430 429 427 425 423

608 604 601 597 592

913 908 903 897 891

491 489 486 483 479

738 734 730 725 720

11 12 13 14 15

483 480 476 473 469

726 721 716 710 704

418 415 412 409 405

628 624 619 614 609

350 347 345 342 339

526 522 519 515 510

279 278 276 274 271

420 417 414 411 408

588 582 577 571 564

883 875 867 858 848

475 471 467 462 457

714 708 701 694 686

16 17 18 19 20

465 460 455 451 445

698 691 684 677 669

402 398 394 390 385

604 598 592 586 579

336 333 330 326 323

506 501 496 491 485

269 266 264 261 258

404 400 396 392 388

557 550 543 535 527

838 827 816 804 792

451 445 439 433 427

678 670 661 651 641

21 22 23 24 25

440 435 429 423 417

662 653 645 636 627

381 376 371 366 361

572 565 558 550 543

319 315 311 307 303

480 474 468 461 455

255 252 249 246 242

384 379 374 369 364

518 510 501 492 482

779 766 753 739 725

420 413 406 399 391

631 621 610 599 588

26 27 28 29 30

411 405 398 392 385

618 608 599 589 579

356 350 345 339 333

535 527 518 510 501

298 294 289 284 280

448 442 435 428 420

239 235 231 228 224

359 353 348 342 337

473 463 453 443 433

711 696 681 666 651

384 376 368 360 352

577 565 553 541 529

32 34 36 38 40

371 357 343 329 314

558 537 516 494 472

322 310 297 285 272

484 465 447 428 409

270 260 250 239 229

406 391 375 360 344

216 208 200 192 184

325 313 301 288 276

412 392 371 350 329

620 589 557 526 495

336 319 302 285 269

504 479 454 429 404

Design

Effective length, KL (ft), with respect to least radius of gyration, r

HSS16-HSS14

Properties 2

Ag , in. I , in.4 r , in. ASD Ωc = 1.67

19.9 606 5.51 LRFD

17.2 526 5.53

14.4 443 5.55

11.5 359 5.58

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

24.5 552 4.75

19.8 453 4.79

AISC_Part 4B:14th Ed.

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Page 70

4–70

DESIGN OF COMPRESSION MEMBERS

Table 4-5 (continued)

Available Strength in Axial Compression, kips HSS14HSS12.750 Shape

t design, in. lb/ft

Round HSS HSS14× 0.312 0.291 45.7

0.375 0.349 54.6

Pn /Ωc φc Pn

0.250 0.233 36.8

Pn /Ωc φc Pn Pn /Ωc

0.500 0.465 65.5

HSS12.750× 0.375 0.349 49.6

0.250 0.233 33.4

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

377

567

314

472

254

382

450

677

342

514

230

346

6 7 8 9 10

372 370 368 366 363

559 557 553 550 546

310 309 307 305 303

466 464 461 458 455

251 249 248 246 245

377 375 373 370 368

443 440 437 433 430

665 661 657 651 646

336 334 332 330 327

506 503 499 495 491

227 225 224 222 220

341 339 336 334 331

11 12 13 14 15

360 357 354 350 346

542 537 532 526 521

300 298 295 292 289

451 448 443 439 434

243 241 238 236 234

365 362 358 355 351

425 421 416 411 405

639 633 625 617 609

324 320 317 313 308

486 481 476 470 464

218 216 213 211 208

328 324 321 317 313

16 17 18 19 20

342 338 334 329 324

515 508 501 494 487

286 282 278 274 270

429 424 418 413 407

231 228 225 222 219

347 343 338 334 329

399 393 387 380 373

600 591 582 572 561

304 300 295 290 285

457 450 443 436 428

205 202 199 196 192

309 304 299 294 289

21 22 23 24 25

319 314 309 303 298

480 472 464 456 447

266 262 258 253 249

400 394 387 380 374

215 212 209 205 201

324 319 313 308 302

366 359 352 344 336

551 540 528 517 505

279 274 268 263 257

420 412 403 395 386

189 185 182 178 174

284 278 273 267 261

26 27 28 29 30

292 286 280 274 268

439 430 421 412 403

244 239 234 229 224

366 359 352 344 337

197 194 190 186 182

297 291 285 279 273

328 320 312 304 296

493 481 469 457 444

251 245 239 233 226

377 368 359 349 340

170 166 162 158 154

255 249 243 237 231

32 34 36 38 40

256 243 231 218 206

385 366 347 328 309

214 204 193 183 172

322 306 290 275 259

173 165 157 148 140

261 248 235 223 210

279 262 246 229 213

419 394 369 345 320

214 201 189 176 164

321 302 284 265 247

145 137 128 120 112

218 206 193 181 168

Design

Effective length, KL (ft), with respect to least radius of gyration, r

Fy = 42 ksi

Properties 2

Ag , in. I , in.4 r , in. ASD Ωc = 1.67

15.0 349 4.83 LRFD

12.5 295 4.85

10.1 239 4.87

17.9 339 4.35

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

13.6 262 4.39

9.16 180 4.43

AISC_Part 4B:14th Ed.

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10:09 AM

Page 71

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–71

Table 4-5 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi

HSS10.750HSS10

Round HSS Shape

t design, in. lb/ft

HSS10.750× 0.375 0.349 41.6

0.500 0.465 54.8

Pn /Ωc φc Pn

Effective length, KL (ft), with respect to least radius of gyration, r

Design

0.250 0.233 28.1

Pn /Ωc φc Pn Pn /Ωc

0.625 0.581 62.6

HSS10× 0.500 0.465 50.8

0.375 0.349 38.6

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

194

291

433

650

350

189 188 186 184 182

284 282 279 276 273

420 416 411 406 400

632 625 618 610 601

340 337 333 328 324

398 392 386 379 372

179 177 174 171 168

269 265 261 257 252

393 386 378 370 362

591 580 569 557 544

243 237 232 226 221

365 357 349 340 332

164 161 157 154 150

247 242 237 231 225

353 344 335 325 315

422 410 398 386 374

215 209 203 197 191

323 314 305 296 287

146 142 138 134 130

220 214 208 201 195

240 232 224 215 207

361 349 336 323 311

184 178 172 166 159

277 268 258 249 239

126 122 117 113 109

190 174 159 144 130

286 262 239 216 195

147 135 123 112 101

221 203 185 168 151

101 92.5 84.6 77.0 69.5

ASD

LRFD

ASD

LRFD

0

377

567

287

431

6 7 8 9 10

368 365 361 357 353

554 549 543 537 530

280 278 275 272 269

421 417 413 409 404

11 12 13 14 15

348 343 337 331 325

523 515 507 497 488

265 261 257 252 248

16 17 18 19 20

318 311 304 296 289

478 468 457 446 434

21 22 23 24 25

281 273 265 257 249

26 27 28 29 30 32 34 36 38 40

ASD

ASD

LRFD

525

267

401

511 506 500 493 486

259 257 254 251 247

390 386 382 377 371

318 313 307 300 294

478 470 461 451 441

243 239 234 230 225

365 359 352 345 338

531 517 503 488 473

287 280 272 264 256

431 420 409 397 385

219 214 208 203 197

330 322 313 304 296

305 295 284 274 264

458 443 427 412 396

248 240 232 224 215

373 361 349 336 324

191 184 178 172 166

287 277 268 259 249

189 183 176 170 164

253 243 232 222 212

380 365 349 334 319

207 199 191 182 174

311 299 286 274 262

159 153 147 141 134

240 230 221 211 202

151 139 127 116 104

192 173 155 139 125

289 260 232 208 188

158 143 128 115 104

238 215 192 173 156

122 111 99.3 89.1 80.4

184 166 149 134 121

Properties 2

Ag , in. I , in.4 r , in. ASD Ωc = 1.67

15.0 199 3.64 LRFD

11.4 154 3.68

7.70 106 3.72

17.2 191 3.34

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

13.9 159 3.38

10.6 123 3.41

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Page 72

4–72

DESIGN OF COMPRESSION MEMBERS

Table 4-5 (continued)

Available Strength in Axial Compression, kips HSS10HSS9.625

Round HSS

Shape

HSS10× 0.250 0.233 26.1

0.312 0.291 32.3

t design, in. lb/ft

Pn /Ωc φc Pn

0.188 0.174 19.7

Pn /Ωc φc Pn Pn /Ωc

0.500 0.465 48.8

HSS9.625× 0.375 0.349 37.1

0.312 0.291 31.1

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

0

223

336

180

270

135

203

337

507

257

6 7 8 9 10

217 215 213 210 207

327 324 320 316 311

175 173 171 169 167

263 261 258 254 251

132 130 129 127 125

198 196 194 191 189

327 323 319 315 310

491 486 480 473 466

249 246 243 240 236

11 12 13 14 15

204 200 197 193 189

306 301 296 290 283

164 162 159 155 152

247 243 238 234 229

124 121 119 117 114

186 183 179 176 172

304 299 292 286 279

457 449 439 429 419

16 17 18 19 20

184 180 175 170 165

277 270 263 256 248

149 145 141 138 134

223 218 212 207 201

112 109 106 104 101

168 164 160 156 151

272 264 257 249 241

21 22 23 24 25

160 155 150 145 140

241 233 226 218 210

130 126 121 117 113

195 189 182 176 170

97.7 94.6 91.6 88.5 85.3

147 142 138 133 128

26 27 28 29 30

134 129 124 119 114

202 194 186 178 171

109 105 100 96.3 92.1

164 157 151 145 138

82.2 79.1 75.9 72.8 69.7

124 119 114 109 105

32 34 36 38 40

103 93.7 84.1 75.5 68.2

155 141 126 114 102

Design

Effective length, KL (ft), with respect to least radius of gyration, r

Fy = 42 ksi

84.0 126 76.2 114 68.5 103 61.5 92.5 55.5 83.4

63.7 57.8 52.1 46.7 42.2

95.7 86.8 78.3 70.2 63.4

LRFD

ASD

LRFD

386

215

322

374 370 366 361 355

208 206 204 201 198

313 310 306 302 297

232 228 223 218 213

349 343 336 328 320

194 191 187 183 179

292 287 281 275 269

408 397 386 374 362

208 202 197 191 185

312 304 295 287 278

174 170 165 160 155

262 255 248 240 233

232 224 216 207 199

349 337 324 312 299

179 172 166 160 153

268 259 250 240 231

150 145 140 134 129

225 218 210 202 194

191 182 174 166 158

287 274 262 249 237

147 141 135 128 122

221 212 202 193 184

124 119 113 108 103

186 178 171 163 155

142 127 113 102 91.8

214 191 170 153 138

111 99.1 88.4 79.3 71.6

166 149 133 119 108

93.4 83.9 74.8 67.1 60.6

140 126 112 101 91.1

Properties 2

Ag , in. I , in.4 r , in. ASD Ωc = 1.67

8.88 105 3.43 LRFD

7.15 85.3 3.45

5.37 64.8 3.47

13.4 141 3.24

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

10.2 110 3.28

8.53 93.0 3.30

AISC_Part 4B:14th Ed.

2/23/11

10:09 AM

Page 73

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–73

Table 4-5 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi

Round HSS HSS9.625× 0.250 0.188 0.233 0.174 25.1 19.0

Shape

t design, in. lb/ft

Pn /Ωc φc Pn

Effective length, KL (ft), with respect to least radius of gyration, r

Design

HSS8.625× 0.500 0.375 0.465 0.349 43.4 33.1

0.625 0.581 53.5

Pn /Ωc φc Pn Pn /Ωc

0.322 0.300 28.6

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

370

556

299

450

228

343

197

297

355 350 345 338 332

534 527 518 509 498

288 284 280 275 269

433 427 420 413 405

220 217 214 210 206

330 326 321 315 309

190 188 185 182 178

286 282 278 273 268

178 174 171 167 163

324 316 308 299 289

487 475 462 449 435

263 257 250 243 236

396 386 376 366 354

201 197 192 186 181

303 296 288 280 272

175 171 166 162 157

262 256 250 243 236

106 103 101 97.7 94.7

160 155 151 147 142

280 270 260 250 239

420 406 390 375 359

228 220 212 204 196

343 331 319 307 294

175 169 163 157 151

263 255 246 236 227

152 147 142 137 131

229 221 213 206 198

182 176 170 164 157

91.7 88.6 85.5 82.4 79.2

138 133 128 124 119

229 218 208 197 187

344 328 312 297 281

188 179 171 163 154

282 269 257 244 232

145 139 132 126 120

218 208 199 189 180

126 121 115 110 105

190 181 173 165 157

151 145 138 132 126

76.1 72.9 69.8 66.8 63.7

114 110 105 100 95.7

177 167 157 148 138

266 251 237 222 208

146 138 130 123 115

220 208 196 185 173

114 108 102 95.9 90.3

171 162 153 144 136

183 162 145 130 117

101 89.7 80.0 71.8 64.8

152 135 120 108 97.5

ASD

LRFD

ASD

LRFD

ASD

0

173

260

130

195

6 7 8 9 10

168 166 164 162 159

252 250 247 243 240

126 125 124 122 120

190 188 186 183 181

11 12 13 14 15

157 154 151 148 144

236 231 227 222 217

118 116 114 111 109

16 17 18 19 20

141 137 133 129 125

211 206 200 194 188

21 22 23 24 25

121 117 113 109 105

26 27 28 29 30

100 96.3 92.1 88.0 83.9

32 34 36 38 40

HSS9.625HSS8.625

76.0 114 68.3 103 61.0 91.7 54.7 82.3 49.4 74.2

57.7 52.0 46.5 41.7 37.6

86.8 122 78.2 108 69.8 96.2 62.7 86.3 56.6 77.9

Pn /Ωc φc Pn ASD

99.3 94.1 89.0 84.0 79.1

LRFD

149 141 134 126 119

79.4 119 70.3 106 62.7 94.3 56.3 84.6 50.8 76.3

69.6 105 61.7 92.7 55.0 82.7 49.4 74.2 44.6 67.0

9.07 77.8 2.93

7.85 68.1 2.95

Properties 2

Ag , in. I , in.4 r , in. ASD Ωc = 1.67

6.87 75.9 3.32 LRFD

5.17 57.7 3.34

14.7 119 2.85

11.9 100 2.89

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 4B:14th Ed.

2/23/11

10:09 AM

Page 74

4–74

DESIGN OF COMPRESSION MEMBERS

Table 4-5 (continued)

Available Strength in Axial Compression, kips HSS8.625HSS7.500

Round HSS HSS8.625× 0.250 0.188 0.233 0.174 22.4 17.0

Shape

t design, in. lb/ft

Pn /Ωc φc Pn

HSS7.625× 0.375 0.328 0.349 0.305 29.1 25.6

Pn /Ωc φc Pn Pn /Ωc

HSS7.500× 0.500 0.375 0.465 0.349 37.4 28.6

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

154

232

116

175

201

302

176

265

259

389

197

296

6 7 8 9 10

149 147 145 142 140

224 221 218 214 210

112 111 109 107 105

169 166 164 161 158

191 188 184 180 176

288 283 277 271 264

168 165 162 158 155

253 248 244 238 232

246 242 236 231 225

370 363 355 347 338

188 184 180 176 172

282 277 271 265 258

11 12 13 14 15

137 134 130 127 123

206 201 196 191 185

103 101 98.3 95.7 93.0

155 151 148 144 140

171 166 160 155 149

257 249 241 232 224

150 146 141 136 131

226 219 212 205 197

218 211 204 196 188

328 317 306 294 282

167 162 156 150 144

251 243 235 226 217

16 17 18 19 20

119 116 112 108 103

180 174 168 162 155

90.2 87.3 84.3 81.3 78.2

136 131 127 122 118

143 137 130 124 118

215 205 196 187 177

126 120 115 110 104

189 181 173 165 156

180 172 163 155 146

270 258 245 233 220

138 132 126 120 113

208 199 189 180 171

149 143 137 130 124

75.1 113 112 72.0 108 105 68.8 103 99.4 65.7 98.8 93.4 62.6 94.1 87.5

148 140 132 124 116

138 130 122 114 106

208 195 183 171 160

107 101 94.9 89.0 83.1

161 152 143 134 125

Design

Effective length, KL (ft), with respect to least radius of gyration, r

Fy = 42 ksi

21 22 23 24 25

99.2 95.0 90.9 86.7 82.5

26 27 28 29 30

78.4 118 74.3 112 70.4 106 66.4 99.9 62.6 94.1

59.5 56.5 53.5 50.6 47.7

89.5 84.9 80.4 76.0 71.7

81.7 123 76.1 114 70.7 106 65.9 99.1 61.6 92.6

72.3 109 67.3 101 62.6 94.1 58.4 87.7 54.5 82.0

98.6 91.4 85.0 79.3 74.1

32 34 36 38 40

55.2 48.9 43.6 39.2 35.3

42.1 37.3 33.3 29.9 26.9

63.3 56.1 50.0 44.9 40.5

54.1 48.0 42.8 38.4 34.7

47.9 42.5 37.9 34.0 30.7

65.1 57.7 51.4 46.2 41.7

83.0 73.5 65.6 58.8 53.1

168 159 149 140 131

81.4 72.1 64.3 57.7 52.1

98.6 93.1 87.8 82.5 77.3

72.0 63.8 56.9 51.1 46.1

148 137 128 119 111 97.8 86.7 77.3 69.4 62.6

Pn /Ωc φc Pn ASD

LRFD

77.5 116 71.9 108 66.8 100 62.3 93.6 58.2 87.5 51.2 45.3 40.4 36.3 32.7

76.9 68.1 60.7 54.5 49.2

Properties 2

Ag , in. I , in.4 r , in. ASD Ωc = 1.67

6.14 54.1 2.97 LRFD

4.62 41.3 2.99

7.98 52.9 2.58

7.01 47.1 2.59

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

10.3 63.9 2.49

7.84 50.2 2.53

AISC_Part 4B:14th Ed.

2/23/11

10:10 AM

Page 75

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–75

Table 4-5 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi

Round HSS Shape

HSS7.500× 0.250 0.233 19.4

0.312 0.291 24.0

t design, in. lb/ft

Pn /Ωc φc Pn

0.188 0.174 14.7

Pn /Ωc φc Pn Pn /Ωc

0.500 0.465 34.7

HSS7× 0.375 0.349 26.6

0.312 0.291 22.3

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

166

249

134

201

101

151

240

361

183

276

154

232

6 7 8 9 10

158 155 152 148 145

237 233 228 223 217

127 125 123 120 117

192 188 185 180 176

95.9 94.3 92.5 90.4 88.2

144 142 139 136 133

226 222 216 210 204

340 333 325 316 306

173 170 165 161 156

260 255 249 242 235

146 143 139 136 132

219 215 210 204 198

11 12 13 14 15

141 136 132 127 122

211 205 198 191 183

114 110 107 103 99.0

171 166 160 155 149

85.8 83.2 80.5 77.7 74.8

129 125 121 117 112

197 190 182 174 166

296 285 273 262 249

151 146 140 134 128

227 219 210 201 192

127 123 118 113 108

192 185 178 170 163

16 17 18 19 20

117 112 107 101 96.2

176 168 160 152 145

95.0 90.9 86.7 82.5 78.3

143 137 130 124 118

71.8 108 68.7 103 65.6 98.6 62.5 93.9 59.4 89.2

158 149 141 133 124

237 225 212 199 187

122 115 109 103 96.6

183 173 164 155 145

103 97.8 92.6 87.3 82.1

155 147 139 131 123

21 22 23 24 25

91.0 85.8 80.7 75.7 70.8

137 129 121 114 106

74.1 111 70.0 105 65.9 99.0 61.9 93.0 57.9 87.1

56.2 53.1 50.1 47.1 44.1

84.5 116 79.9 108 75.3 101 70.8 93.1 66.3 85.8

175 163 151 140 129

90.5 84.5 78.6 72.9 67.2

136 127 118 110 101

26 27 28 29 30

66.1 61.4 57.1 53.2 49.7

99.3 92.2 85.7 79.9 74.7

54.1 50.3 46.8 43.6 40.8

81.3 75.6 70.3 65.5 61.3

41.3 38.4 35.7 33.3 31.1

62.0 57.7 53.7 50.1 46.8

79.4 119 73.6 111 68.4 103 63.8 95.9 59.6 89.6

62.2 57.6 53.6 50.0 46.7

93.4 86.6 80.6 75.1 70.2

53.2 49.3 45.8 42.7 39.9

79.9 74.1 68.9 64.2 60.0

32 34 36 38 40

43.7 38.7 34.5 31.0 28.0

65.7 58.2 51.9 46.6 42.0

35.8 31.7 28.3 25.4 22.9

53.8 47.7 42.5 38.2 34.5

27.4 24.2 21.6 19.4 17.5

41.1 36.4 32.5 29.2 26.3

52.4 46.4 41.4 37.2

41.0 36.4 32.4 29.1

61.7 54.6 48.7 43.7

35.1 31.1 27.7 24.9

52.8 46.7 41.7 37.4

Design

Effective length, KL (ft), with respect to least radius of gyration, r

HSS7.500HSS7

78.8 69.8 62.2 55.8

ASD

LRFD

77.0 116 71.9 108 67.0 101 62.2 93.6 57.5 86.4

Properties 2

Ag , in. I , in.4 r , in. ASD Ωc = 1.67

6.59 42.9 2.55 LRFD

5.32 35.2 2.57

4.00 26.9 2.59

9.55 51.2 2.32

Note: Heavy line indicates KL/r equal to or greater than 200.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7.29 40.4 2.35

6.13 34.6 2.37

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4–76

DESIGN OF COMPRESSION MEMBERS

Table 4-5 (continued)

Available Strength in Axial Compression, kips Round HSS

HSS7– HSS6.875 Shape

HSS7× 0.188 0.174 13.7

0.250 0.233 18.0

t design, in. lb/ft

Pn /Ωc φc Pn

0.125 0.116 9.19

Pn /Ωc φc Pn Pn /Ωc

0.500 0.465 34.1

HSS6.875× 0.375 0.349 26.1

0.312 0.291 21.9

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

124

187

93.8

141

63.1

94.9

235

354

180

271

151

228

6 7 8 9 10

118 115 113 110 107

177 173 169 165 160

88.8 87.1 85.1 82.9 80.6

133 131 128 125 121

59.8 58.7 57.4 55.9 54.3

89.9 88.2 86.2 84.0 81.7

221 216 211 205 198

333 325 317 308 298

170 166 162 157 153

255 250 243 237 229

143 140 136 133 129

215 210 205 199 193

11 12 13 14 15

103 99.6 95.8 91.9 87.9

155 150 144 138 132

78.0 75.3 72.5 69.6 66.6

117 113 109 105 100

52.7 50.9 49.0 47.1 45.1

79.2 76.5 73.7 70.7 67.7

191 184 176 168 160

287 276 265 253 240

147 142 136 130 124

221 212 205 196 186

124 120 115 110 105

187 180 173 165 158

16 17 18 19 20

83.8 79.6 75.4 71.2 67.0

126 120 113 107 101

63.5 60.4 57.3 54.1 51.0

95.5 90.8 86.1 81.4 76.7

43.0 40.9 38.9 36.8 34.7

64.7 61.5 58.4 55.3 52.1

152 143 135 127 118

228 215 203 190 178

118 112 105 99.0 92.8

177 168 158 149 139

99.8 94.5 89.3 84.1 78.9

21 22 23 24 25

62.9 58.8 54.9 51.0 47.2

94.5 88.4 82.5 76.7 71.0

47.9 44.9 41.9 39.0 36.2

72.0 67.5 63.0 58.7 54.4

32.6 30.6 28.6 26.6 24.8

49.0 46.0 43.0 40.0 37.2

110 103 94.9 87.4 80.6

166 154 143 131 121

86.7 80.7 74.9 69.2 63.8

130 121 113 104 95.9

73.8 111 68.8 103 64.0 96.1 59.2 89.0 54.6 82.0

26 27 28 29 30

43.7 40.5 37.6 35.1 32.8

65.6 60.8 56.6 52.7 49.3

33.5 31.0 28.8 26.9 25.1

50.3 46.6 43.4 40.4 37.8

22.9 21.2 19.7 18.4 17.2

34.4 31.9 29.7 27.6 25.8

74.5 112 69.1 104 64.2 96.5 59.9 90.0 55.9 84.1

59.0 54.7 50.9 47.4 44.3

88.7 82.2 76.5 71.3 66.6

50.5 46.8 43.5 40.6 37.9

75.8 70.3 65.4 61.0 57.0

32 34 36 38 40

28.8 25.5 22.8 20.4

43.3 38.4 34.2 30.7

22.1 19.6 17.4 15.7 14.1

33.2 29.4 26.2 23.5 21.2

15.1 13.4 11.9 10.7 9.67

22.7 20.1 17.9 16.1 14.5

49.2 43.5 38.8

38.9 34.5 30.8 27.6

58.5 51.9 46.2 41.5

33.3 29.5 26.3 23.6

50.1 44.4 39.6 35.5

Design

Effective length, KL (ft), with respect to least radius of gyration, r

Fy = 42 ksi

73.9 65.5 58.4

ASD

LRFD

150 142 134 126 119

Properties 2

Ag , in. I , in.4 r , in. ASD Ωc = 1.67

4.95 28.4 2.39 LRFD

3.73 21.7 2.41

2.51 14.9 2.43

9.36 48.3 2.27

Note: Heavy line indicates KL/r equal to or greater than 200.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7.16 38.2 2.31

6.02 32.7 2.33

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–77

Table 4-5 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi

HSS6.875HSS6.625

Round HSS HSS6.875×

Shape

0.250 0.233 17.7

t design, in. lb/ft

Pn /Ωc

Effective length, KL (ft), with respect to least radius of gyration, r

Design

0.188 0.174 13.4

φc Pn

Pn /Ωc

HSS6.625× 0.432 0.402 28.6

0.500 0.465 32.7

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0.375 0.349 25.1

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

122

184

92.0

138

226

340

198

297

173

260

6 7 8 9 10

115 113 110 107 104

173 170 166 161 157

87.0 85.2 83.2 81.0 78.6

131 128 125 122 118

212 207 201 195 188

318 311 302 293 282

185 181 176 170 165

278 272 264 256 247

162 158 154 150 145

244 238 232 225 217

11 12 13 14 15

101 97.1 93.2 89.3 85.2

151 146 140 134 128

76.1 73.4 70.5 67.6 64.6

114 110 106 102 97.1

181 173 165 157 149

272 260 248 236 224

158 152 145 138 131

238 228 218 208 197

139 134 128 122 116

209 201 192 183 174

16 17 18 19 20

81.1 76.9 72.7 68.6 64.4

122 116 109 103 96.8

61.5 58.4 55.3 52.1 49.0

92.5 87.8 83.1 78.4 73.7

141 132 124 116 108

211 199 186 174 162

124 117 109 102 95.2

186 175 164 154 143

109 103 96.7 90.5 84.4

164 155 145 136 127

21 22 23 24 25

60.3 56.3 52.4 48.6 44.8

90.7 84.6 78.7 73.0 67.4

46.0 43.0 40.0 37.2 34.3

69.1 64.6 60.1 55.9 51.6

99.6 92.0 84.4 77.5 71.4

150 138 127 116 107

88.3 81.6 75.1 68.9 63.5

133 123 113 104 95.5

78.4 72.6 66.9 61.4 56.6

118 109 101 92.4 85.1

26 27 28 29 30

41.4 38.4 35.7 33.3 31.1

62.3 57.8 53.7 50.1 46.8

31.7 29.4 27.4 25.5 23.8

47.7 44.2 41.1 38.3 35.8

66.0 61.2 56.9 53.1 49.6

99.3 92.0 85.6 79.8 74.6

58.7 54.5 50.6 47.2 44.1

88.3 81.9 76.1 71.0 66.3

52.4 48.5 45.1 42.1 39.3

78.7 73.0 67.9 63.3 59.1

32 34 36 38

27.4 24.2 21.6 19.4

41.1 36.4 32.5 29.2

21.0 18.6 16.6 14.9

31.5 27.9 24.9 22.3

43.6 38.6 34.4

65.5 58.0 51.8

38.8 34.4 30.6

58.3 51.6 46.1

34.6 30.6 27.3

51.9 46.0 41.0

Properties 2

Ag , in. I , in.4 r , in.

ASD

4.86 26.8 2.35 LRFD

3.66 20.6 2.37

Ωc = 1.67

φc = 0.90

9.00 42.9 2.18

7.86 38.2 2.20

Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

6.88 34.0 2.22

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Page 78

4–78

DESIGN OF COMPRESSION MEMBERS

Table 4-5 (continued)

Available Strength in Axial Compression, kips Round HSS

HSS6.625

Shape

0.312 0.291 21.1

t design, in. lb/ft

Effective length, KL (ft), with respect to least radius of gyration, r

Design

Fy = 42 ksi

HSS6.625× 0.250 0.233 17.0

0.280 0.260 19.0

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

0.188 0.174 12.9

φc Pn

Pn /Ωc

0.125 0.116 8.69

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

146

219

131

197

118

177

88.8

133

59.6

89.6

6 7 8 9 10

137 134 130 126 122

205 201 196 190 183

123 120 117 114 110

185 180 176 171 165

111 108 105 102 99.0

166 163 158 154 149

83.5 81.7 79.6 77.3 74.9

126 123 120 116 113

56.1 54.9 53.6 52.1 50.4

84.4 82.5 80.5 78.2 75.8

11 12 13 14 15

118 113 108 103 97.9

177 170 162 155 147

106 102 97.3 92.9 88.3

159 153 146 140 133

95.5 91.7 87.8 83.8 79.7

143 138 132 126 120

72.3 69.5 66.6 63.6 60.5

109 104 100 95.6 91.0

48.7 46.9 44.9 43.0 40.9

73.2 70.4 67.5 64.6 61.5

16 17 18 19 20

92.7 87.5 82.3 77.1 71.9

139 132 124 116 108

83.6 78.9 74.3 69.6 65.0

126 119 112 105 97.7

75.6 71.4 67.2 63.0 58.9

114 107 101 94.7 88.5

57.4 54.3 51.2 48.0 45.0

86.3 81.6 76.9 72.2 67.6

38.9 36.8 34.7 32.6 30.5

58.4 55.3 52.1 49.0 45.9

21 22 23 24 25

66.9 62.0 57.3 52.6 48.5

101 93.3 86.1 79.1 72.9

60.5 56.1 51.9 47.7 44.0

91.0 84.4 78.0 71.7 66.1

54.8 50.9 47.1 43.3 39.9

82.4 76.5 70.8 65.1 60.0

41.9 39.0 36.1 33.3 30.6

63.0 58.6 54.2 50.0 46.1

28.5 26.5 24.6 22.7 20.9

42.9 39.9 37.0 34.1 31.5

26 27 28 29 30

44.9 41.6 38.7 36.1 33.7

67.4 62.5 58.1 54.2 50.6

40.6 37.7 35.0 32.7 30.5

61.1 56.7 52.7 49.1 45.9

36.9 34.2 31.8 29.7 27.7

55.5 51.4 47.8 44.6 41.7

28.3 26.3 24.4 22.8 21.3

42.6 39.5 36.7 34.2 32.0

19.4 18.0 16.7 15.6 14.5

29.1 27.0 25.1 23.4 21.9

32 34 36 38

29.6 26.2 23.4

44.5 39.4 35.2

26.8 23.8 21.2

40.3 35.7 31.9

24.4 21.6 19.3

36.6 32.4 28.9

18.7 16.6 14.8 13.3

28.1 24.9 22.2 19.9

12.8 11.3 10.1 9.06

19.2 17.0 15.2 13.6

Properties 2

Ag , in. I , in.4 r , in.

ASD

5.79 29.1 2.24 LRFD

5.20 26.4 2.25

Ωc = 1.67

φc = 0.90

4.68 23.9 2.26

3.53 18.4 2.28

Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.37 12.6 2.30

AISC_Part 4B:14th Ed.

2/23/11

10:10 AM

Page 79

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–79

Table 4-5 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi

Round HSS HSS6×

Shape

0.500 0.465 29.4

t design, in. lb/ft

0.375 0.349 22.6

Pn /Ωc φc Pn

0.312 0.291 19.0

Pn /Ωc φc Pn Pn /Ωc

0.280 0.260 17.1

0.250 0.233 15.4

0.188 0.174 11.7

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

203

306

156

234

131

197

118

177

106

160

80.0

120

1 2 3 4 5

203 202 199 196 192

305 303 300 295 289

156 155 153 151 148

234 232 230 226 222

131 130 129 127 124

197 196 194 191 187

118 117 116 114 112

177 176 174 171 168

106 105 104 103 101

159 158 156 154 151

79.8 79.3 78.5 77.4 75.9

120 119 118 116 114

6 7 8 9 10

187 182 176 169 162

281 273 264 254 243

144 140 135 130 125

216 210 203 196 188

121 118 114 110 106

183 177 172 166 159

109 106 103 99.1 95.2

164 160 155 149 143

98.3 95.6 92.6 89.3 85.8

148 144 139 134 129

74.2 72.2 70.0 67.6 64.9

112 109 105 102 97.6

11 12 13 14 15

154 146 138 130 121

231 220 207 195 182

119 113 107 101 94.8

179 170 161 152 143

101 96.1 91.0 85.8 80.6

152 144 137 129 121

91.0 86.6 82.1 77.4 72.8

137 130 123 116 109

82.1 78.2 74.1 70.0 65.8

123 117 111 105 98.9

62.1 59.2 56.2 53.2 50.0

93.4 89.0 84.5 79.9 75.2

16 17 18 19 20

113 105 96.5 88.6 81.0

170 157 145 133 122

88.5 82.3 76.2 70.2 64.4

133 124 114 105 96.8

Design

Effective length, KL (ft), with respect to least radius of gyration, r

HSS6

75.4 113 70.2 105 65.0 97.8 60.0 90.2 55.2 82.9

68.1 102 63.4 95.3 58.8 88.4 54.4 81.7 50.0 75.1

61.6 57.4 53.3 49.3 45.4

92.6 86.3 80.1 74.1 68.2

46.9 43.8 40.7 37.7 34.7

70.5 65.8 61.2 56.6 52.2

21 22 23 24 25

73.6 111 67.0 101 61.3 92.2 56.3 84.6 51.9 78.0

58.7 53.5 48.9 44.9 41.4

88.2 80.4 73.5 67.5 62.3

50.4 45.9 42.0 38.6 35.6

75.8 69.0 63.2 58.0 53.5

45.7 41.7 38.1 35.0 32.3

68.8 62.6 57.3 52.6 48.5

41.6 37.9 34.7 31.8 29.3

62.5 56.9 52.1 47.8 44.1

31.9 29.1 26.6 24.5 22.5

47.9 43.7 40.0 36.8 33.9

26 28 30 32 34

48.0 41.4 36.0 31.7

38.3 33.0 28.8 25.3

57.6 49.6 43.2 38.0

32.9 28.4 24.7 21.7

49.4 42.6 37.1 32.6

29.8 25.7 22.4 19.7

44.9 38.7 33.7 29.6

27.1 23.4 20.4 17.9 15.9

40.8 35.1 30.6 26.9 23.8

20.8 18.0 15.7 13.8 12.2

31.3 27.0 23.5 20.7 18.3

72.1 62.2 54.2 47.6

Properties 2

Ag , in. I , in.4 r , in. ASD Ωc = 1.67

8.09 31.2 1.96 LRFD

6.20 24.8 2.00

5.22 21.3 2.02

4.69 19.3 2.03

Note: Heavy line indicates KL/r equal to or greater than 200.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.22 17.6 2.04

3.18 13.5 2.06

AISC_Part 4B:14th Ed.

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10:10 AM

Page 80

4–80

DESIGN OF COMPRESSION MEMBERS

Table 4-5 (continued)

Available Strength in Axial Compression, kips HSS6HSS5.563 Shape

t design, in. lb/ft

Round HSS HSS6× 0.125 0.116 7.85

0.500 0.465 27.1

Pn /Ωc φc Pn

0.375 0.349 20.8

Pn /Ωc φc Pn Pn /Ωc

HSS5.563× 0.258 0.240 14.6

0.188 0.174 10.8

0.134 0.124 7.78

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

53.8

80.9

187

282

144

216

101

152

74.2

112

53.3

80.1

1 2 3 4 5

53.7 53.4 52.8 52.1 51.1

80.7 80.2 79.4 78.3 76.9

187 185 183 179 175

281 279 275 270 263

143 142 141 138 135

216 214 211 207 203

101 99.8 98.6 96.9 94.7

151 150 148 146 142

74.0 73.5 72.6 71.4 69.8

111 110 109 107 105

53.2 52.8 52.2 51.3 50.2

79.9 79.4 78.4 77.1 75.5

6 7 8 9 10

50.0 48.7 47.2 45.6 43.9

75.2 73.2 71.0 68.5 65.9

170 164 158 151 143

256 247 237 226 215

131 127 122 117 111

197 191 183 175 167

92.2 89.2 85.9 82.3 78.5

139 134 129 124 118

68.0 65.9 63.5 61.0 58.2

102 99.0 95.5 91.6 87.5

48.9 47.4 45.7 43.9 41.9

73.5 71.2 68.7 66.0 63.0

11 12 13 14 15

42.0 40.1 38.1 36.1 34.0

63.2 60.3 57.3 54.2 51.1

135 127 119 110 102

203 191 178 166 153

105 99.2 93.0 86.7 80.4

158 149 140 130 121

74.5 112 70.3 106 66.1 99.3 61.8 92.8 57.4 86.3

55.3 52.3 49.3 46.1 43.0

83.2 78.7 74.0 69.3 64.6

39.9 37.7 35.5 33.3 31.1

59.9 56.7 53.4 50.1 46.7

16 17 18 19 20

31.9 29.8 27.8 25.7 23.8

47.9 44.8 41.7 38.7 35.7

93.9 85.9 78.1 70.6 63.7

141 129 117 106 95.7

74.2 112 68.2 102 62.3 93.6 56.6 85.1 51.1 76.8

53.1 48.9 44.8 40.9 37.0

79.9 73.5 67.4 61.4 55.6

39.9 36.8 33.8 30.9 28.1

59.9 55.3 50.8 46.5 42.2

28.8 26.7 24.5 22.4 20.4

43.4 40.1 36.8 33.7 30.7

21 22 23 24 25

21.8 20.0 18.3 16.8 15.5

32.8 30.0 27.5 25.2 23.2

57.8 52.6 48.2 44.2 40.8

86.8 79.1 72.4 66.5 61.3

46.3 42.2 38.6 35.5 32.7

69.6 63.5 58.1 53.3 49.1

33.5 30.6 28.0 25.7 23.7

50.4 45.9 42.0 38.6 35.6

25.5 23.2 21.2 19.5 18.0

38.3 34.9 31.9 29.3 27.0

18.5 16.9 15.4 14.2 13.1

27.8 25.3 23.2 21.3 19.6

26 28 30 32 34

14.3 12.3 10.7 9.44 8.36

21.5 18.5 16.1 14.2 12.6

37.7 32.5 28.3

56.6 48.8 42.5

30.2 26.1 22.7

45.4 39.2 34.1

21.9 18.9 16.4

32.9 28.4 24.7

16.6 14.3 12.5

25.0 12.1 21.5 10.4 18.8 9.06 7.97

Design

Effective length, KL (ft), with respect to least radius of gyration, r

Fy = 42 ksi

18.1 15.6 13.6 12.0

Properties 2

Ag , in. I , in.4 r , in. ASD Ωc = 1.67

2.14 9.28 2.08 LRFD

7.45 24.4 1.81

5.72 19.5 1.85

4.01 14.2 1.88

Note: Heavy line indicates KL/r equal to or greater than 200.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.95 10.7 1.91

2.12 7.84 1.92

AISC_Part 4B:14th Ed.

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10:10 AM

Page 81

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–81

Table 4-5 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi

HSS5.500HSS5

Round HSS Shape

HSS5.500× 0.375 0.349 20.6

0.500 0.465 26.7

t design, in. lb/ft

Pn /Ωc φc Pn

Pn /Ωc φc Pn Pn /Ωc

0.500 0.465 24.1

HSS5× 0.375 0.349 18.5

0.312 0.291 15.6

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

185

278

142

214

99.8

150

166

250

128

193

108

163

1 2 3 4 5

185 183 181 177 173

277 275 271 266 260

142 141 139 136 133

213 211 209 205 200

99.6 98.8 97.6 95.8 93.7

150 149 147 144 141

166 164 161 158 153

249 247 243 237 230

128 127 125 122 118

192 190 187 183 178

108 107 105 103 99.9

162 160 158 154 150

6 7 8 9 10

168 162 155 148 140

252 243 233 222 211

129 125 120 115 109

194 188 180 172 164

91.1 88.1 84.8 81.2 77.3

137 132 127 122 116

147 141 134 126 118

221 212 201 190 178

114 109 104 98.6 92.7

172 164 157 148 139

96.5 92.6 88.3 83.6 78.8

145 139 133 126 118

11 12 13 14 15

133 124 116 108 99.5

199 187 174 162 150

103 97.1 90.9 84.7 78.4

155 146 137 127 118

73.3 69.1 64.8 60.5 56.2

110 110 104 102 97.4 93.5 90.9 85.3 84.4 77.3

166 153 141 128 116

86.6 80.3 74.1 67.9 61.8

130 121 111 102 92.8

73.7 111 68.5 103 63.3 95.1 58.1 87.3 53.0 79.6

16 17 18 19 20

91.3 83.4 75.7 68.2 61.5

137 125 114 102 92.5

21 22 23 24 25

55.8 50.9 46.5 42.7 39.4

26 28 30

36.4 31.4

Design

Effective length, KL (ft), with respect to least radius of gyration, r

0.258 0.240 14.5

ASD

LRFD

72.3 109 66.2 99.6 60.4 90.8 54.7 82.2 49.4 74.2

51.9 47.7 43.6 39.7 35.8

78.0 71.7 65.6 59.6 53.9

69.5 104 62.0 93.2 55.3 83.1 49.6 74.6 44.8 67.3

55.8 50.2 44.7 40.1 36.2

83.9 75.4 67.2 60.3 54.5

48.0 43.2 38.6 34.7 31.3

72.2 65.0 58.1 52.1 47.0

83.9 76.4 69.9 64.2 59.2

44.8 40.8 37.3 34.3 31.6

67.3 61.3 56.1 51.5 47.5

32.5 29.6 27.1 24.9 22.9

48.9 44.5 40.7 37.4 34.5

40.6 37.0 33.9 31.1 28.7

61.0 55.6 50.9 46.7 43.1

32.9 29.9 27.4 25.2 23.2

49.4 45.0 41.2 37.8 34.9

28.4 25.9 23.7 21.7 20.0

42.7 38.9 35.6 32.7 30.1

54.7 47.2

29.2 25.2 21.9

43.9 37.9 33.0

21.2 18.3 15.9

31.9 27.5 23.9

26.5

39.8

21.4

32.2

18.5

27.8

Properties 2

Ag , in. I , in.4 r , in.

7.36 23.5 1.79

ASD

LRFD

Ωc = 1.67

φc = 0.90

5.65 18.8 1.83

3.97 13.7 1.86

6.62 17.2 1.61

5.10 13.9 1.65

Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.30 12.0 1.67

AISC_Part 4B:14th Ed.

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Page 82

4–82

DESIGN OF COMPRESSION MEMBERS

Table 4-5 (continued)

Available Strength in Axial Compression, kips HSS5HSS4.500

Round HSS HSS5×

Shape

t design, in. lb/ft

0.258 0.240 13.1

0.250 0.233 12.7

Pn /Ωc φc Pn

0.188 0.174 9.67

Pn /Ωc φc Pn Pn /Ωc

HSS4.500× 0.375 0.337 0.349 0.313 16.5 15.0

0.125 0.116 6.51

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

90.3

136

87.8

132

66.4

99.8

44.8

67.3

114

172

104

156

1 2 3 4 5

90.0 89.2 87.8 85.9 83.6

135 134 132 129 126

87.5 86.7 85.4 83.5 81.2

132 130 128 126 122

66.2 65.6 64.6 63.3 61.6

99.5 98.6 97.1 95.1 92.5

44.6 44.2 43.6 42.7 41.6

67.1 66.5 65.5 64.2 62.5

114 113 110 107 103

171 169 166 161 155

103 102 99.9 97.1 93.7

155 153 150 146 141

6 7 8 9 10

80.8 77.6 74.1 70.3 66.2

121 117 111 106 99.6

78.5 75.4 72.0 68.3 64.4

118 113 108 103 96.8

59.5 57.2 54.7 52.0 49.1

89.5 86.0 82.2 78.1 73.7

40.2 38.7 37.1 35.2 33.3

60.5 58.2 55.7 53.0 50.1

98.8 93.6 88.1 82.1 76.0

148 141 132 123 114

89.6 85.0 80.0 74.7 69.2

135 128 120 112 104

11 12 13 14 15

62.1 57.8 53.5 49.2 45.0

93.3 86.9 80.4 74.0 67.6

60.3 56.2 52.0 47.8 43.7

90.7 84.5 78.2 71.9 65.7

46.0 43.0 39.8 36.7 33.6

69.2 64.6 59.9 55.2 50.5

31.3 29.3 27.2 25.1 23.0

47.1 44.0 40.8 37.7 34.6

69.7 105 63.5 95.4 57.3 86.1 51.3 77.1 45.6 68.5

63.6 57.9 52.4 47.0 41.8

95.5 87.1 78.7 70.6 62.8

16 17 18 19 20

40.9 36.9 33.0 29.6 26.8

61.4 55.5 49.6 44.6 40.2

39.7 35.9 32.1 28.8 26.0

59.7 53.9 48.3 43.3 39.1

30.6 27.7 24.9 22.3 20.1

46.0 41.6 37.4 33.5 30.3

21.0 19.1 17.2 15.4 13.9

31.6 28.6 25.8 23.2 20.9

40.1 35.5 31.7 28.4 25.7

60.3 53.4 47.6 42.7 38.6

36.8 32.6 29.1 26.1 23.5

55.3 49.0 43.7 39.2 35.4

21 22 23 24 25

24.3 22.1 20.2 18.6 17.1

36.5 33.2 30.4 27.9 25.7

23.6 21.5 19.7 18.1 16.6

35.5 32.3 29.6 27.1 25.0

18.3 16.6 15.2 14.0 12.9

27.5 25.0 22.9 21.0 19.4

12.6 11.5 10.5 9.65 8.90

19.0 17.3 15.8 14.5 13.4

23.3 21.2 19.4 17.8

35.0 31.9 29.2 26.8

21.4 19.5 17.8 16.4

32.1 29.3 26.8 24.6

26 28

15.8 13.7

23.8 20.5

15.4 13.3

23.1 19.9

11.9 10.3

17.9 15.4

8.23 7.09

12.4 10.7

Design

Effective length, KL (ft), with respect to least radius of gyration, r

Fy = 42 ksi

Pn /Ωc φc Pn ASD

LRFD

Properties 2

Ag , in. I , in.4 r , in.

3.59 10.2 1.69

ASD

LRFD

Ωc = 1.67

φc = 0.90

3.49 9.94 1.69

2.64 7.69 1.71

1.78 5.31 1.73

Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.55 9.87 1.47

4.12 9.07 1.48

AISC_Part 4B:14th Ed.

2/23/11

10:10 AM

Page 83

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–83

Table 4-5 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi

HSS4.500HSS4

Round HSS Shape

t design, in. lb/ft

Pn /Ωc

Effective length, KL (ft), with respect to least radius of gyration, r

Design

HSS4.500× 0.188 0.174 8.67

0.237 0.220 10.8 φc Pn

Pn /Ωc

φc Pn

HSS4× 0.125 0.116 5.85

0.313 0.291 12.3

0.250 0.233 10.0

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

74.4

112

59.4

89.2

40.2

60.5

85.3

128

69.4

104

1 2 3 4 5

74.2 73.3 71.9 70.0 67.6

111 110 108 105 102

59.1 58.5 57.4 55.9 54.0

88.9 87.9 86.2 84.0 81.2

40.1 39.7 38.9 37.9 36.7

60.3 59.6 58.5 57.0 55.2

84.8 83.5 81.4 78.6 75.1

127 126 122 118 113

69.1 68.0 66.4 64.1 61.3

104 102 99.7 96.3 92.1

6 7 8 9 10

64.9 61.7 58.3 54.6 50.8

97.5 92.8 87.6 82.1 76.3

51.8 49.3 46.6 43.7 40.7

77.9 74.1 70.0 65.7 61.1

35.2 33.6 31.8 29.9 27.8

53.0 50.5 47.8 44.9 41.9

71.0 66.5 61.6 56.5 51.3

107 99.9 92.6 84.9 77.1

58.0 54.3 50.4 46.3 42.1

87.1 81.7 75.8 69.6 63.3

11 12 13 14 15

46.8 42.9 39.0 35.2 31.5

70.4 64.5 58.6 52.8 47.3

37.6 34.4 31.3 28.3 25.4

56.5 51.8 47.1 42.5 38.1

25.8 23.7 21.6 19.6 17.6

38.7 35.6 32.5 29.4 26.4

46.1 41.0 36.2 31.5 27.4

69.3 61.7 54.3 47.3 41.2

37.9 33.8 29.8 26.0 22.6

57.0 50.8 44.8 39.1 34.0

16 17 18 19 20

27.9 24.7 22.0 19.8 17.8

41.9 37.1 33.1 29.7 26.8

22.5 20.0 17.8 16.0 14.4

33.9 30.0 26.8 24.0 21.7

15.7 13.9 12.4 11.1 10.0

23.6 20.9 18.6 16.7 15.1

24.1 21.3 19.0 17.1 15.4

36.2 32.1 28.6 25.7 23.2

19.9 17.6 15.7 14.1 12.7

29.9 26.5 23.6 21.2 19.1

21 22 23 24 25

16.2 14.7 13.5 12.4 11.4

24.3 22.2 20.3 18.6 17.2

13.1 11.9 10.9 10.0 9.23

19.7 17.9 16.4 15.0 13.9

13.7 12.5 11.4 10.5 9.65

14.0 12.7

21.0 19.1

11.6 10.5

17.4 15.8

9.10 8.29 7.58 6.97 6.42

Properties 2

Ag , in. I , in.4 r , in.

2.96 6.79 1.52

2.36 5.54 1.53

1.60 3.84 1.55

3.39 5.87 1.32

Note: Heavy line indicates KL/r equal to or greater than 200.

ASD

LRFD

Ωc = 1.67

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.76 4.91 1.33

AISC_Part 4B:14th Ed.

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10:10 AM

Page 84

4–84

DESIGN OF COMPRESSION MEMBERS

Table 4-5 (continued)

Available Strength in Axial Compression, kips Round HSS

HSS4

Shape

t design, in. lb/ft

Effective length, KL (ft), with respect to least radius of gyration, r

Design

Fy = 42 ksi

0.237 0.220 9.53

HSS4× 0.220 0.205 8.89

0.226 0.210 9.12

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0.188 0.174 7.66

Pn /Ωc

φc Pn

0.125 0.116 5.18

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

65.6

98.7

62.9

94.5

61.4

92.2

52.6

79.0

35.7

53.7

1 2 3 4 5

65.3 64.4 62.8 60.7 58.0

98.2 96.7 94.4 91.2 87.2

62.6 61.6 60.1 58.1 55.6

94.0 92.7 90.4 87.3 83.5

61.1 60.2 58.7 56.7 54.3

91.8 90.4 88.2 85.2 81.5

52.3 51.6 50.3 48.6 46.6

78.6 77.5 75.6 73.1 70.0

35.5 35.0 34.2 33.1 31.7

53.4 52.7 51.4 49.8 47.7

6 7 8 9 10

55.0 51.6 47.9 44.0 40.1

82.6 77.5 72.0 66.2 60.3

52.7 49.4 45.9 42.2 38.4

79.1 74.2 68.9 63.4 57.7

51.4 48.2 44.8 41.2 37.5

77.2 72.5 67.3 61.9 56.4

44.1 41.4 38.5 35.5 32.4

66.3 62.3 57.9 53.3 48.6

30.1 28.3 26.4 24.4 22.3

45.3 42.6 39.7 36.6 33.5

11 12 13 14 15

36.2 32.3 28.6 25.0 21.7

54.4 48.5 42.9 37.5 32.7

34.6 30.9 27.4 23.9 20.8

52.1 46.5 41.1 35.9 31.3

33.8 30.2 26.7 23.3 20.3

50.8 45.4 40.1 35.1 30.5

29.2 26.1 23.1 20.3 17.7

43.9 39.3 34.8 30.5 26.6

20.2 18.1 16.1 14.2 12.4

30.3 27.2 24.2 21.3 18.6

16 17 18 19 20

19.1 16.9 15.1 13.6 12.2

28.7 25.4 22.7 20.4 18.4

18.3 16.2 14.5 13.0 11.7

27.5 24.4 21.7 19.5 17.6

17.9 15.8 14.1 12.7 11.4

26.8 23.8 21.2 19.0 17.2

15.5 13.8 12.3 11.0 9.94

23.3 20.7 18.4 16.6 14.9

10.9 9.63 8.59 7.71 6.95

16.3 14.5 12.9 11.6 10.5

21 22

11.1 10.1

16.7 15.2

10.6 9.68

16.0 14.6

10.4 9.45

15.6 14.2

9.02 8.21

13.6 12.3

6.31 5.75

9.48 8.64

Properties 2

Ag , in. I , in.4 r , in.

2.61 4.68 1.34

2.50 4.50 1.34

2.44 4.41 1.34

2.09 3.83 1.35

Note: Heavy line indicates KL/r equal to or greater than 200.

ASD

LRFD

Ωc = 1.67

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.42 2.67 1.37

AISC_Part 4B:14th Ed.

2/23/11

10:10 AM

Page 85

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–85

Table 4-6

Available Strength in Axial Compression, kips

Fy = 35 ksi

Pipe Pipe 12

Shape

t design, in. lb/ft

XS 0.465 65.5

XS 0.465 54.8

Pn /Ωc φc Pn Pn /Ωc

Pipe 8 Std 0.340 40.5

XXS 0.816 72.5

XS 0.465 43.4

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

367

551

287

432

316

476

241

362

419

6 7 8 9 10

362 360 358 355 353

544 541 538 534 530

283 282 280 278 276

426 424 421 418 415

310 308 305 303 299

466 463 459 455 450

236 235 233 231 228

355 353 350 347 343

405 400 394 388 381

11 12 13 14 15

350 347 343 340 336

526 521 516 511 505

274 272 269 266 263

412 408 405 400 396

296 292 288 284 279

445 439 433 427 420

226 223 220 217 213

339 335 330 326 320

16 17 18 19 20

332 328 323 319 314

499 493 486 479 472

260 257 254 250 246

391 386 381 376 370

274 269 264 259 253

413 405 397 389 381

210 206 202 198 194

21 22 23 24 25

309 304 298 293 288

464 457 449 440 432

243 239 235 230 226

365 359 353 346 340

248 242 236 230 224

372 363 354 345 336

26 27 28 29 30

282 276 270 264 258

424 415 406 397 388

222 217 213 208 204

333 327 320 313 306

217 211 205 198 192

32 34 36 38 40

246 234 221 209 197

370 351 333 314 296

194 185 175 165 156

292 277 263 248 234

179 166 154 142 130

Design

Effective length, KL (ft), with respect to least radius of gyration, r

Pipe 10 Std 0.349 49.6

Pn /Ωc φc Pn

PIPE 12-PIPE 8

ASD

LRFD

630

249

375

609 601 593 583 573

242 239 236 232 228

363 359 354 349 343

373 365 357 348 338

561 549 536 523 508

224 220 215 210 204

337 330 323 315 307

315 310 304 298 291

328 318 308 297 286

494 478 463 447 430

199 193 187 181 175

299 290 282 273 263

190 185 181 176 172

285 278 272 265 258

275 264 253 242 231

414 397 380 364 347

169 163 156 150 144

254 245 235 225 216

327 317 308 298 288

167 162 157 153 148

251 244 236 229 222

220 209 198 188 178

331 314 298 283 267

137 131 125 119 113

206 197 188 178 169

269 250 231 213 195

138 128 119 110 101

207 193 179 165 152

158 140 124 112 101

237 210 187 168 152

101 89.7 80.0 71.8 64.8

152 135 120 108 97.5

Properties 2

Ag , in. I , in.4 r , in. ASD Ωc = 1.67

17.5 339 4.35 LRFD

13.7 262 4.39

15.1 199 3.64

11.5 151 3.68

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

20.0 154 2.78

11.9 100 2.89

AISC_Part 4B:14th Ed.

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10:11 AM

Page 86

4–86

DESIGN OF COMPRESSION MEMBERS

Table 4-6 (continued)

Available Strength in Axial Compression, kips Pipe

PIPE 8-PIPE 5 Pipe 8 Std 0.300 28.6

Shape

t design, in. lb/ft

Effective length, KL (ft), with respect to least radius of gyration, r

Design

Fy = 35 ksi

Pipe 6 XS 0.403 28.6

XXS 0.805 53.2

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pipe 5 XXS 0.699 38.6

Std 0.261 19.0

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

165

247

308

463

164

247

109

164

224

337

6 7 8 9 10

160 158 156 154 151

240 237 234 231 227

290 283 276 268 260

436 426 415 403 391

155 152 149 145 141

233 229 224 218 212

103 101 99.3 96.9 94.2

155 153 149 146 142

205 199 192 184 176

309 299 288 277 264

11 12 13 14 15

148 146 143 139 136

223 219 214 209 204

251 241 231 221 210

377 362 347 332 316

136 132 127 122 116

205 198 191 183 175

91.4 88.4 85.2 81.9 78.5

137 133 128 123 118

167 158 149 139 130

251 237 223 209 195

16 17 18 19 20

132 129 125 121 117

199 194 188 182 176

199 188 177 167 156

299 283 267 250 234

111 106 100 94.7 89.2

167 159 151 142 134

75.1 71.6 68.0 64.4 60.9

113 108 102 96.8 91.5

120 111 102 93.1 84.5

181 167 153 140 127

21 22 23 24 25

113 109 105 101 96.9

170 164 158 152 146

145 135 125 115 106

218 203 188 173 160

83.8 78.5 73.3 68.3 63.3

126 118 110 103 95.1

57.3 53.9 50.5 47.1 43.9

86.2 81.0 75.8 70.8 65.9

76.7 69.9 63.9 58.7 54.1

115 105 96.1 88.2 81.3

26 27 28 29 30

92.8 88.7 84.7 80.7 76.8

139 133 127 121 115

98.2 91.1 84.7 78.9 73.8

148 137 127 119 111

58.5 54.3 50.5 47.0 44.0

88.0 81.6 75.8 70.7 66.1

40.6 37.7 35.0 32.7 30.5

61.1 56.7 52.7 49.1 45.9

50.0 46.4 43.1 40.2

75.2 69.7 64.8 60.4

32 34 36 38 40

69.1 61.7 55.0 49.4 44.6

104 92.7 82.7 74.2 67.0

64.8 57.4

38.6 34.2 30.5

58.1 51.4 45.9

26.8 23.8 21.2

40.3 35.7 31.9

97.4 86.3

Properties 2

Ag , in. I , in.4 r , in.

ASD

7.85 68.1 2.95 LRFD

14.7 63.5 2.08

Ωc = 1.67

φc = 0.90

7.83 38.3 2.20

5.20 26.5 2.25

Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

10.7 32.2 1.74

AISC_Part 4B:14th Ed.

2/23/11

10:11 AM

Page 87

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–87

Table 4-6 (continued)

Available Strength in Axial Compression, kips

Fy = 35 ksi

Pipe Pipe 5

Shape

XS 0.349 20.8

t design, in. lb/ft

Pn /Ωc Design

Std 0.241 14.6

φc Pn

Pn /Ωc

Pipe 4 XS 0.315 15.0

XXS 0.628 27.6

φc Pn

Std 0.221 10.8

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

120

180

84.0

126

161

241

86.8

130

62.0

93.2

6 7 8 9 10

111 108 105 101 96.8

167 162 157 152 146

78.0 75.9 73.5 71.0 68.2

117 114 111 107 103

140 133 126 118 110

210 200 189 177 165

76.9 73.6 70.0 66.1 62.0

116 111 105 99.3 93.1

55.2 52.9 50.4 47.7 44.9

83.0 79.6 75.8 71.8 67.5

11 12 13 14 15

92.5 88.1 83.5 78.7 74.0

139 132 125 118 111

65.3 62.2 59.1 55.8 52.6

98.1 93.6 88.8 83.9 79.0

101 92.7 84.3 76.0 68.1

152 139 127 114 102

57.7 53.4 49.1 44.9 40.7

86.8 80.3 73.8 67.4 61.2

42.0 38.9 35.9 32.9 30.0

63.1 58.5 54.0 49.5 45.1

16 17 18 19 20

69.2 64.4 59.8 55.2 50.7

104 96.9 89.8 83.0 76.3

49.3 46.0 42.8 39.6 36.5

74.1 69.1 64.3 59.5 54.9

60.3 53.5 47.7 42.8 38.6

90.7 80.3 71.7 64.3 58.0

36.7 32.8 29.2 26.2 23.7

55.1 49.2 43.9 39.4 35.6

27.1 24.4 21.7 19.5 17.6

40.8 36.6 32.7 29.3 26.5

21 22 23 24 25

46.4 42.3 38.7 35.5 32.8

69.8 63.6 58.2 53.4 49.2

33.5 30.6 28.0 25.7 23.7

50.4 45.9 42.0 38.6 35.6

35.0 31.9 29.2

52.6 48.0 43.9

21.5 19.6 17.9 16.4

32.3 29.4 26.9 24.7

16.0 14.6 13.3 12.2 11.3

24.0 21.9 20.0 18.4 16.9

26 27 28 29 30

30.3 28.1 26.1 24.3 22.7

45.5 42.2 39.2 36.6 34.2

21.9 20.3 18.9 17.6 16.4

32.9 30.5 28.4 26.4 24.7

0

Effective length, KL (ft), with respect to least radius of gyration, r

PIPE 5-PIPE 4

Properties 2

5.73 19.5 1.85

ASD

LRFD

Ωc = 1.67

φc = 0.90

Ag , in. I , in.4 r , in.

4.01 14.3 1.88

7.66 14.7 1.39

4.14 9.12 1.48

Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.96 6.82 1.51

AISC_Part 4B:14th Ed.

2/23/11

10:11 AM

Page 88

4–88

DESIGN OF COMPRESSION MEMBERS

Table 4-6 (continued)

Available Strength in Axial Compression, kips Pipe

PIPE 31⁄ 2 -PIPE 3 Pipe 3 1/2

Shape

t design, in. lb/ft

XS 0.296 12.5

Pn /Ωc

Effective length, KL (ft), with respect to least radius of gyration, r

Design

Fy = 35 ksi

Std 0.211 9.12

φc Pn

Pipe 3 XS 0.280 10.3

XXS 0.559 18.6

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Std 0.201 7.58

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

71.9

108

52.4

78.7

108

163

59.3

89.1

43.4

65.2

6 7 8 9 10

61.6 58.2 54.6 50.8 46.8

92.6 87.5 82.1 76.3 70.3

45.2 42.8 40.3 37.6 34.8

67.9 64.4 60.6 56.5 52.2

85.6 78.6 71.2 63.7 56.2

129 118 107 95.7 84.5

48.4 44.9 41.3 37.5 33.6

72.7 67.5 62.0 56.3 50.6

35.7 33.3 30.7 28.0 25.3

53.7 50.1 46.2 42.2 38.1

11 12 13 14 15

42.8 38.7 34.8 31.0 27.3

64.3 58.2 52.3 46.6 41.0

31.9 29.0 26.2 23.4 20.8

47.9 43.6 39.4 35.2 31.3

49.0 42.1 35.9 30.9 26.9

73.6 63.3 53.9 46.5 40.5

29.9 26.2 22.7 19.6 17.1

44.9 39.4 34.1 29.4 25.6

22.6 20.0 17.5 15.1 13.1

34.0 30.0 26.2 22.7 19.8

16 17 18 19 20

24.0 21.3 19.0 17.0 15.4

36.1 32.0 28.5 25.6 23.1

18.3 16.2 14.5 13.0 11.7

27.5 24.4 21.7 19.5 17.6

23.7 21.0

35.6 31.5

15.0 13.3 11.8 10.6

22.5 20.0 17.8 16.0

11.6 10.2 9.13 8.19

17.4 15.4 13.7 12.3

21 22

13.9

20.9

10.6 9.68

16.0 14.6

Properties 2

Ag , in. I , in.4 r , in.

3.43 5.94 1.31

2.50 4.52 1.34

5.17 5.79 1.06

2.83 3.70 1.14

Note: Heavy line indicates KL/r equal to or greater than 200.

ASD

LRFD

Ωc = 1.67

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.07 2.85 1.17

AISC_Part 4B:14th Ed.

2/23/11

10:11 AM

Page 89

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–89

Table 4-7

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT18× c

lb/ft

X-X Axis Y-Y Axis

c

151

131c

141

123.5c

115.5c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1210

1810

1050

1580

921

1380

813

1220

712

1070

10 12 14 16 18

1170 1150 1130 1110 1080

1750 1730 1700 1670 1630

1020 1000 987 969 949

1530 1510 1480 1460 1430

894 883 870 854 838

1340 1330 1310 1280 1260

791 781 770 758 744

1190 1170 1160 1140 1120

694 686 677 667 655

1040 1030 1020 1000 985

20 22 24 26 28

1060 1030 997 964 931

1590 1540 1500 1450 1400

927 903 878 851 823

1390 1360 1320 1280 1240

819 799 778 756 732

1230 1200 1170 1140 1100

729 712 694 675 656

1090 1070 1040 1020 986

643 629 614 599 583

966 945 924 900 876

30 32 34 36 40

896 860 823 786 711

1350 1290 1240 1180 1070

794 764 733 702 639

1190 1150 1100 1060 961

708 682 657 630 576

1060 1030 987 947 866

635 614 592 570 524

955 923 890 857 788

566 548 530 511 473

850 824 796 768 711

Design

Effective length, KL (ft), with respect to indicated axis

WT18

0

1210

1810

1050

1580

921

1380

813

1220

712

1070

10 12 14 16 18

1040 1020 1000 970 933

1560 1540 1500 1460 1400

899 887 870 846 817

1350 1330 1310 1270 1230

778 769 756 738 715

1170 1160 1140 1110 1070

681 674 664 650 632

1020 1010 998 977 950

592 586 578 568 554

889 881 869 853 832

20 22 24 26 28

892 847 799 749 699

1340 1270 1200 1130 1050

784 747 708 667 625

1180 1120 1060 1000 939

687 657 624 589 554

1030 987 938 886 832

610 585 558 529 499

917 880 839 795 750

536 516 494 470 445

806 776 742 706 669

30 32 34 36 40

649 599 550 502 412

975 900 826 754 619

582 540 498 457 379

875 811 749 687 569

518 481 445 410 342

778 723 669 616 514

468 437 406 376 317

704 657 611 565 477

419 393 367 341 290

630 591 551 512 436

Properties 2

Ag , in. rx , in. ry , in.

ASD

44.5 5.37 3.82 LRFD

41.5 5.36 3.80

Ωc = 1.67

φc = 0.90

c

38.5 5.36 3.76

36.3 5.36 3.74

Shape is slender for compression with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

34.1 5.36 3.71

AISC_Part 4B:14th Ed.

2/23/11

10:11 AM

Page 90

4–90

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT18 Shape

WT18× c

lb/ft

X-X Axis Y-Y Axis

c

128

105c

116

97c

91c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1040

1560

839

1260

735

1100

599

900

509

765

10 12 14 16 18

1000 992 976 959 939

1510 1490 1470 1440 1410

816 806 795 782 768

1230 1210 1190 1180 1150

716 707 698 687 675

1080 1060 1050 1030 1010

585 579 572 564 555

879 870 860 848 835

499 494 489 482 476

749 743 734 725 715

20 22 24 26 28

918 895 870 844 817

1380 1340 1310 1270 1230

752 735 716 697 677

1130 1100 1080 1050 1020

662 647 632 615 598

994 973 949 925 899

545 535 523 511 499

820 804 787 769 749

468 460 451 441 431

703 691 678 663 648

30 32 34 36 40

789 760 730 700 638

1190 1140 1100 1050 960

656 634 611 588 541

985 953 919 884 814

580 562 543 523 483

872 844 816 786 726

485 471 457 442 412

729 708 687 665 619

421 410 399 387 363

633 616 599 582 546

Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

0

1040

1560

839

1260

735

1100

599

900

509

765

10 12 14 16 18

838 797 747 690 630

1260 1200 1120 1040 947

680 650 614 572 527

1020 978 923 860 792

575 552 523 490 452

864 830 787 736 680

472 456 435 411 383

709 685 655 617 576

402 390 375 356 334

604 586 563 535 503

20 22 24 26 28

569 507 447 389 338

855 762 672 585 508

480 432 385 340 296

721 650 579 511 445

413 372 333 294 257

620 560 500 442 386

353 322 291 261 231

531 485 438 392 347

311 286 261 236 212

467 430 393 355 319

30 32 34 36 40

296 261 232 208 169

445 393 349 312 254

260 230 204 183 149

391 345 307 275 224

226 200 178 160 130

339 300 267 240 196

203 180 161 144 118

306 271 242 217 177

188 167 149 134 109

283 251 224 201 164

Properties 2

Ag , in. rx , in. ry , in.

ASD

37.6 5.66 2.65 LRFD

34.0 5.63 2.62

Ωc = 1.67

φc = 0.90

c

30.9 5.65 2.58

28.5 5.62 2.56

Shape is slender for compression with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

26.8 5.62 2.55

AISC_Part 4B:14th Ed.

2/23/11

10:11 AM

Page 91

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–91

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT18× c

lb/ft

X-X Axis Y-Y Axis

c

85

75c

80

67.5c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

424

637

367

552

324

486

271

407

10 12 14 16 18

416 412 408 404 398

625 620 614 607 599

361 358 355 351 347

542 538 533 527 521

318 316 313 310 307

478 475 471 466 461

267 265 263 261 258

401 398 395 392 388

20 22 24 26 28

393 387 380 373 365

590 581 571 560 549

342 337 332 326 320

514 507 499 490 481

303 299 295 290 285

456 449 443 436 428

255 252 248 245 241

383 379 373 368 362

30 32 34 36 40

357 349 340 331 313

537 525 512 498 470

314 307 300 293 278

471 461 451 440 417

279 274 268 262 249

420 412 403 394 375

237 232 228 223 213

356 349 342 335 320

Design

Effective length, KL (ft), with respect to indicated axis

WT18

0

424

637

367

552

324

486

271

407

10 12 14 16 18

335 327 315 302 286

503 491 474 453 429

288 281 272 262 249

432 422 410 393 374

249 244 237 229 218

375 367 357 344 328

197 193 188 181 173

295 290 282 272 261

20 22 24 26 28

268 249 229 209 190

402 374 344 315 285

234 219 203 186 170

352 329 305 280 255

206 194 180 166 152

310 291 271 250 229

165 155 144 133 122

247 233 217 201 184

30 32 34 36 40

171 152 136 122 99.9

256 228 204 183 150

154 138 123 111 91.1

231 207 185 167 137

138 125 112 101 82.9

208 187 168 151 125

111 100 90.5 81.9

168 151 136 123

Properties 2

Ag , in. rx , in. ry , in.

ASD

25.0 5.61 2.53 LRFD

Ωc = 1.67

φc = 0.90

23.5 5.61 2.50

22.1 5.62 2.47

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

19.9 5.66 2.38

AISC_Part 4B:14th Ed.

2/23/11

10:11 AM

Page 92

4–92

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT16.5 Shape

WT16.5× h

lb/ft

X-X Axis Y-Y Axis

h

193.5

177

145.5c

159

131.5c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1710

2570

1560

2340

1400

2110

1270

1910

1040

1570

10 12 14 16 18

1640 1610 1570 1540 1490

2460 2420 2370 2310 2250

1500 1470 1440 1400 1360

2250 2210 2160 2110 2050

1340 1320 1290 1260 1220

2020 1980 1940 1890 1840

1220 1190 1170 1140 1110

1830 1800 1760 1710 1660

1000 986 966 944 919

1510 1480 1450 1420 1380

20 22 24 26 28

1450 1400 1350 1290 1240

2180 2100 2030 1940 1860

1320 1280 1230 1180 1130

1980 1920 1840 1770 1690

1180 1140 1100 1050 1010

1780 1720 1650 1580 1510

1070 1030 995 953 911

1610 1550 1490 1430 1370

892 863 833 801 768

1340 1300 1250 1200 1150

30 32 34 36 40

1180 1120 1060 1000 886

1770 1690 1600 1510 1330

1070 1020 964 910 802

1610 1530 1450 1370 1200

958 909 859 810 712

1440 1370 1290 1220 1070

867 823 778 733 644

1300 1240 1170 1100 968

734 700 664 629 559

1100 1050 999 946 840

Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

0

1710

2560

1560

2340

1400

2110

1270

1910

1040

1570

10 12 14 16 18

1530 1480 1430 1370 1300

2300 2230 2150 2060 1960

1390 1340 1300 1240 1180

2090 2020 1950 1860 1770

1230 1200 1150 1100 1050

1850 1800 1730 1660 1580

1100 1080 1040 1000 956

1650 1620 1570 1510 1440

899 883 861 831 796

1350 1330 1290 1250 1200

20 22 24 26 28

1230 1160 1090 1010 936

1860 1750 1630 1520 1410

1120 1050 983 914 844

1680 1580 1480 1370 1270

992 933 872 810 748

1490 1400 1310 1220 1120

904 849 792 734 676

1360 1280 1190 1100 1020

757 714 670 625 579

1140 1070 1010 939 871

30 32 34 36 40

860 786 714 644 523

1290 1180 1070 968 786

775 708 642 578 470

1170 1060 965 869 706

686 626 567 509 414

1030 940 852 766 622

618 562 508 455 371

929 845 763 684 557

534 489 445 403 328

802 735 670 606 494

Properties 2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

57.0 5.07 3.77 LRFD

52.1 5.03 3.74 h

φc = 0.90

c

46.8 4.99 3.71

42.8 4.96 3.68

38.7 4.93 3.65

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Shape is slender for compression with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 4B:14th Ed.

2/23/11

10:11 AM

Page 93

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–93

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT16.5× c

lb/ft

X-X Axis Y-Y Axis

c

120.5

100.5c

110.5

84.5c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

921

1380

780

1170

638

960

466

700

10 12 14 16 18

887 873 857 838 817

1330 1310 1290 1260 1230

754 742 729 714 698

1130 1120 1100 1070 1050

619 611 601 590 578

930 918 903 887 868

454 449 443 437 429

683 675 666 656 645

20 22 24 26 28

794 770 744 717 689

1190 1160 1120 1080 1040

680 660 640 618 596

1020 993 962 929 896

564 550 535 518 501

848 826 803 779 753

421 412 403 393 382

633 620 605 590 574

30 32 34 36 40

660 631 601 570 510

992 948 903 857 766

573 549 524 500 450

861 825 788 751 677

484 466 447 428 390

727 700 672 643 586

371 360 348 336 311

558 540 523 504 467

Design

Effective length, KL (ft), with respect to indicated axis

WT16.5

0

921

1380

780

1170

638

960

466

700

10 12 14 16 18

774 763 746 724 696

1160 1150 1120 1090 1050

648 640 628 611 591

974 962 944 919 888

524 518 510 499 485

787 779 767 751 729

382 369 353 333 312

574 555 530 501 468

20 22 24 26 28

664 628 591 553 514

997 945 889 831 772

566 538 509 478 446

851 809 765 719 671

468 448 426 403 379

703 673 641 606 570

288 264 240 216 193

433 397 361 325 290

30 32 34 36 40

474 436 398 361 295

713 655 598 543 443

415 383 352 321 264

623 575 528 483 397

354 330 305 281 234

533 496 459 422 352

171 151 134 120 98.1

256 227 202 181 147

Properties 2

Ag , in. rx , in. ry , in.

ASD

35.6 4.96 3.62 LRFD

Ωc = 1.67

φc = 0.90

32.6 4.95 3.59 c

29.7 4.95 3.56

Shape is slender for compression with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

24.7 5.12 2.50

AISC_Part 4B:14th Ed.

2/23/11

10:11 AM

Page 94

4–94

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT16.5 Shape

WT16.5× c

lb/ft

X-X Axis Y-Y Axis

c

76

65c

70.5

59c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

390

586

325

489

284

426

235

353

10 12 14 16 18

381 377 373 368 362

573 567 560 553 544

319 316 312 308 304

479 475 469 464 457

278 276 273 270 266

418 415 410 406 400

231 229 227 225 222

347 344 341 338 334

20 22 24 26 28

356 349 342 334 325

535 524 513 502 489

299 294 289 283 276

450 442 434 425 415

262 258 254 249 244

394 388 381 374 366

219 216 212 209 205

329 324 319 314 308

30 32 34 36 40

317 308 299 289 270

476 463 449 435 405

270 263 256 248 233

405 395 384 373 350

238 232 226 220 208

358 349 340 331 312

201 196 192 187 177

302 295 288 281 267

Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

0

390

586

325

489

284

426

235

353

10 12 14 16 18

311 302 291 277 260

467 454 437 416 391

257 250 242 231 219

386 376 364 348 329

216 212 205 197 187

325 318 308 295 281

172 169 164 158 151

259 253 246 237 227

20 22 24 26 28

242 224 205 186 167

364 336 308 279 251

205 191 175 160 145

308 286 264 241 218

176 164 151 138 125

264 246 227 208 189

143 134 124 114 104

214 201 187 172 157

30 32 34 36 40

149 132 118 106 86.3

223 198 177 159 130

130 116 104 93.2 76.3

196 174 156 140 115

113 101 90.3 81.3

170 152 136 122

94.5 84.8 76.3 68.9

142 127 115 103

Properties 2

Ag , in. rx , in. ry , in.

ASD

22.5 5.14 2.47 LRFD

Ωc = 1.67

φc = 0.90

20.7 5.15 2.43

19.1 5.18 2.38

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

17.4 5.20 2.32

AISC_Part 4B:14th Ed.

2/23/11

10:11 AM

Page 95

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–95

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT15×

lb/ft

195.5

h

178.5

Pn /Ωc φc Pn

X-X Axis Y-Y Axis

h

h

163

Pn /Ωc φc Pn Pn /Ωc

146

130.5

117.5 c

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1720

2590

1570

2360

1440

2160

1290

1940

1150

1730

988

1480

10 12 14 16 18

1640 1610 1560 1520 1470

2470 2410 2350 2280 2210

1490 1460 1420 1380 1330

2250 2200 2140 2080 2010

1360 1330 1300 1260 1220

2050 2010 1950 1890 1830

1220 1190 1160 1130 1090

1840 1790 1750 1690 1630

1090 1070 1040 1010 971

1640 1610 1560 1510 1460

938 917 893 866 836

1410 1380 1340 1300 1260

20 22 24 26 28

1410 1360 1300 1230 1170

2130 2040 1950 1850 1760

1280 1230 1170 1120 1060

1930 1850 1760 1680 1590

1170 1120 1070 1010 959

1760 1680 1610 1520 1440

1040 999 952 903 853

1570 1500 1430 1360 1280

933 892 850 806 761

1400 1340 1280 1210 1140

804 770 734 698 660

1210 1160 1100 1050 992

30 32 34 36 40

1100 1040 973 907 781

1660 1560 1460 1360 1170

997 936 875 815 699

1500 1410 1320 1230 1050

904 848 792 737 630

1360 1270 1190 1110 947

803 752 702 652 556

1210 1130 1060 980 836

716 670 625 580 494

1080 1010 940 872 743

622 583 545 507 434

934 877 819 762 652

Design

Effective length, KL (ft), with respect to indicated axis

WT15

0

1720

2590

1570

2360

1440

2160

1290

1930

1150

1730

988

1480

10 12 14 16 18

1560 1510 1450 1380 1310

2340 2260 2180 2080 1970

1410 1370 1310 1250 1190

2120 2050 1970 1880 1790

1280 1240 1190 1130 1080

1930 1860 1790 1710 1620

1140 1100 1060 1010 956

1710 1660 1590 1520 1440

1010 972 932 889 841

1510 1460 1400 1340 1260

853 835 808 774 735

1280 1250 1210 1160 1100

20 22 24 26 28

1240 1160 1080 1000 922

1860 1750 1630 1510 1390

1120 1050 977 903 830

1680 1580 1470 1360 1250

1010 948 881 814 747

1520 1420 1320 1220 1120

900 841 782 722 662

1350 1260 1180 1080 995

791 739 686 632 579

1190 1110 1030 950 870

693 648 602 556 509

1040 974 905 835 765

30 32 34 36 40

843 766 692 619 503

1270 1150 1040 931 755

758 688 620 555 450

1140 1030 932 834 677

681 617 555 495 402

1020 927 834 744 604

603 546 490 438 356

906 820 737 658 535

526 475 425 380 309

791 714 639 571 464

464 419 376 337 274

697 630 566 506 412

Properties 2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

57.6 4.61 3.67 LRFD φc = 0.90

52.5 4.56 3.64 h

c

48.0 4.52 3.60

43.0 4.48 3.58

38.5 4.46 3.53

34.7 4.41 3.51

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Shape is slender for compression with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 4B:14th Ed.

2/23/11

10:11 AM

Page 96

4–96

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT15 Shape

WT15× c

lb/ft

X-X Axis Y-Y Axis

c

105.5

86.5c

95.5

74 c

66 c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

833

1250

687

1030

557

838

469

704

384

577

10 12 14 16 18

794 778 759 737 713

1190 1170 1140 1110 1070

657 644 630 613 595

987 968 946 922 894

536 527 516 504 490

805 791 775 757 737

452 445 437 428 418

680 669 657 644 628

372 366 360 354 346

558 551 542 531 520

20 22 24 26 28

688 661 632 602 572

1030 993 950 905 860

575 555 532 509 486

865 833 800 766 730

476 460 444 427 409

715 692 667 641 615

407 395 382 369 355

612 594 575 555 534

338 329 319 309 299

508 494 480 465 449

30 32 34 36 40

541 510 478 447 387

813 766 719 672 581

462 437 412 387 339

694 657 620 582 509

391 372 353 334 296

587 559 531 502 445

341 327 312 297 267

513 491 469 446 401

288 277 265 254 230

433 416 399 382 346

Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

0

833

1250

687

1030

557

838

469

704

384

577

10 12 14 16 18

704 692 673 649 620

1060 1040 1010 975 931

574 565 553 536 514

862 850 831 805 773

460 455 446 435 420

691 683 671 654 632

374 355 331 305 277

561 533 498 459 417

297 284 268 249 228

447 428 403 374 343

20 22 24 26 28

587 551 515 477 439

882 829 773 717 660

490 463 434 405 375

736 696 653 609 564

403 383 362 340 317

606 576 544 511 477

249 221 193 167 145

374 332 290 251 218

207 185 163 142 124

310 278 245 214 186

30 32 34 36 40

402 365 330 296 241

604 549 496 445 362

346 316 288 260 212

520 476 433 391 319

295 272 249 228 187

443 408 375 342 281

127 112 99.6 89.1

191 168 150 134

109 96.3 85.8 76.8

164 145 129 115

Properties 2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

31.1 4.43 3.49 LRFD

28.0 4.42 3.46

25.4 4.42 3.42

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

φc = 0.90

21.8 4.63 2.28

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

19.5 4.66 2.25

AISC_Part 4B:14th Ed.

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10:11 AM

Page 97

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–97

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT15× c

lb/ft

X-X Axis Y-Y Axis

c

62

Design

Effective length, KL (ft), with respect to indicated axis

WT15

54c

58

49.5c

45c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

327

492

292

439

256

384

214

322

159

239

10 12 14 16 18

318 314 309 304 298

478 472 465 457 448

284 280 277 272 267

427 422 416 409 401

249 246 243 239 235

374 370 365 360 354

209 207 204 202 198

314 311 307 303 298

156 155 153 152 150

235 233 231 228 225

20 22 24 26 28

291 284 277 269 261

438 427 416 404 392

261 255 249 242 235

393 384 374 364 353

231 226 220 215 209

347 339 331 323 314

195 191 187 183 178

293 287 281 275 268

147 145 143 140 137

222 218 214 210 206

30 32 34 36 40

252 243 234 224 205

379 365 351 337 309

228 220 212 204 188

342 331 319 307 282

203 196 190 183 169

305 295 285 275 255

173 168 163 158 147

261 253 245 238 221

134 131 127 124 117

201 196 192 186 176

0

327

492

292

439

256

384

214

322

159

239

10 12 14 16 18

253 244 231 216 199

381 366 347 325 300

221 213 203 190 176

332 320 305 286 265

187 181 173 163 152

282 272 260 245 228

152 147 141 134 125

229 222 212 201 188

115 112 109 104 98.9

173 169 163 157 149

20 22 24 26 28

182 164 146 129 113

273 247 220 194 169

161 146 130 115 101

242 219 196 173 152

139 126 114 101 88.5

209 190 171 152 133

116 106 95.3 85.1 75.2

174 159 143 128 113

92.9 86.4 79.6 72.6 65.7

140 130 120 109 98.7

100 89.3 80.0

58.7 52.5 47.2

88.3 79.0 70.9

30 32 34 36

99.1 87.7 78.2 70.1

149 132 118 105

88.8 78.8 70.3 63.1

133 118 106 94.8

78.2 69.5 62.2

118 105 93.4

66.6 59.4 53.2

Properties 2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

18.2 4.66 2.23 LRFD

17.1 4.67 2.19

15.9 4.69 2.15

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

φc = 0.90

14.5 4.71 2.10

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

13.2 4.69 2.09

AISC_Part 4B:14th Ed.

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10:12 AM

Page 98

4–98

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT13.5 Shape

WT13.5×

lb/ft

129

117.5

Pn /Ωc φc Pn

X-X Axis Y-Y Axis

108.5

Pn /Ωc φc Pn Pn /Ωc

97c

89c

80.5 c

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1140

1710

1040

1560

958

1440

819

1230

736

1110

605

909

10 12 14 16 18

1070 1040 1000 965 924

1610 1560 1510 1450 1390

973 945 913 878 839

1460 1420 1370 1320 1260

896 870 840 807 771

1350 1310 1260 1210 1160

767 746 721 693 663

1150 1120 1080 1040 997

692 673 651 627 601

1040 1010 979 943 904

571 557 541 522 502

859 837 813 785 755

20 22 24 26 28

879 832 784 734 684

1320 1250 1180 1100 1030

798 756 711 666 620

1200 1140 1070 1000 932

732 692 651 609 566

1100 1040 978 915 851

632 598 563 528 492

949 899 847 794 740

573 544 514 483 451

862 818 772 725 678

481 458 435 411 386

723 689 654 617 580

30 32 34 36 40

635 585 537 490 402

954 880 807 737 604

575 530 486 443 362

864 796 730 666 544

524 482 441 401 327

787 724 663 603 492

457 421 387 353 290

686 633 581 531 435

420 388 358 328 270

631 584 538 493 406

361 336 312 288 242

543 506 469 433 364

Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

0

1140

1710

1040

1560

958

1440

819

1230

736

1110

605

909

10 12 14 16 18

1010 967 922 874 822

1510 1450 1390 1310 1230

908 872 832 788 740

1360 1310 1250 1180 1110

832 800 763 722 679

1250 1200 1150 1090 1020

703 683 657 624 588

1060 1030 987 938 884

616 601 580 553 522

925 904 872 831 784

502 493 478 459 436

755 740 719 690 655

20 22 24 26 28

767 711 653 596 540

1150 1070 982 896 812

690 639 587 535 484

1040 960 882 804 727

633 586 538 490 443

951 880 808 737 666

549 508 467 426 386

825 764 702 640 579

488 452 416 379 343

733 679 625 570 516

411 383 355 326 298

617 576 534 491 448

30 32 34 36 40

486 433 384 343 278

730 651 577 515 418

434 386 343 306 249

653 581 515 460 374

398 353 314 280 228

598 531 472 421 342

346 308 274 245 199

520 463 411 368 299

308 274 244 218 178

463 412 366 328 267

270 243 217 194 158

406 365 326 292 238

Properties 2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

38.1 4.02 3.36 LRFD

34.7 4.00 3.33 c

32.0 3.96 3.32

28.6 3.94 3.29

Shape is slender for compression with Fy = 50 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

26.3 3.97 3.25

23.8 3.95 3.23

AISC_Part 4B:14th Ed.

2/23/11

10:12 AM

Page 99

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–99

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT13.5× c

lb/ft

73

X-X Axis Y-Y Axis

64.5

Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to indicated axis

WT13.5

c

c

57

Pn /Ωc φc Pn Pn /Ωc

51c

47c

42c

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

649

351

527

262

394

217

326

176

264

412 403 394 383 371

619 606 592 575 557

336 330 322 314 305

505 496 485 472 459

253 249 244 239 233

380 374 367 359 350

210 207 204 200 196

316 311 306 300 294

171 169 166 163 160

257 253 250 245 241

604 578 551 524 495

358 344 329 314 298

538 517 495 472 449

296 285 274 263 251

444 429 412 395 377

227 220 213 206 198

341 331 320 309 297

191 186 180 175 169

287 279 271 263 254

157 153 149 145 140

235 230 224 218 211

310 291 272 253 216

467 438 409 381 325

283 267 250 235 203

425 401 376 352 305

239 227 214 202 177

359 341 322 303 266

190 181 173 165 148

285 273 260 247 222

163 156 150 143 130

245 235 225 216 196

136 131 126 121 111

204 197 190 182 167

ASD

LRFD

ASD

0

493

742

432

10 12 14 16 18

469 458 446 433 418

704 689 670 650 628

20 22 24 26 28

402 385 367 348 330

30 32 34 36 40

LRFD

ASD

LRFD

0

493

742

432

649

351

527

262

394

217

326

176

264

10 12 14 16 18

406 399 390 377 361

610 600 586 566 542

341 321 296 269 242

513 482 445 405 363

270 256 239 220 199

406 385 359 330 298

204 195 185 172 158

306 294 277 258 238

167 161 153 144 133

251 242 230 216 200

130 126 121 115 107

196 190 182 172 161

20 22 24 26 28

342 321 300 278 256

514 483 451 418 385

214 186 160 137 119

321 280 240 206 179

177 156 135 117 101

266 234 204 175 152

143 129 114 100 87.1

216 193 172 150 131

122 110 98.9 87.7 76.8

183 166 149 132 115

30 32 34 36 40

234 212 192 172 140

352 319 288 258 211

104 91.8 81.6 72.9

156 138 123 110

88.9 134 78.6 118 69.9 105 62.6 94.0

76.5 115 67.7 102 60.3 90.6

67.6 102 59.9 90.0 53.4 80.3

15.0 4.14 2.15

13.8 4.16 2.12

98.7 90.1 81.3 72.7 64.1

148 135 122 109 96.4

56.6 50.3 45.0

85.1 75.7 67.6

Properties 2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

21.6 3.95 3.20 LRFD φc = 0.90

18.9 4.13 2.21

16.8 4.15 2.18

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

12.4 4.18 2.07

AISC_Part 4B:14th Ed.

2/23/11

10:12 AM

Page 100

4–100

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT12 Shape

WT12× h

lb/ft

185

167.5

Pn /Ωc φc Pn

X-X Axis

Design

Y-Y Axis

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

h

h

139.5h

153

Pn /Ωc φc Pn Pn /Ωc

φc Pn

Pn /Ωc φc Pn

125 Pn /Ωc φc Pn

114.5 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1630

2450

1470

2210

1340

2020

1230

1850

1100

1660

1010

1510

10 12 14 16 18

1520 1470 1410 1350 1290

2280 2210 2120 2030 1930

1360 1320 1270 1210 1150

2050 1980 1900 1820 1730

1240 1200 1160 1100 1050

1870 1810 1740 1660 1570

1130 1100 1050 1000 950

1700 1650 1580 1510 1430

1020 981 940 896 848

1530 1470 1410 1350 1270

927 894 856 815 771

1390 1340 1290 1230 1160

20 22 24 26 28

1220 1140 1070 992 916

1830 1720 1600 1490 1380

1090 1020 951 881 812

1630 1530 1430 1320 1220

987 925 861 797 733

1480 1390 1290 1200 1100

895 837 779 719 661

1340 1260 1170 1080 993

798 745 692 638 585

1200 1120 1040 959 879

724 676 627 577 528

1090 1020 942 868 794

30 32 34 36 40

841 767 696 627 508

1260 1150 1050 943 764

744 677 613 550 446

1120 1020 921 827 670

670 609 550 492 399

1010 915 827 740 599

603 546 492 440 356

906 821 740 661 536

532 482 433 386 313

800 724 651 581 470

480 434 389 347 281

722 652 584 521 422

0

1630

2450

1470

2210

1340

2020

1230

1840

1100

1660

1010

1510

10 12 14 16 18

1460 1400 1330 1260 1180

2200 2110 2000 1890 1770

1310 1260 1190 1120 1050

1970 1890 1790 1690 1580

1190 1140 1080 1020 952

1800 1720 1630 1530 1430

1090 1040 984 925 862

1630 1560 1480 1390 1300

969 926 877 823 767

1460 1390 1320 1240 1150

879 839 794 745 693

1320 1260 1190 1120 1040

20 22 24 26 28

1090 1010 919 833 750

1640 1510 1380 1250 1130

972 894 815 738 662

1460 1340 1230 1110 995

881 809 737 665 596

1320 1220 1110 1000 896

797 731 664 599 535

1200 1100 998 900 805

708 648 588 529 472

1060 974 884 796 710

639 584 529 476 424

961 878 796 715 637

30 32 34 36 40

669 591 524 468 379

1010 889 788 703 570

589 520 460 411 333

886 781 692 618 501

529 466 413 369 299

796 700 621 554 449

474 417 370 330 268

713 627 556 496 402

417 367 325 290 236

627 552 489 437 354

373 328 291 260 211

561 493 438 391 317

Properties 2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

54.5 3.78 3.27 LRFD φc = 0.90

49.1 3.73 3.23 h

44.9 3.69 3.20

41.0 3.65 3.17

36.8 3.61 3.14

33.6 3.58 3.11

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 4B:14th Ed.

2/23/11

10:12 AM

Page 101

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–101

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT12×

lb/ft

103.5

X-X Axis Y-Y Axis

96

88

73c

81

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

907

1360

844

1270

772

1160

716

1080

605

909

10 12 14 16 18

834 804 770 733 692

1250 1210 1160 1100 1040

776 748 715 680 642

1170 1120 1080 1020 965

709 683 653 621 586

1070 1030 982 933 880

657 632 605 574 542

987 950 909 863 814

558 539 516 492 466

839 810 776 740 700

20 22 24 26 28

649 605 561 516 471

976 910 843 775 708

602 561 519 477 435

905 843 780 717 654

549 511 472 433 395

825 768 710 652 594

507 472 436 400 365

763 709 656 602 548

438 409 380 350 321

658 615 571 527 483

30 32 34 36 40

428 386 345 308 249

643 580 518 462 374

395 355 317 283 229

593 534 477 425 345

358 322 287 256 207

538 484 431 385 312

330 297 264 236 191

496 446 397 354 287

292 265 238 212 172

440 398 357 319 258

Design

Effective length, KL (ft), with respect to indicated axis

WT12

0

907

1360

844

1270

772

1160

716

1080

605

909

10 12 14 16 18

787 751 710 665 618

1180 1130 1070 1000 929

728 694 657 616 572

1090 1040 987 925 860

660 629 594 557 517

991 945 893 837 777

605 577 546 512 476

909 867 821 770 715

504 488 466 439 410

758 734 701 660 616

20 22 24 26 28

570 520 470 422 375

856 781 707 634 563

527 481 435 390 346

792 722 653 586 520

475 433 391 350 310

715 651 588 526 467

438 400 362 324 288

659 602 544 488 433

378 345 313 281 250

568 519 470 422 375

30 32 34 36 40

329 290 257 230 186

495 436 387 345 280

304 268 237 212 172

457 402 357 319 259

272 240 213 190 154

409 360 320 286 232

253 223 198 177 144

380 335 297 266 216

220 194 172 154 125

330 291 259 231 188

Properties 2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

30.3 3.55 3.08 LRFD

28.2 3.53 3.07 c

25.8 3.51 3.04

23.9 3.50 3.05

Shape is slender for compression with Fy = 50 ksi.

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

21.5 3.50 3.01

AISC_Part 4B:14th Ed.

2/23/11

10:12 AM

Page 102

4–102

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT12 Shape

WT12× c

lb/ft

X-X Axis Y-Y Axis

c

65.5

52c

58.5

51.5c

47c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

511

769

409

615

317

476

349

525

292

439

10 12 14 16 18

474 459 441 422 401

713 690 663 634 602

382 371 358 344 328

574 557 538 517 493

299 291 282 272 262

449 438 424 410 393

329 320 310 299 287

494 481 467 450 432

276 270 262 254 244

415 405 394 381 367

20 22 24 26 28

379 355 332 308 284

569 534 498 462 426

312 294 277 258 240

468 443 416 388 361

250 238 225 213 199

376 358 339 319 300

274 261 247 232 218

412 392 371 349 327

234 224 212 201 189

352 336 319 302 285

30 32 34 36 40

260 237 214 193 156

391 356 322 289 234

222 204 187 170 138

334 307 280 255 208

186 173 160 147 123

280 260 240 221 185

203 188 174 160 133

305 283 261 240 199

178 166 154 143 121

267 249 232 215 181

Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

0

511

769

409

615

317

476

349

525

292

439

10 12 14 16 18

416 405 389 369 345

625 608 585 554 519

327 320 310 297 280

491 481 466 446 422

249 246 240 232 221

375 369 360 348 333

267 246 222 197 171

401 369 333 296 258

223 207 189 169 149

335 311 284 255 225

20 22 24 26 28

320 294 267 241 215

481 442 402 362 323

262 243 223 203 183

394 365 335 305 275

209 196 182 167 153

314 294 273 252 230

147 124 105 89.6 77.6

221 186 157 135 117

130 110 93.7 80.4 69.7

195 166 141 121 105

30 32 34 36 40

190 168 149 134 109

286 252 224 201 164

164 145 129 116 94.5

246 218 194 174 142

139 125 111 100 81.7

208 188 167 150 123

67.8 59.8

102 89.8

61.0 53.8

Properties 2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

19.3 3.52 2.97 LRFD

17.2 3.51 2.94

15.3 3.51 2.91

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

φc = 0.90

15.1 3.67 1.99

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

13.8 3.67 1.98

91.7 80.9

AISC_Part 4B:14th Ed.

2/23/11

10:12 AM

Page 103

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–103

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT12× c

lb/ft

X-X Axis Y-Y Axis

c

42

34c

38

31c

27.5c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

225

338

180

271

146

219

142

214

109

163

10 12 14 16 18

215 210 205 199 193

323 316 308 300 290

173 170 166 162 157

260 255 249 243 236

140 138 135 132 129

211 207 203 199 194

137 135 132 129 126

206 203 199 194 189

105 104 102 99.9 97.7

158 156 153 150 147

20 22 24 26 28

186 179 171 163 155

280 269 257 245 233

152 147 142 136 130

229 221 213 204 195

125 121 117 113 109

188 183 176 170 163

122 118 114 110 105

184 178 172 165 159

95.3 92.8 90.0 87.1 84.1

143 139 135 131 126

30 32 34 36 40

147 139 130 122 105

221 208 196 183 158

124 117 111 105 92.3

186 176 167 158 139

104 99.2 94.5 89.6 80.0

156 149 142 135 120

101 96.2 91.5 86.7 77.2

152 145 138 130 116

81.0 77.8 74.5 71.1 64.4

122 117 112 107 96.8

0

225

338

180

271

146

219

142

214

10 12 14 16 18

172 162 150 137 122

258 244 226 205 184

136 130 121 112 101

205 195 182 168 152

107 102 96.3 89.3 81.5

160 154 145 134 122

90.2 80.9 70.4 59.7 49.3

136 122 106 89.7 74.1

68.2 62.0 54.9 47.4 39.9

103 93.2 82.6 71.3 59.9

20 22 24 26 28

108 94.0 80.5 69.3 60.2

162 141 121 104 90.4

90.4 79.8 69.3 59.8 52.1

136 120 104 89.9 78.3

73.4 65.2 57.2 49.5 43.3

110 98.0 85.9 74.5 65.1

41.0 34.5

61.6 51.9

33.4 28.3

50.2 42.5

30 32

52.7 46.6

79.3 70.0

45.7 40.4

68.7 60.7

38.1

57.3

Design

Effective length, KL (ft), with respect to indicated axis

WT12

109

163

Properties 2

12.4 3.67 1.95

ASD

LRFD

Ωc = 1.67

φc = 0.90

Ag , in. rx , in. ry , in.

11.2 3.68 1.92

10.00 3.70 1.87

9.11 3.79 1.38

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.10 3.80 1.34

AISC_Part 4B:14th Ed.

2/23/11

10:12 AM

Page 104

4–104

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT10.5 Shape

WT10.5×

lb/ft

100.5 Pn /Ωc φc Pn

X-X Axis

Design

Y-Y Axis

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

91 83 Pn /Ωc φc Pn Pn /Ωc φc Pn

73.5 Pn /Ωc φc Pn

66 Pn /Ωc φc Pn

61 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

886

1330

802

1210

731

1100

647

972

581

873

535

ASD

LRFD 804

10 12 14 16 18

794 757 715 669 621

1190 1140 1070 1010 934

718 683 645 603 559

1080 1030 969 906 840

652 620 584 546 505

980 932 878 820 759

579 551 520 487 451

870 828 782 732 678

519 494 466 436 403

780 742 700 655 606

477 454 428 400 370

717 682 643 601 556

20 22 24 26 28

572 521 471 423 375

859 784 709 635 564

513 467 422 377 334

771 702 634 567 502

463 421 379 338 299

696 633 570 508 449

415 378 341 305 271

624 568 513 459 407

370 337 304 272 241

557 507 457 408 362

339 308 278 248 219

510 464 418 373 330

30 32 34 36 40

330 290 257 229 186

496 436 386 344 279

293 257 228 203 165

440 387 343 306 248

262 230 204 182 147

393 345 306 273 221

238 209 185 165 134

357 314 278 248 201

211 185 164 146 119

317 278 247 220 178

192 169 149 133 108

288 253 225 200 162

0

886

1330

802

1210

731

1100

647

972

581

873

535

804

10 12 14 16 18

774 737 695 649 601

1160 1110 1040 975 903

697 663 625 583 540

1050 996 939 877 811

632 601 566 528 489

949 903 851 794 734

548 521 491 458 423

824 783 738 688 636

486 462 435 406 375

730 694 654 610 563

439 423 401 375 346

660 636 603 563 519

20 22 24 26 28

551 501 451 402 355

828 753 678 605 534

494 449 404 360 317

743 675 607 541 477

448 406 365 325 287

673 611 549 489 431

387 351 315 280 246

582 527 473 420 370

343 311 279 247 217

515 467 419 372 326

315 285 254 225 196

474 428 382 338 295

30 32 34 36 40

311 273 242 216 175

467 411 364 325 264

277 244 216 193 157

417 367 325 290 235

251 220 195 175 142

377 331 294 262 213

215 189 168 150 122

323 284 252 225 183

190 167 148 132 108

285 251 223 199 162

172 151 134 120 97.6

258 227 202 181 147

Properties 2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

29.6 3.10 3.02 LRFD

26.8 3.07 3.00

24.4 3.04 2.99

21.6 3.08 2.95

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

19.4 3.06 2.93

17.9 3.04 2.91

AISC_Part 4B:14th Ed.

2/23/11

10:12 AM

Page 105

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–105

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT10.5×

lb/ft

55.5

c

50.5

Pn /Ωc φc Pn

X-X Axis

Design

Y-Y Axis

Effective length, KL (ft), with respect to indicated axis

WT10.5

c

c

46.5

Pn /Ωc φc Pn Pn /Ωc

41.5c

36.5c

34c

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

552

396

596

312

469

233

351

197

296

334 320 305 288 270

502 481 458 432 405

360 345 328 310 290

541 518 493 465 436

286 275 263 250 236

430 414 396 376 354

217 210 202 193 183

325 315 303 290 275

184 178 172 165 158

276 268 259 249 238

441 404 367 330 295

251 231 212 192 174

377 348 318 289 261

270 249 228 207 186

405 374 342 311 280

221 205 189 174 158

331 308 285 261 238

173 163 152 141 130

260 245 228 212 196

150 142 133 125 116

226 213 200 187 174

174 153 135 121 97.6

261 229 203 181 147

155 138 122 109 88.1

233 207 183 163 132

167 148 131 117 94.4

250 222 196 175 142

143 128 114 102 82.5

215 193 172 153 124

119 109 98.7 88.8 71.9

179 164 148 133 108

107 98.5 90.1 82.0 66.8

161 148 135 123 100

ASD

LRFD

ASD

0

447

671

368

10 12 14 16 18

402 384 364 341 318

604 577 546 513 478

20 22 24 26 28

294 269 244 220 196

30 32 34 36 40

LRFD

ASD

LRFD

0

447

671

368

552

396

596

312

469

233

351

197

296

10 12 14 16 18

364 354 338 318 296

547 531 508 478 445

298 292 281 267 251

448 438 422 401 377

276 243 209 175 142

415 366 314 263 214

222 199 174 149 124

334 299 262 223 186

170 155 138 121 103

256 233 208 181 155

145 134 121 107 92.6

218 201 181 160 139

20 22 24 26 28

272 248 223 199 176

409 372 336 300 265

233 214 195 176 157

350 321 293 264 237

117 97.0 81.9 70.1 60.6

175 102 153 146 84.9 128 123 71.8 108 105 61.4 92.4 91.1 53.2 79.9

30 32 34 36 40

154 136 121 108 88.1

232 205 182 163 132

139 123 109 97.9 79.7

210 185 165 147 120

52.9

79.6

46.5

69.8

86.4 130 72.2 108 61.1 91.9 52.4 78.8 45.4 68.2

78.9 119 66.2 99.5 56.1 84.4 48.2 72.4 41.8 62.8

39.7

36.5

59.7

54.9

Properties 2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

16.3 3.03 2.90 LRFD φc = 0.90

14.9 3.01 2.89

13.7 3.25 1.84

12.2 3.22 1.83

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

10.7 3.21 1.81

10.0 3.20 1.80

AISC_Part 4B:14th Ed.

2/23/11

10:12 AM

Page 106

4–106

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT10.5 Shape

WT10.5× c

lb/ft

X-X Axis

c

27.5 24 Pn /Ωc φc Pn Pn /Ωc φc Pn

28.5c Pn /Ωc φc Pn

25c Pn /Ωc φc Pn

22c Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

158

238

127

190

98.0

147

150

225

117

177

90.0

135

10 12 14 16 18

149 145 141 136 131

224 218 212 204 196

120 117 114 111 107

181 176 172 166 160

93.6 91.7 89.6 87.1 84.5

141 138 135 131 127

141 138 134 129 124

212 207 201 194 186

112 109 106 103 99.4

168 164 160 155 149

86.1 84.4 82.5 80.3 77.9

129 127 124 121 117

20 22 24 26 28

125 119 113 106 99.5

188 179 169 159 150

103 98.1 93.5 88.7 83.8

154 147 140 133 126

81.6 78.5 75.3 71.9 68.4

123 118 113 108 103

119 113 107 101 94.9

178 170 161 152 143

95.6 91.5 87.3 82.9 78.4

144 138 131 125 118

75.3 72.5 69.6 66.6 63.5

113 109 105 100 95.4

30 32 34 36 40

92.9 86.4 79.9 73.5 61.4

133 124 115 106 88.8

73.9 111 69.3 104 64.7 97.3 60.2 90.5 51.5 77.4

60.3 57.0 53.8 50.5 44.1

90.6 85.7 80.8 76.0 66.4

0

Y-Y Axis

c

31 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

10 12 14 16 18 20 22 24 26 28

140 130 120 111 92.2

158

238

117 109 99.6 89.2 78.5

176 164 150 134 118

78.8 118 73.8 111 68.9 103 64.0 96.1 54.5 81.9 127

67.9 102 57.7 86.7 49.0 73.7 42.2 63.4 36.6 55.0

64.9 61.3 57.7 54.1 47.0

97.5 92.1 86.7 81.3 70.7

190

98.0

147

90.7 85.4 78.8 71.3 63.4

136 128 118 107 95.3

66.7 63.3 58.9 53.7 48.2

100 95.1 88.5 80.8 72.4

55.4 47.6 40.6 35.1 30.5

83.3 71.5 61.1 52.7 45.9

42.4 36.7 31.6 27.4

63.8 55.2 47.5 41.2

88.7 82.5 76.5 70.5 59.1 150

225

117

177

90.0

135

96.2 145 83.4 125 70.1 105 57.1 85.9 46.0 69.2

73.3 110 64.3 96.6 54.6 82.0 44.9 67.5 36.5 54.8

55.3 49.2 42.5 35.7 29.3

83.1 74.0 63.9 53.6 44.0

37.8 31.5

30.1

24.3

36.6

56.8 47.4

45.3

Properties 2

Ag , in. rx , in. ry , in.

9.13 3.21 1.77

ASD

LRFD

Ωc = 1.67

φc = 0.90

8.10 3.23 1.73

7.07 3.26 1.66

8.37 3.29 1.35

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7.36 3.30 1.30

6.49 3.31 1.26

AISC_Part 4B:14th Ed.

2/23/11

10:12 AM

Page 107

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–107

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT9×

lb/ft

87.5 Pn /Ωc φc Pn

X-X Axis

Design

Y-Y Axis

Effective length, KL (ft), with respect to indicated axis

WT9

79 71.5 Pn /Ωc φc Pn Pn /Ωc φc Pn

65 Pn /Ωc φc Pn

59.5 Pn /Ωc φc Pn ASD

LRFD

53 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

769

1160

695

1040

629

945

575

864

527

792

467

702

10 12 14 16 18

663 621 575 526 475

997 933 864 790 714

597 558 515 470 424

897 839 775 707 638

538 502 463 422 380

809 755 696 634 571

491 458 422 383 344

738 688 634 576 518

451 421 388 354 318

678 633 584 532 478

399 373 343 313 281

600 560 516 470 422

20 22 24 26 28

424 374 327 281 242

638 563 491 422 364

378 332 289 248 214

568 500 434 372 321

337 296 256 219 189

507 445 385 329 284

305 267 231 197 170

459 402 347 297 256

283 248 215 184 158

425 373 323 276 238

249 219 189 162 139

375 328 284 243 209

30 32 34 36 40

211 185 164 146 119

317 279 247 220 178

186 164 145 129 105

280 246 218 194 157

165 145 128 114 92.6

247 217 193 172 139

148 130 115 103 83.4

223 196 173 155 125

138 121 107 95.8 77.6

207 182 161 144 117

121 107 94.5 84.3 68.3

182 160 142 127 103

0

769

1160

695

1040

629

945

575

864

527

792

467

702

10 12 14 16 18

661 622 580 534 487

993 936 871 803 732

594 559 520 479 436

892 840 782 720 655

535 503 468 430 391

804 756 703 647 588

486 457 424 390 354

730 686 638 586 532

440 414 385 354 321

662 622 578 532 483

385 362 336 308 280

578 544 505 464 421

20 22 24 26 28

439 391 345 300 259

659 588 518 452 390

392 349 307 267 230

589 525 462 401 346

352 312 274 238 205

528 470 412 358 309

318 282 247 214 185

478 424 372 322 278

288 256 224 194 168

433 385 337 292 252

251 222 194 168 145

377 334 292 252 218

30 32 34 36 40

226 199 176 157 127

340 299 265 236 191

201 177 157 140 113

302 266 235 210 170

179 158 140 125 101

269 237 210 187 152

161 142 126 112 91.0

242 213 189 169 137

146 129 114 102 82.6

220 193 172 153 124

126 111 98.7 88.2 71.5

190 167 148 133 108

Properties 2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

25.7 2.66 2.76 LRFD

23.2 2.63 2.74

21.0 2.60 2.72

19.2 2.58 2.70

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

17.6 2.60 2.69

15.6 2.59 2.66

AISC_Part 4B:14th Ed.

2/23/11

10:13 AM

Page 108

4–108

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT9 Shape

WT9×

lb/ft

c

48.5

X-X Axis Y-Y Axis

c

43

Pn /Ωc φc Pn

38

Pn /Ωc φc Pn Pn /Ωc

35.5c

32.5c

30c

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

425

639

356

534

274

412

299

450

250

376

210

315

10 12 14 16 18

362 337 310 282 253

544 507 466 424 380

306 286 264 241 218

459 430 397 363 327

239 226 210 194 177

360 339 316 292 266

262 246 230 212 193

393 370 345 319 291

221 209 196 182 167

332 314 295 273 251

187 178 168 157 145

281 267 252 235 218

20 22 24 26 28

224 195 169 144 124

336 294 253 216 186

194 171 149 128 110

292 257 223 192 165

160 143 126 110 95.3

240 215 190 166 143

175 156 138 120 104

262 234 207 181 156

152 137 122 108 94.1

229 206 184 162 141

133 121 109 97.1 85.9

200 182 164 146 129

30 32 34 36 40

108 94.9 84.0 75.0 60.7

162 143 126 113 91.2

Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

95.8 84.2 74.6 66.5 53.9

144 127 112 100 81.0

83.1 125 73.0 110 64.7 97.2 57.7 86.7 46.7 70.2

90.6 136 79.6 120 70.5 106 62.9 94.5 50.9 76.6

81.9 123 72.0 108 63.8 95.9 56.9 85.5 46.1 69.3

ASD

LRFD

75.1 113 66.0 99.2 58.5 87.9 52.2 78.4 42.3 63.5

0

425

639

356

534

274

412

299

450

250

376

210

315

10 12 14 16 18

347 327 303 279 253

522 491 456 419 380

287 274 258 238 217

431 412 387 358 326

219 212 202 189 174

330 319 304 284 262

200 173 144 117 93.5

301 259 217 176 140

171 150 127 105 84.4

258 225 191 158 127

147 130 112 93.7 76.6

221 195 168 141 115

20 22 24 26 28

226 200 175 151 131

340 301 263 227 196

195 173 152 132 114

293 260 229 198 172

159 143 127 112 97.7

238 215 191 169 147

30 32 34 36 40

114 100 89.1 79.6 64.6

171 151 134 120 97.0

99.8 88.0 78.1 69.8 56.7

150 132 117 105 85.2

76.3 115 63.3 95.2 53.4 80.3 45.7 68.6 39.5 59.3

68.9 104 57.3 86.1 48.4 72.7 41.3 62.1 35.7 53.7

10.4 2.74 1.70

9.55 2.72 1.69

62.6 52.1 44.0 37.6 32.6

94.1 78.3 66.1 56.6 48.9

85.4 128 75.4 113 66.9 101 59.9 90.0 48.7 73.1 Properties

2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

14.2 2.56 2.65 LRFD φc = 0.90

12.7 2.55 2.63

11.1 2.54 2.61

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.82 2.71 1.68

AISC_Part 4B:14th Ed.

2/23/11

10:13 AM

Page 109

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–109

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT9× c

lb/ft

X-X Axis

23c

25

20c

17.5c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

178

267

136

205

129

193

87.3

131

70.9

107

10 12 14 16 18

160 153 145 136 127

241 230 218 204 190

125 120 114 108 102

187 180 172 163 153

118 114 109 103 97.1

177 171 163 155 146

81.5 79.1 76.3 73.3 69.9

123 119 115 110 105

66.6 64.8 62.7 60.4 57.9

100 97.4 94.3 90.8 87.1

20 22 24 26 28

117 107 97.1 87.4 78.0

176 161 146 131 117

95.2 88.3 81.3 74.4 67.5

143 133 122 112 101

90.8 84.4 77.9 71.4 65.0

137 127 117 107 97.7

66.4 62.7 58.8 54.9 51.0

99.8 94.2 88.4 82.6 76.7

55.3 52.5 49.5 46.6 43.5

83.1 78.8 74.5 70.0 65.4

30 32 34 36 40

69.0 60.6 53.7 47.9 38.8

104 91.1 80.7 72.0 58.3

60.9 54.5 48.3 43.1 34.9

58.8 52.7 46.9 41.8 33.9

88.3 79.3 70.5 62.9 50.9

47.1 43.3 39.5 35.9 29.2

70.8 65.0 59.4 54.0 43.9

40.5 37.5 34.5 31.7 26.2

60.9 56.4 51.9 47.6 39.3

0

Y-Y Axis

c

27.5

Design

Effective length, KL (ft), with respect to indicated axis

WT9

178

267

10 12 14 16 18

125 112 97.5 82.8 68.7

188 168 147 125 103

20 22 24 26

56.3 47.0 39.7 34.0

136

84.7 70.6 59.7 51.1

91.5 81.9 72.6 64.8 52.5 205

129

193

87.3

131

70.9

107

98.8 90.0 80.0 69.6 59.3

149 135 120 105 89.1

80.0 67.5 55.0 43.4 34.7

120 101 82.6 65.2 52.2

58.3 51.0 43.3 35.8 28.8

87.7 76.6 65.1 53.7 43.4

45.0 39.6 33.7 27.9 22.6

67.6 59.4 50.6 41.9 34.0

49.4 41.2 34.9 29.9

74.2 62.0 52.5 45.0

28.4

42.6

23.6

35.5

18.7

28.0

Properties 2

Ag , in. rx , in. ry , in.

8.10 2.71 1.67

ASD

LRFD

Ωc = 1.67

φc = 0.90

7.34 2.70 1.65

6.77 2.77 1.29

5.88 2.76 1.27

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5.15 2.79 1.22

AISC_Part 4B:14th Ed.

2/23/11

10:13 AM

Page 110

4–110

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT8 Shape

WT8×

lb/ft

50

X-X Axis

38.5

Pn /Ωc φc Pn Pn /Ωc

33.5c

28.5c

25c

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

440

662

392

590

334

501

252

379

236

355

182

273

10 12 14 16 18

359 329 296 262 228

540 494 445 394 343

320 292 263 232 202

481 439 395 349 304

271 248 222 196 171

408 372 334 295 256

210 194 176 158 139

316 291 265 237 209

199 185 169 153 136

299 278 254 229 204

156 146 135 124 112

235 220 203 186 168

20 22 24 26 28

196 165 138 118 102

294 248 208 177 153

173 146 122 104 89.9

260 219 184 157 135

146 122 103 87.5 75.5

219 184 154 132 113

121 104 87.6 74.7 64.4

182 119 156 104 132 88.3 112 75.2 96.7 64.9

30 32 34 36 40

Y-Y Axis

c

44.5

Pn /Ωc φc Pn Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

88.6 133 77.9 117 69.0 104 61.5 92.5

78.3 118 68.8 103 61.0 91.6 54.4 81.7

65.8 57.8 51.2 45.7

98.8 86.9 76.9 68.6

56.1 49.3 43.7 38.9

84.3 74.1 65.6 58.5

56.5 49.7 44.0 39.2 31.8

180 156 133 113 97.5 84.9 74.7 66.1 59.0 47.8

ASD

LRFD

99.5 150 87.7 132 76.4 115 65.5 98.5 56.5 84.9 49.2 43.3 38.3 34.2 27.7

74.0 65.0 57.6 51.4 41.6

0

440

661

392

589

334

501

252

379

236

355

182

273

10 12 14 16 18

362 337 310 281 252

545 507 466 423 378

319 297 273 247 221

480 447 410 372 332

269 252 232 210 188

404 379 349 316 282

204 194 182 167 151

306 292 273 251 227

153 130 106 84.4 67.2

230 195 160 127 101

122 106 88.7 72.4 57.9

184 159 133 109 87.0

20 22 24 26 28

222 193 166 142 122

334 291 249 213 184

195 170 145 124 107

293 255 218 186 161

165 143 122 105 90.4

248 215 184 157 136

135 119 104 89.6 77.5

203 179 157 135 117

54.8 45.5 38.3 32.7

47.2 39.2 33.1 28.3

71.0 59.0 49.8 42.5

30 32 34 36 40

107 93.8 83.2 74.2 60.2

160 141 125 112 90.5

93.4 140 82.2 123 72.8 109 65.0 97.7 52.7 79.3

78.9 119 69.5 104 61.6 92.6 55.0 82.7 44.7 67.1

82.3 68.3 57.6 49.2

67.7 102 59.7 89.7 52.9 79.6 47.3 71.1 38.4 57.7

Properties 2

Ag , in. rx , in. ry , in. ASD Ωc = 1.67

14.7 2.28 2.51 LRFD φc = 0.90

13.1 2.27 2.49

11.3 2.24 2.47

9.81 2.22 2.46

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.39 2.41 1.60

7.37 2.40 1.59

AISC_Part 4B:14th Ed.

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10:13 AM

Page 111

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–111

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT8× c

lb/ft

X-X Axis

18c

20

15.5c

13c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

144

216

102

153

87.6

132

65.4

98.3

46.6

70.1

10 12 14 16 18

126 118 111 102 93.2

189 178 166 153 140

91.6 87.3 82.5 77.3 71.8

138 131 124 116 108

79.2 75.8 72.0 67.8 63.3

119 114 108 102 95.1

60.1 57.9 55.5 52.7 49.8

90.4 87.1 83.4 79.3 74.9

43.5 42.2 40.7 39.0 37.2

65.4 63.4 61.1 58.6 55.9

20 22 24 26 28

84.2 75.3 66.6 58.3 50.4

127 113 100 87.6 75.8

66.1 60.4 54.6 49.0 43.6

99.4 90.8 82.1 73.7 65.5

58.7 53.9 49.2 44.5 39.9

88.2 81.0 73.9 66.8 60.0

46.7 43.5 40.3 37.1 33.8

70.2 65.4 60.6 55.7 50.9

35.2 33.2 31.2 29.1 26.9

53.0 50.0 46.8 43.7 40.5

30 32 34 36 40

43.9 38.6 34.2 30.5

66.0 58.0 51.4 45.8

38.4 33.7 29.9 26.6

57.7 50.7 44.9 40.0

35.5 31.3 27.7 24.7 20.0

53.4 47.1 41.7 37.2 30.1

30.7 27.7 24.7 22.0 17.9

46.1 41.6 37.1 33.1 26.8

24.8 22.8 20.8 18.8 15.3

37.3 34.2 31.2 28.3 23.0

65.4

98.3

46.6

70.1

41.7 35.7 29.6 23.8 19.1

62.7 53.7 44.6 35.7 28.7

29.2 25.5 21.6 17.6 14.3

43.9 38.3 32.4 26.5 21.5

0

0

Y-Y Axis

c

22.5

Design

Effective length, KL (ft), with respect to indicated axis

WT8

144

216

102

153

87.6

132

10 12 14 16 18

99.0 87.1 74.5 62.1 50.3

149 131 112 93.3 75.7

74.4 67.3 59.4 51.2 43.3

112 101 89.2 77.0 65.1

61.4 55.8 49.4 42.7 36.2

92.3 83.9 74.3 64.2 54.3

20 22 24 26

41.2 34.2 28.9 24.7

61.9 51.5 43.5 37.2

35.8 29.8 25.2 21.6

53.8 44.9 37.9 32.5

29.9 25.0 21.2

45.0 37.6 31.9

Properties 2

Ag , in. rx , in. ry , in.

6.63 2.39 1.57

5.89 2.37 1.56

5.29 2.41 1.52

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

ASD

LRFD

Ωc = 1.67

φc = 0.90

4.56 2.45 1.17

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.84 2.47 1.12

AISC_Part 4B:14th Ed.

2/23/11

10:13 AM

Page 112

4–112

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT7 Shape

WT7×

lb/ft

66 Pn /Ωc φc Pn

X-X Axis

Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

60 54.5 Pn /Ωc φc Pn Pn /Ωc φc Pn LRFD

49.5 Pn /Ωc φc Pn

45 Pn /Ωc φc Pn

ASD

LRFD

ASD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

581

873

530

797

479

720

437

657

395

594

359

540

10 12 14 16 18

409 350 291 236 187

614 526 438 355 281

370 316 262 211 167

556 474 393 317 251

330 280 231 184 145

496 421 347 277 219

300 254 209 166 131

450 381 313 250 197

270 228 187 148 117

405 343 281 223 176

264 231 197 163 132

397 347 295 246 199

20 22 24 26 28

152 125 105 89.7 77.3

228 188 158 135 116

135 112 93.8 79.9 68.9

203 168 141 120 104

118 97.4 81.8 69.7 60.1

177 106 160 146 87.8 132 123 73.8 111 105 62.9 94.5 90.4

94.9 143 107 161 78.4 118 88.6 133 65.9 99.1 74.4 112 56.2 84.4 63.4 95.3 54.7 82.2

30

Y-Y Axis

41 Pn /Ωc φc Pn

47.6

71.6

0

581

873

530

796

479

720

437

657

395

594

359

540

10 12 14 16 18

534 517 497 476 453

802 777 747 715 680

485 470 452 432 411

729 706 679 650 618

438 424 408 390 371

658 637 612 586 557

397 384 370 353 336

597 577 556 531 505

357 345 332 318 302

536 519 500 478 454

297 276 253 228 204

446 415 380 343 306

20 22 24 26 28

428 402 376 349 322

643 604 565 525 484

388 365 341 316 292

584 549 512 475 439

350 329 307 285 263

526 494 461 428 395

317 298 278 258 238

477 448 418 388 357

286 268 250 232 214

429 403 376 349 321

179 155 133 113 97.7

269 234 199 170 147

30 32 34 36 40

296 270 245 220 178

444 405 368 331 268

268 244 221 199 161

402 367 332 298 242

241 219 199 178 145

362 330 299 268 217

218 198 179 161 130

327 298 270 242 196

196 178 161 145 117

294 268 242 217 176

85.2 128 74.9 113 66.4 99.8 59.2 89.0 48.0 72.2

Properties 2

Ag , in. rx , in. ry , in.

19.4 1.73 3.76

ASD

LRFD

Ωc = 1.67

φc = 0.90

17.7 1.71 3.74

16.0 1.68 3.73

14.6 1.67 3.71

Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

13.2 1.66 3.70

12.0 1.85 2.48

AISC_Part 4B:14th Ed.

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10:13 AM

Page 113

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–113

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT7×

lb/ft

37

X-X Axis Y-Y Axis

c

34

Pn /Ωc φc Pn

30.5

Pn /Ωc φc Pn Pn /Ωc

26.5c

24c

21.5c

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

326

491

299

450

260

392

223

336

186

280

146

219

10 12 14 16 18

237 206 175 145 116

357 310 263 217 175

217 188 159 132 106

326 283 240 198 159

190 165 140 116 93.5

286 249 211 175 141

168 148 128 108 88.7

252 223 192 162 133

143 128 111 95.2 79.7

215 192 167 143 120

115 104 92.1 80.0 68.1

173 156 138 120 102

Design

Effective length, KL (ft), with respect to indicated axis

WT7

ASD

LRFD

20 22 24 26 28

94.2 142 77.9 117 65.4 98.3 55.7 83.8 48.1 72.02

85.5 128 70.7 106 59.4 89.2 50.6 76.0 43.6 65.6

75.8 114 62.6 94.1 52.6 79.1 44.8 67.4 38.7 58.1

71.9 108 59.5 89.4 50.0 75.1 42.6 64.0 36.7 55.2

65.2 53.9 45.3 38.6 33.3

98.0 81.0 68.1 58.0 50.0

57.0 47.1 39.6 33.7 29.1

85.6 70.8 59.5 50.7 43.7

30

41.9

38.0

33.7

32.0

29.0

43.6

25.3

38.1

62.9

57.1

50.6

48.1

0

326

490

299

450

260

392

223

336

186

280

146

219

10 12 14 16 18

269 250 229 207 185

404 376 344 311 278

245 227 208 188 168

368 342 313 283 252

212 199 183 165 148

318 299 275 249 222

166 148 128 109 90.5

249 222 193 164 136

140 126 111 95.2 80.1

211 189 166 143 120

112 102 91.0 79.5 68.2

169 154 137 120 103

20 22 24 26 28

163 141 120 103 88.7

244 212 181 154 133

147 127 109 92.6 80.0

221 191 163 139 120

130 113 96.0 82.0 70.9

195 169 144 123 106

30 32 34 36 40

77.3 116 68.0 102 60.3 90.6 53.8 80.8 43.6 65.5

69.7 105 61.3 92.2 54.4 81.7 48.5 72.9 39.3 59.1

61.8 54.4 48.2 43.1 34.9

92.9 81.8 72.5 64.7 52.5

73.8 111 61.2 92.0 51.5 77.5 44.0 66.1 38.0 57.1

66.0 54.8 46.1 39.4 34.0

99.2 82.3 69.3 59.2 51.1

57.4 47.7 40.2 34.3 29.7

86.3 71.7 60.4 51.6 44.6

33.1 29.1

29.7

44.6

25.9

38.9

49.8 43.8

Properties 2

Ag , in. rx , in. ry , in.

10.9 1.82 2.48

ASD

LRFD

Ωc = 1.67

φc = 0.90

10.0 1.81 2.46

8.96 1.80 2.45

7.80 1.88 1.92

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7.07 1.88 1.91

6.31 1.86 1.89

AISC_Part 4B:14th Ed.

2/23/11

10:13 AM

Page 114

4–114

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT7 Shape

WT7× c

lb/ft

X-X Axis

15c

17

13c

11c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

127

190

99.9

150

80.9

122

61.9

93.0

43.6

65.6

10 12 14 16 18

105 96.1 87.0 77.5 68.0

157 144 131 117 102

84.3 78.3 71.7 64.8 57.8

127 118 108 97.4 86.9

69.6 65.1 60.2 55.1 49.7

105 97.9 90.5 82.7 74.7

54.6 51.6 48.4 44.9 41.2

82.0 77.6 72.7 67.4 61.9

39.4 37.6 35.6 33.5 31.2

59.1 56.5 53.6 50.4 47.0

20 22 24 26 28

58.8 50.1 42.1 35.9 30.9

88.4 75.2 63.2 53.9 46.5

50.8 44.1 37.7 32.1 27.7

76.4 66.3 56.7 48.3 41.6

44.4 39.1 34.1 29.2 25.2

66.7 58.8 51.2 44.0 37.9

37.4 33.7 30.0 26.4 23.0

56.2 50.6 45.1 39.7 34.6

28.9 26.5 24.1 21.7 19.4

43.4 39.8 36.2 32.7 29.2

30 32 34

26.9 23.7 21.0

40.5 35.6 31.5

24.1 21.2 18.8

36.3 31.9 28.2

22.0 19.3 17.1

33.0 29.0 25.7

20.1 17.6 15.6

30.2 26.5 23.5

17.3 15.2 13.4

25.9 22.8 20.2

61.9

93.0

43.6

65.6

35.8 29.0 22.6 17.5 14.0

53.8 43.6 33.9 26.4 21.0

25.7 21.4 17.1 13.4

38.6 32.2 25.8 20.2

0

0

Y-Y Axis

c

19

Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

127

190

99.9

150

80.9

122

10 12 14 16 18

86.5 75.2 63.4 52.1 41.8

130 113 95.4 78.3 62.8

69.5 61.5 52.8 44.3 36.1

104 92.4 79.4 66.5 54.2

55.2 49.3 42.7 36.1 29.7

82.9 74.1 64.2 54.2 44.6

20 22 24

34.1 28.3 23.9

51.2 42.5 35.9

29.5 24.5 20.7

44.3 36.9 31.1

24.4 20.3 17.2

36.6 30.5 25.9

Properties 2

Ag , in. rx , in. ry , in.

5.58 2.04 1.55

5.00 2.04 1.53

4.42 2.07 1.49

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

ASD

LRFD

Ωc = 1.67

φc = 0.90

3.85 2.12 1.08

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.25 2.14 1.04

AISC_Part 4B:14th Ed.

2/23/11

10:13 AM

Page 115

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–115

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT6×

lb/ft

29

26.5

Pn /Ωc φc Pn

X-X Axis

20c

17.5c

Pn /Ωc φc Pn

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

255

383

233

350

219

329

196

295

155

233

132

199

4 6 8 10 12

237 216 189 160 130

356 324 284 240 195

216 197 173 147 120

325 296 261 221 180

205 188 168 145 121

308 283 252 218 182

183 169 150 129 108

276 254 226 194 162

146 135 121 106 89.8

219 203 183 159 135

126 119 110 98.9 87.0

190 179 165 149 131

14 16 18 20 22

102 153 78.2 117 61.8 92.8 50.0 75.2 41.3 62.1 34.7

Pn /Ωc φc Pn Pn /Ωc

22.5

LRFD

24 26 28

Y-Y Axis

25

ASD

Design

Effective length, KL (ft), with respect to indicated axis

WT6

52.2

ASD

LRFD

94.2 142 72.3 109 57.1 85.9 46.3 69.6 38.3 57.5

97.6 147 76.2 115 60.2 90.5 48.8 73.3 40.3 60.6

86.8 130 67.6 102 53.4 80.3 43.3 65.0 35.8 53.8

73.8 111 58.7 88.2 46.4 69.7 37.6 56.5 31.0 46.7

74.8 112 62.9 94.5 51.6 77.6 41.8 62.8 34.5 51.9

32.1

33.9 28.9

30.1 25.6

26.1 22.2

29.0 24.7 21.3

48.3

50.9 43.4

45.2 38.5

39.2 33.4

43.6 37.2 32.0

0

255

383

233

350

219

328

196

295

155

233

132

199

4 6 8 10 12

242 235 224 211 197

364 353 337 318 296

219 212 202 191 177

329 318 304 287 267

202 192 178 162 144

304 289 268 244 217

170 167 159 145 129

255 251 239 218 194

133 131 126 117 106

200 197 190 176 159

113 108 99.4 87.4 74.2

169 163 149 131 112

14 16 18 20 22

181 164 147 129 113

272 246 220 194 169

163 147 131 116 100

245 221 198 174 151

125 107 88.8 72.5 60.0

188 112 168 160 95.0 143 133 78.8 118 109 64.2 96.5 90.2 53.2 79.9

24 26 28 30 32

96.5 145 82.3 124 71.1 107 62.0 93.1 54.5 81.9

85.8 129 73.2 110 63.2 95.1 55.1 82.9 48.5 72.9

50.5 43.1 37.2 32.4 28.5

75.9 64.7 55.8 48.7 42.8

44.8 38.2 33.0 28.8 25.3

67.3 57.4 49.6 43.2 38.0

93.4 140 80.6 121 68.2 102 56.4 84.8 46.8 70.3

61.1 48.6 38.7 31.4 26.1

91.8 73.1 58.1 47.3 39.2

39.4 33.6 29.0 25.3 22.3

22.0

33.0

59.2 50.5 43.6 38.0 33.5

Properties 2

Ag , in. rx , in. ry , in.

8.52 1.50 2.51

ASD

LRFD

Ωc = 1.67

φc = 0.90

7.78 1.51 2.48

7.30 1.60 1.96

6.56 1.59 1.95

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5.84 1.57 1.94

5.17 1.76 1.54

AISC_Part 4B:14th Ed.

2/23/11

10:13 AM

Page 116

4–116

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT6 Shape

WT6× c

lb/ft

c

15

X-X Axis Y-Y Axis

c

13

Pn /Ωc φc Pn

11

Pn /Ωc φc Pn Pn /Ωc

9.5c

8c

7c

φc Pn

Pn /Ωc φc Pn

Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

93.1

140

64.7

97.3

68.6

103

49.9

75.0

37.9

57.0

28.1

42.2

4 6 8 10 12

89.6 85.3 79.7 73.0 65.6

135 128 120 110 98.6

62.7 60.4 57.2 53.3 48.9

94.3 90.7 85.9 80.1 73.5

66.4 63.7 60.1 55.8 51.0

99.7 95.7 90.3 83.9 76.6

48.5 46.8 44.6 41.9 38.8

72.9 70.4 67.0 63.0 58.3

37.0 35.9 34.4 32.5 30.4

55.6 54.0 51.7 48.9 45.7

27.5 26.8 25.9 24.7 23.3

41.4 40.3 38.9 37.1 35.1

14 16 18 20 22

57.8 50.0 42.4 35.2 29.1

86.9 75.1 63.7 52.9 43.7

44.2 39.3 34.5 29.7 25.2

66.4 59.1 51.8 44.7 37.9

45.8 40.5 35.2 30.1 25.2

68.8 60.8 52.8 45.2 37.9

35.5 31.9 28.4 24.9 21.5

53.3 48.0 42.6 37.4 32.3

28.1 25.6 23.1 20.5 18.1

42.2 38.5 34.7 30.9 27.1

21.8 20.2 18.5 16.8 15.1

32.8 30.4 27.8 25.2 22.6

24 26 28 30 32

24.4 20.8 17.9

36.7 31.3 27.0

21.2 18.1 15.6

31.9 27.2 23.4

21.2 18.1 15.6 13.6

31.9 27.1 23.4 20.4

18.3 15.6 13.4 11.7

27.4 23.4 20.2 17.6

15.7 13.4 11.6 10.1 8.87

23.6 20.2 17.4 15.2 13.3

13.4 11.8 10.2 8.89 7.82

20.1 17.7 15.3 13.4 11.7

0

93.1

140

64.7

97.3

68.6

49.9

75.0

37.9

57.0

28.1

42.2

4 6 8 10 12

78.1 76.1 71.5 64.5 56.4

117 114 107 97.0 84.7

53.9 53.0 50.8 47.2 42.5

81.0 79.6 76.4 70.9 63.8

52.1 43.5 32.9 22.8 16.2

78.3 65.4 49.4 34.3 24.3

37.0 31.9 25.0 17.9 12.8

55.6 47.9 37.5 27.0 19.3

25.6 22.3 17.6 12.7 9.28

38.5 33.5 26.5 19.2 14.0

18.6 16.5 13.6 10.2 7.54

27.9 24.9 20.4 15.3 11.3

14 16 18 20 22

47.8 39.5 31.8 25.9 21.5

71.9 59.4 47.8 38.9 32.3

37.2 31.9 26.8 22.0 18.3

56.0 48.0 40.2 33.1 27.5

12.0

18.0

24

18.1

27.2

15.4

23.2

Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

103

Pn /Ωc φc Pn

Properties 2

Ag , in. rx , in. ry , in.

4.40 1.75 1.52

ASD

LRFD

Ωc = 1.67

φc = 0.90

3.82 1.75 1.51

3.24 1.90 0.847

2.79 1.90 0.821

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.36 1.92 0.773

2.08 1.92 0.753

AISC_Part 4B:14th Ed.

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–117

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT5×

lb/ft

22.5

16.5

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

199

298

172

258

145

218

132

199

103

154

4 6 8 10 12

178 155 128 100 73.9

267 233 192 150 111

154 134 111 86.5 63.9

231 202 166 130 96.0

131 114 95.0 74.8 55.8

196 172 143 112 83.9

122 111 96.0 80.2 64.3

184 166 144 121 96.7

95.4 87.1 76.6 65.0 53.2

143 131 115 97.7 79.9

14 16 18 20 22

54.3 41.6 32.8 26.6

46.9 35.9 28.4 23.0

70.5 54.0 42.7 34.6

41.0 31.4 24.8 20.1

61.6 47.2 37.3 30.2

49.5 37.9 29.9 24.3 20.0

74.4 57.0 45.0 36.4 30.1

41.9 32.2 25.5 20.6 17.0

63.0 48.4 38.3 31.0 25.6

16.8

25.3

14.3

21.5

81.6 62.5 49.4 40.0

24

Y-Y Axis

13c

15

ASD 0

X-X Axis

19.5

Pn /Ωc Design

Effective length, KL (ft), with respect to indicated axis

WT5

0

199

298

172

258

145

218

132

199

103

154

4 6 8 10 12

187 178 166 151 135

281 267 249 227 203

160 152 141 129 115

241 229 213 193 172

133 126 117 106 94.4

199 189 176 160 142

115 103 89.0 73.3 57.7

173 155 134 110 86.7

86.7 81.3 71.5 59.7 47.8

130 122 107 89.8 71.8

14 16 18 20 22

118 101 84.8 69.5 57.5

177 152 127 105 86.4

99.9 85.3 71.2 58.2 48.2

150 128 107 87.5 72.4

82.0 69.6 57.8 47.1 39.0

123 105 86.9 70.8 58.6

43.5 33.4 26.5 21.5 17.8

65.3 50.2 39.8 32.3 26.7

36.6 28.2 22.4 18.2 15.1

55.0 42.4 33.6 27.3 22.6

24 26 28 30 32

48.4 41.2 35.6 31.0 27.3

72.7 62.0 53.5 46.6 41.0

40.5 34.5 29.8 26.0 22.8

60.9 51.9 44.8 39.0 34.3

32.8 28.0 24.2 21.1 18.5

49.3 42.1 36.3 31.7 27.8

Properties 2

Ag , in. rx , in. ry , in.

6.63 1.24 2.01

5.73 1.24 1.98

4.85 1.26 1.94

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

ASD

LRFD

Ωc = 1.67

φc = 0.90

4.42 1.45 1.37

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.81 1.44 1.36

AISC_Part 4B:14th Ed.

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Page 118

4–118

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT5 Shape

WT5× c

lb/ft

X-X Axis Y-Y Axis

c

11

8.5c

9.5

7.5c

6c

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

80.9

122

73.2

110

62.8

94.4

53.5

80.5

31.4

47.2

4 6 8 10 12

75.7 69.8 62.2 53.6 44.7

114 105 93.4 80.5 67.2

68.8 63.7 57.2 49.7 42.0

103 95.7 85.9 74.8 63.1

59.3 55.1 49.8 43.7 37.2

89.1 82.8 74.8 65.7 56.0

50.7 47.3 42.9 37.9 32.5

76.1 71.0 64.5 56.9 48.9

30.1 28.6 26.7 24.4 21.8

45.3 43.0 40.1 36.6 32.8

14 16 18 20 22

36.1 28.2 22.2 18.0 14.9

54.2 42.3 33.4 27.1 22.4

34.3 27.2 21.5 17.4 14.4

51.6 40.8 32.3 26.1 21.6

30.8 24.8 19.6 15.9 13.1

46.3 37.3 29.5 23.9 19.7

27.2 22.1 17.5 14.2 11.7

40.9 33.2 26.4 21.4 17.7

19.1 16.4 13.8 11.4 9.41

28.7 24.7 20.8 17.1 14.1

24 26

12.5

18.8

12.1

18.2

11.0 9.39

16.6 14.1

14.8 12.6

7.91 6.74

11.9 10.1

0

80.9

62.8

94.4

53.5

80.5

31.4

47.2

4 6 8 10 12

65.1 62.0 55.5 46.9 37.9

97.8 93.2 83.4 70.5 57.0

55.5 44.7 32.2 21.5 15.1

83.5 67.2 48.4 32.3 22.7

45.3 36.6 26.2 17.5 12.4

68.0 55.0 39.3 26.3 18.6

35.7 29.0 20.6 13.9 9.93

53.7 43.5 30.9 20.9 14.9

20.8 18.0 14.0 9.99 7.25

31.3 27.1 21.1 15.0 10.9

14 16 18 20 22

29.3 22.7 18.0 14.7 12.2

44.1 34.1 27.1 22.1 18.3

11.2

16.8

Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

122

73.2

110

9.21

9.87 8.41

13.8

Properties 2

Ag , in. rx , in. ry , in.

3.24 1.46 1.33

2.81 1.54 0.874

2.50 1.56 0.844

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

ASD

LRFD

Ωc = 1.67

φc = 0.90

2.21 1.57 0.810

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.77 1.57 0.785

AISC_Part 4B:14th Ed.

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Page 119

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–119

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT4×

lb/ft

33.5 Pn /Ωc φc Pn

Design

X-X Axis Y-Y Axis

29

24

Pn /Ωc

φc Pn

20

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

17.5 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

295

443

256

384

211

317

176

264

154

231

4 6 8 10 12

253 209 160 113 78.6

380 314 240 170 118

218 179 135 94.6 65.7

328 269 204 142 98.7

177 143 106 71.5 49.7

267 215 159 108 74.7

148 119 88.1 59.8 41.5

222 179 132 89.9 62.4

129 103 75.0 50.3 34.9

193 154 113 75.6 52.5

14 16

57.8 44.2

48.2 36.9

72.5 55.5

36.5 27.9

54.9 42.0

30.5 23.4

45.9 35.1

25.6 19.6

38.6 29.5

0

Effective length, KL (ft), with respect to indicated axis

WT4

86.8 66.5

0

295

443

256

384

211

317

176

264

154

231

4 6 8 10 12

283 270 253 232 210

425 405 380 349 315

245 233 218 200 181

368 351 328 301 271

202 192 180 165 148

303 289 270 247 222

167 159 148 135 121

251 238 222 203 182

145 138 129 118 105

219 208 194 177 158

14 16 18 20 22

186 161 138 115 95.3

279 243 207 173 143

160 138 118 98.1 81.1

240 208 177 147 122

130 113 95.7 79.4 65.6

196 170 144 119 98.7

106 91.4 77.1 63.5 52.5

160 137 116 95.4 78.9

92.5 79.4 66.9 55.0 45.5

139 119 100 82.7 68.4

24 26 28 30 32

80.1 68.2 58.8 51.3 45.1

55.2 47.0 40.6 35.3 31.1

82.9 70.7 61.0 53.1 46.7

44.2 37.6 32.5 28.3 24.9

66.4 56.6 48.8 42.5 37.4

38.3 32.6 28.1 24.5 21.6

57.5 49.0 42.3 36.9 32.4

120 103 88.4 77.0 67.7

68.2 58.1 50.1 43.6 38.4

102 87.3 75.3 65.6 57.7

Properties 2

Ag , in. rx , in. ry , in.

9.84 1.05 2.12

8.54 1.03 2.10

7.05 0.986 2.08

5.87 0.988 2.04

Note: Heavy line indicates KL/r equal to or greater than 200.

ASD

LRFD

Ωc = 1.67

φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5.14 0.968 2.03

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Page 120

4–120

DESIGN OF COMPRESSION MEMBERS

Table 4-7 (continued)

Available Strength in Axial Compression, kips WT-Shapes

WT4 Shape

WT4×

lb/ft

15.5

X-X Axis

12

10.5

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

137

205

123

185

106

159

92.2

139

4 6 8 10 12

114 91.2 66.6 44.7 31.0

171 137 100 67.2 46.6

105 85.1 63.7 43.9 30.5

157 128 95.8 65.9 45.8

89.5 72.5 54.0 36.9 25.6

135 109 81.1 55.4 38.5

80.6 68.2 53.9 39.8 28.0

121 102 81.0 59.9 42.1

14 16 18

22.8 17.5

34.3 26.2

22.4 17.1

33.6 25.8

18.8 14.4

28.3 21.7

20.6 15.8 12.4

30.9 23.7 18.7

0

0

Y-Y Axis

14

Pn /Ωc Design

Effective length, KL (ft), with respect to indicated axis

Fy = 50 ksi

137

205

123

185

4 6 8 10 12

128 122 114 104 92.8

192 183 171 156 140

113 105 93.8 81.4 68.4

170 157 141 122 103

14 16 18 20 22

81.4 69.8 58.7 48.2 39.9

122 105 88.2 72.5 60.0

55.7 43.8 34.6 28.1 23.2

24 26 28 30 32

33.6 28.6 24.7 21.5 18.9

50.5 43.0 37.1 32.4 28.4

19.5 16.7

106

159

92.2

139

96.4 89.2 79.9 69.3 58.2

145 134 120 104 87.4

79.3 69.9 58.5 46.4 34.9

119 105 87.9 69.8 52.4

83.7 65.8 52.1 42.2 34.9

47.2 37.1 29.4 23.8 19.7

71.0 55.7 44.1 35.8 29.6

25.7 19.8 15.6 12.7

38.7 29.7 23.5 19.1

29.4 25.0

16.6 14.1

24.9 21.2

Properties 2

Ag , in. rx , in. ry , in.

4.56 0.969 2.02 ASD

LRFD

Ωc = 1.67

φc = 0.90

4.12 1.01 1.62

3.54 0.999 1.61

Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.08 1.12 1.26

AISC_Part 4B:14th Ed.

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Page 121

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–121

Table 4-7 (continued)

Available Strength in Axial Compression, kips

Fy = 50 ksi

WT-Shapes Shape

WT4×

lb/ft

9

X-X Axis Y-Y Axis

7.5

5c

6.5

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

78.7

118

66.5

99.9

57.5

86.4

32.5

48.8

4 6 8 10 12

69.2 58.8 46.9 35.0 24.8

104 88.4 70.5 52.6 37.2

59.4 51.5 42.3 32.8 24.0

89.2 77.4 63.5 49.2 36.0

51.4 44.7 36.8 28.7 21.1

77.3 67.3 55.3 43.1 31.6

29.8 26.8 23.1 19.0 15.0

44.8 40.3 34.7 28.6 22.6

14 16 18 20

18.2 13.9 11.0

27.4 20.9 16.5

17.6 13.5 10.6 8.62

26.4 20.2 16.0 13.0

15.5 11.8 9.36 7.58

23.3 17.8 14.1 11.4

11.3 8.69 6.87 5.56

17.1 13.1 10.3 8.36

0

78.7

66.5

99.9

57.5

86.4

32.5

48.8

4 6 8 10 12

65.2 57.5 48.0 37.9 28.1

98.0 86.4 72.1 56.9 42.3

48.1 37.6 26.3 17.3 12.1

72.3 56.6 39.6 25.9 18.2

38.5 30.1 20.7 13.6 9.60

57.8 45.2 31.2 20.5 14.4

23.0 19.5 14.7 10.1 7.21

34.5 29.3 22.1 15.2 10.8

14 16 18 20

20.8 16.0 12.7 10.3

31.3 24.1 19.1 15.5

13.4

7.11

10.7

5.37

Design

Effective length, KL (ft), with respect to indicated axis

WT4

118

8.94

8.07

Properties 2

Ag , in. rx , in. ry , in.

2.63 1.14 1.23 ASD

LRFD

Ωc = 1.67

φc = 0.90

2.22 1.22 0.876

1.92 1.23 0.843

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.48 1.20 0.840

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Page 122

4–122

DESIGN OF COMPRESSION MEMBERS

Table 4-8

Available Strength in Axial Compression, kips Double Angles—Equal Legs

2L8

lb/ft

X-X Axis Y-Y Axis

Effective length, KL (ft), with respect to indicated axis

Design 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 0 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57

2L8× 8× 11/8 114 Pn /Ωc φc Pn

7/8

1 102 Pn /Ωc φc Pn

3/4

5/8

9/16 c

90.0 77.8 65.4 59.2 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

724 721 709 691 666 636 600 561 519 475 430 385 342 300 260 226 199 176 157 141 127 724 689 671 647 616 582 532 488 442 396 351 307 265 229 199 175 156 139 125

1090 1080 1070 1040 1000 955 902 843 779 713 646 579 513 451 391 340 299 265 236 212 191 1090 1040 1010 972 927 874 799 733 664 595 527 461 398 344 300 264 234 209 187

651 648 638 622 600 573 541 506 469 429 390 350 311 273 237 207 182 161 144 129 116 651 613 597 576 549 518 473 434 393 352 312 272 235 203 177 156 138 123 111

978 973 959 934 901 861 813 761 704 646 586 526 467 411 357 311 273 242 216 194 175 978 922 898 865 825 778 711 652 591 529 468 410 353 305 266 234 208 185 166

573 571 562 548 529 505 478 448 415 381 346 311 277 244 213 185 163 144 129 115 104 573 532 518 500 477 438 405 370 333 296 260 237 204 176 154 135 120 107 96.4

862 857 845 824 795 760 719 673 624 572 520 468 416 367 320 278 245 217 193 173 157 862 800 779 751 716 658 609 556 501 446 391 356 307 265 231 204 181 161 145

496 493 486 474 458 437 414 388 360 330 300 270 241 213 185 161 142 126 112 101 90.8 496 449 437 422 403 371 343 313 282 251 221 200 172 149 130 115 102 91.0 81.8

745 741 730 712 688 657 622 583 541 497 451 406 362 320 279 243 213 189 168 151 136 745 674 657 634 605 557 515 471 424 378 332 301 259 224 196 173 153 137 123

417 415 409 399 385 369 349 328 304 280 255 230 205 182 159 138 122 108 96.1 86.2 77.8 417 334 332 328 321 304 284 260 234 208 182 165 142 123 108 94.9 82.3 75.4 67.8

627 624 614 600 579 554 525 493 458 421 383 346 309 273 239 208 183 162 144 130 117 627 502 499 493 483 456 426 390 352 312 273 247 213 185 162 143 127 113 102

362 360 355 347 336 322 306 287 268 247 226 205 184 164 144 126 111 98.0 87.4 78.4 70.8 362 280 278 275 270 258 243 225 204 182 160 139 126 109 95.8 84.6 75.2 67.3 60.6

544 541 534 521 504 484 459 432 403 372 340 308 277 246 217 189 166 147 131 118 106 544 420 418 413 406 388 365 337 306 273 241 209 189 164 144 127 113 101 91.1

Properties of 2 angles— 3/8 in. back to back 2

Ag , in. rx, in. ry , in.

33.6 2.41 3.54

30.2 2.43 3.52

rz , in.

1.56

1.56

26.6 2.45 3.50

23.0 2.46 3.47

19.4 2.48 3.45

17.5 2.49 3.44

1.58

1.58

Properties of single angle ASD

LRFD

Ωc = 1.67

φc = 0.90

1.57

1.57

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

No. of connectorsa

Shape

Fy = 36 ksi

b

2

3

AISC_Part 4C:14th Ed.

2/23/11

10:36 AM

Page 123

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–123

Table 4-8 (continued)

Available Strength in Axial Compression, kips Double Angles—Equal Legs

lb/ft

X-X Axis Y-Y Axis

Effective length, KL (ft), with respect to indicated axis

Design 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 0 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57

2L8× 8× 1/2 c

52.8 Pn /Ωc φc Pn

2L6× 6× No. of connectorsa

Shape

2L8-2L6

1 74.8

Pn /Ωc

φc Pn

7/8

3/4

5/8

66.2 Pn /Ωc φc Pn

57.4 Pn /Ωc φc Pn

48.4 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

309 307 303 297 287 276 263 248 232 215 198 180 162 145 129 113 99.2 87.9 78.4 70.4 63.5 309 227 225 223 220 212 202 189 174 156 139 122 110 96.2 84.5 74.8 66.6 59.7 53.8

464 462 456 446 432 415 395 373 349 323 297 270 244 218 194 170 149 132 118 106 95.4 464 341 339 336 331 319 304 284 261 235 209 183 166 145 127 112 100 89.7 80.8

474 470 457 436 408 374 337 298 259 220 184 152 128 109 93.8

713 706 686 655 613 563 507 448 389 331 276 228 192 164 141

420 416 405 387 362 334 301 267 232 199 167 138 116 98.6 85.1 74.1

632 626 609 581 545 501 453 401 349 299 250 207 174 148 128 111

364 361 351 335 315 290 262 233 203 174 146 121 101 86.4 74.5 64.9

548 543 528 504 473 436 394 350 305 261 219 181 152 130 112 97.6

308 306 297 284 267 246 223 199 174 149 126 104 87.7 74.8 64.5 56.1

463 459 447 427 401 370 336 299 261 224 189 157 132 112 96.9 84.4

474 449 429 402 371 327 287 248 209 173 143 120 103 88.5 77.1

713 674 644 605 558 491 432 372 314 260 215 181 154 133 116

420 395 377 354 326 287 252 217 183 151 125 105 89.6 77.3 67.4

632 593 567 532 490 431 379 326 275 227 188 158 135 116 101

364 338 323 303 279 245 215 184 155 128 106 89.0 75.9 65.5

548 508 485 455 419 368 323 277 233 192 159 134 114 98.5

308 280 268 251 231 203 178 153 129 106 87.8 74.0 63.1 54.5

463 421 402 377 347 306 268 230 194 159 132 111 94.9 82.0

b

2

3

Properties of 2 angles— 3/8 in. back to back 2

Ag , in. rx , in. ry , in.

15.7 2.49 3.43

rz , in.

1.59

22.0 1.79 2.72

19.5 1.81 2.70

16.9 1.82 2.67

14.3 1.84 2.65

1.17

1.17

Properties of single angle ASD

LRFD

Ωc = 1.67

φc = 0.90

1.17

1.17

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

No. of connectorsa

Fy = 36 ksi

b

3

AISC_Part 4C:14th Ed.

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Page 124

4–124

DESIGN OF COMPRESSION MEMBERS

Table 4-8 (continued)

Available Strength in Axial Compression, kips Double Angles—Equal Legs

2L6 9/16

1/2

7/16 c

3/8c

5/16 c

43.8 Pn /Ωc φc Pn

39.2 Pn /Ωc φc Pn

34.4 Pn /Ωc φc Pn

29.8 Pn /Ωc φc Pn

24.8 Pn /Ωc φc Pn

0

ASD 278

LRFD 418

ASD 248

LRFD 373

ASD 214

LRFD 322

ASD 172

LRFD 259

ASD 131

LRFD 196

2 4 6 8 10

276 268 257 241 223

414 403 386 363 335

246 239 229 215 199

369 360 344 324 299

212 207 198 187 173

319 311 298 281 260

171 167 160 152 141

257 251 241 228 212

130 127 123 117 109

195 191 184 175 165

12 14 16 18 20

202 180 158 136 115

304 271 237 204 172

181 161 141 122 103

272 243 213 183 155

157 141 124 107 91.2

237 212 186 161 137

130 117 104 90.8 78.1

195 176 156 136 117

101 92.4 83.0 73.6 64.3

152 139 125 111 96.7

55.4 47.0 40.1 34.5 30.1

83.3 70.7 60.2 51.9 45.2

lb/ft

X-X Axis

Effective length, KL (ft), with respect to indicated axis

Design

22 24 26 28 30

95.2 80.0 68.2 58.8 51.2

143 120 102 88.3 77.0

85.8 72.1 61.4 53.0 46.1

129 108 92.3 79.6 69.4

76.1 63.9 54.5 47.0 40.9

114 96.1 81.9 70.6 61.5

66.1 55.5 47.3 40.8 35.5

99.3 83.4 71.1 61.3 53.4

0

278

418

248

373

214

322

172

259

6 9 12 15 18

248 237 218 199 177

373 357 328 299 267

215 206 190 174 155

323 310 286 261 233

167 164 158 148 134

250 247 238 223 202

126 125 121 116 106

190 188 182 174 160

88.0 87.2 85.4 82.5 77.9

132 131 128 124 117

21 24 27 30 33

155 132 115 94.5 78.5

232 198 173 142 118

136 116 101 83.1 69.1

204 174 152 125 104

117 100 87.4 72.0 60.0

177 151 131 108 90.3

142 123 104 90.0 75.4

71.3 63.2 54.5 48.0 40.6

107 95.0 82.0 72.2 61.0

36 39 42

66.1 56.5 48.8

64.0 54.9 47.6

34.6 29.9 26.0

52.1 44.9 39.0

Ag , in.2 rx , in. ry , in.

99.4 84.9 73.3

94.6 81.8 69.0 59.9 50.2

58.3 87.6 50.8 76.3 42.6 49.8 74.9 43.5 65.4 36.5 43.1 64.7 37.6 56.6 31.7 Properties of 2 angles— 3/8 in. back to back

12.9 1.85 2.64

11.5 1.86 2.63

10.2 1.86 2.62

131

Ωc = 1.67

1.18 LRFD φc = 0.90

1.18

8.76 1.87 2.60

7.34 1.88 2.59

1.18

1.19

1.19

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

196

Properties of single angle

rz , in. ASD

No. of connectorsa

2L6× 6×

Shape

Y-Y Axis

Fy = 36 ksi

2

3

AISC_Part 4C:14th Ed.

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Page 125

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–125

Table 4-8 (continued) Fy = 36 ksi

Available Strength in Axial Compression, kips Double Angles—Equal Legs

7/8

lb/ft

X-X Axis

5/8

1/2

7/16

3/8c

5/16 c

54.4 47.2 40.0 32.4 28.6 24.6 20.6 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 0 345 518 302 454 254 382 207 310 182 273 155 232 121 181

2 4 6 8 10

340 327 305 277 245

511 491 458 417 368

298 286 267 243 215

448 430 402 366 324

251 241 226 206 183

377 363 340 310 275

204 196 184 168 149

306 295 276 252 225

180 173 162 148 132

270 260 244 223 199

12 14 16 18 20

211 177 144 114 92.7

317 265 216 172 139

186 156 127 101 82.2

279 234 191 153 124

159 134 110 87.8 71.1

238 201 165 132 107

130 109 90.1 72.2 58.5

195 165 135 109 88.0

115 97.2 80.3 64.5 52.2

173 146 121 96.9 78.5

22 24 26

153 147 138 127 113

230 221 208 191 170

99.0 84.2 69.9 56.5 45.8

149 127 105 84.9 68.8

119 115 109 101 90.9 80.2 69.2 58.3 48.1 39.0

179 173 164 151 137 121 104 87.7 72.3 58.6

518

302

454

254

382

207

310

182

273

155

232

121

181

2 4 6 8 10

337 332 322 310 295

507 498 484 466 443

293 288 280 269 255

440 433 420 404 383

244 239 233 223 212

366 360 350 336 319

192 189 184 177 168

289 284 276 266 252

165 162 158 152 142

248 244 237 228 213

123 123 122 120 116

185 184 183 181 175

89.2 88.9 88.4 87.5 85.4

134 134 133 132 128

12 14 16 18 20

277 251 229 206 183

416 377 344 310 275

239 217 197 177 157

360 326 297 267 237

199 180 164 147 131

299 271 247 221 196

157 143 130 117 103

237 215 195 175 155

132 121 110 98.0 86.2

198 182 165 147 130

110 102 93.1 83.1 73.0

166 154 140 125 110

82.4 77.9 72.1 65.3 58.1

124 117 108 98.2 87.4

22 24 26 28 30

161 140 119 103 89.9

242 210 180 155 135

138 119 102 87.9 76.7

207 179 153 132 115

114 98.6 84.2 72.7 63.4

172 148 127 109 95.3

51.0 46.1 39.8 34.7 30.4

76.6 69.3 59.8 52.1 45.7

32 34 36 38

79.0 70.0 62.5 56.1

90.1 77.5 66.3 57.3 50.0

135 117 99.6 86.1 75.2

74.8 67.3 57.6 49.8 43.5

112 101 86.6 74.9 65.4

63.2 56.7 48.7 42.2 37.0

95.0 85.2 73.2 63.5 55.6

119 67.4 101 55.8 83.9 44.0 66.2 38.4 57.6 32.6 49.0 26.9 40.4 105 59.8 89.8 49.5 74.4 39.1 58.7 34.0 51.2 29.0 43.6 23.9 36.0 93.9 53.3 80.2 44.2 66.4 34.9 52.4 30.4 45.7 25.9 39.0 21.4 32.2 84.3 Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

16.0 1.49 2.30

rz , in. ASD

0.971 LRFD

Ωc = 1.67

b

76.6 115 67.9 102 58.8 88.4 48.4 72.7 43.2 64.9 37.8 56.8 32.2 48.4 64.4 96.7 57.1 85.8 49.4 74.3 40.6 61.1 36.3 54.5 31.8 47.8 27.1 40.7 23.1 34.7

0 345

Y-Y Axis

Effective length, KL (ft), with respect to indicated axis

3/4

No. of connectorsa

2L5× 5×

Shape

Design

2L5

φc = 0.90

14.0 1.50 2.27 0.972

11.8 1.52 2.25

9.58 1.53 2.22

8.44 1.54 2.21

Properties of single angle 0.975 0.980 0.983

a

7.30 1.55 2.20

6.14 1.56 2.19

0.986

0.990

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2

3

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10:37 AM

Page 126

4–126

DESIGN OF COMPRESSION MEMBERS

Table 4-8 (continued)

Available Strength in Axial Compression, kips Double Angles—Equal Legs

2L4 3/4

lb/ft

X-X Axis

1/2

7/16

3/8

5/16

1/4c

37.0 31.4 25.6 22.6 19.6 16.4 13.2 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 0 235 353 199 299 162 243 142 214 123 185 103 155 75.9 114

2 4 6 8 10

230 215 193 166 136

12 107 14 80.8 16 61.9 18 48.9 20 0 235

Y-Y Axis

Effective length, KL (ft), with respect to indicated axis

5/8

No. of connectorsa

2L4× 4×

Shape

Design

Fy = 36 ksi

346 324 290 249 205

195 183 164 142 117

161 121 93.0 73.5

293 275 247 213 176

93.1 70.7 54.1 42.8 34.6

140 106 81.4 64.3 52.1

158 149 134 116 96.3 76.7 58.5 44.8 35.4 28.7

238 224 202 174 145 115 87.9 67.3 53.2 43.1

139 131 118 103 85.5 68.3 52.3 40.1 31.6 25.6

210 197 178 154 128 103 78.6 60.2 47.6 38.5

121 114 103 89.5 74.7 59.9 46.1 35.3 27.9 22.6

182 171 155 134 112 90.1 69.3 53.0 41.9 33.9

353

199

299

162

243

142

214

123

185

134 130 125 117 108

201 196 188 176 163

113 110 106 99.5 92.1

170 166 159 150 138

101 95.4 86.4 75.3 63.1

152 143 130 113 94.8

50.8 39.3 30.1 23.8 19.3

76.4 59.1 45.2 35.7 28.9

103

74.6 112 70.7 106 64.7 97.3 57.2 85.9 48.8 73.3 40.1 31.9 24.6 19.4 15.7

155

75.9 114

82.9 82.4 81.4 79.2 75.1

125 124 122 119 113

55.9 55.7 55.1 54.1 52.3

84.1 83.7 82.8 81.3 78.5

2 4 6 8 10

230 224 215 202 187

345 336 323 304 282

193 188 180 169 156

290 282 270 254 235

154 150 144 135 125

232 226 216 204 188

12 14 16 18 20

166 147 128 109 91.6

249 221 192 164 138

138 122 106 90.1 75.0

208 184 159 135 113

111 97.6 84.5 71.7 59.5

166 147 127 108 89.5

95.8 84.5 73.0 61.8 51.2

144 127 110 92.9 76.9

81.5 71.9 62.2 52.7 43.6

122 108 93.5 79.2 65.5

67.2 59.4 51.2 43.2 35.6

101 89.3 77.0 64.9 53.5

48.3 43.6 38.4 32.9 27.6

72.6 65.6 57.7 49.5 41.5

22 24 26 28 30

75.7 63.7 54.3 46.8 40.8

49.3 41.5 35.4 30.6 26.7

74.1 62.4 53.2 46.0 40.1

42.4 35.7 30.5 26.3 23.0

63.7 53.7 45.8 39.6 34.5

36.2 30.5 26.1 22.5 19.6

54.4 45.9 39.2 33.8 29.5

29.7 25.1 21.5 18.6

44.6 37.7 32.3 27.9

23.1 19.6 16.9 14.6

34.8 29.5 25.3 22.0

114 95.7 81.6 70.4 61.3

62.1 52.2 44.5 38.4 33.5

93.3 78.5 66.9 57.7 50.3

Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

10.9 1.18 1.88

9.22 1.20 1.85

rz , in. ASD

0.774 LRFD

0.774

7.50 1.21 1.83

6.60 1.22 1.81

5.72 1.23 1.80

4.80 1.24 1.79

3.86 1.25 1.78

0.779

0.781

0.783

Properties of single angle

Ωc = 1.67

φc = 0.90

0.776

0.777

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

60.3 47.9 37.0 29.2 23.7

3

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Page 127

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–127

Table 4-8 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Double Angles—Equal Legs 1/2

7/16

3/8

5/16

1/4c

22.2 Pn /Ωc φc Pn

19.6 Pn /Ωc φc Pn

17.0 Pn /Ωc φc Pn

14.4 Pn /Ωc φc Pn

11.6 Pn /Ωc φc Pn

0

ASD 140

LRFD 211

ASD 125

LRFD 187

ASD 108

LRFD 162

ASD 90.5

LRFD 136

ASD 70.7

LRFD 106

1 2 3 4 5

139 136 132 126 118

209 205 198 189 177

124 121 117 112 105

186 182 176 168 158

107 105 102 96.9 91.3

161 158 153 146 137

90.0 88.2 85.4 81.6 77.0

135 133 128 123 116

70.3 69.0 66.9 64.1 60.6

106 104 101 96.3 91.1

6 7 8 9 10

109 100 90.2 80.3 70.4

164 150 136 121 106

11 12 13 14 15

61.0 51.9 44.3 38.2 33.2

16 17 18

29.2 25.9

lb/ft

X-X Axis

Effective length, KL (ft), with respect to indicated axis

Design

97.7 89.5 80.9 72.1 63.5

147 135 122 108 95.4

84.9 77.9 70.6 63.0 55.6

128 117 106 94.8 83.6

71.7 65.8 59.7 53.5 47.3

108 99.0 89.8 80.4 71.0

56.7 52.3 47.7 43.0 38.2

85.2 78.6 71.7 64.6 57.4

91.6 78.1 66.5 57.4 50.0

55.1 47.1 40.1 34.6 30.1

82.8 70.8 60.3 52.0 45.3

48.4 41.5 35.4 30.5 26.6

72.7 62.4 53.1 45.8 39.9

41.2 35.5 30.3 26.1 22.7

62.0 53.4 45.5 39.2 34.2

33.6 29.1 24.9 21.5 18.7

50.5 43.8 37.5 32.3 28.2

43.9 38.9

26.5 23.5

39.8 35.3

23.3 20.7

35.1 31.1

20.0 17.7 15.8

30.0 26.6 23.7

16.5 14.6 13.0

24.8 21.9 19.6

0

140

211

125

187

108

162

90.5

136

70.7

2 4 6 8 10

135 130 123 114 101

203 196 185 172 151

119 115 109 100 88.3

178 172 163 151 133

101 97.6 92.3 85.4 75.3

152 147 139 128 113

82.1 79.5 75.4 69.8 61.8

123 120 113 105 92.8

55.1 54.7 53.9 51.9 47.3

82.8 82.3 80.9 78.0 71.1

54.0 46.0 38.2 30.8 25.1

81.2 69.2 57.4 46.3 37.7

41.8 35.6 29.5 23.9 19.5

62.8 53.6 44.4 35.9 29.3

31.3 26.3 22.5

16.2 13.7 11.7

24.4 20.6 17.6

12 14 16 18 20

88.1 75.1 62.5 50.6 41.0

132 113 93.9 76.0 61.7

22 24 26

34.0 28.6 24.4

51.0 42.9 36.6

Ag , in.2 rx , in. ry , in.

6.50 1.05 1.63

rz , in. ASD

0.679 LRFD

Ωc = 1.67

φc = 0.90

77.1 65.6 54.4 43.9 35.6

116 98.6 81.7 65.9 53.5

65.7 55.9 46.3 37.4 30.4

98.8 84.0 69.6 56.1 45.6

29.5 44.3 25.2 37.8 20.8 24.8 37.3 21.2 31.8 17.5 21.2 31.8 18.1 27.2 15.0 Properties of 2 angles— 3/8 in. back to back 5.78 1.06 1.61

5.00 1.07 1.60

Properties of single angle 0.681 0.683

3.40 1.09 1.57

0.685

0.688

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

106

4.20 1.08 1.59

a

No. of connectorsa

2L31/2 × 31/2 ×

Shape

Y-Y Axis

2L31/2

3

AISC_Part 4C:14th Ed.

2/23/11

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Page 128

4–128

DESIGN OF COMPRESSION MEMBERS

Table 4-8 (continued)

Available Strength in Axial Compression, kips Double Angles—Equal Legs

2L3 1/2

lb/ft

X-X Axis

3/8

5/16

1/4

3/16c

18.8 16.6 14.4 12.2 9.80 7.42 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to indicated axis

7/16

0

ASD 119

LRFD ASD 179 105

LRFD 157

ASD 91.0

LRFD 137

ASD 76.7

LRFD 115

ASD 62.1

LRFD ASD 93.3 42.9

LRFD 64.4

1 2 3 4 5

118 115 109 102 93.9

177 172 164 154 141

156 152 145 136 125

90.1 87.7 83.8 78.6 72.4

135 132 126 118 109

76.1 74.0 70.8 66.5 61.3

114 111 106 99.9 92.1

61.5 59.9 57.3 53.9 49.8

92.5 90.1 86.2 81.0 74.8

42.5 41.5 39.9 37.7 35.1

63.9 62.4 60.0 56.7 52.8

104 101 96.4 90.3 83.0

6 7 8 9 10

84.6 127 74.8 112 64.9 97.6 55.3 83.1 46.2 69.4

75.0 113 66.4 99.8 57.8 86.9 49.3 74.2 41.3 62.1

65.4 58.1 50.6 43.3 36.4

98.3 87.3 76.1 65.1 54.7

55.5 49.4 43.2 37.0 31.2

83.4 74.2 64.9 55.7 46.9

45.2 40.3 35.3 30.3 25.6

67.9 60.5 53.0 45.6 38.5

32.2 29.0 25.8 22.5 19.4

48.4 43.6 38.7 33.9 29.1

11 12 13 14 15

38.1 32.1 27.3 23.5

34.2 28.7 24.5 21.1 18.4

30.1 25.3 21.6 18.6 16.2

45.3 38.1 32.4 28.0 24.4

25.9 21.7 18.5 16.0 13.9

38.9 32.7 27.9 24.0 20.9

21.3 17.9 15.3 13.2 11.5

32.0 26.9 22.9 19.8 17.2

16.4 13.8 11.7 10.1 8.80

24.6 20.7 17.6 15.2 13.2

0

57.3 48.2 41.0 35.4

51.4 43.2 36.8 31.7 27.6

119

179

105

157

91.0

137

76.7

115

62.1

93.3

42.9

64.4

2 4 6 8 10

115 110 102 90.4 78.3

173 165 154 136 118

101 96.2 89.4 78.9 68.3

151 145 134 119 103

86.3 82.6 76.7 67.7 58.6

130 124 115 102 88.0

71.1 68.1 63.3 55.9 48.3

107 102 95.1 84.0 72.5

54.8 52.6 49.1 43.6 37.8

82.3 79.0 73.8 65.5 56.8

31.1 30.8 30.2 28.6 25.8

46.7 46.3 45.4 43.0 38.8

12 14 16 18 20

65.6 53.3 41.8 33.0 26.8

98.6 80.0 62.8 49.7 40.3

57.1 46.3 36.2 28.7 23.3

49.0 39.6 31.0 24.5 19.9

73.6 59.5 46.5 36.9 29.9

40.3 32.5 25.3 20.1 16.3

60.5 48.8 38.0 30.2 24.5

31.7 25.6 20.0 15.9 12.9

47.6 38.5 30.1 23.9 19.5

22.1 18.2 14.4 11.6 9.48

33.3 27.3 21.7 17.4 14.3

22

22.2

33.3

19.2 28.9 16.5 24.8 13.5 20.3 10.7 Properties of 2 angles— 3/8 in. back to back

16.1

7.89

11.9

85.9 69.6 54.4 43.1 35.0

Ag , in.2 rx , in. ry , in.

5.52 0.895 1.43

4.86 0.903 1.42

rz , in. ASD

0.580 LRFD

0.580

4.22 0.910 1.41

3.56 0.918 1.39

2.88 0.926 1.38

2.18 0.933 1.37

0.585

0.586

Properties of single angle

Ωc = 1.67

φc = 0.90

0.581

0.583

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

No. of connectorsa

2L3× 3×

Shape

Y-Y Axis

Fy = 36 ksi

b

3

AISC_Part 4C:14th Ed.

2/23/11

10:37 AM

Page 129

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–129

Table 4-8 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Double Angles—Equal Legs

lb/ft

Y-Y Axis

X-X Axis

Design

1/2

3/8

5/16

1/4

3/16 c

15.4 Pn /Ωc φc Pn

11.8 Pn /Ωc φc Pn

10.0 Pn /Ωc φc Pn

8.20 Pn /Ωc φc Pn

6.14 Pn /Ωc φc Pn

0

ASD 97.4

LRFD 146

ASD 74.6

LRFD 112

ASD 62.9

LRFD 94.6

ASD 51.3

LRFD 77.1

ASD 38.1

LRFD 57.3

1 2 3 4 5

96.1 92.1 85.9 77.8 68.6

144 138 129 117 103

73.6 70.7 66.0 60.1 53.2

111 106 99.3 90.3 80.0

62.1 59.7 55.9 50.9 45.2

93.4 89.7 84.0 76.5 67.9

50.6 48.7 45.6 41.7 37.1

76.1 73.2 68.6 62.6 55.7

37.7 36.3 34.1 31.2 27.9

56.6 54.5 51.2 46.9 41.9

6 7 8 9 10

58.8 49.0 39.7 31.5 25.5

88.4 73.6 59.7 47.3 38.3

45.9 38.5 31.4 25.0 20.3

68.9 57.8 47.2 37.6 30.5

39.0 32.9 26.9 21.5 17.4

58.7 49.4 40.5 32.3 26.2

32.1 27.2 22.3 17.9 14.5

48.3 40.8 33.6 26.9 21.8

24.3 20.6 17.1 13.8 11.2

36.5 31.0 25.7 20.7 16.8

11 12

21.1 17.7

31.7 26.6

16.7 14.1

25.2 21.1

14.4 12.1

21.6 18.2

12.0 10.1

18.0 15.1

0

97.4

146

74.6

112

62.9

94.6

51.3

77.1

38.1

57.3

1 2 3 4 5

95.7 94.3 92.0 88.9 85.0

144 142 138 134 128

72.4 71.3 69.5 67.1 64.1

109 107 105 101 96.4

60.3 59.4 57.9 55.8 53.3

90.6 89.2 86.9 83.9 80.1

47.8 47.1 45.9 44.3 42.3

71.8 70.7 69.0 66.6 63.6

29.9 29.9 29.7 29.4 28.9

45.0 44.9 44.6 44.2 43.5

6 7 8 9 10

80.5 73.6 67.8 61.8 55.7

121 111 102 92.9 83.7

60.7 55.4 51.0 46.4 41.7

91.2 83.3 76.6 69.7 62.6

50.3 45.9 42.2 38.3 34.3

75.7 69.1 63.4 57.5 51.6

40.0 36.6 33.6 30.5 27.4

60.2 55.0 50.5 45.9 41.2

28.1 26.3 24.4 22.2 19.9

42.2 39.5 36.6 33.4 30.0

11 12 13 14 15

49.6 43.7 38.1 32.9 28.7

74.6 65.8 57.3 49.5 43.1

37.0 32.5 28.2 24.4 21.2

55.7 48.9 42.4 36.6 31.9

30.4 26.7 23.0 19.9 17.3

45.7 40.1 34.6 29.9 26.1

24.3 21.3 18.3 15.9 13.9

36.5 31.9 27.6 23.8 20.8

17.7 15.4 13.3 11.6 10.1

26.6 23.2 20.0 17.4 15.2

16 17 18 19 20

25.2 22.3 19.9 17.9 16.2

37.9 33.6 30.0 26.9 24.3

Ag , in.2 rx , in. ry , in.

4.52 0.735 1.23

rz , in. ASD

0.481 LRFD

Ωc = 1.67

φc = 0.90

18.7 28.1 15.3 22.9 12.2 16.6 24.9 13.5 20.3 10.8 14.8 22.2 12.1 18.2 9.66 13.3 20.0 10.9 16.3 8.68 12.0 18.0 Properties of 2 angles— 3/8 in. back to back 3.46 0.749 1.21

2.92 0.756 1.19

Properties of single angle 0.481 0.481

18.3 16.3 14.5 13.1

9.23 7.76

8.95 7.96 7.12 6.40

13.5 12.0 10.7 9.62

1.80 0.771 1.17

0.482

0.482

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

13.9 11.7

2.38 0.764 1.18

a

No. of connectorsa

2L21/2 × 21/2 ×

Shape

Effective length, KL (ft), with respect to indicated axis

2L21/2

3

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DESIGN OF COMPRESSION MEMBERS

Table 4-8 (continued)

Available Strength in Axial Compression, kips Double Angles—Equal Legs

2L2

lb/ft Design

X-X Axis

5/16

1/4

3/16

1/8c

9.40 Pn /Ωc φc Pn

7.84 Pn /Ωc φc Pn

6.38 Pn /Ωc φc Pn

4.88 Pn /Ωc φc Pn

3.30 Pn /Ωc φc Pn

ASD 59.1

LRFD 88.8

ASD 50.0

LRFD 75.2

ASD 40.7

LRFD 61.2

ASD 31.0

LRFD 46.7

ASD 19.3

LRFD 29.0

1 2 3 4 5 6 7 8 9 10

57.8 54.2 48.6 41.7 34.3 27.0 20.4 15.6 12.3

86.9 81.4 73.0 62.7 51.6 40.6 30.6 23.5 18.5

49.0 45.9 41.3 35.6 29.4 23.3 17.7 13.5 10.7

73.6 69.1 62.1 53.5 44.2 35.0 26.6 20.3 16.1

39.9 37.5 33.8 29.3 24.3 19.3 14.7 11.3 8.91 7.22

60.0 56.4 50.8 44.0 36.5 29.1 22.1 17.0 13.4 10.9

30.4 28.6 25.9 22.5 18.7 15.0 11.5 8.80 6.95 5.63

45.7 43.0 38.9 33.7 28.1 22.5 17.3 13.2 10.4 8.46

19.0 18.0 16.4 14.5 12.3 10.1 8.00 6.16 4.86 3.94

28.5 27.0 24.7 21.8 18.5 15.2 12.0 9.25 7.31 5.92

0

59.1

88.8

50.0

75.2

40.7

61.2

31.0

46.7

19.3

29.0

1 2 3 4 5

57.8 56.5 54.5 51.8 48.5

86.9 85.0 81.9 77.8 72.9

48.6 47.5 45.7 43.4 40.6

73.0 71.4 68.7 65.2 61.0

39.0 38.1 36.7 34.8 32.5

58.6 57.3 55.1 52.3 48.8

28.5 27.9 26.9 25.6 23.9

42.9 42.0 40.5 38.4 35.9

14.1 14.1 14.0 13.8 13.4

21.2 21.2 21.0 20.7 20.2

6 7 8 9 10

43.5 39.1 34.6 30.1 25.8

65.3 58.8 52.0 45.3 38.8

36.3 32.6 28.8 25.0 21.3

54.6 49.0 43.3 37.6 32.0

29.1 26.1 23.0 19.9 16.9

43.7 39.2 34.5 29.9 25.4

21.4 19.2 16.9 14.6 12.4

32.2 28.9 25.4 22.0 18.7

12.6 11.6 10.4 9.14 7.85

19.0 17.5 15.7 13.7 11.8

11 12 13 14 15

21.7 18.2 15.5 13.4 11.7

32.6 27.4 23.4 20.1 17.6

17.9 15.0 12.8 11.1 9.63

26.8 22.6 19.3 16.6 14.5

14.1 11.9 10.1 8.76 7.64

21.2 17.9 15.2 13.2 11.5

10.4 8.75 7.47 6.46 5.64

15.6 13.1 11.2 9.71 8.47

6.62 5.62 4.83 4.19 3.67

16

10.3

15.4

8.47 12.7 6.72 10.1 4.96 Properties of 2 angles— 3/8 in. back to back

0

Y-Y Axis

3/8

Ag , in.2 rx , in. ry , in.

2.74 0.591 1.01

2.32 0.598 0.996

rz , in. ASD

0.386 LRFD

0.386

1.89 0.605 0.982

9.94 8.45 7.26 6.30 5.51

7.46

1.44 0.612 0.967

0.982 0.620 0.951

0.389

0.391

Properties of single angle

Ωc = 1.67

φc = 0.90

0.387

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

No. of connectorsa

2L2× 2×

Shape

Effective length, KL (ft), with respect to indicated axis

Fy = 36 ksi

b

3

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–131

Table 4-9

Available Strength in Axial Compression, kips Double Angles—LLBB

Shape lb/ft

X-X Axis Y-Y Axis

Effective length, KL (ft), with respect to indicated axis

Design 0 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 0 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42

2L8 LLBB

2L8× 6× 7/8 3/4 5/8 9/16 c 1/2 c 7/16 c 1 88.4 78.2 67.6 57.0 51.4 46.0 40.4 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 565 554 540 522 500 474 444 413 380 346 313 279 247 216 188 166 147 131 117 106

849 832 812 785 751 712 668 621 571 521 470 420 371 325 283 249 220 197 176 159

496 486 475 459 439 416 391 363 335 305 276 247 218 191 167 147 130 116 104 93.8

745 731 713 690 660 626 588 546 503 459 414 371 328 288 251 220 195 174 156 141

565 528 516 500 480 457 420 389 357 324 291 258 227 197 172 151 134 120 108 97.2 88.3

849 794 776 752 722 686 631 585 536 486 437 388 341 296 258 227 202 180 162 146 133

496 456 446 432 415 394 363 336 308 279 251 223 195 169 148 130 116 103 92.9 83.9

745 685 670 649 623 593 545 505 463 420 377 334 294 255 222 196 174 155 140 126

431 423 413 399 383 363 341 318 293 267 242 217 192 169 147 129 115 102 91.8 82.9 75.2 431 385 377 365 351 334 307 285 261 237 212 188 165 143 125 110 98.1 87.7 78.8 71.3

648 636 621 600 575 546 513 477 440 402 364 326 289 254 221 195 172 154 138 125 113 648 579 566 549 527 502 462 428 393 356 319 283 248 215 188 166 147 132 118 107

361 354 346 335 321 305 287 268 247 226 205 184 164 144 126 110 97.9 87.3 78.3 70.7 64.1 361 302 299 294 286 275 255 236 216 195 174 154 134 116 102 90.1 80.1 71.7 64.6 58.4

543 533 520 503 483 458 431 402 371 340 308 276 246 217 189 166 147 131 118 106 96.4 543 453 449 442 430 414 383 355 325 293 262 231 201 175 153 135 120 108 97.1 87.8

314 309 302 293 281 268 252 236 219 201 183 165 148 131 115 101 89.2 79.6 71.4 64.5 58.5 314 254 252 248 243 234 219 204 188 170 153 135 118 103 90.7 80.3 71.5 64.1 57.7 52.3

472 464 454 440 422 402 379 355 329 302 275 248 222 197 172 151 134 120 107 96.9 87.9 472 382 379 373 365 352 329 307 282 256 230 203 178 155 136 121 107 96.3 86.8 78.6

267 263 257 250 240 229 217 204 189 175 160 145 130 116 103 90.1 79.9 71.2 63.9 57.7 52.3 267 208 206 203 199 194 183 171 159 145 131 117 103 90.0 79.3 70.4 62.8 56.3 50.8 46.1

402 395 387 375 361 345 326 306 285 263 240 218 196 175 154 135 120 107 96.1 86.7 78.6 402 312 310 306 300 291 274 258 239 218 197 176 155 135 119 106 94.4 84.7 76.4 69.2

220 216 212 206 199 191 181 171 160 148 137 125 113 102 90.8 80.2 71.0 63.3 56.8 51.3 46.5 220 162 161 159 156 153 146 138 129 119 109 97.9 87.2 76.8 68.0 60.5 54.1 48.7 44.0 39.9

330 325 319 310 300 287 273 257 240 223 205 188 170 153 136 120 107 95.2 85.4 77.1 69.9 330 244 242 239 235 229 219 207 194 179 163 147 131 115 102 90.9 81.3 73.2 66.1 60.0

Properties of 2 angles— 3/8 in. back to back 2

No. of connectorsa

Fy = 36 ksi

Ag , in. rx , in. ry , in.

26.2 2.49 2.52

23.0 2.50 2.50

rz , in.

1.28

1.28

20.0 2.52 2.47

16.8 2.54 2.45

15.2 2.55 2.44

13.6 2.55 2.43

12.0 2.56 2.42

1.30

1.30

1.31

Properties of single angle ASD

LRFD

Ωc = 1.67

φc = 0.90

1.29

1.29

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

2

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Page 132

4–132

DESIGN OF COMPRESSION MEMBERS

Table 4-9 (continued)

Available Strength in Axial Compression, kips

2L8× 4× 7/8 3/4 5/8 9/16 c 1/2 c 7/16 c 1 74.8 66.2 57.4 48.4 43.8 39.2 34.4 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn

Shape lb/ft

X-X Axis

Effective length, KL (ft), with respect to indicated axis

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 0 479 719 423 635 366 551 307 462 269 404 228 343 187 281

4 6 8 10 12

469 458 443 424 402

706 689 666 638 605

415 405 392 375 356

623 609 589 564 535

360 351 340 326 310

541 528 511 490 466

302 295 285 274 260

453 443 429 412 391

264 258 250 241 229

397 388 376 362 345

224 220 213 206 196

337 330 321 309 295

184 181 176 170 163

277 271 264 255 245

14 16 18 20 22

378 352 324 296 267

568 529 487 444 402

335 312 288 263 238

503 469 433 395 358

292 272 251 230 208

438 409 378 346 313

245 229 212 194 176

368 344 318 291 264

217 203 188 173 158

326 305 283 260 237

186 175 163 151 138

280 263 245 226 207

155 146 137 127 117

233 220 206 191 176

24 26 28 30 32

239 212 186 162 143

360 319 280 244 214

214 190 167 146 128

321 285 251 219 192

187 167 147 128 113

281 250 221 193 169

158 141 124 109 95.5

238 212 187 163 144

143 128 113 99.6 87.5

214 192 170 150 132

125 113 101 89.6 78.7

188 170 152 135 118

107 97.6 88.0 78.7 69.7

162 147 132 118 105

34 126 36 113 38 101 40 91.2 42 0 479

Y-Y Axis

No. of connectorsa

Double Angles—LLBB

2L8 LLBB

Design

Fy = 36 ksi

190 113 169 101 152 90.7 137 81.8 74.2

170 152 136 123 112

99.8 89.0 79.9 72.1 65.4

150 134 120 108 98.3

84.6 75.5 67.7 61.1 55.5

127 113 102 91.9 83.3

77.5 69.2 62.1 56.0 50.8

117 104 93.3 84.2 76.4

69.7 62.2 55.8 50.4 45.7

105 93.5 83.9 75.7 68.7

61.8 55.1 49.5 44.6 40.5

92.9 82.8 74.3 67.1 60.9

719 423

635 366

551

307

462

269

404

228

343

187

281

4 6 8 10 12

429 406 375 330 288

645 610 564 496 432

370 350 323 284 247

557 526 486 427 371

467 442 408 359 312

256 245 227 198 170

385 368 341 298 256

218 209 195 171 148

327 314 293 258 223

178 172 161 143 125

268 258 242 216 188

140 135 128 115 102

210 203 192 173 153

14 16 18 20 22

244 202 163 132 110

367 304 245 199 165

209 172 138 112 93.3

314 176 259 145 208 116 169 94.6 140 78.6

264 217 174 142 118

142 115 92.1 75.5 63.0

213 172 138 113 94.6

124 101 81.6 67.1 56.1

187 152 123 101 84.3

106 87.0 70.6 58.3 48.8

159 131 106 87.6 73.4

24 26

92.5 139 79.0 119

Ag , in.2 rx , in. ry , in.

22.2 2.51 1.60

rz , in. ASD

0.844 LRFD

Ωc = 1.67

φc = 0.90

311 294 272 239 208

87.5 72.9 59.7 49.5 41.7

131 110 89.7 74.4 62.6

78.7 118 66.3 99.7 53.2 80.0 47.5 71.4 41.4 62.3 35.5 53.3 67.2 101 Properties of 2 angles— 3/8 in. back to back 19.6 2.53 1.57 0.846

17.0 2.55 1.55

14.3 2.56 1.52

13.0 2.57 1.51

Properties of single angle 0.850 0.856 0.859

a

11.6 2.58 1.50 0.863

10.2 2.59 1.49 0.867

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

2

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Page 133

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–133

Table 4-9 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Double Angles—LLBB 3/4

5/8

1/2 c

7/16 c

3/8c

52.4 Pn /Ωc φc Pn

44.2 Pn /Ωc φc Pn

35.8 Pn /Ωc φc Pn

31.4 Pn /Ωc φc Pn

27.2 Pn /Ωc φc Pn

0

ASD 334

LRFD 502

ASD 280

LRFD 421

ASD 218

LRFD 328

ASD 182

LRFD 274

ASD 145

LRFD 218

4 6 8 10 12

326 316 303 286 267

490 475 455 430 402

273 265 254 241 225

411 399 382 362 338

213 207 199 189 177

321 312 299 284 267

178 173 167 159 150

268 261 251 239 225

142 139 134 128 121

213 208 201 192 182

14 16 18 20 22

246 225 202 180 158

370 338 304 270 237

208 190 171 152 134

312 285 257 229 201

165 151 137 123 109

247 227 206 184 163

140 129 117 106 94.6

210 193 176 159 142

114 106 97.1 88.4 79.7

171 159 146 133 120

24 26 28 30 32

137 117 101 87.8 77.2

205 176 151 132 116

116 99.8 86.1 75.0 65.9

175 150 129 113 99.0

95.0 82.1 70.8 61.6 54.2

143 123 106 92.7 81.4

83.5 72.9 63.0 54.9 48.2

125 110 94.6 82.4 72.5

71.1 62.8 54.9 47.8 42.0

107 94.4 82.5 71.9 63.2

34 36

68.4 61.0

58.4 52.1

87.7 78.3

48.0 42.8

72.1 64.3

42.7 38.1

64.2 57.3

37.2 33.2

55.9 49.9

lb/ft

X-X Axis

Effective length, KL (ft), with respect to indicated axis

Design

103 91.6

0

334

502

280

421

218

328

182

274

145

218

4 6 8 10 12

295 279 259 228 200

443 420 389 343 300

238 225 209 185 161

357 339 314 277 243

178 172 161 143 125

268 259 243 215 188

143 138 131 117 104

215 208 197 177 156

108 105 100 91.3 81.7

162 158 150 137 123

14 16 18 20 22

171 142 115 93.3 77.4

256 213 172 140 116

138 114 91.9 75.0 62.4

207 171 138 113 93.7

106 87.3 70.4 57.8 48.3

159 131 106 86.9 72.6

24 26

65.3 55.7

Ag , in.2 rx , in. ry , in. rz , in. ASD Ωc = 1.67

98.1 83.8

φc = 0.90

133 111 90.3 74.5 62.4

71.1 60.1 49.6 41.2 34.7

107 90.4 74.5 62.0 52.2

53.0

29.6

44.4

52.6 79.1 40.9 61.5 35.2 45.0 67.6 35.0 52.7 Properties of 2 angles— 3/8 in. back to back

15.5 2.21 1.61 0.855 LRFD

88.6 73.8 60.1 49.6 41.5

13.0 2.23 1.58

10.5 2.25 1.56

Properties of single angle 0.860 0.866

9.26 2.26 1.55

8.00 2.27 1.54

0.869

0.873

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

No. of connectorsa

2L7× 4×

Shape

Y-Y Axis

2L7 LLBB

b

2

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Page 134

4–134

DESIGN OF COMPRESSION MEMBERS

Table 4-9 (continued)

Available Strength in Axial Compression, kips Double Angles—LLBB

2L6 LLBB 7/8

lb/ft

54.4

X-X Axis

5/8

47.2

9/16

40.0

36.2

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 345

LRFD 518

ASD 300

LRFD 450

ASD 252

LRFD 379

ASD 229

LRFD 343

4 6 8 10 12

333 319 300 277 252

501 479 451 416 378

290 277 261 242 220

435 417 393 363 331

244 234 220 204 186

366 351 331 307 279

221 212 200 185 169

332 318 300 278 254

14 16 18 20 22

224 197 170 144 119

337 296 255 216 179

197 173 150 127 106

296 260 225 191 159

166 146 127 108 90.1

250 220 191 162 135

151 133 116 98.6 82.5

228 201 174 148 124

24 26 28 30

100 85.5 73.7 64.2

151 128 111 96.5

0

345

518

300

450

252

379

229

343

4 6 8 10 12

319 304 283 251 222

480 456 425 378 334

273 259 241 214 189

410 390 363 322 284

224 213 198 176 155

336 320 298 264 233

199 189 176 156 138

298 284 265 235 208

14 16 18 20 22

192 162 134 109 89.9

289 244 201 163 135

163 137 112 91.1 75.5

244 205 168 137 113

133 112 91.5 74.5 61.9

200 168 138 112 93.0

119 99.8 81.5 66.5 55.2

179 150 123 99.9 83.0

24 26 28

75.7 64.6 55.7

114 63.5 95.5 52.1 78.3 97.0 54.2 81.5 44.5 66.9 83.7 46.8 70.4 Properties of 2 angles— 3/8 in. back to back

46.6 39.8

70.0 59.8

Design

Effective length, KL (ft), with respect to indicated axis

3/4

Ag , in.2 rx , in. ry , (in.

89.0 75.9 65.4 57.0

16.0 1.86 1.71

134 114 98.3 85.6

13.9 1.88 1.68

75.7 64.5 55.6 48.5

114 97.0 83.6 72.9

11.7 1.89 1.66

69.3 59.1 50.9 44.4

No. of connectorsa

2L6× 4×

Shape

Y-Y Axis

Fy = 36 ksi

104 88.8 76.6 66.7

10.6 1.90 1.65

Properties of single angle

rz , in. ASD

0.854 LRFD

Ωc = 1.67

φc = 0.90

0.856

0.859

a

0.861

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

2

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Page 135

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–135

Table 4-9 (continued) Fy = 36 ksi

Available Strength in Axial Compression, kips Double Angles—LLBB 1/2

lb/ft

32.4

X-X Axis

3/8c

28.6

5/16 c

24.6

20.6

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 205

LRFD 308

ASD 175

LRFD 264

ASD 142

LRFD 213

ASD 108

LRFD 162

4 6 8 10 12

198 190 179 166 152

298 286 269 250 228

170 163 154 144 131

255 245 232 216 198

138 133 126 118 109

207 200 189 177 163

105 102 97.0 91.4 84.9

158 153 146 137 128

14 16 18 20 22

136 120 104 89.2 74.7

205 181 157 134 112

118 105 91.7 78.8 66.5

178 158 138 118 99.9

98.7 88.3 77.8 67.6 57.8

148 133 117 102 86.9

77.9 70.5 62.9 55.5 48.2

117 106 94.6 83.4 72.5

24 26 28 30 32

62.8 53.5 46.1 40.2

55.8 47.6 41.0 35.7 31.4

83.9 71.5 61.7 53.7 47.2

48.7 41.5 35.8 31.2 27.4

73.2 62.4 53.8 46.9 41.2

41.3 35.2 30.4 26.5 23.2

62.1 52.9 45.6 39.8 34.9

Design

Effective length, KL (ft), with respect to indicated axis

7/16 c

94.4 80.4 69.4 60.4

0

205

308

175

264

142

213

4 6 8 10 12

173 164 154 137 121

260 247 231 206 182

143 139 132 118 104

215 209 198 177 156

111 108 103 93.7 83.6

166 162 155 141 126

78.6 77.0 74.2 68.9 62.7

118 116 112 104 94.2

14 16 18 20 22

104 87.7 71.6 58.5 48.7

157 132 108 88.0 73.2

109 92.0 75.6 62.4 52.3

55.4 47.7 40.0 33.3 28.1

83.3 71.7 60.1 50.1 42.2

24 26

41.1 35.1

61.8 35.0 52.6 29.5 44.3 52.8 30.0 45.0 25.3 38.1 Properties of 2 angles— 3/8 in. back to back

24.0 20.7

36.0 31.0

Ag , in.2 rx , in. ry , in.

9.50 1.91 1.64

rz , in. ASD

0.864 LRFD

Ωc = 1.67

φc = 0.90

89.0 74.3 60.3 49.5 41.3

134 112 90.7 74.4 62.1

72.5 61.2 50.3 41.5 34.8

8.36 1.92 1.62

108

No. of connectorsa

2L6× 4×

Shape

Y-Y Axis

2L6 LLBB

162

7.22 1.93 1.61

6.06 1.94 1.60

0.870

0.874

Properties of single angle 0.867 a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

2

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Page 136

4–136

DESIGN OF COMPRESSION MEMBERS

Table 4-9 (continued)

Available Strength in Axial Compression, kips Double Angles—LLBB

2L6 LLBB 1/2

lb/ft

30.6

X-X Axis

5/16 c

23.4

19.6

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 194

LRFD 292

ASD 135

LRFD 203

ASD 103

LRFD 155

2 4 6 8 10

192 188 180 170 158

289 282 271 256 237

134 131 127 120 112

202 197 190 181 169

102 100 96.9 92.5 87.1

154 151 146 139 131

12 14 16 18 20

144 130 115 99.6 85.2

217 195 172 150 128

104 94.0 84.1 74.1 64.4

156 141 126 111 96.8

81.0 74.3 67.2 60.0 52.9

122 112 101 90.2 79.5

22 24 28 30 32

71.6 60.1 44.2 38.5 33.8

55.1 46.4 34.1 29.7 26.1

82.8 69.8 51.3 44.7 39.3

46.0 39.4 29.0 25.2 22.2

69.1 59.2 43.5 37.9 33.3

Design

Effective length, KL (ft), with respect to indicated axis

3/8c

108 90.4 66.4 57.8 50.8

0

194

292

135

203

2 4 6 8 10

166 160 150 133 116

250 240 225 200 175

107 105 101 91.9 81.0

161 158 152 138 122

76.5 75.2 72.6 67.3 60.6

115 113 109 101 91.0

103 84.6 67.2 54.2 44.5

52.5 43.9 35.6 29.0 24.0

78.9 66.0 53.5 43.5 36.0

20.1

30.2

12 14 16 18 20

98.0 79.8 62.8 50.1 40.9

147 120 94.4 75.3 61.4

22

34.0

51.0 24.7 37.2 Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

9.00 1.92 1.40

rz , in. ASD

0.756

68.7 56.3 44.7 36.1 29.6

6.88 1.93 1.38

103

Ωc = 1.67

φc = 0.90

0.763

a

5.78 1.94 1.37 0.767

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

155

Properties of single angle LRFD

No. of connectorsa

2L6× 31/2 ×

Shape

Y-Y Axis

Fy = 36 ksi

2

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–137

Table 4-9 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Double Angles—LLBB 3/4

5/8

1/2

3/8c

5/16 c

39.6 Pn /Ωc φc Pn

33.6 Pn /Ωc φc Pn

27.2 Pn /Ωc φc Pn

20.8 Pn /Ωc φc Pn

17.4 Pn /Ωc φc Pn

0

ASD 252

LRFD 379

ASD 213

LRFD 319

ASD 172

LRFD 259

ASD 129

LRFD 194

ASD 101

2 4 6 8 10

249 240 225 206 184

374 360 338 310 276

210 202 190 174 156

316 304 286 262 234

170 164 155 142 127

256 247 232 213 191

128 123 116 107 96.3

192 185 175 161 145

99.6 96.4 91.3 84.7 76.8

150 145 137 127 115

12 14 16 18 20

160 136 112 90.6 73.4

241 204 169 136 110

136 115 95.7 77.3 62.6

204 173 144 116 94.1

111 95.1 79.3 64.3 52.1

167 143 119 96.7 78.3

84.6 72.5 60.8 49.7 40.2

127 109 91.4 74.7 60.5

68.2 59.3 50.4 42.0 34.2

103 89.1 75.8 63.1 51.4

22 24

60.6 50.9

51.7 43.5

77.8 65.4

43.1 36.2

64.7 54.4

33.3 27.9

50.0 42.0

28.3 23.8

42.5 35.7

lb/ft

X-X Axis

Effective length, KL (ft), with respect to indicated axis

Design

91.1 76.6

101

No. of connectorsa

Shape

Y-Y Axis

2L5 LLBB

2L5× 31/2 ×

LRFD 151

0

252

379

213

319

172

259

129

194

2 4 6 8 10

241 232 218 195 172

362 348 327 293 258

199 192 180 161 141

300 289 271 242 212

157 151 142 127 111

235 227 213 190 167

108 106 102 92.6 81.6

162 159 153 139 123

79.1 78.0 75.5 69.9 62.5

119 117 113 105 94.0

12 14 16 18 20

147 122 98.6 81.9 66.5

221 183 148 123 99.9

120 99.6 79.8 63.3 51.4

181 150 120 95.2 77.3

94.8 78.4 62.6 49.8 40.5

143 118 94.1 74.9 60.9

69.3 56.9 45.2 36.2 29.6

104 85.6 68.0 54.5 44.5

53.9 44.8 36.1 29.1 23.9

80.9 67.4 54.2 43.7 35.9

22 24

55.0 46.3

82.7 69.6

42.6 37.5

64.0 56.4

33.6 28.3

50.5 42.5

24.6 20.8

37.0 31.3

19.9 16.9

30.0 25.4

b

151

2

3

Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

11.7 1.55 1.53

9.86 1.56 1.50

8.00 1.58 1.48

6.10 1.59 1.46

5.12 1.60 1.44

0.755

0.758

Properties of single angle

rz , in. ASD Ωc = 1.67

0.744 LRFD φc = 0.90

0.746

0.750

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 138

4–138

DESIGN OF COMPRESSION MEMBERS

Table 4-9 (continued)

Available Strength in Axial Compression, kips Double Angles—LLBB

2L5 LLBB 1/2

7/16

3/8c

5/16 c

1/4c

25.6 Pn /Ωc φc Pn

22.6 Pn /Ωc φc Pn

19.6 Pn /Ωc φc Pn

16.4 Pn /Ωc φc Pn

13.2 Pn /Ωc φc Pn

0

ASD 162

LRFD 243

ASD 143

LRFD 214

ASD 121

LRFD 182

ASD 94.8

LRFD 142

ASD 67.2

LRFD 101

2 4 6 8 10

160 154 145 133 119

240 231 218 200 179

141 136 128 118 106

212 204 193 177 159

120 116 109 101 90.6

180 174 164 151 136

93.8 90.8 86.1 79.9 72.6

141 136 129 120 109

66.6 64.8 61.9 58.0 53.3

100 97.4 93.0 87.1 80.1

12 14 16 18 20

104 89.2 74.3 60.3 48.9

157 134 112 90.7 73.4

92.7 79.3 66.2 53.9 43.7

139 119 99.5 81.0 65.6

79.7 68.5 57.5 47.2 38.2

120 103 86.5 70.9 57.4

64.5 56.2 47.9 39.9 32.6

97.0 84.4 72.0 60.0 49.0

48.1 42.7 37.1 31.7 26.6

72.3 64.1 55.8 47.6 39.9

22 24

40.4 33.9

60.7 51.0

36.1 30.3

54.2 45.6

31.6 26.5

47.5 39.9

26.9 22.6

40.5 34.0

22.0 18.5

33.0 27.7

lb/ft

X-X Axis

Effective length, KL (ft), with respect to indicated axis

Design

0

162

243

143

214

121

182

94.8

142

67.2

2 4 6 8 10

145 137 125 107 89.1

218 206 189 161 134

124 118 108 92.2 76.8

186 177 162 139 115

102 98.5 91.7 78.6 65.0

153 148 138 118 97.7

75.1 73.1 68.9 60.4 50.8

113 110 104 90.7 76.3

49.3 48.2 46.0 41.4 35.8

74.1 72.4 69.1 62.3 53.9

12 14 16 18 20

71.0 54.0 41.7 33.1 26.9

51.2 38.8 30.2 24.1 19.6

77.0 58.4 45.4 36.2 29.5

40.8 31.4 24.6 19.7 16.1

61.3 47.2 36.9 29.6 24.2

29.6 23.4 18.5 15.0

44.5 35.1 27.8 22.5

107 81.2 62.6 49.7 40.4

61.2 46.6 36.0 28.6 23.3

92.0 70.0 54.1 43.0 35.0

Ag , in. rx , in. ry , in.

7.50 1.58 1.24

6.62 1.59 1.23

5.72 1.60 1.22

4.82 1.61 1.21

3.88 1.62 1.19

0.649

0.652

Properties of single angle

rz , in. ASD Ωc = 1.67

0.642 LRFD φc = 0.90

0.644

0.646

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

101

Properties of 2 angles— 3/8 in. back to back 2

No. of connectorsa

2L5× 3×

Shape

Y-Y Axis

Fy = 36 ksi

2

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Page 139

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–139

Table 4-9 (continued) Fy = 36 ksi

Available Strength in Axial Compression, kips Double Angles—LLBB 1/2

lb/ft

23.8

X-X Axis

5/16 c

18.2

1/4c

15.4

12.4

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 151

LRFD 227

ASD 116

LRFD 174

ASD 96.7

LRFD 145

ASD 71.6

LRFD 108

2 4 6 8 10

148 139 126 109 91.4

222 209 189 165 137

113 107 97.0 84.7 71.1

170 161 146 127 107

94.9 89.5 81.3 71.0 59.6

143 135 122 107 89.6

70.3 66.7 61.2 54.2 46.3

106 100 92.0 81.4 69.6

12 14 16 18 20

73.3 56.4 43.2 34.1 27.6

48.2 37.4 28.7 22.7 18.3

72.4 56.3 43.1 34.0 27.6

38.2 30.5 23.6 18.6 15.1

57.5 45.8 35.4 28.0 22.7

Design

Y-Y Axis

3/8

No. of connectorsa

Shape

Effective length, KL (ft), with respect to indicated axis

2L4 LLBB

2L4× 31/2 ×

b

110 84.8 64.9 51.3 41.5

57.5 44.6 34.1 27.0 21.9

86.4 67.0 51.3 40.6 32.8

0

151

227

116

174

96.7

145

71.6

108

2 4 6 8 10

143 138 130 117 103

215 207 196 176 156

105 102 95.9 86.3 76.6

158 153 144 130 115

79.6 78.8 76.7 70.9 63.2

120 118 115 107 95.0

54.6 54.2 53.1 50.2 45.9

82.1 81.4 79.8 75.5 69.1

12 14 16 18 20

89.2 74.7 60.8 51.0 41.4

134 112 91.4 76.7 62.3

66.1 55.4 45.1 37.8 30.7

99.3 83.2 67.7 56.8 46.2

54.3 45.1 36.3 30.5 24.9

81.6 67.9 54.6 45.8 37.4

40.4 34.2 28.2 23.8 19.5

60.7 51.5 42.3 35.7 29.3

22 24 26

34.3 28.9 24.6

51.6 43.4 37.0

25.5 21.5

38.3 32.3

20.7 17.5

31.1 26.2

16.3 13.8

24.5 20.7

2

3

Properties of 2 angles— 3/8 in. back to back 2

Ag , in. rx , in. ry , in.

7.00 1.23 1.57

rz , in.

0.716

5.36 1.25 1.55

4.50 1.25 1.53

3.64 1.26 1.52

0.721

0.723

Properties of single angle ASD

LRFD

Ωc = 1.67

φc = 0.90

0.719 a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 140

4–140

DESIGN OF COMPRESSION MEMBERS

Table 4-9 (continued)

Available Strength in Axial Compression, kips Double Angles—LLBB

2L4 LLBB 5/8

1/2

3/8

5/16 c

1/4c

27.2 Pn /Ωc φc Pn

22.2 Pn /Ωc φc Pn

17.0 Pn /Ωc φc Pn

14.4 Pn /Ωc φc Pn

11.6 Pn /Ωc φc Pn

0

ASD 172

LRFD 259

ASD 140

LRFD 211

ASD 107

LRFD 161

ASD 89.8

LRFD 135

ASD 66.5

LRFD 99.9

2 4 6 8 10

169 159 144 125 104

253 239 216 188 157

137 129 117 102 85.6

206 195 176 154 129

105 99.5 90.4 79.1 66.6

158 149 136 119 100

88.2 83.3 75.9 66.6 56.2

133 125 114 100 84.5

65.3 62.0 56.9 50.5 43.3

98.2 93.3 85.6 75.9 65.1

45.8 35.9 27.5 21.7 17.6

68.8 53.9 41.3 32.6 26.4

35.8 28.7 22.2 17.6 14.2

53.9 43.1 33.4 26.4 21.4

lb/ft

X-X Axis

Effective length, KL (ft), with respect to indicated axis

Design

12 14 16 18 20

83.6 64.3 49.2 38.9 31.5

126 96.6 74.0 58.5 47.4

68.9 53.2 40.8 32.2 26.1

104 80.0 61.2 48.4 39.2

0

172

259

140

211

2 4 6 8 10

164 157 144 125 106

247 235 217 188 159

131 125 115 99.2 83.7

198 188 173 149 126

12 14 16 18 20

86.3 67.9 54.9 43.4 35.2

130 102 82.4 65.3 52.9

67.9 52.9 42.7 33.8 27.4

102 79.5 64.1 50.8 41.2

22

29.1

43.8

22.7

34.1

54.0 42.1 32.2 25.5 20.6

107

81.1 63.3 48.5 38.3 31.0

161

89.8

135

66.5

99.9

96.5 91.9 84.7 73.2 61.8

145 138 127 110 92.9

75.3 73.8 69.7 60.8 51.1

113 111 105 91.4 76.8

52.1 51.1 49.0 43.8 37.6

78.2 76.9 73.6 65.9 56.5

50.1 39.0 31.4 25.0 20.3

75.4 58.5 47.3 37.5 30.5

41.1 31.6 24.5 19.5 15.9

61.7 47.5 36.9 29.4 23.9

30.8 24.1 18.9 15.1 12.4

46.3 36.3 28.4 22.7 18.6

No. of connectorsa

2L4× 3×

Shape

Y-Y Axis

Fy = 36 ksi

b

2

3

Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

7.98 1.23 1.35

6.50 1.24 1.32

rz , in. ASD

0.631 LRFD

0.633

4.98 1.26 1.30

4.18 1.27 1.29

3.38 1.27 1.27

0.638

0.639

Properties of single angle

Ωc = 1.67

φc = 0.90

0.636

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 141

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–141

Table 4-9 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Double Angles—LLBB 1/2

7/16

3/8

5/16

1/4c

20.4 Pn /Ωc φc Pn

18.2 Pn /Ωc φc Pn

15.8 Pn /Ωc φc Pn

13.2 Pn /Ωc φc Pn

10.8 Pn /Ωc φc Pn

0

ASD 130

LRFD 196

ASD 115

LRFD 173

ASD 100

LRFD 150

ASD 84.1

LRFD 126

ASD 65.7

LRFD 98.8

2 4 6 8 10

127 117 103 85.2 67.2

191 176 154 128 101

112 104 91.1 75.9 60.1

169 156 137 114 90.3

97.5 90.3 79.5 66.5 52.8

147 136 119 99.9 79.4

82.0 75.9 66.8 55.9 44.4

123 114 100 84.0 66.8

64.2 59.7 52.9 44.6 35.9

96.4 89.7 79.5 67.1 54.0

12 14 16 18

50.1 36.8 28.2

45.2 33.2 25.4 20.1

67.9 49.9 38.2 30.2

39.9 29.4 22.5 17.8

60.0 44.1 33.8 26.7

33.5 24.7 18.9 14.9

50.4 37.1 28.4 22.4

27.5 20.4 15.6 12.3

41.4 30.6 23.4 18.5

lb/ft

X-X Axis

Effective length, KL (ft), with respect to indicated axis

Design

0

75.3 55.4 42.4

130

196

115

173

2 4 6 8 10

124 119 110 94.9 80.7

187 178 165 143 121

109 104 95.9 83.0 70.5

163 156 144 125 106

12 14 16 18 20

66.2 54.8 42.5 33.7 27.3

99.5 82.4 63.9 50.6 41.0

57.8 47.7 37.0 29.3 23.8

22

22.6

34.0

19.7

100

150

84.1

126

65.7

98.8

92.7 88.5 81.9 70.9 60.3

139 133 123 107 90.7

75.5 72.1 66.7 57.9 49.2

113 108 100 87.0 74.0

52.8 52.1 50.1 44.8 38.4

79.4 78.3 75.3 67.3 57.7

86.8 71.8 55.6 44.0 35.7

49.4 38.9 31.6 25.0 20.3

74.2 58.5 47.4 37.6 30.6

40.3 31.6 25.6 20.4 16.6

60.5 47.5 38.5 30.6 24.9

31.4 24.6 20.1 16.0 13.1

47.2 37.0 30.2 24.1 19.7

29.6

16.8

25.3

13.7

20.6

10.9

16.3

Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

6.04 1.07 1.37

5.34 1.08 1.36

rz , in. ASD

0.618 LRFD

0.620

4.64 1.09 1.35

3.90 1.09 1.33

3.16 1.10 1.32

0.624

0.628

Properties of single angle

Ωc = 1.67

φc = 0.90

0.622

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

No. of connectorsa

Shape

Y-Y Axis

2L31/2 LLBB

2L31/2 × 3×

b

2

3

AISC_Part 4C:14th Ed.

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Page 142

4–142

DESIGN OF COMPRESSION MEMBERS

Table 4-9 (continued)

Available Strength in Axial Compression, kips Double Angles—LLBB

2L31/2 LLBB 1/2

14.4

1/4c

12.2

9.80

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

X-X Axis

18.8

5/16

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

119 119 116 113 108 102 94.5 86.9 78.8 70.5 62.3 54.4 46.8 39.9 34.4 30.0 26.3 23.3 20.8

179 178 175 169 162 153 142 131 118 106 93.7 81.8 70.4 60.0 51.7 45.1 39.6 35.1 31.3

91.4 90.8 89.1 86.4 82.7 78.2 72.9 67.2 61.2 55.0 48.8 42.8 37.1 31.7 27.3 23.8 20.9 18.5 16.5

137 137 134 130 124 117 110 101 92.0 82.7 73.4 64.4 55.7 47.6 41.1 35.8 31.4 27.9 24.8

77.2 76.7 75.3 73.0 69.9 66.2 61.8 57.1 52.1 46.9 41.7 36.7 31.8 27.2 23.5 20.5 18.0 15.9 14.2

116 115 113 110 105 99.5 92.9 85.8 78.2 70.5 62.7 55.1 47.8 40.9 35.3 30.8 27.0 23.9 21.4

60.3 60.0 58.9 57.2 55.0 52.1 48.9 45.3 41.5 37.6 33.7 29.8 26.0 22.5 19.4 16.9 14.8 13.1 11.7

90.7 90.1 88.6 86.0 82.6 78.4 73.5 68.1 62.4 56.5 50.6 44.8 39.2 33.8 29.1 25.4 22.3 19.7 17.6

b

Y-Y Axis

lb/ft

3/8

No. of connectorsa

2L31/2 × 21/2 ×

Shape

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

119 114 113 109 105 99.8 91.3 83.9 76.1 68.1 60.1 52.4 47.2 40.3 34.8 30.4 26.7 23.7 21.2

179 172 169 164 158 150 137 126 114 102 90.4 78.7 70.9 60.6 52.4 45.7 40.2 35.6 31.8

91.4 84.8 83.4 81.0 77.8 73.9 67.7 62.2 56.4 50.4 44.4 38.6 33.0 29.6 25.6 22.4 19.7 17.5 15.6

137 127 125 122 117 111 102 93.4 84.7 75.7 66.8 58.0 49.6 44.5 38.5 33.6 29.6 26.3 23.4

77.2 69.1 67.9 66.0 63.5 60.3 55.2 50.8 46.0 41.1 36.2 31.4 26.8 22.9 19.8 18.1 16.0 14.2 12.7

116 104 102 99.2 95.4 90.6 83.0 76.3 69.1 61.7 54.3 47.1 40.2 34.4 29.8 27.3 24.0 21.3 19.1

60.3 49.5 49.2 48.6 47.6 46.0 42.8 39.5 35.8 32.0 28.1 24.3 20.8 17.9 15.5 13.6 12.0 10.7 9.56

90.7 74.4 74.0 73.1 71.6 69.1 64.3 59.3 53.8 48.0 42.2 36.6 31.2 26.8 23.3 20.4 18.1 16.1 14.4

2

Design

Effective length, KL (ft), with respect to indicated axis

Fy = 36 ksi

3

Properties of 2 angles— 3/8 in. back to back Ag , in.2 rx , in. ry , in.

5.54 1.08 1.13

rz , in.

0.532

4.24 1.10 1.11

3.58 1.11 1.09

2.90 1.12 1.08

0.538

0.541

Properties of single angle ASD

LRFD

Ωc = 1.67

φc = 0.90

0.535 a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/23/11

10:38 AM

Page 143

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–143

Table 4-9 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Double Angles—LLBB

lb/ft

7/16

3/8

5/16

1/4

X-X Axis

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

ASD 108 107 104 99.3 93.1 85.7 77.5 68.8 60.0 51.3 43.2 35.7 30.0 25.6 22.1 19.2

LRFD 162 161 156 149 140 129 117 103 90.2 77.2 64.9 53.7 45.1 38.4 33.1 28.9

ASD 95.7 94.9 92.3 88.3 82.9 76.4 69.2 61.5 53.8 46.1 38.9 32.2 27.1 23.1 19.9 17.3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

108 105 103 100 96.8 92.3 87.0 79.4 72.8 66.0 59.1 52.3 45.7 39.4 34.0 29.7 26.1 23.1 20.7 18.5

162 158 155 151 145 139 131 119 109 99.2 88.8 78.6 68.7 59.3 51.2 44.6 39.2 34.8 31.0 27.9

95.7 144 83.2 125 70.3 106 56.9 92.3 139 79.3 119 65.4 98.3 50.6 90.8 137 78.0 117 64.4 96.8 49.8 88.4 133 75.9 114 62.7 94.2 48.5 85.1 128 73.0 110 60.3 90.7 46.7 81.0 122 69.5 104 57.4 86.3 44.6 74.2 111 63.6 95.7 52.7 79.2 41.0 68.4 103 58.6 88.2 48.6 73.0 37.8 62.2 93.5 53.3 80.2 44.2 66.4 34.4 55.9 84.0 47.9 72.0 39.7 59.6 30.9 49.6 74.5 42.4 63.8 35.1 52.8 27.4 43.4 65.2 37.1 55.8 30.7 46.2 23.9 39.4 59.2 33.6 50.6 27.8 41.8 21.5 33.9 50.9 28.9 43.4 23.8 35.8 18.5 29.2 43.9 24.9 37.5 20.6 31.0 16.0 25.5 38.3 21.8 32.7 18.0 27.1 14.0 22.4 33.7 19.1 28.8 15.8 23.8 12.3 19.9 29.9 17.0 25.5 14.1 21.1 11.0 17.7 26.7 15.2 22.8 12.6 18.9 9.79 15.9 24.0 13.6 20.5 11.3 17.0 Properties of 2 angles— 3/8 in. back to back

LRFD 144 143 139 133 125 115 104 92.5 80.8 69.3 58.4 48.4 40.7 34.7 29.9 26.0

Ag , in.2 rx , in. ry , in.

5.00 0.910 1.18

4.44 0.917 1.16

rz , in. ASD

0.516 LRFD

0.516

Ωc = 1.67

3/16 c

17.0 15.2 13.2 11.2 9.00 6.78 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn

Y-Y Axis

Effective length, KL (ft), with respect to indicated axis

Design

1/2

φc = 0.90

ASD 83.2 82.5 80.3 76.8 72.2 66.6 60.4 53.9 47.1 40.5 34.2 28.4 23.9 20.4 17.6 15.3

LRFD 125 124 121 115 109 100 90.8 80.9 70.8 60.9 51.5 42.7 35.9 30.6 26.4 23.0

3.86 0.924 1.15

ASD LRFD 70.3 106 69.7 105 67.9 102 65.0 97.6 61.1 91.9 56.5 84.9 51.3 77.1 45.8 68.9 40.2 60.4 34.7 52.1 29.4 44.1 24.4 36.7 20.5 30.9 17.5 26.3 15.1 22.7 13.1 19.7

ASD 56.9 56.4 55.0 52.7 49.6 45.9 41.8 37.4 32.9 28.4 24.1 20.1 16.9 14.4 12.4 10.8

LRFD 85.5 84.8 82.7 79.2 74.6 69.0 62.8 56.2 49.4 42.7 36.3 30.2 25.4 21.7 18.7 16.3

ASD LRFD 39.3 59.1 39.0 58.6 38.1 57.3 36.7 55.1 34.8 52.2 32.4 48.7 29.8 44.8 26.9 40.5 24.0 36.1 21.1 31.7 18.2 27.3 15.5 23.3 13.0 19.5 11.1 16.7 9.55 14.4 8.32 12.5

85.5 76.0 74.8 72.9 70.3 67.0 61.6 56.8 51.7 46.4 41.1 35.9 32.4 27.8 24.1 21.0 18.5 16.5 14.7

39.3 30.4 30.2 30.0 29.6 29.0 27.5 25.9 23.9 21.6 19.3 17.0 14.7 13.3 11.6 10.2 9.00 8.01 7.18

59.1 45.6 45.5 45.1 44.5 43.5 41.4 38.9 35.9 32.5 29.0 25.5 22.1 20.0 15.3 13.5 12.0 10.8

3.26 0.932 1.14

2.64 0.940 1.12

2.00 0.947 1.11

Properties of single angle 0.517 0.518

0.520

0.521

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

No. of connectorsa

Shape

2L3 LLBB

2L3× 21/2 ×

b

2

3

AISC_Part 4C:14th Ed.

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4–144

DESIGN OF COMPRESSION MEMBERS

Table 4-9 (continued)

Available Strength in Axial Compression, kips Double Angles—LLBB

2L3 LLBB

lb/ft

Effective length,KL (ft), with respect to indicated axis X-X Axis

Design

1/2

3/8

5/16

1/4

3/16c

15.4 Pn /Ωc φc Pn

11.8 Pn /Ωc φc Pn

10.0 Pn /Ωc φc Pn

8.20 Pn /Ωc φc Pn

6.14 Pn /Ωc φc Pn

0

ASD 97.4

LRFD 146

ASD 75.4

LRFD 113

ASD 63.8

LRFD 95.9

ASD 51.7

LRFD 77.8

ASD 36.0

LRFD 54.1

1 2 3 4 5

96.6 94.0 89.9 84.5 78.0

145 141 135 127 117

74.8 72.9 69.8 65.7 60.8

112 110 105 98.8 91.4

63.3 61.7 59.1 55.7 51.6

95.1 92.7 88.8 83.7 77.6

51.3 50.0 48.0 45.3 42.0

77.1 75.2 72.1 68.0 63.1

35.7 34.9 33.6 31.9 29.8

53.7 52.5 50.6 48.0 44.8

6 7 8 9 10

70.7 62.9 55.1 47.3 39.9

106 94.6 82.8 71.1 60.0

55.3 49.4 43.4 37.5 31.8

83.1 74.3 65.3 56.3 47.8

47.0 42.1 37.1 32.1 27.3

70.7 63.3 55.7 48.2 41.0

38.3 34.4 30.3 26.3 22.5

57.6 51.7 45.6 39.5 33.7

27.5 24.9 22.3 19.6 17.0

41.3 37.5 33.5 29.5 25.6

11 12 13 14 15

33.1 27.9 23.7 20.5 17.8

49.8 41.9 35.7 30.8 26.8

26.5 22.3 19.0 16.4 14.3

39.8 33.5 28.5 24.6 21.4

22.8 19.2 16.3 14.1 12.3

34.3 28.8 24.5 21.2 18.4

18.8 15.8 13.5 11.6 10.1

28.3 23.7 20.2 17.4 15.2

14.5 12.3 10.4 9.00 7.84

21.9 18.4 15.7 13.5 11.8

6.89

10.4

16 0

97.4

146

75.4

113

63.8

95.9

51.7

77.8

36.0

54.1

1 2 3 4 5

94.0 91.7 88.0 83.0 74.8

141 138 132 125 112

71.1 69.3 66.4 62.4 56.1

107 104 99.7 93.8 84.4

58.6 57.1 54.7 51.4 46.3

88.1 85.8 82.2 77.3 69.5

45.3 44.1 42.3 39.9 36.0

68.0 66.3 63.6 59.9 54.1

28.6 28.3 27.8 26.8 24.8

43.0 42.6 41.7 40.3 37.2

6 7 8 9 10

67.3 59.5 51.5 43.7 38.3

101 89.4 77.4 65.7 57.6

50.3 44.2 38.1 32.1 27.8

75.7 66.5 57.2 48.2 41.8

41.5 36.4 31.3 26.3 22.7

62.3 54.7 47.0 39.5 34.1

32.3 28.4 24.4 20.5 17.6

48.5 42.6 36.6 30.8 26.5

22.5 19.9 17.2 14.5 12.0

33.8 29.9 25.8 21.8 18.1

11 12 13 14 15

31.7 26.7 22.8 19.7 17.1

47.7 40.1 34.2 29.5 25.8

23.0 19.4 16.6 14.3 12.5

34.6 29.2 24.9 21.5 18.8

18.8 15.9 13.6 11.7

28.3 23.9 20.4 17.6

14.7 12.4 10.6 9.17

22.0 18.6 15.9 13.8

10.1 8.57 7.36 6.39

15.2 12.9 11.1 9.60

No. of connectorsa

2L3× 2×

Shape

Y-Y Axis

Fy = 36 ksi

b

2

3

Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

4.52 0.922 0.940

rz , in. ASD

0.425 LRFD

Ωc = 1.67

φc = 0.90

3.50 0.937 0.911

2.96 0.945 0.897

Properties of single angle 0.426 0.428

2.40 0.953 0.883

1.83 0.961 0.869

0.431

0.435

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 145

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–145

Table 4-9 (continued) Fy = 36 ksi

Available Strength in Axial Compression, kips Double Angles—LLBB 3/8

lb/ft

10.6

X-X Axis

1/4

9.00

3/16 c

7.24

5.50

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 66.8

LRFD 100

ASD 56.9

LRFD 85.5

ASD 46.1

LRFD 69.3

ASD 34.8

LRFD 52.2

1 2 3 4 5

66.0 63.5 59.5 54.3 48.4

99.2 95.4 89.4 81.7 72.7

56.2 54.1 50.8 46.5 41.5

84.5 81.3 76.3 69.9 62.3

45.6 43.9 41.3 37.8 33.8

68.5 66.0 62.0 56.9 50.9

34.3 33.1 31.2 28.7 25.8

51.6 49.8 46.9 43.1 38.8

6 7 8 9 10

42.0 35.5 29.2 23.4 19.0

63.1 53.3 43.9 35.2 28.5

36.1 30.6 25.3 20.4 16.5

54.2 46.0 38.1 30.6 24.8

29.5 25.1 20.9 16.9 13.7

44.4 37.8 31.4 25.3 20.5

22.6 19.4 16.2 13.2 10.7

34.0 29.1 24.3 19.8 16.1

11 12 13

15.7 13.2

23.6 19.8

13.6 11.5

20.5 17.2

11.3 9.49 8.08

17.0 14.3 12.1

0

66.8

56.9

85.5

46.1

69.3

34.8

52.2

1 2 3 4 5

64.4 62.8 60.4 57.0 53.1

96.7 94.4 90.7 85.7 79.7

54.0 52.7 50.6 47.8 43.1

81.1 79.2 76.0 71.8 64.8

42.4 41.4 39.8 37.6 34.0

63.8 62.3 59.8 56.5 51.1

28.4 28.2 27.7 26.9 24.8

42.7 42.3 41.7 40.4 37.3

6 7 8 9 10

47.4 42.3 37.1 31.9 27.0

71.3 63.6 55.7 48.0 40.6

38.9 34.4 29.9 25.4 22.3

58.5 51.7 44.9 38.2 33.5

30.7 27.1 23.5 20.0 17.5

46.1 40.8 35.4 30.1 26.3

22.6 20.0 17.3 14.6 12.7

33.9 30.0 25.9 21.9 19.0

11 12 13 14 15

22.4 18.9 16.1 13.9 12.1

33.7 28.4 24.2 20.9 18.2

18.5 15.6 13.3 11.5 10.0

27.8 23.4 20.0 17.3 15.1

14.5 12.3 10.5 9.05 7.89

21.8 18.4 15.7 13.6 11.9

10.6 8.97 7.68 6.66 5.82

15.9 13.5 11.5 10.0 8.75

Design

Effective length, KL (ft), with respect to indicated axis

5/16

100

8.83 7.42 6.32

No. of connectorsa

2L21/2 × 2×

Shape

Y-Y Axis

2L21/2 LLBB

b

13.3 11.2 9.50

2

3

Properties of 2 angles— 3/8 in. back to back 2

Ag , in. rx , in. ry , in.

3.10 0.766 0.957

rz , in. ASD

0.419 LRFD

Ωc = 1.67

φc = 0.90

2.64 0.774 0.943

2.14 0.782 0.930

1.64 0.790 0.916

0.423

0.426

Properties of single angle 0.420 a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 146

4–146

DESIGN OF COMPRESSION MEMBERS

Table 4-10

Available Strength in Axial Compression, kips

2L8× 6× 7/8 3/4 5/8 9/16 c 1/2 c 7/16 c 1 88.4 78.2 67.6 57.0 51.4 46.0 40.4 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn

Shape lb/ft

X-X Axis

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 0 565 849 496 745 431 648 361 543 314 472 267 402 220 330

4 6 8 10 12

542 515 479 437 391

815 774 720 657 587

476 453 422 386 346

716 681 635 580 520

414 394 368 337 302

623 593 553 506 454

347 331 309 284 255

522 498 465 426 383

303 289 271 250 226

455 435 408 375 339

258 247 233 215 196

388 372 350 324 295

213 205 194 180 165

320 308 291 271 248

14 16 18 20 22

342 293 246 202 167

514 441 370 304 251

304 261 220 182 150

456 393 331 273 226

265 229 193 160 132

399 344 291 240 199

225 195 165 137 114

338 293 248 206 171

200 175 149 126 104

301 262 225 189 156

175 154 133 113 94.0

263 231 200 170 141

149 132 115 99.2 83.8

224 199 174 149 126

24 140 26 120 28 103 30 0 565

Y-Y Axis

Effective length, KL (ft), with respect to indicated axis

No. of connectorsa

Double Angles—SLBB

2L8 SLBB

Design

Fy = 36 ksi

211 126 190 111 167 180 108 162 94.6 142 155 92.7 139 81.5 123

95.4 143 81.3 122 70.1 105

87.3 131 79.0 119 70.5 106 74.4 112 67.3 101 60.0 90.2 64.1 96.4 58.0 87.2 51.8 77.8 45.1 67.8

849 496

745 431

648 361

543

314

472

267

402

220

330

4 6 8 10 12

552 546 538 528 516

829 821 809 793 775

481 476 469 461 450

723 716 705 692 676

414 410 404 396 387

622 616 607 595 582

300 300 300 299 298

451 451 450 449 447

253 252 252 251 251

380 379 379 378 377

206 206 206 205 205

310 310 309 309 308

160 160 160 160 159

241 241 241 240 240

16 20 24 28 32

486 438 394 348 301

731 659 593 523 453

424 382 344 303 262

638 574 517 456 394

365 329 296 261 225

548 494 445 392 339

292 272 246 217 187

439 408 369 326 281

247 234 214 191 166

371 352 322 286 249

203 195 182 164 144

304 293 273 246 216

158 154 147 135 120

238 232 221 203 181

36 40 44 48 52

256 222 184 155 132

385 334 276 232 198

223 193 160 134 115

335 290 240 202 172

191 165 137 115 98.1

287 158 248 136 205 113 173 95.1 147 81.2

238 205 170 143 122

141 122 101 85.5 73.0

212 183 152 128 110

123 104 89.7 75.7 64.7

185 156 135 114 97.3

105 89.3 77.6 65.7 56.3

157 134 117 98.7 84.6

56 114 171 60 99.1 149

98.8 148 84.6 127 70.1 105 63.1 94.8 56.0 84.1 48.7 73.2 86.1 129 73.8 111 61.2 91.9 55.0 82.7 48.9 73.4 42.5 63.9 Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

26.2 1.72 3.77

23.0 1.74 3.75

rz , in. ASD

1.28 LRFD

1.28

Ωc = 1.67

φc = 0.90

20.0 1.75 3.72

16.8 1.77 3.70

b

15.2 1.78 3.69

13.6 1.79 3.68

12.0 1.80 3.66

Properties of single angle 1.29 1.29 1.30

1.30

1.31

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3

4

AISC_Part 4C:14th Ed.

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Page 147

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–147

Table 4-10 (continued)

Available Strength in Axial Compression, kips Double Angles—SLBB

2L8× 4× 7/8 3/4 5/8 9/16 c 1/2 c 7/16 c 1 74.8 66.2 57.4 48.4 43.8 39.2 34.4 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn

Shape lb/ft

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 0 479 719 423 635 366 551 307 462 269 404 228 343 187 281

4 6 8 10 12

427 370 303 234 171

642 556 455 352 257

378 328 270 210 154

568 493 405 315 231

14 125 189 113 170 16 96.0 144 86.4 130 18 0 479

Y-Y Axis

Effective length, KL (ft), with respect to indicated axis

X-X Axis

Design

2L8 SLBB No. of connectorsa

Fy = 36 ksi

328 286 236 184 136

493 430 355 277 204

99.8 150 76.4 115

276 241 200 157 116

415 363 300 236 175

243 214 179 142 108

365 321 269 214 162

207 184 156 126 97.1

312 277 235 189 146

171 154 132 109 85.6

258 231 199 163 129

85.6 129 79.3 119 72.1 108 64.5 97.0 65.5 98.5 60.7 91.2 55.2 82.9 49.4 74.3 43.6 65.5 39.0 58.7

719 423

635 366

551

307

462

269

404

228

343

187

281

4 6 8 10 12

474 469 463 456 447

712 705 696 685 672

417 413 408 402 394

627 621 614 604 592

361 358 353 347 340

542 537 531 522 511

258 258 258 258 257

388 387 387 387 387

218 218 218 218 218

328 328 328 328 328

178 178 178 178 178

268 268 268 268 268

139 139 139 139 139

209 209 209 209 209

16 20 24 28 32

425 389 356 320 283

638 585 535 481 426

374 343 313 282 249

562 515 471 423 374

323 296 270 243 214

485 445 406 365 322

256 245 225 202 179

385 369 339 304 268

217 215 198 179 159

327 323 298 269 239

178 176 168 154 137

267 265 253 231 206

139 138 135 127 115

208 207 203 192 174

36 40 44 48 52

247 211 182 153 131

371 318 274 230 196

217 185 160 134 114

325 279 240 202 172

186 159 137 115 97.8

280 239 205 172 147

155 132 111 93.0 79.2

233 199 166 140 119

138 119 100 84.1 71.7

208 179 150 126 108

120 104 88.3 74.3 63.4

181 156 133 112 95.3

102 89.3 76.8 64.9 55.4

154 134 115 97.6 83.3

56 113 60 98.1 64 86.3 68 76.4

169 147 130 115

98.6 148 85.9 129 75.5 113

b

6

84.4 127 68.4 103 61.9 93.0 54.7 82.2 47.8 71.9 73.5 110 61.0 91.7 53.9 81.0 47.7 71.7 41.7 62.7 64.6 97.1 53.6 80.6 47.4 71.3 41.9 63.0 36.7 55.1 7

Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

22.2 1.03 4.08

rz , in. ASD

0.844 LRFD

19.6 1.04 4.06

17.0 1.05 4.03

14.3 1.06 4.00

13.0 1.07 3.99

11.6 1.08 3.97

10.2 1.09 3.96

Properties of single angle

Ωc = 1.67

φc = 0.90

0.846

0.850

0.856

0.859

a

0.863

0.867

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/23/11

10:39 AM

Page 148

4–148

DESIGN OF COMPRESSION MEMBERS

Table 4-10 (continued)

Available Strength in Axial Compression, kips Double Angles—SLBB

2L7 SLBB

3/4

5/8

1/2 c

7/16 c

3/8c

52.4 Pn /Ωc φc Pn

44.2 Pn /Ωc φc Pn

35.8 Pn /Ωc φc Pn

31.4 Pn /Ωc φc Pn

27.2 Pn /Ωc φc Pn

0

ASD 334

LRFD 502

ASD 280

LRFD 421

ASD 218

LRFD 328

ASD 182

LRFD 274

ASD 145

LRFD 218

4 6 8 10 12

301 264 220 174 131

453 397 331 262 197

254 224 188 150 114

381 336 282 225 171

199 176 149 121 92.9

299 265 225 181 140

167 149 128 105 82.3

251 224 192 158 124

134 121 105 87.2 69.7

201 181 157 131 105

lb/ft

X-X Axis

Design

Y-Y Axis

14 16 18

96.3 73.7 58.2

145 111 87.5

83.8 64.1 50.7

126 96.4 76.2

68.9 52.7 41.7

104 79.3 62.6

61.9 47.4 37.4

93.0 71.2 56.2

53.4 40.9 32.3

b

80.3 61.5 48.6

0

334

502

280

421

218

328

182

274

145

218

4 6 8 10 12

328 324 318 311 303

493 487 479 468 455

273 270 265 260 253

411 406 399 390 380

179 179 179 178 178

269 269 268 268 267

142 142 142 142 142

214 214 214 214 213

107 107 107 107 106

161 161 160 160 160

16 20 24 28 32

283 251 222 192 163

425 378 334 289 245

236 209 185 160 135

354 315 278 241 204

176 163 145 126 107

264 245 218 189 161

141 135 122 107 92.0

212 203 184 161 138

106 104 97.9 87.7 76.2

159 156 147 132 115

36 40 44 48 52

145 113 93.1 78.3 66.7

203 169 140 118 100

112 93.4 77.3 65.0 55.4

168 140 116 97.6 83.2

88.6 72.2 59.7 50.2 42.8

133 108 89.8 75.5 64.4

77.1 63.2 52.3 44.0 37.6

116 94.9 78.6 66.2 56.4

64.7 53.8 44.6 37.6 32.1

97.3 80.8 67.0 56.4 48.2

56

57.5

47.8

71.8

37.0

55.5

32.4

48.7

27.7

41.6

86.5

No. of connectorsa

2L7× 4×

Shape

Effective length, KL (ft), with respect to indicated axis

Fy = 36 ksi

5

6

Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

15.5 1.08 3.48

13.0 1.10 3.46

10.5 1.11 3.43

9.26 1.12 3.42

8.00 1.12 3.40

0.869

0.873

Properties of single angle

rz , in. ASD Ωc = 1.67

0.855 LRFD φc = 0.90

0.860

0.866

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–149

Table 4-10 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Double Angles—SLBB 7/8

lb/ft

54.4

X-X Axis

5/8

47.2

9/16

40.0

36.2

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 345

LRFD 518

ASD 300

LRFD 450

ASD 252

LRFD 379

ASD 229

LRFD 343

4 6 8 10 12

312 275 231 184 140

469 414 347 277 210

272 241 204 164 126

409 362 306 246 189

229 204 172 139 107

345 306 259 209 161

208 185 157 128 98.6

313 278 236 192 148

14 16 18

103 78.9 62.4

155 119 93.7

0

345

518

300

450

252

379

229

343

4 6 8 10 12

338 332 324 314 303

508 499 487 473 455

293 288 281 272 262

440 432 422 409 394

245 240 235 227 219

368 361 353 342 329

221 217 211 205 197

331 326 318 308 296

16 20 24 28 32

268 233 197 161 132

402 350 296 242 198

231 201 169 138 113

348 302 255 208 170

193 168 141 115 93.1

290 252 212 172 140

174 151 127 103 83.7

262 227 191 155 126

36 40 44 48

104 84.3 69.7 58.6

156 127 105 88.0

Design

Y-Y Axis

3/4

92.9 71.1 56.2

140 107 84.4

89.2 72.3 59.8 50.2

134 109 89.8 75.5

79.6 60.9 48.1

120 91.6 72.3

73.6 59.7 49.3 41.5

111 89.7 74.2 62.3

73.4 56.2 44.4

No. of connectorsa

2L6× 4×

Shape

Effective length, KL (ft), with respect to indicated axis

2L6 SLBB

66.2 53.7 44.4 37.3

99.5 80.7 66.7 56.1

Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

16.0 1.10 2.96

13.9 1.12 2.94

11.7 1.13 2.91

10.6 1.14 2.90

Properties of single angle

rz , in. ASD

0.854 LRFD

Ωc = 1.67

φc = 0.90

0.856

0.859

a

0.861

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

110 84.4 66.7

4

5

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Page 150

4–150

DESIGN OF COMPRESSION MEMBERS

Table 4-10 (continued)

Available Strength in Axial Compression, kips Double Angles—SLBB

2L6 SLBB

1/2

lb/ft

32.4

X-X Axis

3/8c

28.6

5/16 c

24.6

20.6

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 205

LRFD 308

ASD 175

LRFD 264

ASD 142

LRFD 213

ASD 108

LRFD 162

4 6 8 10 12

187 166 141 114 88.4

280 249 212 172 133

160 143 123 100 78.5

241 216 184 151 118

131 118 102 84.9 67.7

197 177 154 128 102

100 91.5 80.5 68.3 55.8

151 138 121 103 83.9

14 16 18

65.7 50.3 39.8

44.0 33.8 26.7

66.2 50.8 40.2

Design

Y-Y Axis

7/16 c

98.8 75.7 59.8

58.9 45.1 35.6

88.5 67.8 53.5

51.7 39.6 31.3

77.8 59.5 47.0

0

205

308

175

264

142

213

4 6 8 10 12

196 193 188 182 175

295 289 283 274 263

143 143 143 142 141

215 215 215 214 212

110 110 110 109 109

166 165 165 165 164

77.9 77.8 77.7 77.5 77.2

117 117 117 116 116

16 20 24 28 32

155 134 113 91.8 72.2

233 202 170 138 108

132 116 97.7 79.7 62.8

198 174 147 120 94.4

105 94.4 80.8 66.7 53.3

157 142 121 100 80.1

75.7 71.4 63.3 53.5 43.8

114 107 95.1 80.4 65.9

36 40 44 48

57.1 47.8 39.5 33.2

49.8 40.4 33.5 28.1

74.8 60.8 50.3 42.3

42.3 34.4 28.5

63.6 51.7 42.8

35.0 28.5 23.7

52.7 42.9 35.6

85.9 71.8 59.4 50.0

108

No. of connectorsa

2L6× 4×

Shape

Effective length, KL (ft), with respect to indicated axis

Fy = 36 ksi

162

Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

9.50 1.14 2.89

rz , in. ASD

0.864 LRFD

Ωc = 1.67

φc = 0.90

8.36 1.15 2.88

7.22 1.16 2.86

6.06 1.17 2.85

0.870

0.874

Properties of single angle 0.867 a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

4

5

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–151

Table 4-10 (continued) Fy = 36 ksi

Available Strength in Axial Compression, kips Double Angles—SLBB 1/2

23.4

19.6

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

X-X Axis

30.6

5/16 c

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

194 192 188 180 170 158 145 131 116 101 86.4 72.7 61.1 52.1 44.9 39.1 34.4

292 289 282 271 256 238 218 196 174 151 130 109 91.9 78.3 67.5 58.8 51.7

135 134 131 127 121 113 105 95.3 85.6 75.9 66.2 57.0 48.3 41.1 35.5 30.9 27.2

203 202 198 191 181 170 157 143 129 114 99.5 85.7 72.6 61.8 53.3 46.4 40.8

103 102 100 97.2 92.9 87.8 81.8 75.3 68.4 61.4 54.4 47.6 41.1 35.1 30.2 26.3 23.1

155 154 151 146 140 132 123 113 103 92.3 81.8 71.5 61.8 52.7 45.4 39.6 34.8

b

Y-Y Axis

lb/ft

3/8c

No. of connectorsa

2L6× 31/2 ×

Shape

0 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 38 42 46 48

194 185 180 175 169 161 150 141 131 121 111 101 91.0 81.5 72.3 64.1 51.3 42.0 35.1 32.2

292 278 271 263 253 242 225 211 197 182 166 151 137 122 109 96.3 77.1 63.2 52.7 48.4

135 105 105 105 105 104 102 98.1 92.8 86.6 80.1 73.4 66.8 60.4 54.2 48.1 38.6 31.7 26.5 24.3

203 158 158 158 157 156 153 148 139 130 120 110 100 90.8 81.4 72.4 58.1 47.6 39.8 36.5

103 74.7 74.6 74.5 74.3 74.1 73.4 72.3 70.2 66.8 62.7 58.1 53.4 48.8 44.2 39.7 31.9 26.2 21.9 20.1

155 112 112 112 112 111 110 109 106 100 94.2 87.4 80.3 73.3 66.4 59.7 48.0 39.4 32.9 30.3

5

Design

Effective length, KL (ft), with respect to indicated axis

2L6 SLBB

Properties of 2 angles— 3/8 in. back to back Ag , in.2 rx , in. ry , in.

9.00 0.968 2.96

rz , in.

0.756

6.88 0.984 2.94

5.78 0.991 2.92

Properties of single angle ASD

LRFD

Ωc = 1.67

φc = 0.90

0.763

a

0.767

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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10:39 AM

Page 152

4–152

DESIGN OF COMPRESSION MEMBERS

Table 4-10 (continued)

Available Strength in Axial Compression, kips Double Angles—SLBB

2L5 SLBB

X-X Axis

Effective length, KL (ft), with respect to indicated axis

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Y-Y Axis

Design

0 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 38

Ag , in.2 rx , in. ry , in. rz , in. ASD Ωc = 1.67

3/4

5/8

1/2

3/8c

5/16 c

39.6 Pn /Ωc φc Pn

33.6 Pn /Ωc φc Pn

27.2 Pn /Ωc φc Pn

20.8 Pn /Ωc φc Pn

17.4 Pn /Ωc φc Pn

ASD 252 250 244 235 222 207 189 170 151 132 113 95.7 80.5 68.6 59.1 51.5 45.3

LRFD 379 376 367 353 334 310 284 256 227 198 170 144 121 103 88.8 77.4 68.0

ASD 213 211 206 198 188 175 161 145 129 113 97.6 82.9 69.6 59.3 51.2 44.6 39.2

ASD 172 171 167 161 153 143 131 119 106 93.3 80.8 68.9 58.0 49.4 42.6 37.1 32.6

ASD 129 128 126 121 115 108 99.9 91.0 81.7 72.4 63.2 54.3 46.0 39.2 33.8 29.4 25.9 22.9

LRFD 194 193 189 182 173 162 150 137 123 109 94.9 81.7 69.1 58.9 50.8 44.3 38.9 34.5

ASD 101 100 98.0 94.8 90.5 85.3 79.2 72.7 65.8 58.8 51.8 45.0 38.6 32.9 28.4 24.7 21.7 19.2

LRFD 151 150 147 143 136 128 119 109 98.9 88.3 77.8 67.7 58.0 49.4 42.6 37.1 32.6 28.9

252 239 231 221 210 191 176 161 145 129 114 99.0 85.4 74.4 65.4 58.0 46.4

379 360 348 333 315 288 265 241 217 194 171 149 128 112 98.3 87.1 69.8

213 319 172 259 129 201 302 161 243 106 194 292 156 234 106 185 279 149 224 104 176 264 141 212 102 160 241 128 193 94.8 147 222 118 177 87.5 134 202 107 161 79.6 121 181 96.4 145 71.5 107 161 85.6 129 63.5 94.5 142 75.1 113 55.7 82.2 123 65.1 97.8 48.2 70.9 107 56.2 84.4 41.6 61.8 92.8 49.0 73.6 36.3 54.3 81.6 43.1 64.7 32.0 48.1 72.3 38.2 57.4 28.4 38.5 57.9 30.6 46.0 22.7 Properties of 2 angles— 3/8 in. back to back

194 159 159 157 153 142 132 120 108 95.4 83.7 72.4 62.6 54.6 48.1 42.6 34.2

101 77.7 77.4 76.9 75.9 72.8 68.4 63.1 57.2 51.3 45.4 39.8 34.5 30.1 26.5 23.5 18.9

151 117 116 116 114 109 103 94.8 86.0 77.1 68.3 59.8 51.8 45.3 39.9 35.4 28.4

11.7 0.974 2.47 0.744 LRFD φc = 0.90

LRFD 319 317 310 298 282 263 241 218 194 170 147 125 105 89.2 76.9 67.0 58.9

9.86 0.987 2.45

LRFD 259 257 251 242 230 214 197 179 160 140 121 104 87.2 74.3 64.0 55.8 49.0

8.00 1.00 2.42

Properties of single angle 0.746 0.750

6.10 1.02 2.39

5.12 1.02 2.38

0.755

0.758

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

No. of connectorsa

2L5× 31/2 ×

Shape lb/ft

Fy = 36 ksi

b

4

AISC_Part 4C:14th Ed.

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Page 153

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–153

Table 4-10 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Double Angles—SLBB 1/2

7/16

3/8c

5/16 c

1/4c

25.6 Pn /Ωc φc Pn

22.6 Pn /Ωc φc Pn

19.6 Pn /Ωc φc Pn

16.4 Pn /Ωc φc Pn

13.2 Pn /Ωc φc Pn

0

ASD 162

LRFD 243

ASD 143

LRFD 214

ASD 121

LRFD 182

ASD 94.8

LRFD 142

ASD 67.2

LRFD 101

1 2 3 4 5

160 155 146 135 122

240 232 220 203 184

141 137 129 120 108

212 205 194 180 163

120 116 110 102 93.0

180 175 166 154 140

93.8 91.2 86.9 81.2 74.4

141 137 131 122 112

66.7 65.0 62.4 58.8 54.5

100 97.7 93.7 88.4 82.0

6 7 8 9 10

108 93.6 79.1 65.4 53.2

163 141 119 98.4 79.9

96.1 83.3 70.7 58.7 47.7

144 125 106 88.2 71.7

82.7 72.1 61.5 51.3 41.9

124 108 92.4 77.1 63.0

66.9 59.0 51.1 43.3 36.0

101 88.7 76.8 65.1 54.1

49.7 44.6 39.3 34.1 29.1

74.8 67.0 59.1 51.3 43.7

11 12 13 14

43.9 36.9 31.5

66.0 55.5 47.3

39.4 33.1 28.2

59.3 49.8 42.4

34.7 29.1 24.8

52.1 43.8 37.3

29.8 25.0 21.3 18.4

44.7 37.6 32.0 27.6

24.4 20.5 17.4 15.0

36.6 30.8 26.2 22.6

lb/ft

Y-Y Axis

X-X Axis

Design

0

162

243

143

214

121

182

94.8

142

67.2

6 8 10 12 14

153 148 142 134 123

230 222 213 202 185

134 130 124 118 108

202 195 187 177 162

100 99.8 99.2 97.4 91.3

150 150 149 146 137

73.7 73.5 73.3 72.7 70.5

111 111 110 109 106

48.1 48.0 47.9 47.6 47.1

72.3 72.2 72.0 71.5 70.7

16 18 20 22 24

114 104 94.0 84.0 74.3

171 156 141 126 112

26 28 30 32 34

65.1 56.3 49.0 43.1 38.2

38

30.6

99.6 90.9 82.1 73.3 64.8

150 137 123 110 97.4

84.7 77.5 70.0 62.6 55.3

127 116 105 94.1 83.2

66.7 61.7 56.3 50.8 45.3

100 92.8 84.7 76.3 68.1

45.9 43.8 40.7 37.2 33.5

69.0 65.8 61.1 55.8 50.4

97.8 84.6 73.7 64.8 57.4

56.6 48.9 42.6 37.5 33.2

85.1 73.5 64.1 56.4 49.9

48.4 41.8 36.5 32.1 28.5

72.7 62.9 54.9 48.3 42.8

40.0 34.9 30.4 26.8 23.8

60.1 52.4 45.7 40.3 35.7

29.9 27.3 24.0 21.1 18.8

44.9 41.1 36.0 31.8 28.2

46.0

26.6

40.0

22.8

34.3

19.1

28.6

15.1

22.6

Ag , in. rx , in. ry , in.

7.50 0.824 2.50

rz , in. ASD

0.642 LRFD

Ωc = 1.67

φc = 0.90

6.62 0.831 2.48

5.72 0.838 2.47

Properties of single angle 0.644 0.646

4.82 0.846 2.46

3.88 0.853 2.44

0.649

0.652

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

101

Properties of 2 angles— 3/8 in. back to back 2

No. of connectorsa

2L5× 3×

Shape

Effective length, KL (ft), with respect to indicated axis

2L5 SLBB

4

5

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Page 154

4–154

DESIGN OF COMPRESSION MEMBERS

Table 4-10 (continued)

Available Strength in Axial Compression, kips Double Angles—SLBB

2L4 SLBB

1/2

lb/ft

23.8

X-X Axis

5/16

18.2

1/4c

15.4

12.4

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 151

LRFD 227

ASD 116

LRFD 174

ASD 96.7

LRFD 145

ASD 71.6

LRFD 108

1 2 3 4 5

150 147 142 135 127

225 221 213 203 190

115 112 109 104 97.3

172 169 163 156 146

96.1 94.1 91.0 86.8 81.7

144 142 137 131 123

71.1 69.9 67.8 65.0 61.5

107 105 102 97.7 92.5

6 7 8 9 10

117 107 96.4 85.5 74.9

176 161 145 129 113

90.2 82.5 74.4 66.2 58.1

136 124 112 99.5 87.3

75.9 69.6 62.9 56.1 49.4

114 105 94.5 84.3 74.2

57.6 53.2 48.6 43.9 39.1

86.5 80.0 73.1 65.9 58.8

11 12 13 14 15

64.6 54.9 46.8 40.3 35.1

97.1 82.5 70.3 60.6 52.8

50.3 42.8 36.5 31.5 27.4

75.6 64.4 54.9 47.3 41.2

42.9 36.7 31.2 26.9 23.5

64.4 55.1 46.9 40.5 35.3

34.5 30.0 25.7 22.2 19.3

51.8 45.1 38.7 33.4 29.1

16 17

30.9 27.3

46.4 41.1

24.1 21.3

36.2 32.1

20.6 18.3

31.0 27.4

17.0 15.1

25.5 22.6

Design

Effective length, KL (ft), with respect to indicated axis

3/8

0

151

227

116

174

96.7

145

71.6

6 8 10 12 14

137 129 117 106 93.8

205 194 176 159 141

102 96.2 87.4 78.9 69.9

153 145 131 119 105

78.3 76.7 71.8 65.4 58.0

118 115 108 98.3 87.1

53.6 52.9 50.9 47.6 43.1

80.6 79.5 76.5 71.5 64.7

16 18 20 22 24

81.6 69.7 58.3 48.3 40.6

50.3 42.7 35.4 29.5 24.8

75.6 64.2 53.3 44.3 37.3

38.0 32.7 27.6 23.0 19.5

57.0 49.2 41.5 34.6 29.3

26 28 30

34.6 29.9 26.1

52.1 25.7 38.6 21.2 31.9 44.9 22.2 33.3 18.4 27.6 39.2 19.3 29.1 16.0 24.1 Properties of 2 angles— 3/8 in. back to back

16.7 14.4 12.6

25.1 21.7 19.0

123 105 87.7 72.6 61.1

Ag , in.2 rx , in. ry , in.

7.00 1.04 1.89

rz , in. ASD

0.716 LRFD

Ωc = 1.67

φc = 0.90

60.7 51.7 43.1 35.7 30.1

91.3 77.7 64.8 53.7 45.2

5.36 1.05 1.86

4.50 1.06 1.85

Properties of single angle 0.719 0.721 a

No. of connectorsa

2L4× 31/2 ×

Shape

Y-Y Axis

Fy = 36 ksi

108

3.64 1.07 1.83 0.723

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

3

AISC_Part 4C:14th Ed.

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10:39 AM

Page 155

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–155

Table 4-10 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Double Angles—SLBB 5/8

1/2

3/8

5/16

1/4c

27.2 Pn /Ωc φc Pn

22.2 Pn /Ωc φc Pn

17.0 Pn /Ωc φc Pn

14.4 Pn /Ωc φc Pn

11.6 Pn /Ωc φc Pn

0

ASD 172

LRFD 259

ASD 140

LRFD 211

ASD 107

LRFD 161

ASD 89.8

LRFD 135

ASD 66.5

LRFD 99.9

1 2 3 4 5

170 165 156 145 132

256 248 235 218 198

139 134 128 119 108

208 202 192 179 163

106 103 98.2 91.6 83.7

160 155 148 138 126

89.0 86.4 82.3 76.8 70.4

134 130 124 116 106

65.9 64.2 61.4 57.7 53.3

99.0 96.4 92.3 86.8 80.2

6 7 8 9 10

117 102 87.2 72.8 59.5

176 154 131 109 89.4

96.7 84.6 72.5 60.8 49.9

145 127 109 91.5 75.1

75.0 65.9 56.8 48.0 39.6

113 99.1 85.4 72.1 59.5

63.2 55.7 48.1 40.7 33.8

95.0 83.7 72.3 61.2 50.8

48.4 43.2 37.9 32.6 27.6

72.8 64.9 56.9 49.0 41.5

11 12 13 14

49.2 41.3 35.2 30.3

73.9 62.1 52.9 45.6

41.3 34.7 29.6 25.5

62.0 52.1 44.4 38.3

32.7 27.5 23.4 20.2

49.2 41.3 35.2 30.4

27.9 23.5 20.0 17.2

42.0 35.3 30.0 25.9

22.9 19.3 16.4 14.2

34.5 29.0 24.7 21.3

lb/ft

X-X Axis

Effective length, KL (ft), with respect to indicated axis

Design

0

172

259

140

211

6 8 10 12 14

159 151 141 126 113

239 227 212 189 170

129 122 113 101 90.5

193 183 171 152 136

97.0 91.8 85.5 76.4 68.2

120 103 87.5 72.8 61.3

59.9 51.6 43.7 36.3 30.6

16 18 20 22 24

99.4 86.1 73.3 61.3 51.5

149 129 110 92.1 77.4

26 28 30 32

43.9 37.9 33.0 29.0

66.0 56.9 49.6 43.6

79.5 68.6 58.2 48.5 40.8

107

161

89.8

135

66.5

99.9

146 138 129 115 103

74.1 73.0 68.4 62.3 55.4

111 110 103 93.7 83.2

51.1 50.7 49.0 46.0 41.7

76.8 76.1 73.7 69.1 62.6

48.2 41.1 35.8 29.7 25.1

72.4 61.7 53.8 44.7 37.7

36.8 31.9 27.1 23.6 19.9

55.3 47.9 40.7 35.5 29.9

32.2 27.8 24.2

17.0 14.7 12.9

25.6 22.1 19.3

90.0 77.5 65.6 54.6 45.9

34.7 52.2 26.1 39.2 21.4 30.0 45.1 22.5 33.8 18.5 26.1 39.3 19.6 29.5 16.1 23.0 34.5 17.2 25.9 Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

7.98 0.845 1.98

6.50 0.858 1.95

rz , in. ASD

0.631 LRFD

0.633

4.98 0.873 1.93

4.18 0.880 1.91

3.38 0.887 1.90

0.638

0.639

Properties of single angle

Ωc = 1.67

φc = 0.90

0.636

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

No. of connectorsa

2L4× 3×

Shape

Y-Y Axis

2L4 SLBB

b

3

4

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Page 156

4–156

DESIGN OF COMPRESSION MEMBERS

Table 4-10 (continued)

Available Strength in Axial Compression, kips Double Angles—SLBB

2L31/2 SLBB

1/2

7/16

3/8

5/16

1/4c

20.4 Pn /Ωc φc Pn

18.2 Pn /Ωc φc Pn

15.8 Pn /Ωc φc Pn

13.2 Pn /Ωc φc Pn

10.8 Pn /Ωc φc Pn

0

ASD 130

LRFD 196

ASD 115

LRFD 173

ASD 100

1 2 3 4 5

129 125 119 111 102

194 188 179 167 153

114 111 106 98.6 90.4

171 166 159 148 136

lb/ft

X-X Axis

Effective length, KL (ft), with respect to indicated axis

Design

LRFD 150

ASD 84.1

LRFD 126

ASD 65.7

LRFD 98.8

99.1 96.3 91.8 85.9 78.8

149 145 138 129 118

83.3 81.0 77.3 72.4 66.5

125 122 116 109 100

65.2 63.4 60.7 57.0 52.7

97.9 95.4 91.2 85.7 79.1

6 7 8 9 10

91.3 80.3 69.3 58.6 48.5

137 121 104 88.1 72.9

81.2 71.6 62.0 52.6 43.7

122 108 93.1 79.0 65.6

71.0 62.7 54.4 46.2 38.5

107 94.3 81.7 69.5 57.9

60.0 53.1 46.2 39.4 33.0

90.2 79.9 69.4 59.2 49.6

47.8 42.6 37.3 32.0 27.1

71.8 64.0 56.0 48.2 40.7

11 12 13 14 15

40.1 33.7 28.7 24.7

60.2 50.6 43.1 37.2

36.1 30.3 25.8 22.3

54.2 45.6 38.8 33.5

31.8 26.8 22.8 19.7

47.9 40.2 34.3 29.6

27.3 22.9 19.5 16.8 14.7

41.0 34.4 29.3 25.3 22.0

22.5 18.9 16.1 13.9 12.1

33.8 28.4 24.2 20.9 18.2

0

130

196

115

173

6 8 10 12 14

117 108 95.7 84.1 72.2

175 163 144 126 109

102 95.0 83.7 73.4 62.9

154 143 126 110 94.5

16 18 20 22 24

60.5 49.5 41.7 34.5 29.0

91.0 74.4 62.6 51.8 43.6

52.6 42.8 36.0 29.8 25.1

26 28

24.7 21.3

37.1 32.0

21.4

100

150

84.1

126

65.7

98.8

87.9 81.6 72.0 63.1 54.0

132 123 108 94.9 81.2

72.6 67.5 59.6 52.3 44.8

109 101 89.5 78.6 67.3

51.7 50.2 45.9 40.7 35.0

77.7 75.5 69.1 61.2 52.5

79.0 64.3 54.1 44.8 37.7

45.1 36.7 29.8 24.6 20.7

67.8 55.1 44.7 37.0 31.2

37.4 30.4 24.7 20.4 17.2

56.2 45.6 37.1 30.7 25.9

29.2 23.8 19.4 16.1 13.6

43.9 35.7 29.1 24.2 20.4

32.1

17.7

26.6

14.7

22.1

11.6

17.4

No. of connectorsa

2L31/2 × 3×

Shape

Y-Y Axis

Fy = 36 ksi

b

3

4

Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

6.04 0.877 1.69

5.34 0.885 1.67

4.64 0.892 1.66

3.90 0.900 1.65

3.16 0.908 1.63

0.624

0.628

Properties of single angle

rz , in. ASD Ωc = 1.67

0.618 LRFD φc = 0.90

0.620

0.622

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 4C:14th Ed.

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Page 157

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–157

Table 4-10 (continued) Fy = 36 ksi

Available Strength in Axial Compression, kips Double Angles—SLBB 1/2

lb/ft

18.8

X-X Axis

5/16

14.4

1/4 c

12.2

9.80

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 119

LRFD 179

ASD 91.4

LRFD 137

ASD 77.2

LRFD 116

ASD 60.3

LRFD 90.7

1 2 3 4 5

118 112 104 93.3 81.2

177 169 156 140 122

90.1 86.2 80.0 72.1 63.2

135 129 120 108 94.9

76.1 72.8 67.7 61.2 53.7

114 109 102 92.0 80.7

59.5 57.1 53.3 48.5 42.8

89.4 85.8 80.2 72.8 64.4

6 7 8 9 10

68.5 56.1 44.4 35.1 28.4

103 84.3 66.7 52.7 42.7

53.7 44.3 35.5 28.0 22.7

80.7 66.6 53.3 42.1 34.1

45.8 37.9 30.5 24.1 19.5

68.8 57.0 45.8 36.2 29.4

36.9 30.8 25.1 20.0 16.2

55.4 46.4 37.8 30.0 24.3

11 12

23.5

35.3

18.8

28.2

16.1 13.6

24.3 20.4

13.4 11.2

20.1 16.9

Design

Effective length, KL (ft), with respect to indicated axis

3/8

0

119

179

91.4

137

77.2

116

60.3

90.7

2 4 6 8 10

117 114 108 101 90.4

176 171 163 152 136

88.8 86.2 82.1 76.5 68.2

134 130 123 115 102

74.1 72.0 68.5 63.9 57.0

111 108 103 96.1 85.7

48.6 48.5 48.2 47.3 44.0

73.0 72.9 72.4 71.1 66.1

12 14 16 18 20

80.3 69.8 59.3 49.4 40.3

121 105 89.2 74.2 60.5

60.4 52.3 44.3 36.7 29.8

50.5 43.7 37.0 30.6 24.9

75.9 65.7 55.6 46.0 37.4

39.4 34.2 29.0 24.1 19.6

59.2 51.5 43.7 36.2 29.5

22 24 26 28

33.3 28.0 23.8 20.6

50.0 24.7 37.1 20.6 31.0 42.0 20.7 31.2 17.3 26.0 35.8 17.7 26.6 14.8 22.2 30.9 15.3 22.9 12.7 19.2 Properties of 2 angles— 3/8 in. back to back

16.3 13.7 11.7 10.1

24.4 20.6 17.6 15.2

Ag , in.2 rx , in. ry , in.

5.54 0.701 1.76

rz , in. ASD

0.532 LRFD

Ωc = 1.67

φc = 0.90

90.8 78.6 66.6 55.1 44.8

4.24 0.716 1.73

3.58 0.723 1.72

2.90 0.731 1.70

0.538

0.541

No. of connectorsa

2L31/2 × 21/2 ×

Shape

Y-Y Axis

2L31/2 SLBB

Properties of single angle 0.535 a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

4

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Page 158

4–158

DESIGN OF COMPRESSION MEMBERS

Table 4-10 (continued)

Available Strength in Axial Compression, kips Double Angles—SLBB

2L3 SLBB

1/2

lb/ft

X-X Axis

3/8

5/16

1/4

3/16c

17.0 15.2 13.2 11.2 9.00 6.78 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to indicated axis

7/16

0

ASD 108

LRFD 162

ASD 95.7

LRFD 144

ASD 83.2

LRFD 125

ASD 70.3

LRFD ASD 106 56.9

LRFD ASD 85.5 39.3

LRFD 59.1

1 2 3 4 5

106 102 94.4 85.2 74.6

160 153 142 128 112

94.3 90.3 84.0 75.9 66.7

142 136 126 114 100

82.0 78.6 73.2 66.3 58.4

123 118 110 99.7 87.7

69.3 66.5 62.0 56.3 49.7

104 99.9 93.2 84.6 74.7

56.1 53.9 50.3 45.8 40.5

84.4 81.0 75.7 68.8 60.8

38.8 37.4 35.2 32.4 29.0

58.4 56.3 53.0 48.6 43.6

6 7 8 9 10

63.5 52.4 42.0 33.2 26.9

95.4 78.8 63.2 49.9 40.4

56.9 47.1 37.9 30.0 24.3

85.5 70.8 57.0 45.1 36.5

49.9 41.5 33.6 26.6 21.5

75.0 62.4 50.4 39.9 32.4

42.6 35.6 28.9 22.9 18.6

64.1 53.5 43.4 34.5 27.9

34.9 29.2 23.8 18.9 15.3

52.4 43.9 35.8 28.5 23.0

25.3 21.6 18.0 14.6 11.8

38.1 32.5 27.1 22.0 17.8

11 12

22.2

33.4

20.1 16.9

30.2 25.4

17.8 15.0

26.7 22.5

15.4 12.9

23.1 12.7 19.4 10.6

19.0 16.0

0

9.78 8.22

162

95.7

144

83.2

125

70.3

106

56.9

85.5

39.3

59.1

2 4 6 8 10

105 101 94.5 83.5 72.8

158 152 142 126 109

93.1 89.4 83.5 73.7 64.2

140 134 125 111 96.5

80.4 77.1 71.9 63.4 55.1

121 116 108 95.3 82.7

67.1 64.3 60.0 53.0 46.0

101 96.7 90.2 79.6 69.1

52.9 50.8 47.5 42.0 36.5

79.5 76.4 71.4 63.1 54.9

29.9 29.7 29.3 27.9 25.2

44.9 44.7 44.1 42.0 37.9

12 14 16 18 20

61.5 50.4 41.6 32.9 26.7

92.4 75.7 62.6 49.5 40.1

54.1 44.2 36.5 28.8 23.4

81.3 66.5 54.8 43.3 35.1

46.3 37.7 30.9 24.4 19.8

69.6 56.6 46.4 36.7 29.8

38.6 31.4 25.7 20.3 16.5

58.0 47.2 38.6 30.5 24.8

30.7 25.0 20.4 16.2 13.1

46.2 37.5 30.6 24.3 19.7

21.6 17.9 14.2 11.8 9.59

32.5 26.8 21.4 17.7 14.4

22 24

22.1 18.5

33.1 27.9

19.3 16.2

29.1 24.4

16.4 13.8

24.6 20.7

13.6 11.5

20.5 10.9 17.2 9.15

16.3 13.8

7.96

12.0

Properties of 2 angles— 3/8 in. back to back 5.00 0.718 1.49

4.44 0.724 1.48

rz , in. ASD

0.516 LRFD

0.516

3.86 0.731 1.46

3.26 0.739 1.45

2.64 0.746 1.44

2.00 0.753 1.42

0.520

0.521

Properties of single angle

Ωc = 1.67

φc = 0.90

0.517

0.518

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

14.7 12.4

108

Ag , in.2 rx , in. ry , in.

No. of connectorsa

2L3× 21/2 ×

Shape

Y-Y Axis

Fy = 36 ksi

3

4

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–159

Table 4-10 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Double Angles—SLBB

lb/ft Design

3/8

5/16

1/4

3/16 c

15.4 Pn /Ωc φc Pn

11.8 Pn /Ωc φc Pn

10.0 Pn /Ωc φc Pn

8.20 Pn /Ωc φc Pn

6.14 Pn /Ωc φc Pn

0

ASD 97.4

LRFD 146

ASD 75.4

LRFD 113

ASD 63.8

LRFD 95.9

ASD 51.7

LRFD 77.8

ASD 36.0

LRFD 54.1

1 2 3 4 5

95.0 87.9 77.3 64.6 51.2

143 132 116 97.1 77.0

73.6 68.4 60.5 50.9 40.8

111 103 90.9 76.5 61.3

62.3 58.0 51.4 43.5 35.0

93.6 87.1 77.3 65.3 52.6

50.5 47.1 41.9 35.6 28.8

76.0 70.8 63.0 53.5 43.3

35.2 33.1 29.8 25.8 21.4

53.0 49.8 44.9 38.8 32.2

6 7 8 9

38.6 28.4 21.7 17.2

58.0 42.7 32.7 25.8

31.1 23.0 17.6 13.9

46.8 34.5 26.4 20.9

26.9 19.9 15.2 12.0

40.4 29.9 22.9 18.1

22.3 16.6 12.7 10.0

33.5 24.9 19.0 15.0

17.0 13.0 9.94 7.85

25.6 19.5 14.9 11.8

0

97.4

146

75.4

113

63.8

95.9

51.7

77.8

36.0

54.1

2 4 6 8 10

95.8 92.3 86.7 77.4 68.2

144 139 130 116 103

73.8 71.0 66.7 59.4 52.2

111 107 100 89.3 78.5

62.0 59.7 56.0 49.8 43.7

93.2 89.7 84.1 74.8 65.6

49.6 47.8 44.8 39.9 35.0

74.6 71.8 67.3 60.0 52.6

27.9 27.8 27.7 26.8 24.5

41.9 41.8 41.6 40.3 36.9

12 14 16 18 20

58.4 48.6 40.7 32.4 26.2

87.8 73.1 61.1 48.6 39.4

44.6 37.0 30.8 24.4 19.8

67.0 55.6 46.3 36.7 29.8

37.2 30.7 25.5 20.2 16.4

55.9 46.2 38.3 30.3 24.6

29.8 24.6 19.7 16.1 13.1

44.8 37.0 29.6 24.3 19.7

21.3 17.8 14.5 11.9 9.69

32.0 26.8 21.8 17.9 14.6

22 24 26

21.7 18.2 15.5

32.6 27.4 23.3

16.4 13.8

24.6 20.7

13.5 11.4

20.3 17.1

10.8 9.11

16.3 13.7

8.03 6.76

12.1 10.2

X-X Axis Y-Y Axis

1/2

No. of connectorsa

2L3× 2×

Shape

Effective length, KL (ft), with respect to indicated axis

2L3 SLBB

b

Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

4.52 0.543 1.56

3.50 0.555 1.54

rz , in. ASD

0.425 LRFD

0.426

2.96 0.562 1.52

2.40 0.569 1.51

1.83 0.577 1.49

0.431

0.435

Properties of single angle

Ωc = 1.67

φc = 0.90

0.428

a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4

5

AISC_Part 4C:14th Ed.

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10:40 AM

Page 160

4–160

DESIGN OF COMPRESSION MEMBERS

Table 4-10 (continued)

Available Strength in Axial Compression, kips Double Angles—SLBB

2L21/2 SLBB

3/8

lb/ft

10.6

X-X Axis

1/4

9.00

3/16 c

7.24

5.50

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

Pn /Ωc

φc Pn

0

ASD 66.8

LRFD 100

ASD 56.9

LRFD 85.5

ASD 46.1

LRFD 69.3

ASD 34.8

LRFD 52.2

1 2 3 4 5

65.3 61.0 54.3 46.2 37.6

98.2 91.6 81.7 69.5 56.5

55.6 52.0 46.5 39.7 32.5

83.6 78.2 69.9 59.7 48.8

45.1 42.3 37.9 32.5 26.7

67.8 63.5 57.0 48.9 40.2

34.0 32.0 28.8 24.9 20.6

51.2 48.0 43.3 37.4 31.0

6 7 8 9

29.2 21.8 16.7 13.2

43.9 32.7 25.0 19.8

25.4 19.0 14.5 11.5

38.1 28.5 21.8 17.3

21.0 15.8 12.1 9.57

31.6 23.8 18.2 14.4

16.4 12.5 9.53 7.53

24.6 18.7 14.3 11.3

0

66.8

56.9

85.5

46.1

69.3

34.8

52.2

2 4 6 8 10

64.8 61.3 55.9 47.7 39.7

97.4 92.2 84.0 71.7 59.7

54.8 51.8 47.2 40.3 33.5

82.4 77.9 71.0 60.5 50.3

43.8 41.4 36.8 31.6 26.0

65.9 62.2 55.3 47.5 39.0

28.0 27.7 26.6 23.5 19.4

42.0 41.7 39.9 35.3 29.1

12 14 16 18 20

31.8 24.3 18.6 14.7 11.9

47.7 36.5 28.0 22.1 17.9

26.7 20.4 15.6 12.3 10.0

40.1 30.6 23.5 18.6 15.0

20.4 16.0 12.3 9.71 7.87

30.6 24.0 18.4 14.6 11.8

15.2 11.9 9.20 7.29 5.92

22.9 18.0 13.8 11.0 8.90

Design

Effective length, KL (ft), with respect to indicated axis

5/16

100

No. of connectorsa

2L2 1/2 × 2×

Shape

Y-Y Axis

Fy = 36 ksi

Properties of 2 angles— 3/8 in. back to back

Ag , in.2 rx , in. ry , in.

3.10 0.574 1.27

rz , in. ASD

0.419 LRFD

Ωc = 1.67

φc = 0.90

2.64 0.581 1.26

2.14 0.589 1.24

1.64 0.597 1.23

0.423

0.426

Properties of single angle 0.420 a

For Y-Y axis, welded or pretensioned bolted intermediate connectors must be used. b For required number of intermediate connectors, see the discussion of Table 4-8. c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/r equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

b

3

4

AISC_Part 4C:14th Ed.

4/12/11

3:30 PM

Page 161

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–161

Table 4-11

Available Strength in Axial Compression, kips

Fy = 36 ksi

Concentrically Loaded Single Angles L8× 8×

Shape

11/8

lb/ft

ASD

78 /

1

56.9 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L8

51.0 45.0 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

9 16c /

3 4 /

5 8 /

38.9 Pn /Ωc φc Pn

32.7 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

29.6 Pn /Ωc φc Pn ASD

LRFD

0

362

544

326

489

287

431

248

373

208

313

181

272

1 2 3 4 5

361 358 352 345 335

543 538 529 518 504

324 321 317 310 301

488 483 476 465 453

286 283 279 273 265

430 426 419 410 399

247 245 241 236 230

371 368 362 355 345

208 206 203 198 193

312 309 305 298 290

181 179 177 173 169

272 269 265 260 253

6 7 8 9 10

324 311 297 281 265

487 467 446 423 399

291 279 267 253 238

437 420 401 380 358

257 247 235 223 211

386 371 354 336 317

222 213 204 193 182

334 320 306 290 274

187 180 172 163 154

281 270 258 245 231

163 157 150 143 135

245 236 226 215 204

11 12 13 14 15

248 231 214 197 180

373 348 322 296 270

223 208 192 177 161

336 312 289 266 243

198 184 170 157 144

297 277 256 236 216

171 159 147 136 124

257 239 222 204 187

144 135 125 115 105

217 202 188 173 158

127 119 111 102 94.2

192 179 167 154 142

16 17 18 19 20

163 147 132 118 107

245 221 198 178 160

147 132 118 106 95.9

220 199 178 160 144

130 118 106 94.8 85.5

196 177 159 142 129

113 102 91.3 82.0 74.0

170 153 137 123 111

145 133 121 111 103

87.0 79.2 72.5 66.6 61.4

131 119 109 100 92.2

56.7

85.3

21 22 23 24 25

96.8 88.2 80.7 74.1 68.3

26

63.1

94.9

95.9 86.8 77.9 69.9 63.1

144 130 117 105 94.9

86.0 129 78.1 117 70.5 106 63.3 95.1 57.1 85.9

77.6 117 70.7 106 64.7 97.2 59.4 89.3 54.8 82.3

67.1 101 61.1 91.9 55.9 84.1 51.4 77.2 47.3 71.2

57.3 52.2 47.7 43.8 40.4

86.1 78.4 71.7 65.9 60.7

51.8 47.2 43.2 39.7 36.6

77.9 71.0 64.9 59.6 55.0

50.6

43.8

37.4

56.1

33.8

50.8

76.1

65.8

Properties

Ag , in.2 rz , in. ASD Ωc = 1.67

16.8 1.56 LRFD

15.1 1.56 c

13.3 1.57

11.5 1.57

Shape is slender for compression with Fy = 36 ksi.

φc = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.69 1.58

8.77 1.58

AISC_Part 4C:14th Ed.

4/12/11

3:30 PM

Page 162

4–162

DESIGN OF COMPRESSION MEMBERS

Table 4-11 (continued)

Available Strength in Axial Compression, kips Concentrically Loaded Single Angles

L8

L8× 8×

Shape

L8× 6×

1 2c /

lb/ft

ASD

78 /

1

26.4 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

44.2 39.1 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

9 16c /

3 4 /

5 8 /

33.8 Pn /Ωc φc Pn

28.5 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

25.7 Pn /Ωc φc Pn ASD

LRFD

0

154

232

282

424

248

373

215

324

181

272

157

236

1 2 3 4 5

154 152 150 148 144

231 229 226 222 216

281 277 271 262 252

422 417 407 394 378

247 243 238 230 221

371 366 357 346 332

214 211 207 200 192

322 318 311 301 289

180 177 174 168 161

270 267 261 253 243

157 155 151 147 141

235 232 227 221 212

6 7 8 9 10

140 135 129 124 117

210 203 194 186 176

239 225 210 194 178

359 338 316 292 267

210 198 184 170 156

315 297 277 256 235

183 172 161 149 137

275 259 242 224 205

153 145 135 125 115

231 217 203 188 172

135 127 119 111 102

203 192 180 167 154

11 12 13 14 15

111 104 97.1 90.2 83.3

166 156 146 136 125

161 145 129 114 99.6

242 218 194 171 150

142 127 113 100 87.4

213 191 170 150 131

124 112 99.7 88.2 77.1

187 168 150 133 116

104 94.0 83.9 74.2 64.9

157 141 126 112 97.6

93.5 84.7 76.0 67.7 59.7

141 127 114 102 89.7

16 17 18 19 20

76.5 115 69.9 105 63.5 95.5 57.3 86.1 51.7 77.7

87.5 132 77.5 117 69.1 104 62.1 93.3 56.0 84.2

76.8 115 68.1 102 60.7 91.2 54.5 81.9 49.2 73.9

67.8 102 60.0 90.2 53.6 80.5 48.1 72.2 43.4 65.2

57.1 50.5 45.1 40.5 36.5

85.8 76.0 67.8 60.8 54.9

52.4 46.5 41.4 37.2 33.6

78.8 69.8 62.3 55.9 50.4

21 22 23 24 25

46.9 42.7 39.1 35.9 33.1

70.5 64.2 58.8 54.0 49.8

50.8

44.6

39.3

33.1

49.8

30.4

45.8

26

30.6

46.0

76.4

67.0

59.1

Properties

Ag , in.2 rz , in. ASD Ωc = 1.67

7.84 1.59 LRFD φc = 0.90

13.1 1.28

11.5 1.28

9.99 1.29

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.41 1.29

7.61 1.30

AISC_Part 4C:14th Ed.

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3:30 PM

Page 163

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–163

Table 4-11 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Concentrically Loaded Single Angles L8× 6×

Shape

1 2c /

lb/ft

Effective length, KL (ft), with respect to least radius of gyration, rz

Design

ASD

L8× 4× 7 16c /

23.0 Pn /Ωc φc Pn

ASD

78 /

3 4 /

33.1 Pn /Ωc φc Pn

28.7 Pn /Ωc φc Pn

1

20.2 37.4 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

L8

LRFD

ASD

LRFD

ASD

LRFD

ASD

5 8 /

LRFD

24.2 Pn /Ωc φc Pn ASD

LRFD

0

134

201

110

165

239

360

211

317

183

275

154

231

1 2 3 4 5

133 132 129 125 121

200 198 194 188 181

109 108 106 103 99.9

164 163 159 155 150

237 229 217 202 183

356 345 327 303 276

209 202 192 178 162

314 304 288 268 243

181 175 167 155 141

272 264 250 233 212

152 148 140 130 119

229 222 211 196 179

115 109 103 96.0 88.8

173 164 155 144 133

95.9 91.3 86.3 81.0 75.4

144 137 130 122 113

163 142 121 101 82.5

245 214 182 152 124

144 126 107 89.5 73.1

217 189 161 135 110

125 109 93.5 78.2 64.0

189 106 165 92.8 141 79.5 118 66.7 96.2 54.8

6 7 8 9 10 11 12 13 14 15

81.5 122 74.2 111 67.0 101 60.0 90.1 53.3 80.0

69.7 105 63.9 96.1 58.2 87.5 52.6 79.0 47.2 70.9

16 17 18 19 20

46.9 41.5 37.0 33.2 30.0

70.4 62.4 55.6 49.9 45.1

41.9 37.1 33.1 29.7 26.8

63.0 55.8 49.8 44.7 40.3

21

27.2

40.9

24.3

36.6

68.2 103 57.3 86.1 48.8 73.4 42.1 63.3

60.4 50.8 43.3 37.3

90.8 76.3 65.0 56.1

52.9 44.5 37.9 32.7

79.5 66.8 56.9 49.1

45.3 38.0 32.4 27.9

160 140 120 100 82.3 68.0 57.2 48.7 42.0

Properties

Ag , in.2 rz , in. ASD Ωc = 1.67

6.80 1.30 LRFD φc = 0.90

5.99 1.31

11.1 0.844

9.79 0.846

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.49 0.850

7.16 0.856

AISC_Part 4C:14th Ed.

4/12/11

3:31 PM

Page 164

4–164

DESIGN OF COMPRESSION MEMBERS

Table 4-11 (continued)

Available Strength in Axial Compression, kips L8-L7

Concentrically Loaded Single Angles L8× 4×

Shape

9 16c /

lb/ft

Effective length, KL (ft), with respect to least radius of gyration, rz

1 2c /

21.9 Pn /Ωc φc Pn

Design

Fy = 36 ksi

ASD

L7× 4× 7 16c /

19.6 17.2 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

1 2c /

3 4 /

5 8 /

26.2 Pn /Ωc φc Pn

22.1 Pn /Ωc φc Pn

LRFD

ASD

LRFD

0

134

202

114

171

93.6

141

167

251

140

211

109

164

1 2 3 4 5

133 129 123 115 105

200 194 185 172 158

113 110 105 98.3 90.4

170 165 158 148 136

92.8 90.5 86.7 81.6 75.6

140 136 130 123 114

165 160 152 141 129

248 241 228 212 194

139 134 128 119 108

208 202 192 179 163

108 105 100 93.6 85.7

163 158 151 141 129

103 115 92.5 100 81.3 85.9 70.3 72.0 59.7 59.1

6 7 8 9 10

94.1 141 82.8 124 71.4 107 60.4 90.8 50.0 75.1

81.6 123 72.4 109 62.9 94.6 53.8 80.8 45.1 67.7

68.8 61.5 54.1 46.8 39.7

11 12 13 14

41.3 34.7 29.6 25.5

37.3 31.3 26.7 23.0

33.1 27.8 23.7 20.5

62.1 52.2 44.5 38.3

56.0 47.1 40.1 34.6

49.8 41.8 35.7 30.7

ASD

48.8 41.0 34.9 30.1

LRFD

173 151 129 108 88.8 73.4 61.6 52.5 45.3

ASD

LRFD

17.9 Pn /Ωc φc Pn ASD

LRFD

96.9 146 84.8 127 72.7 109 61.1 91.8 50.2 75.4

77.0 116 67.8 102 58.6 88.1 49.7 74.6 41.2 61.9

41.5 34.8 29.7 25.6

34.0 28.6 24.4 21.0

62.3 52.4 44.6 38.5

51.1 43.0 36.6 31.6

Properties

Ag , in.2 rz , in. ASD Ωc = 1.67

6.49 0.859 LRFD φc = 0.90

5.80 0.863

5.11 0.867

7.74 0.855

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

6.50 0.860

5.26 0.866

AISC_Part 4C:14th Ed.

4/12/11

3:31 PM

Page 165

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–165

Table 4-11 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Concentrically Loaded Single Angles L7× 4×

Shape

7 16c /

lb/ft

Effective length, KL (ft), with respect to least radius of gyration, rz

Design

L6× 6× 3 8c /

15.7 Pn /Ωc φc Pn

L7-L6

78 /

3 4 /

33.1 Pn /Ωc φc Pn

28.7 Pn /Ωc φc Pn

1

13.6 37.4 Pn /Ωc φc Pn Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

91.0

137

72.4

109

237

356

210

316

182

274

154

231

1 2 3 4 5

90.2 87.8 83.8 78.6 72.4

136 132 126 118 109

71.8 70.1 67.2 63.4 58.8

108 105 101 95.2 88.3

236 232 226 217 206

354 349 339 326 310

209 206 200 192 183

314 309 301 289 275

181 178 174 167 159

273 268 261 251 239

153 150 146 141 134

230 226 220 211 201

6 7 8 9 10

65.5 58.1 50.7 43.4 36.4

98.4 87.4 76.1 65.2 54.8

53.6 48.1 42.4 36.8 31.4

80.6 72.3 63.8 55.3 47.2

194 181 166 151 136

292 272 250 228 205

172 160 147 134 121

259 241 222 202 182

149 139 128 116 105

225 209 192 175 158

126 117 108 98.1 88.3

189 176 162 148 133

11 12 13 14 15

30.2 25.3 21.6 18.6

45.3 38.1 32.5 28.0

26.3 22.1 18.8 16.2

39.5 121 33.2 107 28.3 93.0 24.4 80.2 69.9

182 161 140 121 105

108 94.7 82.4 71.1 61.9

162 142 124 107 93.1

54.4 48.2 43.0 38.6

81.8 72.5 64.6 58.0

61.4 54.4 48.5 43.5

LRFD

92.3 81.7 72.9 65.4

ASD

LRFD

ASD

LRFD

24.2 Pn /Ωc φc Pn

0

16 17 18 19

ASD

5 8 /

ASD

LRFD

93.3 140 82.2 123 71.5 108 61.7 92.7 53.7 80.7

78.6 118 69.2 104 60.3 90.6 52.0 78.1 45.3 68.1

47.2 41.8 37.3 33.5

39.8 35.3 31.4 28.2

71.0 62.9 56.1 50.3

59.8 53.0 47.3 42.4

Properties

Ag , in.2 rz , in. ASD Ωc = 1.67

4.63 0.869 LRFD φc = 0.90

4.00 0.873

11.0 1.17

9.75 1.17

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.46 1.17

7.13 1.17

AISC_Part 4C:14th Ed.

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3:32 PM

Page 166

4–166

DESIGN OF COMPRESSION MEMBERS

Table 4-11 (continued)

Available Strength in Axial Compression, kips Concentrically Loaded Single Angles

L6

L6× 6×

Shape

9 16 /

lb/ft

ASD

7 16c /

12 /

21.9 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

19.6 17.2 Pn /Ωc φc Pn Pn /Ωc φc Pn ASD

LRFD

ASD

5 16c /

14.9 Pn /Ωc φc Pn

12.4 Pn /Ωc φc Pn

78 /

27.2 Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

0

139

209

124

187

107

160

86.1

129

65.3

98.2

172

259

1 2 3 4 5

138 136 132 127 121

208 204 199 192 182

124 122 118 114 109

186 183 178 171 163

106 104 102 97.9 93.3

159 157 153 147 140

85.7 84.4 82.4 79.6 76.2

129 127 124 120 115

65.1 64.2 62.8 60.9 58.5

97.8 96.5 94.4 91.5 87.9

171 165 157 146 133

257 249 236 219 200

114 106 98.1 89.5 80.7

172 160 147 134 121

102 95.3 87.8 80.0 72.2

154 143 132 120 108

88.1 82.2 75.9 69.4 62.7

132 124 114 104 94.3

72.2 67.8 63.0 58.0 52.8

109 102 94.7 87.2 79.4

55.7 52.6 49.2 45.7 42.0

83.8 79.1 74.0 68.7 63.1

119 104 88.7 74.3 60.9

178 156 133 112 91.5

50.3 42.3 36.0 31.1

75.6 63.6 54.2 46.7

6 7 8 9 10

LRFD

L6× 4× 3 8c /

11 12 13 14 15

72.0 108 63.5 95.4 55.4 83.3 47.8 71.9 41.7 62.6

64.4 56.8 49.6 42.8 37.3

96.7 85.4 74.5 64.3 56.0

56.1 49.7 43.5 37.7 32.8

84.4 74.7 65.4 56.6 49.3

47.7 42.6 37.7 33.0 28.8

71.7 64.1 56.7 49.6 43.2

38.3 34.6 31.0 27.5 24.1

57.5 52.0 46.5 41.3 36.2

16 17 18 19

36.6 32.4 28.9 26.0

32.8 29.0 25.9 23.2

49.2 43.6 38.9 34.9

28.8 25.5 22.8 20.5

43.3 38.4 34.2 30.7

25.3 22.4 20.0 17.9

38.0 33.7 30.0 27.0

21.2 18.8 16.7 15.0

31.8 28.2 25.2 22.6

55.0 48.8 43.5 39.0

ASD

LRFD

Properties

Ag , in.2 rz , in. ASD Ωc = 1.67

6.45 1.18 LRFD φc = 0.90

5.77 1.18

5.08 1.18

4.38 1.19

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.67 1.19

8.00 0.854

AISC_Part 4C:14th Ed.

4/12/11

3:32 PM

Page 167

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–167

Table 4-11 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Concentrically Loaded Single Angles L6× 4×

Shape lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L6

3 4 /

5 8 /

9 16 /

12 /

7 16c /

23.6 Pn /Ωc φc Pn

20.0 Pn /Ωc φc Pn

18.1 Pn /Ωc φc Pn

16.2 Pn /Ωc φc Pn

14.3 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

0

150

225

126

190

114

ASD

172

LRFD

102

ASD

154

87.7

132

1 2 3 4 5

148 144 136 127 116

223 216 205 191 174

125 121 115 107 97.7

188 182 173 161 147

113 110 104 97.2 88.6

170 165 157 146 133

101 98.3 93.5 87.0 79.4

152 148 140 131 119

86.8 84.3 80.3 74.9 68.6

130 127 121 113 103

6 7 8 9 10

103 90.1 77.2 64.7 53.1

155 135 116 97.3 79.8

87.3 76.4 65.5 55.0 45.1

131 115 98.4 82.6 67.8

79.2 69.4 59.5 50.0 41.1

119 104 89.4 75.1 61.8

71.0 62.3 53.5 45.0 37.0

107 93.6 80.3 67.6 55.6

61.6 54.2 46.8 39.6 32.8

92.6 81.5 70.3 59.5 49.3

11 12 13 14

43.9 36.9 31.4 27.1

65.9 55.4 47.2 40.7

37.3 31.3 26.7 23.0

56.1 47.1 40.1 34.6

34.0 28.5 24.3 21.0

51.0 42.9 36.5 31.5

30.6 25.7 21.9 18.9

46.0 38.6 32.9 28.4

27.1 22.8 19.4 16.7

40.7 34.2 29.2 25.1

Properties

Ag , in.2 rz , in. ASD Ωc = 1.67

6.94 0.856 LRFD

5.86 0.859

5.31 0.861

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

φc = 0.90

4.75 0.864

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.18 0.867

AISC_Part 4C:14th Ed.

4/12/11

3:32 PM

Page 168

4–168

DESIGN OF COMPRESSION MEMBERS

Table 4-11 (continued)

Available Strength in Axial Compression, kips Concentrically Loaded Single Angles

L6

L6× 31/2 ×

L6× 4×

Shape lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

3 8c /

5 16c /

12 /

3 8c /

5 16c /

12.3 Pn /Ωc φc Pn

10.3 Pn /Ωc φc Pn

15.3 Pn /Ωc φc Pn

11.7 Pn /Ωc φc Pn

9.80 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

71.0

107

54.0

81.1

97.0

146

67.6

102

51.5

77.3

1 2 3 4 5

70.3 68.4 65.4 61.3 56.5

106 103 98.3 92.2 84.9

53.5 52.2 50.1 47.3 44.0

80.4 78.5 75.3 71.1 66.1

95.7 92.0 86.1 78.5 69.6

144 138 129 118 105

66.8 64.5 60.8 55.9 50.3

100 96.9 91.3 84.1 75.5

50.9 49.3 46.8 43.4 39.4

76.5 74.1 70.3 65.2 59.3

6 7 8 9 10

51.1 45.4 39.6 33.9 28.5

76.8 68.2 59.5 50.9 42.8

40.2 36.1 31.9 27.8 23.8

60.4 54.3 48.0 41.7 35.7

60.2 50.6 41.5 33.1 26.8

90.4 76.1 62.4 49.8 40.3

44.1 37.8 31.6 25.8 20.9

66.3 56.8 47.5 38.8 31.4

35.1 30.5 26.0 21.7 17.7

52.7 45.9 39.1 32.7 26.7

11 12 13 14

23.6 19.8 16.9 14.6

35.4 29.8 25.4 21.9

20.0 16.8 14.3 12.3

30.0 25.2 21.5 18.5

22.2 18.6

33.3 28.0

17.3 14.5

26.0 21.8

14.7 12.3

22.0 18.5

Properties 2

Ag , in. rz , in.

ASD

3.61 0.870 LRFD

3.03 0.874

Ωc = 1.67

φc = 0.90

4.50 0.756

3.44 0.763

c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.89 0.767

AISC_Part 4C:14th Ed.

4/12/11

3:33 PM

Page 169

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–169

Table 4-11 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Concentrically Loaded Single Angles L5× 5×

Shape

78 /

lb/ft

3 4 /

27.2 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L5

ASD

5 8 /

23.6 20.0 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

3 8c /

12 /

7 16 /

16.2 Pn /Ωc φc Pn

14.3 Pn /Ωc φc Pn

ASD

12.3 Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

0

172

259

150

226

127

191

103

155

91.0

137

77.3

116

1 2 3 4 5

171 167 160 152 141

257 251 241 228 212

149 146 140 132 123

224 219 210 199 185

126 123 118 112 104

190 185 178 168 157

102 100 96.2 91.0 84.8

154 150 145 137 127

90.3 88.2 84.8 80.2 74.8

136 133 127 121 112

76.8 75.0 72.2 68.4 63.9

115 113 109 103 96.0

6 7 8 9 10

129 116 103 89.9 77.2

194 175 155 135 116

113 102 90.0 78.6 67.4

169 153 135 118 101

77.7 117 70.1 105 62.3 93.6 54.5 81.9 46.9 70.5

68.6 61.9 55.1 48.2 41.5

103 93.1 82.8 72.4 62.4

58.7 53.1 47.4 41.6 35.9

88.2 79.9 71.2 62.5 54.0

11 12 13 14 15

65.1 54.7 46.6 40.2 35.0

97.8 82.2 70.0 60.4 52.6

56.9 47.8 40.7 35.1 30.6

16

30.8

46.2

26.9

95.4 86.0 76.3 66.7 57.3

143 129 115 100 86.1

85.5 71.8 61.2 52.8 46.0

48.4 40.7 34.6 29.9 26.0

72.7 61.1 52.1 44.9 39.1

39.7 33.3 28.4 24.5 21.3

59.6 50.1 42.7 36.8 32.1

35.2 29.6 25.2 21.7 18.9

52.9 44.4 37.9 32.6 28.4

30.6 25.7 21.9 18.9 16.5

46.0 38.7 32.9 28.4 24.7

40.4

22.9

34.4

18.8

28.2

16.6

25.0

14.5

21.7

Properties 2

Ag , in. rz , in. ASD Ωc = 1.67

8.00 0.971 LRFD φc = 0.90

6.98 0.972

5.90 0.975

4.79 0.980

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.22 0.983

3.65 0.986

AISC_Part 4C:14th Ed.

4/12/11

3:33 PM

Page 170

4–170

DESIGN OF COMPRESSION MEMBERS

Table 4-11 (continued)

Available Strength in Axial Compression, kips Concentrically Loaded Single Angles

L5

L5× 31/2 ×

L5× 5×

Shape

5 16c /

lb/ft

3 4 /

10.3 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

19.8 16.8 Pn /Ωc φc Pn Pn /Ωc φc Pn ASD

12 /

3 8c /

13.6 Pn /Ωc φc Pn

10.4 Pn /Ωc φc Pn

5 8 /

LRFD

8.70 Pn /Ωc φc Pn

ASD

LRFD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

60.4

90.7

126

190

106

160

86.2

130

64.6

97.1

50.3

75.6

1 2 3 4 5

59.9 58.7 56.6 53.9 50.6

90.1 88.2 85.1 81.0 76.0

124 119 111 101 89.5

187 179 168 152 135

105 101 94.0 85.5 75.6

158 151 141 128 114

85.1 81.7 76.4 69.5 61.6

128 123 115 104 92.5

63.8 61.3 57.5 52.4 46.6

95.9 92.2 86.4 78.8 70.1

49.7 48.0 45.2 41.5 37.3

74.7 72.1 67.9 62.4 56.0

6 7 8 9 10

46.8 42.7 38.4 34.1 29.8

70.4 64.2 57.8 51.2 44.8

77.0 116 64.5 96.9 52.5 78.9 41.7 62.7 33.8 50.8

65.1 54.5 44.4 35.4 28.6

97.8 81.9 66.8 53.1 43.0

53.1 44.6 36.4 29.0 23.5

79.8 67.0 54.7 43.6 35.3

40.4 34.1 28.0 22.4 18.1

60.7 51.2 42.1 33.7 27.3

32.6 27.9 23.3 19.0 15.4

49.1 41.9 35.0 28.5 23.1

11 12 13 14 15

25.7 21.8 18.6 16.0 14.0

38.6 32.8 27.9 24.1 21.0

27.9 23.5

23.7 19.9

35.6 29.9

19.4 16.3

29.2 24.5

15.0 12.6

22.5 18.9

12.7 10.7

19.1 16.0

16

12.3

18.4

42.0 35.3

ASD

5 16c /

Properties 2

Ag , in. rz , in. ASD Ωc = 1.67

3.07 0.990 LRFD φc = 0.90

5.85 0.744

4.93 0.746

4.00 0.750

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.05 0.755

2.56 0.758

AISC_Part 4C:14th Ed.

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3:33 PM

Page 171

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–171

Table 4-11 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Concentrically Loaded Single Angles L5× 31/2 ×

Shape

12 /

7.00 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L5× 3×

1 4c /

lb/ft

ASD

L5

7 16 /

12.8 11.3 Pn /Ωc φc Pn Pn /Ωc φc Pn

3 8c /

5 16c /

9.80 Pn /Ωc φc Pn

8.20 Pn /Ωc φc Pn

1 4c /

6.60 Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

35.9

53.9

80.8

122

71.4

107

60.6

91.1

47.4

71.2

33.6

ASD

LRFD 50.5

1 2 3 4 5

35.5 34.4 32.6 30.3 27.6

53.4 51.7 49.0 45.6 41.4

79.4 75.1 68.5 60.2 51.0

119 113 103 90.5 76.7

70.1 66.3 60.5 53.3 45.2

105 99.7 91.0 80.0 67.9

59.5 56.4 51.6 45.5 38.8

89.5 84.8 77.6 68.5 58.3

46.6 44.4 40.9 36.4 31.4

70.1 66.7 61.4 54.8 47.2

33.1 31.7 29.6 26.7 23.5

49.8 47.7 44.4 40.2 35.3

6 7 8 9 10

24.6 21.4 18.3 15.3 12.5

36.9 32.2 27.5 23.0 18.8

41.7 32.8 25.2 19.9 16.1

62.7 49.3 37.9 29.9 24.2

37.0 29.1 22.4 17.7 14.3

55.5 43.8 33.7 26.6 21.5

31.9 25.3 19.5 15.4 12.5

47.9 38.0 29.3 23.1 18.7

26.2 21.2 16.6 13.1 10.6

39.4 31.9 24.9 19.7 15.9

20.1 16.7 13.4 10.6 8.61

30.2 25.0 20.2 16.0 12.9

11 12

10.3 8.69

15.5 13.1

Properties 2

Ag , in. rz , in. ASD Ωc = 1.67

2.07 0.761 LRFD φc = 0.90

3.75 0.642

3.31 0.644

2.86 0.646

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.41 0.649

1.94 0.652

AISC_Part 4C:14th Ed.

4/12/11

3:34 PM

Page 172

4–172

DESIGN OF COMPRESSION MEMBERS

Table 4-11 (continued)

Available Strength in Axial Compression, kips Concentrically Loaded Single Angles

L4

L4× 4×

Shape

3 4 /

lb/ft

5 8 /

18.5 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

ASD

12 /

15.7 12.8 Pn /Ωc φc Pn Pn /Ωc φc Pn

7 16 /

3 8 /

5 16 /

11.3 Pn /Ωc φc Pn

9.80 Pn /Ωc φc Pn

8.20 Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

117

176

99.4

149

80.8

122

71.1

107

61.7

92.7

51.6

ASD

LRFD 77.5

1 2 3 4 5

116 111 105 95.8 85.5

174 168 157 144 128

98.1 94.5 88.7 81.2 72.4

147 142 133 122 109

79.8 76.9 72.2 66.1 59.0

120 116 108 99.3 88.7

70.3 67.7 63.5 58.2 52.0

106 102 95.5 87.5 78.1

60.9 58.6 55.1 50.5 45.1

91.5 88.1 82.8 75.9 67.8

50.9 49.1 46.1 42.3 37.8

76.6 73.8 69.3 63.6 56.9

6 7 8 9 10

74.4 112 63.1 94.8 52.2 78.4 42.0 63.1 34.0 51.1

63.0 53.5 44.2 35.6 28.8

94.7 80.3 66.5 53.5 43.3

51.4 43.6 36.1 29.1 23.6

77.2 65.6 54.3 43.7 35.4

45.3 38.4 31.8 25.7 20.8

68.0 57.8 47.9 38.6 31.3

39.3 33.4 27.7 22.4 18.1

59.1 50.2 41.7 33.6 27.2

33.0 28.1 23.3 18.9 15.3

49.6 42.2 35.1 28.4 23.0

11 12 13

28.1 23.6

23.8 20.0

35.8 30.1

19.5 16.4

29.3 24.6

17.2 14.4

25.8 21.7

15.0 12.6

22.5 18.9

12.6 10.6 9.04

19.0 15.9 13.6

42.3 35.5

Properties 2

Ag , in. rz , in. ASD Ωc = 1.67

5.44 0.774 LRFD

4.61 0.774

3.75 0.776

3.30 0.777

Note: Heavy line indicates KL/rz equal to or greater than 200.

φc = 0.90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.86 0.779

2.40 0.781

AISC_Part 4C:14th Ed.

4/12/11

3:34 PM

Page 173

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–173

Table 4-11 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Concentrically Loaded Single Angles

1 4c /

lb/ft

12 /

6.60 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L4× 31/2 ×

L4× 4×

Shape

ASD

L4

11.9 9.10 Pn /Ωc φc Pn Pn /Ωc φc Pn

L4× 3× 5 16 /

1 4c /

7.70 Pn /Ωc φc Pn

6.20 Pn /Ωc φc Pn

3 8 /

ASD

LRFD

ASD

5 8 /

13.6 Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

0

37.9

57.0

75.4

113

57.8

86.8

48.4

72.7

35.8

53.8

86.0

129

1 2 3 4 5

37.5 36.3 34.3 31.7 28.6

56.4 54.5 51.5 47.6 43.0

74.3 71.1 66.0 59.6 52.1

112 107 99.3 89.5 78.4

56.9 54.5 50.6 45.7 40.0

85.6 81.9 76.1 68.7 60.2

47.7 45.6 42.4 38.3 33.6

71.6 68.6 63.8 57.6 50.5

35.3 33.9 31.8 29.0 25.7

53.1 51.0 47.7 43.5 38.6

84.4 79.7 72.5 63.4 53.4

127 120 109 95.3 80.3

6 7 8 9 10

25.3 21.8 18.4 15.2 12.4

38.0 32.8 27.7 22.9 18.6

44.3 36.6 29.3 23.1 18.7

66.6 54.9 44.0 34.8 28.1

34.1 28.2 22.6 17.9 14.5

51.2 42.3 34.0 26.8 21.7

28.7 23.7 19.1 15.1 12.2

43.1 35.6 28.7 22.7 18.3

22.2 18.7 15.3 12.3 9.93

33.4 28.1 23.1 18.4 14.9

43.3 33.8 25.9 20.5 16.6

65.1 50.9 38.9 30.8 24.9

11 12 13

10.2 8.58 7.31

15.3 12.9 11.0

15.5

23.3

12.0

18.0

10.1 8.48

15.2 12.7

8.21 6.90

12.3 10.4

Properties 2

Ag , in. rz , in. ASD Ωc = 1.67

1.93 0.783 LRFD φc = 0.90

3.50 0.716

2.68 0.719

2.25 0.721

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.82 0.723

3.99 0.631

AISC_Part 4C:14th Ed.

4/12/11

3:35 PM

Page 174

4–174

DESIGN OF COMPRESSION MEMBERS

Table 4-11 (continued)

Available Strength in Axial Compression, kips L4–L31/2

Concentrically Loaded Single Angles L31/2 × 31/2 ×

L4× 3×

Shape

12 /

lb/ft

3 8 /

11.1 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

1 4c /

12 /

5.80 Pn /Ωc φc Pn

11.1 Pn /Ωc φc Pn

5 16 /

8.50 7.20 Pn /Ωc φc Pn Pn /Ωc φc Pn ASD

LRFD

ASD

7 16 /

9.80 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

ASD

LRFD

0

70.1

105

53.7

80.7

44.9

67.5

33.2

49.9

70.1

105

62.3

93.6

1 2 3 4 5

68.7 65.0 59.1 51.8 43.7

103 97.6 88.8 77.8 65.6

52.7 49.8 45.3 39.8 33.6

79.2 74.8 68.2 59.8 50.5

44.1 41.7 38.0 33.4 28.2

66.3 62.7 57.1 50.2 42.4

32.7 31.0 28.5 25.3 21.8

49.1 46.7 42.9 38.1 32.7

68.9 65.6 60.4 53.9 46.4

104 98.6 90.8 80.9 69.8

61.3 58.4 53.8 48.0 41.4

92.1 87.7 80.8 72.1 62.2

6 7 8 9 10

35.5 27.7 21.2 16.8 13.6

53.3 41.7 31.9 25.2 20.4

27.3 21.4 16.4 13.0 10.5

41.1 32.2 24.7 19.5 15.8

23.0 18.1 13.9 11.0 8.88

34.6 27.2 20.9 16.5 13.3

18.1 14.5 11.3 8.89 7.20

27.1 21.8 16.9 13.4 10.8

38.8 31.3 24.4 19.3 15.6

58.3 47.0 36.7 29.0 23.5

34.6 28.0 21.9 17.3 14.0

52.0 42.0 32.9 26.0 21.0

12.9

19.4

11.6

17.4

11

Properties 2

Ag , in. rz , in. ASD Ωc = 1.67

3.25 0.633 LRFD φc = 0.90

2.49 0.636

2.09 0.638

1.69 0.639

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.25 0.679

2.89 0.681

AISC_Part 4C:14th Ed.

4/12/11

3:35 PM

Page 175

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–175

Table 4-11 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Concentrically Loaded Single Angles L31/2 × 31/2 ×

Shape

3 8 /

lb/ft

Effective length, KL (ft), with respect to least radius of gyration, rz

Design

L31/2 × 3× 1 4c /

5 16 /

8.50 Pn /Ωc φc Pn

7.20 5.80 Pn /Ωc φc Pn Pn /Ωc φc Pn ASD

ASD

12 /

7 16 /

3 8 /

10.2 Pn /Ωc φc Pn

9.10 Pn /Ωc φc Pn

7.90 Pn /Ωc φc Pn

ASD

LRFD

LRFD

ASD

LRFD

ASD

LRFD

0

53.9

81.0

45.3

68.0

35.4

53.2

65.1

97.8

57.6

86.5

50.0

75.2

1 2 3 4 5

53.0 50.5 46.6 41.6 35.9

79.7 75.9 70.0 62.5 54.0

44.5 42.4 39.1 35.0 30.2

66.9 63.8 58.8 52.5 45.4

34.8 33.2 30.8 27.6 24.0

52.3 50.0 46.3 41.5 36.1

63.8 60.1 54.5 47.4 39.6

95.9 90.4 81.8 71.2 59.6

56.4 53.2 48.2 42.0 35.2

84.8 79.9 72.4 63.1 52.8

49.0 46.2 41.9 36.6 30.6

73.7 69.5 63.0 54.9 46.1

6 7 8 9 10

30.0 24.3 19.0 15.0 12.2

45.1 36.5 28.6 22.6 18.3

25.3 20.5 16.1 12.7 10.3

38.0 30.8 24.2 19.1 15.5

20.3 16.6 13.1 10.4 8.40

30.5 24.9 19.7 15.6 12.6

31.9 24.6 18.8 14.9 12.0

47.9 36.9 28.3 22.3 18.1

28.3 21.9 16.7 13.2 10.7

42.5 32.9 25.2 19.9 16.1

24.7 19.1 14.6 11.6 9.37

37.1 28.7 22.0 17.4 14.1

11

10.1

15.1

12.8

6.94

10.4

8.50

LRFD

L31/2

ASD

LRFD

Properties 2

Ag , in. rz , in. ASD Ωc = 1.67

2.50 0.683 LRFD φc = 0.90

2.10 0.685

1.70 0.688

3.02 0.618

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.67 0.620

2.32 0.622

AISC_Part 4C:14th Ed.

4/12/11

3:35 PM

Page 176

4–176

DESIGN OF COMPRESSION MEMBERS

Table 4-11 (continued)

Available Strength in Axial Compression, kips Concentrically Loaded Single Angles

L31/2

L31/2 × 3×

Shape

6.60 Pn /Ωc φc Pn

Design

ASD

L31/2 × 21/2 × 1 4c /

5 16 /

lb/ft

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

12 /

5.40 9.40 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

1 4c /

3 8 /

5 16 /

7.20 Pn /Ωc φc Pn

6.10 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

4.90 Pn /Ωc φc Pn

LRFD

ASD

LRFD

0

42.0

63.2

32.9

49.4

59.7

89.7

45.7

68.7

38.6

58.0

30.2

ASD

45.3

LRFD

1 2 3 4 5

41.2 38.9 35.3 30.8 25.8

62.0 58.4 53.0 46.3 38.8

32.3 30.5 27.8 24.4 20.7

48.5 45.9 41.8 36.7 31.1

58.1 53.6 46.9 38.9 30.6

87.4 80.6 70.5 58.5 45.9

44.5 41.1 36.0 29.9 23.6

66.9 61.8 54.1 45.0 35.4

37.6 34.7 30.5 25.4 20.0

56.5 52.2 45.8 38.1 30.1

29.4 27.3 24.1 20.2 16.1

44.2 41.0 36.2 30.4 24.3

6 7 8 9 10

20.9 16.2 12.4 9.78 7.93

31.3 24.3 18.6 14.7 11.9

16.9 13.2 10.2 8.03 6.50

25.3 19.9 15.3 12.1 9.78

22.7 16.7 12.8

34.2 25.1 19.2

17.6 12.9 9.90

26.4 19.4 14.9

15.0 11.0 8.45

22.6 16.6 12.7

12.3 18.4 9.04 13.6 6.92 10.4 5.47 8.22

Properties 2

Ag , in. rz , in. ASD Ωc = 1.67

1.95 0.624 LRFD φc = 0.90

1.58 0.628

2.77 0.532

2.12 0.535

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.79 0.538

1.45 0.541

AISC_Part 4C:14th Ed.

4/12/11

3:36 PM

Page 177

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–177

Table 4-11 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Concentrically Loaded Single Angles L3× 3×

Shape

12 /

lb/ft

7 16 /

9.40 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L3

3 8 /

8.30 7.20 Pn /Ωc φc Pn Pn /Ωc φc Pn ASD

LRFD

3 16c /

5 16 /

14 /

6.10 Pn /Ωc φc Pn

4.90 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

3.71 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

0

59.5

89.4

52.4

78.7

45.5

68.4

38.4

57.7

31.0

46.7

21.4

ASD

32.2

LRFD

1 2 3 4 5

58.2 54.4 48.6 41.5 33.9

87.4 81.7 73.0 62.4 50.9

51.2 47.9 42.8 36.5 29.8

77.0 71.9 64.3 54.9 44.8

44.5 41.6 37.2 31.8 25.9

66.8 62.5 55.9 47.7 39.0

37.5 35.1 31.4 26.9 22.0

56.4 52.7 47.2 40.4 33.0

30.4 28.4 25.4 21.8 17.8

45.6 42.7 38.2 32.7 26.8

21.0 19.8 17.9 15.5 13.0

31.6 29.7 26.9 23.3 19.5

6 7 8 9

26.4 19.8 15.1 12.0

39.7 29.7 22.8 18.0

23.3 17.4 13.3 10.5

35.0 26.2 20.0 15.8

20.3 15.2 11.6 9.18

30.5 22.8 17.5 13.8

17.2 12.9 9.87 7.80

25.8 19.4 14.8 11.7

14.0 21.0 10.4 15.6 10.5 15.8 7.97 12.0 8.04 12.1 6.10 9.18 6.35 9.54 4.82 7.25

Properties 2

Ag , in. rz , in. ASD Ωc = 1.67

2.76 0.580 LRFD φc = 0.90

2.43 0.580

2.11 0.581

1.78 0.583

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.44 0.585

1.09 0.586

AISC_Part 4C:14th Ed.

4/12/11

3:36 PM

Page 178

4–178

DESIGN OF COMPRESSION MEMBERS

Table 4-11 (continued)

Available Strength in Axial Compression, kips Concentrically Loaded Single Angles

L3

L3× 21/2 ×

Shape

12 /

lb/ft

7 16 /

8.50 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

3 8 /

7.60 6.60 Pn /Ωc φc Pn Pn /Ωc φc Pn ASD

LRFD

ASD

LRFD

3 16c /

5 16 /

14 /

5.60 Pn /Ωc φc Pn

4.50 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

3.39 Pn /Ωc φc Pn

ASD

LRFD

0

53.9

81.0

47.9

71.9

41.6

62.5

35.1

52.8

28.5

42.8

19.7

ASD

29.5

LRFD

1 2 3 4 5

52.4 48.1 41.7 34.2 26.4

78.7 72.3 62.7 51.4 39.8

46.5 42.7 37.0 30.3 23.5

69.9 64.2 55.7 45.6 35.3

40.4 37.1 32.2 26.4 20.5

60.8 55.8 48.4 39.7 30.8

34.2 31.4 27.2 22.4 17.3

51.3 47.2 41.0 33.6 26.1

27.7 25.4 22.1 18.2 14.1

41.6 38.2 33.2 27.3 21.2

19.2 17.8 15.6 13.1 10.4

28.8 26.7 23.5 19.7 15.6

6 7 8

19.3 14.2 10.9

29.0 21.3 16.3

17.1 12.6 9.64

25.8 18.9 14.5

15.0 11.0 8.41

22.5 16.5 12.6

12.7 9.32 7.13

19.1 14.0 10.7

10.3 15.6 7.60 11.4 5.82 8.75

7.86 11.8 5.78 8.69 4.43 6.65

Properties 2

Ag , in. rz , in. ASD Ωc = 1.67

2.50 0.516 LRFD φc = 0.90

2.22 0.516

1.93 0.517

1.63 0.518

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.32 0.520

1.00 0.521

AISC_Part 4C:14th Ed.

4/12/11

3:36 PM

Page 179

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–179

Table 4-11 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Concentrically Loaded Single Angles

L21/2 × 21/2 ×

L3× 2×

Shape

12 /

lb/ft

3 8 /

7.70 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L3-L21/2

ASD

5.90 5.00 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

14 /

3 16c /

4.10 Pn /Ωc φc Pn

3.07 Pn /Ωc φc Pn

5 16 /

LRFD

ASD

LRFD

ASD

LRFD

ASD

12 /

LRFD

7.70 Pn /Ωc φc Pn ASD

LRFD

0

48.7

73.2

37.7

56.7

31.9

48.0

25.9

38.9

18.0

27.1

48.7

73.2

1 2 3 4 5

46.7 41.2 33.4 24.9 17.0

70.2 61.9 50.2 37.4 25.6

36.2 31.9 25.9 19.3 13.3

54.4 48.0 38.9 29.1 19.9

30.6 27.0 22.0 16.5 11.3

46.0 40.6 33.0 24.7 17.0

24.8 22.0 17.9 13.5 9.31

37.3 33.0 26.9 20.2 14.0

17.4 15.6 13.0 10.0 7.23

26.1 23.4 19.5 15.1 10.9

47.1 42.7 36.3 28.8 21.5

70.9 64.2 54.5 43.3 32.3

6 7 8

11.8 8.70

17.8 13.1

9.21 6.77

13.8 10.2

7.86 11.8 5.78 8.68

6.46 4.75

9.71 7.14

5.03 3.70

7.56 15.2 5.56 11.1 8.53

22.8 16.7 12.8

Properties 2

Ag , in. rz , in. ASD Ωc = 1.67

2.26 0.425 LRFD φc = 0.90

1.75 0.426

1.48 0.428

1.20 0.431

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

0.917 0.435

2.26 0.481

AISC_Part 4C:14th Ed.

4/12/11

3:37 PM

Page 180

4–180

DESIGN OF COMPRESSION MEMBERS

Table 4-11 (continued)

Available Strength in Axial Compression, kips Concentrically Loaded Single Angles

L21/2

L21/2 × 21/2 ×

Shape lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

L21/2 × 2×

3 8 /

5 16 /

14 /

3 16c /

3 8 /

5.90 Pn /Ωc φc Pn

5.00 Pn /Ωc φc Pn

4.10 Pn /Ωc φc Pn

3.07 Pn /Ωc φc Pn

5.30 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

37.3

56.1

31.5

47.3

25.7

38.6

19.1

28.7

33.4

50.2

1 2 3 4 5

36.1 32.7 27.8 22.1 16.4

54.2 49.2 41.7 33.2 24.7

30.5 27.6 23.4 18.6 13.9

45.8 41.5 35.2 28.0 20.9

24.8 22.5 19.1 15.2 11.3

37.3 33.8 28.7 22.9 17.1

18.5 16.8 14.3 11.4 8.56

27.8 25.2 21.5 17.2 12.9

32.0 28.1 22.7 16.7 11.4

48.1 42.3 34.0 25.2 17.1

6 7 8

11.6 8.53 6.53

17.4 12.8 9.81

12.0 8.85 6.78

6.07 4.46 3.41

9.79 7.20 5.51

14.7 10.8 8.28

8.02 5.89 4.51

9.12 6.70 5.13

7.89

11.9

Properties 2

Ag , in. rz , in.

ASD

1.73 0.481 LRFD

1.46 0.481

Ωc = 1.67

φc = 0.90

1.19 0.482

0.901 0.482

c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.55 0.419

AISC_Part 4C:14th Ed.

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3:37 PM

Page 181

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–181

Table 4-11 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Concentrically Loaded Single Angles L21/2 × 2×

Shape lb/ft

Effective length, KL (ft), with respect to least radius of gyration, rz

Design

L21/2

L21/2 × 11/2 ×

5 16 /

14 /

3 16c /

14 /

3 16c /

4.50 Pn /Ωc φc Pn

3.62 Pn /Ωc φc Pn

2.75 Pn /Ωc φc Pn

3.19 Pn /Ωc φc Pn

2.44 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

28.5

42.8

23.1

34.7

17.3

26.1

20.4

30.7

15.3

23.1

1 2 3 4 5

27.3 24.0 19.3 14.3 9.72

41.0 36.0 29.0 21.5 14.6

22.1 19.5 15.8 11.7 7.99

33.2 29.3 23.7 17.6 12.0

16.6 14.7 12.0 8.99 6.20

25.0 22.1 18.0 13.5 9.32

19.0 15.2 10.5 6.37 4.07

28.5 22.9 15.8 9.57 6.12

14.3 11.5 8.10 4.96 3.17

21.5 17.4 12.2 7.45 4.77

6 7

6.75 4.96

10.1 7.46

5.55 4.08

4.30 3.16

6.47 4.75

8.34 6.13

Properties 2

Ag , in. rz , in.

ASD

1.32 0.420 LRFD

1.07 0.423

Ωc = 1.67

φc = 0.90

0.818 0.426

0.947 0.321

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

0.724 0.324

AISC_Part 4C:14th Ed.

4/12/11

3:37 PM

Page 182

4–182

DESIGN OF COMPRESSION MEMBERS

Table 4-11 (continued)

Available Strength in Axial Compression, kips Concentrically Loaded Single Angles

L2

L2× 2×

Shape lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

3 8 /

5 16 /

14 /

3 16 /

1 8c /

4.70 Pn /Ωc φc Pn

3.92 Pn /Ωc φc Pn

3.19 Pn /Ωc φc Pn

2.44 Pn /Ωc φc Pn

1.65 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

29.5

44.4

25.0

37.6

20.3

30.6

15.6

23.4

9.65

14.5

1 2 3 4 5

28.1 24.1 18.7 13.1 8.52

42.2 36.2 28.1 19.7 12.8

23.8 20.4 15.8 11.1 7.22

35.7 30.7 23.8 16.7 10.8

19.3 16.6 12.9 9.05 5.90

29.1 25.0 19.4 13.6 8.87

14.8 12.7 9.92 6.98 4.56

22.2 19.1 14.9 10.5 6.86

9.23 8.06 6.43 4.68 3.13

13.9 12.1 9.66 7.04 4.71

6

5.92

4.10

6.16

3.17

4.76

2.18

3.27

8.90

5.01

7.53

Properties 2

Ag , in. rz , in.

ASD

1.37 0.386 LRFD

1.16 0.386

Ωc = 1.67

φc = 0.90

0.944 0.387

0.722 0.389

c Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

0.491 0.391

AISC_Part 4D:14th Ed.

4/12/11

3:14 PM

Page 183

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–183

Table 4-12

Available Strength in Axial Compression, kips

Fy = 36 ksi

Eccentrically Loaded Single Angles L8× 8×

Shape

11/8

lb/ft

ASD

78 /

1

56.9 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L8

51.0 45.0 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

9 16c /

3 4 /

5 8 /

38.9 Pn /Ωc φc Pn

32.7 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

29.6 Pn /Ωc φc Pn ASD

LRFD

0

174

262

167

251

159

240

149

224

127

191

109

165

1 2 3 4 5

173 172 169 165 161

261 258 254 249 242

166 165 162 158 154

250 248 244 238 232

159 157 155 151 147

239 237 233 227 221

149 147 145 141 137

223 221 217 212 206

127 126 125 124 123

190 190 189 187 185

109 109 108 107 106

164 164 163 161 159

6 7 8 9 10

155 149 143 136 129

234 225 216 206 195

148 142 136 129 122

224 215 206 196 185

141 136 129 123 116

213 205 195 186 176

132 126 120 114 107

199 191 182 172 163

121 115 110 104 97.8

181 174 166 157 148

103 99.4 96.1 92.7 89.4

154 149 144 139 134

11 12 13 14 15

122 114 107 100 93.7

185 174 163 153 143

115 108 101 94.6 88.1

175 165 154 144 134

109 102 95.5 89.0 82.7

166 155 145 136 126

101 94.2 87.8 81.6 75.6

153 143 134 124 116

91.7 85.6 79.6 73.9 68.4

139 130 121 113 104

84.6 79.0 73.6 68.3 63.2

128 120 112 104 96.5

16 17 18 19 20

87.3 81.1 75.1 69.6 64.7

133 124 115 106 99.0

21 22 23 24 25

60.3 56.3 52.6 49.3 46.3

92.2 86.1 80.5 75.5 70.9

81.9 125 75.9 116 70.1 107 64.9 99.3 60.2 92.1

76.7 117 71.0 109 65.5 100 60.5 92.5 56.0 85.6

70.0 107 64.6 98.8 59.4 90.9 54.7 83.7 50.5 77.3

63.1 58.1 53.4 49.0 45.2

96.5 88.9 81.6 75.0 69.1

58.4 53.8 49.5 45.4 41.8

89.2 82.3 75.7 69.4 63.9

56.0 52.2 48.8 45.7 42.8

52.0 48.4 45.1 42.2 39.5

79.5 74.0 69.0 64.5 60.4

46.8 43.5 40.5 37.8 35.4

71.6 66.5 62.0 57.8 54.1

41.8 38.7 36.0 33.5 31.3

63.9 59.2 55.0 51.3 47.9

38.6 35.7 33.2 30.9 28.8

59.0 54.7 50.7 47.2 44.1

37.1

56.7

33.1

50.7

29.3

44.8

27.0

41.2

85.7 79.9 74.6 69.9 65.5

26

Properties

Ag , in.2 rz , in.

16.8 1.56

ASD

LRFD

Ωc = 1.67

φc = 0.90

15.1 1.56

13.3 1.57

11.5 1.57

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.69 1.58

8.77 1.58

AISC_Part 4D:14th Ed.

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10:44 AM

Page 184

4–184

DESIGN OF COMPRESSION MEMBERS

Table 4-12 (continued)

Available Strength in Axial Compression, kips L8

L8× 6×

1 2 c,f /

lb/ft

78 /

1

26.4 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Eccentrically Loaded Single Angles L8× 8×

Shape

Fy = 36 ksi

44.2 39.1 Pn /Ωc φc Pn Pn /Ωc φc Pn ASD

LRFD

ASD

LRFD

9 16c /

3 4 /

5 8 /

33.8 Pn /Ωc φc Pn

28.5 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

25.7 Pn /Ωc φc Pn

ASD

LRFD

0

91.0

137

161

241

158

238

157

236

153

231

155

ASD

233

LRFD

1 2 3 4 5

90.8 90.4 89.8 89.0 87.9

137 136 135 134 132

160 158 155 151 146

240 238 234 228 221

158 155 152 147 138

237 234 229 223 209

156 154 150 144 136

235 231 226 218 206

152 148 142 135 126

229 224 215 204 192

153 148 141 133 124

230 223 213 201 189

6 7 8 9 10

85.6 82.7 79.8 76.8 73.8

129 124 120 115 111

135 124 114 105 95.5

205 189 174 160 146

128 118 108 98.3 89.3

194 180 165 151 137

125 115 104 94.2 85.0

190 175 159 144 131

118 108 97.1 87.1 78.0

181 165 149 134 120

115 104 93.4 83.6 74.7

175 159 143 129 115

11 12 13 14 15

70.9 67.9 64.9 62.0 58.2

106 101 96.6 91.9 87.2

87.0 79.1 71.8 65.1 58.9

134 122 110 100 90.7

16 17 18 19 20

53.9 49.7 45.8 42.1 38.7

82.3 76.0 70.1 64.4 59.2

53.6 48.9 44.8 41.2 38.0

21 22 23 24 25

35.7 33.0 30.6 28.5 26.6

54.6 50.5 46.8 43.6 40.6

35.1

26

24.8

37.9

81.0 124 73.3 113 66.3 102 60.0 92.4 54.1 83.4

76.7 118 69.1 106 62.2 96.0 56.0 86.5 50.4 77.8

69.8 108 62.6 96.7 56.1 86.7 50.3 77.8 45.0 69.7

66.7 103 59.7 92.3 53.4 82.7 47.9 74.2 42.9 66.5

82.5 75.2 68.9 63.4 58.5

49.0 44.6 40.8 37.4 34.5

75.6 68.8 62.9 57.7 53.1

45.5 41.3 37.7 34.5 31.7

70.3 63.8 58.2 53.2 48.9

40.5 36.7 33.4 30.5 27.9

62.7 56.7 51.6 47.1 43.2

38.5 34.8 31.6 28.8 26.4

59.7 53.9 48.9 44.6 40.8

54.1

31.9

49.1

29.2

45.1

25.7

39.7

24.3

37.5

Properties

Ag , in.2 rz , in.

7.84 1.59

ASD

LRFD

Ωc = 1.67

φc = 0.90

13.1 1.28

11.5 1.28

9.99 1.29

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.41 1.29

7.61 1.30

AISC_Part 4D:14th Ed.

2/23/11

10:44 AM

Page 185

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–185

Table 4-12 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Eccentrically Loaded Single Angles L8× 6×

Shape

1 2 c,f /

lb/ft

Effective length, KL (ft), with respect to least radius of gyration, rz

Design

ASD

L8× 4× 7 16 c,f /

23.0 Pn /Ωc φc Pn

L8

78 /

3 4 /

33.1 Pn /Ωc φc Pn

28.7 Pn /Ωc φc Pn

1

20.2 37.4 Pn /Ωc φc Pn Pn /Ωc φc Pn

5 8 /

24.2 Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

122

184

89.5

134

68.2

102

65.8

98.8

63.6

95.6

61.8

93.0

1 2 3 4 5

122 121 121 121 119

183 182 181 180 181

89.5 89.2 88.1 86.9 86.0

134 134 132 130 128

67.6 65.8 63.0 59.4 55.5

102 99.0 94.9 89.7 84.0

65.1 63.3 60.4 57.0 53.0

97.9 95.2 91.1 86.1 80.3

63.0 61.3 58.5 54.8 50.7

94.7 92.2 88.2 82.9 76.9

61.2 59.3 56.3 52.4 48.1

92.0 89.3 84.9 79.3 73.0

6 7 8 9 10

108 97.6 87.5 78.1 69.6

165 149 134 120 107

85.8 88.1 82.8 73.7 65.5

127 128 127 114 101

51.2 46.9 42.5 38.3 34.2

77.7 71.3 64.8 58.4 52.2

48.7 44.3 40.0 35.9 31.9

73.9 67.5 61.0 54.8 48.8

46.3 41.9 37.6 33.5 29.6

70.4 63.8 57.4 51.2 45.4

43.6 39.1 34.9 30.9 27.2

66.3 59.7 53.3 47.3 41.6

11 12 13 14 15

62.1 55.4 49.5 44.3 39.8

96.0 85.8 76.8 68.8 61.7

58.3 51.9 46.4 41.5 37.2

90.3 80.6 72.1 64.5 57.9

30.6 27.5 24.9 22.5

46.8 42.1 38.0 34.5

28.4 25.5 22.9 20.7

43.5 39.0 35.1 31.8

26.3 23.5 21.1 19.0

40.3 36.0 32.3 29.1

24.0 21.3 19.0 17.1

36.8 32.7 29.2 26.2

16 17 18 19 20

35.6 32.1 29.1 26.5 24.3

55.3 49.9 45.2 41.1 37.6

33.4 30.0 27.2 24.7 22.6

51.9 46.7 42.2 38.4 35.0

21

22.3

34.5

20.7

32.1

Properties

Ag , in.2 rz , in.

6.80 1.30

ASD

LRFD

Ωc = 1.67

φc = 0.90

5.99 1.31

11.1 0.844

9.79 0.846

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.49 0.850

7.16 0.856

AISC_Part 4D:14th Ed.

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10:44 AM

Page 186

4–186

DESIGN OF COMPRESSION MEMBERS

Table 4-12 (continued)

Available Strength in Axial Compression, kips L8-L7

9 16c /

lb/ft

1 2 c,f /

21.9 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Eccentrically Loaded Single Angles L8× 4×

Shape

Fy = 36 ksi

L7× 4× 7 16 c,f /

19.6 17.2 Pn /Ωc φc Pn Pn /Ωc φc Pn

1 2c /

3 4 /

5 8 /

26.2 Pn /Ωc φc Pn

22.1 Pn /Ωc φc Pn

17.9 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

60.0

90.2

57.5

86.4

54.7

82.2

65.2

98.0

62.1

93.4

59.2

89.0

1 2 3 4 5

59.3 57.4 54.4 50.5 46.2

89.2 86.4 82.0 76.4 70.1

56.8 54.9 51.9 48.1 43.9

85.4 82.6 78.3 72.8 66.6

54.1 52.1 49.2 45.5 41.4

81.3 78.5 74.3 68.9 62.8

64.4 62.2 58.8 54.9 50.4

96.9 93.6 88.7 83.0 76.5

61.4 59.4 56.2 52.1 47.5

92.4 89.5 84.8 78.8 72.1

58.5 56.3 52.8 48.6 43.8

87.9 84.8 79.8 73.6 66.7

6 7 8 9 10

41.7 37.4 33.2 29.4 25.8

63.6 57.0 50.8 45.0 39.6

39.5 35.3 31.3 27.6 24.3

60.2 53.9 47.9 42.4 37.3

37.2 33.1 29.3 25.8 22.7

56.6 50.6 44.9 39.6 34.9

45.8 41.1 36.7 32.6 28.7

69.6 62.7 56.1 49.8 43.9

42.7 38.1 33.8 29.7 26.0

65.1 58.2 51.7 45.6 39.9

39.1 34.6 30.4 26.6 23.2

59.7 52.9 46.6 40.9 35.6

11 12 13 14

22.7 20.1 17.9 16.1

34.8 30.8 27.5 24.7

21.3 18.8 16.7 14.9

32.7 28.9 25.7 23.0

19.9 17.5 15.5 13.8

30.5 26.9 23.8 21.3

25.3 22.5 20.1 18.1

38.8 34.5 30.9 27.8

22.9 20.2 18.0 16.2

35.1 31.1 27.7 24.8

20.2 17.8 15.8 14.1

31.1 27.4 24.2 21.6

Properties

Ag , in.2 rz , in.

6.49 0.859

ASD

LRFD

Ωc = 1.67

φc = 0.90

5.80 0.863

5.11 0.867

7.74 0.855

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

6.50 0.860

5.26 0.866

AISC_Part 4D:14th Ed.

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10:44 AM

Page 187

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–187

Table 4-12 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Eccentrically Loaded Single Angles L7× 4×

Shape

7 16 c,f /

lb/ft

Effective length, KL (ft), with respect to least radius of gyration, rz

Design

L6× 6× 3 8 c,f /

15.7 Pn /Ωc φc Pn

L7-L6

78 /

3 4 /

33.1 Pn /Ωc φc Pn

28.7 Pn /Ωc φc Pn

1

13.6 37.4 Pn /Ωc φc Pn Pn /Ωc φc Pn

24.2 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

56.3

84.6

53.1

79.9

102

153

98.9

149

93.5

141

87.3

131

1 2 3 4 5

55.6 53.4 50.0 45.8 41.2

83.6 80.4 75.6 69.4 62.7

52.4 50.3 47.0 42.9 38.4

78.8 75.7 71.0 65.0 58.5

101 99.5 96.9 93.4 89.1

152 150 146 141 135

98.3 96.7 94.0 90.4 86.1

148 145 141 136 130

92.9 91.3 88.6 85.1 80.9

140 137 133 128 122

86.7 85.1 82.5 79.1 75.0

130 128 124 119 113

6 7 8 9 10

36.6 32.3 28.3 24.7 21.5

55.9 49.4 43.4 38.0 33.2

34.0 29.9 26.1 22.8 19.8

52.0 45.8 40.2 35.1 30.6

84.4 79.3 73.9 68.5 63.2

128 120 112 104 96.3

81.3 76.1 70.7 65.3 60.0

123 115 107 99.3 91.4

76.2 71.1 65.9 60.6 55.5

115 108 100 92.2 84.6

70.4 65.5 60.4 55.4 50.5

106 99.2 91.8 84.3 77.0

11 12 13 14 15

18.7 16.4 14.5 12.9

28.8 25.3 22.3 19.9

17.2 15.1 13.3 11.8

26.6 23.2 20.5 18.1

58.0 53.1 48.3 43.8 39.8

88.5 81.0 73.8 66.9 60.9

54.9 50.0 45.3 40.9 37.1

83.7 76.3 69.3 62.6 56.8

50.6 45.9 41.4 37.3 33.7

77.2 70.1 63.4 57.1 51.6

45.8 41.4 37.2 33.4 30.1

69.9 63.2 56.9 51.0 46.0

36.4 33.4 30.7 28.3

55.7 51.0 46.9 43.3

33.8 30.9 28.4 26.1

51.7 47.3 43.4 39.9

30.6 27.9 25.6 23.5

46.9 42.8 39.1 36.0

27.2 24.7 22.6 20.7

41.6 37.8 34.5 31.7

16 17 18 19

ASD

5 8 /

Properties

Ag , in.2 rz , in.

4.63 0.869

ASD

LRFD

Ωc = 1.67

φc = 0.90

4.00 0.873

11.0 1.17

9.75 1.17

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.46 1.17

7.13 1.17

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4–188

DESIGN OF COMPRESSION MEMBERS

Table 4-12 (continued)

Available Strength in Axial Compression, kips L6

Eccentrically Loaded Single Angles L6× 6×

Shape

9 16 /

lb/ft

7 16c /

12 /

21.9 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

19.6 17.2 Pn /Ωc φc Pn Pn /Ωc φc Pn

L6× 4× 3 8 c,f /

5 16 c,f /

14.9 Pn /Ωc φc Pn

12.4 Pn /Ωc φc Pn

78 /

27.2 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

83.3

125

77.6

117

64.8

97.4

50.7

76.2

36.0

54.0

71.9

108

1 2 3 4 5

82.8 81.3 78.8 75.5 71.6

124 122 119 114 108

77.4 76.9 74.8 71.6 67.8

116 116 113 108 102

64.6 64.2 63.5 62.5 59.9

97.1 96.5 95.3 93.8 89.8

50.6 50.2 49.6 48.7 46.6

76.0 75.4 74.5 73.2 70.0

35.9 35.6 35.2 34.6 33.9

53.9 53.5 52.9 52.0 50.9

71.0 68.3 64.2 59.3 53.9

107 103 96.9 89.7 81.8

6 7 8 9 10

67.2 62.4 57.6 52.7 48.0

102 94.6 87.4 80.2 73.2

63.5 58.9 54.2 49.6 45.0

96.1 89.3 82.4 75.4 68.6

57.3 53.7 49.4 45.1 40.9

85.8 81.3 75.0 68.6 62.4

44.4 42.2 40.0 37.8 35.5

66.7 63.3 59.9 56.4 52.9

33.0 31.8 30.0 28.3 26.5

49.5 47.7 45.1 42.4 39.7

48.5 43.5 38.7 34.2 30.0

73.9 66.3 59.1 52.4 46.1

11 12 13 14 15

43.5 39.2 35.3 31.6 28.4

66.4 60.0 53.9 48.3 43.4

40.7 36.6 32.8 29.3 26.3

62.1 55.9 50.2 44.8 40.2

37.0 33.2 29.8 26.6 23.8

56.4 50.8 45.6 40.6 36.4

33.3 30.2 27.1 24.2 21.7

49.3 45.7 41.5 37.1 33.1

24.7 23.0 21.2 19.4 17.5

37.0 34.3 31.5 28.7 25.9

26.5 23.5 21.0 18.9

40.6 36.1 32.2 28.9

16 17 18 19

25.6 23.3 21.2 19.4

39.2 35.6 32.5 29.7

23.7 21.5 19.5 17.9

36.2 32.8 29.9 27.3

21.4 19.4 17.6 16.1

32.8 29.6 26.9 24.6

19.4 17.6 15.9 14.5

29.7 26.8 24.3 22.2

15.7 14.2 12.9 11.7

23.3 21.1 19.1 17.4

Properties

Ag , in.2 rz , in.

6.45 1.18

ASD

LRFD

Ωc = 1.67

φc = 0.90

5.77 1.18

5.08 1.18

4.38 1.19

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.67 1.19

8.00 0.854

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–189

Table 4-12 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Eccentrically Loaded Single Angles L6× 4×

Shape lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L6

3 4 /

5 8 /

9 16 /

12 /

7 16c /

23.6 Pn /Ωc φc Pn

20.0 Pn /Ωc φc Pn

18.1 Pn /Ωc φc Pn

16.2 Pn /Ωc φc Pn

14.3 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

70.1

105

67.4

101

66.2

99.5

64.0

96.2

62.4

93.7

1 2 3 4 5

69.1 66.2 61.9 56.7 51.4

104 99.8 93.5 85.9 78.0

66.3 63.2 58.7 53.8 48.5

99.7 95.3 88.7 81.6 73.7

65.1 61.9 57.8 52.7 47.1

97.9 93.2 87.3 79.9 71.7

63.1 60.5 56.2 50.9 45.3

95.0 91.1 85.0 77.3 69.0

61.4 58.6 54.2 48.8 43.1

92.4 88.4 82.0 74.1 65.7

6 7 8 9 10

46.1 41.0 36.2 31.8 27.8

70.2 62.6 55.4 48.8 42.6

43.1 38.0 33.3 29.0 25.2

65.8 58.1 51.0 44.6 38.8

41.6 36.5 31.8 27.6 23.9

63.6 55.9 48.8 42.5 36.8

39.7 34.6 30.0 26.0 22.4

60.7 53.1 46.1 39.9 34.4

37.6 32.5 28.1 24.2 20.8

57.5 50.0 43.2 37.3 32.1

11 12 13 14

24.4 21.5 19.2 17.2

37.4 33.1 29.4 26.4

22.0 19.4 17.1 15.3

33.8 29.8 26.4 23.5

20.8 18.2 16.1 14.3

32.0 28.0 24.8 22.1

19.4 17.0 15.0 13.3

29.9 26.1 23.0 20.5

17.9 15.6 13.8 12.2

27.7 24.1 21.2 18.8

Properties

Ag , in.2 rz , in.

6.94 0.856

5.86 0.859

ASD

LRFD

Ωc = 1.67

φc = 0.90

5.31 0.861

4.75 0.864

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.18 0.867

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Page 190

4–190

DESIGN OF COMPRESSION MEMBERS

Table 4-12 (continued)

Available Strength in Axial Compression, kips L6

Eccentrically Loaded Single Angles

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L6× 31/2 ×

L6× 4×

Shape lb/ft

Fy = 36 ksi

3 8 c,f /

5 16 c,f /

12 /

3 8 c,f /

5 16 c,f /

12.3 Pn /Ωc φc Pn

10.3 Pn /Ωc φc Pn

15.3 Pn /Ωc φc Pn

11.7 Pn /Ωc φc Pn

9.80 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

58.9

88.5

53.3

80.2

47.1

70.8

43.6

65.6

40.4

60.7

1 2 3 4 5

57.9 55.2 50.9 45.6 40.1

87.1 83.2 77.0 69.3 61.2

53.3 51.0 47.0 42.0 36.7

80.1 77.0 71.1 63.8 56.1

46.4 44.3 41.0 37.0 32.7

69.8 66.7 61.9 56.1 49.8

42.9 40.6 37.3 33.2 29.1

64.5 61.3 56.4 50.5 44.4

39.6 37.5 34.3 30.5 26.6

59.6 56.5 51.9 46.3 40.6

6 7 8 9 10

34.8 30.0 25.8 22.2 19.0

53.3 46.1 39.8 34.2 29.4

31.7 27.2 23.3 20.0 17.2

48.7 41.9 36.0 31.0 26.6

28.6 24.8 21.3 18.2 15.7

43.7 37.9 32.7 28.0 24.1

25.2 21.6 18.5 15.7 13.4

38.5 33.2 28.4 24.2 20.7

22.9 19.6 16.7 14.2 12.1

35.1 30.1 25.7 22.0 18.7

11 12 13 14

16.4 14.2 12.5 11.0

25.3 22.0 19.3 17.0

14.8 12.8 11.2 9.83

22.9 19.8 17.3 15.2

13.7 12.0

21.0 18.4

11.6 10.1

17.8 15.6

10.4 9.03

16.1 13.9

Properties

Ag , in.2 rz , in.

3.61 0.870

3.03 0.874

ASD

LRFD

Ωc = 1.67

φc = 0.90

4.50 0.756

3.44 0.763

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.89 0.767

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–191

Table 4-12 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Eccentrically Loaded Single Angles L5× 5×

Shape

78 /

lb/ft

3 4 /

27.2 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L5

5 8 /

23.6 20.0 Pn /Ωc φc Pn Pn /Ωc φc Pn

3 8c /

12 /

7 16 /

16.2 Pn /Ωc φc Pn

14.3 Pn /Ωc φc Pn

12.3 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

71.6

108

68.9

104

65.7

98.7

60.6

91.0

56.6

85.1

46.5

69.8

1 2 3 4 5

71.1 69.4 66.9 63.5 59.5

107 104 101 95.8 90.0

68.4 66.7 64.1 60.7 56.7

103 100 96.6 91.6 85.8

65.1 63.4 60.8 57.4 53.4

97.9 95.5 91.6 86.7 80.8

60.0 58.4 55.9 52.6 48.8

90.2 87.9 84.2 79.5 73.9

56.1 54.6 52.2 49.1 45.5

84.3 82.2 78.7 74.1 68.8

46.3 45.8 45.1 43.4 41.2

69.6 68.9 67.7 65.1 61.7

6 7 8 9 10

55.2 50.7 46.2 41.8 37.6

83.7 77.0 70.3 63.8 57.4

52.4 47.9 43.5 39.1 35.0

79.4 72.8 66.2 59.7 53.5

49.1 44.7 40.3 36.1 32.1

74.5 67.9 61.4 55.1 49.1

44.7 40.5 36.3 32.3 28.6

67.8 61.5 55.3 49.3 43.7

41.6 37.6 33.6 29.8 26.3

63.0 57.1 51.2 45.6 40.3

38.3 34.6 30.9 27.4 24.1

58.1 52.5 47.0 41.7 36.8

11 12 13 14 15

33.6 29.9 26.8 24.2 21.9

51.3 45.8 41.0 36.9 33.4

31.1 27.6 24.7 22.1 20.0

47.6 42.2 37.7 33.9 30.5

28.4 25.1 22.3 19.9 17.9

43.4 38.4 34.1 30.5 27.4

25.1 22.1 19.5 17.3 15.5

38.5 33.7 29.8 26.5 23.8

23.1 20.2 17.8 15.8 14.1

35.3 30.9 27.3 24.2 21.6

21.1 18.4 16.1 14.3 12.7

32.2 28.1 24.7 21.9 19.5

16

19.9

30.4

18.1

27.7

16.2

24.7

14.0

21.4

12.7

19.4

11.4

17.5

Properties

Ag , in.2 rz , in.

8.00 0.971

ASD

LRFD

Ωc = 1.67

φc = 0.90

6.98 0.972

5.90 0.975

4.79 0.980

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.22 0.983

3.65 0.986

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Page 192

4–192

DESIGN OF COMPRESSION MEMBERS

Table 4-12 (continued)

Available Strength in Axial Compression, kips L5

L5× 31/2 ×

5 16 c,f /

lb/ft

3 4 /

10.3 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Eccentrically Loaded Single Angles L5× 5×

Shape

Fy = 36 ksi

ASD

12 /

3 8c /

13.6 Pn /Ωc φc Pn

10.4 Pn /Ωc φc Pn

5 8 /

19.8 16.8 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

35.4

53.2

55.4

83.3

54.6

82.0

52.9

79.5

49.7

74.7

46.9

70.5

1 2 3 4 5

35.2 34.9 34.3 32.8 31.0

53.0 52.4 51.5 49.3 46.5

54.9 53.4 49.0 43.9 38.7

82.6 80.5 74.1 66.6 59.0

54.0 51.3 46.6 41.3 36.3

81.3 77.3 70.5 62.7 55.4

51.6 48.1 43.6 38.6 33.5

77.7 72.6 66.1 58.7 51.1

48.7 45.6 40.9 35.4 30.1

73.2 68.8 62.0 54.0 46.1

45.9 42.8 38.2 32.8 27.7

69.1 64.7 57.9 50.1 42.4

6 7 8 9 10

29.1 27.3 25.4 23.5 21.1

43.7 40.8 37.8 34.9 31.8

33.9 29.5 25.4 21.8 18.9

51.8 45.1 39.0 33.5 29.0

31.5 27.1 23.2 19.8 17.0

48.2 41.6 35.7 30.4 26.1

28.7 24.4 20.7 17.5 14.9

43.9 37.5 31.8 26.9 23.0

25.3 21.2 17.8 14.9 12.6

38.9 32.7 27.5 23.0 19.4

23.1 19.2 16.1 13.4 11.3

35.6 29.7 24.9 20.8 17.5

11 12 13 14 15

18.5 16.2 14.2 12.5 11.1

28.3 24.7 21.7 19.1 17.0

16.5 14.5

25.3 22.3

14.8 12.9

22.7 19.9

12.9 11.2

19.8 17.3

10.8 9.34

16.6 14.4

9.96

LRFD

8.70 Pn /Ωc φc Pn

0

16

ASD

5 16 c,f /

ASD

9.62 8.30

LRFD

14.9 12.8

15.2

Properties

Ag , in.2 rz , in.

3.07 0.990

ASD

LRFD

Ωc = 1.67

φc = 0.90

5.85 0.744

4.93 0.746

4.00 0.750

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.05 0.755

2.56 0.758

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–193

Table 4-12 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Eccentrically Loaded Single Angles L5× 31/2 ×

Shape

12 /

7.00 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L5× 3×

1 4 c,f /

lb/ft

ASD

L5

12.8 11.3 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

3 8c /

5 16c,f /

9.80 Pn /Ωc φc Pn

8.20 Pn /Ωc φc Pn

7 16 /

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

1 4 c,f /

6.60 Pn /Ωc φc Pn ASD

LRFD

0

31.0

46.5

35.9

54.0

34.7

52.2

33.8

50.7

31.8

47.7

28.8

43.3

1 2 3 4 5

31.0 30.9 30.8 29.2 24.5

46.6 46.3 45.8 44.6 37.6

35.0 32.8 29.7 26.2 22.6

52.7 49.5 45.0 39.8 34.5

34.0 31.9 28.7 25.0 21.4

51.1 48.1 43.5 38.1 32.7

33.0 30.7 27.4 23.7 20.1

49.6 46.3 41.5 36.1 30.7

31.0 28.7 25.4 21.8 18.4

46.6 43.3 38.6 33.3 28.1

28.1 25.9 22.9 19.5 16.3

42.2 39.2 34.7 29.8 25.0

6 7 8 9 10

20.3 16.9 14.0 11.7 9.85

31.4 26.1 21.8 18.2 15.3

19.3 16.2 13.6 11.5 9.90

29.5 24.9 20.9 17.7 15.2

18.1 15.2 12.6 10.7 9.12

27.7 23.3 19.4 16.4 14.0

16.8 14.0 11.6 9.72 8.28

25.8 21.5 17.8 15.0 12.7

15.3 12.7 10.5 8.74 7.40

23.5 19.5 16.1 13.5 11.4

13.5 11.2 9.22 7.63 6.43

20.8 17.2 14.3 11.8 9.93

11 12

8.36 7.18

13.0 11.1

Properties

Ag , in.2 rz , in.

2.07 0.761

ASD

LRFD

Ωc = 1.67

φc = 0.90

3.75 0.642

3.31 0.644

2.86 0.646

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.41 0.649

1.94 0.652

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10:45 AM

Page 194

4–194

DESIGN OF COMPRESSION MEMBERS

Table 4-12 (continued)

Available Strength in Axial Compression, kips L4

Eccentrically Loaded Single Angles L4× 4×

Shape

3 4 /

lb/ft

5 8 /

18.5 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

12 /

15.7 12.8 Pn /Ωc φc Pn Pn /Ωc φc Pn

7 16 /

3 8 /

11.3 Pn /Ωc φc Pn

9.80 Pn /Ωc φc Pn ASD

5 16 /

LRFD

8.20 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

45.8

68.9

44.5

66.9

41.2

62.0

39.6

59.5

36.9

55.4

31.9

ASD

48.0

1 2 3 4 5

45.3 43.7 41.3 38.3 34.9

68.1 65.9 62.4 57.9 52.9

43.9 42.3 39.8 36.6 33.1

66.0 63.7 60.0 55.4 50.3

40.7 39.1 36.6 33.5 30.1

61.2 58.8 55.2 50.7 45.7

39.0 37.4 35.0 31.9 28.6

58.7 56.3 52.8 48.3 43.3

36.3 34.8 32.5 29.6 26.4

54.7 52.4 49.0 44.8 40.1

31.8 31.3 29.3 26.6 23.7

47.7 47.0 44.2 40.3 35.9

6 7 8 9 10

31.4 27.9 24.5 21.3 18.6

47.7 42.4 37.4 32.5 28.4

29.5 26.0 22.7 19.6 16.9

44.9 39.6 34.6 29.9 25.8

26.7 23.3 20.1 17.2 14.8

40.6 35.5 30.8 26.4 22.6

25.1 21.9 18.8 16.0 13.7

38.3 33.3 28.7 24.5 20.9

23.2 20.0 17.2 14.5 12.4

35.2 30.6 26.2 22.3 18.9

20.7 17.8 15.2 12.8 10.9

31.5 27.2 23.3 19.6 16.6

11 12 13

16.3 14.4

24.9 22.0

14.7 13.0

22.6 19.8

12.8 11.2

19.6 17.2

11.8 10.3

18.1 15.7

10.7 9.26

16.3 14.2

9.33 8.08 7.06

LRFD

14.3 12.4 10.8

Properties

Ag , in.2 rz , in.

5.44 0.774

ASD

LRFD

Ωc = 1.67

φc = 0.90

4.61 0.774

3.75 0.776

3.30 0.777

Note: Heavy line indicates KL/rz equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.86 0.779

2.40 0.781

AISC_Part 4D:14th Ed.

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Page 195

STEEL COMPRESSION—MEMBER SELECTION TABLES

4–195

Table 4-12 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Eccentrically Loaded Single Angles

1 4 c,f /

lb/ft

12 /

6.60 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L4× 31/2 ×

L4× 4×

Shape

ASD

L4

11.9 9.10 Pn /Ωc φc Pn Pn /Ωc φc Pn

1 4 c,f /

7.70 Pn /Ωc φc Pn

6.20 Pn /Ωc φc Pn

LRFD

ASD

LRFD

LRFD

ASD

LRFD

33.8

50.4

75.7

47.8

71.9

35.7

53.6

24.5

36.8

39.1

58.8

1 2 3 4 5

22.3 22.0 21.2 19.7 18.2

33.6 33.0 31.8 29.6 27.3

49.7 47.7 44.6 40.7 35.0

74.8 72.0 67.8 62.3 53.7

48.0 48.1 43.3 37.7 32.2

72.1 72.9 66.1 57.9 49.7

35.6 35.4 34.3 35.1 29.7

53.5 53.0 51.0 51.0 46.1

24.4 23.6 22.3 21.1 20.4

36.7 35.4 33.4 31.5 29.8

38.6 37.2 34.4 29.5 25.0

58.1 56.2 52.2 45.0 38.2

6 7 8 9 10

16.8 15.2 13.0 11.0 9.29

25.0 22.7 19.9 16.9 14.2

28.7 23.6 19.4 16.1 13.5

44.3 36.5 30.0 24.8 20.9

25.8 20.7 16.8 13.7 11.4

39.9 32.2 26.1 21.3 17.7

23.9 19.0 15.3 12.4 10.3

37.2 29.6 23.8 19.3 15.9

21.1 16.6 13.3 10.8 8.86

32.9 26.0 20.8 16.8 13.8

21.0 17.5 14.6 12.3 10.5

32.2 26.9 22.4 18.9 16.1

11.5

17.8

9.68

15.0

ASD

8.64 7.38

LRFD

ASD

13.6 Pn /Ωc φc Pn

22.5

7.93 12.1 6.84 10.5 5.96 9.10

LRFD

5 8 /

0

11 12 13

ASD

L4× 3× 5 16 /

3 8 /

13.4 11.4

7.44 11.6 6.33 9.86

Properties

Ag , in.2 rz , in.

1.93 0.783

ASD

LRFD

Ωc = 1.67

φc = 0.90

3.50 0.716

2.68 0.719

2.25 0.721

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.82 0.723

3.99 0.631

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4–196

DESIGN OF COMPRESSION MEMBERS

Table 4-12 (continued)

Available Strength in Axial Compression, kips L4-L31/2

Eccentrically Loaded Single Angles L31/2 × 31/2 ×

L4× 3×

Shape

12 /

lb/ft

3 8 /

11.1 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

ASD

5 16 /

8.50 7.20 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

1 4 c,f /

12 /

5.80 Pn /Ωc φc Pn

11.1 Pn /Ωc φc Pn

ASD

LRFD

ASD

7 16 /

LRFD

9.80 Pn /Ωc φc Pn ASD

LRFD

0

39.1

58.8

38.2

57.4

37.6

56.5

30.6

46.0

33.3

50.1

32.0

48.1

1 2 3 4 5

38.5 36.8 32.8 27.8 23.2

58.0 55.7 49.8 42.3 35.5

37.4 35.2 30.6 25.4 20.7

56.4 53.3 46.6 38.8 31.8

36.3 32.9 29.0 23.6 19.0

54.7 49.9 44.1 36.2 29.2

30.4 30.4 26.4 21.3 16.9

45.6 45.2 40.3 32.6 26.0

32.8 31.2 28.7 25.8 22.7

49.3 46.9 43.4 39.1 34.4

31.5 29.9 27.5 24.6 21.5

47.3 45.0 41.5 37.2 32.7

6 7 8 9 10

19.2 15.8 13.0 10.8 9.20

29.5 24.3 20.0 16.7 14.2

16.8 13.6 11.0 9.13 7.68

25.9 21.0 17.0 14.1 11.8

15.2 12.2 9.83 8.09 6.78

23.5 18.9 15.2 12.5 10.5

13.4 10.7 8.57 7.00 5.84

20.7 16.6 13.3 10.9 9.04

19.6 16.7 14.0 11.9 10.2

29.8 25.5 21.5 18.2 15.5

18.5 15.7 13.1 11.0 9.41

28.2 23.9 20.0 16.9 14.4

13.4

8.11

12.4

11

8.78

Properties

Ag , in.2 rz , in.

3.25 0.633

ASD

LRFD

Ωc = 1.67

φc = 0.90

2.49 0.636

2.09 0.638

1.69 0.639

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.25 0.679

2.89 0.681

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–197

Table 4-12 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Eccentrically Loaded Single Angles L31/2 × 31/2 ×

Shape

3 8 /

lb/ft

Effective length, KL (ft), with respect to least radius of gyration, rz

Design

ASD

L31/2 × 3× 1 4c /

5 16 /

8.50 Pn /Ωc φc Pn

7.20 5.80 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

LRFD

L31/2

ASD

LRFD

12 /

7 16 /

10.2 Pn /Ωc φc Pn

9.10 Pn /Ωc φc Pn

ASD

LRFD

ASD

3 8 /

LRFD

7.90 Pn /Ωc φc Pn ASD

LRFD

0

30.6

46.0

28.0

42.1

21.2

31.8

36.8

55.2

37.9

56.9

38.7

58.1

1 2 3 4 5

30.1 28.5 26.1 23.2 20.2

45.2 42.9 39.4 35.2 30.7

27.5 26.0 23.8 21.1 18.3

41.4 39.2 35.9 32.0 27.8

21.0 20.6 19.3 17.9 16.0

31.6 30.9 29.0 26.7 24.2

36.2 34.6 32.1 28.5 23.2

54.5 52.3 48.9 43.7 35.7

37.2 35.2 32.3 28.2 22.6

56.0 53.3 49.3 43.3 34.8

37.8 35.4 31.8 27.3 21.5

57.0 53.7 48.6 42.1 33.2

6 7 8 9 10

17.3 14.5 12.1 10.1 8.57

26.3 22.2 18.5 15.5 13.1

15.5 13.0 10.7 8.93 7.54

23.6 19.8 16.4 13.7 11.5

13.5 11.3 9.30 7.69 6.46

20.6 17.2 14.2 11.8 9.88

18.8 15.2 12.3 10.2 8.62

29.0 23.4 19.0 15.8 13.3

18.0 14.4 11.6 9.59 8.04

27.9 22.3 18.0 14.8 12.4

17.0 13.4 10.8 8.81 7.36

26.3 20.8 16.7 13.6 11.4

11

7.36

11.3

6.45

5.50

8.41

9.86

Properties

Ag , in.2 rz , in.

2.50 0.683

ASD

LRFD

Ωc = 1.67

φc = 0.90

2.10 0.685

1.70 0.688

3.02 0.618

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.67 0.620

2.32 0.622

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4–198

DESIGN OF COMPRESSION MEMBERS

Table 4-12 (continued)

Available Strength in Axial Compression, kips L31/2

Eccentrically Loaded Single Angles L31/2 × 3×

Shape

6.60 Pn /Ωc φc Pn

Effective length, KL (ft), with respect to least radius of gyration, rz

Design

ASD

L31/2 × 21/2 × 1 4c /

5 16 /

lb/ft

Fy = 36 ksi

12 /

5.40 9.40 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

3 8 /

5 16 /

7.20 Pn /Ωc φc Pn

6.10 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

1 4c /

4.90 Pn /Ωc φc Pn ASD

LRFD

0

34.5

51.8

24.3

36.5

28.1

42.3

27.5

41.4

27.2

40.9

26.0

39.1

1 2 3 4 5

34.6 35.3 30.2 25.5 20.0

52.0 53.1 46.3 39.3 31.0

24.3 23.3 22.4 22.8 18.1

36.4 34.8 33.3 34.4 28.1

27.6 25.5 21.7 18.0 14.7

41.6 38.6 33.0 27.4 22.5

26.9 23.6 19.9 16.1 12.9

40.5 35.8 30.2 24.7 19.8

25.9 22.8 18.9 15.1 11.9

38.9 34.5 28.8 23.1 18.3

24.9 21.7 17.6 13.7 10.6

37.5 32.9 26.8 21.1 16.4

6 7 8 9 10

15.5 12.2 9.67 7.87 6.54

24.1 18.9 15.0 12.2 10.1

13.9 10.8 8.49 6.87 5.68

21.6 11.8 16.8 9.55 13.2 7.86 10.7 8.82

18.2 14.7 12.1

10.2 8.12 6.61

15.7 12.5 10.2

9.30 14.3 7.33 11.3 5.93 9.14

8.26 12.8 6.44 9.96 5.17 7.98 4.24 6.54

1.79 0.538

1.45 0.541

Properties

Ag , in.2 rz , in.

1.95 0.624

ASD

LRFD

Ωc = 1.67

φc = 0.90

1.58 0.628

2.77 0.532

2.12 0.535

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–199

Table 4-12 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Eccentrically Loaded Single Angles L3× 3×

Shape

12 /

lb/ft

7 16 /

9.40 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L3

ASD

3 8 /

8.30 7.20 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

LRFD

3 16 c,f /

5 16 /

14 /

6.10 Pn /Ωc φc Pn

4.90 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

3.71 Pn /Ωc φc Pn

LRFD

ASD

0

25.3

38.1

24.3

36.5

23.2

34.9

21.7

32.6

19.4

29.2

12.7

ASD

19.1

LRFD

1 2 3 4 5

24.8 23.2 21.0 18.3 15.7

37.3 35.0 31.7 27.8 23.8

23.8 22.2 19.9 17.3 14.7

35.7 33.5 30.2 26.3 22.4

22.7 21.1 18.9 16.3 13.7

34.1 31.8 28.5 24.7 20.9

21.2 19.7 17.5 15.0 12.5

31.9 29.7 26.5 22.8 19.1

19.1 17.7 15.7 13.4 11.1

28.7 26.7 23.7 20.3 16.9

12.6 12.2 11.2 10.0 8.95

18.9 18.3 16.7 15.0 13.3

6 7 8 9

13.1 10.8 8.99 7.58

20.0 16.5 13.7 11.6

12.2 10.0 8.27 6.93

18.7 15.3 12.6 10.6

11.3 17.3 10.3 15.7 9.19 14.1 8.27 12.7 7.55 11.5 6.75 10.3 6.30 9.64 5.60 8.57

8.97 13.7 7.17 11.0 5.80 8.88 4.79 7.32

7.29 11.1 5.83 8.92 4.68 7.16 3.84 5.86

1.44 0.585

1.09 0.586

Properties

Ag , in.2 rz , in.

2.76 0.580

ASD

LRFD

Ωc = 1.67

φc = 0.90

2.43 0.580

2.11 0.581

1.78 0.583

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 200

4–200

DESIGN OF COMPRESSION MEMBERS

Table 4-12 (continued)

Available Strength in Axial Compression, kips L3

Eccentrically Loaded Single Angles L3× 21/2 ×

Shape

12 /

lb/ft

7 16 /

8.50 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

ASD

3 8 /

7.60 6.60 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

LRFD

ASD

LRFD

3 16 c,f /

5 16 /

14 /

5.60 Pn /Ωc φc Pn

4.50 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

3.39 Pn /Ωc φc Pn ASD

LRFD

0

24.8

37.3

25.5

38.4

26.1

39.3

26.7

40.2

24.2

36.4

14.7

22.2

1 2 3 4 5

24.4 23.2 21.3 17.4 13.8

36.7 35.1 32.5 26.6 21.2

25.0 23.5 21.3 16.9 13.2

37.6 35.6 32.5 25.9 20.4

25.5 23.7 20.9 16.3 12.5

38.4 35.9 31.9 25.0 19.3

25.9 23.6 20.1 15.4 11.7

39.0 35.9 30.8 23.8 18.0

24.5 22.0 18.1 14.0 10.4

36.7 33.5 27.9 21.7 16.1

14.5 13.7 13.3 11.9 8.70

21.7 20.4 19.5 18.6 13.6

6 7 8

10.9 8.70 7.09

16.8 13.4 10.9

10.3 8.15 6.61

15.9 12.6 10.2

9.65 14.9 7.56 11.7 6.08 9.38

8.84 13.7 6.85 10.6 5.46 8.44

7.77 12.1 5.96 9.24 4.72 7.31

6.47 10.1 4.91 7.65 3.86 6.00

1.63 0.518

1.32 0.520

1.00 0.521

Properties

Ag , in.2 rz , in.

2.50 0.516

ASD

LRFD

Ωc = 1.67

φc = 0.90

2.22 0.516

1.93 0.517

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–201

Table 4-12 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Eccentrically Loaded Single Angles

L21/2 × 21/2 ×

L3× 2×

Shape

12 /

lb/ft

3 8 /

7.70 Pn /Ωc φc Pn

Design

Effective length, KL (ft), with respect to least radius of gyration, rz

L3-L21/2

ASD

5.90 5.00 Pn /Ωc φc Pn Pn /Ωc φc Pn

LRFD

ASD

14 /

3 16 c,f /

4.10 Pn /Ωc φc Pn

3.07 Pn /Ωc φc Pn

5 16 /

LRFD

ASD

LRFD

ASD

0

18.3

27.5

17.6

26.4

17.0

25.5

1 2 3 4 5

17.4 15.3 12.7 10.2 7.97

26.2 23.1 19.3 15.5 12.2

16.6 14.2 11.5 9.04 6.93

25.0 21.5 17.5 13.8 10.6

15.9 13.5 10.8 8.35 6.32

24.0 15.4 20.5 12.9 16.5 10.0 12.8 7.58 9.72 5.64

6 7 8

6.29 5.08

9.65 7.79

5.38 4.28

8.26 6.58

4.85 3.84

7.46 5.90

16.3

LRFD 24.5

4.27 3.35

ASD 15.3

23.2 14.3 19.6 11.8 15.4 8.95 11.6 6.61 8.69 4.87 6.58 5.15

3.63 2.81

LRFD

12 /

7.70 Pn /Ωc φc Pn ASD

LRFD

23.0

18.1

27.2

21.6 17.9 13.7 10.2 7.53

17.6 16.1 14.1 11.9 9.78

26.4 24.4 21.4 18.1 14.9

5.61 4.34

7.85 12.0 6.38 9.76 5.28 8.07

Properties

Ag , in.2 rz , in.

2.26 0.425

ASD

LRFD

Ωc = 1.67

φc = 0.90

1.75 0.426

1.48 0.428

1.20 0.431

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

0.917 0.435

2.26 0.481

AISC_Part 4D:14th Ed.

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Page 202

4–202

DESIGN OF COMPRESSION MEMBERS

Table 4-12 (continued)

Available Strength in Axial Compression, kips L21/2

Eccentrically Loaded Single Angles L21/2 × 21/2 ×

Shape lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

L21/2 × 2×

3 8 /

5 16 /

14 /

3 16c /

3 8 /

5.90 Pn /Ωc φc Pn

5.00 Pn /Ωc φc Pn

4.10 Pn /Ωc φc Pn

3.07 Pn /Ωc φc Pn

5.30 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

17.0

25.5

16.0

24.1

14.8

22.2

11.7

17.5

16.9

25.4

1 2 3 4 5

16.4 14.9 12.9 10.6 8.55

24.7 22.5 19.5 16.2 13.1

15.5 14.0 11.9 9.77 7.76

23.3 21.1 18.1 14.9 11.9

14.3 12.8 10.8 8.77 6.88

21.5 19.3 16.4 13.4 10.5

11.5 10.9 9.16 7.33 5.68

17.3 16.4 13.9 11.2 8.69

16.4 15.0 11.9 8.94 6.65

24.7 22.8 18.1 13.7 10.2

6 7 8

6.73 5.39 4.40

10.3 8.24 6.74

6.04 4.80 3.89

4.32 3.36 2.69

6.61 5.14 4.11

5.06

9.24 7.34 5.96

5.29 4.16 3.36

8.10 6.37 5.13

7.79

Properties

Ag , in.2 rz , in.

1.73 0.481

1.46 0.481

ASD

LRFD

Ωc = 1.67

φc = 0.90

1.19 0.482

0.901 0.482

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.55 0.419

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STEEL COMPRESSION—MEMBER SELECTION TABLES

4–203

Table 4-12 (continued)

Available Strength in Axial Compression, kips

Fy = 36 ksi

Eccentrically Loaded Single Angles L21/2 × 2×

Shape lb/ft

Effective length, KL (ft), with respect to least radius of gyration, rz

Design

L21/2

L2 1/2 × 11/2 ×

5 16 /

14 /

3 16c /

14 /

3 16c /

4.50 Pn /Ωc φc Pn

3.62 Pn /Ωc φc Pn

2.75 Pn /Ωc φc Pn

3.19 Pn /Ωc φc Pn

2.44 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

17.5

26.3

17.4

26.2

15.4

23.2

9.06

13.6

8.63

13.0

1 2 3 4 5

16.8 15.1 11.5 8.46 6.18

25.4 23.0 17.7 13.0 9.53

16.6 14.3 10.7 7.65 5.49

25.1 21.8 16.4 11.8 8.49

15.4 12.7 9.55 6.63 4.67

23.0 19.4 14.7 10.3 7.25

8.27 6.61 4.86 3.43 2.50

12.5 10.1 7.44 5.27 3.84

7.84 6.04 4.29 2.95 2.11

11.8 9.21 6.58 4.54 3.25

6 7

4.64

7.15

4.07 3.14

6.29 4.84

3.41 2.61

5.29 4.03

Properties

Ag , in.2 rz , in.

1.32 0.420

1.07 0.423

ASD

LRFD

Ωc = 1.67

φc = 0.90

0.818 0.426

0.947 0.321

Shape is slender for compression with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

0.724 0.324

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Page 204

4–204

DESIGN OF COMPRESSION MEMBERS

Table 4-12 (continued)

Available Strength in Axial Compression, kips L2

Eccentrically Loaded Single Angles L2× 2×

Shape lb/ft Design

Effective length, KL (ft), with respect to least radius of gyration, rz

Fy = 36 ksi

3 8 /

5 16 /

14 /

3 16 /

1 8 c,f /

4.70 Pn /Ωc φc Pn

3.92 Pn /Ωc φc Pn

3.19 Pn /Ωc φc Pn

2.44 Pn /Ωc φc Pn

1.65 Pn /Ωc φc Pn

ASD

LRFD

ASD

LRFD

0

11.6

17.5

11.2

16.8

1 2 3 4 5

11.1 9.70 7.93 6.18 4.67

16.7 14.7 12.0 9.42 7.14

10.6 9.21 7.42 5.69 4.24

16.0 13.9 11.3 8.69 6.48

6

3.62

5.54

3.25

4.97

ASD

LRFD

ASD

LRFD

ASD

LRFD

15.8

9.44

14.2

5.58

8.39

9.95 8.52 6.76 5.09 3.74

15.0 12.9 10.3 7.78 5.71

8.91 7.57 5.90 4.37 3.14

13.4 11.4 8.98 6.67 4.81

5.45 4.88 4.12 3.36 2.39

8.19 7.32 6.16 4.95 3.64

2.83

4.33

2.35

3.59

1.76

2.67

10.5

Properties

Ag , in.2 rz , in.

1.37 0.386

1.16 0.386

ASD

LRFD

Ωc = 1.67

φc = 0.90

0.944 0.387

0.722 0.389

Shape is slender for compression with Fy = 36 ksi. f Shape exceeds compact limit for flexure with Fy = 36 ksi. Note: Heavy line indicates KL/rz equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

0.491 0.391

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–205

Table 4-13 Fy = 46 ksi fc′ = 4 ksi

Available Strength in Axial Compression, kips Concrete Filled Rectangular HSS HSS20× 12×

Shape

5 8 /

t design, in. Steel, lb/ft

Effective length, (KL )y , with respect to weak axis (ft)

Design 0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

COMPOSITE HSS20-HSS16

HSS16× 12×

12 /

3 8 /

5 8 /

12 /

3 8 /

0.581 0.465 0.349 0.581 0.465 0.349 127 103 78.5 110 89.7 68.3 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 1150 1730 1010 1510 865 1300 970 1450 849 1270 724 1090 1130 1700 993 1490 850 1280 954 1430 835 1250 711 1070 1130 1690 987 1480 845 1270 948 1420 830 1240 707 1060 1120 1680 980 1470 839 1260 941 1410 824 1240 702 1050 1110 1660 972 1460 832 1250 934 1400 817 1230 696 1040 1100 1650 964 1450 825 1240 925 1390 810 1210 690 1030 1090 1630 955 1430 817 1230 916 1370 802 1200 683 1020 1080 1620 945 1420 808 1210 906 1360 793 1190 675 1010 1070 1600 934 1400 798 1200 896 1340 784 1180 667 1000 1050 1580 922 1380 788 1180 885 1330 774 1160 658 987 1040 1560 910 1360 777 1170 873 1310 763 1150 649 974 1020 1540 897 1350 766 1150 860 1290 752 1130 639 959 1010 1510 883 1330 754 1130 847 1270 741 1110 629 944 994 1490 869 1300 741 1110 833 1250 728 1090 619 928 977 1470 855 1280 728 1090 819 1230 716 1070 608 911 960 1440 839 1260 715 1070 804 1210 703 1050 596 894 942 1410 824 1240 701 1050 788 1180 689 1030 584 877 924 1390 807 1210 687 1030 773 1160 675 1010 572 858 905 1360 791 1190 672 1010 756 1130 661 992 560 840 886 1330 774 1160 658 986 740 1110 647 970 547 821 866 1300 757 1130 642 964 723 1080 632 948 534 802 846 1270 739 1110 627 940 706 1060 617 925 521 782 826 1240 721 1080 611 917 689 1030 602 902 508 762 806 1210 703 1050 595 893 671 1010 586 879 495 742 785 1180 685 1030 580 869 653 980 571 856 481 722 764 1150 666 1000 563 845 636 953 555 832 468 701 722 1080 629 944 531 797 600 899 523 785 440 661 680 1020 592 888 499 748 564 845 492 737 413 620 638 957 555 833 467 700 528 791 460 690 386 579 597 895 519 778 435 652 492 738 429 643 359 539 556 834 483 724 404 605 457 686 398 598 333 499 Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

589 401

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

72300 30500 4.93 1.54

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

885 603

491 331

738 498

62800 26400 4.99 1.54

386 260

581 391

52500 21900 5.04 1.55

416 335

626 504

40300 24900 4.80 1.27

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

347 279

521 420

35200 21600 4.86 1.28

274 219

412 329

29300 18000 4.91 1.28

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DESIGN OF COMPRESSION MEMBERS

Table 4-13 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS16-HSS14

HSS16× 8×

5 16 /

t design, in. Steel, lb/ft Design

Effective length, (KL )y , with respect to weak axis (ft)

Concrete Filled Rectangular HSS HSS16× 12×

Shape

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

Fy = 46 ksi fc′ = 4 ksi

5 8 /

12 /

HSS14× 10× 3 8 /

5 16 /

5 8 /

0.291 0.581 0.465 0.349 0.291 0.581 57.4 93.3 76.1 58.1 48.9 93.3 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 660 990 763 1140 662 992 558 837 503 754 783 1180 649 973 736 1100 638 957 538 807 484 726 765 1150 644 967 726 1090 630 945 531 796 478 717 758 1140 640 959 715 1070 620 931 523 784 471 706 750 1130 634 951 703 1050 610 915 514 771 462 694 742 1110 628 942 689 1030 598 898 504 756 453 680 732 1100 622 933 675 1010 586 879 493 740 444 666 722 1080 615 922 659 989 573 859 482 723 433 650 711 1070 607 911 643 964 558 838 470 705 422 634 699 1050 599 898 625 938 543 815 457 686 411 616 686 1030 590 886 607 911 528 792 444 666 399 598 673 1010 581 872 588 883 512 768 430 645 386 579 659 988 572 858 569 854 495 743 416 624 373 560 644 966 562 843 549 824 478 717 402 602 360 540 629 943 552 828 529 793 461 691 387 580 347 520 613 920 541 812 508 763 443 664 372 558 333 500 597 896 530 796 488 731 425 638 357 535 319 479 581 871 519 779 467 700 407 611 341 512 306 459 564 846 508 761 446 669 389 584 326 489 292 438 547 821 496 744 425 638 371 557 311 467 278 417 530 795 484 726 405 607 353 530 296 444 264 397 513 769 472 708 384 577 336 504 281 422 251 376 495 743 460 689 366 550 318 478 266 400 238 356 478 717 447 671 348 523 301 452 252 378 225 337 460 691 435 652 330 497 285 427 238 357 212 318 443 664 422 633 313 471 268 402 224 336 199 299 426 638 397 595 280 421 236 355 197 296 175 263 391 587 372 558 248 373 209 314 175 262 155 233 358 537 347 520 221 333 187 280 156 234 139 208 325 488 322 483 199 299 168 252 140 210 124 187 294 440 298 447 179 269 151 227 126 189 112 168 266 399 Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

235 187

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

26200 16000 4.94 1.28

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

353 281

322 192

484 288

29100 9060 3.27 1.79

270 160

406 241

25700 7950 3.32 1.80

215 126

323 190

21600 6630 3.37 1.80

185 108

19200 5900 3.40 1.80

Note: Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

278 162

300 233

450 351

24500 13900 3.98 1.33

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Table 4-13 (continued) Fy = 46 ksi fc′ = 4 ksi

Available Strength in Axial Compression, kips Concrete Filled Rectangular HSS HSS14× 10×

Shape

12 /

t design, in. Steel, lb/ft Design

Effective length, (KL )y , with respect to weak axis (ft)

COMPOSITE HSS14-HSS12

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

3 8 /

HSS12× 10×

5 16 /

1 4 c,f /

12 /

3 8 /

0.465 0.349 0.291 0.233 0.465 0.349 76.1 58.1 48.9 39.4 69.3 53.0 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 682 1020 578 867 523 784 468 701 607 911 514 772 666 998 564 846 510 765 456 684 593 889 502 752 660 990 559 839 505 758 452 677 587 881 497 746 653 980 553 830 500 750 447 670 581 872 492 738 646 969 547 820 494 741 441 662 574 862 486 729 638 957 540 810 488 732 435 653 567 851 480 720 629 943 532 798 481 721 429 643 559 838 473 709 619 929 524 786 473 709 422 633 550 825 465 698 609 913 515 773 465 697 414 621 541 811 457 686 598 897 506 758 456 684 406 610 531 796 449 673 586 880 496 744 447 670 398 597 520 781 440 660 574 862 485 728 437 656 389 584 509 764 430 645 562 843 474 712 427 641 380 570 498 747 421 631 549 823 463 695 417 626 371 556 486 729 410 616 535 803 452 677 407 610 361 542 474 711 400 600 522 782 440 660 396 593 351 527 461 692 389 584 507 761 428 641 385 577 341 511 449 673 378 567 493 740 415 623 373 560 331 496 436 653 367 551 478 718 403 604 362 542 320 480 422 633 356 534 464 695 390 585 350 525 309 464 409 613 344 516 449 673 377 565 338 507 299 448 395 593 333 499 434 650 364 546 326 490 288 432 382 573 321 482 418 628 351 527 315 472 277 416 368 552 309 464 403 605 338 507 303 454 267 400 354 532 298 447 388 582 325 488 291 436 256 384 341 511 286 429 373 560 312 468 279 419 245 368 327 491 275 412 343 515 287 430 256 384 224 337 300 451 252 378 314 471 262 393 234 350 204 306 274 412 230 345 286 429 238 357 212 318 185 277 249 374 208 313 259 388 215 322 191 286 166 249 225 337 188 281 234 350 194 291 172 258 150 224 203 304 169 254 Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

251 195

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

21600 12300 4.04 1.33

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

c f

377 293

199 154

298 231

18000 10200 4.09 1.33

171 132

257 198

16000 9040 4.12 1.33

141 108

212 163

14000 7860 4.14 1.33

Shape is noncompact for compression with Fy = 46 ksi. Shape is noncompact for flexure with Fy = 46 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

198 173

298 260

14500 10700 3.96 1.16

157 137

236 206

12100 8900 4.01 1.17

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DESIGN OF COMPRESSION MEMBERS

Table 4-13 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS12

5 16 /

t design, in. Steel, lb/ft Design

Effective length, (KL )y , with respect to weak axis (ft)

Concrete Filled Rectangular HSS HSS12× 10×

Shape

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

Fy = 46 ksi fc′ = 4 ksi

HSS12× 8×

14 /

5 8 /

12 /

0.291 0.233 0.581 0.465 44.6 36.0 76.3 62.5 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD 463 695 415 622 608 913 528 793 452 678 404 606 586 878 509 763 448 671 400 600 578 866 502 753 443 664 396 594 568 853 494 741 438 656 391 586 558 837 485 728 432 648 386 578 547 821 476 714 425 638 380 570 535 803 466 698 419 628 373 560 522 783 455 682 411 617 367 550 508 763 443 664 404 605 360 539 494 741 431 646 395 593 352 528 479 718 418 627 387 580 344 516 463 695 404 607 378 567 336 504 447 671 391 586 369 553 328 492 431 647 377 565 359 539 319 479 414 622 362 544 349 524 310 465 398 596 348 522 340 509 301 452 381 571 333 500 329 494 292 438 364 545 319 478 319 479 282 424 347 520 304 456 309 463 273 409 331 497 290 434 298 447 263 395 315 474 275 413 288 432 254 381 300 451 261 391 277 416 244 366 285 429 247 370 267 400 235 352 270 406 233 350 256 384 225 338 256 385 220 329 246 368 216 324 242 363 206 310 225 338 197 296 214 321 181 272 205 308 179 269 189 285 161 241 186 279 162 243 169 254 143 215 167 251 145 218 152 228 129 193 151 226 131 197 137 206 116 174

3 8 /

14 /

0.349 47.9 Pn /Ωc φc Pn ASD LRFD 444 666 427 641 422 632 415 622 408 611 400 599 391 586 382 572 372 558 361 542 351 526 339 509 328 492 316 474 304 456 292 438 280 420 267 401 255 383 243 364 231 346 219 328 207 310 195 293 184 276 173 259 152 228 135 202 120 180 108 162 97.3 146

0.233 32.6 Pn /Ωc φc Pn ASD LRFD 354 531 340 510 335 503 330 495 324 486 317 476 310 465 303 454 295 442 286 429 277 416 268 402 259 388 249 374 239 359 229 344 220 329 210 314 200 299 190 285 180 270 170 255 161 241 151 227 142 214 133 200 117 176 104 156 92.6 139 83.1 125 75.0 113

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

135 117

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

10800 7920 4.04 1.17

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

203 176

112 97.0

168 146

9390 6890 4.07 1.17

202 150

304 226

13600 6900 3.16 1.40

171 126

257 136 190 100

12000 6100 3.21 1.40

10100 5110 3.27 1.41

Note: Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

204 150

97.3 146 71.1 107 7880 3940 3.32 1.41

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Table 4-13 (continued) Fy = 46 ksi fc′ = 4 ksi

Available Strength in Axial Compression, kips COMPOSITE HSS12-HSS10

Concrete Filled Rectangular HSS HSS12× 6×

Shape

t design, in. Steel, lb/ft

Effective length, (KL )y , with respect to weak axis (ft)

Design 0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

HSS10× 8×

5 8 /

12 /

3 8 /

14 /

5 8 /

12 /

0.581 67.8 Pn /Ωc φc Pn ASD LRFD 519 778 485 728 474 712 462 695 449 675 435 653 420 631 403 606 387 581 369 555 352 529 334 502 316 474 297 447 279 420 261 393 244 366 227 341 210 316 194 291 178 268 165 248 153 230 142 214 133 199 124 186 109 164 96.4 145 86.0 129 77.2 116

0.465 55.7 Pn /Ωc φc Pn ASD LRFD 447 670 419 628 409 614 398 597 386 579 373 559 359 539 344 517 329 494 313 470 297 446 281 422 265 397 249 374 234 352 220 330 206 309 192 288 178 268 165 248 152 229 141 211 130 196 121 182 113 170 106 159 92.9 140 82.2 124 73.4 110 65.8 99.0 59.4 89.3

0.349 42.8 Pn /Ωc φc Pn ASD LRFD 373 560 350 525 342 513 333 499 323 484 312 468 301 451 289 433 276 414 263 394 250 375 236 354 223 334 209 314 196 294 183 274 170 255 157 236 145 218 133 200 123 184 114 170 105 158 97.9 147 91.2 137 85.3 128 74.9 112 66.4 99.6 59.2 88.8 53.1 79.7 48.0 71.9

0.233 29.2 Pn /Ωc φc Pn ASD LRFD 293 440 275 412 268 402 261 391 253 380 244 367 235 353 226 339 216 324 205 308 195 292 184 276 173 260 163 244 152 228 142 213 132 197 122 183 112 168 103 154 94.9 142 87.7 132 81.3 122 75.6 113 70.5 106 65.9 98.8 57.9 86.8 51.3 76.9 45.7 68.6 41.1 61.6 37.1 55.6

0.581 67.8 Pn /Ωc φc Pn ASD LRFD 532 799 512 767 504 756 496 744 487 730 477 715 466 699 454 681 442 663 429 643 415 623 401 602 387 580 372 558 357 537 343 516 329 495 315 474 301 453 287 432 273 411 259 390 246 370 233 349 219 330 207 311 182 274 161 242 144 216 129 194 116 175

0.465 55.7 Pn /Ωc φc Pn ASD LRFD 461 691 443 665 437 655 430 645 422 633 413 620 404 606 394 591 384 576 373 559 361 542 349 524 337 506 325 487 312 468 299 449 286 429 273 410 260 390 247 371 235 352 222 333 210 315 198 296 186 279 174 262 154 231 136 205 121 183 109 164 98.4 148

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

168 101

253 143 215 151 85.0 128

10800 3380 2.39 1.79

9520 2980 2.44 1.79

114 171 67.8 102 8120 2520 2.49 1.80

82.2 124 152 48.2 72.5 129 6330 1950 2.54 1.80

8440 5820 3.09 1.20

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

229 129 194 109

194 164

7480 5140 3.14 1.21

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DESIGN OF COMPRESSION MEMBERS

Table 4-13 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS10

Fy = 46 ksi fc′ = 4 ksi

Concrete Filled Rectangular HSS HSS10× 8×

Shape

HSS10× 6×

3 8 /

5 16 /

14 /

3 16 /

5 8 /

1 2 /

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

0.349 42.8 Pn /Ωc φc Pn ASD LRFD 387 580 372 558 367 550 361 542 355 532 348 521 340 510 332 497 323 484 314 470 304 456 294 441 284 426 274 410 263 394 252 378 241 362 231 346 220 330 209 313 198 297 188 282 177 266 167 251 157 236 148 221 130 195 115 172 103 154 92.0 138 83.0 125

0.291 36.1 Pn /Ωc φc Pn ASD LRFD 347 520 334 500 329 493 324 486 318 477 311 467 304 457 297 445 289 434 281 421 272 408 263 395 254 381 245 367 235 353 225 338 216 324 206 309 196 294 187 280 177 265 167 251 158 237 149 224 140 210 131 197 115 173 102 153 91.2 137 81.9 123 73.9 111

0.233 29.2 Pn /Ωc φc Pn ASD LRFD 307 460 295 442 291 436 286 429 281 421 275 412 268 403 262 393 255 382 247 371 239 359 231 347 223 335 215 322 206 309 198 296 189 283 180 270 171 257 163 244 154 231 146 219 138 206 129 194 122 182 114 171 99.9 150 88.5 133 79.0 118 70.9 106 64.0 95.9

0.174 22.2 Pn /Ωc φc Pn ASD LRFD 265 397 254 381 250 376 246 369 241 362 236 354 231 346 225 337 218 328 212 318 205 307 198 297 190 286 183 274 175 263 168 252 160 240 152 229 145 217 137 206 130 195 122 184 115 173 108 162 101 152 94.6 142 83.1 125 73.7 110 65.7 98.5 59.0 88.4 53.2 79.8

0.581 59.3 Pn /Ωc φc Pn ASD LRFD 452 679 424 637 414 623 403 606 391 588 378 569 365 548 350 526 335 504 319 480 303 456 287 432 271 407 255 383 239 359 223 335 207 311 192 288 177 266 163 245 150 225 139 208 129 193 120 180 111 168 104 157 91.5 138 81.1 122 72.3 109 64.9 97.6

0.465 48.9 Pn /Ωc φc Pn ASD LRFD 388 583 363 545 354 531 345 517 334 501 322 483 310 464 297 445 283 425 269 404 255 382 241 362 228 342 215 323 202 303 189 284 176 265 164 246 152 228 140 210 129 194 119 179 110 166 103 154 95.7 144 89.4 134 78.6 118 69.6 105 62.1 93.3 55.7 83.8

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

103 154 86.9 131

88.5 133 74.8 112

73.6 111 62.1 93.3

6340 4360 3.19 1.21

5660 3880 3.22 1.21

4910 3360 3.25 1.21

t design, in. Steel, lb/ft

Effective length, (KL )y , with respect to weak axis (ft)

Design

Properties

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

57.5 48.2

86.4 125 187 72.4 85.6 129

4100 2800 3.28 1.21

6600 2810 2.34 1.53

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

106 159 72.7 109 5860 2500 2.39 1.53

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Table 4-13 (continued) Fy = 46 ksi fc′ = 4 ksi

Available Strength in Axial Compression, kips COMPOSITE HSS10

Concrete Filled Rectangular HSS HSS10× 6×

Shape

3 8 /

t design, in. Steel, lb/ft

Effective length, (KL )y , with respect to weak axis (ft)

Design 0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

5 16 /

0.349 0.291 37.7 31.8 Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD 323 484 288 432 302 453 270 405 295 443 264 395 287 431 256 385 278 418 249 373 269 403 240 360 259 388 231 347 248 372 222 333 237 355 212 318 225 338 202 303 214 321 191 287 202 303 181 271 190 285 170 255 178 268 160 240 167 250 149 224 155 233 139 209 144 216 129 194 133 200 119 179 122 183 110 165 112 169 101 151 104 155 93.0 139 95.7 144 86.0 129 88.8 133 79.7 120 82.5 124 74.1 111 76.9 116 69.1 104 71.9 108 64.6 96.9 63.2 94.9 56.7 85.1 56.0 84.0 50.3 75.4 49.9 75.0 44.8 67.3 44.8 67.3 40.2 60.4 40.4 60.7 36.3 54.5

HSS10× 5× 14 /

3 16 /

3 8 /

5 16 /

0.233 25.8 Pn /Ωc φc Pn ASD LRFD 253 379 237 355 231 347 225 337 218 327 210 315 202 303 194 291 185 278 176 264 167 250 158 236 148 222 139 208 130 195 121 181 112 168 103 155 95.0 142 87.2 131 80.4 121 74.3 111 68.9 103 64.1 96.1 59.7 89.6 55.8 83.7 49.1 73.6 43.5 65.2 38.8 58.1 34.8 52.2 31.4 47.1

0.174 19.6 Pn /Ωc φc Pn ASD LRFD 216 324 202 303 197 295 191 287 185 278 179 268 172 257 164 246 157 235 149 223 141 211 133 199 125 187 116 175 109 163 101 151 93.2 140 85.8 129 78.6 118 72.2 108 66.5 99.8 61.5 92.3 57.0 85.6 53.0 79.6 49.4 74.2 46.2 69.3 40.6 60.9 36.0 54.0 32.1 48.1 28.8 43.2 26.0 39.0

0.349 35.1 Pn /Ωc φc Pn ASD LRFD 290 435 264 397 256 384 246 369 235 353 224 336 212 318 200 300 187 281 175 262 162 243 150 224 137 206 126 190 116 174 106 159 96.2 145 87.6 132 80.2 121 73.6 111 67.9 102 62.7 94.3 58.2 87.5 54.1 81.3 50.4 75.8 47.1 70.8 41.4 62.3 36.7 55.2

0.291 29.7 Pn /Ωc φc Pn ASD LRFD 259 388 236 354 228 342 219 329 210 315 200 300 190 284 179 268 168 252 156 235 145 218 134 201 123 185 113 169 103 154 92.6 139 84.0 126 76.5 115 70.0 105 64.3 96.5 59.3 88.9 54.8 82.2 50.8 76.2 47.2 70.9 44.0 66.1 41.2 61.7 36.2 54.3 32.0 48.1

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

85.2 128 58.1 87.4

73.7 111 50.0 75.2

5020 2130 2.44 1.54

4530 1910 2.47 1.54

61.6 41.6

92.6 62.6

3920 1650 2.49 1.54

48.3 32.4

72.6 48.7

3270 1370 2.52 1.54

76.2 115 45.4 68.2 4320 1350 2.05 1.79

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

66.2 39.2

99.5 58.9

3930 1220 2.07 1.79

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DESIGN OF COMPRESSION MEMBERS

Table 4-13 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS10-HSS9

t design, in. Steel, lb/ft Design

Effective length, (KL )y , with respect to weak axis (ft)

Concrete Filled Rectangular HSS HSS10× 5×

Shape

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

Fy = 46 ksi fc′ = 4 ksi

HSS9× 7×

14 /

3 16 /

5 8 /

12 /

3 8 /

5 16 /

0.233 24.1 Pn /Ωc φc Pn ASD LRFD 226 339 206 309 199 299 192 287 183 275 175 262 165 248 156 234 146 219 136 205 127 190 117 175 107 161 98.2 147 89.3 134 80.6 121 73.1 110 66.6 99.9 61.0 91.4 56.0 84.0 51.6 77.4 47.7 71.6 44.2 66.4 41.1 61.7 38.3 57.5 35.8 53.7 31.5 47.2 27.9 41.8

0.174 18.4 Pn /Ωc φc Pn ASD LRFD 192 288 174 261 168 253 162 243 155 232 147 221 139 209 131 196 123 184 114 171 106 159 97.4 146 89.2 134 81.3 122 73.6 110 66.5 99.7 60.3 90.4 54.9 82.4 50.3 75.4 46.2 69.2 42.5 63.8 39.3 59.0 36.5 54.7 33.9 50.9 31.6 47.4 29.5 44.3 26.0 38.9 23.0 34.5

0.581 59.3 Pn /Ωc φc Pn ASD LRFD 454 682 431 647 423 636 414 623 405 609 395 593 384 577 372 559 360 541 347 521 334 501 320 481 306 460 292 439 278 417 263 396 249 375 235 353 221 333 208 312 194 292 182 273 169 253 157 236 146 220 137 205 120 180 106 160 94.9 143 85.1 128 76.8 115

0.465 48.9 Pn /Ωc φc Pn ASD LRFD 393 590 374 561 367 550 359 539 351 526 341 512 331 497 320 481 309 464 297 446 285 428 273 410 260 391 248 372 235 353 222 334 210 315 198 298 187 281 176 264 165 248 154 232 144 217 134 201 125 188 117 175 103 154 90.8 137 81.0 122 72.7 109 65.6 98.7

0.349 37.7 Pn /Ωc φc Pn ASD LRFD 328 492 312 468 306 459 300 450 293 439 285 428 277 416 268 402 259 389 250 374 240 359 230 344 219 329 209 313 198 297 188 282 177 266 167 251 157 235 147 220 137 206 128 192 118 178 110 165 103 154 95.9 144 84.3 126 74.7 112 66.6 99.9 59.8 89.7 54.0 80.9

0.291 31.8 Pn /Ωc φc Pn ASD LRFD 293 440 279 418 274 411 268 402 262 393 255 383 248 372 240 360 232 348 223 335 214 322 205 308 196 294 187 280 177 266 168 252 159 238 150 224 140 211 132 197 123 184 114 172 106 159 98.7 148 92.0 138 86.0 129 75.5 113 66.9 100 59.7 89.5 53.6 80.4 48.4 72.5

99.7 150 82.8 124

79.9 120 66.1 99.4

69.1 104 57.1 85.9

5080 3320 2.73 1.24

4330 2840 2.78 1.23

3880 2540 2.81 1.24

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

55.3 32.7

83.1 49.1

3430 1060 2.10 1.80

43.6 25.4

65.5 117 176 38.1 97.5 147

2860 873 2.13 1.81

5690 3740 2.68 1.23

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 4D:14th Ed.

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Page 213

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–213

Table 4-13 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

COMPOSITE HSS9

Concrete Filled Rectangular HSS HSS9× 5×

Shape

5 8 /

t design, in. Steel, lb/ft

3 8 /

5 16 /

14 /

3 16 /

0.581 0.465 0.349 0.291 0.233 0.174 50.8 42.1 32.6 27.6 22.4 17.1 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

12 /

0

386

580

322

483

267

400

238

357

208

311

176

264

6 7 8 9 10

351 339 326 312 297

527 510 490 468 446

292 283 272 261 249

439 425 409 392 374

243 235 225 216 205

364 352 338 323 308

216 209 201 193 183

325 314 302 289 275

189 183 176 168 160

284 274 264 252 240

160 154 148 142 135

240 231 222 212 202

11 12 13 14 15

281 264 247 230 214

422 397 372 346 321

236 223 210 196 182

355 335 315 294 274

194 183 171 159 148

291 274 257 239 221

174 163 153 143 132

260 245 230 214 199

151 143 134 125 116

227 214 201 187 173

127 120 112 104 96.4

191 180 168 156 145

16 17 18 19 20

197 180 165 149 135

296 271 247 224 202

169 155 142 130 117

253 233 214 195 177

136 125 115 106 96.5

204 188 173 159 145

122 112 102 93.0 83.9

183 168 154 140 126

107 97.8 89.3 81.1 73.1

160 147 134 122 110

88.8 81.3 74.1 67.0 60.5

133 122 111 100 90.7

21 22 23 24 25

122 111 102 93.5 86.2

184 167 153 141 130

107 97.1 88.8 81.6 75.2

160 146 134 123 113

87.5 79.7 72.9 67.0 61.7

131 120 110 101 92.8

76.1 114 69.4 104 63.5 95.2 58.3 87.4 53.7 80.6

66.3 60.4 55.3 50.8 46.8

99.5 90.7 82.9 76.2 70.2

54.8 50.0 45.7 42.0 38.7

82.3 75.0 68.6 63.0 58.0

26 27 28 29 30

79.7 120 73.9 111 68.7 103 64.1 96.3 59.9 90.0

69.5 104 64.5 96.9 59.9 90.1 55.9 84.0 52.2 78.5

57.1 52.9 49.2 45.9 42.9

85.8 79.5 74.0 69.0 64.4

49.7 46.1 42.8 39.9 37.3

74.5 69.1 64.2 59.9 56.0

43.3 40.1 37.3 34.8 32.5

64.9 60.2 56.0 52.2 48.8

35.8 33.2 30.8 28.8 26.9

53.7 49.8 46.3 43.1 40.3

32 34

52.6

45.9

37.7

56.6

32.8 29.0

49.2 43.6

28.6 25.3

42.9 38.0

23.6 20.9

35.4 31.4

96.4 62.4

55.7 35.8

83.7 53.8

46.7 29.8

70.2 44.7

36.6 23.3

55.0 35.0

79.1

69.0

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

92.8 140 60.0 90.2

79.4 119 51.5 77.4

4270 1600 1.92 1.63

3840 1430 1.97 1.64

64.1 41.5

3280 1220 2.03 1.64

2960 1100 2.05 1.64

2600 961 2.08 1.64

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2160 794 2.10 1.65

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Page 214

4–214

DESIGN OF COMPRESSION MEMBERS

Table 4-13 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS8

Concrete Filled Rectangular HSS HSS8× 6×

Shape

t design, in. Steel, lb/ft Design

Effective length, (KL )y , with respect to weak axis (ft)

Fy = 46 ksi fc′ = 4 ksi

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

5 8 /

12 /

3 8 /

5 16 /

14 /

3 16 /

0.581 50.8 Pn /Ωc φc Pn ASD LRFD 386 580 360 542 352 529 342 514 331 498 320 480 307 462 294 442 281 422 267 401 253 380 238 358 224 337 210 315 196 294 182 273 168 253 155 233 142 214 131 196 120 181 111 167 103 155 96.0 144 89.5 135 83.7 126 73.5 111 65.1 97.9 58.1 87.3

0.465 42.1 Pn /Ωc φc Pn ASD LRFD 327 491 305 458 298 446 289 433 280 419 269 404 259 388 247 371 236 354 225 337 213 320 202 303 190 285 178 268 167 251 156 234 144 217 134 201 123 185 113 170 104 157 96.4 145 89.4 134 83.1 125 77.5 116 72.4 109 63.6 95.7 56.4 84.7 50.3 75.6 45.1 67.8

0.349 32.6 Pn /Ωc φc Pn ASD LRFD 272 408 254 381 248 372 241 361 233 350 225 337 216 324 207 310 197 296 187 281 177 266 167 251 157 236 147 221 137 206 127 191 118 177 109 163 100 150 92.1 138 84.9 128 78.5 118 72.8 109 67.6 102 63.1 94.8 58.9 88.6 51.8 77.8 45.9 69.0 40.9 61.5 36.7 55.2

0.291 27.6 Pn /Ωc φc Pn ASD LRFD 243 364 227 340 221 332 215 323 208 313 201 302 193 290 185 278 177 265 168 252 159 239 150 225 141 212 132 198 123 185 114 172 106 159 97.8 147 89.6 134 82.3 123 75.9 114 70.1 105 65.0 97.6 60.5 90.7 56.4 84.6 52.7 79.0 46.3 69.5 41.0 61.5 36.6 54.9 32.8 49.3 29.6 44.5

0.233 22.4 Pn /Ωc φc Pn ASD LRFD 213 319 199 298 194 291 188 283 182 274 176 264 169 254 162 243 155 232 147 220 139 208 131 197 123 185 115 173 107 161 99.8 150 92.4 139 85.1 128 78.0 117 71.7 107 66.0 99.1 61.1 91.6 56.6 84.9 52.6 79.0 49.1 73.6 45.9 68.8 40.3 60.5 35.7 53.6 31.8 47.8 28.6 42.9 25.8 38.7

0.174 17.1 Pn /Ωc φc Pn ASD LRFD 181 271 169 253 164 247 160 240 155 232 149 223 143 214 137 205 130 195 124 185 117 175 110 165 103 155 96.4 145 89.7 135 83.1 125 76.8 115 70.6 106 64.6 96.9 59.3 89.0 54.7 82.0 50.5 75.8 46.9 70.3 43.6 65.4 40.6 60.9 38.0 56.9 33.4 50.1 29.6 44.3 26.4 39.5 23.7 35.5 21.4 32.0

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

87.0 131 70.5 106

74.5 112 60.2 90.4

3650 2260 2.27 1.27

3270 2020 2.32 1.27

60.0 48.6

90.2 73.0

2790 1730 2.38 1.27

52.0 41.9

78.1 63.0

2520 1560 2.40 1.27

43.4 35.0

2200 1360 2.43 1.27

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

65.3 52.6

34.2 27.4

51.4 41.2

1830 1120 2.46 1.28

AISC_Part 4D:14th Ed.

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–215

Table 4-13 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

COMPOSITE HSS8

Concrete Filled Rectangular HSS HSS8× 4×

Shape

5 8 /

t design, in. Steel, lb/ft

3 8 /

5 16 /

14 /

3 16 /

0.581 0.465 0.349 0.291 0.233 0.174 42.3 35.2 27.5 23.3 19.0 14.5 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

12 /

0

322

484

268

403

215

323

191

286

166

249

139

209

6 7 8 9 10

277 262 246 228 211

416 393 369 343 317

232 221 208 194 180

349 332 313 292 271

185 176 165 154 144

278 264 248 232 216

165 157 147 138 127

247 235 221 206 191

143 136 128 120 111

215 204 192 180 166

120 114 107 100 92.7

180 171 161 150 139

11 12 13 14 15

193 175 157 140 124

290 263 236 211 186

166 151 137 123 110

249 227 206 185 165

133 122 111 100 90.1

200 183 167 151 135

117 107 96.3 86.7 78.0

175 160 144 130 117

102 93.0 84.1 75.5 67.2

153 139 126 113 101

16 17 18 19 20

109 96.4 85.9 77.1 69.6

163 145 129 116 105

21 22 23 24 25

63.1 57.5 52.6 48.3 44.6

94.9 86.5 79.1 72.7 67.0

26 27 28

96.6 85.6 76.4 68.5 61.9

145 129 115 103 93.0

56.1 51.1 46.8 43.0 39.6

85.2 128 77.6 116 70.2 105 62.9 94.3 55.9 83.9

80.1 120 71.0 107 63.3 95.1 56.8 85.4 51.3 77.1

69.6 105 61.7 92.7 55.0 82.7 49.4 74.2 44.6 67.0

59.2 52.4 46.8 42.0 37.9

88.8 78.7 70.2 63.0 56.8

49.3 43.6 38.9 34.9 31.5

73.9 65.5 58.4 52.4 47.3

84.3 76.8 70.3 64.6 59.5

46.5 42.4 38.8 35.6 32.8

69.9 63.7 58.3 53.5 49.3

40.4 36.8 33.7 31.0 28.5

60.8 55.4 50.7 46.5 42.9

34.4 31.3 28.6 26.3 24.2

51.5 47.0 43.0 39.5 36.4

28.6 26.1 23.8 21.9 20.2

42.9 39.1 35.8 32.8 30.3

36.6

55.0

30.3

45.6

26.4 24.5

39.6 36.8

22.4 20.8

33.6 31.2

18.7 17.3 16.1

28.0 25.9 24.1

56.8 33.9

85.4 51.0

69.6 41.5

40.2 24.0

60.5 36.1

33.9 20.1

50.9 30.2

26.7 15.7

40.1 23.6

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

65.5 39.1

98.4 58.7

2570 800 1.51 1.79

2330 727 1.56 1.79

46.3 27.6

2010 628 1.61 1.79

1820 568 1.63 1.79

1610 498 1.66 1.80

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1350 414 1.69 1.81

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Page 216

4–216

DESIGN OF COMPRESSION MEMBERS

Table 4-13 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS7

Concrete Filled Rectangular HSS HSS7× 5×

Shape

12 /

t design, in. Steel, lb/ft

3 8 /

5 16 /

14 /

3 16 /

1 8 c,f /

0.465 0.349 0.291 0.233 0.174 0.116 35.2 27.5 23.3 19.0 14.5 9.86 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

Fy = 46 ksi fc′ = 4 ksi

0

268

403

220

330

196

294

171

256

144

216

117

175

6 7 8 9 10

244 236 226 216 206

366 354 340 325 309

200 193 185 176 167

299 289 277 264 251

178 172 165 157 149

267 257 247 236 224

155 150 144 137 131

233 225 216 206 196

131 126 121 115 110

196 189 181 173 164

105 102 97.3 92.7 87.7

158 152 146 139 132

11 12 13 14 15

195 183 171 159 148

292 275 257 240 222

158 148 138 129 119

237 222 208 193 179

141 133 124 115 107

212 199 186 173 160

123 116 108 101 93.3

185 174 163 151 140

103 97.1 90.7 84.2 77.8

155 146 136 126 117

16 17 18 19 20

136 125 113 103 92.7

204 187 171 154 139

110 101 93.0 84.8 76.8

166 153 140 127 115

97.9 89.6 81.5 73.5 66.4

147 134 122 110 99.9

82.6 124 77.3 116 72.0 108 66.6 99.9 61.3 91.9

85.9 129 78.6 118 71.5 107 64.6 97.0 58.3 87.5

71.5 107 65.3 97.9 59.3 89.0 53.5 80.2 48.3 72.4

56.1 51.0 46.1 41.4 37.4

84.1 76.5 69.2 62.1 56.0

21 22 23 24 25

84.1 126 76.6 115 70.1 105 64.4 96.8 59.3 89.2

69.6 105 63.4 95.4 58.0 87.2 53.3 80.1 49.1 73.8

60.3 54.9 50.2 46.1 42.5

90.6 82.5 75.5 69.4 63.9

52.9 48.2 44.1 40.5 37.3

79.4 72.3 66.2 60.8 56.0

43.8 39.9 36.5 33.5 30.9

65.7 59.8 54.7 50.3 46.3

33.9 30.9 28.3 25.9 23.9

50.8 46.3 42.4 38.9 35.9

26 27 28 29 30

54.9 50.9 47.3 44.1 41.2

45.4 42.1 39.2 36.5 34.1

68.3 63.3 58.9 54.9 51.3

39.3 36.5 33.9 31.6 29.5

59.1 54.8 51.0 47.5 44.4

34.5 32.0 29.8 27.7 25.9

51.8 48.0 44.6 41.6 38.9

28.6 26.5 24.6 23.0 21.5

42.8 39.7 36.9 34.4 32.2

22.1 20.5 19.1 17.8 16.6

33.2 30.8 28.6 26.7 24.9

30.0

45.1

26.0

39.0

22.8

34.2

18.9 16.7

28.3 25.1

14.6 12.9

21.9 19.4

43.1 33.5

64.8 50.4

56.3 43.9

31.5 24.4

47.3 36.7

24.8 19.2

37.2 28.8

17.6 13.5

26.5 20.2

82.5 76.5 71.1 66.3 61.9

32 34

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy ASD Ωc = 2.00

53.0 41.4

kip-in.2 kip-in.2

LRFD φc = 0.75

79.7 62.3

1960 1120 1.91 1.32 c

1690 967 1.97 1.32

37.4 29.2

1530 872 1.99 1.32

1350 766 2.02 1.33

1120 634 2.05 1.33

872 491 2.07 1.33

Shape is noncompact for compression with Fy = 46 ksi. f Shape is noncompact for flexure with Fy = 46 ksi.

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 4D:14th Ed.

2/23/11

10:46 AM

Page 217

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–217

Table 4-13 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

COMPOSITE HSS7

Concrete Filled Rectangular HSS HSS7× 4×

Shape

12 /

t design, in. Steel, lb/ft

5 16 /

14 /

3 16 /

1 8 c,f /

0.465 0.349 0.291 0.233 0.174 0.116 31.8 24.9 21.2 17.3 13.3 9.01 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

3 8 /

0

243

365

193

290

172

258

149

223

125

187

99.9

150

6 7 8 9 10

209 198 186 174 160

314 298 280 261 241

166 157 148 138 129

249 236 222 208 193

148 140 132 123 114

222 210 198 184 170

129 122 115 107 99.1

193 183 172 161 149

108 102 95.9 89.4 82.7

161 153 144 134 124

85.7 81.0 76.0 70.7 65.2

128 122 114 106 97.7

11 12 13 14 15

147 134 121 108 95.6

221 201 181 162 144

119 108 98.4 88.6 79.2

178 163 148 133 119

104 94.7 85.7 77.5 69.5

156 142 129 116 104

90.9 82.8 74.8 67.0 59.5

136 124 112 100 89.3

75.9 114 69.0 104 62.3 93.5 55.8 83.6 49.5 74.2

59.6 54.0 48.5 43.2 38.1

89.4 81.0 72.8 64.9 57.2

16 17 18 19 20

84.1 126 74.5 112 66.4 99.9 59.6 89.6 53.8 80.9

70.0 105 62.0 93.2 55.3 83.2 49.7 74.6 44.8 67.4

61.8 54.8 48.9 43.8 39.6

92.9 82.3 73.4 65.9 59.5

52.4 46.4 41.4 37.2 33.5

78.6 69.6 62.1 55.8 50.3

43.5 38.6 34.4 30.9 27.9

65.3 57.9 51.6 46.3 41.8

33.5 29.7 26.5 23.8 21.5

50.3 44.5 39.7 35.7 32.2

21 22 23 24 25

48.8 44.5 40.7 37.4 34.4

40.7 37.0 33.9 31.1 28.7

61.1 55.7 50.9 46.8 43.1

35.9 32.7 29.9 27.5 25.3

53.9 49.2 45.0 41.3 38.1

30.4 27.7 25.4 23.3 21.5

45.6 41.6 38.0 34.9 32.2

25.3 23.0 21.1 19.4 17.8

37.9 34.5 31.6 29.0 26.8

19.5 17.7 16.2 14.9 13.7

29.2 26.6 24.3 22.3 20.6

26.5

39.9

23.4

35.2

19.8 18.4

29.8 27.6

16.5 15.3

24.7 12.7 22.9 11.8 10.9

19.0 17.7 16.4

37.0 24.5

55.7 36.8

48.9 32.2

27.3 18.0

41.0 27.0

21.6 14.1

32.5 15.4 21.2 9.93

23.2 14.9

73.4 66.8 61.2 56.2 51.8

26 27 28

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy ASD Ωc = 2.00

45.3 29.9

kip-in.2 kip-in.2

LRFD φc = 0.75

68.1 44.9

1620 637 1.53 1.59 c

1410 553 1.58 1.60

32.5 21.4

1280 501 1.61 1.60

1130 440 1.64 1.60

946 366 1.66 1.61

735 282 1.69 1.61

Shape is noncompact for compression with Fy = 46 ksi. f Shape is noncompact for flexure with Fy = 46 ksi.

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 4D:14th Ed.

2/23/11

10:47 AM

Page 218

4–218

DESIGN OF COMPRESSION MEMBERS

Table 4-13 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS6

Concrete Filled Rectangular HSS HSS6× 5×

Shape

t design, in. Steel, lb/ft Design

Effective length, (KL )y , with respect to weak axis (ft)

Fy = 46 ksi fc′ = 4 ksi

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

12 /

3 8 /

5 16 /

14 /

3 16 /

18 /

0.465 31.8 Pn /Ωc φc Pn ASD LRFD 243 365 242 364 240 361 237 356 232 349 226 340 220 330 212 318 203 305 194 291 184 276 174 261 163 245 152 228 141 212 130 196 119 179 109 164 98.9 149 89.1 134 80.4 121 72.9 110 66.4 99.9 60.8 91.4 55.8 83.9 51.5 77.3 47.6 71.5 44.1 66.3 41.0 61.6 38.2 57.5 35.7 53.7

0.349 24.9 Pn /Ωc φc Pn ASD LRFD 197 295 196 294 195 292 192 288 188 282 183 275 178 267 171 257 164 246 156 235 148 222 140 210 131 196 122 183 113 170 105 158 96.7 145 88.7 133 80.9 122 73.3 110 66.2 99.5 60.0 90.2 54.7 82.2 50.0 75.2 46.0 69.1 42.4 63.7 39.2 58.9 36.3 54.6 33.8 50.8 31.5 47.3 29.4 44.2

0.291 21.2 Pn /Ωc φc Pn ASD LRFD 175 263 175 262 173 260 171 256 167 251 163 245 158 238 153 229 147 220 140 210 133 199 125 188 117 176 109 164 101 152 93.6 140 85.8 129 78.3 117 71.0 107 64.2 96.6 58.0 87.2 52.7 79.1 48.0 72.1 43.9 66.0 40.3 60.6 37.2 55.8 34.3 51.6 31.9 47.9 29.6 44.5 27.6 41.5 25.8 38.8

0.233 17.3 Pn /Ωc φc Pn ASD LRFD 152 228 152 228 151 226 149 223 146 219 142 213 138 207 133 200 128 192 122 183 116 174 109 164 103 154 95.7 144 88.9 133 82.0 123 75.3 113 68.8 103 62.5 93.8 56.3 84.5 50.8 76.3 46.1 69.2 42.0 63.0 38.4 57.7 35.3 53.0 32.5 48.8 30.1 45.1 27.9 41.8 25.9 38.9 24.2 36.3 22.6 33.9

0.174 13.3 Pn /Ωc φc Pn ASD LRFD 128 192 128 192 127 190 125 187 123 184 120 179 116 174 112 168 107 161 102 153 97.0 146 91.5 137 85.8 129 80.1 120 74.3 111 68.5 103 62.9 94.3 57.3 86.0 52.0 78.0 46.8 70.3 42.3 63.4 38.3 57.5 34.9 52.4 32.0 47.9 29.4 44.0 27.1 40.6 25.0 37.5 23.2 34.8 21.6 32.3 20.1 30.2 18.8 28.2

0.116 9.01 Pn /Ωc φc Pn ASD LRFD 103 155 103 155 102 153 101 151 98.6 148 96.1 144 93.1 140 89.6 134 85.8 129 81.7 122 77.3 116 72.7 109 68.0 102 63.3 94.9 58.5 87.7 53.8 80.6 49.1 73.7 44.6 67.0 40.3 60.5 36.2 54.3 32.7 49.0 29.6 44.4 27.0 40.5 24.7 37.0 22.7 34.0 20.9 31.4 19.3 29.0 17.9 26.9 16.7 25.0 15.5 23.3 14.5 21.8

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

41.4 36.4

62.2 54.7

1310 968 1.87 1.16

33.8 29.6

50.8 44.5

1130 838 1.92 1.16

29.5 25.8

44.3 38.7

1030 758 1.95 1.17

24.8 21.7

37.3 32.6

905 668 1.98 1.16

19.6 17.1

755 555 2.01 1.17

Note: Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

29.5 25.7

13.9 12.1

21.0 18.2

584 429 2.03 1.17

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–219

Table 4-13 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

COMPOSITE HSS6

Concrete Filled Rectangular HSS HSS6× 4×

Shape

12 /

t design, in. Steel, lb/ft

5 16 /

14 /

3 16 /

1 8 /

0.465 0.349 0.291 0.233 0.174 0.116 28.4 22.4 19.1 15.6 12.0 8.16 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

3 8 /

0

217

326

172

258

152

229

132

198

110

166

88.2 132

1 2 3 4 5

216 213 209 203 195

325 321 314 305 293

171 169 165 160 154

256 253 248 240 231

152 150 147 142 137

228 225 220 214 206

132 130 127 124 119

197 195 191 185 178

110 109 106 103 99.6

165 163 160 155 149

87.8 86.7 84.8 82.3 79.2

6 7 8 9 10

186 176 165 153 141

279 264 248 230 212

147 140 132 123 114

221 210 198 185 171

131 124 116 108 99.7

196 186 174 162 150

114 108 101 94.1 86.9

170 161 152 141 130

95.1 90.1 84.6 78.8 72.8

143 135 127 118 109

75.5 113 71.4 107 66.9 100 62.1 93.2 57.2 85.8

11 12 13 14 15

129 117 105 93.3 82.3

194 176 158 140 124

105 95.3 86.1 77.2 68.7

157 143 129 116 103

91.2 82.9 75.2 67.7 60.5

137 125 113 102 91.0

132 130 127 123 119

79.6 119 72.3 108 65.1 97.7 58.2 87.2 51.5 77.3

66.7 100 60.6 91.0 54.6 82.0 48.8 73.2 43.3 64.9

52.2 47.3 42.4 37.8 33.2

78.4 70.9 63.7 56.6 49.9

16 17 18 19 20

72.3 109 64.0 96.2 57.1 85.9 51.3 77.1 46.3 69.5

60.5 53.6 47.8 42.9 38.7

91.0 80.6 71.9 64.5 58.2

53.5 47.4 42.3 38.0 34.3

80.5 71.3 63.6 57.1 51.5

45.4 40.3 35.9 32.2 29.1

68.3 60.5 54.0 48.4 43.7

38.0 33.7 30.0 27.0 24.3

57.0 50.5 45.1 40.4 36.5

29.2 25.9 23.1 20.7 18.7

43.8 38.8 34.6 31.1 28.0

21 22 23 24 25

42.0 38.2 35.0 32.1 29.6

35.1 32.0 29.3 26.9 24.8

52.8 48.1 44.0 40.4 37.3

31.1 28.3 25.9 23.8 21.9

46.7 42.6 38.9 35.8 33.0

26.4 24.0 22.0 20.2 18.6

39.7 36.1 33.1 30.4 28.0

22.1 20.1 18.4 16.9 15.6

33.1 30.2 27.6 25.3 23.4

17.0 15.5 14.1 13.0 12.0

25.4 23.2 21.2 19.5 17.9

20.3

30.5

17.2

25.9

14.4 13.4

21.6 11.1 20.0 10.3

16.6 15.4

38.2 28.2

21.4 15.8

32.1 16.9 23.8 12.5

63.1 57.5 52.6 48.3 44.5

26 27

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

35.0 26.1

52.6 39.2

1070 546 1.50 1.40

29.0 21.5

43.6 32.3

935 475 1.55 1.40

25.4 18.8

849 433 1.58 1.40

752 380 1.61 1.41

634 320 1.63 1.41

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

25.5 12.1 18.2 18.8 8.85 13.3 489 246 1.66 1.41

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4–220

DESIGN OF COMPRESSION MEMBERS

Table 4-13 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS6

Concrete Filled Rectangular HSS HSS6× 3×

Shape

12 /

t design, in. Steel, lb/ft

3 8 /

5 16 /

14 /

3 16 /

18 /

0.465 0.349 0.291 0.233 0.174 0.116 25.0 19.8 17.0 13.9 10.7 7.31 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

Fy = 46 ksi fc′ = 4 ksi

0

191

288

151

227

130

195

112

168

92.8

139

73.1 110

1 2 3 4 5

190 186 179 169 158

286 279 268 254 237

150 147 142 135 126

225 221 213 203 190

129 126 121 116 109

193 189 182 174 163

111 109 105 99.8 93.5

167 163 157 150 140

92.2 90.2 87.1 82.8 77.7

138 135 131 124 117

72.6 109 71.0 107 68.5 103 65.1 97.6 61.0 91.5

145 131 117 102 88.4

218 197 176 154 133

117 107 96.0 85.1 74.4

176 160 144 128 112

101 92.2 83.2 74.1 65.0

151 139 125 111 97.8

86.3 129 78.5 118 70.4 106 62.4 93.8 55.2 82.9

71.9 65.5 58.9 52.2 45.6

108 98.3 88.3 78.3 68.4

56.3 51.2 45.9 40.6 35.4

84.4 76.8 68.9 60.9 53.0

6 7 8 9 10 11 12 13 14 15

75.2 113 63.2 95.0 53.8 80.9 46.4 69.8 40.4 60.8

64.1 54.4 46.3 39.9 34.8

96.4 81.7 69.6 60.0 52.3

56.3 48.0 40.9 35.3 30.7

84.7 72.2 61.5 53.0 46.2

48.1 41.4 35.3 30.4 26.5

72.3 62.3 53.1 45.7 39.9

39.3 33.3 28.4 24.4 21.3

58.9 49.9 42.5 36.7 31.9

30.4 25.7 21.9 18.8 16.4

45.5 38.5 32.8 28.3 24.6

16 17 18 19 20

35.5 31.5 28.1

30.6 27.1 24.2 21.7

46.0 40.7 36.3 32.6

27.0 23.9 21.4 19.2

40.6 36.0 32.1 28.8

23.3 20.6 18.4 16.5 14.9

35.0 31.0 27.7 24.8 22.4

18.7 16.6 14.8 13.3 12.0

28.1 24.9 22.2 19.9 18.0

14.4 12.8 11.4 10.2 9.23

21.6 19.2 17.1 15.3 13.9

53.4 47.3 42.2

21

8.38 12.6

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

28.8 17.1

43.3 25.7

833 260 1.12 1.79

23.9 14.3

36.0 21.5

736 230 1.17 1.79

21.1 31.7 12.6 18.9 673 210 1.19 1.79

17.9 10.6

26.9 14.2 16.0 8.45

597 186 1.22 1.79

507 157 1.25 1.80

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

21.4 10.2 15.4 12.7 6.00 9.01 395 121 1.27 1.81

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Page 221

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–221

Table 4-13 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

COMPOSITE HSS5

Concrete Filled Rectangular HSS HSS5× 4×

Shape

12 /

t design, in. Steel, lb/ft

5 16 /

14 /

3 16 /

18 /

0.465 0.349 0.291 0.233 0.174 0.116 25.0 19.8 17.0 13.9 10.7 7.31 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

3 8 /

0

191

288

151

227

133

200

115

173

96.2 144

76.5

115

1 2 3 4 5

191 188 184 178 171

286 283 276 268 257

150 148 145 141 136

226 223 218 212 204

133 131 128 124 119

199 196 192 186 179

115 113 111 108 104

172 170 167 162 155

95.8 94.6 92.6 89.9 86.5

144 142 139 135 130

76.2 75.2 73.5 71.3 68.5

114 113 110 107 103

6 7 8 9 10

163 153 143 132 122

244 230 215 199 183

130 123 115 107 99.3

195 185 173 162 149

114 107 100 93.1 85.7

170 161 150 140 129

148 140 131 122 112

82.5 78.1 73.2 68.1 62.8

124 117 110 102 94.2

65.3 61.7 57.7 53.6 49.3

97.9 92.5 86.6 80.3 73.9

11 12 13 14 15

110 99.5 88.8 78.6 68.7

166 150 133 118 103

16 17 18 19 20

60.4 53.5 47.7 42.8 38.7

21 22 23 24 25

35.1 31.9 29.2 26.8

98.8 93.4 87.6 81.4 75.0

90.9 137 82.5 124 74.3 112 66.4 99.7 58.7 88.3

78.6 118 71.6 108 64.6 97.2 57.9 87.0 51.4 77.3

68.5 103 62.0 93.0 55.6 83.4 49.5 74.2 43.7 65.7

57.4 52.1 46.8 41.7 36.8

86.2 78.1 70.2 62.6 55.2

44.9 40.6 36.3 32.3 28.3

67.4 60.9 54.5 48.4 42.5

90.8 80.4 71.7 64.4 58.1

51.6 45.7 40.8 36.6 33.0

77.6 68.7 61.3 55.0 49.7

45.3 40.1 35.8 32.1 29.0

68.0 60.3 53.7 48.2 43.5

38.6 34.2 30.5 27.4 24.7

58.0 51.4 45.8 41.1 37.1

32.4 28.7 25.6 22.9 20.7

48.5 43.0 38.4 34.4 31.1

24.9 22.1 19.7 17.7 15.9

37.4 33.1 29.5 26.5 23.9

52.7 48.0 43.9 40.4

30.0 27.3 25.0 22.9 21.1

45.0 41.0 37.5 34.5 31.8

26.3 23.9 21.9 20.1 18.5

39.5 36.0 32.9 30.2 27.9

22.4 20.4 18.7 17.2 15.8

33.7 30.7 28.1 25.8 23.8

18.8 17.1 15.7 14.4 13.3

28.2 25.7 23.5 21.6 19.9

14.5 13.2 12.1 11.1 10.2

21.7 19.8 18.1 16.6 15.3

14.6

22.0

12.3

18.4

9.43 8.75

14.1 13.1

16.1 13.7

24.2 20.5

12.8 10.8

19.2 16.3

9.17 7.73

13.8 11.6

26 27 Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

26.0 22.2

39.1 33.3

658 456 1.46 1.20

21.7 18.4

32.6 27.7

579 400 1.52 1.20

19.0 16.2

28.6 24.3

527 363 1.54 1.20

468 322 1.57 1.21

397 272 1.60 1.21

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

306 209 1.62 1.21

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Page 222

4–222

DESIGN OF COMPRESSION MEMBERS

Table 4-13 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS5

Fy = 46 ksi fc′ = 4 ksi

Concrete Filled Rectangular HSS HSS5× 3×

Shape

12 /

t design, in. Steel, lb/ft

3 8 /

5 16 /

14 /

3 16 /

18 /

0.465 0.349 0.291 0.233 0.174 0.116 21.6 17.3 14.8 12.2 9.42 6.46 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

166

249

132

198

113

170

97.0

145

80.3

120

63.1

94.7

1 2 3 4 5

164 160 154 146 135

247 241 232 219 203

131 128 123 117 109

196 192 185 176 164

112 110 106 101 94.6

169 165 159 152 142

96.2 94.1 90.7 86.0 80.4

144 141 136 129 121

79.7 78.0 75.2 71.4 66.9

120 117 113 107 100

62.7 61.3 59.1 56.1 52.5

94.0 91.9 88.6 84.1 78.7

6 7 8 9 10

124 111 98.4 85.7 73.4

186 167 148 129 110

101 91.4 81.7 72.0 62.5

151 137 123 108 93.9

87.5 132 79.8 120 71.8 108 63.7 95.7 55.7 83.7

74.1 67.3 60.1 53.3 46.8

111 101 90.2 80.2 70.4

61.7 56.1 50.3 44.4 38.7

92.6 84.2 75.4 66.6 58.0

48.4 43.9 39.3 34.7 30.1

72.6 65.9 59.0 52.0 45.2

11 12 13 14 15

61.7 51.8 44.2 38.1 33.2

92.7 77.9 66.4 57.2 49.9

53.4 45.0 38.4 33.1 28.8

80.3 67.7 57.7 49.7 43.3

48.0 40.7 34.7 29.9 26.0

72.1 61.1 52.1 44.9 39.1

40.6 34.6 29.5 25.4 22.1

61.0 52.0 44.3 38.2 33.3

33.2 28.0 23.9 20.6 17.9

49.8 42.0 35.8 30.9 26.9

25.8 21.8 18.5 16.0 13.9

38.7 32.7 27.8 24.0 20.9

16 17 18 19 20

29.2 25.8 23.0

43.8 38.8 34.6

25.3 22.4 20.0 18.0

38.1 33.7 30.1 27.0

22.9 20.3 18.1 16.2

34.4 30.5 27.2 24.4

19.5 17.2 15.4 13.8

29.2 25.9 23.1 20.7

15.8 14.0 12.5 11.2 10.1

23.6 12.2 20.9 10.8 18.7 9.68 16.8 8.68 15.1 7.84

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

20.9 14.3

31.5 21.5

17.7 12.1

26.5 18.2

Effective length, (KL )y , with respect to weak axis (ft)

0

18.4 16.3 14.5 13.0 11.8

Properties

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

503 214 1.09 1.53

450 192 1.14 1.53

15.6 10.7

23.5 13.3 19.9 10.6 16.0 16.1 9.11 13.7 7.26 10.9

413 176 1.17 1.53

367 157 1.19 1.53

313 132 1.22 1.54

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7.65 11.5 5.19 7.80 245 103 1.25 1.54

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10:47 AM

Page 223

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–223

Table 4-13 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

COMPOSITE HSS5-HSS4

Concrete Filled Rectangular HSS HSS5× 21/2 ×

Shape

14 /

t design, in. Steel, lb/ft

18 /

3 8 /

5 16 /

14 /

0.233 0.174 0.116 0.349 0.291 0.233 11.4 8.78 6.03 14.7 12.7 10.5 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

HSS4× 3×

3 16 /

0

87.8

132

72.4 109

56.3

84.5 113

169

97.0

146

82.1

123

1 2 3 4 5

86.9 84.1 79.8 74.0 67.8

130 126 120 111 102

71.7 107 69.5 104 66.0 98.9 61.3 92.0 55.9 83.8

55.7 54.0 51.3 47.7 43.5

83.6 112 81.1 109 77.0 105 71.6 99.3 65.3 92.5

168 164 158 149 139

96.2 94.1 90.6 85.9 80.2

145 141 136 129 121

81.4 79.5 76.5 72.4 67.5

122 119 115 109 101

6 7 8 9 10

61.0 53.8 46.5 39.4 32.7

91.7 80.8 69.8 59.2 49.2

49.9 43.6 37.3 31.3 26.2

74.8 65.4 56.0 47.0 39.3

38.9 34.0 29.1 24.4 20.1

58.3 51.0 43.7 36.7 30.1

84.9 128 76.6 115 68.1 102 59.6 89.6 51.3 77.1

73.8 66.9 59.7 52.4 45.4

111 100 89.7 78.8 68.2

61.9 56.3 50.6 44.7 39.0

93.0 84.7 76.0 67.2 58.6

11 12 13 14 15

27.0 22.7 19.4 16.7 14.5

40.6 34.1 29.1 25.1 21.9

21.6 18.2 15.5 13.4 11.6

32.5 27.3 23.3 20.1 17.5

16.6 13.9 11.9 10.2 8.91

24.9 20.9 17.8 15.4 13.4

43.5 36.5 31.1 26.8 23.4

65.3 54.9 46.8 40.3 35.1

38.7 32.6 27.8 23.9 20.9

58.2 49.0 41.7 36.0 31.3

33.5 28.4 24.2 20.9 18.2

50.4 42.7 36.3 31.3 27.3

16 17 18 19

12.8

19.2 10.2 15.4 9.06 13.6

7.84 11.8 6.94 10.4

20.5 18.2 16.2

30.9 18.3 27.4 16.2 24.4 14.5

27.5 16.0 24.4 14.1 21.8 12.6 11.3

24.0 21.3 19.0 17.0

11.9 7.06

17.8 10.6

16.3 13.3

14.0 11.3

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

317 99.3 0.999 1.79

9.50 14.3 6.89 10.4 12.2 18.4 10.9 5.65 8.50 4.06 6.10 9.91 14.9 8.82 271 84.3 1.02 1.79

214 65.9 1.05 1.80

248 153 1.11 1.27

229 142 1.13 1.27

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.30 7.54

205 127 1.16 1.27

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Page 224

4–224

DESIGN OF COMPRESSION MEMBERS

Table 4-13 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS4

Concrete Filled Rectangular HSS HSS4× 21/2 ×

HSS4× 3×

Shape

3 16 /

t design, in. Steel, lb/ft

1 8 /

3 8 /

5 16 /

14 /

3 16 /

0.174 0.116 0.349 0.291 0.233 0.174 8.15 5.61 13.4 11.6 9.66 7.51 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

Fy = 46 ksi fc′ = 4 ksi

0

67.9 102

53.1

79.7 103

155.0 89.0

134

73.6 111

60.7

91.0

1 2 3 4 5

67.4 101 65.9 98.9 63.5 95.2 60.2 90.3 56.2 84.3

52.7 51.5 49.6 47.1 44.0

79.1 102 77.3 98.4 74.4 93.0 70.6 85.8 65.9 77.5

153 148 140 129 116

132 128 121 112 102

72.8 109 70.6 106 67.1 101 62.4 93.8 56.9 85.6

60.0 58.1 55.1 51.1 46.4

90.1 87.2 82.7 76.7 69.6

6 7 8 9 10

51.7 46.8 41.8 36.7 31.8

77.5 70.3 62.7 55.1 47.7

40.5 36.7 32.7 28.8 24.9

60.7 55.0 49.1 43.2 37.4

68.4 103 58.9 88.6 49.7 74.7 40.9 61.5 33.2 49.9

60.3 52.4 44.6 37.1 30.2

90.6 78.8 67.0 55.7 45.4

50.9 44.5 38.2 32.1 26.4

76.5 67.0 57.4 48.3 39.7

41.3 35.9 30.6 25.9 21.5

61.9 53.9 45.9 38.9 32.3

11 12 13 14 15

27.1 23.0 19.6 16.9 14.7

40.7 34.6 29.4 25.4 22.1

21.3 17.9 15.2 13.1 11.4

31.9 26.8 22.9 19.7 17.2

27.4 23.0 19.6 16.9 14.7

25.0 21.0 17.9 15.4 13.4

37.6 31.6 26.9 23.2 20.2

21.8 18.3 15.6 13.5 11.7

32.8 27.5 23.5 20.2 17.6

17.7 14.9 12.7 10.9 9.54

26.7 22.4 19.1 16.5 14.3

16 17 18 19 20

12.9 11.5 10.2 9.17

19.4 10.1 17.2 8.91 15.4 7.95 13.8 7.14 6.44

10.3

15.5

41.2 34.6 29.5 25.4 22.2

88.0 85.2 80.7 74.8 67.9

15.1 13.4 11.9 10.7 9.66

8.38 12.6

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

7.47 11.2 5.42 6.04 9.08 4.35 174 108 1.19 1.27

8.15 10.7 16.0 6.54 7.54 11.3

137 84.6 1.21 1.27

210 95.5 0.922 1.48

9.54 6.76

14.3 10.2

195 88.8 0.947 1.48

8.22 12.4 6.62 10.0 5.82 8.75 4.69 7.05 175 80.0 0.973 1.48

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

150 68.3 0.999 1.48

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Table 4-13 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

COMPOSITE HSS4

Concrete Filled Rectangular HSS HSS4× 21/2 ×

Shape

HSS4× 2×

1 8 /

t design, in. Steel, lb/ft

3 8 /

5 16 /

14 /

3 16 /

1 8 /

0.116 0.349 0.291 0.233 0.174 0.116 5.18 12.2 10.6 8.81 6.87 4.75 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

47.2

70.8

93.4 140

81.0 122

67.2 101

53.7

80.5

41.2

61.8

1 2 3 4 5

46.7 45.2 42.9 39.8 36.2

70.0 67.8 64.3 59.7 54.3

91.7 86.8 79.2 69.7 59.2

138 130 119 105 89.0

79.6 120 75.6 114 69.5 104 61.7 92.7 52.9 79.5

66.1 63.0 58.2 52.1 45.1

99.4 94.8 87.5 78.2 67.8

52.8 50.2 46.3 41.2 35.8

79.2 75.4 69.4 61.8 53.8

40.6 38.6 35.7 31.9 27.6

60.8 58.0 53.5 47.8 41.4

6 7 8 9 10

32.2 28.1 24.0 20.0 16.4

48.4 42.1 36.0 30.0 24.6

48.4 38.2 29.4 23.2 18.8

72.8 57.5 44.2 34.9 28.3

43.9 35.1 27.3 21.5 17.4

37.8 30.7 24.1 19.1 15.5

56.9 46.2 36.3 28.7 23.2

30.4 25.0 19.9 15.7 12.8

45.6 37.5 29.9 23.7 19.2

23.2 18.8 14.8 11.7 9.46

34.8 28.2 22.2 17.5 14.2

11 12 13 14 15

13.5 11.4 9.69 8.36 7.28

20.3 17.1 14.5 12.5 10.9

15.5 13.1

23.4 14.4 19.6 12.1

16 17

6.40 5.67

9.60 8.50

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

4.82 3.38

7.24 5.08

Effective length, (KL )y , with respect to weak axis (ft)

0

65.9 52.8 41.0 32.4 26.2

21.7 12.8 18.2 10.7

19.2 10.5 15.8 16.1 8.86 13.3 7.55 11.3

7.82 11.7 6.57 9.85 5.60 8.39

Properties

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

119 53.8 1.03 1.49

9.10 13.7 8.20 12.3 7.11 10.7 5.77 5.40 8.12 4.89 7.36 4.25 6.38 3.43 172 53.3 0.729 1.80

161 50.2 0.754 1.79

146 45.6 0.779 1.79

125 39.1 0.804 1.79

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.67 5.16

4.23 2.50

6.35 3.75

100 31.1 0.830 1.79

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DESIGN OF COMPRESSION MEMBERS

Table 4-14

Available Strength in Axial Compression, kips COMPOSITE HSS20-HSS16

5 8 /

t design, in. Steel, lb/ft Design

Effective length, (KL )y , with respect to weak axis (ft)

Concrete Filled Rectangular HSS HSS20× 12×

Shape

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

Fy = 46 ksi fc′ = 5 ksi

HSS16× 12×

12 /

0.581 127 Pn /Ωc φc Pn ASD LRFD 1240 1860 1220 1830 1210 1810 1200 1800 1190 1790 1180 1770 1170 1750 1160 1730 1140 1710 1130 1690 1110 1670 1100 1640 1080 1620 1060 1590 1040 1560 1020 1530 1000 1500 982 1470 961 1440 940 1410 918 1380 896 1340 874 1310 851 1280 828 1240 805 1210 759 1140 712 1070 666 999 621 931 576 864

3 8 /

5 8 /

0.465 0.349 103 78.5 Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD 1100 1650 958 1440 1080 1620 940 1410 1070 1610 934 1400 1070 1600 927 1390 1060 1580 919 1380 1050 1570 910 1370 1040 1550 900 1350 1020 1540 890 1330 1010 1520 879 1320 999 1500 867 1300 985 1480 854 1280 970 1450 841 1260 954 1430 826 1240 938 1410 812 1220 921 1380 797 1190 904 1360 781 1170 886 1330 765 1150 868 1300 748 1120 849 1270 731 1100 829 1240 714 1070 810 1210 696 1040 790 1180 678 1020 770 1150 660 990 749 1120 642 963 729 1090 624 935 708 1060 605 908 666 1000 568 852 625 937 531 796 583 875 494 741 543 814 458 688 503 754 423 635

12 /

3 8 /

0.581 0.465 0.349 110 89.7 68.3 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD 1040 1560 920 1380 797 1200 1020 1530 904 1360 783 1170 1010 1520 898 1350 777 1170 1010 1510 891 1340 771 1160 998 1500 883 1330 765 1150 988 1480 875 1310 757 1140 978 1470 866 1300 749 1120 967 1450 856 1280 740 1110 955 1430 846 1270 731 1100 943 1410 834 1250 720 1080 929 1390 822 1230 710 1060 915 1370 810 1210 698 1050 901 1350 796 1190 687 1030 885 1330 783 1170 674 1010 869 1300 768 1150 661 992 853 1280 754 1130 648 972 836 1250 738 1110 635 952 818 1230 723 1080 621 931 800 1200 707 1060 606 910 782 1170 690 1040 592 888 764 1150 674 1010 577 865 745 1120 657 985 562 843 726 1090 640 959 547 820 706 1060 622 933 531 797 687 1030 605 907 516 774 667 1000 587 881 500 751 628 941 552 828 469 704 588 882 517 775 438 657 549 824 482 723 408 612 511 766 448 672 378 566 473 709 414 621 348 522

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

599 405

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

74500 31200 4.93 1.55

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

901 609

500 335

752 503

64900 27100 4.99 1.55

394 263

593 395

54700 22600 5.04 1.56

423 339

636 509

41400 25500 4.80 1.27

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

353 283

530 425

36300 22200 4.86 1.28

279 222

419 334

30400 18600 4.91 1.28

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Table 4-14 (continued) Fy = 46 ksi fc′ = 5 ksi

Available Strength in Axial Compression, kips Concrete Filled Rectangular HSS HSS16× 12×

Shape

Design

Effective length, (KL )y , with respect to weak axis (ft)

HSS16× 8×

5 16 /

t design, in. Steel, lb/ft

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

COMPOSITE HSS16-HSS14

5 8 /

12 /

HSS14× 10× 38 /

5 16 /

5 8 /

0.291 0.581 0.465 0.349 0.291 0.581 57.4 93.3 76.1 58.1 48.9 93.3 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 735 1100 806 1210 707 1060 605 908 551 827 832 1250 721 1080 776 1160 681 1020 582 873 530 795 811 1220 716 1070 765 1150 671 1010 574 861 522 783 803 1200 710 1070 753 1130 661 991 565 848 514 771 795 1190 704 1060 740 1110 649 974 555 832 504 757 785 1180 697 1050 725 1090 636 954 544 816 494 741 775 1160 689 1030 709 1060 622 934 532 797 483 724 763 1150 681 1020 692 1040 608 911 519 778 471 706 751 1130 672 1010 674 1010 592 888 505 757 458 687 738 1110 662 993 655 983 575 863 490 736 445 667 724 1090 652 978 636 953 558 837 475 713 431 646 709 1060 641 962 615 923 540 810 460 690 416 625 694 1040 630 945 594 891 522 783 444 666 402 602 678 1020 618 928 573 859 503 754 428 641 387 580 661 992 606 909 551 826 484 726 411 616 371 557 644 967 594 891 528 793 464 697 394 591 356 534 627 940 581 871 506 759 445 667 377 566 340 510 609 914 568 852 484 725 425 638 360 540 324 487 591 886 554 832 461 692 406 608 343 515 309 463 572 858 541 811 439 658 386 579 326 490 293 440 554 830 527 790 417 625 367 550 310 464 278 417 535 802 513 769 395 592 348 521 293 440 263 394 516 774 498 747 373 560 329 493 277 415 248 372 497 745 484 726 352 528 310 465 261 392 234 351 478 717 469 704 332 498 292 438 246 368 220 329 459 689 455 682 313 471 275 412 230 345 205 308 440 661 426 639 280 421 241 362 202 303 181 271 403 605 397 595 248 373 214 321 179 269 160 240 368 551 368 552 221 333 191 286 160 240 143 214 333 499 340 510 199 299 171 257 143 215 128 192 299 449 313 470 179 269 154 232 129 194 116 173 270 405 Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

239 190

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

27300 16600 4.94 1.28

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

359 285

327 193

492 291

29700 9200 3.27 1.80

275 162

413 243

26400 8110 3.32 1.80

219 127

329 191

22300 6800 3.37 1.81

189 109

20000 6070 3.40 1.82

Note: Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

284 164

304 236

457 355

25000 14200 3.98 1.33

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DESIGN OF COMPRESSION MEMBERS

Table 4-14 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS14-HSS12

Concrete Filled Rectangular HSS HSS14× 10×

Shape

12 /

t design, in. Steel, lb/ft Design

Effective length, (KL )y , with respect to weak axis (ft)

Fy = 46 ksi fc′ = 5 ksi

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

3 8 /

HSS12× 10×

5 16 /

1 4 c,f /

12 /

3 8 /

0.465 0.349 0.291 0.233 0.465 0.349 76.1 58.1 48.9 39.4 69.3 53.0 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 732 1100 631 946 577 865 522 784 650 975 559 838 714 1070 614 922 561 842 508 762 633 950 544 817 707 1060 609 913 556 834 503 755 627 941 539 809 700 1050 602 903 550 825 497 746 621 931 533 800 692 1040 595 892 543 814 491 736 613 920 527 790 683 1020 587 880 535 803 484 726 605 907 519 779 673 1010 578 867 527 790 476 714 596 894 511 767 662 993 568 852 518 777 468 701 586 879 503 754 650 975 558 837 508 763 459 688 576 863 494 740 638 957 547 821 498 748 449 674 565 847 484 726 625 938 536 804 488 732 439 659 553 829 474 711 612 918 524 786 477 715 429 643 541 811 463 694 598 897 511 767 465 698 418 627 528 792 452 678 583 875 499 748 453 680 407 610 515 772 440 661 568 852 485 728 441 661 395 593 501 752 429 643 553 829 472 708 428 642 384 576 488 731 416 625 537 806 458 687 415 623 372 558 473 710 404 606 521 782 444 666 402 603 360 539 459 689 391 587 505 757 430 645 389 583 347 521 444 667 379 568 489 733 415 623 376 563 335 503 430 645 366 549 472 708 401 601 362 543 323 484 415 622 353 529 455 683 386 580 349 523 310 465 400 600 340 510 439 658 372 558 335 503 298 447 385 577 327 490 422 633 357 536 322 483 285 428 370 555 314 471 406 608 343 514 308 463 273 410 355 533 301 452 389 584 328 493 295 443 261 391 340 511 288 432 357 535 300 450 269 404 237 356 311 467 263 395 325 488 273 409 244 366 214 321 283 425 239 358 295 442 246 370 220 329 192 288 256 384 215 323 265 397 221 332 197 296 172 258 230 345 193 290 239 359 200 299 178 267 155 233 208 311 174 261 Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

255 197

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

22200 12600 4.04 1.33

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

c f

383 297

202 156

304 234

18600 10500 4.09 1.33

174 133

262 200

16700 9340 4.12 1.34

144 110

217 165

14600 8160 4.14 1.34

Shape is noncompact for compression with Fy = 46 ksi. Shape is noncompact for flexure with Fy = 46 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

201 175

302 264

14800 10900 3.96 1.17

160 139

240 209

12500 9160 4.01 1.17

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Table 4-14 (continued) Fy = 46 ksi fc′ = 5 ksi

Available Strength in Axial Compression, kips Concrete Filled Rectangular HSS HSS12× 10×

Shape

5 16 /

t design, in. Steel, lb/ft

Effective length, (KL )y , with respect to weak axis (ft)

Design 0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

COMPOSITE HSS12

HSS12× 8×

14 /

5 8 /

12 /

0.291 0.233 0.581 0.465 44.6 36.0 76.3 62.5 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD 509 763 461 692 640 960 562 842 495 743 449 673 615 922 540 810 491 736 444 666 606 909 532 799 485 728 439 658 596 894 524 786 479 718 433 650 585 878 514 771 472 708 427 640 573 860 504 755 465 697 420 630 560 840 492 738 457 685 412 619 546 819 480 720 448 673 404 607 531 797 467 701 439 659 396 594 516 773 454 680 430 645 387 581 499 749 440 659 420 630 378 567 483 724 425 637 410 615 368 553 465 698 410 615 399 599 359 538 448 672 395 592 388 582 348 522 430 645 379 569 377 566 338 507 412 618 363 545 366 548 327 491 394 590 347 521 354 531 317 475 375 563 332 497 342 513 306 458 357 536 316 474 330 496 295 442 339 509 300 450 319 478 284 425 321 482 284 427 307 460 273 409 304 456 269 404 295 442 262 392 287 430 254 381 283 424 251 376 270 406 239 359 271 406 240 360 256 385 225 337 259 389 229 344 242 363 210 316 236 354 208 312 214 321 185 277 214 321 188 281 189 285 164 246 192 288 168 252 169 254 146 219 173 259 151 226 152 228 131 197 156 234 136 204 137 206 118 178

3 8 /

14 /

0.349 47.9 Pn /Ωc φc Pn ASD LRFD 479 718 460 690 454 680 446 669 438 657 429 643 419 629 409 613 397 596 386 579 374 561 361 542 348 522 335 503 322 483 308 462 295 442 281 421 267 401 254 381 241 361 227 341 215 322 202 303 190 284 177 266 156 234 138 207 123 185 111 166 99.7 150

0.233 32.6 Pn /Ωc φc Pn ASD LRFD 391 586 375 562 369 554 363 544 356 534 348 522 340 509 331 496 321 482 311 467 301 452 291 436 280 420 269 403 257 386 246 369 235 352 223 335 212 318 201 301 190 284 179 268 168 252 158 237 147 221 138 207 121 182 107 161 95.7 144 85.9 129 77.5 116

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

137 119

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

11200 8180 4.04 1.17

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

206 179

114 98.4

171 148

9770 7150 4.07 1.17

205 151

308 228

13900 7000 3.16 1.41

173 128

261 138 192 101

12300 6220 3.21 1.41

10500 5240 3.27 1.42

Note: Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

208 152

99.2 149 71.9 108 8180 4070 3.32 1.42

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DESIGN OF COMPRESSION MEMBERS

Table 4-14 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS12-HSS10

Concrete Filled Rectangular HSS HSS12× 6×

Shape

t design, in. Steel, lb/ft Design

Effective length, (KL )y , with respect to weak axis (ft)

Fy = 46 ksi fc′ = 5 ksi

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

HSS10× 8×

5 8 /

12 /

3 8 /

14 /

5 8 /

12 /

0.581 67.8 Pn /Ωc φc Pn ASD LRFD 541 811 505 757 493 739 479 718 463 695 447 670 429 644 411 616 392 587 372 558 352 529 334 502 316 474 297 447 279 420 261 393 244 366 227 341 210 316 194 291 178 268 165 248 153 230 142 214 133 199 124 186 109 164 96.4 145 86.0 129 77.2 116

0.465 55.7 Pn /Ωc φc Pn ASD LRFD 471 706 440 660 429 644 417 626 404 606 390 585 375 563 359 539 343 514 326 489 308 463 291 437 274 410 256 384 239 358 222 333 206 309 192 288 178 268 165 248 152 229 141 211 130 196 121 182 113 170 106 159 92.9 140 82.2 124 73.4 110 65.8 99.0 59.4 89.3

0.349 42.8 Pn /Ωc φc Pn ASD LRFD 399 598 373 559 364 545 354 530 343 514 331 496 318 477 305 457 291 436 276 414 262 393 247 371 232 348 218 326 203 305 189 283 175 262 161 242 148 222 136 204 125 188 116 174 107 161 99.9 150 93.1 140 87.0 130 76.5 115 67.7 102 60.4 90.6 54.2 81.3 48.9 73.4

0.233 29.2 Pn /Ωc φc Pn ASD LRFD 320 480 299 448 291 437 283 425 274 411 264 396 254 380 243 364 231 347 219 329 207 311 195 293 183 275 171 257 160 239 148 222 137 205 126 189 115 173 106 159 97.5 146 90.2 135 83.6 125 77.7 117 72.5 109 67.7 102 59.5 89.3 52.7 79.1 47.0 70.5 42.2 63.3 38.1 57.1

0.581 67.8 Pn /Ωc φc Pn ASD LRFD 558 837 535 803 528 791 519 778 509 763 498 747 486 729 473 710 460 690 446 669 432 648 417 625 401 602 386 578 370 555 354 530 337 506 321 482 305 458 289 434 274 411 259 390 246 370 233 349 219 330 207 311 182 274 161 242 144 216 129 194 116 175

0.465 55.7 Pn /Ωc φc Pn ASD LRFD 488 732 468 703 462 693 454 681 445 668 436 654 426 639 415 623 404 605 391 587 379 568 366 549 353 529 339 509 325 488 311 467 297 446 283 425 269 404 256 383 242 363 228 343 215 323 202 304 190 285 177 266 156 234 138 207 123 185 111 166 99.7 150

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

171 101

256 145 218 152 85.7 129

10900 3410 2.39 1.79

9730 3020 2.44 1.79

116 175 68.4 103 8350 2570 2.49 1.80

84.0 126 154 48.7 73.2 130 6560 2000 2.54 1.81

8590 5900 3.09 1.21

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

231 131 196 110

196 166

7640 5240 3.14 1.21

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

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Table 4-14 (continued) Fy = 46 ksi fc′ = 5 ksi

Available Strength in Axial Compression, kips COMPOSITE HSS10

Concrete Filled Rectangular HSS HSS10× 8×

Shape

HSS10× 6×

3 8 /

5 16 /

14 /

3 16 /

5 8 /

12 /

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

0.349 42.8 Pn /Ωc φc Pn ASD LRFD 416 623 399 599 393 590 387 580 379 569 371 557 363 544 354 530 344 516 334 500 323 484 312 468 301 451 289 434 277 416 265 398 254 380 242 362 230 345 218 327 206 310 195 292 184 275 173 259 162 243 151 227 133 200 118 177 105 158 94.3 141 85.1 128

0.291 36.1 Pn /Ωc φc Pn ASD LRFD 376 565 361 542 356 534 350 525 343 515 336 504 328 492 320 479 311 466 301 452 292 437 281 422 271 407 260 391 250 375 239 358 228 342 217 326 206 310 196 293 185 278 175 262 164 247 154 232 145 217 135 203 119 178 105 158 93.8 141 84.2 126 76.0 114

0.233 29.2 Pn /Ωc φc Pn ASD LRFD 337 506 323 485 318 478 313 469 307 460 300 450 293 439 285 427 277 415 268 402 259 389 250 375 240 361 231 346 221 331 211 317 201 302 191 287 182 272 172 258 162 243 153 229 144 215 135 202 126 189 117 176 103 155 91.4 137 81.6 122 73.2 110 66.1 99.1

0.174 22.2 Pn /Ωc φc Pn ASD LRFD 296 444 283 425 279 418 274 411 268 402 262 393 255 383 248 372 241 361 233 349 225 337 216 324 208 312 199 298 190 285 181 272 172 258 163 245 155 232 146 219 137 206 129 194 121 181 113 169 105 158 98.3 147 86.4 130 76.6 115 68.3 102 61.3 91.9 55.3 83.0

0.581 59.3 Pn /Ωc φc Pn ASD LRFD 467 701 435 653 424 636 412 618 398 597 383 575 368 552 351 527 335 504 319 480 303 456 287 432 271 407 255 383 239 359 223 335 207 311 192 288 177 266 163 245 150 225 139 208 129 193 120 180 111 168 104 157 91.5 138 81.1 122 72.3 109 64.9 97.6

0.465 48.9 Pn /Ωc φc Pn ASD LRFD 408 612 380 570 371 556 360 540 349 523 336 504 323 484 308 463 294 441 279 418 264 395 248 372 233 349 218 326 203 304 189 284 176 265 164 246 152 228 140 210 129 194 119 179 110 166 103 154 95.7 144 89.4 134 78.6 118 69.6 105 62.1 93.3 55.7 83.8

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

104 157 88.0 132

89.9 135 75.8 114

74.9 113 62.9 94.6

6520 4470 3.19 1.21

5830 3990 3.22 1.21

5080 3470 3.25 1.21

t design, in. Steel, lb/ft

Effective length, (KL )y , with respect to weak axis (ft)

Design

Properties

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

58.5 48.8

87.9 126 190 73.4 86.2 130

4280 2910 3.28 1.21

6700 2840 2.34 1.54

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

108 162 73.4 110 5970 2540 2.39 1.53

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DESIGN OF COMPRESSION MEMBERS

Table 4-14 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS10

Fy = 46 ksi fc′ = 5 ksi

Concrete Filled Rectangular HSS HSS10× 6×

Shape

HSS10× 5×

3 8 /

5 16 /

14 /

3 16 /

3 8 /

5 16 /

0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

0.349 37.7 Pn /Ωc φc Pn ASD LRFD 344 516 321 481 313 470 304 456 294 442 284 426 273 409 261 392 249 373 236 354 224 335 211 316 198 297 185 278 172 259 160 240 148 222 136 204 125 187 115 172 106 158 97.6 146 90.5 136 84.2 126 78.5 118 73.3 110 64.4 96.7 57.1 85.6 50.9 76.4 45.7 68.6 41.2 61.9

0.291 31.8 Pn /Ωc φc Pn ASD LRFD 310 465 289 434 282 423 274 411 265 398 256 384 246 369 235 353 224 336 213 319 201 302 190 285 178 267 167 250 155 233 144 216 133 200 123 184 112 169 103 155 95.2 143 88.0 132 81.6 122 75.9 114 70.7 106 66.1 99.1 58.1 87.1 51.5 77.2 45.9 68.9 41.2 61.8 37.2 55.8

0.233 25.8 Pn /Ωc φc Pn ASD LRFD 275 413 257 385 250 375 243 364 235 352 226 340 217 326 208 312 198 297 188 281 177 266 167 250 156 235 146 219 136 204 126 189 116 174 107 160 97.6 146 89.6 134 82.6 124 76.4 115 70.8 106 65.9 98.8 61.4 92.1 57.4 86.1 50.4 75.6 44.7 67.0 39.8 59.8 35.8 53.6 32.3 48.4

0.174 19.6 Pn /Ωc φc Pn ASD LRFD 239 359 222 334 217 325 210 315 203 304 195 293 187 280 178 268 169 254 160 241 151 227 142 213 133 199 123 185 114 172 106 159 97.2 146 88.8 133 81.3 122 74.6 112 68.8 103 63.6 95.4 59.0 88.4 54.8 82.2 51.1 76.7 47.8 71.6 42.0 63.0 37.2 55.8 33.2 49.7 29.8 44.6 26.9 40.3

0.349 35.1 Pn /Ωc φc Pn ASD LRFD 307 461 279 418 269 404 259 388 247 370 235 352 222 333 208 313 195 292 181 272 168 251 154 231 141 212 128 192 116 174 106 159 96.2 145 87.6 132 80.2 121 73.6 111 67.9 102 62.7 94.3 58.2 87.5 54.1 81.3 50.4 75.8 47.1 70.8 41.4 62.3 36.7 55.2

0.291 29.7 Pn /Ωc φc Pn ASD LRFD 276 414 251 376 242 363 233 349 222 333 211 317 200 299 188 282 176 263 163 245 151 227 139 208 127 191 116 174 105 157 94.5 142 85.7 129 78.1 117 71.4 107 65.6 98.4 60.5 90.7 55.9 83.9 51.8 77.8 48.2 72.3 44.9 67.4 42.0 63.0 36.9 55.4 32.7 49.0

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

86.6 130 58.7 88.2

75.0 113 50.6 76.0

77.5 116 45.8 68.8

67.4 101 39.5 59.4

5150 2170 2.44 1.54

4670 1950 2.47 1.55

4430 1370 2.05 1.80

4040 1240 2.07 1.81

t design, in. Steel, lb/ft

Effective length, (KL )y , with respect to weak axis (ft)

Design

Properties

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

62.8 42.1

94.4 63.3

4060 1700 2.49 1.55

49.3 32.7

74.1 49.2

3410 1410 2.52 1.56

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–233

Table 4-14 (continued) Fy = 46 ksi fc′ = 5 ksi

Available Strength in Axial Compression, kips COMPOSITE HSS10-HSS9

Concrete Filled Rectangular HSS HSS10× 5×

Shape

t design, in. Steel, lb/ft

Effective length, (KL )y , with respect to weak axis (ft)

Design 0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

HSS9× 7×

14 /

3 16 /

5 8 /

12 /

3 8 /

5 16 /

0.233 24.1 Pn /Ωc φc Pn ASD LRFD 244 366 222 332 214 321 205 308 196 294 186 279 176 264 165 248 154 232 144 215 133 199 122 183 111 167 101 152 91.5 137 82.6 124 74.9 112 68.3 102 62.5 93.7 57.4 86.0 52.9 79.3 48.9 73.3 45.3 68.0 42.1 63.2 39.3 58.9 36.7 55.1 32.3 48.4 28.6 42.9

0.174 18.4 Pn /Ωc φc Pn ASD LRFD 211 316 190 286 184 275 176 264 168 252 159 238 150 225 140 211 131 196 121 182 112 167 102 153 93.2 140 84.4 127 75.9 114 68.5 103 62.1 93.1 56.6 84.9 51.8 77.7 47.5 71.3 43.8 65.7 40.5 60.8 37.6 56.3 34.9 52.4 32.6 48.8 30.4 45.6 26.7 40.1 23.7 35.5

0.581 59.3 Pn /Ωc φc Pn ASD LRFD 474 711 449 673 440 660 430 645 419 629 408 611 395 592 381 572 367 551 353 529 338 506 322 483 307 460 292 439 278 417 263 396 249 375 235 353 221 333 208 312 194 292 182 273 169 253 157 236 146 220 137 205 120 180 106 160 94.9 143 85.1 128 76.8 115

0.465 48.9 Pn /Ωc φc Pn ASD LRFD 414 621 393 589 385 578 377 565 367 551 357 536 346 520 335 502 323 484 310 465 297 446 284 426 270 405 257 385 243 364 229 344 216 324 203 304 190 284 177 265 165 248 154 232 144 217 134 201 125 188 117 175 103 154 90.8 137 81.0 122 72.7 109 65.6 98.7

0.349 37.7 Pn /Ωc φc Pn ASD LRFD 350 525 332 498 326 489 319 478 311 467 303 454 294 440 284 426 274 411 263 395 252 378 241 362 230 345 218 328 207 310 196 293 184 276 173 260 162 243 151 227 141 211 131 196 121 182 113 169 105 157 98.1 147 86.2 129 76.3 115 68.1 102 61.1 91.7 55.2 82.7

0.291 31.8 Pn /Ωc φc Pn ASD LRFD 316 474 300 450 294 441 288 432 281 421 273 410 265 397 256 384 247 370 237 356 228 341 217 326 207 311 197 295 186 280 176 264 166 249 156 234 146 219 136 204 127 190 117 176 109 163 101 152 94.4 142 88.2 132 77.5 116 68.7 103 61.2 91.9 55.0 82.5 49.6 74.4

81.1 122 66.9 101

70.2 106 57.8 86.9

4440 2900 2.78 1.24

4000 2610 2.81 1.24

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

56.4 33.0

84.8 49.6

3550 1090 2.10 1.80

44.5 25.6

66.9 119 178 101 152 38.5 98.4 148 83.7 126

2970 899 2.13 1.82

5780 3790 2.68 1.23

5180 3380 2.73 1.24

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF COMPRESSION MEMBERS

Table 4-14 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS9

Concrete Filled Rectangular HSS HSS9× 5×

Shape

5 8 /

t design, in. Steel, lb/ft

12 /

3 8 /

5 16 /

14 /

3 16 /

0.581 0.465 0.349 0.291 0.233 0.174 50.8 42.1 32.6 27.6 22.4 17.1 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

Fy = 46 ksi fc′ = 5 ksi

0

386

580

336

504

282

423

253

380

224

336

193

289

6 7 8 9 10

351 339 326 312 297

527 510 490 468 446

304 293 281 268 254

456 440 422 402 381

256 247 237 226 215

383 370 355 339 322

230 222 213 203 193

345 333 319 305 290

203 196 188 179 170

304 294 282 269 255

174 168 161 153 145

261 252 241 230 218

11 12 13 14 15

281 264 247 230 214

422 397 372 346 321

240 225 210 196 182

359 337 315 294 274

203 190 178 165 152

304 285 266 247 229

182 171 160 149 138

274 257 240 223 206

161 151 141 131 121

241 226 211 196 181

137 128 119 111 102

205 192 179 166 153

16 17 18 19 20

197 180 165 149 135

296 271 247 224 202

169 155 142 130 117

253 233 214 195 177

140 128 116 106 96.5

210 192 174 159 145

126 116 105 94.9 85.6

190 173 158 142 128

111 101 92.1 83.0 74.9

166 152 138 125 112

21 22 23 24 25

122 111 102 93.5 86.2

184 167 153 141 130

107 97.1 88.8 81.6 75.2

160 146 134 123 113

87.5 79.7 72.9 67.0 61.7

131 120 110 101 92.8

93.2 84.8 76.8 69.0 62.3

140 127 115 104 93.4

77.6 116 70.8 106 64.7 97.1 59.5 89.2 54.8 82.2

68.0 102 61.9 92.9 56.7 85.0 52.0 78.0 47.9 71.9

56.5 51.5 47.1 43.2 39.9

84.7 77.2 70.6 64.9 59.8

26 27 28 29 30

79.7 120 73.9 111 68.7 103 64.1 96.3 59.9 90.0

69.5 104 64.5 96.9 59.9 90.1 55.9 84.0 52.2 78.5

57.1 52.9 49.2 45.9 42.9

85.8 79.5 74.0 69.0 64.4

50.7 47.0 43.7 40.7 38.0

76.0 70.5 65.5 61.1 57.1

44.3 41.1 38.2 35.6 33.3

66.5 61.7 57.3 53.5 49.9

36.9 34.2 31.8 29.6 27.7

55.3 51.3 47.7 44.4 41.5

32 34

52.6

45.9

37.7

56.6

33.4 29.6

50.2 44.4

29.3 25.9

43.9 38.9

24.3 21.5

36.5 32.3

97.9 62.9

56.6 36.1

85.1 54.3

47.6 30.1

71.5 45.2

37.4 23.5

56.2 35.4

79.1

69.0

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

93.8 141 60.4 90.8

80.4 121 51.9 78.0

4330 1610 1.92 1.64

3900 1450 1.97 1.64

65.1 41.9

3350 1240 2.03 1.64

3040 1120 2.05 1.65

2680 984 2.08 1.65

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2240 818 2.10 1.65

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–235

Table 4-14 (continued) Fy = 46 ksi fc′ = 5 ksi

Available Strength in Axial Compression, kips COMPOSITE HSS8

Concrete Filled Rectangular HSS HSS8× 6×

Shape

t design, in. Steel, lb/ft

Effective length, (KL )y , with respect to weak axis (ft)

Design 0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40

5 8 /

12 /

3 8 /

5 16 /

14 /

3 16 /

0.581 50.8 Pn /Ωc φc Pn ASD LRFD 392 588 364 545 354 531 343 515 331 498 320 480 307 462 294 442 281 422 267 401 253 380 238 358 224 337 210 315 196 294 182 273 168 253 155 233 142 214 131 196 120 181 111 167 103 155 96.0 144 89.5 135 83.7 126 73.5 111 65.1 97.9 58.1 87.3

0.465 42.1 Pn /Ωc φc Pn ASD LRFD 343 514 319 478 310 466 301 452 291 437 280 420 269 403 256 385 244 366 231 346 218 327 205 307 191 287 178 268 167 251 156 234 144 217 134 201 123 185 113 170 104 157 96.4 145 89.4 134 83.1 125 77.5 116 72.4 109 63.6 95.7 56.4 84.7 50.3 75.6 45.1 67.8

0.349 32.6 Pn /Ωc φc Pn ASD LRFD 288 433 269 403 262 393 254 381 246 369 237 355 227 341 217 325 207 310 196 294 185 277 174 261 163 244 152 228 141 212 131 196 121 181 111 166 101 152 93.1 140 85.8 129 79.3 119 73.5 110 68.4 103 63.7 95.6 59.6 89.3 52.3 78.5 46.4 69.6 41.4 62.0 37.1 55.7

0.291 27.6 Pn /Ωc φc Pn ASD LRFD 260 390 242 363 236 354 229 344 222 332 213 320 205 307 196 294 186 280 177 265 167 250 157 236 147 221 137 206 128 192 118 177 109 164 100 150 91.7 138 84.2 126 77.6 116 71.8 108 66.5 99.8 61.9 92.8 57.7 86.5 53.9 80.8 47.4 71.1 42.0 62.9 37.4 56.1 33.6 50.4 30.3 45.5

0.233 22.4 Pn /Ωc φc Pn ASD LRFD 230 346 214 322 209 313 203 304 196 294 189 283 181 272 173 259 164 247 156 234 147 221 138 207 129 194 121 181 112 168 104 156 95.6 143 87.6 131 80.2 120 73.6 110 67.8 102 62.7 94.1 58.2 87.3 54.1 81.1 50.4 75.6 47.1 70.7 41.4 62.1 36.7 55.0 32.7 49.1 29.4 44.0 26.5 39.8

0.174 17.1 Pn /Ωc φc Pn ASD LRFD 199 299 185 277 180 270 175 262 168 253 162 243 155 233 148 222 140 211 133 199 125 188 117 176 109 164 102 153 94.3 141 87.0 130 79.9 120 72.9 109 66.7 100 61.3 91.9 56.5 84.7 52.2 78.3 48.4 72.6 45.0 67.5 42.0 63.0 39.2 58.8 34.5 51.7 30.5 45.8 27.2 40.9 24.4 36.7 22.1 33.1

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

87.9 132 71.1 107

75.4 113 60.7 91.3

3700 2290 2.27 1.27

3320 2050 2.32 1.27

60.9 49.1

91.5 73.8

2860 1760 2.38 1.27

52.8 42.4

79.4 63.8

2590 1590 2.40 1.28

44.2 35.4

2270 1390 2.43 1.28

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

66.4 53.2

34.9 27.8

52.4 41.7

1900 1160 2.46 1.28

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4–236

DESIGN OF COMPRESSION MEMBERS

Table 4-14 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS8

Concrete Filled Rectangular HSS HSS8× 4×

Shape

5 8 /

t design, in. Steel, lb/ft

12 /

3 8 /

5 16 /

14 /

3 16 /

0.581 0.465 0.349 0.291 0.233 0.174 42.3 35.2 27.5 23.3 19.0 14.5 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

Fy = 46 ksi fc′ = 5 ksi

0

322

484

270

405

225

338

202

302

177

265

151

226

6 7 8 9 10

277 262 246 228 211

416 393 369 343 317

232 221 208 194 180

349 332 313 292 271

193 183 171 159 147

290 274 257 239 221

173 164 154 143 132

260 246 231 215 198

152 144 135 126 116

228 216 203 189 174

129 122 115 107 98.3

194 183 172 160 147

11 12 13 14 15

193 175 157 140 124

290 263 236 211 186

166 151 137 123 110

249 227 206 185 165

134 122 111 100 90.1

202 183 167 151 135

121 110 99.0 88.3 78.1

182 165 148 133 117

106 96.6 87.0 77.7 68.7

160 145 131 117 103

16 17 18 19 20

109 96.4 85.9 77.1 69.6

163 145 129 116 105

21 22 23 24 25

63.1 57.5 52.6 48.3 44.6

94.9 86.5 79.1 72.7 67.0

26 27 28

96.6 85.6 76.4 68.5 61.9

145 129 115 103 93.0

56.1 51.1 46.8 43.0 39.6

89.9 135 81.4 122 73.2 110 65.2 97.8 57.5 86.2

80.1 120 71.0 107 63.3 95.1 56.8 85.4 51.3 77.1

69.6 105 61.7 92.7 55.0 82.7 49.4 74.2 44.6 67.0

60.4 53.5 47.7 42.8 38.7

90.6 80.3 71.6 64.2 58.0

50.5 44.8 39.9 35.8 32.3

75.8 67.1 59.9 53.8 48.5

84.3 76.8 70.3 64.6 59.5

46.5 42.4 38.8 35.6 32.8

69.9 63.7 58.3 53.5 49.3

40.4 36.8 33.7 31.0 28.5

60.8 55.4 50.7 46.5 42.9

35.1 31.9 29.2 26.8 24.7

52.6 47.9 43.8 40.3 37.1

29.3 26.7 24.5 22.5 20.7

44.0 40.1 36.7 33.7 31.0

36.6

55.0

30.3

45.6

26.4 24.5

39.6 36.8

22.9 21.2

34.3 31.8

19.1 17.7 16.5

28.7 26.6 24.8

57.5 34.1

86.4 51.3

70.6 41.8

40.9 24.2

61.4 36.4

34.5 20.3

51.8 30.4

27.2 15.9

40.9 23.9

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

66.1 39.3

99.3 59.0

2600 805 1.51 1.80

2360 733 1.56 1.79

47.0 27.8

2050 636 1.61 1.80

1860 577 1.63 1.80

1650 508 1.66 1.80

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1390 425 1.69 1.81

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–237

Table 4-14 (continued) Fy = 46 ksi fc′ = 5 ksi

Available Strength in Axial Compression, kips COMPOSITE HSS7

Concrete Filled Rectangular HSS HSS7× 5×

Shape

12 /

t design, in. Steel, lb/ft

5 16 /

14 /

3 16 /

1 8 c,f /

0.465 0.349 0.291 0.233 0.174 0.116 35.2 27.5 23.3 19.0 14.5 9.86 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

3 8 /

0

276

414

232

348

208

312

183

275

157

236

131

196

6 7 8 9 10

248 239 229 218 206

373 359 343 327 309

209 202 193 184 174

314 302 290 276 262

188 181 174 165 157

282 272 260 248 235

166 160 153 146 138

249 240 230 219 208

142 136 131 124 118

212 205 196 186 176

117 112 107 102 95.9

175 168 161 153 144

11 12 13 14 15

195 183 171 159 148

292 275 257 240 222

164 154 143 133 122

246 231 215 199 183

148 139 129 120 110

222 208 194 179 165

130 122 114 106 97.3

196 183 171 158 146

111 104 96.3 89.0 81.8

166 155 144 134 123

89.9 83.7 77.5 71.3 65.2

135 126 116 107 97.8

16 17 18 19 20

136 125 113 103 92.7

204 187 171 154 139

112 102 93.0 84.8 76.8

168 153 140 127 115

101 92.0 83.4 75.0 67.7

152 138 125 112 101

89.2 134 81.3 122 73.6 110 66.2 99.3 59.7 89.6

74.8 112 67.9 102 61.4 92.1 55.1 82.6 49.7 74.5

59.2 53.5 47.9 43.0 38.8

88.8 80.2 71.8 64.5 58.2

21 22 23 24 25

84.1 126 76.6 115 70.1 105 64.4 96.8 59.3 89.2

69.6 105 63.4 95.4 58.0 87.2 53.3 80.1 49.1 73.8

61.4 55.9 51.2 47.0 43.3

92.0 83.9 76.7 70.5 64.9

54.2 49.4 45.2 41.5 38.2

81.3 74.1 67.8 62.2 57.4

45.1 41.1 37.6 34.5 31.8

67.6 61.6 56.4 51.8 47.7

35.2 32.1 29.3 26.9 24.8

52.8 48.1 44.0 40.4 37.2

26 27 28 29 30

54.9 50.9 47.3 44.1 41.2

45.4 42.1 39.2 36.5 34.1

68.3 63.3 58.9 54.9 51.3

40.0 37.1 34.5 32.2 30.1

60.0 55.7 51.8 48.3 45.1

35.4 32.8 30.5 28.4 26.6

53.0 49.2 45.7 42.6 39.8

29.4 27.3 25.4 23.6 22.1

44.1 40.9 38.0 35.5 33.1

23.0 21.3 19.8 18.5 17.2

34.4 31.9 29.7 27.7 25.9

30.0

45.1

26.4

39.6

23.3

35.0

19.4 17.2

29.1 25.8

15.2 13.4

22.7 20.1

43.7 33.9

65.7 50.9

57.1 44.4

32.0 24.7

48.1 37.2

25.2 19.4

37.9 29.2

18.0 13.6

27.0 20.5

82.5 76.5 71.1 66.3 61.9

32 34

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy ASD Ωc = 2.00

53.6 41.8

kip-in.2 kip-in.2

LRFD φc = 0.75

80.5 62.8

1990 1130 1.91 1.33 c

1720 982 1.97 1.32

38.0 29.5

1570 889 1.99 1.33

1390 785 2.02 1.33

1160 653 2.05 1.33

910 510 2.07 1.34

Shape is noncompact for compression with Fy = 46 ksi. f Shape is noncompact for flexure with Fy = 46 ksi.

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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10:49 AM

Page 238

4–238

DESIGN OF COMPRESSION MEMBERS

Table 4-14 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS7

Concrete Filled Rectangular HSS HSS7× 4×

Shape

12 /

t design, in. Steel, lb/ft

3 8 /

5 16 /

14 /

3 16 /

1 8 c,f /

0.465 0.349 0.291 0.233 0.174 0.116 31.8 24.9 21.2 17.3 13.3 9.01 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

Fy = 46 ksi fc′ = 5 ksi

0

243

365

202

303

181

272

159

238

135

203

6 7 8 9 10

209 198 186 174 160

314 298 280 261 241

173 163 153 142 131

259 245 230 213 196

155 147 138 128 118

233 220 206 192 177

136 129 121 112 104

204 193 181 169 155

116 109 102 95.1 87.5

173 164 153 143 131

11 12 13 14 15

147 134 121 108 95.6

221 201 181 162 144

119 108 98.4 88.6 79.2

179 163 148 133 119

108 97.6 87.6 78.1 69.5

162 146 131 117 104

94.8 85.9 77.3 68.9 60.8

142 129 116 103 91.2

111 93.9 88.5 82.6 76.4 70.0

166 141 133 124 115 105

79.9 120 72.3 108 64.9 97.4 57.7 86.6 50.8 76.2

63.6 57.2 51.0 45.1 39.4

95.4 85.9 76.6 67.7 59.1

16 17 18 19 20

84.1 126 74.5 112 66.4 99.9 59.6 89.6 53.8 80.9

70.0 105 62.0 93.2 55.3 83.2 49.7 74.6 44.8 67.4

61.8 54.8 48.9 43.8 39.6

92.9 82.3 73.4 65.9 59.5

53.4 47.3 42.2 37.9 34.2

80.2 71.0 63.3 56.8 51.3

44.7 39.6 35.3 31.7 28.6

67.0 59.3 52.9 47.5 42.9

34.7 30.7 27.4 24.6 22.2

52.0 46.0 41.1 36.9 33.3

21 22 23 24 25

48.8 44.5 40.7 37.4 34.4

40.7 37.0 33.9 31.1 28.7

61.1 55.7 50.9 46.8 43.1

35.9 32.7 29.9 27.5 25.3

53.9 49.2 45.0 41.3 38.1

31.0 28.3 25.9 23.7 21.9

46.5 42.4 38.8 35.6 32.8

25.9 23.6 21.6 19.8 18.3

38.9 35.4 32.4 29.8 27.4

20.1 18.3 16.8 15.4 14.2

30.2 27.5 25.2 23.1 21.3

26.5

39.9

23.4

35.2

20.2 18.8

30.4 28.1

16.9 15.7

25.4 23.5

13.1 12.2 11.3

19.7 18.3 17.0

37.5 24.7

56.4 37.1

49.6 32.4

27.8 18.1

41.7 27.3

22.0 14.3

33.1 21.4

15.8 10.0

23.7 15.1

73.4 66.8 61.2 56.2 51.8

26 27 28

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy ASD Ωc = 2.00

45.8 30.1

kip-in.2 kip-in.2

LRFD φc = 0.75

68.8 45.2

1640 642 1.53 1.60 c

1430 560 1.58 1.60

33.0 21.6

1300 508 1.61 1.60

1160 449 1.64 1.61

977 375 1.66 1.61

766 291 1.69 1.62

Shape is noncompact for compression with Fy = 46 ksi. f Shape is noncompact for flexure with Fy = 46 ksi.

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 239

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–239

Table 4-14 (continued) Fy = 46 ksi fc′ = 5 ksi

Available Strength in Axial Compression, kips COMPOSITE HSS6

Concrete Filled Rectangular HSS HSS6× 5×

Shape

t design, in. Steel, lb/ft

Effective length, (KL )y , with respect to weak axis (ft)

Design 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

12 /

3 8 /

5 16 /

14 /

3 16 /

18 /

0.465 31.8 Pn /Ωc φc Pn ASD LRFD 246 369 245 368 243 365 239 359 234 352 228 342 221 331 212 318 203 305 194 291 184 276 174 261 163 245 152 228 141 212 130 196 119 179 109 164 98.9 149 89.1 134 80.4 121 72.9 110 66.4 99.9 60.8 91.4 55.8 83.9 51.5 77.3 47.6 71.5 44.1 66.3 41.0 61.6 38.2 57.5 35.7 53.7

0.349 24.9 Pn /Ωc φc Pn ASD LRFD 206 310 206 309 204 306 201 302 197 296 192 288 186 279 179 268 171 257 163 244 154 231 145 217 135 203 125 189 116 175 107 160 97.6 146 88.7 133 80.9 122 73.3 110 66.2 99.5 60.0 90.2 54.7 82.2 50.0 75.2 46.0 69.1 42.4 63.7 39.2 58.9 36.3 54.6 33.8 50.8 31.5 47.3 29.4 44.2

0.291 21.2 Pn /Ωc φc Pn ASD LRFD 185 278 185 277 183 275 180 271 177 265 172 259 167 250 161 241 154 231 147 220 139 208 131 196 122 183 114 170 105 158 96.6 145 88.4 133 80.3 120 72.6 109 65.1 97.7 58.8 88.2 53.3 80.0 48.6 72.9 44.4 66.7 40.8 61.2 37.6 56.4 34.8 52.2 32.3 48.4 30.0 45.0 28.0 41.9 26.1 39.2

0.233 17.3 Pn /Ωc φc Pn ASD LRFD 163 244 162 244 161 242 159 238 156 233 152 227 147 220 142 212 136 203 129 194 122 183 115 173 108 162 100 150 92.8 139 85.4 128 78.1 117 71.0 107 64.2 96.3 57.7 86.5 52.0 78.1 47.2 70.8 43.0 64.5 39.3 59.0 36.1 54.2 33.3 50.0 30.8 46.2 28.6 42.8 26.5 39.8 24.7 37.1 23.1 34.7

0.174 13.3 Pn /Ωc φc Pn ASD LRFD 139 209 139 208 138 207 136 204 133 199 129 194 125 188 121 181 115 173 110 165 104 156 97.6 146 91.2 137 84.8 127 78.3 117 71.9 108 65.7 98.5 59.6 89.4 53.7 80.6 48.2 72.3 43.5 65.3 39.5 59.2 36.0 53.9 32.9 49.3 30.2 45.3 27.8 41.8 25.7 38.6 23.9 35.8 22.2 33.3 20.7 31.0 19.3 29.0

0.116 9.01 Pn /Ωc φc Pn ASD LRFD 115 172 115 172 114 170 112 168 109 164 106 160 103 154 98.7 148 94.2 141 89.4 134 84.2 126 78.9 118 73.4 110 67.9 102 62.5 93.7 57.1 85.6 51.8 77.7 46.8 70.1 41.8 62.8 37.6 56.3 33.9 50.8 30.7 46.1 28.0 42.0 25.6 38.4 23.5 35.3 21.7 32.5 20.1 30.1 18.6 27.9 17.3 25.9 16.1 24.2 15.1 22.6

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

41.8 36.7

62.8 55.1

1330 978 1.87 1.17

34.2 29.9

51.4 45.0

1150 850 1.92 1.16

29.9 26.1

44.9 39.2

1050 772 1.95 1.17

25.2 22.0

37.9 33.0

928 684 1.98 1.16

19.9 17.3

779 571 2.01 1.17

Note: Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

30.0 26.0

14.2 12.2

21.3 18.4

608 445 2.03 1.17

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Page 240

4–240

DESIGN OF COMPRESSION MEMBERS

Table 4-14 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS6

Concrete Filled Rectangular HSS HSS6× 4×

Shape

12 /

t design, in. Steel, lb/ft

3 8 /

5 16 /

14 /

3 16 /

18 /

0.465 0.349 0.291 0.233 0.174 0.116 28.4 22.4 19.1 15.6 12.0 8.16 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

Fy = 46 ksi fc′ = 5 ksi

0

217

326

179

269

160

240

140

211

119

179

97.4

146

1 2 3 4 5

216 213 209 203 195

325 321 314 305 293

178 176 172 167 160

267 264 258 250 240

159 157 154 149 144

239 236 231 224 215

140 138 135 131 126

210 207 202 196 189

119 117 115 111 107

178 176 172 167 160

97.0 95.7 93.5 90.5 86.8

145 143 140 136 130

6 7 8 9 10

186 176 165 153 141

279 264 248 230 212

152 144 134 124 114

229 216 202 187 171

137 129 121 112 103

205 194 181 168 155

120 113 106 98.6 90.7

180 170 159 148 136

102 96.2 90.1 83.6 76.9

153 144 135 125 115

82.5 77.7 72.5 67.0 61.3

124 117 109 100 92.0

11 12 13 14 15

129 117 105 93.3 82.3

194 176 158 140 124

105 95.3 86.1 77.2 68.7

157 143 129 116 103

94.1 85.1 76.3 67.7 60.5

141 128 114 102 91.0

82.8 124 74.9 112 67.1 101 59.7 89.5 52.5 78.7

70.1 105 63.4 95.1 56.8 85.2 50.5 75.7 44.4 66.5

55.7 50.0 44.6 39.3 34.3

83.5 75.1 66.9 59.0 51.5

16 17 18 19 20

72.3 109 64.0 96.2 57.1 85.9 51.3 77.1 46.3 69.5

60.5 53.6 47.8 42.9 38.7

91.0 80.6 71.9 64.5 58.2

53.5 47.4 42.3 38.0 34.3

80.5 71.3 63.6 57.1 51.5

46.1 40.9 36.4 32.7 29.5

69.2 61.3 54.7 49.1 44.3

39.0 34.5 30.8 27.6 25.0

58.5 51.8 46.2 41.5 37.4

30.2 26.7 23.9 21.4 19.3

45.3 40.1 35.8 32.1 29.0

21 22 23 24 25

42.0 38.2 35.0 32.1 29.6

35.1 32.0 29.3 26.9 24.8

52.8 48.1 44.0 40.4 37.3

31.1 28.3 25.9 23.8 21.9

46.7 42.6 38.9 35.8 33.0

26.8 24.4 22.3 20.5 18.9

40.2 36.6 33.5 30.8 28.3

22.6 20.6 18.9 17.3 16.0

33.9 30.9 28.3 26.0 24.0

17.5 16.0 14.6 13.4 12.4

26.3 24.0 21.9 20.1 18.5

20.3

30.5

17.5

26.2

14.8 13.7

22.1 11.4 20.5 10.6

17.1 15.9

38.7 28.5

21.7 16.0

32.6 24.0

17.2 12.6

25.9 12.4 19.0 8.95

18.6 13.5

63.1 57.5 52.6 48.3 44.5

26 27

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

35.3 26.3

53.1 39.5

1080 551 1.50 1.40

29.3 21.7

44.1 32.5

950 481 1.55 1.41

25.7 19.0

865 440 1.58 1.40

770 388 1.61 1.41

654 328 1.63 1.41

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

509 254 1.66 1.42

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Page 241

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–241

Table 4-14 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 5 ksi

COMPOSITE HSS6

Concrete Filled Rectangular HSS HSS6× 3×

Shape

12 /

t design, in. Steel, lb/ft

5 16 /

14 /

3 16 /

18 /

0.465 0.349 0.291 0.233 0.174 0.116 25.0 19.8 17.0 13.9 10.7 7.31 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

3 8 /

0

191

288

152

228

135

203

118

177

99.2

149

79.9 120

1 2 3 4 5

190 186 179 169 158

286 279 268 254 237

151 147 142 135 126

226 221 213 203 190

134 131 126 120 112

201 197 189 180 168

117 115 110 105 97.8

176 172 165 157 147

98.4 96.3 92.8 88.0 82.3

148 144 139 132 123

79.3 77.5 74.5 70.6 65.9

119 116 112 106 98.8

145 131 117 102 88.4

218 197 176 154 133

117 107 96.0 85.1 74.4

176 160 144 128 112

103 92.9 83.2 74.1 65.0

154 139 125 111 97.8

90.0 135 81.6 122 72.9 109 64.1 96.2 55.6 83.4

75.9 68.9 61.6 54.3 47.1

114 103 92.4 81.4 70.7

60.5 54.7 48.7 42.7 36.9

90.8 82.1 73.1 64.1 55.4

6 7 8 9 10 11 12 13 14 15

75.2 113 63.2 95.0 53.8 80.9 46.4 69.8 40.4 60.8

64.1 54.4 46.3 39.9 34.8

96.4 81.7 69.6 60.0 52.3

56.3 48.0 40.9 35.3 30.7

84.7 72.2 61.5 53.0 46.2

48.1 41.4 35.3 30.4 26.5

72.3 62.3 53.1 45.7 39.9

40.3 34.0 28.9 24.9 21.7

60.4 50.9 43.4 37.4 32.6

31.4 26.4 22.5 19.4 16.9

47.1 39.6 33.7 29.1 25.3

16 17 18 19 20

35.5 31.5 28.1

30.6 27.1 24.2 21.7

46.0 40.7 36.3 32.6

27.0 23.9 21.4 19.2

40.6 36.0 32.1 28.8

23.3 20.6 18.4 16.5 14.9

35.0 31.0 27.7 24.8 22.4

19.1 16.9 15.1 13.5 12.2

28.6 25.4 22.6 20.3 18.3

14.8 13.1 11.7 10.5 9.49

22.2 19.7 17.6 15.8 14.2

53.4 47.3 42.2

21

8.61 12.9

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

29.1 17.2

43.7 25.8

841 261 1.12 1.80

24.2 14.4

36.4 21.6

746 232 1.17 1.79

21.3 12.7

32.1 19.1

685 213 1.19 1.79

18.1 10.7

27.3 14.5 16.1 8.52

609 189 1.22 1.80

521 161 1.25 1.80

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

21.8 10.5 15.7 12.8 6.05 9.10 410 125 1.27 1.81

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Page 242

4–242

DESIGN OF COMPRESSION MEMBERS

Table 4-14 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS5

Concrete Filled Rectangular HSS HSS5× 4×

Shape

12 /

t design, in. Steel, lb/ft

3 8 /

5 16 /

14 /

3 16 /

18 /

0.465 0.349 0.291 0.233 0.174 0.116 25.0 19.8 17.0 13.9 10.7 7.31 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

Fy = 46 ksi fc′ = 5 ksi

0

191

288

156

234

140

209

122

183

103

155

84.2

126

1 2 3 4 5

191 188 184 178 171

286 283 276 268 257

155 153 150 145 139

233 230 224 217 208

139 137 134 130 124

208 206 201 195 187

122 120 117 114 109

183 180 176 171 164

103 102 99.4 96.3 92.5

154 152 149 144 139

83.8 82.6 80.7 78.1 74.8

126 124 121 117 112

6 7 8 9 10

163 153 143 132 122

244 230 215 199 183

132 124 116 107 99.3

198 186 174 162 149

118 112 104 96.4 88.4

178 167 156 145 133

104 98.1 91.7 85.0 78.0

156 147 138 127 117

88.1 83.1 77.7 72.0 66.1

132 125 117 108 99.2

71.1 66.9 62.3 57.6 52.6

107 100 93.5 86.3 79.0

11 12 13 14 15

110 99.5 88.8 78.6 68.7

166 150 133 118 103

16 17 18 19 20

60.4 53.5 47.7 42.8 38.7

21 22 23 24 25

35.1 31.9 29.2 26.8

90.9 137 82.5 124 74.3 112 66.4 99.7 58.7 88.3

80.3 120 72.3 108 64.6 97.2 57.9 87.0 51.4 77.3

71.0 107 64.0 96.0 57.2 85.8 50.7 76.0 44.4 66.6

60.2 54.3 48.6 43.1 37.7

90.3 81.5 72.9 64.6 56.6

47.7 42.8 38.1 33.6 29.3

71.6 64.2 57.1 50.3 43.9

90.8 80.4 71.7 64.4 58.1

51.6 45.7 40.8 36.6 33.0

77.6 68.7 61.3 55.0 49.7

45.3 40.1 35.8 32.1 29.0

68.0 60.3 53.7 48.2 43.5

39.0 34.6 30.8 27.7 25.0

58.5 51.9 46.3 41.5 37.5

33.2 29.4 26.2 23.5 21.2

49.8 44.1 39.3 35.3 31.8

25.7 22.8 20.3 18.2 16.5

38.6 34.2 30.5 27.4 24.7

52.7 48.0 43.9 40.4

30.0 27.3 25.0 22.9 21.1

45.0 41.0 37.5 34.5 31.8

26.3 23.9 21.9 20.1 18.5

39.5 36.0 32.9 30.2 27.9

22.7 20.6 18.9 17.3 16.0

34.0 31.0 28.3 26.0 24.0

19.3 17.5 16.1 14.7 13.6

28.9 26.3 24.1 22.1 20.4

14.9 13.6 12.4 11.4 10.5

22.4 20.4 18.7 17.2 15.8

14.8

22.2

12.6

18.8

9.74 9.03

14.6 13.6

16.3 13.8

24.5 20.8

13.0 11.0

19.5 16.5

9.33 7.83

14.0 11.8

26 27 Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

26.2 22.3

39.4 33.5

664 459 1.46 1.20

21.9 18.6

32.9 27.9

587 404 1.52 1.21

19.3 16.3

29.0 24.5

536 368 1.54 1.21

478 328 1.57 1.21

409 279 1.60 1.21

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

317 216 1.62 1.21

AISC_Part 4D:14th Ed.

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Page 243

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–243

Table 4-14 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 5 ksi

COMPOSITE HSS5

Concrete Filled Rectangular HSS HSS5× 3×

Shape

12 /

t design, in. Steel, lb/ft

3 8 /

5 16 /

14 /

3 16 /

18 /

0.465 0.349 0.291 0.233 0.174 0.116 21.6 17.3 14.8 12.2 9.42 6.46 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

166

249

132

198

117

175

102

153

85.5

128

68.7 103

1 2 3 4 5

164 160 154 146 135

247 241 232 219 203

131 128 123 117 109

196 192 185 176 164

116 113 109 103 95.9

174 170 163 154 144

101 98.7 95.0 90.0 83.9

152 148 142 135 126

84.9 82.9 79.8 75.7 70.7

127 124 120 114 106

68.2 102 66.6 99.9 64.1 96.1 60.6 91.0 56.5 84.8

6 7 8 9 10

124 111 98.4 85.7 73.4

186 167 148 129 110

101 91.4 81.7 72.0 62.5

151 137 123 108 93.9

11 12 13 14 15

61.7 51.8 44.2 38.1 332

92.7 77.9 66.4 57.2 49.9

53.4 45.0 38.4 33.1 28.8

16 17 18 19 20

29.2 25.8 23.0

43.8 38.8 34.6

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

21.1 14.4

31.7 21.6

Effective length, (KL )y , with respect to weak axis (ft)

0

87.9 132 79.8 120 71.8 108 63.7 95.7 55.7 83.7

77.1 116 69.7 105 62.1 93.1 54.4 81.7 47.0 70.5

65.0 58.8 52.5 46.1 39.9

97.5 88.3 78.7 69.1 59.8

51.8 46.8 41.6 36.5 31.4

77.8 70.2 62.5 54.7 47.1

80.3 67.7 57.7 49.7 43.3

48.0 40.7 34.7 29.9 26.0

72.1 61.1 52.1 44.9 39.1

40.6 34.6 29.5 25.4 22.1

61.0 52.0 44.3 38.2 33.3

34.0 28.6 24.3 21.0 18.3

51.0 42.9 36.5 31.5 27.4

26.6 22.4 19.1 16.4 14.3

39.9 33.6 28.6 24.7 21.5

25.3 22.4 20.0 18.0

38.1 33.7 30.1 27.0

22.9 20.3 18.1 16.2

34.4 30.5 27.2 24.4

19.5 17.2 15.4 13.8

29.2 25.9 23.1 20.7

16.1 14.2 12.7 11.4 10.3

24.1 12.6 21.4 11.1 19.0 9.94 17.1 8.93 15.4 8.06

17.8 12.2

26.8 18.3

18.9 16.7 14.9 13.4 12.1

Properties

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

507 215 1.09 1.54

455 194 1.14 1.53

15.8 10.8

23.7 13.5 20.2 10.8 16.2 9.19 13.8 7.33

420 178 1.17 1.54

374 159 1.19 1.53

321 135 1.22 1.54

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

16.2 11.0

7.80 11.7 5.25 7.89 253 106 1.25 1.54

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DESIGN OF COMPRESSION MEMBERS

Table 4-14 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS5-HSS4

Concrete Filled Rectangular HSS HSS5× 21/2 ×

Shape

14 /

t design, in. Steel, lb/ft

HSS4× 3×

3 16 /

18 /

3 8 /

5 16 /

14 /

0.233 0.174 0.116 0.349 0.291 0.233 11.4 8.78 6.03 14.7 12.7 10.5 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

Fy = 46 ksi fc′ = 5 ksi

0

91.7

138

76.6 115

60.9

91.4 113

169

98.4

148

85.9

129

1 2 3 4 5

90.7 87.8 83.1 76.9 69.6

136 132 125 115 104

75.8 114 73.4 110 69.6 104 64.5 96.8 58.5 87.8

60.2 58.3 55.2 51.2 46.4

90.4 112 87.5 109 82.8 105 76.8 99.3 69.6 92.5

168 164 158 149 139

97.6 95.2 91.3 86.1 80.2

146 143 137 129 121

85.2 83.1 79.8 75.5 70.2

128 125 120 113 105

6 7 8 9 10

61.7 53.8 46.5 39.4 32.7

92.6 80.8 69.8 59.2 49.2

52.0 45.2 38.5 32.0 26.2

78.0 67.8 57.7 48.0 39.3

41.2 35.7 30.4 25.2 20.6

61.8 53.6 45.5 37.9 30.8

84.9 128 76.6 115 68.1 102 59.6 89.6 51.3 77.1

73.8 66.9 59.7 52.4 45.4

111 100 89.7 78.8 68.2

64.2 57.8 51.2 44.7 39.0

96.3 86.7 76.9 67.2 58.6

11 12 13 14 15

27.0 22.7 19.4 16.7 14.5

40.6 34.1 29.1 25.1 21.9

21.6 18.2 15.5 13.4 11.6

32.5 27.3 23.3 20.1 17.5

17.0 14.3 12.2 10.5 9.13

25.5 21.4 18.2 15.7 13.7

43.5 36.5 31.1 26.8 23.4

65.3 54.9 46.8 40.3 35.1

38.7 32.6 27.8 23.9 20.9

58.2 49.0 41.7 36.0 31.3

33.5 28.4 24.2 20.9 18.2

50.4 42.7 36.3 31.3 27.3

16 17 18 19

12.8

19.2 10.2 15.4 9.06 13.6

8.03 12.0 7.11 10.7

20.5 18.2 16.2

30.9 18.3 27.4 16.2 24.4 14.5

27.5 16.0 24.4 14.1 21.8 12.6 11.3

24.0 21.3 19.0 17.0

12.0 7.11

18.1 10.7

16.5 13.4

14.2 11.4

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

323 100 0.999 1.80

9.66 14.5 7.02 10.6 12.3 18.5 11.0 5.70 8.57 4.10 6.16 9.98 15.0 8.89 277 85.7 1.02 1.80

221 67.5 1.05 1.81

250 155 1.11 1.27

232 143 1.13 1.27

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.42 7.61

208 128 1.16 1.27

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Table 4-14 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 5 ksi

COMPOSITE HSS4

Concrete Filled Rectangular HSS 3 16 /

t design, in. Steel, lb/ft

18 /

3 8 /

5 16 /

14 /

3 16 /

0.174 0.116 0.349 0.291 0.233 0.174 8.15 5.61 13.4 11.6 9.66 7.51 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, (KL )y , with respect to weak axis (ft)

HSS4× 21/2 ×

HSS4× 3×

Shape

0

72.0 108

57.6

86.3 103

155

89.0

134

76.6 115

64.0

96.0

1 2 3 4 5

71.5 107 69.8 105 67.1 101 63.5 95.2 59.1 88.7

57.1 55.7 53.6 50.7 47.1

85.7 102 83.6 98.4 80.3 93.0 76.0 85.8 70.7 77.5

153 148 140 129 116

88.0 85.2 80.7 74.8 67.9

132 128 121 112 102

75.7 114 73.2 110 69.1 104 63.8 95.7 57.6 86.3

63.3 61.2 57.9 53.6 48.5

95.0 91.9 86.9 80.4 72.7

6 7 8 9 10

54.2 48.9 43.5 38.0 32.8

81.3 73.4 65.2 57.0 49.1

43.2 38.9 34.5 30.1 25.9

64.8 58.4 51.8 45.2 38.9

68.4 103 58.9 88.6 49.7 74.7 40.9 61.5 33.2 49.9

60.3 52.4 44.6 37.1 30.2

90.6 78.8 67.0 55.7 45.4

50.9 44.5 38.2 32.1 26.4

76.5 67.0 57.4 48.3 39.7

42.9 37.1 31.4 26.0 21.5

64.3 55.7 47.1 39.0 32.3

11 12 13 14 15

27.7 23.3 19.8 17.1 14.9

41.5 34.9 29.7 25.6 22.3

21.9 18.4 15.7 13.5 11.8

32.8 27.6 23.5 20.3 17.6

27.4 23.0 19.6 16.9 14.7

25.0 21.0 17.9 15.4 13.4

37.6 31.6 26.9 23.2 20.2

21.8 18.3 15.6 13.5 11.7

32.8 27.5 23.5 20.2 17.6

17.7 14.9 12.7 10.9 9.54

26.7 22.4 19.1 16.5 14.3

16 17 18 19 20

13.1 11.6 10.3 9.28

19.6 10.3 17.4 9.16 15.5 8.17 13.9 7.33 6.62

10.3

15.5

41.2 34.6 29.5 25.4 22.2

15.5 13.7 12.3 11.0 9.92

8.38 12.6

Properties

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

7.58 11.4 5.52 6.11 9.18 4.41 178 110 1.19 1.27

8.29 10.7 16.2 6.63 7.58 11.4

141 86.9 1.21 1.27

212 96.1 0.922 1.49

9.63 6.80

14.5 10.2

197 89.5 0.947 1.48

8.32 12.5 6.72 10.1 5.87 8.82 4.73 7.11 178 80.9 0.973 1.48

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

153 69.4 0.999 1.48

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DESIGN OF COMPRESSION MEMBERS

Table 4-14 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS4

Fy = 46 ksi fc′ = 5 ksi

Concrete Filled Rectangular HSS HSS4× 21/2 ×

Shape

HSS4× 2×

1 8 /

t design, in. Steel, lb/ft

3 8 /

5 16 /

14 /

3 16 /

1 8 /

0.116 0.349 0.291 0.233 0.174 0.116 5.18 12.2 10.6 8.81 6.87 4.75 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

50.8

76.2

93.4 140

81.0 122

67.5 101

56.2

84.4

44.0

66.0

1 2 3 4 5

50.2 48.6 46.0 42.5 38.5

75.3 72.9 68.9 63.8 57.7

91.7 86.8 79.2 69.7 59.2

138 130 119 105 89.0

79.6 120 75.6 114 69.5 104 61.7 92.7 52.9 79.5

66.4 63.0 58.2 52.1 45.1

99.5 94.8 87.5 78.2 67.8

55.3 52.5 48.2 42.8 36.7

82.9 78.8 72.3 64.1 55.0

43.3 41.2 37.9 33.7 29.0

64.9 61.8 56.8 50.5 43.4

6 7 8 9 10

34.0 29.5 24.9 20.6 16.8

51.1 44.2 37.4 31.0 25.2

48.4 38.2 29.4 23.2 18.8

72.8 57.5 44.2 34.9 28.3

43.9 35.1 27.3 21.5 17.4

37.8 30.7 24.1 19.1 15.5

56.9 46.2 36.3 28.7 23.2

30.4 25.0 19.9 15.7 12.8

45.6 37.5 29.9 23.7 19.2

24.1 19.4 15.1 11.9 9.65

36.1 29.1 22.6 17.9 14.5

11 12 13 14 15

13.9 11.7 9.93 8.56 7.46

20.8 17.5 14.9 12.8 11.2

15.5 13.1

23.4 14.4 19.6 12.1

16 17

6.55 5.81

9.83 8.71

Mnx /Ωb φb Mnx kip-ft Mny /Ωb φb Mny kip-ft

4.90 3.42

7.37 5.13

Effective length, (KL )y , with respect to weak axis (ft)

0

65.9 52.8 41.0 32.4 26.2

21.7 12.8 18.2 10.7

19.2 10.5 15.8 16.1 8.86 13.3 7.55 11.3

7.98 12.0 6.70 10.1 5.71 8.57

Properties

Pex (Kx Lx )2/104 Pey (Ky Ly )2/104 rmy , in. rmx /rmy

kip-in.2 kip-in.2

ASD

LRFD

Ωc = 2.00

φc = 0.75

123 55.1 1.03 1.49

9.16 13.8 8.27 12.4 7.19 10.8 5.85 5.42 8.15 4.92 7.39 4.27 6.42 3.46 173 53.5 0.729 1.80

163 50.5 0.754 1.80

148 46.0 0.779 1.79

128 39.6 0.804 1.80

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

8.79 5.20

4.30 2.52

6.47 3.79

103 31.7 0.830 1.80

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–247

Table 4-15

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

Concrete Filled Square HSS HSS16× 16×

Shape

12 /

t design, in. Steel, lb/ft

HSS14× 14× 5 16 /

5 8 /

12 /

3 8 /

0.465 0.349 0.291 0.581 0.465 0.349 103 78.5 65.9 110 89.7 68.3 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design 0

Effective length, KL (ft)

3 8 /

COMPOSITE HSS16-HSS14

1040 1550

892

1340

820

1230

977

1460

856

1280

731

1100

6 7 8 9 10

1030 1020 1020 1010 1010

1540 1530 1530 1520 1510

883 880 876 872 867

1320 1320 1310 1310 1300

812 808 805 801 796

1220 1210 1210 1200 1190

964 959 954 948 942

1450 1440 1430 1420 1410

845 841 836 831 825

1270 1260 1250 1250 1240

721 717 713 709 704

1080 1080 1070 1060 1060

11 12 13 14 15

1000 996 989 981 973

1500 1490 1480 1470 1460

862 856 850 843 836

1290 1280 1270 1260 1250

791 786 780 774 767

1190 1180 1170 1160 1150

935 927 919 910 901

1400 1390 1380 1360 1350

819 812 805 797 789

1230 1220 1210 1200 1180

698 693 686 679 672

1050 1040 1030 1020 1010

16 17 18 19 20

965 956 946 937 926

1450 1430 1420 1410 1390

828 821 812 804 795

1240 1230 1220 1210 1190

760 753 745 737 728

1140 1130 1120 1100 1090

891 880 869 857 845

1340 1320 1300 1290 1270

780 771 761 751 740

1170 1160 1140 1130 1110

664 656 648 639 629

996 984 971 958 944

21 22 23 24 25

916 905 894 882 870

1370 1360 1340 1320 1300

785 775 765 755 744

1180 1160 1150 1130 1120

719 710 701 691 681

1080 1070 1050 1040 1020

833 820 807 793 780

1250 1230 1210 1190 1170

729 718 706 694 682

1090 1080 1060 1040 1020

620 610 600 589 579

930 915 900 884 868

26 27 28 29 30

857 845 832 819 805

1290 1270 1250 1230 1210

733 722 711 699 687

1100 1080 1070 1050 1030

671 660 649 638 627

1010 990 974 958 941

765 751 736 721 706

1150 1130 1100 1080 1060

669 657 644 630 617

1000 985 965 946 926

568 557 545 534 522

852 835 818 801 784

32 34 36 38 40

778 749 720 691 661

1170 1120 1080 1040 992

663 638 613 587 561

994 957 919 880 841

605 581 557 533 509

907 872 836 800 764

675 644 612 580 549

1010 966 918 870 823

590 562 534 506 478

885 843 802 760 718

499 475 451 426 402

748 712 676 640 604

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

422 634 44500

331 498 37100

283 425 33200

378 569 32700

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

316 475 28400

248 373 23600

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4–248

DESIGN OF COMPRESSION MEMBERS

Table 4-15 (continued)

COMPOSITE HSS14-HSS12

HSS12× 12×

5 16 /

t design, in. Steel, lb/ft

Fy = 46 ksi fc′ = 4 ksi

Concrete Filled Square HSS HSS14× 14×

Shape

5 8 /

12 /

3 8 /

5 16 /

14 /

0.291 0.581 0.465 0.349 0.291 0.233 57.4 93.3 76.1 58.1 48.9 39.4 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Available Strength in Axial Compression, kips

0

667

1000

790

1190

689

1030

585

877

530

795

474

712

6 7 8 9 10

658 655 651 647 642

987 982 976 970 963

776 771 766 759 752

1160 1160 1150 1140 1130

677 672 667 662 656

1010 1010 1000 993 984

575 571 567 562 556

862 856 850 843 835

520 517 513 508 503

780 775 769 762 755

466 462 459 455 450

698 694 688 682 675

11 12 13 14 15

637 631 625 619 612

955 947 938 929 918

744 736 727 717 707

1120 1100 1090 1080 1060

649 642 634 626 617

973 963 951 938 925

551 544 537 530 523

826 816 806 795 784

498 492 486 479 472

747 738 729 719 709

445 440 434 428 422

668 660 651 642 633

16 17 18 19 20

605 597 590 581 573

908 896 884 872 859

696 685 673 661 648

1040 1030 1010 991 972

607 598 587 577 566

911 896 881 865 849

515 506 497 488 479

772 759 746 732 718

465 457 449 441 432

697 686 674 661 648

415 408 400 393 385

622 612 601 589 577

21 22 23 24 25

564 555 545 536 526

846 832 818 803 788

635 622 608 594 580

953 933 912 891 870

555 543 531 519 507

832 815 797 779 760

469 459 449 438 428

703 688 673 657 641

423 414 405 395 385

635 621 607 593 578

377 368 360 351 342

565 552 539 526 513

26 27 28 29 30

516 505 495 484 473

773 758 742 726 710

565 551 536 521 506

848 826 804 781 759

494 482 469 456 443

741 722 703 684 664

417 406 395 384 373

625 609 592 576 559

375 365 355 345 335

563 548 533 518 502

333 324 315 305 296

499 486 472 458 444

32 34 36 38 40

451 429 407 385 363

677 644 611 577 544

476 446 416 386 358

714 669 624 580 537

417 390 365 339 314

625 586 547 508 471

350 328 305 284 262

525 491 458 425 393

314 294 274 254 234

472 441 411 381 352

277 259 240 223 205

416 388 361 334 308

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

212 319 21100

270 406 19200

226 339 16900

178 268 14100

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

153 230 12500

126 190 10900

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–249

Table 4-15 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

Concrete Filled Square HSS HSS10× 10×

Shape

5 8 /

t design, in. Steel, lb/ft

12 /

3 8 /

5 16 /

14 /

3 16 /

0.581 0.465 0.349 0.291 0.233 0.174 76.3 62.5 47.9 40.4 32.6 24.7 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

COMPOSITE HSS10

0

615

923

535

803

451

676

406

609 361

541 314

471

6 7 8 9 10

599 594 587 580 572

899 891 881 870 859

522 517 511 505 498

782 775 767 758 748

439 435 430 425 420

659 653 646 638 629

396 392 388 383 378

593 588 581 574 567

351 348 344 340 335

527 522 516 509 502

305 302 299 295 291

458 453 448 442 436

11 12 13 14 15

564 554 545 534 523

846 832 817 801 784

491 483 474 465 456

736 725 712 698 684

413 407 399 392 384

620 610 599 588 576

372 366 359 352 345

558 549 539 529 518

330 324 318 312 305

495 486 477 468 458

286 281 276 270 264

429 421 413 405 396

16 17 18 19 20

511 499 487 474 461

767 749 730 711 691

446 436 425 414 403

669 653 637 621 604

376 367 358 348 339

563 550 537 523 508

337 330 321 313 304

506 494 482 469 456

298 291 284 276 268

448 437 426 414 402

258 251 245 238 231

387 377 367 357 346

21 22 23 24 25

447 434 420 406 392

671 650 630 609 587

391 379 367 355 343

587 569 551 533 515

329 319 309 299 289

494 479 464 449 433

295 286 277 268 259

443 429 416 402 388

260 252 244 236 227

390 378 366 353 341

224 216 209 202 194

335 325 313 302 291

26 27 28 29 30

377 363 349 335 321

566 545 524 503 482

331 319 306 294 282

496 478 459 441 423

279 268 258 248 238

418 402 387 372 356

249 240 230 221 212

374 360 346 332 318

219 210 202 194 185

328 316 303 291 278

187 179 172 164 157

280 269 258 247 236

32 34 36 38 40

294 267 242 219 198

440 400 364 329 297

258 235 213 191 173

387 353 319 287 259

217 198 179 161 145

326 297 269 242 218

194 176 159 143 129

291 264 239 214 193

169 153 138 124 112

254 230 207 186 168

143 129 116 104 93.7

214 194 173 156 141

Properties φb Mn kip-ft 179 270 151 227 120 180 103 155 85.5 129 Pe (KL )2/104 kip-in.2 10300 9070 7640 6780 5880 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

66.3 99.7 4920

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4–250

DESIGN OF COMPRESSION MEMBERS

Table 4-15 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS9

Concrete Filled Square HSS HSS9× 9×

Shape

5 8 /

t design, in. Steel, lb/ft

12 /

3 8 /

5 16 /

14 /

3 16 /

0.581 0.465 0.349 0.291 0.233 0.174 67.8 55.7 42.8 36.1 29.2 22.2 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 46 ksi fc′ = 4 ksi

0

534

801

462

693 388

583 349

523 308

463 267

400

6 7 8 9 10

517 511 504 496 488

776 766 756 745 732

448 443 437 430 423

672 664 655 646 635

376 372 367 362 356

565 558 551 543 534

338 334 329 324 319

506 501 494 487 479

299 295 291 287 282

448 443 437 430 423

258 255 251 247 243

387 382 377 371 364

11 12 13 14 15

479 469 459 448 436

718 704 688 671 654

416 407 398 389 379

623 611 598 583 569

349 343 335 327 319

524 514 503 491 479

313 307 300 293 286

470 460 450 440 429

277 271 265 259 252

415 406 397 388 378

238 233 228 222 216

357 350 342 333 324

16 17 18 19 20

424 412 399 386 372

636 617 598 579 559

369 358 347 336 325

553 538 521 505 487

311 302 293 283 274

466 453 439 425 411

278 270 262 254 245

417 405 393 380 367

245 238 230 223 215

367 357 346 334 323

210 204 197 190 184

315 305 296 286 275

21 22 23 24 25

359 345 332 318 305

538 518 497 478 459

313 302 290 278 267

470 453 435 417 400

264 255 245 235 225

396 382 367 352 338

236 227 219 210 201

354 341 328 315 301

207 200 192 184 176

311 299 287 276 264

177 170 163 156 149

265 255 244 234 223

26 27 28 29 30

292 280 267 255 242

439 420 401 383 364

255 243 232 220 209

382 365 348 331 314

215 206 196 186 177

323 308 294 280 266

192 183 175 166 158

288 275 262 249 236

168 160 152 145 137

252 240 229 217 206

142 135 128 122 115

213 203 192 182 173

32 34 36 38 40

218 195 174 156 141

328 293 262 235 212

188 167 149 133 120

281 250 223 200 181

159 141 126 113 102

238 212 189 170 153

141 126 112 100 90.7

212 123 188 109 168 97.1 151 87.2 136 78.7

184 102 163 90.7 146 80.9 131 72.6 118 65.5

154 136 121 109 98.3

Properties φb Mn kip-ft 142 213 120 180 95.2 143 81.9 123 68.0 102 Pe (KL )2/104 kip-in.2 7140 6330 5360 4770 4130 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

53.1 79.8 3440

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10:52 AM

Page 251

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–251

Table 4-15 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

COMPOSITE HSS8

Concrete Filled Square HSS HSS8× 8×

Shape

5 8 /

12 /

3 8 /

5 16 /

14 /

0.581 59.3 Pn /Ωc φc Pn ASD LRFD

0.465 48.9 Pn /Ωc φc Pn ASD LRFD

0.349 37.7 Pn /Ωc φc Pn ASD LRFD

0.291 31.8 Pn /Ωc φc Pn ASD LRFD

0.233 25.8 Pn /Ωc φc Pn ASD LRFD

0

456

684

395

593

330

494

295

442

260

390

6 7 8 9 10

438 431 424 415 406

656 646 635 623 609

379 374 368 361 353

569 561 551 541 529

317 312 307 301 295

475 468 461 452 443

283 279 275 270 264

425 419 412 404 396

249 246 242 237 232

374 369 363 356 348

11 12 13 14 15

396 386 376 365 354

596 581 565 549 532

345 336 326 317 306

517 504 490 475 460

288 281 273 265 257

433 422 410 398 386

258 251 245 237 230

387 377 367 356 345

227 221 215 208 202

340 331 322 312 302

16 17 18 19 20

342 330 318 306 293

514 496 478 459 440

296 285 274 263 251

444 428 411 394 377

248 239 230 221 212

373 359 346 332 318

222 214 206 198 189

333 321 309 297 284

195 188 180 173 166

292 281 271 260 248

21 22 23 24 25

280 267 255 242 230

421 402 383 364 345

240 229 217 206 195

360 343 326 309 293

202 193 184 174 165

304 290 275 262 248

181 172 164 156 148

271 259 246 234 221

158 151 143 136 129

237 226 215 204 193

26 27 28 29 30

217 205 193 182 170

326 308 290 273 256

184 173 163 154 145

276 260 246 231 217

156 147 139 130 122

234 221 208 195 182

139 131 124 116 109

209 197 186 174 163

121 114 108 101 94.2

182 172 161 151 141

32 34 36 38 40

149 132 118 106 95.6

225 199 177 159 144

127 113 100 90.2 81.4

191 169 151 136 122

107 94.6 84.4 75.8 68.4

160 142 127 114 103

t design, in. Steel, lb/ft

Effective length, KL (ft)

Design

95.4 84.5 75.4 67.7 61.1

143 127 113 101 91.6

82.8 73.3 65.4 58.7 53.0

124 110 98.1 88.0 79.4

Properties φb Mn kip-ft 108 163 91.9 138 73.4 110 63.5 95.4 Pe (KL )2/104 kip-in.2 4730 4220 3590 3210 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

52.7 79.3 2780

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10:52 AM

Page 252

4–252

DESIGN OF COMPRESSION MEMBERS

Table 4-15 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS8-HSS7

Concrete Filled Square HSS HSS8× 8×

Shape

HSS7× 7×

3 16 /

5 8 /

12 /

3 8 /

5 16 /

0.174 19.6 Pn /Ωc φc Pn ASD LRFD

0.581 50.8 Pn /Ωc φc Pn ASD LRFD

0.465 42.1 Pn /Ωc φc Pn ASD LRFD

0.349 32.6 Pn /Ωc φc Pn ASD LRFD

0.291 27.6 Pn /Ωc φc Pn ASD LRFD

0

223

335

386

580

329

494

274

410

244

367

6 7 8 9 10

214 211 207 203 199

321 316 311 304 298

366 359 351 343 333

550 540 528 515 501

312 306 299 292 283

468 459 449 437 425

260 255 249 243 237

390 382 374 365 355

232 228 223 218 212

348 342 334 326 317

11 12 13 14 15

194 189 183 178 172

291 283 275 266 258

323 313 302 290 278

486 470 453 436 418

275 265 256 245 235

412 398 383 368 352

229 222 214 206 197

344 333 321 309 296

205 199 192 184 177

308 298 287 276 265

16 17 18 19 20

166 159 153 147 140

248 239 230 220 210

266 253 241 228 215

399 381 362 343 324

224 214 203 193 182

337 320 305 290 274

188 180 171 162 153

283 269 256 243 229

169 161 153 145 137

253 242 230 218 206

21 22 23 24 25

134 127 121 114 108

200 191 181 171 162

203 191 179 167 155

305 287 268 251 233

172 162 152 143 133

259 244 229 214 200

144 135 127 118 110

216 203 190 177 165

129 122 114 106 99.2

194 182 171 160 149

26 27 28 29 30

102 95.6 89.6 83.7 78.2

152 143 134 126 117

144 133 124 116 108

216 201 186 174 162

124 115 107 99.6 93.1

186 173 161 150 140

102 94.6 88.0 82.0 76.6

153 142 132 123 115

92.0 85.3 79.3 73.9 69.1

138 128 119 111 104

32 34 36 38 40

68.8 60.9 54.3 48.8 44.0

101 89.5 79.8 71.6 64.7

60.7 53.8 48.0 43.1 38.9

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 46 ksi fc′ = 4 ksi

103 91.4 81.5 73.1 66.0

95.0 84.1 75.1 67.4 60.8

143 126 113 101 91.4

81.8 72.4 64.6 58.0 52.3

123 109 97.1 87.2 78.7

67.4 59.7 53.2 47.8 43.1

91.1 80.7 72.0 64.6 58.3

Properties φb Mn kip-ft 41.3 62.0 79.5 120 67.9 102 54.7 82.2 Pe (KL )2/104 kip-in.2 2310 2970 2650 2270 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

47.4 71.2 2040

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10:52 AM

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–253

Table 4-15 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

COMPOSITE HSS7-HSS6

Concrete Filled Square HSS HSS7× 7×

Shape

3 16 /

1 8 c,f /

5 8 /

12 /

0.233 22.4 Pn /Ωc φc Pn ASD LRFD

0.174 17.1 Pn /Ωc φc Pn ASD LRFD

0.116 11.6 Pn /Ωc φc Pn ASD LRFD

0.581 42.3 Pn /Ωc φc Pn ASD LRFD

0.465 35.2 Pn /Ωc φc Pn ASD LRFD

0

214

322

183

274

151

226

322

484

268

403

6 7 8 9 10

203 200 195 191 185

305 299 293 286 278

173 170 166 162 157

260 255 249 243 236

142 139 136 132 129

213 209 204 199 193

299 291 283 273 262

450 438 425 410 394

250 244 237 229 221

376 367 356 344 332

11 12 13 14 15

180 174 168 161 155

270 261 251 242 232

152 147 142 136 131

229 221 213 204 196

124 120 115 110 106

187 180 173 166 158

251 240 228 215 203

378 360 342 324 305

212 203 193 183 173

319 305 290 275 260

16 17 18 19 20

148 141 134 127 120

222 211 201 190 180

125 119 113 107 100

187 178 169 160 151

100 95.4 90.2 85.1 80.0

151 143 135 128 120

190 178 165 153 142

286 267 249 231 213

163 153 143 133 123

245 230 215 200 185

21 22 23 24 25

113 106 99.3 92.7 86.3

169 159 149 139 130

94.5 88.7 82.9 77.3 71.8

142 133 124 116 108

75.0 70.1 65.3 60.6 56.0

113 105 97.9 90.9 84.0

130 119 109 99.8 92.0

196 179 163 150 138

114 104 95.6 87.8 80.9

171 157 144 132 122

26 27 28 29 30

80.0 74.2 69.0 64.3 60.1

120 111 103 96.5 90.1

66.4 61.6 57.3 53.4 49.9

99.6 92.4 85.9 80.1 74.8

51.8 48.0 44.6 41.6 38.9

77.6 72.0 66.9 62.4 58.3

85.1 78.9 73.4 68.4 63.9

128 119 110 103 96.0

74.8 69.4 64.5 60.1 56.2

112 104 96.9 90.4 84.4

32 34 36 38 40

52.8 46.8 41.7 37.5 33.8

79.2 70.2 62.6 56.2 50.7

43.8 38.8 34.6 31.1 28.1

65.8 58.3 52.0 46.6 42.1

34.2 30.3 27.0 24.2 21.9

51.2 45.4 40.5 36.3 32.8

56.2 49.7 44.4

84.4 74.8 66.7

49.4 43.7 39.0

74.2 65.7 58.6

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

HSS6× 6×

14 /

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

39.5 59.3 1780 c

31.0 46.6 1470

21.7 32.7 1150

55.3 83.2 1720

47.8 71.8 1550

Shape is noncompact for compression with Fy = 46 ksi. f Shape is noncompact for flexure with Fy = 46 ksi.

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 254

4–254

DESIGN OF COMPRESSION MEMBERS

Table 4-15 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS6

Concrete Filled Square HSS HSS6× 6×

Shape

3 8 /

5 16 /

14 /

3 16 /

18 /

0.349 27.5 Pn /Ωc φc Pn ASD LRFD

0.291 23.3 Pn /Ωc φc Pn ASD LRFD

0.233 19.0 Pn /Ωc φc Pn ASD LRFD

0.174 14.5 Pn /Ωc φc Pn ASD LRFD

0.116 9.86 Pn /Ωc φc Pn ASD LRFD

0

222

333

198

297

173

259

146

219

119

178

6 7 8 9 10

206 201 195 189 182

310 302 293 283 272

184 179 174 168 162

276 269 261 253 243

161 157 152 147 142

241 235 228 221 213

136 132 128 124 119

204 198 192 186 179

110 107 104 100 96.2

165 161 156 150 144

11 12 13 14 15

174 166 158 150 141

261 249 237 225 212

156 149 141 134 127

233 223 212 201 190

136 130 124 117 111

204 195 186 176 166

114 109 104 98.5 93.0

172 164 156 148 139

92.0 87.7 83.2 78.7 74.0

138 132 125 118 111

16 17 18 19 20

133 124 116 108 99.4

199 186 174 161 149

119 112 104 96.7 89.5

179 167 156 145 134

104 97.7 91.3 84.8 78.6

156 147 137 127 118

87.4 81.8 76.3 70.8 65.5

131 123 114 106 98.2

69.4 64.7 60.1 55.6 51.3

104 97.1 90.2 83.5 76.9

21 22 23 24 25

91.8 84.7 77.8 71.4 65.8

138 127 117 107 98.9

82.5 75.7 69.2 63.6 58.6

124 114 104 95.4 87.9

72.5 66.6 60.9 55.9 51.5

109 99.8 91.4 83.9 77.3

60.3 55.3 50.6 46.4 42.8

90.5 82.9 75.9 69.7 64.2

47.0 42.9 39.3 36.0 33.2

70.6 64.4 58.9 54.1 49.8

26 27 28 29 30

60.8 56.4 52.5 48.9 45.7

91.4 84.8 78.8 73.5 68.7

54.2 50.2 46.7 43.6 40.7

81.3 75.4 70.1 65.3 61.0

47.7 44.2 41.1 38.3 35.8

71.5 66.3 61.6 57.5 53.7

39.6 36.7 34.1 31.8 29.7

59.4 55.0 51.2 47.7 44.6

30.7 28.5 26.5 24.7 23.1

46.1 42.7 39.7 37.0 34.6

32 34 36 38

40.2 35.6 31.7 28.5

60.4 53.5 47.7 42.8

35.8 31.7 28.3 25.4

53.7 47.5 42.4 38.1

31.5 27.9 24.9 22.3

47.2 41.8 37.3 33.5

26.1 23.1 20.6 18.5

39.2 34.7 31.0 27.8

20.3 18.0 16.0 14.4

30.4 26.9 24.0 21.6

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 46 ksi fc′ = 4 ksi

Properties φb Mn kip-ft 38.7 58.2 33.7 50.7 28.2 42.4 22.2 33.4 Pe (KL )2/104 kip-in.2 1330 1200 1060 879 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

15.7 23.6 682

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10:52 AM

Page 255

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–255

Table 4-15 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

Concrete Filled Square HSS HSS51/2 × 51/2 ×

Shape

3 8 /

t design, in. Steel, lb/ft

5 16 /

HSS5× 5×

14 /

3 16 /

1 8 /

12 /

0.349 0.291 0.233 0.174 0.116 0.465 24.9 21.2 17.3 13.3 9.01 28.4 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

COMPOSITE HSS51/2 -HSS5

0

197

296

176

263

153

229

129

193

104

156

217

326

1 2 3 4 5

197 195 193 190 186

295 293 290 285 279

175 174 172 169 165

263 261 258 253 248

152 151 150 147 144

229 227 224 221 216

128 127 126 124 121

192 191 189 186 182

103 103 101 99.7 97.5

155 154 152 150 146

216 215 211 207 202

325 322 318 311 303

6 7 8 9 10

181 175 169 162 155

271 263 254 243 232

161 156 151 145 138

242 234 226 217 208

140 136 131 126 121

211 204 197 189 181

118 115 111 106 102

177 172 166 159 152

94.9 91.9 88.6 84.9 81.0

142 138 133 127 122

195 188 180 171 162

294 283 271 257 244

11 12 13 14 15

147 139 131 123 115

221 209 197 184 172

132 125 118 110 103

198 187 176 165 154

115 109 103 96.5 90.2

173 164 154 145 135

145 137 129 121 113

76.9 115 72.7 109 68.3 103 63.9 95.9 59.5 89.3

152 142 132 122 112

229 214 199 184 169

16 17 18 19 20

107 99.2 91.7 84.5 77.4

161 149 138 127 116

95.6 88.4 81.3 74.5 67.8

143 133 122 112 102

96.6 91.5 86.3 80.9 75.6

83.9 126 77.6 116 71.5 107 65.6 98.4 59.9 89.8

70.2 105 65.0 97.5 59.8 89.7 54.8 82.2 50.0 74.9

55.1 50.8 46.6 42.5 38.5

82.7 103 76.2 93.2 69.9 84.1 63.8 75.5 57.8 68.1

154 140 126 113 102

21 22 23 24 25

70.5 106 64.2 96.5 58.7 88.3 53.9 81.1 49.7 74.7

61.6 56.2 51.4 47.2 43.5

92.7 84.4 77.2 70.9 65.4

54.3 49.5 45.3 41.6 38.3

81.4 74.2 67.9 62.3 57.5

45.3 41.3 37.8 34.7 32.0

68.0 61.9 56.7 52.0 48.0

35.0 31.9 29.1 26.8 24.7

52.4 47.8 43.7 40.1 37.0

61.8 56.3 51.5 47.3 43.6

92.9 84.6 77.4 71.1 65.5

26 27 28 29 30

46.0 42.6 39.6 36.9 34.5

40.2 37.3 34.7 32.3 30.2

60.4 56.0 52.1 48.6 45.4

35.4 32.8 30.5 28.5 26.6

53.1 49.3 45.8 42.7 39.9

29.6 27.4 25.5 23.8 22.2

44.3 41.1 38.2 35.6 33.3

22.8 21.1 19.7 18.3 17.1

34.2 31.7 29.5 27.5 25.7

40.3 37.4 34.8 32.4 30.3

60.6 56.2 52.2 48.7 45.5

69.1 64.1 59.6 55.5 51.9

Properties φb Mn kip-ft 31.9 48.0 27.9 41.9 23.3 35.1 18.4 27.6 13.0 19.6 Pe (KL )2/104 kip-in.2 986 891 786 656 506 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

31.3 47.0 813

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Page 256

4–256

DESIGN OF COMPRESSION MEMBERS

Table 4-15 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS5

Concrete Filled Square HSS HSS5× 5×

Shape

3 8 /

5 16 /

14 /

3 16 /

18 /

0.349 22.4 Pn /Ωc φc Pn ASD LRFD

0.291 19.1 Pn /Ωc φc Pn ASD LRFD

0.233 15.6 Pn /Ωc φc Pn ASD LRFD

0.174 12.0 Pn /Ωc φc Pn ASD LRFD

0.116 8.16 Pn /Ωc φc Pn ASD LRFD

0

173

260

154

231

134

201

112

168

89.9

135

1 2 3 4 5

173 171 169 165 161

259 257 253 248 242

154 152 150 147 143

230 228 225 221 215

133 132 130 128 125

200 198 196 192 187

112 111 109 107 104

168 166 164 161 157

89.7 88.9 87.6 85.8 83.5

134 133 131 129 125

6 7 8 9 10

156 150 144 137 129

234 225 215 205 194

139 134 128 122 115

208 200 192 183 173

121 116 111 106 101

181 175 167 159 151

101 97.6 93.5 89.1 84.5

152 146 140 134 127

80.9 77.8 74.4 70.8 66.9

121 117 112 106 100

11 12 13 14 15

122 114 107 98.9 91.3

183 172 160 149 137

109 102 94.4 87.3 80.3

163 152 142 131 120

94.8 88.8 82.7 76.6 70.5

142 133 124 115 106

79.6 74.5 69.4 64.3 59.2

119 112 104 96.5 88.8

62.9 58.8 54.6 50.4 46.3

94.4 88.2 81.9 75.6 69.4

16 17 18 19 20

83.8 76.4 69.4 62.5 56.4

126 115 104 93.9 84.8

73.4 66.7 60.7 54.9 49.6

110 100 91.3 82.5 74.5

64.5 58.8 53.2 47.8 43.1

96.8 88.1 79.8 71.7 64.7

54.2 49.4 44.7 40.2 36.3

81.4 74.1 67.1 60.3 54.4

42.2 38.3 34.5 31.0 28.0

63.4 57.5 51.8 46.5 41.9

21 22 23 24 25

51.2 46.6 42.6 39.2 36.1

76.9 70.0 64.1 58.9 54.2

44.9 41.0 37.5 34.4 31.7

67.6 61.5 56.3 51.7 47.7

39.1 35.6 32.6 29.9 27.6

58.7 53.5 48.9 44.9 41.4

32.9 30.0 27.4 25.2 23.2

49.3 45.0 41.1 37.8 34.8

25.4 23.1 21.1 19.4 17.9

38.0 34.7 31.7 29.1 26.8

26 27 28 29 30

33.4 30.9 28.8 26.8 25.1

50.2 46.5 43.2 40.3 37.7

29.3 27.2 25.3 23.6 22.0

44.1 40.9 38.0 35.4 33.1

25.5 23.7 22.0 20.5 19.2

38.3 35.5 33.0 30.8 28.8

21.5 19.9 18.5 17.2 16.1

32.2 29.8 27.8 25.9 24.2

16.5 15.3 14.3 13.3 12.4

24.8 23.0 21.4 19.9 18.6

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 46 ksi fc′ = 4 ksi

Properties φb Mn kip-ft 25.7 38.6 22.5 33.7 18.9 28.4 14.9 22.5 Pe (KL )2/104 kip-in.2 708 641 566 476 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

10.6 16.0 367

AISC_Part 4E:14th Ed.

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10:53 AM

Page 257

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–257

Table 4-15 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

COMPOSITE HSS41/2

Concrete Filled Square HSS HSS41/2 × 41/2 ×

Shape

12 /

t design, in. Steel, lb/ft

5 16 /

14 /

3 16 /

1 8 /

0.465 0.349 0.291 0.233 0.174 0.116 25.0 19.8 17.0 13.9 10.7 7.31 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

3 8 /

0

191

288

151

227

134

200

116

174

96.7 145

76.9

115

1 2 3 4 5

191 189 185 180 174

287 283 278 271 262

150 149 146 143 138

226 224 220 215 208

133 132 129 126 122

200 198 194 189 183

115 114 112 110 106

173 171 168 164 159

96.3 95.3 93.7 91.4 88.6

144 143 140 137 133

76.7 75.8 74.5 72.6 70.3

115 114 112 109 105

6 7 8 9 10

167 159 151 141 132

252 240 227 213 198

133 127 121 114 107

200 191 182 171 160

117 112 106 99.8 93.2

176 168 159 150 140

102 97.4 92.4 87.0 81.3

153 146 139 130 122

85.2 81.5 77.3 72.9 68.2

128 122 116 109 102

67.6 64.5 61.1 57.5 53.7

101 96.8 91.7 86.2 80.5

11 12 13 14 15

122 112 102 92.0 82.6

183 168 153 138 124

149 138 126 115 104

86.4 79.6 73.2 66.8 60.6

130 120 110 100 91.1

99.2 91.5 83.9 76.4 69.1

75.5 113 69.6 104 63.7 95.5 57.9 86.8 52.2 78.3

63.4 58.5 53.6 48.8 44.1

95.0 87.7 80.4 73.2 66.1

49.8 45.8 41.9 38.0 34.2

74.7 68.7 62.8 57.0 51.3

16 17 18 19 20

73.5 110 65.1 97.8 58.0 87.2 52.1 78.3 47.0 70.7

62.0 55.2 49.2 44.2 39.9

93.2 83.0 74.0 66.4 59.9

54.7 48.8 43.6 39.1 35.3

82.1 73.4 65.5 58.8 53.0

46.8 41.5 37.0 33.3 30.0

70.2 62.4 55.6 49.9 45.1

39.6 35.2 31.4 28.2 25.4

59.3 52.8 47.1 42.2 38.1

30.6 27.1 24.2 21.7 19.6

45.9 40.7 36.3 32.6 29.4

21 22 23 24 25

42.6 38.9 35.5 32.6 30.1

64.1 58.4 53.4 49.1 45.2

36.2 33.0 30.2 27.7 25.5

54.4 49.5 45.3 41.6 38.4

32.0 29.2 26.7 24.5 22.6

48.1 43.8 40.1 36.8 34.0

27.2 24.8 22.7 20.8 19.2

40.9 37.3 34.1 31.3 28.8

23.1 21.0 19.2 17.7 16.3

34.6 31.5 28.8 26.5 24.4

17.8 16.2 14.8 13.6 12.6

26.7 24.3 22.2 20.4 18.8

26 27 28 29

27.8

41.8

23.6 21.9

35.5 32.9

20.9 19.4 18.0

31.4 29.1 27.1

17.8 16.5 15.3

26.7 15.0 24.7 13.9 23.0 13.0 12.1

22.6 11.6 20.9 10.8 19.5 10.0 18.1 9.33

17.4 16.1 15.0 14.0

Properties φb Mn kip-ft 24.3 36.5 20.2 30.3 17.7 26.6 15.0 22.5 11.9 17.8 Pe (KL )2/104 kip-in.2 558 491 446 394 334 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

Dashed line indicates the KL beyond which bare steel strength controls.

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DESIGN OF COMPRESSION MEMBERS

Table 4-15 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS4

Concrete Filled Square HSS HSS4× 4×

Shape

12 /

t design, in. Steel, lb/ft

3 8 /

5 16 /

14 /

3 16 /

1 8 /

0.465 0.349 0.291 0.233 0.174 0.116 21.6 17.3 14.8 12.2 9.42 6.46 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 46 ksi fc′ = 4 ksi

0

166

249

132

198

114

171

98.7 148

82.0

123

64.8

97.2

1 2 3 4 5

165 163 159 153 147

248 244 239 231 221

131 129 126 123 118

197 194 190 184 177

114 112 109 106 102

170 168 164 159 152

98.2 96.9 94.7 91.8 88.1

147 145 142 138 132

81.6 80.5 78.8 76.4 73.4

122 121 118 115 110

64.5 63.7 62.2 60.3 57.9

96.8 95.5 93.4 90.5 86.9

6 7 8 9 10

139 131 121 112 102

209 196 182 168 153

112 106 98.8 91.6 84.1

168 159 149 138 126

145 137 128 119 110

83.8 79.1 73.9 68.4 62.8

126 119 111 103 94.2

69.9 66.0 61.8 57.3 52.7

105 99.0 92.6 85.9 79.0

55.1 52.0 48.6 45.0 41.3

82.7 78.0 72.9 67.5 62.0

96.5 91.2 85.4 79.3 73.0

11 12 13 14 15

92.0 138 82.2 124 72.8 109 63.7 95.8 55.5 83.5

76.5 115 69.0 104 61.7 92.8 54.7 82.2 47.9 72.0

66.6 100 60.3 90.6 54.0 81.2 48.0 72.2 42.2 63.5

57.1 51.5 46.0 40.8 36.1

85.7 77.2 68.9 61.3 54.3

48.0 43.4 38.8 34.5 30.2

72.0 65.0 58.2 51.7 45.4

37.6 33.9 30.3 26.8 23.5

56.4 50.8 45.4 40.2 35.2

16 17 18 19 20

48.8 43.2 38.6 34.6 31.2

73.3 65.0 58.0 52.0 46.9

42.1 37.3 33.3 29.9 27.0

63.3 56.1 50.0 44.9 40.5

37.1 32.9 29.3 26.3 23.8

55.8 49.4 44.1 39.6 35.7

31.7 28.1 25.1 22.5 20.3

47.7 42.3 37.7 33.8 30.5

26.6 23.5 21.0 18.8 17.0

39.9 35.3 31.5 28.3 25.5

20.6 18.3 16.3 14.6 13.2

30.9 27.4 24.4 21.9 19.8

21 22 23 24 25

28.3 25.8 23.6

42.6 38.8 35.5

24.4 22.3 20.4 18.7

36.7 33.5 30.6 28.1

21.5 19.6 18.0 16.5

32.4 29.5 27.0 24.8

18.4 16.8 15.4 14.1 13.0

27.7 25.2 23.1 21.2 19.5

15.4 14.1 12.9 11.8 10.9

23.1 12.0 21.1 10.9 19.3 9.98 17.7 9.17 16.3 8.45

26

18.0 16.4 15.0 13.8 12.7

7.81 11.7

Properties φb Mn kip-ft 18.2 27.4 15.3 23.0 13.5 20.3 11.5 17.3 Pe (KL )2/104 kip-in.2 362 325 296 263 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

9.17 13.8 223

Dashed line indicates the KL beyond which bare steel strength controls.

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4–259

Table 4-15 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

COMPOSITE HSS31/2

Concrete Filled Square HSS HSS31/2 × 31/2 ×

Shape

t design, in. Steel, lb/ft

Effective length, KL (ft)

Design

3 8 /

5 16 /

14 /

3 16 /

18 /

0.349 14.7 Pn /Ωc φc Pn ASD LRFD

0.291 12.7 Pn /Ωc φc Pn ASD LRFD

0.233 10.5 Pn /Ωc φc Pn ASD LRFD

0.174 8.15 Pn /Ωc φc Pn ASD LRFD

0.116 5.61 Pn /Ωc φc Pn ASD LRFD

0

113

169

97.0

146

82.5

124

68.4

103

53.6

80.3

1 2 3 4 5

112 110 107 102 96.7

168 165 160 154 145

96.4 94.7 92.0 88.3 83.8

145 142 138 133 126

82.0 80.5 78.2 74.9 71.0

123 121 117 112 107

68.0 66.8 64.9 62.3 59.1

102 100 97.3 93.4 88.6

53.2 52.3 50.8 48.8 46.3

79.9 78.5 76.2 73.2 69.4

6 7 8 9 10

90.4 83.5 76.2 68.7 61.2

136 126 115 103 92.0

78.6 72.9 66.8 60.5 54.2

118 110 100 90.9 81.4

66.5 61.5 56.2 51.1 46.0

99.7 92.2 84.4 76.8 69.1

55.4 51.4 47.1 42.6 38.1

83.1 77.0 70.6 63.9 57.2

43.4 40.3 36.9 33.4 29.9

65.1 60.4 55.3 50.1 44.9

11 12 13 14 15

53.8 46.8 40.1 34.6 30.1

80.9 70.3 60.3 52.0 45.3

47.9 41.9 36.2 31.2 27.2

72.1 63.0 54.4 46.9 40.8

40.9 36.0 31.3 27.0 23.5

61.5 54.1 47.1 40.6 35.4

33.7 29.5 25.4 21.9 19.1

50.6 44.3 38.2 32.9 28.7

26.5 23.1 20.0 17.2 15.0

39.7 34.7 30.0 25.8 22.5

16 17 18 19 20

26.5 23.5 20.9 18.8 16.9

39.8 35.2 31.4 28.2 25.5

23.9 21.2 18.9 16.9 15.3

35.9 31.8 28.4 25.5 23.0

20.7 18.3 16.3 14.7 13.2

31.1 27.5 24.6 22.0 19.9

16.8 14.9 13.3 11.9 10.8

25.2 22.3 19.9 17.9 16.1

13.2 11.7 10.4 9.35 8.44

19.8 17.5 15.6 14.0 12.7

21 22

15.4

23.1

13.9

20.8

12.0 10.9

18.0 16.4

14.6 13.3

7.65 6.97

11.5 10.5

9.75 8.89

Properties φb Mn kip-ft 11.2 16.8 10.0 15.0 8.51 12.8 Pe (KL )2/104 kip-in.2 201 185 166 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

6.83 10.3 141

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF COMPRESSION MEMBERS

Table 4-15 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS3

Concrete Filled Square HSS HSS3× 3×

Shape

3 8 /

5 16 /

14 /

3 16 /

18 /

0.349 12.2 Pn /Ωc φc Pn ASD LRFD

0.291 10.6 Pn /Ωc φc Pn ASD LRFD

0.233 8.81 Pn /Ωc φc Pn ASD LRFD

0.174 6.87 Pn /Ωc φc Pn ASD LRFD

0.116 4.75 Pn /Ωc φc Pn ASD LRFD

0

93.4

140

81.0

122

67.2

101

55.4

83.1

42.9

64.4

1 2 3 4 5

92.6 90.2 86.4 81.3 75.3

139 136 130 122 113

80.3 78.3 75.1 70.9 65.8

121 118 113 107 98.9

66.7 65.1 62.6 59.3 55.2

100 97.9 94.1 89.1 83.0

54.9 53.6 51.5 48.7 45.3

82.4 80.4 77.3 73.0 67.9

42.6 41.6 40.0 37.8 35.3

63.9 62.4 60.0 56.8 52.9

6 7 8 9 10

68.5 61.2 53.8 46.4 39.4

103 92.0 80.8 69.8 59.3

60.1 53.9 47.6 41.3 35.3

90.3 81.0 71.5 62.1 53.0

50.6 45.7 40.6 35.6 30.6

76.1 68.7 61.1 53.4 46.0

41.5 37.4 33.1 28.9 24.8

62.2 56.0 49.7 43.3 37.2

32.3 29.2 26.0 22.7 19.6

48.5 43.8 38.9 34.1 29.4

11 12 13 14 15

32.9 27.6 23.5 20.3 17.7

49.4 41.5 35.4 30.5 26.6

29.6 24.9 21.2 18.3 15.9

44.5 37.4 31.8 27.4 23.9

25.9 21.8 18.6 16.0 13.9

39.0 32.8 27.9 24.1 21.0

21.1 17.8 15.2 13.1 11.4

31.8 26.8 22.8 19.7 17.1

16.6 13.9 11.9 10.2 8.92

24.9 20.9 17.8 15.4 13.4

16 17 18 19

15.5 13.8

23.3 20.7

14.0 12.4 11.0

21.0 18.6 16.6

12.3 10.9 9.69

18.4 16.3 14.6

10.0 8.87 7.91 7.10

15.1 13.3 11.9 10.7

7.84 6.94 6.19 5.56

11.8 10.4 9.29 8.34

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 46 ksi fc′ = 4 ksi

Properties φb Mn kip-ft 7.69 11.6 6.92 10.4 5.98 8.99 Pe (KL )2/104 kip-in.2 115 107 96.9 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

4.83 7.26 83.1

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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4–261

Table 4-15 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 4 ksi

Concrete Filled Square HSS HSS21/2 × 21/2 ×

Shape

HSS21/4 × 21/4 ×

5 16 /

14 /

3 16 /

1 8 /

14 /

0.291 8.45 Pn /Ωc φc Pn ASD LRFD

0.233 7.11 Pn /Ωc φc Pn ASD LRFD

0.174 5.59 Pn /Ωc φc Pn ASD LRFD

0.116 3.90 Pn /Ωc φc Pn ASD LRFD

0.233 6.26 Pn /Ωc φc Pn ASD LRFD

0

64.7

97.3

54.3

81.6

43.2

64.9

33.3

50.0

47.9

72.0

1 2 3 4 5

63.9 61.6 57.8 53.0 47.3

96.1 92.5 86.9 79.6 71.2

53.6 51.8 48.8 45.0 40.4

80.6 77.8 73.4 67.6 60.8

42.7 41.2 38.9 35.8 32.2

64.1 61.9 58.3 53.7 48.4

33.0 31.9 30.1 27.8 25.1

49.4 47.8 45.1 41.7 37.6

47.2 45.2 41.9 37.8 33.0

71.0 67.9 63.0 56.7 49.6

6 7 8 9 10

41.3 35.1 29.1 23.5 19.0

62.0 52.7 43.7 35.2 28.6

35.5 30.5 25.6 20.9 17.0

53.4 45.9 38.5 31.5 25.5

28.5 24.7 20.9 17.4 14.1

42.9 37.1 31.5 26.1 21.2

22.1 19.1 16.1 13.3 10.8

33.2 28.7 24.2 19.9 16.2

28.0 23.1 18.4 14.6 11.8

42.1 34.7 27.7 21.9 17.7

11 12 13 14 15

15.7 13.2 11.2 9.69

23.6 19.8 16.9 14.6

14.0 11.8 10.0 8.65 7.53

21.1 17.7 15.1 13.0 11.3

11.7 9.80 8.35 7.20 6.27

17.5 14.7 12.6 10.8 9.43

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

COMPOSITE HSS21/2 -HSS21/4

16

8.90 7.48 6.37 5.49 4.79

13.3 11.2 9.56 8.24 7.18

4.21

6.31

9.75 8.19 6.98

14.7 12.3 10.5

Properties φb Mn kip-ft 4.45 6.69 3.90 5.85 3.20 4.81 Pe (KL )2/104 kip-in.2 55.4 50.9 44.1 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

2.36 3.54 35.4

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.04 4.57 34.9

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DESIGN OF COMPRESSION MEMBERS

Table 4-15 (continued)

COMPOSITE HSS21/4 -HSS2

Available Strength in Axial Compression, kips Concrete Filled Square HSS HSS21/4 × 21/4 ×

Shape

HSS2× 2×

3 16 /

1 8 /

14 /

3 16 /

1 8 /

0.174 4.96 Pn /Ωc φc Pn ASD LRFD

0.116 3.48 Pn /Ωc φc Pn ASD LRFD

0.233 5.41 Pn /Ωc φc Pn ASD LRFD

0.174 4.32 Pn /Ωc φc Pn ASD LRFD

0.116 3.05 Pn /Ωc φc Pn ASD LRFD

0

37.7

56.7

28.9

43.3

41.6

62.5

32.8

49.3

24.6

36.9

1 2 3 4 5

37.2 35.7 33.3 30.2 26.7

55.9 53.6 50.0 45.4 40.1

28.5 27.3 25.4 23.0 20.3

42.7 41.0 38.2 34.6 30.4

40.8 38.5 34.9 30.4 25.5

61.3 57.8 52.4 45.7 38.3

32.2 30.5 27.9 24.6 20.9

48.4 45.8 41.9 36.9 31.4

24.2 22.9 20.9 18.4 15.7

36.3 34.3 31.4 27.6 23.5

6 7 8 9 10

22.9 19.1 15.5 12.3 9.97

34.4 28.7 23.3 18.5 15.0

17.4 14.5 11.7 9.26 7.50

26.0 21.7 17.5 13.9 11.3

20.6 15.9 12.2 9.64 7.81

30.9 24.0 18.3 14.5 11.7

17.1 13.5 10.4 8.24 6.67

25.7 20.4 15.7 12.4 10.0

12.8 10.2 7.93 6.27 5.08

19.3 15.3 11.9 9.42 7.63

11 12 13 14

8.24 6.92 5.90

12.4 10.4 8.87

6.20 5.21 4.44 3.83

4.20 3.53

6.31 5.30

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 46 ksi fc′ = 4 ksi

9.30 7.81 6.66 5.74

6.46

9.70

5.52 4.63

8.29 6.97

Properties φb Mn kip-ft 2.51 3.77 1.86 2.80 2.28 3.43 Pe (KL )2/104 kip-in.2 30.6 24.6 22.7 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

1.91 2.87 20.2

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.43 2.15 16.4

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–263

Table 4-16

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 5 ksi

Concrete Filled Square HSS HSS16× 16×

Shape

12 /

t design, in. Steel, lb/ft

HSS14× 14× 5 16 /

5 8 /

12 /

3 8 /

0.465 0.349 0.291 0.581 0.465 0.349 103 78.5 65.9 110 89.7 68.3 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design 0

Effective length, KL (ft)

3 8 /

COMPOSITE HSS16-HSS14

1130 1700

992

1490

921

1380 1050 1570

928

1390

806

1210

6 7 8 9 10

1120 1120 1110 1110 1100

1680 1680 1670 1660 1650

981 977 972 967 962

1470 1470 1460 1450 1440

911 907 903 898 892

1370 1360 1350 1350 1340

1550 1540 1530 1520 1510

916 911 906 900 894

1370 1370 1360 1350 1340

794 790 786 780 774

1190 1190 1180 1170 1160

11 12 13 14 15

1090 1090 1080 1070 1060

1640 1630 1620 1600 1590

955 948 941 933 925

1430 1420 1410 1400 1390

886 880 873 865 857

1330 1000 1500 1320 991 1490 1310 982 1470 1300 972 1460 1290 961 1440

886 879 870 861 852

1330 1320 1310 1290 1280

768 761 754 746 737

1150 1140 1130 1120 1110

16 17 18 19 20

1050 1040 1030 1020 1010

1580 1560 1540 1530 1510

916 907 897 887 876

1370 1360 1350 1330 1310

849 840 830 820 810

1270 1260 1250 1230 1220

950 939 926 913 900

1430 1410 1390 1370 1350

842 831 820 809 797

1260 1250 1230 1210 1190

728 718 709 698 687

1090 1080 1060 1050 1030

21 22 23 24 25

994 981 968 955 941

1490 1470 1450 1430 1410

865 853 842 829 817

1300 1280 1260 1240 1230

800 789 777 766 754

1200 1180 1170 1150 1130

886 872 857 842 827

1330 1310 1290 1260 1240

784 771 758 745 731

1180 1160 1140 1120 1100

676 665 653 641 629

1010 997 980 962 943

26 27 28 29 30

927 912 897 882 867

1390 1370 1350 1320 1300

804 791 777 764 750

1210 1190 1170 1150 1120

742 729 716 703 690

1110 1090 1070 1050 1040

811 795 779 762 746

1220 1190 1170 1140 1120

717 702 688 673 658

1070 1050 1030 1010 987

616 603 590 577 564

924 905 885 866 845

32 34 36 38 40

836 803 771 737 704

1250 1210 1160 1110 1060

722 693 663 633 603

1080 1040 995 950 905

663 636 608 580 551

995 954 912 869 827

712 1070 677 1020 642 963 607 911 573 859

627 596 565 534 503

941 894 848 801 755

537 509 482 454 427

805 764 722 681 640

287 431 34600

384 577 33500

321 482 29200

1030 1030 1020 1020 1010

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

428 644 45900

336 506 38500

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

252 379 24500

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DESIGN OF COMPRESSION MEMBERS

Table 4-16 (continued)

COMPOSITE HSS14-HSS12

HSS12× 12×

5 16 /

t design, in. Steel, lb/ft

Fy = 46 ksi fc′ = 5 ksi

Concrete Filled Square HSS HSS14× 14×

Shape

5 8 /

12 /

3 8 /

5 16 /

14 /

0.291 0.581 0.465 0.349 0.291 0.233 57.4 93.3 76.1 58.1 48.9 39.4 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Available Strength in Axial Compression, kips

0

744

1120

840

1260

741

1110

639

959

585

878

531

796

6 7 8 9 10

733 729 724 719 714

1100 1090 1090 1080 1070

825 819 813 806 798

1240 1230 1220 1210 1200

727 722 717 710 704

1090 1080 1080 1070 1060

627 623 618 612 606

941 934 927 918 909

574 570 565 560 554

861 855 848 840 831

520 517 512 507 502

780 775 768 761 753

11 12 13 14 15

708 701 694 686 678

1060 1050 1040 1030 1020

789 780 770 759 748

1180 1170 1150 1140 1120

696 688 679 670 660

1040 1030 1020 1000 990

599 592 584 576 567

899 888 877 864 851

548 541 534 526 518

822 812 801 789 777

496 490 483 475 468

744 734 724 713 702

16 17 18 19 20

670 661 651 642 631

1000 991 977 962 947

736 724 711 697 684

1100 1090 1070 1050 1030

649 638 627 615 603

974 958 941 923 904

558 548 538 528 517

837 822 807 792 775

509 500 491 481 471

764 750 736 721 706

460 451 442 433 424

689 677 664 650 636

21 22 23 24 25

621 610 599 588 576

931 915 898 881 864

669 655 640 624 609

1000 982 959 936 913

590 577 564 551 537

886 866 846 826 806

506 494 483 471 459

759 742 724 706 688

460 450 439 428 417

691 675 658 642 625

414 404 394 384 373

621 606 591 576 560

26 27 28 29 30

564 552 540 527 515

846 828 810 791 772

593 577 561 545 528

889 865 841 817 792

523 509 495 481 466

785 764 742 721 699

447 434 422 409 396

670 651 632 614 595

405 394 382 371 359

608 591 573 556 538

363 352 341 331 320

544 528 512 496 480

32 34 36 38 40

489 464 438 412 387

734 695 657 618 580

496 463 431 399 368

743 694 646 599 552

437 409 380 352 325

656 613 571 529 488

371 346 321 297 273

557 519 482 446 410

336 312 289 267 245

503 468 434 401 368

298 277 256 235 216

447 415 384 353 323

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

216 324 21900

274 412 19600

229 344 17400

181 272 14500

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

155 233 13000

128 193 11400

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–265

Table 4-16 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 5 ksi

Concrete Filled Square HSS HSS10× 10×

Shape

5 8 /

t design, in. Steel, lb/ft

12 /

3 8 /

5 16 /

14 /

3 16 /

0.581 0.465 0.349 0.291 0.233 0.174 76.3 62.5 47.9 40.4 32.6 24.7 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

COMPOSITE HSS10

0

648

973

570

855

487

731

444

665 399

599 353

530

6 7 8 9 10

631 625 618 610 602

947 938 927 915 902

555 550 544 537 529

833 825 815 805 794

474 470 464 459 452

711 705 697 688 678

432 427 422 417 411

647 641 634 625 616

388 384 379 374 369

582 576 569 562 553

343 339 335 330 325

515 509 503 496 488

11 12 13 14 15

592 582 571 560 548

888 873 857 840 822

521 512 503 493 482

782 768 754 739 724

445 438 429 421 412

668 656 644 631 618

404 397 390 382 374

607 596 585 573 560

363 356 349 342 334

544 534 524 513 501

320 314 307 300 293

479 470 461 451 440

16 17 18 19 20

535 522 509 495 481

803 783 763 742 721

472 460 448 436 424

707 690 672 654 636

402 393 382 372 361

604 589 574 558 542

365 356 346 337 327

547 534 519 505 490

326 318 309 300 291

489 477 464 450 437

286 278 270 262 254

429 417 405 393 380

21 22 23 24 25

466 451 436 421 406

699 677 655 632 609

411 398 385 372 359

617 597 578 558 538

350 339 328 317 305

526 509 492 475 458

317 306 296 286 275

475 460 444 428 413

282 272 263 253 244

423 409 394 380 366

245 237 228 219 210

368 355 342 329 316

26 27 28 29 30

391 376 361 346 331

586 564 541 518 496

345 332 319 306 293

518 498 478 458 439

294 282 271 260 249

441 424 407 390 373

265 254 244 233 223

397 381 365 350 334

234 225 215 206 196

351 337 323 308 294

202 193 185 176 168

303 290 277 264 251

32 34 36 38 40

301 273 245 220 199

452 410 368 330 298

267 242 218 195 176

400 363 327 293 265

227 205 185 166 149

340 308 277 248 224

203 183 164 148 133

304 275 247 221 200

178 160 143 129 116

267 241 215 193 174

151 135 121 108 97.8

227 203 181 163 147

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

182 273 10400

153 230 9270

122 183 7850

105 157 7000

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

86.9 131 6100

67.4 101 5140

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DESIGN OF COMPRESSION MEMBERS

Table 4-16 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS9

Concrete Filled Square HSS HSS9× 9×

Shape

5 8 /

t design, in. Steel, lb/ft

12 /

3 8 /

5 16 /

14 /

3 16 /

0.581 0.465 0.349 0.291 0.233 0.174 67.8 55.7 42.8 36.1 29.2 22.2 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 46 ksi fc′ = 5 ksi

0

560

840

490

735 418

626 379

568 339

509 298

448

6 7 8 9 10

542 535 528 519 510

812 803 792 779 765

474 468 462 455 447

711 703 693 682 671

404 399 394 388 381

606 599 591 582 572

366 362 357 351 345

549 543 535 527 517

328 324 319 314 308

492 486 479 471 463

288 284 280 275 270

432 426 420 413 405

11 12 13 14 15

500 490 479 467 454

751 735 718 700 681

439 429 420 409 399

658 644 630 614 598

374 366 358 349 340

561 549 537 524 510

338 331 324 316 307

507 497 485 473 461

302 296 289 281 274

453 444 433 422 410

264 258 252 245 238

396 387 378 368 357

16 17 18 19 20

441 428 414 400 386

662 642 621 600 579

388 376 364 352 340

581 564 546 528 510

330 321 311 300 290

496 481 466 450 435

298 289 280 271 261

448 434 420 406 392

266 257 249 240 231

398 386 373 360 347

231 223 216 208 200

346 335 323 312 300

21 22 23 24 25

372 357 342 328 313

557 536 514 492 470

327 315 302 289 277

491 472 453 434 415

279 268 257 247 236

419 402 386 370 354

251 241 232 222 212

377 362 347 332 318

223 214 205 196 187

334 320 307 293 280

192 184 176 167 159

288 275 263 251 239

26 27 28 29 30

299 284 270 256 242

448 426 405 384 364

264 251 239 227 215

396 377 359 340 323

225 214 204 194 183

338 322 306 290 275

202 192 183 173 164

303 288 274 260 246

178 169 160 152 143

267 253 240 228 215

151 144 136 128 121

227 215 204 193 181

32 34 36 38 40

218 195 174 156 141

328 293 262 235 212

192 170 152 136 123

288 255 227 204 184

164 145 129 116 105

246 218 194 174 157

146 129 115 104 93.4

219 127 194 113 173 101 155 90.2 140 81.4

191 107 169 94.5 151 84.3 135 75.6 122 68.3

160 142 126 113 102

Properties φb Mn kip-ft 143 215 121 182 96.6 145 83.2 125 69.1 104 Pe (KL )2/104 kip-in.2 7260 6450 5510 4910 4280 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

53.9 81.0 3590

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–267

Table 4-16 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 5 ksi

COMPOSITE HSS8

Concrete Filled Square HSS HSS8× 8×

Shape

5 8 /

12 /

3 8 /

5 16 /

14 /

0.581 59.3 Pn /Ωc φc Pn ASD LRFD

0.465 48.9 Pn /Ωc φc Pn ASD LRFD

0.349 37.7 Pn /Ωc φc Pn ASD LRFD

0.291 31.8 Pn /Ωc φc Pn ASD LRFD

0.233 25.8 Pn /Ωc φc Pn ASD LRFD

0

476

714

416

624

352

528

318

477

284

426

6 7 8 9 10

456 449 441 432 422

684 673 661 648 633

399 393 386 379 370

599 590 579 568 556

338 333 327 321 314

507 499 491 481 471

305 301 295 290 283

458 451 443 434 425

272 268 263 258 252

408 402 394 387 378

11 12 13 14 15

412 401 389 377 364

618 601 583 565 546

361 352 342 331 320

542 528 513 497 480

306 298 290 281 272

460 448 435 421 408

276 269 261 253 245

415 404 392 380 367

246 239 232 225 217

369 359 348 337 326

16 17 18 19 20

350 337 323 309 295

526 505 485 464 443

309 297 285 273 261

463 445 428 409 391

262 252 242 232 222

393 379 364 348 333

236 227 218 209 200

354 341 327 314 300

209 201 193 185 176

314 302 289 277 264

21 22 23 24 25

281 267 255 242 230

421 402 383 364 345

249 236 224 212 200

373 355 336 318 301

212 202 191 181 171

318 302 287 272 257

191 181 172 163 154

286 272 258 244 231

168 159 151 143 135

252 239 227 214 202

26 27 28 29 30

217 205 193 182 170

326 308 290 273 256

189 178 166 155 145

283 266 250 233 218

161 152 143 133 124

242 228 214 200 187

145 136 128 119 112

217 204 192 179 167

127 119 112 104 97.2

190 179 167 156 146

32 34 36 38 40

149 132 118 106 95.6

225 199 177 159 144

128 113 101 90.5 81.7

191 170 151 136 123

109 96.9 86.4 77.6 70.0

164 145 130 116 105

t design, in. Steel, lb/ft

Effective length, KL (ft)

Design

98.1 86.9 77.5 69.5 62.8

147 130 116 104 94.1

85.4 75.7 67.5 60.6 54.7

128 114 101 90.9 82.0

Properties φb Mn kip-ft 109 164 93.0 140 74.4 112 64.4 96.8 Pe (KL )2/104 kip-in.2 4800 4290 3680 3300 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

53.5 80.5 2870

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4–268

DESIGN OF COMPRESSION MEMBERS

Table 4-16 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS8-HSS7

Concrete Filled Square HSS HSS8× 8×

Shape

HSS7× 7×

3 16 /

5 8 /

12 /

3 8 /

5 16 /

0.174 19.6 Pn /Ωc φc Pn ASD LRFD

0.581 50.8 Pn /Ωc φc Pn ASD LRFD

0.465 42.1 Pn /Ωc φc Pn ASD LRFD

0.349 32.6 Pn /Ωc φc Pn ASD LRFD

0.291 27.6 Pn /Ωc φc Pn ASD LRFD

0

248

372

394

591

345

517

290

436

262

393

6 7 8 9 10

237 233 229 224 219

356 350 343 336 328

372 364 356 346 336

558 547 534 520 504

326 320 312 304 295

489 479 468 456 443

275 270 264 257 250

413 405 395 385 375

248 243 238 232 225

372 365 357 348 338

11 12 13 14 15

213 207 201 194 187

320 311 301 291 281

325 314 302 290 278

488 470 453 436 418

286 276 266 255 244

429 414 398 382 365

242 234 225 216 207

363 350 337 324 310

218 211 203 195 187

327 316 305 292 280

16 17 18 19 20

180 173 166 158 151

270 260 248 237 226

266 253 241 228 215

399 381 362 343 324

232 221 209 197 186

348 331 314 296 279

197 188 178 168 159

296 281 267 252 238

178 169 161 152 143

267 254 241 228 215

21 22 23 24 25

143 136 128 121 114

215 204 193 182 171

203 191 179 167 155

305 287 268 251 233

174 163 152 143 133

262 245 229 214 200

149 140 130 121 113

223 209 196 182 169

135 126 118 110 102

202 189 177 165 153

26 27 28 29 30

107 100 93.3 87.0 81.3

160 150 140 130 122

144 133 124 116 108

216 201 186 174 162

124 115 107 99.6 93.1

186 173 161 150 140

104 96.6 89.8 83.7 78.3

156 145 135 126 117

94.3 87.4 81.3 75.8 70.8

32 34 36 38 40

71.4 63.3 56.4 50.6 45.7

103 91.4 81.5 73.2 66.0

62.3 55.1 49.2 44.1 39.8

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 46 ksi fc′ = 5 ksi

107 94.9 84.6 76.0 68.6

95.0 84.1 75.1 67.4 60.8

143 126 113 101 91.4

81.8 72.4 64.6 58.0 52.3

123 109 97.1 87.2 78.7

68.8 60.9 54.3 48.8 44.0

141 131 122 114 106 93.4 82.7 73.8 66.2 59.8

Properties φb Mn kip-ft 41.9 63.0 80.3 121 68.6 103 55.4 83.3 Pe (KL )2/104 kip-in.2 2400 3000 2690 2310 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

48.0 72.2 2090

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–269

Table 4-16 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 5 ksi

COMPOSITE HSS7-HSS6

Concrete Filled Square HSS HSS7× 7×

Shape

3 16 /

1 8 c,f /

5 8 /

12 /

0.233 22.4 Pn /Ωc φc Pn ASD LRFD

0.174 17.1 Pn /Ωc φc Pn ASD LRFD

0.116 11.6 Pn /Ωc φc Pn ASD LRFD

0.581 42.3 Pn /Ωc φc Pn ASD LRFD

0.465 35.2 Pn /Ωc φc Pn ASD LRFD

0

233

349

201

302

170

255

322

484

278

417

6 7 8 9 10

220 216 211 205 199

330 324 316 308 299

190 186 182 177 172

285 279 273 266 258

160 156 152 148 143

240 235 229 222 215

299 291 283 273 262

450 438 425 410 394

258 251 243 234 225

386 376 364 351 337

11 12 13 14 15

193 186 179 172 165

290 280 269 258 247

166 160 154 147 141

249 240 231 221 211

138 133 127 122 116

207 199 191 182 174

251 240 228 215 203

378 360 342 324 305

215 205 194 183 173

322 307 291 275 260

16 17 18 19 20

157 149 142 134 126

236 224 212 201 189

134 127 120 113 107

201 191 180 170 160

110 104 97.8 91.8 85.9

165 156 147 138 129

190 178 165 153 142

286 267 249 231 213

163 153 143 133 123

245 230 215 200 185

21 22 23 24 25

118 111 103 96.2 89.1

177 166 155 144 134

99.9 93.3 86.8 80.6 74.4

150 140 130 121 112

80.1 74.4 68.9 63.5 58.5

120 112 103 95.2 87.8

130 119 109 99.8 92.0

196 179 163 150 138

114 104 95.6 87.8 80.9

171 157 144 132 122

26 27 28 29 30

82.4 76.4 71.0 66.2 61.9

124 115 107 99.3 92.8

68.8 63.8 59.3 55.3 51.7

103 95.7 89.0 82.9 77.5

54.1 50.2 46.6 43.5 40.6

81.1 75.2 70.0 65.2 60.9

85.1 78.9 73.4 68.4 63.9

128 119 110 103 96.0

74.8 69.4 64.5 60.1 56.2

112 104 96.9 90.4 84.4

32 34 36 38 40

54.4 48.2 43.0 38.6 34.8

81.6 72.2 64.4 57.8 52.2

45.4 40.2 35.9 32.2 29.1

68.1 60.3 53.8 48.3 43.6

35.7 31.6 28.2 25.3 22.9

53.6 47.4 42.3 38.0 34.3

56.2 49.7 44.4

84.4 74.8 66.7

49.4 43.7 39.0

74.2 65.7 58.6

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

HSS6× 6×

14 /

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

40.1 60.2 1830 c

31.5 47.3 1530

22.1 33.2 1200

55.8 83.8 1730

48.2 72.5 1570

Shape is noncompact for compression with Fy = 46 ksi. f Shape is noncompact for flexure with Fy = 46 ksi.

Note: Heavy line indicates KL/rmy equal to or greater than 200. Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 270

4–270

DESIGN OF COMPRESSION MEMBERS

Table 4-16 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS6

Concrete Filled Square HSS HSS6× 6×

Shape

3 8 /

5 16 /

14 /

3 16 /

18 /

0.349 27.5 Pn /Ωc φc Pn ASD LRFD

0.291 23.3 Pn /Ωc φc Pn ASD LRFD

0.233 19.0 Pn /Ωc φc Pn ASD LRFD

0.174 14.5 Pn /Ωc φc Pn ASD LRFD

0.116 9.86 Pn /Ωc φc Pn ASD LRFD

0

234

351

210

315

185

278

159

239

133

199

6 7 8 9 10

217 211 205 198 190

325 317 307 296 285

195 190 184 178 171

293 285 276 267 256

172 168 163 157 151

258 252 244 236 226

148 144 139 134 129

222 215 209 201 193

122 119 115 110 106

184 178 172 166 159

11 12 13 14 15

182 173 165 156 147

273 260 247 233 220

164 156 148 140 132

246 234 222 210 198

145 138 131 124 117

217 207 196 186 175

123 117 111 105 98.9

185 176 167 158 148

101 96.0 90.7 85.4 80.0

152 144 136 128 120

16 17 18 19 20

137 128 119 110 102

206 192 179 166 153

124 116 108 99.9 92.1

186 174 162 150 138

110 102 95.2 88.2 81.4

164 153 143 132 122

92.7 86.4 80.2 74.2 68.3

139 130 120 111 102

74.6 69.2 64.0 58.8 53.9

112 104 95.9 88.3 80.8

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 46 ksi fc′ = 5 ksi

21 22 23 24 25

93.5 85.3 78.1 71.7 66.1

140 128 117 108 99.1

84.7 77.3 70.7 65.0 59.9

127 116 106 97.5 89.8

74.8 68.3 62.5 57.4 52.9

112 103 93.8 86.1 79.4

62.6 57.1 52.2 47.9 44.2

93.9 85.6 78.3 71.9 66.3

49.0 44.7 40.9 37.5 34.6

73.5 67.0 61.3 56.3 51.9

26 27 28 29 30

61.1 56.7 52.7 49.1 45.9

91.7 85.0 79.0 73.7 68.8

55.4 51.3 47.7 44.5 41.6

83.0 77.0 71.6 66.8 62.4

48.9 45.4 42.2 39.3 36.8

73.4 68.1 63.3 59.0 55.1

40.9 37.9 35.2 32.8 30.7

61.3 56.8 52.8 49.3 46.0

32.0 29.7 27.6 25.7 24.0

48.0 44.5 41.4 38.6 36.0

32 34 36 38

40.3 35.7 31.9 28.6

60.5 53.6 47.8 42.9

36.5 32.4 28.9 25.9

54.8 48.6 43.3 38.9

32.3 28.6 25.5 22.9

48.5 42.9 38.3 34.4

27.0 23.9 21.3 19.1

40.5 35.8 32.0 28.7

21.1 18.7 16.7 15.0

31.7 28.1 25.0 22.5

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

39.2 58.9 1360

34.2 51.4 1230

28.6 43.0 1090

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

22.5 33.9 907

16.0 24.0 710

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10:54 AM

Page 271

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–271

Table 4-16 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 5 ksi

Concrete Filled Square HSS HSS51/2 ×51/2 ×

Shape

3 8 /

t design, in. Steel, lb/ft

5 16 /

HSS5× 5×

14 /

3 16 /

1 8 /

12 /

0.349 0.291 0.233 0.174 0.116 0.465 24.9 21.2 17.3 13.3 9.01 28.4 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

COMPOSITE HSS51/2 -HSS5

0

207

311

186

279

163

245

140

210

116

173

217

326

1 2 3 4 5

207 205 202 199 195

310 307 304 298 292

185 184 182 179 175

278 276 273 268 262

163 162 160 157 154

245 243 240 236 231

139 138 137 134 131

209 208 205 202 197

115 114 113 111 108

173 171 169 166 162

216 215 211 207 202

325 322 318 311 303

6 7 8 9 10

189 183 177 169 161

284 275 265 254 242

170 165 159 152 145

255 247 238 228 218

150 145 140 134 128

225 218 210 201 192

128 124 119 114 109

192 186 179 171 163

105 101 97.5 93.2 88.7

158 152 146 140 133

195 188 180 171 162

294 283 271 257 244

11 12 13 14 15

153 145 136 127 118

230 217 204 191 177

138 130 123 115 107

207 195 184 172 160

122 115 108 101 94.3

182 172 162 152 141

103 97.7 91.8 85.8 79.8

155 146 138 129 120

83.9 78.9 73.9 68.8 63.7

126 118 111 103 95.5

152 142 132 122 112

229 214 199 184 169

16 17 18 19 20

109 101 92.4 84.5 77.4

164 151 139 127 116

148 137 125 115 104

87.4 80.6 74.0 67.6 61.3

131 121 111 101 92.0

98.9 91.2 83.6 76.3 69.2

73.9 111 68.0 102 62.4 93.5 56.9 85.3 51.5 77.2

58.7 53.8 49.0 44.4 40.1

88.0 103 80.6 93.2 73.5 84.1 66.6 75.5 60.1 68.1

154 140 126 113 102

21 22 23 24 25

70.5 106 64.2 96.5 58.7 88.3 53.9 81.1 49.7 74.7

62.8 57.2 52.3 48.1 44.3

94.1 85.8 78.5 72.1 66.4

55.6 50.7 46.4 42.6 39.3

83.5 76.0 69.6 63.9 58.9

46.7 42.5 38.9 35.8 32.9

70.0 63.8 58.4 53.6 49.4

36.3 33.1 30.3 27.8 25.6

54.5 49.7 45.4 41.7 38.5

61.8 56.3 51.5 47.3 43.6

92.9 84.6 77.4 71.1 65.5

26 27 28 29 30

46.0 42.6 39.6 36.9 34.5

40.9 38.0 35.3 32.9 30.8

61.4 57.0 53.0 49.4 46.1

36.3 33.7 31.3 29.2 27.3

54.4 50.5 46.9 43.8 40.9

30.5 28.2 26.3 24.5 22.9

45.7 42.4 39.4 36.7 34.3

23.7 22.0 20.4 19.1 17.8

35.6 33.0 30.7 28.6 26.7

40.3 37.4 34.8 32.4 30.3

60.6 56.2 52.2 48.7 45.5

69.1 64.1 59.6 55.5 51.9

Properties φb Mn kip-ft 32.3 48.5 28.2 42.4 23.7 35.5 18.7 28.0 13.3 19.9 Pe (KL )2/104 kip-in.2 1000 909 806 676 526 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF COMPRESSION MEMBERS

Table 4-16 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS5

Fy = 46 ksi fc′ = 5 ksi

Concrete Filled Square HSS HSS5× 5×

Shape

3 8 /

5 16 /

14 /

3 16 /

18 /

0.349 22.4 Pn /Ωc φc Pn ASD LRFD

0.291 19.1 Pn /Ωc φc Pn ASD LRFD

0.233 15.6 Pn /Ωc φc Pn ASD LRFD

0.174 12.0 Pn /Ωc φc Pn ASD LRFD

0.116 8.16 Pn /Ωc φc Pn ASD LRFD

0

181

272

162

243

142

214

121

182

99.6

149

1 2 3 4 5

181 179 176 173 168

271 269 265 259 252

162 160 158 155 151

243 241 237 232 226

142 141 139 136 132

213 211 208 204 198

121 120 118 116 113

182 180 177 174 169

99.3 98.3 96.8 94.7 92.0

149 147 145 142 138

6 7 8 9 10

162 156 149 142 134

244 234 224 213 201

146 140 134 127 120

219 210 201 191 180

128 123 118 112 106

192 185 177 168 159

109 105 100 95.3 90.0

164 157 150 143 135

88.9 85.3 81.4 77.1 72.7

133 128 122 116 109

11 12 13 14 15

125 117 108 99.9 91.4

188 175 163 150 137

113 105 97.8 90.2 82.7

169 158 147 135 124

99.5 93.0 86.3 79.7 73.1

149 139 129 120 110

84.6 79.0 73.3 67.6 62.0

127 118 110 101 93.0

68.0 63.3 58.5 53.7 49.0

102 94.9 87.7 80.5 73.5

16 17 18 19 20

83.8 76.4 69.4 62.5 56.4

126 115 104 93.9 84.8

75.4 68.3 61.4 55.1 49.7

113 102 92.0 82.6 74.5

66.7 60.5 54.4 48.9 44.1

100 90.7 81.7 73.3 66.2

56.5 51.2 46.1 41.3 37.3

84.8 76.8 69.1 62.0 56.0

44.4 40.1 35.8 32.1 29.0

66.7 60.1 53.7 48.2 43.5

21 22 23 24 25

51.2 46.6 42.6 39.2 36.1

76.9 70.0 64.1 58.9 54.2

45.1 41.1 37.6 34.5 31.8

67.6 61.6 56.4 51.8 47.7

40.0 36.4 33.3 30.6 28.2

60.0 54.7 50.0 45.9 42.3

33.8 30.8 28.2 25.9 23.9

50.8 46.2 42.3 38.9 35.8

26.3 24.0 21.9 20.1 18.6

39.5 35.9 32.9 30.2 27.8

26 27 28 29 30

33.4 30.9 28.8 26.8 25.1

50.2 46.5 43.2 40.3 37.7

29.4 27.3 25.4 23.6 22.1

44.1 40.9 38.0 35.5 33.1

26.1 24.2 22.5 21.0 19.6

39.1 36.3 33.8 31.5 29.4

22.1 20.5 19.0 17.7 16.6

33.1 30.7 28.6 26.6 24.9

17.2 15.9 14.8 13.8 12.9

25.7 23.9 22.2 20.7 19.3

φb Mn kip-ft 26.0 39.0 22.7 34.1 19.2 28.8 15.2 22.8 Pe (KL )2/104 kip-in.2 719 653 579 490 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

10.8

t design, in. Steel, lb/ft

Effective length, KL (ft)

Design

Properties

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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4–273

Table 4-16 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 5 ksi

COMPOSITE HSS41/2

Concrete Filled Square HSS HSS41/2 ×41/2 ×

Shape

12 /

t design, in. Steel, lb/ft

5 16 /

14 /

3 16 /

1 8 /

0.465 0.349 0.291 0.233 0.174 0.116 25.0 19.8 17.0 13.9 10.7 7.31 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

3 8 /

0

191

288

157

235

140

210

123

184

104

156

84.7

127

1 2 3 4 5

191 189 185 180 174

287 283 278 271 262

156 154 151 147 142

234 231 227 221 214

140 138 135 132 128

209 207 203 198 191

122 121 119 116 112

184 182 178 174 168

104 102 101 98.1 94.9

155 154 151 147 142

84.4 83.4 81.8 79.6 77.0

127 125 123 119 115

6 7 8 9 10

167 159 151 141 132

252 240 227 213 198

137 130 123 115 107

205 195 184 173 161

123 117 110 104 96.6

184 175 166 155 145

108 103 97.0 91.1 85.0

161 154 146 137 127

91.1 86.9 82.3 77.3 72.1

137 130 123 116 108

73.8 70.2 66.3 62.1 57.7

111 105 99.4 93.2 86.6

11 12 13 14 15

122 112 102 92.0 82.6

183 168 153 138 124

149 138 126 115 104

89.3 82.0 74.7 67.5 60.6

134 123 112 101 91.1

99.2 91.5 83.9 76.4 69.1

78.7 118 72.3 108 65.9 98.9 59.7 89.5 53.6 80.5

66.8 100 61.4 92.1 56.1 84.1 50.8 76.2 45.7 68.5

53.3 48.8 44.3 40.0 35.8

79.9 73.2 66.5 60.0 53.7

16 17 18 19 20

73.5 110 65.1 97.8 58.0 87.2 52.1 78.3 47.0 70.7

62.0 55.2 49.2 44.2 39.9

93.2 83.0 74.0 66.4 59.9

54.7 48.8 43.6 39.1 35.3

82.1 73.4 65.5 58.8 53.0

47.8 42.4 37.8 33.9 30.6

71.8 63.6 56.7 50.9 45.9

40.8 36.1 32.2 28.9 26.1

61.2 54.2 48.3 43.4 39.1

31.7 28.1 25.1 22.5 20.3

47.6 42.1 37.6 33.7 30.4

21 22 23 24 25

42.6 38.9 35.5 32.6 30.1

64.1 58.4 53.4 49.1 45.2

36.2 33.0 30.2 27.7 25.5

54.4 49.5 45.3 41.6 38.4

32.0 29.2 26.7 24.5 22.6

48.1 43.8 40.1 36.8 34.0

27.8 25.3 23.2 21.3 19.6

41.7 38.0 34.7 31.9 29.4

23.7 21.6 19.7 18.1 16.7

35.5 32.4 29.6 27.2 25.1

18.4 16.8 15.3 14.1 13.0

27.6 25.2 23.0 21.1 19.5

26 27 28 29

27.8

41.8

23.6 21.9

35.5 32.9

20.9 19.4 18.0

31.4 29.1 27.1

18.1 16.8 15.6

27.2 25.2 23.4

15.4 14.3 13.3 12.4

23.2 12.0 21.5 11.1 20.0 10.4 18.6 9.65

18.0 16.7 15.5 14.5

Properties φb Mn kip-ft 24.4 36.7 20.4 30.6 17.9 26.9 15.2 22.8 Pe (KL )2/104 kip-in.2 563 497 454 402 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

12.0 18.1 343

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF COMPRESSION MEMBERS

Table 4-16 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS4

Concrete Filled Square HSS HSS4× 4×

Shape

12 /

t design, in. Steel, lb/ft

3 8 /

5 16 /

14 /

3 16 /

1 8 /

0.465 0.349 0.291 0.233 0.174 0.116 21.6 17.3 14.8 12.2 9.42 6.46 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 46 ksi fc′ = 5 ksi

0

166

249

133

199

119

178

104

156

87.6

131

70.9

106

1 2 3 4 5

165 163 159 153 147

248 244 239 231 221

132 130 127 123 118

198 195 191 184 177

118 117 114 110 106

178 175 171 165 158

103 102 99.7 96.5 92.5

155 153 149 145 139

87.2 86.0 84.1 81.4 78.1

131 129 126 122 117

70.5 69.5 67.9 65.6 62.9

106 104 102 98.5 94.3

6 7 8 9 10

139 131 121 112 102

209 196 182 168 153

112 106 98.8 91.6 84.1

168 159 149 138 126

100 94.2 87.6 80.8 73.8

150 141 131 121 111

87.8 82.7 77.1 71.2 65.1

132 124 116 107 97.7

74.2 69.9 65.2 60.3 55.2

111 105 97.8 90.4 82.8

59.7 56.1 52.2 48.1 44.0

89.5 84.1 78.3 72.2 66.0

11 12 13 14 15

92.0 138 82.2 124 72.8 109 63.7 95.8 55.5 83.5

76.5 115 69.0 104 61.7 92.8 54.7 82.2 47.9 72.0

66.8 100 60.3 90.6 54.0 81.2 48.0 72.2 42.2 63.5

59.0 53.0 47.1 41.6 36.3

88.5 79.5 70.7 62.3 54.4

50.1 45.1 40.2 35.5 31.0

75.2 67.6 60.3 53.2 46.5

39.8 35.6 31.6 27.8 24.2

59.7 53.5 47.5 41.7 36.3

16 17 18 19 20

48.8 43.2 38.6 34.6 31.2

73.3 65.0 58.0 52.0 46.9

42.1 37.3 33.3 29.9 27.0

63.3 56.1 50.0 44.9 40.5

37.1 32.9 29.3 26.3 23.8

55.8 49.4 44.1 39.6 35.7

31.9 28.2 25.2 22.6 20.4

47.8 42.3 37.8 33.9 30.6

27.2 24.1 21.5 19.3 17.4

40.8 36.2 32.3 29.0 26.1

21.3 18.9 16.8 15.1 13.6

31.9 28.3 25.2 22.6 20.4

21 22 23 24 25

28.3 25.8 23.6

42.6 38.8 35.5

24.4 22.3 20.4 18.7

36.7 33.5 30.6 28.1

21.5 19.6 18.0 16.5

32.4 29.5 27.0 24.8

18.5 16.9 15.4 14.2 13.1

27.7 25.3 23.1 21.2 19.6

15.8 14.4 13.2 12.1 11.2

23.7 12.4 21.6 11.3 19.8 10.3 18.1 9.46 16.7 8.72

18.5 16.9 15.5 14.2 13.1

8.06

12.1

26

Properties φb Mn kip-ft 18.3 27.6 15.5 23.2 13.7 20.5 11.6 17.5 Pe (KL )2/104 kip-in.2 365 328 300 268 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

9.29 14.0 229

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Table 4-16 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 5 ksi

COMPOSITE HSS31/2

Concrete Filled Square HSS HSS31/2 × 31/2 ×

Shape

t design, in. Steel, lb/ft

Effective length, KL (ft)

Design

3 8 /

5 16 /

14 /

3 16 /

18 /

0.349 14.7 Pn /Ωc φc Pn ASD LRFD

0.291 12.7 Pn /Ωc φc Pn ASD LRFD

0.233 10.5 Pn /Ωc φc Pn ASD LRFD

0.174 8.15 Pn /Ωc φc Pn ASD LRFD

0.116 5.61 Pn /Ωc φc Pn ASD LRFD

0

113

169

98.9

148

86.4

130

72.6

109

58.1

87.1

1 2 3 4 5

112 110 107 102 96.7

168 165 160 154 145

98.3 96.4 93.4 89.3 84.4

147 145 140 134 127

85.9 84.3 81.7 78.2 74.0

129 126 122 117 111

72.1 70.8 68.7 65.9 62.4

108 106 103 98.8 93.5

57.7 56.7 55.0 52.7 49.8

86.6 85.0 82.5 79.0 74.7

6 7 8 9 10

90.4 83.5 76.2 68.7 61.2

136 126 115 103 92.0

78.7 72.9 66.8 60.5 54.2

118 110 100 90.9 81.4

69.1 63.8 58.2 52.4 46.5

104 95.7 87.2 78.5 69.8

58.3 53.9 49.2 44.4 39.6

87.5 80.9 73.8 66.6 59.4

46.6 43.0 39.2 35.3 31.5

69.9 64.5 58.8 53.0 47.2

11 12 13 14 15

53.8 46.8 40.1 34.6 30.1

80.9 70.3 60.3 52.0 45.3

47.9 41.9 36.2 31.2 27.2

72.1 63.0 54.4 46.9 40.8

40.9 36.0 31.3 27.0 23.5

61.5 54.1 47.1 40.6 35.4

34.8 30.3 26.0 22.4 19.5

52.3 45.5 39.0 33.6 29.3

27.6 24.0 20.6 17.7 15.4

41.5 36.0 30.8 26.6 23.2

16 17 18 19 20

26.5 23.5 20.9 18.8 16.9

39.8 35.2 31.4 28.2 25.5

23.9 21.2 18.9 16.9 15.3

35.9 31.8 28.4 25.5 23.0

20.7 18.3 16.3 14.7 13.2

31.1 27.5 24.6 22.0 19.9

17.2 15.2 13.6 12.2 11.0

25.7 22.8 20.3 18.2 16.5

13.6 12.0 10.7 9.63 8.69

20.4 18.0 16.1 14.4 13.0

21 22

15.4

23.1

13.9

20.8

12.0 10.9

18.0 16.4

14.9 13.6

7.88 7.18

11.8 10.8

9.96 9.07

Properties φb Mn kip-ft 11.3 16.9 10.0 15.1 8.60 12.9 Pe (KL )2/104 kip-in.2 203 188 168 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

6.92 10.4 144

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.99 7.50 114

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DESIGN OF COMPRESSION MEMBERS

Table 4-16 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS3

Concrete Filled Square HSS HSS3× 3×

Shape

3 8 /

5 16 /

14 /

3 16 /

18 /

0.349 12.2 Pn /Ωc φc Pn ASD LRFD

0.291 10.6 Pn /Ωc φc Pn ASD LRFD

0.233 8.81 Pn /Ωc φc Pn ASD LRFD

0.174 6.87 Pn /Ωc φc Pn ASD LRFD

0.116 4.75 Pn /Ωc φc Pn ASD LRFD

0

93.4

140

81.0

122

69.7

104

58.4

87.5

46.2

69.2

1 2 3 4 5

92.6 90.2 86.4 81.3 75.3

139 136 130 122 113

80.3 78.3 75.1 70.9 65.8

121 118 113 107 98.9

69.1 67.3 64.5 60.7 56.2

104 101 96.7 91.1 84.4

57.9 56.4 54.1 51.1 47.4

86.8 84.7 81.2 76.6 71.1

45.8 44.7 42.9 40.5 37.6

68.7 67.0 64.3 60.7 56.4

6 7 8 9 10

68.5 61.2 53.8 46.4 39.4

103 92.0 80.8 69.8 59.3

60.1 53.9 47.6 41.3 35.3

90.3 81.0 71.5 62.1 53.0

51.2 45.8 40.6 35.6 30.6

76.8 68.7 61.1 53.4 46.0

43.3 38.8 34.3 29.7 25.4

64.9 58.2 51.4 44.6 38.1

34.3 30.8 27.3 23.7 20.3

51.5 46.3 40.9 35.6 30.4

11 12 13 14 15

32.9 27.6 23.5 20.3 17.7

49.4 41.5 35.4 30.5 26.6

29.6 24.9 21.2 18.3 15.9

44.5 37.4 31.8 27.4 23.9

25.9 21.8 18.6 16.0 13.9

39.0 32.8 27.9 24.1 21.0

21.3 17.9 15.2 13.1 11.4

31.9 26.8 22.9 19.7 17.2

17.0 14.3 12.2 10.5 9.16

25.5 21.5 18.3 15.8 13.7

16 17 18 19

15.5 13.8

23.3 20.7

14.0 12.4 11.0

21.0 18.6 16.6

12.3 10.9 9.69

18.4 16.3 14.6

10.1 8.91 7.95 7.13

15.1 13.4 11.9 10.7

8.05 7.13 6.36 5.71

12.1 10.7 9.54 8.56

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 46 ksi fc′ = 5 ksi

Properties φb Mn kip-ft 7.74 11.6 6.97 10.5 6.04 9.07 Pe (KL )2/104 kip-in.2 116 108 98.1 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

4.89 7.35 84.6

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.58 5.37 67.7

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–277

Table 4-16 (continued)

Available Strength in Axial Compression, kips

Fy = 46 ksi fc′ = 5 ksi

Concrete Filled Square HSS HSS21/2 × 21/2 ×

Shape

HSS21/4 × 21/4 ×

5 16 /

14 /

3 16 /

18 /

14 /

0.291 8.45 Pn /Ωc φc Pn ASD LRFD

0.233 7.11 Pn /Ωc φc Pn ASD LRFD

0.174 5.59 Pn /Ωc φc Pn ASD LRFD

0.116 3.90 Pn /Ωc φc Pn ASD LRFD

0.233 6.26 Pn /Ωc φc Pn ASD LRFD

0

64.7

97.3

54.3

81.6

45.2

67.8

35.5

53.3

47.9

72.0

1 2 3 4 5

63.9 61.6 57.8 53.0 47.3

96.1 92.5 86.9 79.6 71.2

53.6 51.8 48.8 45.0 40.4

80.6 77.8 73.4 67.6 60.8

44.7 43.1 40.5 37.2 33.3

67.0 64.6 60.8 55.8 50.0

35.1 33.9 31.9 29.4 26.4

52.6 50.8 47.9 44.1 39.6

47.2 45.2 41.9 37.8 33.0

71.0 67.9 63.0 56.7 49.6

6 7 8 9 10

41.3 35.1 29.1 23.5 19.0

62.0 52.7 43.7 35.2 28.6

35.5 30.5 25.6 20.9 17.0

53.4 45.9 38.5 31.5 25.5

29.2 24.9 20.9 17.4 14.1

43.7 37.3 31.5 26.1 21.2

23.2 19.9 16.6 13.6 11.0

34.8 29.8 25.0 20.4 16.5

28.0 23.1 18.4 14.6 11.8

42.1 34.7 27.7 21.9 17.7

11 12 13 14 15

15.7 13.2 11.2 9.69

23.6 19.8 16.9 14.6

14.0 11.8 10.0 8.65 7.53

21.1 17.7 15.1 13.0 11.3

11.7 9.80 8.35 7.20 6.27

17.5 14.7 12.6 10.8 9.43

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

COMPOSITE HSS21/2 -HSS21/4

16

9.10 7.65 6.52 5.62 4.89

13.7 11.5 9.77 8.43 7.34

4.30

6.45

9.75 8.19 6.98

14.7 12.3 10.5

Properties φb Mn kip-ft 4.48 6.73 3.93 5.90 3.24 4.86 Pe (KL )2/104 kip-in.2 55.8 51.4 44.7 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

2.39 3.59 36.2

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.07 4.61 35.2

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DESIGN OF COMPRESSION MEMBERS

Table 4-16 (continued)

COMPOSITE HSS21/4 -HSS2

Available Strength in Axial Compression, kips Concrete Filled Square HSS HSS21/4 × 21/4 ×

Shape

HSS2× 2×

3 16 /

18 /

14 /

3 16 /

18 /

0.174 4.96 Pn /Ωc φc Pn ASD LRFD

0.116 3.48 Pn /Ωc φc Pn ASD LRFD

0.233 5.41 Pn /Ωc φc Pn ASD LRFD

0.174 4.32 Pn /Ωc φc Pn ASD LRFD

0.116 3.05 Pn /Ωc φc Pn ASD LRFD

0

39.1

58.7

30.6

45.9

41.6

62.5

33.1

49.7

25.9

38.9

1 2 3 4 5

38.5 36.8 34.1 30.7 26.7

57.8 55.2 51.2 46.0 40.1

30.2 28.9 26.8 24.2 21.2

45.3 43.3 40.2 36.3 31.8

40.8 38.5 34.9 30.4 25.5

61.3 57.8 52.4 45.7 38.3

32.5 30.6 27.9 24.6 20.9

48.7 45.9 41.9 36.9 31.4

25.5 24.1 21.9 19.2 16.2

38.2 36.1 32.9 28.8 24.4

6 7 8 9 10

22.9 19.1 15.5 12.3 9.97

34.4 28.7 23.3 18.5 15.0

18.0 14.9 12.0 9.45 7.65

27.1 22.4 17.9 14.2 11.5

20.6 15.9 12.2 9.64 7.81

30.9 24.0 18.3 14.5 11.7

17.1 13.5 10.4 8.24 6.67

25.7 20.4 15.7 12.4 10.0

13.2 10.4 7.95 6.28 5.09

19.8 15.5 11.9 9.42 7.63

11 12 13 14

8.24 6.92 5.90

12.4 10.4 8.87

6.33 5.31 4.53 3.90

4.20 3.53

6.31 5.30

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 46 ksi fc′ = 5 ksi

9.49 7.97 6.79 5.86

6.46

9.70

5.52 4.63

8.29 6.97

Properties φb Mn kip-ft 2.53 3.81 1.89 2.84 2.30 3.45 Pe (KL )2/104 kip-in.2 31.0 25.1 22.9 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

1.93 2.90 20.4

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.45 2.18 16.7

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–279

Table 4-17

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 4 ksi

COMPOSITE HSS18HSS16

Concrete Filled Round HSS HSS18×

Shape

0.500

t design, in. Steel, lb/ft

0.375

0.625

0.500

0.438

0.375

0.465 0.349 0.581 0.465 0.407 0.349 93.5 70.7 103 82.9 72.9 62.6 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design 0

Effective length, KL (ft)

HSS16×

972 1460

854

1280

919

1380

816

1220

762

1140

711

1070

6 7 8 9 10

962 958 954 949 944

1440 1440 1430 1420 1420

844 841 837 833 828

1270 1260 1260 1250 1240

907 903 898 893 887

1360 1350 1350 1340 1330

805 801 797 792 786

1210 1200 1200 1190 1180

752 748 744 739 734

1130 1120 1120 1110 1100

701 697 693 689 684

1050 1050 1040 1030 1030

11 12 13 14 15

938 932 925 918 910

1410 1400 1390 1380 1360

822 817 810 803 796

1230 1220 1220 1210 1190

880 873 865 857 848

1320 1310 1300 1290 1270

780 774 767 759 751

1170 1160 1150 1140 1130

728 722 715 708 701

1090 1080 1070 1060 1050

678 672 666 659 651

1020 1010 999 988 977

16 17 18 19 20

902 893 884 874 864

1350 1340 1330 1310 1300

788 780 772 763 754

1180 1170 1160 1140 1130

839 829 819 808 797

1260 1240 1230 1210 1200

743 734 724 714 704

1110 1100 1090 1070 1060

692 684 675 666 656

1040 1030 1010 999 984

644 636 627 618 609

966 953 941 927 913

21 22 23 24 25

854 843 832 820 809

1280 1260 1250 1230 1210

744 734 724 714 703

1120 1100 1090 1070 1050

786 774 761 749 736

1180 1160 1140 1120 1100

694 683 672 660 649

1040 1020 1010 990 973

646 636 625 614 603

969 954 938 921 905

599 590 579 569 558

899 884 869 853 838

26 27 28 29 30

796 784 771 759 746

1190 1180 1160 1140 1120

692 680 669 657 645

1040 1020 1000 985 967

723 709 696 682 667

1080 1060 1040 1020 1000

637 624 612 599 586

955 936 918 899 880

592 580 568 556 544

887 870 852 834 816

547 536 525 514 502

821 805 788 771 753

32 34 36 38 40

719 1080 691 1040 663 995 635 952 606 909

620 595 570 544 518

931 893 855 816 778

639 609 580 550 521

958 914 870 825 781

560 534 507 480 454

840 801 761 720 680

519 494 469 444 419

779 741 704 666 628

479 455 431 407 383

718 682 647 611 575

350 525 39700

274 412 33000

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

326 490 31200

271 407 26800

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

242 364 24500

213 320 22200

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4–280

DESIGN OF COMPRESSION MEMBERS

Table 4-17 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS16HSS14

Concrete Filled Round HSS HSS16×

Shape

0.312

t design, in. Steel, lb/ft

HSS14× 0.250

f

0.625

0.500

0.375

0.312

0.291 0.233 0.581 0.465 0.349 0.291 52.3 42.1 89.4 72.2 54.6 45.7 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 4 ksi

0

657

986

602

903

760

1140

671

1010

579

868

531

797

6 7 8 9 10

648 644 640 636 631

971 966 961 954 947

593 589 586 582 577

889 884 879 872 865

748 743 738 733 726

1120 1120 1110 1100 1090

659 655 651 646 640

989 983 976 968 960

569 565 561 556 551

853 848 842 835 827

522 518 514 510 505

782 777 771 765 757

11 12 13 14 15

626 620 614 607 600

939 930 921 911 901

572 566 561 554 548

858 850 841 831 821

719 712 704 695 686

1080 1070 1060 1040 1030

634 627 619 612 603

950 940 929 917 905

546 539 533 526 518

818 809 799 789 778

500 494 488 481 474

749 741 731 721 711

16 17 18 19 20

593 585 577 569 560

890 878 866 853 840

540 533 525 517 509

811 800 788 776 763

676 666 655 644 633

1010 999 983 966 949

595 585 576 566 556

892 878 864 849 834

511 502 494 485 476

766 753 741 727 713

467 459 451 442 434

700 688 676 664 651

21 22 23 24 25

551 541 532 522 512

826 812 797 783 767

500 491 482 473 463

750 737 723 709 695

621 609 596 583 570

931 913 894 875 856

545 534 523 512 500

818 801 785 767 750

466 456 446 436 426

699 685 670 654 639

425 416 406 397 387

637 623 609 595 580

26 27 28 29 30

501 491 480 469 458

752 736 720 704 687

453 443 433 423 413

680 665 650 635 619

557 544 530 517 503

836 816 795 775 754

488 476 464 452 439

732 714 696 677 659

415 405 394 383 372

623 607 591 574 558

377 367 357 347 337

566 551 535 520 505

32 34 36 38 40

436 414 391 369 346

654 620 587 553 519

392 371 350 329 308

588 556 524 493 462

475 447 419 391 364

712 670 629 587 547

414 389 365 340 316

622 584 547 510 474

350 328 306 285 264

525 492 459 427 396

316 296 275 255 236

474 443 413 383 354

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

182 274 19800 f

149 225 17300

244 367 19900

203 305 17200

Shape is noncompact for flexure with Fy = 42 ksi.

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

160 240 14200

137 206 12600

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–281

Table 4-17 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 4 ksi

COMPOSITE HSS14HSS10.750

Concrete Filled Round HSS HSS14×

Shape

0.250

t design, in. Steel, lb/ft

0.500

0.375

HSS10.750× 0.250

0.500

0.375

0.233 0.465 0.349 0.233 0.465 0.349 36.8 65.5 49.6 33.4 54.8 41.6 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

HSS12.750×

0

485

728

584

877

502

754 418

626

459

688 390

585

6 7 8 9 10

476 473 469 465 460

714 709 704 697 690

573 569 564 559 553

859 853 846 838 829

492 488 484 479 474

738 732 726 719 711

408 405 401 397 392

612 607 602 595 588

446 442 437 431 425

669 663 655 646 637

379 375 371 366 360

569 563 556 549 540

11 12 13 14 15

455 450 444 437 431

683 674 665 656 646

546 539 532 524 515

819 809 798 786 773

468 462 455 448 441

702 693 683 672 661

387 381 376 369 363

580 572 563 554 544

418 410 402 394 385

627 615 604 591 578

354 348 341 334 326

531 522 511 500 489

16 17 18 19 20

424 416 408 401 392

635 624 613 601 588

507 497 488 478 467

760 746 732 717 701

433 425 416 407 398

649 637 624 611 597

356 348 341 333 325

533 522 511 499 487

376 367 357 347 336

564 550 535 520 504

318 310 301 292 283

477 464 452 438 425

21 22 23 24 25

384 375 366 357 348

576 563 549 536 522

457 446 435 424 412

685 669 652 635 618

389 379 369 359 349

583 568 554 539 524

317 308 300 291 282

475 462 449 436 423

326 315 304 293 282

489 472 456 440 423

274 265 256 246 237

411 397 383 369 355

26 27 28 29 30

339 329 320 310 301

508 494 480 465 451

401 389 377 365 353

601 583 566 548 530

339 329 318 308 297

508 493 477 462 446

273 264 255 246 237

410 396 383 369 356

271 260 249 239 228

407 390 374 358 342

227 218 208 199 190

341 327 313 299 285

32 34 36 38 40

281 262 243 225 207

422 393 365 338 311

330 306 283 261 239

495 460 425 391 359

277 256 236 217 198

415 384 354 325 297

220 202 185 169 153

329 303 278 253 229

207 187 167 150 135

310 280 251 225 203

172 155 138 124 112

258 232 207 186 168

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

113 170 11000

166 249 12600

130 196 10400

92.6 139 8020

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

114 172 7110

90.2 136 5880

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4–282

DESIGN OF COMPRESSION MEMBERS

Table 4-17 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS10.750HSS10

Concrete Filled Round HSS HSS10.750×

Shape

0.250

t design, in. Steel, lb/ft

HSS10× 0.625

0.500

0.375

0.312

0.250

0.233 0.581 0.465 0.349 0.291 0.233 28.1 62.6 50.8 38.6 32.3 26.1 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 4 ksi

0

320

479

478

717 415

622 352

528 319

478

286

429

6 7 8 9 10

310 306 302 298 293

465 460 454 447 440

463 457 451 444 437

694 686 676 666 655

402 397 392 386 379

602 595 587 579 569

340 336 332 327 321

510 504 497 490 481

308 305 300 296 290

462 457 450 443 436

276 272 269 264 259

414 409 403 396 389

11 12 13 14 15

288 282 276 270 263

432 424 415 405 395

428 420 410 400 390

643 629 615 601 585

372 365 356 348 339

558 547 535 522 509

315 308 301 294 286

472 462 452 441 429

285 279 272 265 258

427 418 408 398 387

254 248 242 236 230

381 373 364 354 344

16 17 18 19 20

257 249 242 234 227

385 374 363 352 340

379 368 357 345 333

569 552 535 518 500

330 320 310 300 290

495 480 465 450 435

278 270 261 253 244

417 405 392 379 366

251 243 235 227 219

376 365 353 341 329

223 216 208 201 194

334 323 313 302 290

21 22 23 24 25

219 211 203 195 187

328 316 304 292 280

321 309 297 284 272

482 463 445 427 408

279 269 258 248 237

419 403 387 371 355

235 226 216 207 198

352 338 325 311 297

211 203 194 186 178

316 304 291 279 266

186 178 171 163 155

279 267 256 245 233

26 27 28 29 30

179 171 163 155 148

268 256 245 233 221

260 248 236 224 212

390 372 354 336 319

226 216 205 195 185

340 324 308 293 278

189 180 171 163 154

284 270 257 244 231

169 161 153 145 137

254 242 230 218 206

148 140 133 126 119

222 211 200 189 178

32 34 36 38 40

133 118 106 94.7 85.5

199 177 158 142 128

192 173 155 139 125

289 260 232 208 188

166 147 131 118 106

249 137 221 122 197 109 177 97.5 159 88.0

183 162 145 130 117

105 93.1 83.1 74.5 67.3

158 140 125 112 101

206 122 183 108 163 96.5 146 86.6 132 78.1

Properties φb Mn kip-ft 64.2 96.5 117 176 97.6 147 77.1 116 66.2 99.6 Pe (KL )2/104 kip-in.2 4490 6400 5580 4620 4100 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

54.9 82.6 3530

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–283

Table 4-17 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 4 ksi

COMPOSITE HSS10HSS9.625

Concrete Filled Round HSS HSS10×

Shape

0.188

t design, in. Steel, lb/ft

0.500

0.375

0.312

0.250

0.188

0.174 0.465 0.349 0.291 0.233 0.174 19.7 48.8 37.1 31.1 25.1 19.0 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

HSS9.625×

0

252

378

394

591 333

500 301

452

269

404

237

355

6 7 8 9 10

243 239 236 232 227

364 359 354 347 341

381 376 370 364 358

571 564 556 547 537

322 317 313 308 302

482 476 469 461 453

290 287 282 278 272

436 430 424 416 408

260 256 252 248 243

389 384 378 371 364

228 224 221 217 212

342 337 331 325 318

11 12 13 14 15

222 217 211 206 200

333 325 317 308 299

351 343 335 326 317

526 514 502 489 475

296 289 282 275 267

444 434 423 412 401

267 261 254 247 240

400 391 381 371 360

237 232 226 220 213

356 348 339 329 320

207 202 197 191 185

311 303 295 286 277

16 17 18 19 20

193 187 180 173 167

290 280 270 260 250

308 298 288 278 268

461 447 432 417 401

259 251 242 234 225

389 376 364 351 337

233 225 217 209 201

349 338 326 314 302

206 199 192 185 177

309 299 288 277 266

179 172 166 159 152

268 258 248 238 228

21 22 23 24 25

160 153 146 139 132

239 229 219 208 198

257 247 236 226 215

386 370 354 338 323

216 207 198 189 180

324 311 297 284 271

193 185 177 169 161

290 278 265 253 241

170 163 155 148 140

255 244 233 222 210

145 139 132 125 119

218 208 198 188 178

26 27 28 29 30

125 119 112 106 99.3

188 178 168 158 149

205 195 184 175 165

307 292 277 262 247

172 163 154 146 138

257 244 232 219 207

152 145 137 129 122

229 217 205 194 183

133 126 119 112 105

200 189 178 168 158

112 106 99.5 93.4 87.3

168 159 149 140 131

146 129 115 103 93.4

219 122 194 108 173 96.2 155 86.3 140 77.9

32 34 36 38 40

87.3 131 77.4 116 69.0 103 61.9 92.9 55.9 83.8

183 107 162 95.0 144 84.7 130 76.0 117 68.6

161 142 127 114 103

92.5 139 82.0 123 73.1 110 65.6 98.4 59.2 88.8

76.8 115 68.0 102 60.7 91.0 54.4 81.7 49.1 73.7

50.6 76.0 3110

39.5 59.3 2580

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

42.8 64.4 2940

89.8 135 4910

71.0 107 4090

61.0 91.7 3610

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF COMPRESSION MEMBERS

Table 4-17 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS8.625

Concrete Filled Round HSS HSS8.625×

Shape

0.625

t design, in. Steel, lb/ft

0.500

0.375

0.322

0.250

0.188

0.581 0.465 0.349 0.300 0.233 0.174 53.5 43.4 33.1 28.6 22.4 17.0 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 4 ksi

0

392

588 338

507 284

426

261

391

228

342

199

299

6 7 8 9 10

375 369 362 355 347

562 554 544 532 520

324 319 313 307 300

486 478 470 460 450

272 268 263 258 252

408 402 395 387 378

250 246 241 236 231

374 369 362 354 346

218 214 210 206 201

327 322 316 309 301

190 187 183 179 174

285 280 274 268 261

11 12 13 14 15

338 329 319 309 298

507 493 478 463 447

293 285 276 267 258

439 427 414 401 387

245 239 232 224 216

368 358 347 336 325

225 219 212 205 198

337 328 318 308 297

196 190 184 178 171

293 285 276 267 257

169 164 159 153 147

254 246 238 230 221

16 17 18 19 20

287 276 264 252 241

430 413 396 379 361

249 239 229 219 209

373 359 344 329 314

208 200 192 184 175

313 300 288 275 263

190 183 175 167 160

286 274 263 251 239

165 158 151 144 137

247 237 226 216 206

141 135 129 123 116

212 203 193 184 174

21 22 23 24 25

229 218 208 197 187

344 328 312 297 281

199 189 179 169 160

299 284 269 254 240

167 158 150 141 133

250 237 225 212 200

152 144 136 129 121

228 216 204 193 182

130 123 116 109 103

195 185 174 164 154

110 104 97.7 91.8 85.9

165 156 147 138 129

26 27 28 29 30

177 167 157 148 138

266 251 237 222 208

150 141 132 123 115

225 211 198 185 173

125 118 110 102 95.7

188 176 165 154 144

114 106 99.4 92.6 86.6

171 160 149 139 130

32 34 36 38 40

122 108 96.2 86.3 77.9

183 101 162 89.7 145 80.0 130 71.8 117 64.8

152 135 120 108 97.5

84.1 126 74.5 112 66.4 99.7 59.6 89.5 53.8 80.7

76.1 114 67.4 101 60.1 90.2 54.0 80.9 48.7 73.0

96.3 90.0 83.7 78.1 72.9 64.1 56.8 50.7 45.5 41.0

144 135 126 117 109 96.2 85.2 76.0 68.2 61.5

80.2 120 74.5 112 69.3 104 64.6 96.9 60.4 90.5 53.1 47.0 41.9 37.6 34.0

79.6 70.5 62.9 56.4 50.9

Properties φb Mn kip-ft 84.4 127 70.6 106 55.9 84.0 49.3 74.1 39.9 60.0 Pe (KL )2/104 kip-in.2 3880 3400 2830 2560 2160 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

31.2 46.9 1780

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Page 285

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–285

Table 4-17 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 4 ksi

COMPOSITE HSS7.625HSS7.500

Concrete Filled Round HSS HSS7.625×

Shape

0.375

t design, in. Steel, lb/ft

0.328

0.500

0.375

0.312

0.250

0.349 0.305 0.465 0.349 0.291 0.233 29.1 25.6 37.4 28.6 24.0 19.4 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

HSS7.500×

0

239

359

221

331

281

421

234

351

210

315

186

278

6 7 8 9 10

226 222 217 211 205

339 333 325 317 307

209 205 200 195 189

313 307 300 292 283

265 259 253 247 239

397 389 380 370 359

221 216 211 205 199

331 324 316 308 299

198 194 189 184 179

297 291 284 276 268

175 171 167 162 157

262 257 250 244 236

11 12 13 14 15

198 191 184 177 169

298 287 276 265 253

183 177 170 163 156

274 265 255 244 234

231 223 214 205 196

347 334 321 308 294

193 186 178 171 163

289 278 268 256 245

173 167 160 153 146

259 250 240 230 219

152 146 140 134 128

228 219 211 201 192

16 17 18 19 20

161 153 145 137 129

241 229 217 205 193

148 141 134 126 119

223 212 200 189 178

186 177 167 157 148

279 265 251 236 222

155 147 139 131 123

233 221 209 197 185

139 132 125 118 110

209 198 187 176 166

122 115 109 102 95.9

182 173 163 153 144

21 22 23 24 25

121 113 106 98.2 90.9

181 170 158 147 136

111 104 97.2 90.4 83.6

167 156 146 136 125

139 130 122 114 106

208 195 183 171 160

115 108 100 93.1 85.9

173 162 151 140 129

103 96.5 89.8 83.3 76.8

155 145 135 125 115

89.6 83.5 77.5 71.7 66.1

134 125 116 108 99.1

26 27 28 29 30

84.0 77.9 72.4 67.5 63.1

126 117 109 101 94.6

32 34 36 38 40

55.5 49.1 43.8 39.3 35.5

83.2 73.7 65.7 59.0 53.2

77.3 116 71.7 108 66.7 100 62.2 93.2 58.1 87.1

98.6 91.4 85.0 79.3 74.1

51.1 45.2 40.3 36.2 32.7

65.1 57.7 51.4 46.2 41.7

76.6 67.8 60.5 54.3 49.0

148 137 128 119 111 97.8 86.7 77.3 69.4 62.6

79.4 119 73.6 110 68.5 103 63.8 95.7 59.6 89.5

71.0 106 65.8 98.7 61.2 91.8 57.1 85.6 53.3 80.0

61.1 56.6 52.7 49.1 45.9

91.6 84.9 79.0 73.6 68.8

52.4 46.4 41.4 37.2 33.5

46.9 41.5 37.0 33.2 30.0

40.3 35.7 31.9 28.6 25.8

60.5 53.6 47.8 42.9 38.7

78.6 69.7 62.1 55.8 50.3

70.3 62.3 55.5 49.9 45.0

Properties φb Mn kip-ft 42.7 64.2 38.3 57.5 51.9 78.1 41.2 61.9 35.5 53.4 Pe (KL )2/104 kip-in.2 1860 1720 2110 1760 1580 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

29.5 44.4 1360

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Page 286

4–286

DESIGN OF COMPRESSION MEMBERS

Table 4-17 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS7.500HSS7

Concrete Filled Round HSS HSS7.500×

Shape

HSS7×

0.188

0.500

0.375

0.312

0.250

0.174 14.7 Pn /Ωc φc Pn ASD LRFD

0.465 34.7 Pn /Ωc φc Pn ASD LRFD

0.349 26.6 Pn /Ωc φc Pn ASD LRFD

0.291 22.3 Pn /Ωc φc Pn ASD LRFD

0.233 18.0 Pn /Ωc φc Pn ASD LRFD

0

160

241

256

383

212

319

190

285

168

251

6 7 8 9 10

151 147 144 139 135

226 221 215 209 202

239 233 227 220 213

359 350 341 330 319

199 194 189 183 177

298 291 283 275 265

178 174 169 164 158

267 261 254 246 237

157 153 149 144 139

235 229 223 216 208

11 12 13 14 15

130 125 120 114 109

195 187 179 171 163

204 196 187 178 169

307 294 281 267 253

170 163 156 148 141

255 245 234 222 211

152 146 139 133 126

228 219 209 199 189

134 128 122 116 110

200 192 183 174 165

16 17 18 19 20

103 97.2 91.5 85.8 80.2

154 146 137 129 120

159 150 141 133 124

239 225 212 199 187

133 125 117 110 102

199 188 176 164 153

119 112 105 98.0 91.3

178 168 157 147 137

104 97.5 91.3 85.2 79.2

156 146 137 128 119

21 22 23 24 25

74.7 69.3 64.1 59.0 54.4

112 104 96.2 88.5 81.5

116 108 101 93.1 85.8

175 163 151 140 129

94.6 87.5 80.4 73.8 68.0

142 131 121 111 102

84.6 78.2 71.9 66.0 60.8

127 117 108 99.0 91.3

73.3 67.6 62.0 56.9 52.5

110 101 93.0 85.4 78.7

26 27 28 29 30

50.3 46.6 43.3 40.4 37.7

75.4 69.9 65.0 60.6 56.6

79.4 73.6 68.4 63.8 59.6

119 111 103 95.9 89.6

62.9 58.3 54.2 50.6 47.2

94.4 87.5 81.4 75.8 70.9

56.2 52.2 48.5 45.2 42.2

84.4 78.2 72.7 67.8 63.4

48.5 45.0 41.8 39.0 36.4

72.8 67.5 62.8 58.5 54.7

32 34 36 38 40

33.2 29.4 26.2 23.5 21.2

49.8 44.1 39.3 35.3 31.9

52.4 46.4 41.4 37.2

78.8 69.8 62.2 55.8

41.5 36.8 32.8 29.4

62.3 55.2 49.2 44.2

37.1 32.9 29.3 26.3

55.7 49.3 44.0 39.5

32.0 28.4 25.3 22.7

48.1 42.6 38.0 34.1

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 4 ksi

Properties φb Mn kip-ft 23.1 34.7 44.6 67.0 35.4 53.3 Pe (KL )2/104 kip-in.2 1120 1670 1400 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

30.6 45.9 1250

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

25.4 38.2 1080

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–287

Table 4-17 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 4 ksi

COMPOSITE HSS7HSS6.875

Concrete Filled Round HSS HSS7×

Shape

0.188

0.125

0.500

0.375

0.312

0.174 13.7 Pn /Ωc φc Pn ASD LRFD

0.116 9.19 Pn /Ωc φc Pn ASD LRFD

0.465 34.1 Pn /Ωc φc Pn ASD LRFD

0.349 26.1 Pn /Ωc φc Pn ASD LRFD

0.291 21.9 Pn /Ωc φc Pn ASD LRFD

0

144

217

121

182

249

374

207

311

186

278

6 7 8 9 10

134 131 127 123 119

202 197 191 185 178

112 109 106 102 97.9

168 164 158 153 147

233 227 221 214 206

349 341 331 320 309

194 189 184 178 171

290 283 275 267 257

173 169 164 159 153

260 253 246 239 230

11 12 13 14 15

114 109 104 98.2 92.7

171 163 155 147 139

93.6 89.1 84.5 79.8 75.0

140 134 127 120 113

198 189 181 171 162

297 284 271 257 243

165 158 150 143 135

247 237 226 214 203

147 141 134 128 121

221 212 202 192 181

16 17 18 19 20

87.2 81.7 76.3 70.9 65.7

131 123 114 106 98.5

70.2 65.5 60.8 56.2 51.7

105 98.2 91.1 84.2 77.5

153 144 135 127 118

229 215 203 190 178

127 120 112 104 96.9

191 180 168 157 145

114 107 100 93.3 86.6

171 161 150 140 130

21 22 23 24 25

60.6 55.6 50.9 46.7 43.1

90.9 83.4 76.3 70.1 64.6

47.4 43.1 39.5 36.3 33.4

71.0 64.7 59.2 54.4 50.1

110 103 94.9 87.4 80.6

166 154 143 131 121

89.7 82.6 75.7 69.5 64.1

135 124 114 104 96.1

80.1 73.8 67.6 62.1 57.2

120 111 101 93.2 85.9

26 27 28 29 30

39.8 36.9 34.3 32.0 29.9

59.7 55.4 51.5 48.0 44.9

30.9 28.6 26.6 24.8 23.2

46.3 43.0 40.0 37.2 34.8

74.5 69.1 64.2 59.9 55.9

112 104 96.5 90.0 84.1

59.2 54.9 51.1 47.6 44.5

88.9 82.4 76.6 71.4 66.7

52.9 49.1 45.6 42.5 39.7

79.4 73.6 68.4 63.8 59.6

32 34 36 38 40

26.3 23.3 20.8 18.6 16.8

39.4 34.9 31.2 28.0 25.2

20.4 18.1 16.1 14.5 13.1

30.6 27.1 24.2 21.7 19.6

49.2 43.5 38.8

73.9 65.5 58.4

39.1 34.6 30.9 27.7

58.7 52.0 46.3 41.6

34.9 30.9 27.6 24.8

52.4 46.4 41.4 37.2

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

HSS6.875×

Properties φb Mn kip-ft 19.9 29.9 14.1 21.2 42.9 64.4 Pe (KL )2/104 kip-in.2 884 686 1570 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

34.1 51.2 1320

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

29.4 44.2 1170

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4–288

DESIGN OF COMPRESSION MEMBERS

Table 4-17 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS6.875HSS6.625

Concrete Filled Round HSS HSS6.875×

Shape

HSS6.625×

0.250

0.188

0.500

0.432

0.375

0.233 17.7 Pn /Ωc φc Pn ASD LRFD

0.174 13.4 Pn /Ωc φc Pn ASD LRFD

0.465 32.7 Pn /Ωc φc Pn ASD LRFD

0.402 28.6 Pn /Ωc φc Pn ASD LRFD

0.349 25.1 Pn /Ωc φc Pn ASD LRFD

0

163

245

140

211

237

356

216

323

197

295

6 7 8 9 10

152 149 144 140 135

228 223 216 209 202

131 127 123 119 115

196 191 185 179 172

220 215 208 201 193

331 322 312 301 290

200 195 189 183 176

300 293 284 274 263

183 178 173 167 160

274 267 259 250 241

11 12 13 14 15

129 123 118 112 105

194 185 176 167 158

110 105 99.7 94.4 89.0

165 157 150 142 133

185 176 168 158 149

277 265 251 238 224

168 161 152 144 136

252 241 229 216 204

154 147 139 132 124

231 220 209 198 186

141 132 124 116 108

211 199 186 174 162

128 119 111 103 95.2

191 179 166 154 143

117 109 102 94.1 86.9

175 164 152 141 130

150 138 127 116 107

88.3 81.6 75.1 68.9 63.5

133 123 113 104 95.5

79.9 73.0 66.9 61.4 56.6

120 110 101 92.4 85.1

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 4 ksi

16 17 18 19 20

99.3 93.1 87.0 81.0 75.1

149 140 131 121 113

83.5 78.1 72.8 67.5 62.4

125 117 109 101 93.6

21 22 23 24 25

69.3 63.8 58.3 53.6 49.4

104 95.6 87.5 80.3 74.0

57.4 52.5 48.0 44.1 40.7

86.1 78.7 72.0 66.2 61.0

99.6 92.0 84.4 77.5 71.4

26 27 28 29 30

45.6 42.3 39.3 36.7 34.3

68.5 63.5 59.0 55.0 51.4

37.6 34.9 32.4 30.2 28.2

56.4 52.3 48.6 45.3 42.3

66.0 61.2 56.9 53.1 49.6

99.3 92.0 85.6 79.8 74.6

58.7 54.5 50.6 47.2 44.1

88.3 81.9 76.1 71.0 66.3

52.4 48.5 45.1 42.1 39.3

78.7 73.0 67.9 63.3 59.1

32 34 36 38

30.1 26.7 23.8 21.4

45.2 40.0 35.7 32.0

24.8 22.0 19.6 17.6

37.2 33.0 29.4 26.4

43.6 38.6 34.4

65.5 58.0 51.8

38.8 34.4 30.6

58.3 51.6 46.1

34.6 30.6 27.3

51.9 46.0 41.0

Properties φb Mn kip-ft 24.4 36.7 19.1 28.8 39.5 59.3 Pe (KL )2/104 kip-in.2 1010 834 1390 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

35.2 52.9 1270

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

31.4 47.2 1160

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–289

Table 4-17 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 4 ksi

COMPOSITE HSS6.625

Concrete Filled Round HSS HSS6.625×

Shape

0.312

0.280

0.250

0.188

0.125

0.291 21.1 Pn /Ωc φc Pn ASD LRFD

0.260 19.0 Pn /Ωc φc Pn ASD LRFD

0.233 17.0 Pn /Ωc φc Pn ASD LRFD

0.174 12.9 Pn /Ωc φc Pn ASD LRFD

0.116 8.69 Pn /Ωc φc Pn ASD LRFD

0

176

264

165

247

155

232

133

199

111

166

6 7 8 9 10

164 159 154 149 143

245 239 232 224 215

153 149 145 140 134

230 224 217 209 201

144 140 136 131 126

216 210 203 196 189

123 120 116 111 107

184 179 174 167 160

102 98.7 95.3 91.6 87.6

153 148 143 137 131

11 12 13 14 15

137 131 125 118 111

206 197 187 177 167

129 123 116 110 104

193 184 175 165 156

120 115 109 103 96.9

181 172 163 154 145

102 97.2 92.1 86.9 81.6

153 146 138 130 122

83.4 79.0 74.5 69.9 65.3

125 119 112 105 98.0

16 17 18 19 20

104 97.4 90.7 84.0 77.6

156 146 136 126 116

97.4 91.0 84.7 78.5 72.5

146 137 127 118 109

90.9 84.8 78.9 73.0 67.3

136 127 118 110 101

76.2 71.0 65.8 60.7 55.8

114 106 98.7 91.1 83.7

60.7 56.2 51.8 47.5 43.3

91.1 84.3 77.7 71.2 65.0

21 22 23 24 25

71.3 65.2 59.6 54.8 50.5

107 97.8 89.4 82.2 75.7

66.6 60.8 55.7 51.1 47.1

99.9 91.3 83.5 76.7 70.7

61.8 56.4 51.6 47.4 43.7

92.7 84.6 77.4 71.1 65.5

51.0 46.4 42.5 39.0 36.0

76.4 69.6 63.7 58.5 53.9

39.3 35.8 32.8 30.1 27.7

58.9 53.7 49.1 45.1 41.6

26 27 28 29 30

46.7 43.3 40.2 37.5 35.1

70.0 64.9 60.4 56.3 52.6

43.6 40.4 37.6 35.0 32.7

65.3 60.6 56.3 52.5 49.1

40.4 37.4 34.8 32.5 30.3

60.6 56.2 52.2 48.7 45.5

33.2 30.8 28.7 26.7 25.0

49.9 46.2 43.0 40.1 37.5

25.6 23.8 22.1 20.6 19.3

38.5 35.7 33.2 30.9 28.9

32 34 36 38

30.8 27.3 24.3

46.2 40.9 36.5

28.8 25.5 22.7

43.1 38.2 34.1

26.7 23.6 21.1

40.0 35.4 31.6

21.9 19.4 17.3 15.6

32.9 29.2 26.0 23.3

16.9 15.0 13.4 12.0

25.4 22.5 20.1 18.0

t design, in. Steel, lb/ft

Effective length, KL (ft)

Design

Properties φb Mn kip-ft 27.1 40.7 24.7 37.1 22.6 33.9 Pe (KL )2/104 kip-in.2 1040 967 896 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

17.7 26.6 738

12.5 18.8 569

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Page 290

4–290

DESIGN OF COMPRESSION MEMBERS

Table 4-17 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS6

Concrete Filled Round HSS HSS6×

Shape

0.500

t design, in. Steel, lb/ft

0.375

0.312

0.280

0.250

0.188

0.465 0.349 0.291 0.260 0.233 0.174 29.4 22.5 19.0 17.1 15.4 11.7 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 4 ksi

0

208

312

172

258

153

230

143

215

134

201

114

172

1 2 3 4 5

208 206 204 200 195

312 309 305 300 293

172 170 168 165 162

258 256 252 248 243

153 152 150 147 144

230 228 225 221 216

143 142 140 138 135

214 213 210 207 202

134 133 131 129 126

201 199 197 194 189

114 113 112 110 107

171 170 168 165 161

6 7 8 9 10

190 184 177 170 162

285 276 266 255 243

157 152 147 141 134

236 228 220 211 201

140 136 131 125 120

210 204 196 188 179

131 127 122 117 112

196 190 183 175 167

123 119 114 110 105

184 178 172 164 157

104 101 96.9 92.7 88.2

156 151 145 139 132

11 12 13 14 15

154 146 138 130 121

231 220 207 195 182

127 120 113 105 98.1

191 180 169 158 147

113 107 101 94.1 87.5

170 161 151 141 131

106 99.9 93.8 87.7 81.6

159 150 141 132 122

149 140 132 123 115

83.5 78.6 73.6 68.6 63.6

125 118 110 103 95.5

16 17 18 19 20

113 105 96.5 88.6 81.0

170 157 145 133 122

90.8 83.6 76.6 70.2 64.4

136 125 115 105 96.8

99.2 93.6 88.0 82.2 76.4

81.0 121 74.6 112 68.3 102 62.3 93.5 56.4 84.6

75.5 113 69.5 104 63.7 95.5 58.0 87.0 52.5 78.8

70.7 106 65.1 97.7 59.7 89.5 54.4 81.6 49.2 73.8

58.7 53.8 49.2 44.6 40.3

88.0 80.8 73.7 66.9 60.4

21 22 23 24 25

73.6 111 67.0 101 61.3 92.2 56.3 84.6 51.9 78.0

58.7 53.5 48.9 44.9 41.4

88.2 80.4 73.5 67.5 62.3

51.2 46.6 42.6 39.2 36.1

76.7 69.9 64.0 58.7 54.1

47.6 43.4 39.7 36.5 33.6

71.4 65.1 59.6 54.7 50.4

44.6 40.7 37.2 34.2 31.5

66.9 61.0 55.8 51.3 47.2

36.5 33.3 30.4 28.0 25.8

54.8 49.9 45.7 41.9 38.6

26 28 30 32 34

48.0 41.4 36.0 31.7

38.3 33.0 28.8 25.3

57.6 49.6 43.2 38.0

33.4 28.8 25.1 22.0

50.1 43.2 37.6 33.0

31.1 26.8 23.3 20.5

46.6 40.2 35.0 30.8

29.1 25.1 21.9 19.2 17.0

43.7 37.7 32.8 28.8 25.5

23.8 20.5 17.9 15.7 13.9

35.7 30.8 26.8 23.6 20.9

72.1 62.2 54.2 47.6

Properties φb Mn kip-ft 31.7 47.6 25.3 38.0 21.8 32.8 19.9 29.9 Pe (KL )2/104 kip-in.2 994 830 741 690 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

18.2 27.3 646

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

14.3 21.4 529

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–291

Table 4-17 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 4 ksi

COMPOSITE HSS6HSS5.563

Concrete Filled Round HSS HSS6×

Shape

0.125

t design, in. Steel, lb/ft

0.500

0.375

0.258

0.188

0.134

0.116 0.465 0.349 0.240 0.174 0.124 7.85 27.1 20.8 14.6 10.8 7.78 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

HSS5.563×

0

94.6 142

188

283

155

233

123

184

103

154

86.7

130

1 2 3 4 5

94.3 93.5 92.2 90.4 88.2

141 140 138 136 132

188 186 184 180 175

282 279 275 270 263

155 154 151 148 145

232 230 227 223 217

122 121 120 117 114

184 182 179 176 171

102 101 99.8 97.7 95.1

153 152 150 147 143

86.4 85.6 84.2 82.4 80.1

130 128 126 124 120

6 7 8 9 10

85.5 82.4 79.0 75.4 71.4

128 124 119 113 107

170 164 158 151 143

256 247 237 226 215

140 135 129 123 116

210 202 194 184 174

111 106 102 97.0 91.7

166 160 153 145 138

92.0 88.5 84.6 80.4 75.9

138 133 127 121 114

77.3 74.2 70.7 67.0 63.1

116 111 106 101 94.6

11 12 13 14 15

67.4 101 63.1 94.7 58.9 88.3 54.6 81.9 50.3 75.5

135 127 119 110 102

203 191 178 166 153

109 102 95.0 87.8 80.7

164 153 143 132 121

86.3 80.7 75.0 69.4 63.7

129 121 113 104 95.6

71.3 107 66.5 99.8 61.7 92.6 56.9 85.4 52.2 78.3

59.0 54.9 50.7 46.5 42.4

88.5 82.3 76.0 69.8 63.6

16 17 18 19 20

46.1 42.0 38.1 34.3 30.9

69.2 63.1 57.2 51.4 46.4

93.9 85.9 78.1 70.6 63.7

141 129 117 106 95.7

74.2 112 68.2 102 62.3 93.6 56.6 85.1 51.1 76.8

58.2 52.9 47.8 42.9 38.7

87.4 79.4 71.6 64.3 58.0

47.5 43.1 38.7 34.7 31.3

71.3 64.6 58.0 52.1 47.0

38.4 34.6 30.9 27.7 25.0

57.7 51.9 46.4 41.6 37.6

21 22 23 24 25

28.1 25.6 23.4 21.5 19.8

42.1 38.3 35.1 32.2 29.7

57.8 52.6 48.2 44.2 40.8

86.8 79.1 72.4 66.5 61.3

46.3 42.2 38.6 35.5 32.7

69.6 63.5 58.1 53.3 49.1

35.1 32.0 29.2 26.9 24.8

52.6 47.9 43.9 40.3 37.1

28.4 25.9 23.7 21.8 20.1

42.6 38.9 35.5 32.6 30.1

22.7 20.7 18.9 17.4 16.0

34.1 31.0 28.4 26.1 24.0

26 28 30 32 34

18.3 15.8 13.7 12.1 10.7

27.5 23.7 20.6 18.1 16.1

37.7 32.5 28.3

56.6 48.8 42.5

30.2 26.1 22.7

45.4 39.2 34.1

22.9 19.7 17.2

34.3 29.6 25.8

18.5 16.0 13.9

27.8 14.8 24.0 12.8 20.9 11.1 9.78

22.2 19.2 16.7 14.7

Properties φb Mn kip-ft 10.1 15.2 26.7 40.2 21.4 32.2 15.8 23.8 Pe (KL )2/104 kip-in.2 406 769 643 508 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

12.1 18.2 412

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.11 13.7 329

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4–292

DESIGN OF COMPRESSION MEMBERS

Table 4-17 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS5.500HSS5

Concrete Filled Round HSS HSS5.500×

Shape

0.500

t design, in. Steel, lb/ft

0.375

HSS5× 0.258

0.500

0.375

0.312

0.465 0.349 0.240 0.465 0.349 0.291 26.7 20.6 14.5 24.1 18.5 15.6 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 4 ksi

0

186

279

153

230

121

181

166

250

135

202

119

179

1 2 3 4 5

185 183 181 177 173

278 275 271 266 260

153 151 149 146 142

229 227 224 219 213

121 120 118 115 112

181 179 177 173 168

166 164 161 158 153

249 247 243 237 230

134 133 130 127 123

201 199 196 191 185

119 118 116 113 109

179 177 173 169 164

6 7 8 9 10

168 162 155 148 140

252 243 233 222 211

137 132 126 120 114

206 198 190 180 170

109 105 99.9 95.0 89.8

163 157 150 143 135

147 141 134 126 118

221 212 201 190 178

118 113 107 101 93.9

177 169 160 151 141

105 100 94.9 89.3 83.4

157 150 142 134 125

11 12 13 14 15

133 124 116 108 99.5

199 187 174 162 150

107 99.6 92.5 85.3 78.4

160 149 139 128 118

84.3 78.7 73.1 67.4 61.8

166 153 141 128 116

87.1 80.3 74.1 67.9 61.8

131 121 111 102 92.8

16 17 18 19 20

91.3 83.4 75.7 68.2 61.5

137 125 114 102 92.5

21 22 23 24 25

55.8 50.9 46.5 42.7 39.4

26 28 30

36.4 31.4

126 110 118 102 110 93.5 101 85.3 92.7 77.3

77.4 116 71.3 107 65.2 97.7 59.1 88.7 53.3 79.9

72.3 109 66.2 99.6 60.4 90.8 54.7 82.2 49.4 74.2

56.4 51.1 45.9 41.2 37.2

84.5 76.6 68.9 61.8 55.8

69.5 104 62.0 93.2 55.3 83.1 49.6 74.6 44.8 67.3

55.8 50.2 44.7 40.1 36.2

83.9 75.4 67.2 60.3 54.5

48.0 43.2 38.6 34.7 31.3

72.2 65.0 58.1 52.1 47.0

83.9 76.4 69.9 64.2 59.2

44.8 40.8 37.3 34.3 31.6

67.3 61.3 56.1 51.5 47.5

33.8 30.8 28.1 25.8 23.8

50.6 46.1 42.2 38.8 35.7

40.6 37.0 33.9 31.1 28.7

61.0 55.6 50.9 46.7 43.1

32.9 29.9 27.4 25.2 23.2

49.4 45.0 41.2 37.8 34.9

28.4 25.9 23.7 21.7 20.0

42.7 38.9 35.6 32.7 30.1

54.7 47.2

29.2 25.2 21.9

43.9 37.9 33.0

22.0 19.0 16.5

33.0 28.5 24.8

26.5

39.8

21.4

32.2

18.5

27.8

Properties φb Mn kip-ft 26.1 39.2 20.9 31.4 15.4 23.2 21.0 31.6 Pe (KL )2/104 kip-in.2 739 619 489 534 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

16.9 25.4 14.6 22.0 450 401

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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4–293

Table 4-17 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 4 ksi

COMPOSITE HSS5HSS4.500

Concrete Filled Round HSS HSS5×

Shape

0.258

t design, in. Steel, lb/ft

0.188

0.125

0.375

0.337

0.240 0.233 0.174 0.116 0.349 0.313 13.1 12.7 9.67 6.51 16.5 15.0 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

0.250

HSS4.500×

0

106

159

104

156

87.7

132

71.3

107

117

176

109

163

1 2 3 4 5

105 104 103 100 96.8

158 157 154 150 145

104 102 101 98.2 95.0

155 154 151 147 143

87.4 86.5 84.9 82.7 80.1

131 130 127 124 120

71.0 70.2 68.8 67.0 64.7

107 105 103 100 97.0

117 115 112 109 105

175 173 169 163 157

108 107 105 101 97.4

163 160 157 152 146

6 7 8 9 10

93.0 88.8 84.1 79.2 73.9

140 133 126 119 111

91.4 87.2 82.6 77.7 72.6

137 131 124 117 109

76.9 73.3 69.4 65.2 60.8

115 110 104 97.8 91.3

62.0 58.9 55.5 52.0 48.3

92.9 88.3 83.3 78.0 72.4

99.6 94.0 88.1 82.1 76.0

149 141 132 123 114

92.7 87.5 81.8 75.8 69.7

139 131 123 114 105

11 12 13 14 15

68.6 103 63.1 94.7 57.7 86.6 52.4 78.6 47.2 70.8

67.3 101 62.0 93.0 56.7 85.0 51.4 77.1 46.3 69.5

56.3 51.8 47.3 42.8 38.5

84.5 77.7 70.9 64.2 57.8

44.5 40.7 36.9 33.2 29.6

66.7 61.0 55.3 49.8 44.5

69.7 105 63.5 95.4 57.3 86.1 51.3 77.1 45.6 68.5

63.6 57.9 52.4 47.0 41.8

95.5 87.1 78.7 70.6 62.8

16 17 18 19 20

42.2 37.5 33.4 30.0 27.1

63.4 56.2 50.1 45.0 40.6

41.4 36.8 32.8 29.4 26.6

62.2 55.1 49.2 44.1 39.8

34.4 30.4 27.2 24.4 22.0

51.6 45.7 40.7 36.6 33.0

26.2 23.2 20.7 18.6 16.8

39.3 34.8 31.1 27.9 25.2

40.1 35.5 31.7 28.4 25.7

60.3 53.4 47.6 42.7 38.6

36.8 32.6 29.1 26.1 23.5

55.3 49.0 43.7 39.2 35.4

21 22 23 24 25

24.5 22.4 20.5 18.8 17.3

36.8 33.5 30.7 28.2 26.0

24.1 21.9 20.1 18.4 17.0

36.1 32.9 30.1 27.7 25.5

20.0 18.2 16.6 15.3 14.1

29.9 27.3 24.9 22.9 21.1

15.2 13.9 12.7 11.6 10.7

22.8 20.8 19.0 17.5 16.1

23.3 21.2 19.4 17.8

35.0 31.9 29.2 26.8

21.4 19.5 17.8 16.4

32.1 29.3 26.8 24.6

26 28

16.0 13.8

24.0 20.7

15.7 13.5

23.6 13.0 20.3 11.2

19.5 16.8

9.92 8.56

14.9 12.8

Properties φb Mn kip-ft 12.5 18.8 12.2 18.4 9.61 14.4 6.84 10.3 Pe (KL )2/104 kip-in.2 355 349 289 220 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

13.4 20.1 314

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF COMPRESSION MEMBERS

Table 4-17 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS4.500HSS4

Concrete Filled Round HSS HSS4.500×

Shape

HSS4×

0.237

0.188

0.125

0.313

0.250

0.220 10.8 Pn /Ωc φc Pn ASD LRFD

0.174 8.67 Pn /Ωc φc Pn ASD LRFD

0.116 5.85 Pn /Ωc φc Pn ASD LRFD

0.291 12.3 Pn /Ωc φc Pn ASD LRFD

0.233 10.0 Pn /Ωc φc Pn ASD LRFD

0

86.8

130

75.3

113

60.8

91.2

88.6

133

76.6

115

1 2 3 4 5

86.4 85.2 83.4 80.8 77.6

130 128 125 121 116

75.0 74.0 72.3 70.1 67.4

112 111 108 105 101

60.5 59.6 58.2 56.3 54.0

90.7 89.5 87.4 84.5 81.0

88.1 86.6 84.2 80.9 76.9

132 130 126 121 115

76.2 74.9 72.8 70.0 66.5

114 112 109 105 99.8

6 7 8 9 10

73.9 69.8 65.3 60.6 55.7

111 105 98.0 90.8 83.5

64.1 60.5 56.6 52.5 48.2

96.2 90.8 84.9 78.7 72.3

51.3 48.2 44.9 41.4 37.9

76.9 72.3 67.4 62.2 56.8

72.3 67.2 61.7 56.5 51.3

108 101 92.6 84.9 77.1

62.6 58.2 53.5 48.6 43.7

93.8 87.2 80.2 72.9 65.5

11 12 13 14 15

50.7 45.8 41.0 36.4 31.9

76.1 68.7 61.5 54.5 47.9

43.9 39.6 35.5 31.4 27.6

65.9 59.4 53.2 47.2 41.3

34.3 30.8 27.3 24.0 21.0

51.4 46.1 41.0 36.1 31.4

46.1 41.0 36.2 31.5 27.4

69.3 61.7 54.3 47.3 41.2

38.8 34.1 29.8 26.0 22.6

58.2 51.1 44.8 39.1 34.0

16 17 18 19 20

28.0 24.8 22.2 19.9 17.9

42.1 37.3 33.2 29.8 26.9

24.2 21.5 19.1 17.2 15.5

36.3 32.2 28.7 25.8 23.3

18.4 16.3 14.6 13.1 11.8

27.6 24.5 21.8 19.6 17.7

24.1 21.3 19.0 17.1 15.4

36.2 32.1 28.6 25.7 23.2

19.9 17.6 15.7 14.1 12.7

29.9 26.5 23.6 21.2 19.1

21 22 23 24 25

16.3 14.8 13.6 12.5 11.5

24.4 22.2 20.4 18.7 17.2

14.1 12.8 11.7 10.8 9.92

21.1 19.2 17.6 16.1 14.9

10.7 9.74 8.92 8.19 7.55

16.0 14.6 13.4 12.3 11.3

14.0 12.7

21.0 19.1

11.6 10.5

17.4 15.8

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 4 ksi

Properties φb Mn kip-ft 9.27 13.9 7.65 11.5 5.45 8.19 Pe (KL )2/104 kip-in.2 236 204 155 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

8.94 13.4 189

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7.50 11.3 164

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–295

Table 4-17 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 4 ksi

COMPOSITE HSS4

Concrete Filled Round HSS HSS4×

Shape

0.237

0.226

0.220

0.188

0.125

0.220 9.53 Pn /Ωc φc Pn ASD LRFD

0.210 9.12 Pn /Ωc φc Pn ASD LRFD

0.205 8.89 Pn /Ωc φc Pn ASD LRFD

0.174 7.66 Pn /Ωc φc Pn ASD LRFD

0.116 5.18 Pn /Ωc φc Pn ASD LRFD

0

73.7

111

71.6

107

70.5

106

63.8

95.7

51.0

76.5

1 2 3 4 5

73.3 72.1 70.1 67.4 64.1

110 108 105 101 96.1

71.2 70.0 68.1 65.5 62.2

107 105 102 98.2 93.4

70.1 68.9 67.0 64.4 61.3

105 103 101 96.6 91.9

63.4 62.4 60.6 58.3 55.4

95.2 93.6 91.0 87.5 83.1

50.7 49.8 48.4 46.4 44.0

76.0 74.7 72.6 69.6 66.0

6 7 8 9 10

60.2 56.0 51.5 46.8 42.1

90.4 84.0 77.2 70.2 63.1

58.5 54.4 50.0 45.5 40.9

87.8 81.6 75.0 68.2 61.3

57.6 53.5 49.2 44.8 40.2

86.4 80.3 73.8 67.1 60.3

52.1 48.4 44.5 40.4 36.3

78.2 72.6 66.8 60.7 54.5

41.3 38.2 35.0 31.7 28.3

61.9 57.4 52.5 47.5 42.5

11 12 13 14 15

37.4 32.9 28.6 25.0 21.7

56.1 49.3 42.9 37.5 32.7

36.3 31.9 27.7 23.9 20.8

54.5 47.9 41.6 35.9 31.3

35.8 31.4 27.3 23.5 20.5

53.6 47.2 41.0 35.3 30.8

32.3 28.4 24.6 21.2 18.5

48.4 42.6 36.9 31.9 27.8

25.0 21.9 18.8 16.2 14.2

37.6 32.8 28.3 24.4 21.2

16 17 18 19 20

19.1 16.9 15.1 13.6 12.2

28.7 25.4 22.7 20.4 18.4

18.3 16.2 14.5 13.0 11.7

27.5 24.4 21.7 19.5 17.6

18.0 16.0 14.2 12.8 11.5

27.0 23.9 21.4 19.2 17.3

16.3 14.4 12.8 11.5 10.4

24.4 21.6 19.3 17.3 15.6

12.4 11.0 9.83 8.82 7.96

18.7 16.5 14.7 13.2 11.9

21 22

11.1 10.1

16.7 15.2

10.6 9.68

16.0 14.6

10.5 9.53

15.7 14.3

14.2 12.9

7.22 6.58

10.8 9.87

t design, in. Steel, lb/ft

Effective length, KL (ft)

Design

9.44 8.60

Properties φb Mn kip-ft 7.16 10.8 6.90 10.4 6.76 10.2 Pe (KL )2/104 kip-in.2 158 154 152 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

5.92 8.89 137

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.23 6.35 105

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DESIGN OF COMPRESSION MEMBERS

Table 4-18

Available Strength in Axial Compression, kips

COMPOSITE HSS18HSS16

Concrete Filled Round HSS HSS18×

Shape

0.500

t design, in. Steel, lb/ft

HSS16× 0.375

0.625

0.500

0.438

0.375

0.465 0.349 0.581 0.465 0.407 0.349 93.5 70.7 103 82.9 72.9 62.6 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design 0

Effective length, KL (ft)

Fy = 42 ksi fc′ = 5 ksi

1080 1620

966

1450 1000 1500

900

1350

848

1270

798

1200

6 7 8 9 10

1070 1060 1060 1050 1050

1600 1600 1590 1580 1570

954 950 945 940 933

1430 1420 1420 1410 1400

987 983 977 971 964

1480 1470 1470 1460 1450

888 883 878 872 866

1330 1320 1320 1310 1300

836 832 827 821 815

1250 1250 1240 1230 1220

786 782 777 771 765

1180 1170 1170 1160 1150

11 12 13 14 15

1040 1030 1020 1020 1010

1560 1550 1540 1520 1510

927 920 912 904 895

1390 1380 1370 1360 1340

956 948 939 930 920

1430 1420 1410 1390 1380

859 851 843 834 824

1290 1280 1260 1250 1240

808 800 792 784 775

1210 1200 1190 1180 1160

759 751 744 735 726

1140 1130 1120 1100 1090

16 17 18 19 20

997 986 976 964 952

1500 1480 1460 1450 1430

885 876 865 854 843

1330 1310 1300 1280 1260

909 898 886 874 861

1360 1350 1330 1310 1290

814 804 793 781 770

1220 1210 1190 1170 1150

765 755 744 733 722

1150 1130 1120 1100 1080

717 707 697 686 675

1080 1060 1050 1030 1010

21 22 23 24 25

940 927 914 901 887

1410 1390 1370 1350 1330

832 820 807 794 781

1250 1230 1210 1190 1170

848 834 820 806 791

1270 1250 1230 1210 1190

757 745 732 718 705

1140 1120 1100 1080 1060

710 698 685 672 659

1070 1050 1030 1010 989

664 652 640 627 615

996 978 960 941 922

26 27 28 29 30

872 858 843 828 813

1310 1290 1260 1240 1220

768 754 740 726 712

1150 1130 1110 1090 1070

776 761 745 729 713

1160 1140 1120 1090 1070

691 676 662 647 632

1040 1010 993 971 949

646 632 618 604 590

969 948 928 907 885

602 589 575 562 548

903 883 863 843 822

32 34 36 38 40

781 749 717 684 651

1170 1120 1070 1030 976

682 653 622 592 561

1020 979 933 888 842

681 1020 648 972 614 922 581 872 548 822

602 572 541 511 481

904 858 812 766 721

561 532 503 474 445

842 798 755 711 668

520 493 465 437 409

781 739 697 655 614

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

357 536 41100

280 421 34300

333 500 32000

277 416 27700

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

247 372 25400

217 327 23100

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–297

Table 4-18 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 5 ksi

COMPOSITE HSS16HSS14

Concrete Filled Round HSS HSS16×

Shape

0.312

t design, in. Steel, lb/ft

0.250

0.625

0.500

0.375

0.312

0.291 0.233 0.581 0.465 0.349 0.291 52.3 42.1 89.4 72.2 54.6 45.7 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

HSS14× f

0

746

1120

692

1040

822

1230

734

1100

645

967

598

898

6 7 8 9 10

734 730 725 720 714

1100 1090 1090 1080 1070

680 676 672 666 661

1020 1010 1010 1000 991

808 803 797 790 783

1210 1200 1200 1190 1170

721 717 711 705 699

1080 1070 1070 1060 1050

633 628 624 618 612

949 943 935 927 918

587 583 578 572 566

880 874 867 859 850

11 12 13 14 15

707 700 693 685 676

1060 1050 1040 1030 1010

654 647 640 632 624

981 971 960 948 936

775 766 757 747 737

1160 1150 1140 1120 1110

691 683 675 666 656

1040 1030 1010 999 984

605 598 590 581 573

907 897 885 872 859

560 553 545 537 529

840 829 818 806 793

16 17 18 19 20

667 657 648 637 626

1000 986 971 956 940

615 606 596 586 576

922 909 894 879 863

726 714 702 690 677

1090 1070 1050 1030 1020

646 636 625 613 601

969 953 937 920 902

563 554 543 533 522

845 830 815 799 783

520 510 501 491 480

780 766 751 736 720

21 22 23 24 25

615 604 592 580 568

923 906 888 870 852

565 554 542 531 519

847 831 814 796 779

664 650 636 622 607

995 975 954 932 910

589 576 564 551 537

884 865 845 826 806

511 499 488 476 463

766 749 731 713 695

470 459 447 436 424

704 688 671 654 637

26 27 28 29 30

555 543 530 517 504

833 814 795 775 756

507 495 482 470 457

760 742 724 705 686

592 577 562 547 531

888 866 843 820 797

524 510 496 482 468

786 765 744 723 702

451 439 426 413 401

677 658 639 620 601

413 401 389 377 365

619 601 583 565 547

32 34 36 38 40

477 451 424 397 371

716 676 636 596 557

432 407 381 356 332

648 610 572 534 497

500 469 438 408 378

750 704 657 612 567

440 412 384 357 330

660 618 576 535 495

375 350 325 300 277

563 525 487 451 415

341 317 293 270 248

511 475 440 406 372

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

186 280 20600 f

153 229 18100

248 373 20400

207 311 17700

Shape is noncompact for flexure with Fy = 42 ksi.

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

163 245 14700

140 210 13100

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DESIGN OF COMPRESSION MEMBERS

Table 4-18 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS14HSS10.750

Concrete Filled Round HSS HSS14×

Shape

0.250

t design, in. Steel, lb/ft

HSS12.750× 0.500

0.375

HSS10.750× 0.250

0.500

0.375

0.233 0.465 0.349 0.233 0.465 0.349 36.8 65.5 49.6 33.4 54.8 41.6 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 5 ksi

0

554

831

637

955

557

835 474

711

495

742 428

642

6 7 8 9 10

542 538 533 528 522

813 807 800 792 784

623 618 613 607 600

935 928 919 910 900

544 540 535 529 523

816 810 802 794 784

462 458 454 448 443

693 687 680 672 664

481 475 470 463 456

721 713 704 695 684

415 410 405 399 393

622 616 608 599 589

11 12 13 14 15

516 509 502 494 486

774 764 753 741 729

593 585 576 567 557

889 877 864 850 836

516 509 501 492 484

774 763 751 739 725

436 429 422 414 406

654 644 633 622 609

448 440 431 421 412

672 660 646 632 617

386 378 370 362 353

579 568 556 543 530

16 17 18 19 20

477 468 459 449 439

716 702 688 673 658

547 536 525 514 502

821 805 788 771 753

474 465 455 444 434

711 697 682 666 650

398 389 380 370 360

597 583 570 555 541

401 391 380 368 357

602 586 569 552 535

344 334 325 315 304

516 502 487 472 456

21 22 23 24 25

428 418 407 396 385

643 627 611 594 578

490 478 465 453 440

735 717 698 679 659

423 411 400 388 377

634 617 600 583 565

350 340 330 320 309

526 511 495 479 464

345 333 321 309 297

517 499 481 463 445

294 283 273 262 251

441 425 409 393 377

26 27 28 29 30

374 362 351 340 328

561 544 527 509 492

427 413 400 387 374

640 620 600 580 560

365 353 341 329 317

547 530 512 494 476

298 288 277 267 256

448 432 416 400 384

284 272 260 248 237

427 408 390 373 355

240 230 219 209 199

361 345 329 313 298

32 34 36 38 40

305 283 261 239 218

458 424 391 359 328

347 321 295 271 247

521 481 443 406 370

294 270 248 226 204

440 406 372 339 307

235 215 195 176 159

353 322 293 264 238

214 192 171 153 139

321 288 257 230 208

179 159 142 128 115

268 239 213 191 173

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

116 174 11500

169 254 13000

133 200 10700

94.6 142 8350

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

116 175 7280

92.0 138 6050

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–299

Table 4-18 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 5 ksi

COMPOSITE HSS10.750HSS10

Concrete Filled Round HSS HSS10.750×

Shape

0.250

t design, in. Steel, lb/ft

0.625

0.500

0.375

0.312

0.250

0.233 0.581 0.465 0.349 0.291 0.233 28.1 62.6 50.8 38.6 32.3 26.1 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

HSS10×

0

359

538

507

760 445

668 384

576 352

528 320

480

6 7 8 9 10

347 343 338 333 327

521 515 507 499 491

490 484 477 470 461

735 726 716 705 692

431 425 419 413 405

646 638 629 619 608

371 366 361 355 348

556 549 541 532 522

339 335 330 324 318

509 503 495 487 478

308 304 299 294 288

462 455 448 440 432

11 12 13 14 15

321 314 307 299 291

481 471 460 449 437

452 443 432 422 410

679 664 649 632 615

397 389 380 370 360

596 583 570 556 541

341 334 326 317 308

512 501 489 476 463

312 305 297 289 281

468 457 446 434 421

281 275 268 260 252

422 412 401 390 378

16 17 18 19 20

283 275 266 257 248

425 412 399 385 371

399 386 374 361 348

598 580 561 542 522

350 339 328 317 306

525 509 492 476 458

299 290 280 270 260

449 435 420 405 390

272 263 254 245 236

408 395 382 368 354

244 236 227 219 210

366 354 341 328 315

21 22 23 24 25

238 229 220 210 201

358 344 330 315 301

335 322 308 295 282

502 483 463 443 423

294 282 271 259 247

441 424 406 388 371

250 240 229 219 209

375 359 344 329 313

226 217 207 198 188

339 325 311 296 282

201 192 183 174 166

302 288 275 262 248

26 27 28 29 30

192 182 173 164 156

288 274 260 247 234

269 256 243 230 218

403 383 364 345 327

236 224 213 202 191

354 336 319 303 286

199 189 179 169 160

298 283 268 254 240

179 170 160 152 143

268 254 241 227 214

157 148 140 132 124

236 223 210 198 186

32 34 36 38 40

139 123 110 98.3 88.7

208 184 164 147 133

193 173 155 139 125

290 260 232 208 188

170 150 134 120 109

254 225 201 180 163

141 125 112 100 90.4

212 126 188 112 167 99.5 150 89.3 136 80.6

189 109 167 96.5 149 86.1 134 77.3 121 69.7

163 145 129 116 105

Properties φb Mn kip-ft 65.6 98.6 119 178 99.3 149 78.6 118 67.6 102 Pe (KL )2/104 kip-in.2 4660 6510 5700 4750 4230 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

56.1 84.3 3660

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4–300

DESIGN OF COMPRESSION MEMBERS

Table 4-18 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS10HSS9.625

Concrete Filled Round HSS HSS10×

Shape

0.188

t design, in. Steel, lb/ft

HSS9.625× 0.500

0.375

0.312

0.250

0.188

0.174 0.465 0.349 0.291 0.233 0.174 19.7 48.8 37.1 31.1 25.1 19.0 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 5 ksi

0

287

430

422

634 363

544 332

498

301

451

269

404

6 7 8 9 10

275 271 267 262 256

413 407 400 392 384

407 402 396 389 382

611 603 594 583 572

349 345 339 333 327

524 517 509 500 490

319 315 310 304 298

479 472 464 456 447

289 285 280 275 269

433 427 420 412 403

258 254 249 244 239

387 380 374 366 358

11 12 13 14 15

250 244 237 230 222

375 365 355 345 334

373 365 356 346 336

560 547 534 519 504

320 312 304 296 287

480 469 456 444 431

291 284 277 269 260

437 426 415 403 391

262 256 249 241 233

394 384 373 362 350

233 226 220 212 205

349 339 329 319 308

16 17 18 19 20

215 207 199 191 183

322 310 298 286 274

326 315 304 293 281

488 472 456 439 422

278 269 259 249 239

417 403 389 374 359

252 243 234 225 216

378 365 351 337 324

225 217 209 200 192

338 326 313 301 288

198 190 182 174 166

296 285 273 261 249

21 22 23 24 25

174 166 158 150 142

261 249 237 225 212

270 258 247 235 224

405 387 370 353 336

229 219 209 199 189

344 329 314 299 284

206 197 188 179 169

310 296 282 268 254

183 174 166 157 149

275 262 249 236 223

158 150 142 134 127

237 225 213 202 190

26 27 28 29 30

134 126 118 111 104

201 189 178 166 156

212 201 190 180 169

319 302 286 269 254

180 170 161 151 142

269 255 241 227 213

160 151 143 134 126

240 227 214 201 189

141 132 124 117 109

211 199 187 175 164

119 112 105 97.4 91.1

179 168 157 146 137

149 132 118 106 95.3

223 125 198 111 177 98.8 158 88.7 143 80.0

32 34 36 38 40

91.1 137 80.7 121 72.0 108 64.6 96.9 58.3 87.5

188 111 166 97.9 148 87.3 133 78.4 120 70.7

166 147 131 118 106

95.8 84.9 75.7 68.0 61.3

144 127 114 102 92.0

80.0 120 70.9 106 63.2 94.8 56.8 85.1 51.2 76.8

51.7 77.7 3220

40.3 60.6 2690

Properties φb Mn kip-ft Pe (KL )2/104 kip-in.2 ASD LRFD

Mn /Ωb

Ωc = 2.00

43.8 65.8 3060

91.3 137 5010

72.3 109 4210

62.2 93.5 3720

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–301

Table 4-18 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 5 ksi

COMPOSITE HSS8.625

Concrete Filled Round HSS HSS8.625×

Shape

0.625

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

0.500

0.375

0.322

0.250

0.188

0.581 0.465 0.349 0.300 0.233 0.174 53.5 43.4 33.1 28.6 22.4 17.0 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 0

413

619 360

541

308

462

285

427

253

380

225

337

6 7 8 9 10

394 388 380 372 364

591 582 571 559 545

344 339 333 326 318

517 508 499 488 477

294 289 284 277 271

441 433 425 416 406

272 267 262 256 250

408 401 393 385 375

241 237 232 227 221

361 355 348 340 331

213 209 205 200 194

320 314 307 300 291

11 12 13 14 15

354 344 333 322 310

531 516 500 483 466

310 301 291 282 272

464 451 437 423 408

264 256 248 239 231

395 384 372 359 346

243 236 229 221 212

365 354 343 331 319

214 208 201 194 186

322 312 301 290 279

188 182 176 169 162

283 273 263 253 243

16 17 18 19 20

298 286 274 261 249

448 429 411 392 373

261 251 240 229 218

392 376 360 344 327

222 213 203 194 184

333 319 305 291 277

204 195 187 178 169

306 293 280 267 254

178 170 162 154 146

267 256 244 232 220

155 147 140 133 125

232 221 210 199 188

21 22 23 24 25

236 224 211 199 187

354 336 317 299 281

207 196 185 175 164

311 294 278 262 247

175 166 156 147 138

263 248 235 221 207

160 151 143 134 126

240 227 214 201 189

138 130 123 115 108

208 196 184 172 161

118 111 104 96.9 90.2

177 166 156 145 135

26 27 28 29 30

177 167 157 148 138

266 251 237 222 208

154 144 134 125 117

231 216 202 188 176

130 121 113 105 98.1

194 182 169 157 147

118 110 102 95.3 89.0

177 165 153 143 134

100 93.0 86.5 80.7 75.4

150 140 130 121 113

83.6 77.5 72.1 67.2 62.8

125 116 108 101 94.2

32 34 36 38 40

122 108 96.2 86.3 77.9

183 103 162 91.1 145 81.3 130 72.9 117 65.8

55.2 48.9 43.6 39.1 35.3

82.8 73.3 65.4 58.7 53.0

154 137 122 109 98.7

86.2 129 76.4 115 68.1 102 61.1 91.7 55.2 82.8

78.2 117 69.3 104 61.8 92.7 55.5 83.2 50.1 75.1

66.2 58.7 52.3 47.0 42.4

99.4 88.0 78.5 70.5 63.6

Properties φb Mn kip-ft 85.4 128 71.7 108 56.9 85.5 50.3 75.6 40.8 61.3 Pe (KL )2/104 kip-in.2 3930 3460 2900 2630 2230 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

31.9 47.9 1860

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DESIGN OF COMPRESSION MEMBERS

Table 4-18 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS7.625HSS7.500

Concrete Filled Round HSS HSS7.625×

Shape

0.375

t design, in. Steel, lb/ft

HSS7.500×

0.328

0.500

0.375

0.312

0.250

0.349 0.305 0.465 0.349 0.291 0.233 29.1 25.6 37.4 28.6 24.0 19.4 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 5 ksi

0

257

386

239

359

297

445

251

376

228

341

204

306

6 7 8 9 10

242 237 232 225 219

364 356 348 338 328

225 221 215 209 203

338 331 323 314 304

279 273 267 259 251

419 410 400 389 377

236 231 225 219 212

354 347 338 329 318

214 209 204 198 192

321 314 306 298 288

191 187 182 177 171

287 281 273 265 257

11 12 13 14 15

211 203 195 187 178

317 305 293 280 267

196 189 181 173 165

294 283 272 260 248

243 233 224 214 204

364 350 336 321 306

205 197 189 181 172

307 296 283 271 258

185 178 171 163 155

278 267 256 245 233

165 158 152 144 137

247 237 227 217 206

16 17 18 19 20

170 161 152 143 134

254 241 228 214 201

157 149 141 132 124

236 223 211 199 186

194 183 173 162 152

291 275 259 244 229

163 154 146 137 128

245 232 218 205 192

147 139 131 123 115

221 209 197 185 173

130 123 115 108 101

195 184 173 162 151

21 22 23 24 25

126 117 109 101 92.9

188 176 163 151 139

116 108 101 93.1 85.8

174 162 151 140 129

142 132 123 114 106

213 199 184 171 160

120 111 103 95.2 87.8

179 167 155 143 132

108 100 92.8 85.5 78.8

162 150 139 128 118

26 27 28 29 30

85.9 79.6 74.0 69.0 64.5

129 119 111 104 96.7

32 34 36 38 40

56.7 50.2 44.8 40.2 36.3

85.0 75.3 67.2 60.3 54.4

79.3 119 73.5 110 68.4 103 63.7 95.6 59.6 89.3

98.6 91.4 85.0 79.3 74.1

52.3 46.4 41.4 37.1 33.5

65.1 57.7 51.4 46.2 41.7

78.5 69.6 62.0 55.7 50.3

148 137 128 119 111 97.8 86.7 77.3 69.4 62.6

93.9 87.0 80.4 73.8 68.1

141 131 121 111 102

81.1 122 75.2 113 70.0 105 65.2 97.8 60.9 91.4

72.8 109 67.5 101 62.8 94.2 58.6 87.8 54.7 82.1

62.9 58.3 54.3 50.6 47.3

94.4 87.5 81.4 75.9 70.9

53.6 47.4 42.3 38.0 34.3

48.1 42.6 38.0 34.1 30.8

41.5 36.8 32.8 29.5 26.6

62.3 55.2 49.2 44.2 39.9

80.3 71.2 63.5 57.0 51.4

72.1 63.9 57.0 51.2 46.2

Properties φb Mn kip-ft 43.5 65.3 39.0 58.5 52.7 79.1 41.9 63.0 36.2 54.3 Pe (KL )2/104 kip-in.2 1910 1760 2150 1800 1620 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

30.1 45.3 1400

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–303

Table 4-18 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 5 ksi

COMPOSITE HSS7.500HSS7

Concrete Filled Round HSS HSS7.500×

Shape

0.188

0.500

0.375

0.312

0.250

0.174 14.7 Pn /Ωc φc Pn ASD LRFD

0.465 34.7 Pn /Ωc φc Pn ASD LRFD

0.349 26.6 Pn /Ωc φc Pn ASD LRFD

0.291 22.3 Pn /Ωc φc Pn ASD LRFD

0.233 18.0 Pn /Ωc φc Pn ASD LRFD

0

179

269

269

404

227

341

206

308

184

275

6 7 8 9 10

168 164 159 154 149

252 246 239 231 223

251 245 238 231 222

377 368 357 346 334

212 207 201 194 187

318 310 301 292 281

192 187 182 176 169

288 280 272 264 254

171 166 162 156 150

256 250 242 234 226

11 12 13 14 15

143 137 131 124 118

215 206 196 187 177

214 204 195 185 175

320 307 292 278 263

180 172 164 156 147

270 258 246 234 221

163 156 148 141 133

244 233 222 211 199

144 138 131 124 117

216 207 197 186 176

16 17 18 19 20

111 105 97.9 91.3 84.9

167 157 147 137 127

165 155 145 135 125

247 232 217 202 188

139 130 122 114 105

208 196 183 170 158

125 117 110 102 94.7

188 176 165 153 142

110 103 96.1 89.3 82.6

165 155 144 134 124

21 22 23 24 25

78.7 72.6 66.6 61.1 56.3

118 109 99.9 91.7 84.5

116 108 101 93.1 85.8

175 163 151 140 129

97.3 89.6 82.0 75.3 69.4

146 134 123 113 104

87.5 80.5 73.6 67.6 62.3

131 121 110 101 93.5

76.1 69.7 63.8 58.6 54.0

114 105 95.7 87.9 81.0

26 27 28 29 30

52.1 48.3 44.9 41.9 39.1

78.1 72.5 67.4 62.8 58.7

79.4 73.6 68.4 63.8 59.6

119 111 103 95.9 89.6

64.2 59.5 55.3 51.6 48.2

96.3 89.3 83.0 77.4 72.3

57.6 53.4 49.7 46.3 43.3

86.4 80.1 74.5 69.5 64.9

49.9 46.3 43.1 40.1 37.5

74.9 69.4 64.6 60.2 56.3

32 34 36 38 40

34.4 30.5 27.2 24.4 22.0

51.6 45.7 40.8 36.6 33.0

52.4 46.4 41.4 37.2

78.8 69.8 62.2 55.8

42.4 37.5 33.5 30.0

63.6 56.3 50.2 45.1

38.0 33.7 30.1 27.0

57.1 50.5 45.1 40.5

33.0 29.2 26.0 23.4

49.4 43.8 39.1 35.1

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

HSS7×

Properties φb Mn kip-ft 23.6 35.5 45.2 67.9 36.0 54.1 Pe (KL )2/104 kip-in.2 1160 1700 1420 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

31.1 46.7 1280

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

25.9 39.0 1110

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DESIGN OF COMPRESSION MEMBERS

Table 4-18 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS7HSS6.875

Concrete Filled Round HSS HSS7×

Shape

HSS6.875×

0.188

0.125

0.500

0.375

0.312

0.174 13.7 Pn /Ωc φc Pn ASD LRFD

0.116 9.19 Pn /Ωc φc Pn ASD LRFD

0.465 34.1 Pn /Ωc φc Pn ASD LRFD

0.349 26.1 Pn /Ωc φc Pn ASD LRFD

0.291 21.9 Pn /Ωc φc Pn ASD LRFD

0

161

241

138

207

262

394

222

332

200

300

6 7 8 9 10

149 145 140 135 130

224 218 211 203 195

127 123 119 114 109

191 185 179 172 164

244 238 231 224 215

367 357 347 335 323

206 201 195 189 182

309 301 293 283 272

186 182 176 170 164

279 272 264 255 246

11 12 13 14 15

124 119 112 106 99.9

187 178 169 159 150

104 98.8 93.3 87.6 81.9

156 148 140 131 123

206 197 188 178 168

310 296 282 267 252

174 166 158 150 142

261 249 237 225 212

157 150 143 135 128

236 225 214 203 191

16 17 18 19 20

93.5 87.2 81.0 74.9 68.9

140 131 121 112 103

76.2 70.6 65.0 59.7 54.5

114 106 97.6 89.5 81.8

158 148 138 128 119

237 222 207 192 178

133 125 116 108 99.9

200 187 174 162 150

120 112 105 97.0 89.7

180 168 157 146 135

21 22 23 24 25

63.2 57.6 52.7 48.4 44.6

94.8 86.4 79.0 72.6 66.9

49.5 45.1 41.2 37.9 34.9

74.2 67.6 61.9 56.8 52.4

110 103 94.9 87.4 80.6

166 154 143 131 121

92.1 84.4 77.2 70.9 65.3

138 127 116 106 98.0

82.7 75.7 69.2 63.6 58.6

124 114 104 95.4 87.9

26 27 28 29 30

41.2 38.2 35.5 33.1 31.0

61.8 57.3 53.3 49.7 46.4

32.3 29.9 27.8 25.9 24.2

48.4 44.9 41.7 38.9 36.4

74.5 69.1 64.2 59.9 55.9

112 104 96.5 90.0 84.1

60.4 56.0 52.1 48.6 45.4

90.6 84.0 78.1 72.8 68.1

54.2 50.2 46.7 43.6 40.7

81.3 75.4 70.1 65.3 61.1

32 34 36 38 40

27.2 24.1 21.5 19.3 17.4

40.8 36.2 32.3 28.9 26.1

21.3 18.9 16.8 15.1 13.6

32.0 28.3 25.2 22.7 20.5

49.2 43.5 38.8

73.9 65.5 58.4

39.9 35.3 31.5 28.3

59.8 53.0 47.3 42.4

35.8 31.7 28.3 25.4

53.7 47.5 42.4 38.1

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 5 ksi

Properties φb Mn kip-ft 20.3 30.5 14.4 21.6 43.4 65.2 Pe (KL )2/104 kip-in.2 915 716 1600 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

34.6 52.0 1340

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

29.9 44.9 1200

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–305

Table 4-18 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 5 ksi

COMPOSITE HSS6.875HSS6.625

Concrete Filled Round HSS HSS6.875×

Shape

0.250

0.188

0.500

0.432

0.375

0.233 17.7 Pn /Ωc φc Pn ASD LRFD

0.174 13.4 Pn /Ωc φc Pn ASD LRFD

0.465 32.7 Pn /Ωc φc Pn ASD LRFD

0.402 28.6 Pn /Ωc φc Pn ASD LRFD

0.349 25.1 Pn /Ωc φc Pn ASD LRFD

0

179

268

156

234

249

374

228

342

210

315

6 7 8 9 10

166 161 157 151 145

249 242 235 227 218

145 140 136 131 126

217 211 204 196 189

231 225 218 210 201

347 337 326 315 302

211 206 199 192 184

317 308 299 288 277

194 189 183 177 170

292 284 275 265 254

11 12 13 14 15

139 133 126 119 112

209 199 189 179 168

120 114 108 102 95.7

180 171 162 153 143

193 183 174 164 154

289 275 261 246 231

176 168 159 150 141

264 252 239 225 212

162 154 146 138 130

243 231 219 207 195

16 17 18 19 20

105 98.3 91.5 84.7 78.2

158 147 137 127 117

89.4 83.2 77.1 71.1 65.3

134 125 116 107 97.9

144 135 125 116 108

217 202 187 174 162

132 123 114 106 97.2

198 185 171 158 146

121 113 105 97.0 89.2

182 170 157 146 134

21 22 23 24 25

71.8 65.6 60.0 55.1 50.8

108 98.3 90.0 82.6 76.2

59.6 54.3 49.7 45.6 42.1

89.4 81.5 74.5 68.5 63.1

99.6 92.0 84.4 77.5 71.4

150 138 127 116 107

89.0 81.6 75.1 68.9 63.5

134 123 113 104 95.5

81.7 74.4 68.1 62.6 57.6

123 112 102 93.8 86.5

26 27 28 29 30

46.9 43.5 40.5 37.7 35.3

70.4 65.3 60.7 56.6 52.9

38.9 36.1 33.5 31.3 29.2

58.3 54.1 50.3 46.9 43.8

66.0 61.2 56.9 53.1 49.6

99.3 92.0 85.6 79.8 74.6

58.7 54.5 50.6 47.2 44.1

88.3 81.9 76.1 71.0 66.3

53.3 49.4 46.0 42.8 40.0

80.0 74.1 68.9 64.3 60.1

32 34 36 38

31.0 27.5 24.5 22.0

46.5 41.2 36.7 33.0

25.7 22.7 20.3 18.2

38.5 34.1 30.4 27.3

43.6 38.6 34.4

65.5 58.0 51.8

38.8 34.4 30.6

58.3 51.6 46.1

35.2 31.2 27.8

52.8 46.8 41.7

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

HSS6.625×

Properties φb Mn kip-ft 24.9 37.5 19.5 29.4 40.0 60.1 Pe (KL )2/104 kip-in.2 1040 863 1410 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

35.7 53.6 1290

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

31.9 48.0 1180

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4–306

DESIGN OF COMPRESSION MEMBERS

Table 4-18 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS6.625

Concrete Filled Round HSS HSS6.625×

Shape

0.312

0.280

0.250

0.188

0.125

0.291 21.1 Pn /Ωc φc Pn ASD LRFD

0.260 19.0 Pn /Ωc φc Pn ASD LRFD

0.233 17.0 Pn /Ωc φc Pn ASD LRFD

0.174 12.9 Pn /Ωc φc Pn ASD LRFD

0.116 8.69 Pn /Ωc φc Pn ASD LRFD

0

190

285

179

268

169

254

148

221

126

189

6 7 8 9 10

176 171 165 159 153

263 256 248 239 229

165 161 156 150 144

248 241 233 225 216

156 152 147 141 135

234 228 220 212 203

136 132 127 122 117

204 198 191 183 175

115 111 107 102 97.6

172 167 160 154 146

11 12 13 14 15

146 139 132 124 117

219 209 198 186 175

137 131 124 117 110

206 196 186 175 164

129 123 116 110 103

194 184 174 164 154

111 106 99.5 93.5 87.3

167 158 149 140 131

92.5 87.2 81.8 76.3 70.9

139 131 123 114 106

16 17 18 19 20

109 102 94.3 87.1 80.0

164 153 141 131 120

103 95.4 88.4 81.6 75.0

154 143 133 122 112

96.0 89.2 82.6 76.1 69.8

144 134 124 114 105

81.3 75.2 69.3 63.6 58.1

122 113 104 95.4 87.1

65.5 60.2 55.0 50.0 45.2

98.2 90.2 82.5 75.0 67.8

21 22 23 24 25

73.2 66.7 61.0 56.0 51.6

110 100 91.5 84.1 77.5

68.5 62.4 57.1 52.4 48.3

103 93.6 85.7 78.7 72.5

63.6 58.0 53.0 48.7 44.9

95.4 86.9 79.5 73.1 67.3

52.7 48.0 43.9 40.3 37.2

79.0 72.0 65.9 60.5 55.8

41.0 37.4 34.2 31.4 28.9

61.5 56.0 51.3 47.1 43.4

26 27 28 29 30

47.7 44.3 41.2 38.4 35.9

71.6 66.4 61.8 57.6 53.8

44.7 41.4 38.5 35.9 33.6

67.0 62.2 57.8 53.9 50.4

41.5 38.5 35.8 33.4 31.2

62.2 57.7 53.7 50.0 46.8

34.4 31.9 29.6 27.6 25.8

51.6 47.8 44.5 41.4 38.7

26.7 24.8 23.1 21.5 20.1

40.1 37.2 34.6 32.2 30.1

32 34 36 38

31.5 27.9 24.9

47.3 41.9 37.4

29.5 26.1 23.3

44.3 39.2 35.0

27.4 24.3 21.6

41.1 36.4 32.5

22.7 20.1 17.9 16.1

34.0 30.1 26.9 24.1

17.7 15.6 13.9 12.5

26.5 23.5 20.9 18.8

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 5 ksi

Properties φb Mn kip-ft 27.6 41.4 25.2 37.8 23.0 34.6 Pe (KL )2/104 kip-in.2 1060 992 921 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

18.0 27.1 763

12.8 19.2 594

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–307

Table 4-18 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 5 ksi

COMPOSITE HSS6

Concrete Filled Round HSS HSS6×

Shape

0.500

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

0.375

0.312

0.280

0.250

0.188

0.465 0.349 0.291 0.260 0.233 0.174 29.4 22.6 19.0 17.1 15.4 11.7 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD 0

218

327

183

274

164

247

155

232

146

219

126

190

1 2 3 4 5

217 216 213 209 204

326 323 319 313 306

182 181 178 175 171

273 271 268 263 257

164 163 161 158 154

246 244 241 236 231

154 153 151 148 145

231 229 226 222 217

145 144 142 140 136

218 216 213 210 205

126 125 123 121 118

189 187 185 181 177

6 7 8 9 10

198 192 184 176 168

297 287 276 264 252

166 161 155 148 141

249 241 232 222 211

150 145 139 133 126

224 217 209 199 190

141 136 130 125 119

211 204 196 187 178

132 128 123 118 112

199 192 185 176 168

114 110 106 101 95.6

171 165 159 151 143

11 12 13 14 15

159 150 140 131 121

238 224 210 196 182

133 125 118 110 102

200 188 176 164 152

120 113 106 98.4 91.2

180 169 158 148 137

112 106 98.9 92.1 85.3

168 159 148 138 128

106 99.5 93.1 86.7 80.3

159 149 140 130 120

90.1 84.5 78.8 73.1 67.4

135 127 118 110 101

16 17 18 19 20

113 105 96.5 88.6 81.0

170 157 145 133 122

93.7 86.0 78.5 71.3 64.4

141 129 118 107 96.8

84.1 126 77.1 116 70.3 106 63.8 95.7 57.6 86.4

78.6 118 72.1 108 65.7 98.6 59.5 89.3 53.7 80.6

74.0 111 67.8 102 61.8 92.7 55.9 83.9 50.5 75.7

61.8 56.4 51.1 46.0 41.5

92.8 84.6 76.7 69.0 62.3

21 22 23 24 25

73.6 111 67.0 101 61.3 92.2 56.3 84.6 51.9 78.0

58.7 53.5 48.9 44.9 41.4

88.2 80.4 73.5 67.5 62.3

52.2 47.6 43.5 40.0 36.9

78.3 71.4 65.3 60.0 55.3

48.7 44.4 40.6 37.3 34.4

73.1 66.6 61.0 56.0 51.6

45.8 41.7 38.2 35.1 32.3

68.7 62.6 57.3 52.6 48.5

37.7 34.3 31.4 28.8 26.6

56.5 51.5 47.1 43.3 39.9

26 28 30 32 34

48.0 41.4 36.0 31.7

38.3 33.0 28.8 25.3

57.6 49.6 43.2 38.0

34.1 29.4 25.6 22.5

51.1 44.1 38.4 33.7

31.8 27.4 23.9 21.0

47.7 41.1 35.8 31.5

29.9 25.8 22.4 19.7 17.5

44.8 38.6 33.7 29.6 26.2

24.6 21.2 18.5 16.2 14.4

36.9 31.8 27.7 24.3 21.6

72.1 62.2 54.2 47.6

Properties φb Mn kip-ft 32.0 48.1 25.6 38.5 22.2 33.3 20.3 30.4 Pe (KL )2/104 kip-in.2 1010 844 756 706 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

18.5 27.8 663

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF COMPRESSION MEMBERS

Table 4-18 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS6HSS5.563

Concrete Filled Round HSS HSS6×

Shape

0.125

t design, in. Steel, lb/ft

HSS5.563× 0.500

0.375

0.258

0.188

0.134

0.116 0.465 0.349 0.240 0.174 0.124 7.85 27.1 20.8 14.6 10.8 7.78 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 5 ksi

0

107

161

196

295

164

246

132

199

113

169

97.2

146

1 2 3 4 5

107 106 104 102 99.1

160 159 156 153 149

196 194 191 187 182

294 291 287 281 273

164 162 160 156 152

246 243 240 235 228

132 131 129 126 123

198 196 193 189 184

112 111 109 107 104

168 167 164 161 156

96.9 95.9 94.3 92.0 89.2

145 144 141 138 134

6 7 8 9 10

95.9 92.2 88.0 83.6 78.9

144 138 132 125 118

176 169 162 153 145

264 254 242 230 217

147 142 135 129 121

221 212 203 193 182

119 114 109 103 97.4

178 171 163 155 146

100 96.3 91.8 86.9 81.8

151 144 138 130 123

85.9 82.2 78.0 73.6 69.0

129 123 117 110 103

11 12 13 14 15

74.0 111 69.0 103 63.9 95.9 58.9 88.3 53.9 80.8

136 127 119 110 102

204 191 178 166 153

114 106 98.4 90.7 83.1

171 159 148 136 125

91.3 85.1 78.8 72.6 66.4

137 128 118 109 99.6

16 17 18 19 20

49.0 44.3 39.7 35.7 32.2

73.5 66.5 59.6 53.5 48.3

93.9 85.9 78.1 70.6 63.7

141 129 117 106 95.7

75.6 113 68.4 103 62.3 93.6 56.6 85.1 51.1 76.8

60.4 54.5 48.9 43.9 39.6

21 22 23 24 25

29.2 26.6 24.3 22.4 20.6

43.8 39.9 36.5 33.5 30.9

57.8 52.6 48.2 44.2 40.8

86.8 79.1 72.4 66.5 61.3

46.3 42.2 38.6 35.5 32.7

69.6 63.5 58.1 53.3 49.1

26 28 30 32 34

19.1 16.4 14.3 12.6 11.1

28.6 24.6 21.5 18.9 16.7

37.7 32.5 28.3

56.6 48.8 42.5

30.2 26.1 22.7

45.4 39.2 34.1

76.5 115 71.0 107 65.6 98.4 60.2 90.2 54.8 82.2

64.2 59.3 54.4 49.6 44.9

96.2 88.9 81.6 74.4 67.3

90.5 81.8 73.3 65.8 59.4

49.6 44.7 39.9 35.8 32.3

74.5 67.0 59.8 53.7 48.4

40.4 36.0 32.1 28.8 26.0

60.5 53.9 48.1 43.2 39.0

35.9 32.7 29.9 27.5 25.3

53.9 49.1 44.9 41.2 38.0

29.3 26.7 24.4 22.4 20.7

43.9 40.0 36.6 33.6 31.0

23.6 21.5 19.6 18.0 16.6

35.3 32.2 29.5 27.1 24.9

23.4 20.2 17.6

35.1 30.3 26.4

19.1 16.5 14.4

28.7 15.4 24.7 13.3 21.5 11.5 10.1

23.1 19.9 17.3 15.2

Properties φb Mn kip-ft 10.3 15.6 27.0 40.6 21.7 32.6 16.1 24.2 Pe (KL )2/104 kip-in.2 423 777 653 520 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

12.4 18.6 424

Dashed line indicates the KL beyond which bare steel strength controls.

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–309

Table 4-18 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 5 ksi

COMPOSITE HSS5.500HSS5

Concrete Filled Round HSS HSS5.500×

Shape

0.500

t design, in. Steel, lb/ft

0.258

0.500

0.375

0.312

0.465 0.349 0.240 0.465 0.349 0.291 26.7 20.6 14.5 24.1 18.5 15.6 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

0.375

HSS5×

0

194

290

162

242

130

196

170

255

142

212

127

190

1 2 3 4 5

193 191 188 184 179

289 287 282 276 268

161 160 157 154 150

242 239 236 231 224

130 129 127 124 121

195 193 190 186 181

169 167 164 160 155

254 251 246 240 232

141 140 137 133 129

212 209 205 200 193

126 125 123 119 115

189 187 184 179 173

6 7 8 9 10

173 166 158 150 142

259 249 238 225 212

145 139 133 126 119

217 208 199 189 178

116 112 107 101 95.2

175 168 160 152 143

148 141 134 126 118

222 212 201 190 178

124 118 111 105 97.4

186 177 167 157 146

111 105 99.7 93.6 87.2

166 158 150 140 131

11 12 13 14 15

133 124 116 108 99.5

199 187 174 162 150

111 103 95.7 88.0 80.5

167 155 144 132 121

89.1 82.9 76.7 70.4 64.3

166 153 141 128 116

90.0 82.6 75.2 68.0 61.8

135 124 113 102 92.8

16 17 18 19 20

91.3 83.4 75.7 68.2 61.5

137 125 114 102 92.5

21 22 23 24 25

55.8 50.9 46.5 42.7 39.4

26 28 30

36.4 31.4

134 110 124 102 115 93.5 106 85.3 96.4 77.3

80.6 121 73.9 111 67.3 101 60.9 91.3 54.6 81.9

73.1 110 66.2 99.6 60.4 90.8 54.7 82.2 49.4 74.2

58.3 52.6 47.0 42.2 38.1

87.5 78.9 70.5 63.3 57.1

69.5 104 62.0 93.2 55.3 83.1 49.6 74.6 44.8 67.3

55.8 50.2 44.7 40.1 36.2

83.9 75.4 67.2 60.3 54.5

48.6 43.2 38.6 34.7 31.3

72.9 65.0 58.1 52.1 47.0

83.9 76.4 69.9 64.2 59.2

44.8 40.8 37.3 34.3 31.6

67.3 61.3 56.1 51.5 47.5

34.5 31.5 28.8 26.4 24.4

51.8 47.2 43.2 39.7 36.6

40.6 37.0 33.9 31.1 28.7

61.0 55.6 50.9 46.7 43.1

32.9 29.9 27.4 25.2 23.2

49.4 45.0 41.2 37.8 34.9

28.4 25.9 23.7 21.7 20.0

42.7 38.9 35.6 32.7 30.1

54.7 47.2

29.2 25.2 21.9

43.9 37.9 33.0

22.5 19.4 16.9

33.8 29.1 25.4

26.5

39.8

21.4

32.2

18.5

27.8

Properties φb Mn kip-ft 26.3 39.6 21.1 31.8 15.7 23.6 21.2 31.9 Pe (KL )2/104 kip-in.2 747 629 500 539 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

17.1 25.7 456

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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4–310

DESIGN OF COMPRESSION MEMBERS

Table 4-18 (continued)

Available Strength in Axial Compression, kips

COMPOSITE HSS5HSS4.500

Concrete Filled Round HSS HSS5×

Shape

0.258

t design, in. Steel, lb/ft

0.250

HSS4.500× 0.188

0.125

0.375

0.337

0.240 0.233 0.174 0.116 0.349 0.313 13.1 12.7 9.67 6.51 16.5 15.0 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 5 ksi

0

113

170

112

167

95.8

144

79.8

120

123

184

115

172

1 2 3 4 5

113 112 110 107 103

170 168 165 160 155

111 110 108 105 102

167 165 162 158 152

95.4 94.3 92.5 90.0 86.9

143 141 139 135 130

79.4 78.5 76.8 74.6 71.8

119 118 115 112 108

122 120 117 114 109

183 180 176 171 164

114 112 110 106 102

171 169 165 159 153

146 139 132 123 115

83.3 79.2 74.7 69.9 64.9

125 119 112 105 97.4

68.6 64.9 60.9 56.7 52.4

103 104 97.4 97.6 91.4 91.0 85.1 84.1 78.5 77.0

6 7 8 9 10

99.1 94.4 89.2 83.6 77.9

149 142 134 125 117

97.4 92.8 87.7 82.2 76.5

11 12 13 14 15

71.9 108 66.0 98.9 60.0 90.0 54.2 81.3 48.6 72.9

70.7 106 64.8 97.2 59.0 88.5 53.3 79.9 47.7 71.6

59.9 54.7 49.7 44.7 40.0

89.8 82.1 74.5 67.1 59.9

47.9 43.5 39.2 34.9 30.9

71.9 65.3 58.7 52.4 46.4

69.9 105 63.5 95.4 57.3 86.1 51.3 77.1 45.6 68.5

65.4 58.8 52.4 47.0 41.8

98.1 88.1 78.7 70.6 62.8

16 17 18 19 20

43.2 38.2 34.1 30.6 27.6

64.8 57.4 51.2 45.9 41.5

42.4 37.6 33.5 30.1 27.1

63.6 56.3 50.3 45.1 40.7

35.3 31.3 27.9 25.1 22.6

53.0 47.0 41.9 37.6 33.9

27.2 24.1 21.5 19.3 17.4

40.7 36.1 32.2 28.9 26.1

40.1 35.5 31.7 28.4 25.7

60.3 53.4 47.6 42.7 38.6

36.8 32.6 29.1 26.1 23.5

55.3 49.0 43.7 39.2 35.4

21 22 23 24 25

25.1 22.8 20.9 19.2 17.7

37.6 34.3 31.3 28.8 26.5

24.6 22.4 20.5 18.8 17.4

36.9 33.6 30.8 28.3 26.0

20.5 18.7 17.1 15.7 14.5

30.8 28.0 25.7 23.6 21.7

15.8 14.4 13.1 12.1 11.1

23.7 21.6 19.7 18.1 16.7

23.3 21.2 19.4 17.8

35.0 31.9 29.2 26.8

21.4 19.5 17.8 16.4

32.1 29.3 26.8 24.6

26 28

16.4 14.1

24.5 21.1

16.1 13.8

24.1 13.4 20.8 11.5

20.1 10.3 17.3 8.87

155 146 137 126 116

96.9 91.3 85.1 78.7 72.1

145 137 128 118 108

15.4 13.3

Properties φb Mn kip-ft 12.7 19.1 12.4 18.7 9.80 14.7 6.99 10.5 Pe (KL )2/104 kip-in.2 363 356 297 228 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

13.5 20.3 318

Dashed line indicates the KL beyond which bare steel strength controls.

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COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–311

Table 4-18 (continued)

Available Strength in Axial Compression, kips

Fy = 42 ksi fc′ = 5 ksi

COMPOSITE HSS4.500HSS4

Concrete Filled Round HSS HSS4.500×

Shape

0.237

0.188

0.125

0.313

0.250

0.220 10.8 Pn /Ωc φc Pn ASD LRFD

0.174 8.67 Pn /Ωc φc Pn ASD LRFD

0.116 5.85 Pn /Ωc φc Pn ASD LRFD

0.291 12.3 Pn /Ωc φc Pn ASD LRFD

0.233 10.0 Pn /Ωc φc Pn ASD LRFD

0

92.9

139

81.7

123

67.6

101

93.0

139

81.3

122

1 2 3 4 5

92.5 91.2 89.1 86.2 82.7

139 137 134 129 124

81.3 80.2 78.3 75.8 72.6

122 120 117 114 109

67.2 66.2 64.5 62.3 59.5

101 99.3 96.8 93.4 89.3

92.4 90.8 88.2 84.7 80.3

139 136 132 127 120

80.8 79.4 77.1 74.0 70.2

121 119 116 111 105

6 7 8 9 10

78.6 74.0 69.0 63.7 58.3

118 111 103 95.6 87.5

69.0 64.9 60.4 55.8 51.0

103 97.3 90.7 83.7 76.5

56.3 52.7 48.8 44.8 40.6

84.4 79.0 73.2 67.1 61.0

75.3 69.8 63.9 57.8 51.7

113 105 95.9 86.8 77.6

65.8 61.0 55.8 50.5 45.2

98.7 91.4 83.8 75.8 67.8

11 12 13 14 15

52.9 47.5 42.3 37.3 32.6

79.3 71.3 63.5 56.0 48.8

46.2 41.5 36.8 32.4 28.3

69.3 62.2 55.3 48.7 42.4

36.5 32.5 28.6 24.9 21.7

54.8 48.7 42.9 37.3 32.5

46.1 41.0 36.2 31.5 27.4

69.3 61.7 54.3 47.3 41.2

40.0 34.9 30.1 26.0 22.6

60.0 52.4 45.2 39.1 34.0

16 17 18 19 20

28.6 25.4 22.6 20.3 18.3

42.9 38.0 33.9 30.4 27.5

24.9 22.0 19.6 17.6 15.9

37.3 33.0 29.5 26.4 23.9

19.1 16.9 15.1 13.5 12.2

28.6 25.3 22.6 20.3 18.3

24.1 21.3 19.0 17.1 15.4

36.2 32.1 28.6 25.7 23.2

19.9 17.6 15.7 14.1 12.7

29.9 26.5 23.6 21.2 19.1

21 22 23 24 25

16.6 15.1 13.8 12.7 11.7

24.9 22.7 20.8 19.1 17.6

14.4 13.1 12.0 11.0 10.2

21.6 19.7 18.0 16.6 15.3

11.1 10.1 9.22 8.47 7.81

16.6 15.1 13.8 12.7 11.7

14.0 12.7

21.0 19.1

11.6 10.5

17.4 15.8

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

HSS4×

Properties φb Mn kip-ft 9.42 14.2 7.79 11.7 5.57 8.37 Pe (KL )2/104 kip-in.2 241 209 160 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

9.04 13.6 191

Dashed line indicates the KL beyond which bare steel strength controls.

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DESIGN OF COMPRESSION MEMBERS

Table 4-18 (continued)

Available Strength in Axial Compression, kips COMPOSITE HSS4

Concrete Filled Round HSS HSS4×

Shape

0.237

0.226

0.220

0.188

0.125

0.220 9.53 Pn /Ωc φc Pn ASD LRFD

0.210 9.12 Pn /Ωc φc Pn ASD LRFD

0.205 8.89 Pn /Ωc φc Pn ASD LRFD

0.174 7.66 Pn /Ωc φc Pn ASD LRFD

0.116 5.18 Pn /Ωc φc Pn ASD LRFD

0

78.5

118

76.4

115

75.3

113

68.8

103

56.3

84.4

1 2 3 4 5

78.0 76.6 74.4 71.4 67.8

117 115 112 107 102

76.0 74.6 72.5 69.5 66.0

114 112 109 104 98.9

74.8 73.5 71.4 68.5 65.0

112 110 107 103 97.5

68.4 67.2 65.2 62.5 59.3

103 101 97.8 93.8 88.9

55.9 54.9 53.2 50.9 48.1

83.9 82.3 79.8 76.4 72.2

6 7 8 9 10

63.5 58.9 53.9 48.8 43.6

95.3 88.3 80.9 73.2 65.5

61.8 57.3 52.5 47.5 42.5

92.8 85.9 78.7 71.2 63.7

60.9 56.5 51.7 46.8 41.8

91.4 84.7 77.5 70.2 62.8

55.6 51.4 47.1 42.6 38.0

83.3 77.2 70.6 63.8 57.0

44.9 41.4 37.6 33.8 30.0

67.3 62.0 56.5 50.7 45.0

11 12 13 14 15

38.6 33.7 29.1 25.1 21.8

57.9 50.6 43.6 37.6 32.7

37.5 32.8 28.2 24.4 21.2

56.3 49.2 42.4 36.5 31.8

37.0 32.3 27.8 24.0 20.9

55.5 48.5 41.8 36.0 31.4

33.6 29.3 25.2 21.7 18.9

50.4 43.9 37.8 32.6 28.4

26.3 22.8 19.4 16.8 14.6

39.5 34.1 29.2 25.1 21.9

16 17 18 19 20

19.2 17.0 15.2 13.6 12.3

28.8 25.5 22.7 20.4 18.4

18.6 16.5 14.7 13.2 11.9

28.0 24.8 22.1 19.8 17.9

18.4 16.3 14.5 13.0 11.8

27.6 24.4 21.8 19.5 17.6

16.6 14.7 13.1 11.8 10.7

25.0 22.1 19.7 17.7 16.0

12.8 11.4 10.1 9.10 8.22

19.3 17.1 15.2 13.7 12.3

21 22

11.1 10.1

16.7 15.2

10.8 9.86

16.2 14.8

10.7 9.72

16.0 14.6

14.5 13.2

7.45 6.79

11.2 10.2

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 42 ksi fc′ = 5 ksi

9.66 8.80

Properties φb Mn kip-ft 7.27 10.9 7.00 10.5 6.87 10.3 Pe (KL )2/104 kip-in.2 161 157 154 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

6.02 9.05 140

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.31 6.48 108

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10:58 AM

Page 313

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–313

Table 4-19

Available Strength in Axial Compression, kips

Fy = 35 ksi fc′ = 4 ksi

COMPOSITE PIPE 12-PIPE 8

Concrete Filled Pipe Pipe 12

Shape

XS

t design, in. Steel, lb/ft

Std

XS

Pipe 8 Std

XXS

XS

0.465 0.349 0.465 0.340 0.816 0.465 65.5 49.6 54.8 40.5 72.5 43.4 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Pipe 10

0

517

776

458

687 410

614 353

530 423

635 297

445

6 7 8 9 10

508 505 501 497 493

763 758 752 746 739

450 446 443 439 435

674 670 664 659 652

400 396 392 387 382

599 594 588 581 573

344 341 337 333 329

516 512 506 500 493

407 402 395 388 381

611 602 593 583 573

286 282 277 273 267

429 423 416 409 401

11 12 13 14 15

487 482 476 470 463

731 723 714 705 695

430 425 419 413 407

645 637 629 620 610

377 371 364 358 351

565 556 547 537 526

324 318 312 306 300

485 477 469 459 450

373 365 357 348 338

561 549 536 523 508

261 255 248 241 234

392 383 373 362 351

16 17 18 19 20

456 449 441 433 425

684 673 661 649 637

400 393 386 379 371

600 590 579 568 556

343 335 327 319 311

515 503 491 479 466

293 286 279 272 264

440 429 418 407 396

328 318 308 297 286

494 478 463 447 430

227 219 211 203 195

340 328 316 304 292

21 22 23 24 25

416 407 399 389 380

624 611 598 584 570

363 355 346 338 329

544 532 520 507 494

302 293 284 275 266

453 440 426 413 399

256 248 240 232 224

384 372 360 348 336

275 264 253 242 231

414 397 380 364 347

187 178 170 162 154

280 267 255 243 231

26 27 28 29 30

371 361 351 342 332

556 542 527 512 498

321 312 303 294 285

481 468 454 441 427

257 247 238 229 220

385 371 357 343 330

216 208 199 191 183

324 311 299 287 275

220 209 198 188 178

331 314 298 283 267

146 138 130 122 115

218 207 195 184 172

32 34 36 38 40

312 292 273 254 235

468 439 409 380 352

267 249 231 214 197

400 373 346 320 295

202 184 167 151 136

303 276 251 226 204

167 152 137 123 111

251 228 206 184 166

158 140 124 112 101

237 101 210 89.7 187 80.0 168 71.8 152 64.8

152 135 120 108 97.5

Properties φb Mn kip-ft 141 213 111 168 97.6 147 75.5 113 92.0 138 Pe (KL )2/104 kip-in.2 12600 10400 7140 5830 4770 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

59.7 89.7 3400

AISC_Part 4E:14th Ed.

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10:58 AM

Page 314

4–314

DESIGN OF COMPRESSION MEMBERS

Table 4-19 (continued)

Available Strength in Axial Compression, kips COMPOSITE PIPE 8-PIPE 5

Concrete Filled Pipe Pipe 8

Shape

Pipe 6

Pipe 5

Std

XXS

XS

Std

XXS

0.300 28.6 Pn /Ωc φc Pn ASD LRFD

0.805 53.2 Pn /Ωc φc Pn ASD LRFD

0.403 28.6 Pn /Ωc φc Pn ASD LRFD

0.261 19.0 Pn /Ωc φc Pn ASD LRFD

0.699 38.6 Pn /Ωc φc Pn ASD LRFD

0

234

350

308

463

188

282

147

220

224

337

6 7 8 9 10

225 221 218 214 209

337 332 327 321 314

290 283 276 268 260

436 426 415 403 391

176 172 168 163 157

264 258 251 244 236

137 134 131 127 122

206 201 196 190 183

205 199 192 184 176

309 299 288 277 264

11 12 13 14 15

204 199 194 188 182

307 299 291 282 274

251 241 231 221 210

377 362 347 332 316

151 145 139 132 126

227 218 208 199 189

118 113 108 103 97.4

177 169 162 154 146

167 158 149 139 130

251 237 223 209 195

16 17 18 19 20

176 170 164 157 150

264 255 245 236 226

199 188 177 167 156

299 283 267 250 234

119 112 105 98.7 92.1

179 168 158 148 138

92.0 86.6 81.3 76.0 70.8

138 130 122 114 106

120 111 102 93.1 84.5

181 167 153 140 127

21 22 23 24 25

144 137 131 124 117

216 206 196 186 176

145 135 125 115 106

218 203 188 173 160

85.6 79.3 73.3 68.3 63.3

128 119 110 103 95.1

65.7 60.7 55.9 51.3 47.3

98.5 91.1 83.8 77.0 70.9

76.7 69.9 63.9 58.7 54.1

115 105 96.1 88.2 81.3

26 27 28 29 30

111 105 98.6 92.6 86.6

167 157 148 139 130

98.2 91.1 84.7 78.9 73.8

148 137 127 119 111

58.5 54.3 50.5 47.0 44.0

88.0 81.6 75.8 70.7 66.1

43.7 40.5 37.7 35.1 32.8

65.6 60.8 56.5 52.7 49.3

50.0 46.4 43.1 40.2

75.2 69.7 64.8 60.4

32 34 36 38 40

76.1 67.4 60.2 54.0 48.7

114 101 90.2 81.0 73.1

64.8 57.4

38.6 34.2 30.5

58.1 51.4 45.9

28.9 25.6 22.8

43.3 38.3 34.2

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 35 ksi fc′ = 4 ksi

97.4 86.3

Properties φb Mn kip-ft 41.8 62.8 49.8 74.8 29.8 44.7 Pe (KL )2/104 kip-in.2 2560 1910 1270 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

21.0 31.5 970

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

30.1 45.2 967

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10:58 AM

Page 315

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–315

Table 4-19 (continued)

Available Strength in Axial Compression, kips

Fy = 35 ksi fc′ = 4 ksi

COMPOSITE PIPE 5-PIPE 4

Concrete Filled Pipe Pipe 5

Shape

Pipe 4

XS

Std

XXS

XS

Std

0.349 20.8 Pn /Ωc φc Pn ASD LRFD

0.241 14.6 Pn /Ωc φc Pn ASD LRFD

0.628 27.6 Pn /Ωc φc Pn ASD LRFD

0.315 15.0 Pn /Ωc φc Pn ASD LRFD

0.221 10.8 Pn /Ωc φc Pn ASD LRFD

0

136

203

109

163

161

241

94.8

142

76.4

6 7 8 9 10

124 120 115 110 105

186 179 173 165 158

99.1 95.8 92.2 88.3 84.1

149 144 138 132 126

140 133 126 118 110

210 200 189 177 165

82.5 78.4 74.0 69.3 64.4

124 118 111 104 96.6

66.4 63.1 59.5 55.7 51.8

99.6 94.7 89.3 83.6 77.6

152 139 127 114 102

59.3 54.3 49.3 44.9 40.7

89.0 81.4 73.9 67.4 61.2

47.7 43.6 39.6 35.6 31.8

71.5 65.4 59.3 53.4 47.7

t design, in. Steel, lb/ft Design

115

99.7 94.0 88.2 82.4 76.5

149 141 132 124 115

79.7 75.1 70.4 65.7 61.0

120 113 106 98.6 91.5

101 92.7 84.3 76.0 68.1

16 17 18 19 20

70.7 65.0 59.8 55.2 50.7

106 97.6 89.8 83.0 76.3

56.3 51.8 47.3 43.0 38.9

84.5 77.7 71.0 64.6 58.3

60.3 53.5 47.7 42.8 38.6

90.7 80.3 71.7 64.3 58.0

36.7 32.8 29.2 26.2 23.7

55.1 49.2 43.9 39.4 35.6

28.1 24.9 22.2 19.9 18.0

42.2 37.4 33.3 29.9 27.0

21 22 23 24 25

46.4 42.3 38.7 35.5 32.8

69.8 63.6 58.2 53.4 49.2

35.3 32.1 29.4 27.0 24.9

52.9 48.2 44.1 40.5 37.3

35.0 31.9 29.2

52.6 48.0 43.9

21.5 19.6 17.9 16.4

32.3 29.4 26.9 24.7

16.3 14.9 13.6 12.5 11.5

24.5 22.3 20.4 18.8 17.3

26 27 28 29 30

30.3 28.1 26.1 24.3 22.7

45.5 42.2 39.2 36.6 34.2

23.0 21.3 19.8 18.5 17.3

34.5 32.0 29.7 27.7 25.9

φb Mn kip-ft

18.0

27.1

13.4

17.1

25.7

10.4

Effective length, KL (ft)

11 12 13 14 15

Properties

Mn /Ωb

Pe (KL )2/104 ASD Ωc = 2.00

20.1

kip-in.2 643 511 438 Note: Heavy line indicates KL/r equal to or greater than 200. LRFD φc = 0.75

15.6 295

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7.85 236

11.8

AISC_Part 4E:14th Ed.

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10:58 AM

Page 316

4–316

DESIGN OF COMPRESSION MEMBERS

Table 4-19 (continued)

Available Strength in Axial Compression, kips COMPOSITE PIPE 31/2 -PIPE 3

Concrete Filled Pipe Pipe 31/2

Shape

Pipe 3

XS

Std

XXS

XS

Std

0.296 12.5 Pn /Ωc φc Pn ASD LRFD

0.211 9.12 Pn /Ωc φc Pn ASD LRFD

0.559 18.6 Pn /Ωc φc Pn ASD LRFD

0.280 10.3 Pn /Ωc φc Pn ASD LRFD

0.201 7.58 Pn /Ωc φc Pn ASD LRFD

0

77.4

62.9

94.3

108

163

62.4

93.6

50.6

75.9

6 7 8 9 10

64.9 60.9 56.6 52.1 47.4

97.3 91.3 84.9 78.1 71.1

52.7 49.4 45.9 42.2 38.5

79.0 74.1 68.9 63.4 57.7

85.6 78.6 71.2 63.7 56.2

129 118 107 95.7 84.5

49.6 45.6 41.4 37.5 33.6

74.3 68.4 62.1 56.3 50.6

40.2 37.0 33.6 30.2 26.7

60.3 55.5 50.4 45.3 40.1

11 12 13 14 15

42.8 38.7 34.8 31.0 27.3

64.3 58.2 52.3 46.6 41.0

34.7 31.0 27.4 24.0 20.9

52.1 46.5 41.1 36.0 31.3

49.0 42.1 35.9 30.9 26.9

73.6 63.3 53.9 46.5 40.5

29.9 26.2 22.7 19.6 17.1

44.9 39.4 34.1 29.4 25.6

23.4 20.2 17.5 15.1 13.1

35.1 30.3 26.2 22.7 19.8

16 17 18 19 20

24.0 21.3 19.0 17.0 15.4

36.1 32.0 28.5 25.6 23.1

18.4 16.3 14.5 13.0 11.7

27.5 24.4 21.8 19.5 17.6

23.7 21.0

35.6 31.5

15.0 13.3 11.8 10.6

22.5 20.0 17.8 16.0

11.6 10.2 9.13 8.19

17.4 15.4 13.7 12.3

21 22

13.9

20.9

10.7 9.71

16.0 14.6

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 35 ksi fc′ = 4 ksi

116

Properties φb Mn kip-ft 7.62 11.4 5.84 8.78 8.74 13.1 Pe (KL )2/104 kip-in.2 191 154 171 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

5.42 8.14 117

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.19 6.29 95.6

AISC_Part 4E:14th Ed.

2/23/11

10:59 AM

Page 317

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–317

Table 4-20

Available Strength in Axial Compression, kips

Fy = 35 ksi fc′ = 5 ksi

COMPOSITE PIPE 12-PIPE 8

Concrete Filled Pipe Pipe 12

Shape

XS

t design, in. Steel, lb/ft

Std

XS

Pipe 8 Std

XXS

XS

0.465 0.349 0.465 0.340 0.816 0.465 65.5 49.6 54.8 40.5 72.5 43.4 Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn Pn /Ωc φc Pn ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Design

Effective length, KL (ft)

Pipe 10

0

570

855

513

769 446

669 392

587 441

662 319

478

6 7 8 9 10

560 556 551 546 541

839 834 827 820 811

502 499 494 490 484

754 748 742 734 726

434 430 425 420 414

651 645 638 630 622

381 377 372 367 362

571 565 558 551 543

424 418 411 404 395

636 627 617 605 593

306 302 297 291 285

460 453 446 437 428

11 12 13 14 15

535 528 521 514 506

802 793 782 771 759

479 472 466 458 451

718 708 698 688 676

408 401 394 386 378

612 602 591 579 567

356 350 343 336 328

534 524 514 503 492

386 376 366 355 344

579 565 549 533 516

279 272 264 257 248

418 408 396 385 373

16 17 18 19 20

498 489 480 471 461

747 734 721 707 692

443 435 426 417 408

664 652 639 626 612

369 361 351 342 332

554 541 527 513 498

320 312 304 295 286

480 468 455 442 429

333 321 309 297 286

499 481 463 447 430

240 231 223 214 205

360 347 334 320 307

21 22 23 24 25

451 441 431 420 410

677 662 646 630 614

398 389 379 369 359

598 583 568 553 538

322 312 302 292 282

484 469 453 438 422

277 268 258 249 240

415 402 388 374 360

275 264 253 242 231

414 397 380 364 347

195 186 177 168 159

293 279 266 252 239

26 27 28 29 30

399 388 376 365 354

598 581 565 548 531

348 338 327 317 306

522 507 491 475 459

271 261 251 240 230

407 391 376 360 345

230 221 212 202 193

345 331 317 303 290

220 209 198 188 178

331 314 298 283 267

151 142 133 125 117

226 213 200 188 176

32 34 36 38 40

332 309 287 265 244

497 464 431 398 367

285 265 244 224 205

428 397 366 337 308

210 191 172 154 139

315 286 258 231 209

175 158 141 127 114

263 237 212 190 172

158 140 124 112 101

237 103 210 91.2 187 81.3 168 73.0 152 65.9

154 137 122 109 98.8

Properties φb Mn kip-ft 144 217 114 171 99.4 149 77.0 116 92.9 140 Pe (KL )2/104 kip-in.2 13000 10800 7310 6010 4820 Note: Dashed line indicates the KL beyond which bare steel strength controls. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

60.7 91.2 3460

AISC_Part 4E:14th Ed.

2/23/11

10:59 AM

Page 318

4–318

DESIGN OF COMPRESSION MEMBERS

Table 4-20 (continued)

Available Strength in Axial Compression, kips COMPOSITE PIPE 8-PIPE 5

Concrete Filled Pipe Pipe 8

Shape

Pipe 6

Pipe 5

Std

XXS

XS

Std

XXS

0.300 28.6 Pn /Ωc φc Pn ASD LRFD

0.805 53.2 Pn /Ωc φc Pn ASD LRFD

0.403 28.6 Pn /Ωc φc Pn ASD LRFD

0.261 19.0 Pn /Ωc φc Pn ASD LRFD

0.699 38.6 Pn /Ωc φc Pn ASD LRFD

0

258

386

308

463

200

301

161

241

224

337

6 7 8 9 10

247 243 239 234 229

370 365 358 351 343

290 283 276 268 260

436 426 415 403 391

187 183 178 172 166

281 274 267 258 249

150 146 142 137 132

225 219 213 206 198

205 199 192 184 176

309 299 288 277 264

11 12 13 14 15

223 217 211 204 198

335 326 317 307 296

251 241 231 221 210

377 362 347 332 316

160 153 146 139 132

240 230 219 208 197

127 121 116 110 104

190 182 173 165 156

167 158 149 139 130

251 237 223 209 195

16 17 18 19 20

190 183 176 168 161

286 275 264 252 241

199 188 177 167 156

299 283 267 250 234

124 117 109 102 94.9

186 175 164 153 142

97.6 91.6 85.5 79.6 73.8

146 137 128 119 111

120 111 102 93.1 84.5

181 167 153 140 127

21 22 23 24 25

153 146 138 131 123

230 218 207 196 185

145 135 125 115 106

218 203 188 173 160

87.9 81.1 74.4 68.3 63.3

132 122 112 103 95.1

68.1 62.7 57.3 52.6 48.5

102 94.0 86.0 78.9 72.7

76.7 69.9 63.9 58.7 54.1

115 105 96.1 88.2 81.3

26 27 28 29 30

116 109 102 95.3 89.1

174 164 153 143 134

98.2 91.1 84.7 78.9 73.8

148 137 127 119 111

58.5 54.3 50.5 47.0 44.0

88.0 81.6 75.8 70.7 66.1

44.8 41.6 38.7 36.0 33.7

67.3 62.4 58.0 54.1 50.5

50.0 46.4 43.1 40.2

75.2 69.7 64.8 60.4

32 34 36 38 40

78.3 69.3 61.8 55.5 50.1

117 104 92.8 83.3 75.1

64.8 57.4

38.6 34.2 30.5

58.1 51.4 45.9

29.6 26.2 23.4

44.4 39.3 35.1

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 35 ksi fc′ = 5 ksi

97.4 86.3

Properties φb Mn kip-ft 42.6 64.1 50.2 75.4 30.2 45.4 Pe (KL )2/104 kip-in.2 2630 1930 1290 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

21.4 32.2 995

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

30.3 45.5 973

AISC_Part 4E:14th Ed.

2/23/11

10:59 AM

Page 319

COMPOSITE COMPRESSION—MEMBER SELECTION TABLES

4–319

Table 4-20 (continued)

Available Strength in Axial Compression, kips

Fy = 35 ksi fc′ = 5 ksi

COMPOSITE PIPE 5-PIPE 4

Concrete Filled Pipe Pipe 5

Shape

XS

Std

XXS

XS

Std

0.349 20.8 Pn /Ωc φc Pn ASD LRFD

0.241 14.6 Pn /Ωc φc Pn ASD LRFD

0.628 27.6 Pn /Ωc φc Pn ASD LRFD

0.315 15.0 Pn /Ωc φc Pn ASD LRFD

0.221 10.8 Pn /Ωc φc Pn ASD LRFD

0

144

216

118

177

161

241

100

151

82.5

124

6 7 8 9 10

131 127 122 116 111

197 190 183 174 166

107 104 99.4 94.8 90.1

161 155 149 142 135

140 133 126 118 110

210 200 189 177 165

86.8 82.3 77.5 72.3 67.0

130 124 116 109 100

71.2 67.4 63.4 59.1 54.7

107 101 95.1 88.7 82.0

11 12 13 14 15

105 98.4 92.0 85.6 79.3

157 148 138 128 119

85.0 79.9 74.6 69.3 64.0

128 120 112 104 96.0

101 92.7 84.3 76.0 68.1

152 139 127 114 102

61.5 56.1 50.7 45.4 40.7

92.3 84.1 76.0 68.2 61.2

50.1 45.6 41.1 36.8 32.6

75.2 68.4 61.7 55.2 49.0

16 17 18 19 20

73.0 66.8 60.9 55.2 50.7

109 100 91.3 83.0 76.3

58.8 53.8 48.9 44.1 39.8

88.2 80.6 73.3 66.1 59.7

60.3 53.5 47.7 42.8 38.6

90.7 80.3 71.7 64.3 58.0

36.7 32.8 29.2 26.2 23.7

55.1 49.2 43.9 39.4 35.6

28.7 25.4 22.7 20.4 18.4

43.1 38.1 34.0 30.5 27.6

21 22 23 24 25

46.4 42.3 38.7 35.5 32.8

69.8 63.6 58.2 53.4 49.2

36.1 32.9 30.1 27.6 25.5

54.1 49.3 45.1 41.4 38.2

35.0 31.9 29.2

52.6 48.0 43.9

21.5 19.6 17.9 16.4

32.3 29.4 26.9 24.7

16.7 15.2 13.9 12.8 11.8

25.0 22.8 20.8 19.1 17.6

26 27 28 29 30

30.3 28.1 26.1 24.3 22.7

45.5 42.2 39.2 36.6 34.2

23.5 21.8 20.3 18.9 17.7

35.3 32.7 30.4 28.4 26.5

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Pipe 4

Properties φb Mn kip-ft 18.3 27.5 13.6 20.5 17.2 25.8 Pe (KL )2/104 kip-in.2 653 522 440 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

10.5 15.8 299

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7.99 12.0 241

AISC_Part 4E:14th Ed.

2/23/11

10:59 AM

Page 320

4–320

DESIGN OF COMPRESSION MEMBERS

Table 4-20 (continued)

Available Strength in Axial Compression, kips COMPOSITE PIPE 31/2 -PIPE 3

Concrete Filled Pipe Pipe 31/2

Shape

Pipe 3

XS

Std

XXS

XS

Std

0.296 12.5 Pn /Ωc φc Pn ASD LRFD

0.211 9.12 Pn /Ωc φc Pn ASD LRFD

0.559 18.6 Pn /Ωc φc Pn ASD LRFD

0.280 10.3 Pn /Ωc φc Pn ASD LRFD

0.201 7.58 Pn /Ωc φc Pn ASD LRFD

0

81.7

123

67.7

108

163

65.7

98.5

54.2

81.2

6 7 8 9 10

68.0 63.6 58.9 54.0 49.1

102 95.5 88.4 81.1 73.6

56.1 52.5 48.5 44.5 40.3

84.2 78.7 72.8 66.7 60.4

85.6 78.6 71.2 63.7 56.2

129 118 107 95.7 84.5

51.6 47.3 42.8 38.2 33.7

77.5 71.0 64.3 57.4 50.6

42.5 39.0 35.2 31.4 27.7

63.8 58.5 52.9 47.2 41.5

11 12 13 14 15

44.1 39.2 34.8 31.0 27.3

66.1 58.8 52.3 46.6 41.0

36.1 32.1 28.2 24.4 21.3

54.2 48.1 42.2 36.7 31.9

49.0 42.1 35.9 30.9 26.9

73.6 63.3 53.9 46.5 40.5

29.9 26.2 22.7 19.6 17.1

44.9 39.4 34.1 29.4 25.6

24.0 20.6 17.5 15.1 13.2

36.1 30.8 26.3 22.7 19.8

16 17 18 19 20

24.0 21.3 19.0 17.0 15.4

36.1 32.0 28.5 25.6 23.1

18.7 16.6 14.8 13.3 12.0

28.1 24.9 22.2 19.9 18.0

23.7 21.0

35.6 31.5

15.0 13.3 11.8 10.6

22.5 20.0 17.8 16.0

11.6 10.2 9.14 8.20

17.4 15.4 13.7 12.3

21 22

13.9

20.9

10.9 9.89

16.3 14.8

t design, in. Steel, lb/ft Design

Effective length, KL (ft)

Fy = 35 ksi fc′ = 5 ksi

101

Properties φb Mn kip-ft 7.72 11.6 5.94 8.93 8.79 13.2 Pe (KL )2/104 kip-in.2 193 157 171 Note: Heavy line indicates KL/r equal to or greater than 200. ASD LRFD

Mn /Ωb

Ωc = 2.00

φc = 0.75

5.48 8.24 119

Dashed line indicates the KL beyond which bare steel strength controls.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.25 6.39 97.3

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Table 4-21

Stiffness Reduction Factor ASD

LRFD

Pa ᎏᎏ Ag

Pu ᎏᎏ Ag

τ

b

Fy , ksi 35

36

42

46

50

45 44 43 42 41 40

ASD – – – – – –

LRFD – – – – – –

ASD – – – – – –

LRFD – – – – – –

ASD – – – – – –

LRFD – – – – 0.0930 0.181

ASD – – – – – –

LRFD 0.0851 0.166 0.244 0.318 0.388 0.454

ASD – – – – – –

LRFD 0.360 0.422 0.482 0.538 0.590 0.640

39 38 37 36 35

– – – – –

– – – – –

– – – – –

– – – – 0.108

– – – – –

0.265 0.345 0.420 0.490 0.556

– – – – –

0.516 0.575 0.629 0.681 0.728

– – – – –

0.686 0.730 0.770 0.806 0.840

34 33 32 31 30

– – – – –

0.111 0.216 0.313 0.405 0.490

– – – – –

0.210 0.306 0.395 0.478 0.556

– – – – –

0.617 0.673 0.726 0.773 0.816

– – – – –

0.771 0.811 0.847 0.879 0.907

– – – 0.0317 0.154

0.870 0.898 0.922 0.942 0.960

29 28 27 26 25

– – – – –

0.568 0.640 0.705 0.764 0.816

– – – – –

0.627 0.691 0.750 0.802 0.849

– – – 0.0377 0.181

0.855 0.889 0.918 0.943 0.964

– 0.102 0.229 0.346 0.454

0.932 0.953 0.970 0.983 0.992

0.267 0.373 0.470 0.559 0.640

0.974 0.986 0.994 0.998 1.00

24 23 22 21 20

– – – 0.154 0.313

0.862 0.901 0.934 0.960 0.980

– – 0.0869 0.249 0.395

0.889 0.923 0.951 0.972 0.988

0.313 0.434 0.543 0.640 0.726

0.980 0.991 0.998 1.00

0.552 0.640 0.719 0.788 0.847

0.998 1.00

0.713 0.777 0.834 0.882 0.922

19 18 17 16 15

0.457 0.583 0.693 0.786 0.862

0.993 0.999 1.00

0.525 0.640 0.739 0.822 0.889

0.997 1.00

0.800 0.862 0.913 0.952 0.980

0.896 0.936 0.967 0.987 0.998

14 13 12 11 10

0.922 0.964 0.991 1.00

0.996 1.00

1.00

0.940 0.976 0.996 1.00

0.953 0.977 0.992 0.999 1.00

9 8 7 6 5 – Indicates the stiffness reduction parameter is not applicable because the required strength exceeds the available strength for KL/r = 0.

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DESIGN OF COMPRESSION MEMBERS

Table 4-22

Available Critical Stress for Compression Members Fy = 35 ksi KL r 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Fcr /Ωc φc Fcr ksi ASD 21.0 21.0 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.8 20.8 20.8 20.7 20.7 20.7 20.7 20.6 20.6 20.5 20.5 20.4 20.4 20.3 20.3 20.2 20.2 20.1 20.1 20.0 20.0 19.9 19.8 19.8 19.7 19.6 19.5 19.5 19.4 19.3

ksi LRFD 31.5 31.5 31.5 31.5 31.5 31.4 31.4 31.4 31.4 31.3 31.3 31.3 31.2 31.2 31.1 31.1 31.0 31.0 30.9 30.9 30.8 30.7 30.7 30.6 30.5 30.4 30.3 30.3 30.2 30.1 30.0 29.9 29.8 29.7 29.6 29.5 29.4 29.3 29.1 29.0

Fy = 36 ksi KL r 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Fcr /Ωc φc Fcr ksi ASD 21.6 21.6 21.5 21.5 21.5 21.5 21.5 21.5 21.5 21.4 21.4 21.4 21.4 21.3 21.3 21.3 21.2 21.2 21.2 21.1 21.1 21.0 21.0 20.9 20.9 20.8 20.7 20.7 20.6 20.6 20.5 20.4 20.4 20.3 20.2 20.1 20.1 20.0 19.9 19.8

ksi LRFD 32.4 32.4 32.4 32.4 32.4 32.3 32.3 32.3 32.3 32.2 32.2 32.2 32.1 32.1 32.0 32.0 31.9 31.9 31.8 31.7 31.7 31.6 31.5 31.4 31.4 31.3 31.2 31.1 31.0 30.9 30.8 30.7 30.6 30.5 30.4 30.3 30.1 30.0 29.9 29.8

Fy = 42 ksi KL r 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Fcr /Ωc φc Fcr ksi ASD 25.1 25.1 25.1 25.1 25.1 25.1 25.1 25.1 25.0 25.0 25.0 24.9 24.9 24.8 24.8 24.8 24.7 24.7 24.6 24.5 24.5 24.4 24.3 24.3 24.2 24.1 24.0 24.0 23.9 23.8 23.7 23.6 23.5 23.4 23.3 23.2 23.1 23.0 22.9 22.8

ksi LRFD 37.8 37.8 37.8 37.8 37.7 37.7 37.7 37.7 37.6 37.6 37.5 37.5 37.4 37.3 37.3 37.2 37.1 37.1 37.0 36.9 36.8 36.7 36.6 36.5 36.4 36.3 36.1 36.0 35.9 35.8 35.6 35.5 35.4 35.2 35.1 34.9 34.8 34.6 34.4 34.3

Fy = 46 ksi KL r 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Fcr /Ωc φc Fcr ksi ASD 27.5 27.5 27.5 27.5 27.5 27.5 27.5 27.4 27.4 27.4 27.3 27.3 27.2 27.2 27.1 27.1 27.0 27.0 26.9 26.8 26.7 26.7 26.6 26.5 26.4 26.3 26.2 26.1 26.0 25.9 25.8 25.7 25.6 25.5 25.4 25.2 25.1 25.0 24.9 24.7

ASD LRFD Ωc = 1.67 φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ksi LRFD 41.4 41.4 41.4 41.4 41.3 41.3 41.3 41.2 41.2 41.1 41.1 41.0 40.9 40.9 40.8 40.7 40.6 40.5 40.4 40.3 40.2 40.1 40.0 39.8 39.7 39.6 39.4 39.3 39.1 39.0 38.8 38.6 38.5 38.3 38.1 37.9 37.8 37.6 37.4 37.2

Fy = 50 ksi KL r 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Fcr /Ωc φc Fcr ksi ASD 29.9 29.9 29.9 29.9 29.9 29.9 29.8 29.8 29.8 29.7 29.7 29.6 29.6 29.5 29.5 29.4 29.3 29.2 29.2 29.1 29.0 28.9 28.8 28.7 28.6 28.5 28.4 28.3 28.2 28.0 27.9 27.8 27.7 27.5 27.4 27.2 27.1 26.9 26.8 26.6

ksi LRFD 45.0 45.0 45.0 44.9 44.9 44.9 44.8 44.8 44.7 44.7 44.6 44.5 44.4 44.4 44.3 44.2 44.1 43.9 43.8 43.7 43.6 43.4 43.3 43.1 43.0 42.8 42.7 42.5 42.3 42.1 41.9 41.8 41.6 41.4 41.2 40.9 40.7 40.5 40.3 40.0

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Table 4-22 (continued)

Available Critical Stress for Compression Members Fy = 35 ksi KL r 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Fcr /Ωc φc Fcr ksi ASD 19.2 19.2 19.1 19.0 18.9 18.8 18.7 18.6 18.5 18.4 18.3 18.3 18.2 18.1 18.0 17.9 17.7 17.6 17.5 17.4 17.3 17.2 17.1 17.0 16.9 16.8 16.7 16.5 16.4 16.3 16.2 16.1 16.0 15.8 15.7 15.6 15.5 15.4 15.2 15.1

ksi LRFD 28.9 28.8 28.7 28.5 28.4 28.3 28.1 28.0 27.9 27.7 27.6 27.4 27.3 27.1 27.0 26.8 26.7 26.5 26.4 26.2 26.0 25.9 25.7 25.5 25.4 25.2 25.0 24.9 24.7 24.5 24.3 24.2 24.0 23.8 23.6 23.4 23.3 23.1 22.9 22.7

Fy = 36 ksi KL r 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Fcr /Ωc φc Fcr ksi ASD 19.7 19.6 19.6 19.5 19.4 19.3 19.2 19.1 19.0 18.9 18.8 18.7 18.6 18.5 18.4 18.3 18.2 18.1 17.9 17.8 17.7 17.6 17.5 17.4 17.3 17.1 17.0 16.9 16.8 16.7 16.5 16.4 16.3 16.2 16.0 15.9 15.8 15.6 15.5 15.4

ksi LRFD 29.7 29.5 29.4 29.3 29.1 29.0 28.9 28.7 28.5 28.4 28.3 28.1 28.0 27.8 27.6 27.5 27.3 27.1 27.0 26.8 26.6 26.5 26.3 26.1 25.9 25.8 25.6 25.4 25.2 25.0 24.8 24.7 24.5 24.3 24.1 23.9 23.7 23.5 23.3 23.1

Fy = 42 ksi KL r 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Fcr /Ωc φc Fcr ksi ASD 22.7 22.6 22.5 22.3 22.2 22.1 22.0 21.8 21.7 21.6 21.4 21.3 21.2 21.0 20.9 20.7 20.6 20.5 20.3 20.2 20.0 19.9 19.7 19.6 19.4 19.2 19.1 18.9 18.8 18.6 18.5 18.3 18.1 18.0 17.8 17.6 17.5 17.3 17.1 17.0

ksi LRFD 34.1 33.9 33.7 33.6 33.4 33.2 33.0 32.8 32.6 32.4 32.2 32.0 31.8 31.6 31.4 31.2 31.0 30.7 30.5 30.3 30.1 29.9 29.6 29.4 29.2 28.9 28.7 28.5 28.2 28.0 27.7 27.5 27.2 27.0 26.8 26.5 26.3 26.0 25.8 25.5

Fy = 46 ksi KL r 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Fcr /Ωc φc Fcr ksi ASD 24.6 24.5 24.3 24.2 24.0 23.9 23.8 23.6 23.4 23.3 23.1 23.0 22.8 22.6 22.5 22.3 22.1 22.0 21.8 21.6 21.4 21.3 21.1 20.9 20.7 20.5 20.4 20.2 20.0 19.8 19.6 19.4 19.2 19.1 18.9 18.7 18.5 18.3 18.1 17.9

ASD LRFD Ωc = 1.67 φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ksi LRFD 37.0 36.8 36.6 36.3 36.1 35.9 35.7 35.4 35.2 35.0 34.8 34.5 34.3 34.0 33.8 33.5 33.3 33.0 32.8 32.5 32.2 32.0 31.7 31.4 31.2 30.9 30.6 30.3 30.1 29.8 29.5 29.2 28.9 28.6 28.4 28.1 27.8 27.5 27.2 26.9

Fy = 50 ksi KL r 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Fcr /Ωc φc Fcr ksi ASD 26.5 26.3 26.2 26.0 25.8 25.6 25.5 25.3 25.1 24.9 24.8 24.6 24.4 24.2 24.0 23.8 23.6 23.4 23.2 23.0 22.8 22.6 22.4 22.2 22.0 21.8 21.6 21.4 21.1 20.9 20.7 20.5 20.3 20.1 19.8 19.6 19.4 19.2 19.0 18.8

ksi LRFD 39.8 39.5 39.3 39.1 38.8 38.5 38.3 38.0 37.7 37.5 37.2 36.9 36.7 36.4 36.1 35.8 35.5 35.2 34.9 34.6 34.3 34.0 33.7 33.4 33.0 32.7 32.4 32.1 31.8 31.4 31.1 30.8 30.5 30.2 29.8 29.5 29.2 28.8 28.5 28.2

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DESIGN OF COMPRESSION MEMBERS

Table 4-22 (continued)

Available Critical Stress for Compression Members Fy = 35 ksi KL r 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

Fcr /Ωc φc Fcr ksi ASD 15.0 14.9 14.7 14.6 14.5 14.4 14.2 14.1 14.0 13.8 13.7 13.6 13.5 13.3 13.2 13.1 13.0 12.8 12.7 12.6 12.4 12.3 12.2 12.1 11.9 11.8 11.7 11.5 11.4 11.3 11.2 11.0 10.9 10.8 10.7 10.5 10.4 10.3 10.2 10.0

ksi LRFD 22.5 22.3 22.1 22.0 21.8 21.6 21.4 21.2 21.0 20.8 20.6 20.4 20.2 20.0 19.9 19.7 19.5 19.3 19.1 18.9 18.7 18.5 18.3 18.1 17.9 17.7 17.5 17.3 17.2 17.0 16.8 16.6 16.4 16.2 16.0 15.8 15.6 15.5 15.3 15.1

Fy = 36 ksi KL r 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

Fcr /Ωc φc Fcr ksi ASD 15.3 15.1 15.0 14.9 14.7 14.6 14.5 14.3 14.2 14.1 13.9 13.8 13.7 13.5 13.4 13.3 13.1 13.0 12.9 12.7 12.6 12.5 12.3 12.2 12.1 11.9 11.8 11.7 11.5 11.4 11.3 11.1 11.0 10.9 10.7 10.6 10.5 10.4 10.2 10.1

ksi LRFD 22.9 22.7 22.5 22.3 22.1 22.0 21.8 21.6 21.4 21.2 21.0 20.8 20.5 20.3 20.1 19.9 19.7 19.5 19.3 19.1 18.9 18.7 18.5 18.3 18.1 17.9 17.7 17.5 17.3 17.1 16.9 16.7 16.5 16.3 16.2 16.0 15.8 15.6 15.4 15.2

Fy = 42 ksi KL r 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

Fcr /Ωc φc Fcr ksi ASD 16.8 16.6 16.5 16.3 16.1 16.0 15.8 15.6 15.5 15.3 15.1 15.0 14.8 14.6 14.4 14.3 14.1 13.9 13.8 13.6 13.4 13.3 13.1 12.9 12.8 12.6 12.4 12.3 12.1 12.0 11.8 11.6 11.5 11.3 11.2 11.0 10.8 10.7 10.5 10.4

ksi LRFD 25.3 25.0 24.8 24.5 24.3 24.0 23.7 23.5 23.2 23.0 22.7 22.5 22.2 22.0 21.7 21.5 21.2 21.0 20.7 20.5 20.2 20.0 19.7 19.5 19.2 19.0 18.7 18.5 18.2 18.0 17.7 17.5 17.3 17.0 16.8 16.5 16.3 16.1 15.8 15.6

Fy = 46 ksi KL r 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

Fcr /Ωc φc Fcr ksi ASD 17.7 17.5 17.3 17.1 16.9 16.7 16.6 16.4 16.2 16.0 15.8 15.6 15.4 15.2 15.0 14.8 14.6 14.4 14.2 14.1 13.9 13.7 13.5 13.3 13.1 12.9 12.8 12.6 12.4 12.2 12.0 11.8 11.7 11.5 11.3 11.1 11.0 10.8 10.6 10.4

ASD LRFD Ωc = 1.67 φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ksi LRFD 26.6 26.3 26.0 25.8 25.5 25.2 24.9 24.6 24.3 24.0 23.7 23.4 23.1 22.8 22.6 22.3 22.0 21.7 21.4 21.1 20.8 20.6 20.3 20.0 19.7 19.4 19.2 18.9 18.6 18.3 18.1 17.8 17.5 17.3 17.0 16.7 16.5 16.2 16.0 15.7

Fy = 50 ksi KL r 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

Fcr /Ωc φc Fcr ksi ASD 18.5 18.3 18.1 17.9 17.7 17.4 17.2 17.0 16.8 16.6 16.3 16.1 15.9 15.7 15.5 15.3 15.0 14.8 14.6 14.4 14.2 14.0 13.8 13.6 13.4 13.2 13.0 12.8 12.6 12.4 12.2 12.0 11.8 11.6 11.4 11.2 11.0 10.8 10.6 10.4

ksi LRFD 27.9 27.5 27.2 26.9 26.5 26.2 25.9 25.5 25.2 24.9 24.6 24.2 23.9 23.6 23.3 22.9 22.6 22.3 22.0 21.7 21.3 21.0 20.7 20.4 20.1 19.8 19.5 19.2 18.9 18.6 18.3 18.0 17.7 17.4 17.1 16.8 16.5 16.2 16.0 15.7

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Table 4-22 (continued)

Available Critical Stress for Compression Members Fy = 35 ksi KL r 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

Fcr /Ωc φc Fcr ksi ASD 9.91 9.79 9.67 9.55 9.43 9.31 9.19 9.07 8.95 8.83 8.71 8.60 8.48 8.37 8.25 8.13 8.01 7.89 7.78 7.67 7.56 7.45 7.35 7.25 7.15 7.05 6.96 6.86 6.77 6.68 6.59 6.51 6.42 6.34 6.26 6.18 6.10 6.02 5.95 5.87

ksi LRFD 14.9 14.7 14.5 14.3 14.2 14.0 13.8 13.6 13.4 13.3 13.1 12.9 12.7 12.6 12.4 12.2 12.0 11.9 11.7 11.5 11.4 11.2 11.0 10.9 10.7 10.6 10.5 10.3 10.2 10.0 9.91 9.78 9.65 9.53 9.40 9.28 9.17 9.05 8.94 8.82

Fy = 36 ksi KL r 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

Fcr /Ωc φc Fcr ksi ASD 10.0 9.85 9.72 9.59 9.47 9.35 9.22 9.10 8.98 8.86 8.73 8.61 8.49 8.37 8.25 8.13 8.01 7.89 7.78 7.67 7.56 7.45 7.35 7.25 7.15 7.05 6.96 6.86 6.77 6.68 6.59 6.51 6.42 6.34 6.26 6.18 6.10 6.02 5.95 5.87

ksi LRFD 15.0 14.8 14.6 14.4 14.2 14.0 13.9 13.7 13.5 13.3 13.1 12.9 12.8 12.6 12.4 12.2 12.0 11.9 11.7 11.5 11.4 11.2 11.0 10.9 10.7 10.6 10.5 10.3 10.2 10.0 9.91 9.78 9.65 9.53 9.40 9.28 9.17 9.05 8.94 8.82

Fy = 42 ksi KL r 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

Fcr /Ωc φc Fcr ksi ASD 10.2 10.1 9.93 9.78 9.62 9.47 9.32 9.17 9.03 8.89 8.76 8.63 8.50 8.37 8.25 8.13 8.01 7.89 7.78 7.67 7.56 7.45 7.35 7.25 7.15 7.05 6.96 6.86 6.77 6.68 6.59 6.51 6.42 6.34 6.26 6.18 6.10 6.02 5.95 5.87

ksi LRFD 15.4 15.2 14.9 14.7 14.5 14.2 14.0 13.8 13.6 13.4 13.2 13.0 12.8 12.6 12.4 12.2 12.0 11.9 11.7 11.5 11.4 11.2 11.0 10.9 10.7 10.6 10.5 10.3 10.2 10.0 9.91 9.78 9.65 9.53 9.40 9.28 9.17 9.05 8.94 8.82

Fy = 46 ksi KL r 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

Fcr /Ωc φc Fcr ksi ASD 10.3 10.1 9.94 9.78 9.62 9.47 9.32 9.17 9.03 8.89 8.76 8.63 8.50 8.37 8.25 8.13 8.01 7.89 7.78 7.67 7.56 7.45 7.35 7.25 7.15 7.05 6.96 6.86 6.77 6.68 6.59 6.51 6.42 6.34 6.26 6.18 6.10 6.02 5.95 5.87

ASD LRFD Ωc = 1.67 φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ksi LRFD 15.4 15.2 14.9 14.7 14.5 14.2 14.0 13.8 13.6 13.4 13.2 13.0 12.8 12.6 12.4 12.2 12.0 11.9 11.7 11.5 11.4 11.2 11.0 10.9 10.7 10.6 10.5 10.3 10.2 10.0 9.91 9.78 9.65 9.53 9.40 9.28 9.17 9.05 8.94 8.82

Fy = 50 ksi KL r 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

Fcr /Ωc φc Fcr ksi ASD 10.3 10.1 9.94 9.78 9.62 9.47 9.32 9.17 9.03 8.89 8.76 8.63 8.50 8.37 8.25 8.13 8.01 7.89 7.78 7.67 7.56 7.45 7.35 7.25 7.15 7.05 6.96 6.86 6.77 6.68 6.59 6.51 6.42 6.34 6.26 6.18 6.10 6.02 5.95 5.87

ksi LRFD 15.4 15.2 14.9 14.7 14.5 14.2 14.0 13.8 13.6 13.4 13.2 13.0 12.8 12.6 12.4 12.2 12.0 11.9 11.7 11.5 11.4 11.2 11.0 10.9 10.7 10.6 10.5 10.3 10.2 10.0 9.91 9.78 9.65 9.53 9.40 9.28 9.17 9.05 8.94 8.82

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DESIGN OF COMPRESSION MEMBERS

Table 4–22 (continued)

Available Critical Stress for Compression Members Fy = 35 ksi KL r 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

Fcr /Ωc φc Fcr ksi ASD 5.80 5.73 5.66 5.59 5.52 5.45 5.39 5.33 5.25 5.20 5.14 5.08 5.02 4.96 4.91 4.85 4.80 4.74 4.69 4.64 4.59 4.54 4.49 4.44 4.39 4.34 4.30 4.25 4.21 4.16 4.12 4.08 4.04 3.99 3.95 3.91 3.87 3.83 3.80 3.76

ksi LRFD 8.72 8.61 8.50 8.40 8.30 8.20 8.10 8.00 7.89 7.82 7.73 7.64 7.55 7.46 7.38 7.29 7.21 7.13 7.05 6.97 6.90 6.82 6.75 6.67 6.60 6.53 6.46 6.39 6.32 6.26 6.19 6.13 6.06 6.00 5.94 5.88 5.82 5.76 5.70 5.65

Fy = 36 ksi KL r 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

Fcr /Ωc φc Fcr ksi ASD 5.80 5.73 5.66 5.59 5.52 5.45 5.39 5.33 5.25 5.20 5.14 5.08 5.02 4.96 4.91 4.85 4.80 4.74 4.69 4.64 4.59 4.54 4.49 4.44 4.39 4.34 4.30 4.25 4.21 4.16 4.12 4.08 4.04 3.99 3.95 3.91 3.87 3.83 3.80 3.76

ksi LRFD 8.72 8.61 8.50 8.40 8.30 8.20 8.10 8.00 7.89 7.82 7.73 7.64 7.55 7.46 7.38 7.29 7.21 7.13 7.05 6.97 6.90 6.82 6.75 6.67 6.60 6.53 6.46 6.39 6.32 6.26 6.19 6.13 6.06 6.00 5.94 5.88 5.82 5.76 5.70 5.65

Fy = 42 ksi KL r 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

Fcr /Ωc φc Fcr ksi ASD 5.80 5.73 5.66 5.59 5.52 5.45 5.39 5.33 5.25 5.20 5.14 5.08 5.02 4.96 4.91 4.85 4.80 4.74 4.69 4.64 4.59 4.54 4.49 4.44 4.39 4.34 4.30 4.25 4.21 4.16 4.12 4.08 4.04 3.99 3.95 3.91 3.87 3.83 3.80 3.76

ksi LRFD 8.72 8.61 8.50 8.40 8.30 8.20 8.10 8.00 7.89 7.82 7.73 7.64 7.55 7.46 7.38 7.29 7.21 7.13 7.05 6.97 6.90 6.82 6.75 6.67 6.60 6.53 6.46 6.39 6.32 6.26 6.19 6.13 6.06 6.00 5.94 5.88 5.82 5.76 5.70 5.65

Fy = 46 ksi KL r 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

Fcr /Ωc φc Fcr ksi ASD 5.80 5.73 5.66 5.59 5.52 5.45 5.39 5.33 5.25 5.20 5.14 5.08 5.02 4.96 4.91 4.85 4.80 4.74 4.69 4.64 4.59 4.54 4.49 4.44 4.39 4.34 4.30 4.25 4.21 4.16 4.12 4.08 4.04 3.99 3.95 3.91 3.87 3.83 3.80 3.76

ASD LRFD Ωc = 1.67 φc = 0.90 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ksi LRFD 8.72 8.61 8.50 8.40 8.30 8.20 8.10 8.00 7.89 7.82 7.73 7.64 7.55 7.46 7.38 7.29 7.21 7.13 7.05 6.97 6.90 6.82 6.75 6.67 6.60 6.53 6.46 6.39 6.32 6.26 6.19 6.13 6.06 6.00 5.94 5.88 5.82 5.76 5.70 5.65

Fy = 50 ksi KL r 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

Fcr /Ωc φc Fcr ksi ASD 5.80 5.73 5.66 5.59 5.52 5.45 5.39 5.33 5.25 5.20 5.14 5.08 5.02 4.96 4.91 4.85 4.80 4.74 4.69 4.64 4.59 4.54 4.49 4.44 4.39 4.34 4.30 4.25 4.21 4.16 4.12 4.08 4.04 3.99 3.95 3.91 3.87 3.83 3.80 3.76

ksi LRFD 8.72 8.61 8.50 8.40 8.30 8.20 8.10 8.00 7.89 7.82 7.73 7.64 7.55 7.46 7.38 7.29 7.21 7.13 7.05 6.97 6.90 6.82 6.75 6.67 6.60 6.53 6.46 6.39 6.32 6.26 6.19 6.13 6.06 6.00 5.94 5.88 5.82 5.76 5.70 5.65

AISC_PART 5:14th Ed.

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DESIGN OF TENSION MEMBERS

5–1

PART 5 DESIGN OF TENSION MEMBERS SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–2 GROSS AREA, NET AREA AND EFFECTIVE NET AREA . . . . . . . . . . . . . . . . . . . . 5–2 Gross Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–2 Effective Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–2 TENSILE STRENGTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–2 Yielding Limit State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–2 Rupture Limit State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–3 OTHER SPECIFICATION REQUIREMENTS AND DESIGN CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–3 Special Requirements for Heavy Shapes and Plates . . . . . . . . . . . . . . . . . . . . . . . . . 5–3 Slenderness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–3 DESIGN TABLE DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–3 STEEL TENSION MEMBER SELECTION TABLES . . . . . . . . . . . . . . . . . . . . . . . . . 5–5 Table 5-1. W-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–5 Table 5-2. Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–14 Table 5-3. WT-Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–18 Table 5-4. Rectangular HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–27 Table 5-5. Square HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–36 Table 5-6. Round HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–39 Table 5-7. Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–44 Table 5-8. Double Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–46

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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1/20/11

7:40 AM

Page 2

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DESIGN OF TENSION MEMBERS

SCOPE The specification requirements and other design considerations summarized in this Part apply to the design of members subject to static axial tension. For fatigue applications, see AISC Specification Appendix 3. For the design of members subject to eccentric tension or combined tension and flexure, see Part 6.

GROSS AREA, NET AREA AND EFFECTIVE NET AREA In the determination of the available strength of a tension member, the gross area, Ag, is needed for the tensile yielding limit state and the effective net area, Ae, is needed for the tensile rupture limit state, as stipulated in AISC Specification Section D2.

Gross Area The gross area, Ag, is determined as specified in AISC Specification Section B4.3a.

Effective Net Area The effective net area, Ae, is determined from AISC Specification Section D3 by multiplying the net area, An, by the shear lag coefficient, U, where An is determined for tension members per AISC Specification Section B4.3b and U is determined from AISC Specification Table D3.1. Shear lag parameters are illustrated in AISC Specification Commentary Figures C-D3.1, C-D3.2 and C-D3.4.

TENSILE STRENGTH The limit-state of tensile yielding will control the available tensile strength over tensile rupture when the following relationship is satisfied: LRFD

ASD

0.90Fy Ag ≤ 0.75Fu Ae

(5-1a)

Fy Ag Fu Ae ≤ 1.67 2.00

(5-1b)

These expressions are both reduced to: Ae F ≥ 1.2 y Ag Fu

(5-2)

Otherwise, the limit state of tensile rupture will control over tensile yielding.

Yielding Limit State The available tensile strength due to tensile yielding, which must equal or exceed the required strength, Pu or Pa, is determined for tension members, per AISC Specification Section D2(a), using Equation D2-1.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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1/20/11

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DESIGN TABLE DISCUSSION

5–3

Rupture Limit State The available tensile strength due to tensile rupture, which must equal or exceed the required strength, Pu or Pa, is determined for tension members, per AISC Specification Section D2(b) using Equation D2-2.

OTHER SPECIFICATION REQUIREMENTS AND DESIGN CONSIDERATIONS Special Requirements for Heavy Shapes and Plates For tension members with complete-joint-penetration groove welded joints and made from heavy shapes with a flange thickness exceeding 2 in. or built-up sections consisting of plates with a thickness exceeding 2 in., see AISC Specification Sections A3.1c and Section A3.1d.

Slenderness Tension member slenderness ratio, L/r, should preferably be limited to a maximum of 300 per the User Note in AISC Specification Section D1. The intent of this recommendation is explained in the corresponding Commentary.

DESIGN TABLE DISCUSSION Available tensile strengths for various types of tension members (see individual descriptions below) are given in Tables 5-1 through 5-8 for the limit states of tensile yielding and tensile rupture. In each case, the tabulated values for available tensile rupture strength are based upon the assumption that Ae = 0.75Ag, which is arbitrarily selected as a value that is practical to achieve with typical end connections. Such consideration of the effective net area during the design of the member will simplify the design of its end connections, which can be difficult to configure and costly if tension members are selected based upon available tensile yielding strength only, without considering the reduction in strength due to the connection. When Ae > 0.75Ag, either the tabulated values for available tensile rupture strength can be used conservatively or the available tensile rupture strength can be calculated based upon the actual value of Ae. When Ae < 0.75Ag, the tabulated values of the available tensile rupture strength cannot be used, but rather must be calculated based upon the actual value of Ae.

Table 5-1. W-Shapes Available strengths in axial tension are given for W-shapes with Fy = 50 ksi and Fu = 65 ksi (ASTM A992). Note that tensile rupture will control over tensile yielding for W-shapes with Fy = 50 ksi and Fu = 65 ksi when Ae /Ag < 0.923. Otherwise, tensile yielding will control over tensile rupture.

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DESIGN OF TENSION MEMBERS

Table 5-2. Angles Available strengths in axial tension are given for single angles with Fy = 36 ksi and Fu = 58 ksi (ASTM A36). Note that tensile rupture will control over tensile yielding for single angles with Fy = 36 ksi and Fu = 58 ksi when Ae /Ag < 0.745. Otherwise, tensile yielding will control over tensile rupture.

Table 5-3. WT-Shapes Table 5-3 is similar to Table 5-1, except that it covers WT-shapes with Fy = 50 ksi and Fu = 65 ksi (ASTM A992).

Table 5-4. Rectangular HSS Available strengths in axial tension are given for rectangular HSS with Fy = 46 ksi and Fu = 58 ksi (ASTM A500 Grade B). Note that tensile rupture will control over tensile yielding for rectangular HSS with Fy = 46 ksi and Fu = 58 ksi when Ae /Ag < 0.952. Otherwise, tensile yielding will control over tensile rupture.

Table 5-5. Square HSS Table 5-5 is similar to Table 5-4, except that it covers square HSS with Fy = 46 ksi and Fu = 58 ksi (ASTM A500 Grade B).

Table 5-6. Round HSS Available strengths in axial tension are given for ASTM A500 round HSS with Fy = 42 ksi and Fu = 58 ksi (ASTM A500 Grade B). Note that tensile rupture will control over tensile yielding for round HSS with Fy = 42 ksi and Fu = 58 ksi when Ae /Ag < 0.869. Otherwise, tensile yielding will control over tensile rupture.

Table 5-7. Pipe Available strengths in axial tension are given for pipe with Fy = 35 ksi and Fu = 60 ksi (ASTM A53 Grade B). Note that tensile rupture will control over tensile yielding for pipe with Fy = 35 ksi and Fu = 60 ksi when Ae /Ag < 0.700. Otherwise, tensile yielding will control over tensile rupture.

Table 5-8. Double Angles Available strengths in axial tension are given for double angles with Fy = 36 ksi and Fu = 58 ksi (ASTM A36). Note that tensile rupture will control over tensile yielding for double angles with Fy = 36 ksi and Fu = 58 ksi when Ae /Ag < 0.745. Otherwise, tensile yielding will control over tensile rupture.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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1/20/11

7:40 AM

Page 5

5–5

STEEL TENSION MEMBER SELECTION TABLES

Table 5-1

Available Strength in Axial Tension

Fy = 50 ksi Fu = 65 ksi

W-Shapes

Shape

Gross Area, Ag

Ae = 0.75Ag

in.

W44-W40

Yielding kips

Rupture kips

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.

ASD

LRFD

ASD

LRFD

W44×335 ×290 ×262 ×230

98.5 85.4 77.2 67.8

73.9 64.1 57.9 50.9

2950 2560 2310 2030

4430 3840 3470 3050

2400 2080 1880 1650

3600 3120 2820 2480

W40×593h ×503h ×431h ×397h ×372h ×362h ×324 ×297 ×277 ×249 ×215 ×199

174 148 127 117 110 106 95.3 87.3 81.5 73.5 63.5 58.8

131 111 95.3 87.8 82.5 79.5 71.5 65.5 61.1 55.1 47.6 44.1

5210 4430 3800 3500 3290 3170 2850 2610 2440 2200 1900 1760

7830 6660 5720 5270 4950 4770 4290 3930 3670 3310 2860 2650

4260 3610 3100 2850 2680 2580 2320 2130 1990 1790 1550 1430

6390 5410 4650 4280 4020 3880 3490 3190 2980 2690 2320 2150

W40×392h ×331h ×327h ×294 ×278 ×264 ×235 ×211 ×183 ×167 ×149

116 97.7 95.9 86.2 82.3 77.4 69.1 62.1 53.3 49.3 43.8

87.0 73.3 71.9 64.7 61.7 58.1 51.8 46.6 40.0 37.0 32.9

3470 2930 2870 2580 2460 2320 2070 1860 1600 1480 1310

5220 4400 4320 3880 3700 3480 3110 2790 2400 2220 1970

2830 2380 2340 2100 2010 1890 1680 1510 1300 1200 1070

4240 3570 3510 3150 3010 2830 2530 2270 1950 1800 1600

2

2

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

h

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with A e ≥ 0.923A g.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 6

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DESIGN OF TENSION MEMBERS

Table 5-1 (continued)

Available Strength in Axial Tension

Fy = 50 ksi Fu = 65 ksi

W-Shapes

W36-W33

Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

W36×652h ×529h ×487h ×441h ×395h ×361h ×330 ×302 ×282 ×262 ×247 ×231

192 156 143 130 116 106 96.9 89.0 82.9 77.2 72.5 68.2

144 117 107 97.5 87.0 79.5 72.7 66.8 62.2 57.9 54.4 51.2

5750 4670 4280 3890 3470 3170 2900 2660 2480 2310 2170 2040

8640 7020 6440 5850 5220 4770 4360 4010 3730 3470 3260 3070

4680 3800 3480 3170 2830 2580 2360 2170 2020 1880 1770 1660

7020 5700 5220 4750 4240 3880 3540 3260 3030 2820 2650 2500

W36×256 ×232 ×210 ×194 ×182 ×170 ×160 ×150 ×135

75.3 68.0 61.9 57.0 53.6 50.0 47.0 44.3 39.9

56.5 51.0 46.4 42.8 40.2 37.5 35.3 33.2 29.9

2250 2040 1850 1710 1600 1500 1410 1330 1190

3390 3060 2790 2570 2410 2250 2120 1990 1800

1840 1660 1510 1390 1310 1220 1150 1080 972

2750 2490 2260 2090 1960 1830 1720 1620 1460

W33×387h ×354h ×318 ×291 ×263 ×241 ×221 ×201

114 104 93.7 85.6 77.4 71.1 65.3 59.1

85.5 78.0 70.3 64.2 58.1 53.3 49.0 44.3

3410 3110 2810 2560 2320 2130 1960 1770

5130 4680 4220 3850 3480 3200 2940 2660

2780 2540 2280 2090 1890 1730 1590 1440

4170 3800 3430 3130 2830 2600 2390 2160

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

h

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with A e ≥ 0.923A g.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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1/20/11

7:40 AM

Page 7

5–7

STEEL TENSION MEMBER SELECTION TABLES

Table 5-1 (continued)

Available Strength in Axial Tension

Fy = 50 ksi Fu = 65 ksi

W-Shapes

Shape

Gross Area, Ag

Ae = 0.75Ag

in.

W33-W27

Yielding kips

Rupture kips

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.

ASD

LRFD

ASD

LRFD

W33×169 ×152 ×141 ×130 ×118

49.5 44.9 41.5 38.3 34.7

37.1 33.7 31.1 28.7 26.0

1480 1340 1240 1150 1040

2230 2020 1870 1720 1560

1210 1100 1010 933 845

1810 1640 1520 1400 1270

W30×391h ×357h ×326h ×292 ×261 ×235 ×211 ×191 ×173

115 105 95.9 86.0 77.0 69.3 62.3 56.1 50.9

86.3 78.8 71.9 64.5 57.8 52.0 46.7 42.1 38.2

3440 3140 2870 2570 2310 2070 1870 1680 1520

5180 4730 4320 3870 3470 3120 2800 2520 2290

2800 2560 2340 2100 1880 1690 1520 1370 1240

4210 3840 3510 3140 2820 2540 2280 2050 1860

W30×148 ×132 ×124 ×116 ×108 ×99 ×90

43.6 38.8 36.5 34.2 31.7 29.0 26.3

32.7 29.1 27.4 25.7 23.8 21.8 19.7

1310 1160 1090 1020 949 868 787

1960 1750 1640 1540 1430 1310 1180

1060 946 891 835 774 709 640

1590 1420 1340 1250 1160 1060 960

W27×539h ×368h ×336h ×307h ×281 ×258 ×235 ×217 ×194 ×178 ×161 ×146

159 109 99.2 90.2 83.1 76.1 69.4 63.9 57.1 52.5 47.6 43.2

119 81.8 74.4 67.7 62.3 57.1 52.1 47.9 42.8 39.4 35.7 32.4

4760 3230 2970 2700 2490 2280 2080 1910 1710 1570 1430 1290

7160 4910 4460 4060 3740 3420 3120 2880 2570 2360 2140 1940

3870 2660 2420 2200 2020 1860 1690 1560 1390 1280 1160 1050

5800 3990 3630 3300 3040 2780 2540 2340 2090 1920 1740 1580

2

2

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

h

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with A e ≥ 0.923A g.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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1/20/11

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Page 8

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DESIGN OF TENSION MEMBERS

Table 5-1 (continued)

Available Strength in Axial Tension

Fy = 50 ksi Fu = 65 ksi

W-Shapes

W27-W21

Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

W27×129 ×114 ×102 ×94 ×84

37.8 33.6 30.0 27.6 24.7

28.4 25.2 22.5 20.7 18.5

1130 1010 898 826 740

1700 1510 1350 1240 1110

923 819 731 673 601

1380 1230 1100 1010 902

W24×370h ×335h ×306h ×279h ×250 ×229 ×207 ×192 ×176 ×162 ×146 ×131 ×117 ×104

109 98.3 89.7 81.9 73.5 67.2 60.7 56.5 51.7 47.8 43.0 38.6 34.4 30.7

81.8 73.7 67.3 61.4 55.1 50.4 45.5 42.4 38.8 35.9 32.3 29.0 25.8 23.0

3260 2940 2690 2450 2200 2010 1820 1690 1550 1430 1290 1160 1030 919

4910 4420 4040 3690 3310 3020 2730 2540 2330 2150 1940 1740 1550 1380

2660 2400 2190 2000 1790 1640 1480 1380 1260 1170 1050 943 839 748

3990 3590 3280 2990 2690 2460 2220 2070 1890 1750 1570 1410 1260 1120

W24×103 ×94 ×84 ×76 ×68

30.3 27.7 24.7 22.4 20.1

22.7 20.8 18.5 16.8 15.1

907 829 740 671 602

1360 1250 1110 1010 905

738 676 601 546 491

1110 1010 902 819 736

W24×62 ×55

18.2 16.2

13.7 12.2

545 485

819 729

445 397

668 595

W21×201 ×182 ×166 ×147 ×132 ×122 ×111 ×101

59.3 53.6 48.8 43.2 38.8 35.9 32.6 29.8

44.5 40.2 36.6 32.4 29.1 26.9 24.5 22.4

1780 1600 1460 1290 1160 1070 976 892

2670 2410 2200 1940 1750 1620 1470 1340

1450 1310 1190 1050 946 874 796 728

2170 1960 1780 1580 1420 1310 1190 1090

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

h

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with A e ≥ 0.923A g.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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1/20/11

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Page 9

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STEEL TENSION MEMBER SELECTION TABLES

Table 5-1 (continued)

Available Strength in Axial Tension

Fy = 50 ksi Fu = 65 ksi

W-Shapes

W21-W18

Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

W21×93 ×83 ×73 ×68 ×62 ×55 ×48

27.3 24.4 21.5 20.0 18.3 16.2 14.1

20.5 18.3 16.1 15.0 13.7 12.2 10.6

817 731 644 599 548 485 422

1230 1100 968 900 824 729 635

666 595 523 488 445 397 345

999 892 785 731 668 595 517

W21×57 ×50 ×44

16.7 14.7 13.0

12.5 11.0 9.75

500 440 389

752 662 585

406 358 317

609 536 475

W18×311h ×283h ×258h ×234h ×211 ×192 ×175 ×158 ×143 ×130 ×119 ×106 ×97 ×86 ×76

91.6 83.3 76.0 68.6 62.3 56.2 51.4 46.3 42.0 38.3 35.1 31.1 28.5 25.3 22.3

68.7 62.5 57.0 51.5 46.7 42.2 38.6 34.7 31.5 28.7 26.3 23.3 21.4 19.0 16.7

2740 2490 2280 2050 1870 1680 1540 1390 1260 1150 1050 931 853 757 668

4120 3750 3420 3090 2800 2530 2310 2080 1890 1720 1580 1400 1280 1140 1000

2230 2030 1850 1670 1520 1370 1250 1130 1020 933 855 757 696 618 543

3350 3050 2780 2510 2280 2060 1880 1690 1540 1400 1280 1140 1040 926 814

W18×71 ×65 ×60 ×55 ×50

20.9 19.1 17.6 16.2 14.7

15.7 14.3 13.2 12.2 11.0

626 572 527 485 440

941 860 792 729 662

510 465 429 397 358

765 697 644 595 536

W18×46 ×40 ×35

13.5 11.8 10.3

10.1 8.85 7.73

404 353 308

608 531 464

328 288 251

492 431 377

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

h

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with A e ≥ 0.923A g.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:40 AM

Page 10

5–10

DESIGN OF TENSION MEMBERS

Table 5-1 (continued)

Available Strength in Axial Tension

Fy = 50 ksi Fu = 65 ksi

W-Shapes

W16-W14

Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

W16×100 ×89 ×77 ×67

29.4 26.2 22.6 19.6

22.1 19.7 17.0 14.7

880 784 677 587

1320 1180 1020 882

718 640 553 478

1080 960 829 717

W16×57 ×50 ×45 ×40 ×36

16.8 14.7 13.3 11.8 10.6

12.6 11.0 9.98 8.85 7.95

503 440 398 353 317

756 662 599 531 477

410 358 324 288 258

614 536 487 431 388

6.85 5.76

273 230

411 346

223 187

334 281

6440 5870 5330 4850 4400 4010 3740 3500 3260 3020 2740 2490 2260 2050 1860 1700 1550 1400 1280

9680 8820 8010 7290 6620 6030 5630 5270 4910 4550 4110 3750 3400 3080 2790 2560 2330 2100 1920

5230 4780 4360 3970 3580 3280 3050 2850 2660 2460 2230 2030 1840 1670 1510 1380 1260 1140 1040

7850 7170 6530 5950 5360 4920 4570 4280 3990 3700 3340 3050 2760 2510 2270 2080 1900 1710 1560

Shape

W16×31 ×26

9.13 7.68

W14×730h ×665h ×605h ×550h ×500h ×455h ×426h ×398h ×370h ×342h ×311h ×283h ×257 ×233 ×211 ×193 ×176 ×159 ×145

215 196 178 162 147 134 125 117 109 101 91.4 83.3 75.6 68.5 62.0 56.8 51.8 46.7 42.7

161 147 134 122 110 101 93.8 87.8 81.8 75.8 68.6 62.5 56.7 51.4 46.5 42.6 38.9 35.0 32.0

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

h

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with A e ≥ 0.923A g.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:40 AM

Page 11

5–11

STEEL TENSION MEMBER SELECTION TABLES

Table 5-1 (continued)

Available Strength in Axial Tension

Fy = 50 ksi Fu = 65 ksi

W-Shapes

W14-W12

Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

W14×132 ×120 ×109 ×99 ×90

38.8 35.3 32.0 29.1 26.5

29.1 26.5 24.0 21.8 19.9

1160 1060 958 871 793

1750 1590 1440 1310 1190

946 861 780 709 647

1420 1290 1170 1060 970

W14×82 ×74 ×68 ×61

24.0 21.8 20.0 17.9

18.0 16.4 15.0 13.4

719 653 599 536

1080 981 900 806

585 533 488 436

878 800 731 653

W14×53 ×48 ×43

15.6 14.1 12.6

11.7 10.6 9.45

467 422 377

702 635 567

380 345 307

570 517 461

W14×38 ×34 ×30

11.2 10.0 8.85

8.40 7.50 6.64

335 299 265

504 450 398

273 244 216

410 366 324

W14×26 ×22

7.69 6.49

5.77 4.87

230 194

346 292

188 158

281 237

2960 2680 2450 2220 2030 1850 1680 1500 1340 1190 1050 934 844 766 695 632 572

4450 4030 3690 3330 3050 2780 2520 2250 2010 1800 1580 1400 1270 1150 1040 950 860

2410 2180 2000 1810 1650 1510 1370 1220 1090 972 858 761 689 624 566 514 465

3620 3270 2990 2710 2480 2260 2050 1830 1630 1460 1290 1140 1030 936 848 770 697

Shape

W12×336h ×305h ×279h ×252h ×230h ×210 ×190 ×170 ×152 ×136 ×120 ×106 ×96 ×87 ×79 ×72 ×65

98.9 89.5 81.9 74.1 67.7 61.8 56.0 50.0 44.7 39.9 35.2 31.2 28.2 25.6 23.2 21.1 19.1

74.2 67.1 61.4 55.6 50.8 46.4 42.0 37.5 33.5 29.9 26.4 23.4 21.2 19.2 17.4 15.8 14.3

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

h

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with A e ≥ 0.923A g.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:40 AM

Page 12

5–12

DESIGN OF TENSION MEMBERS

Table 5-1 (continued)

Available Strength in Axial Tension

Fy = 50 ksi Fu = 65 ksi

W-Shapes

W12-W10

Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

W12×58 ×53

17.0 15.6

12.8 11.7

509 467

765 702

416 380

624 570

W12×50 ×45 ×40

14.6 13.1 11.7

11.0 9.83 8.78

437 392 350

657 590 527

358 319 285

536 479 428

W12×35 ×30 ×26

10.3 8.79 7.65

7.73 6.59 5.74

308 263 229

464 396 344

251 214 187

377 321 280

W12×22 ×19 ×16 ×14

6.48 5.57 4.71 4.16

4.86 4.18 3.53 3.12

194 167 141 125

292 251 212 187

158 136 115 101

237 204 172 152

985 877 778 680 596 530 473 431

1480 1320 1170 1020 896 797 711 648

803 715 634 553 484 432 387 351

1200 1070 951 829 726 648 580 527

Shape

W10×112 ×100 ×88 ×77 ×68 ×60 ×54 ×49

32.9 29.3 26.0 22.7 19.9 17.7 15.8 14.4

24.7 22.0 19.5 17.0 14.9 13.3 11.9 10.8

W10×45 ×39 ×33

13.3 11.5 9.71

9.98 8.63 7.28

398 344 291

599 518 437

324 280 237

487 421 355

W10×30 ×26 ×22

8.84 7.61 6.49

6.63 5.71 4.87

265 228 194

398 342 292

215 186 158

323 278 237

W10×19 ×17 ×15 ×12

5.62 4.99 4.41 3.54

4.22 3.74 3.31 2.66

168 149 132 106

253 225 198 159

137 122 108 86.5

206 182 161 130

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with A e ≥ 0.923A g.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:40 AM

Page 13

5–13

STEEL TENSION MEMBER SELECTION TABLES

Table 5-1 (continued)

Available Strength in Axial Tension

Fy = 50 ksi Fu = 65 ksi

W-Shapes

W8

Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

W8×67 ×58 ×48 ×40 ×35 ×31

19.7 17.1 14.1 11.7 10.3 9.13

14.8 12.8 10.6 8.78 7.73 6.85

590 512 422 350 308 273

887 770 635 527 464 411

481 416 345 285 251 223

722 624 517 428 377 334

W8×28 ×24

8.25 7.08

6.19 5.31

247 212

371 319

201 173

302 259

W8×21 ×18

6.16 5.26

4.62 3.95

184 157

277 237

150 128

225 193

W8×15 ×13 ×10

4.44 3.84 2.96

3.33 2.88 2.22

133 115 88.6

200 173 133

108 93.6 72.2

162 140 108

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with A e ≥ 0.923A g.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:40 AM

Page 14

5–14

DESIGN OF TENSION MEMBERS

Table 5-2

Available Strength in Axial Tension

Fy = 36 ksi Fu = 58 ksi

Angles

L8-L6 Gross Area, Ag

Ae = 0.75Ag

in.2

in.2

L8×8×11/8 ×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2

16.8 15.1 13.3 11.5 9.69 8.77 7.84

L8×6×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16

Shape

Yielding kips

Rupture kips

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

ASD

LRFD

ASD

LRFD

12.6 11.3 9.98 8.63 7.27 6.58 5.88

362 326 287 248 209 189 169

544 489 431 373 314 284 254

365 328 289 250 211 191 171

548 492 434 375 316 286 256

13.1 11.5 9.99 8.41 7.61 6.80 5.99

9.83 8.63 7.49 6.31 5.71 5.10 4.49

282 248 215 181 164 147 129

424 373 324 272 247 220 194

285 250 217 183 166 148 130

428 375 326 274 248 222 195

L8×4×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16

11.1 9.79 8.49 7.16 6.49 5.80 5.11

8.33 7.34 6.37 5.37 4.87 4.35 3.83

239 211 183 154 140 125 110

360 317 275 232 210 188 166

242 213 185 156 141 126 111

362 319 277 234 212 189 167

L7×4×3/4 ×5/8 ×1/2 ×7/16 ×3/8

7.74 6.50 5.26 4.63 4.00

5.81 4.88 3.95 3.47 3.00

167 140 113 99.8 86.2

251 211 170 150 130

168 142 115 101 87.0

253 212 172 151 131

L6×6×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16 ×3/8 ×5/16

11.0 9.75 8.46 7.13 6.45 5.77 5.08 4.38 3.67

8.25 7.31 6.35 5.35 4.84 4.33 3.81 3.29 2.75

237 210 182 154 139 124 110 94.4 79.1

356 316 274 231 209 187 165 142 119

239 212 184 155 140 126 110 95.4 79.8

359 318 276 233 211 188 166 143 120

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.745Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:40 AM

Page 15

5–15

STEEL TENSION MEMBER SELECTION TABLES

Table 5-2 (continued)

Available Strength in Axial Tension

Fy = 36 ksi Fu = 58 ksi

Angles

Shape

Gross Area, Ag

Ae = 0.75Ag

in.

2

L6-L5

Yielding kips

Rupture kips

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.

ASD

LRFD

ASD

LRFD

2

L6×4×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16 ×3/8 ×5/16

8.00 6.94 5.86 5.31 4.75 4.18 3.61 3.03

6.00 5.21 4.40 3.98 3.56 3.14 2.71 2.27

172 150 126 114 102 90.1 77.8 65.3

259 225 190 172 154 135 117 98.2

174 151 128 115 103 91.1 78.6 65.8

261 227 191 173 155 137 118 98.7

L6×31/2×1/2 ×3/8 ×5/16

4.50 3.44 2.89

3.38 2.58 2.17

97.0 74.2 62.3

146 111 93.6

98.0 74.8 62.9

147 112 94.4

L5×5×7/8 ×3/4 ×5/8 ×1/2 ×7/16 ×3/8 ×5/16

8.00 6.98 5.90 4.79 4.22 3.65 3.07

6.00 5.24 4.43 3.59 3.17 2.74 2.30

172 150 127 103 91.0 78.7 66.2

259 226 191 155 137 118 99.5

174 152 128 104 91.9 79.5 66.7

261 228 193 156 138 119 100

L5×31/2×3/4 ×5/8 ×1/2 ×3/8 ×5/16 ×1/4

5.85 4.93 4.00 3.05 2.56 2.07

4.39 3.70 3.00 2.29 1.92 1.55

126 106 86.2 65.7 55.2 44.6

190 160 130 98.8 82.9 67.1

127 107 87.0 66.4 55.7 45.0

191 161 131 99.6 83.5 67.4

L5×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4

3.75 3.31 2.86 2.41 1.94

2.81 2.48 2.15 1.81 1.46

80.8 71.4 61.7 52.0 41.8

122 107 92.7 78.1 62.9

81.5 71.9 62.4 52.5 42.3

122 108 93.5 78.7 63.5

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.745Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:40 AM

Page 16

5–16

DESIGN OF TENSION MEMBERS

Table 5-2 (continued)

Available Strength in Axial Tension

Fy = 36 ksi Fu = 58 ksi

Angles

L4-L31/2

Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

L4×4×3/4 ×5/8 ×1/2 ×7/16 ×3/8 ×5/16 ×1/4

5.44 4.61 3.75 3.30 2.86 2.40 1.93

4.08 3.46 2.81 2.48 2.15 1.80 1.45

117 99.4 80.8 71.1 61.7 51.7 41.6

176 149 122 107 92.7 77.8 62.5

118 100 81.5 71.9 62.4 52.2 42.1

177 151 122 108 93.5 78.3 63.1

L4×31/2×1/2 ×3/8 ×5/16 ×1/4

3.50 2.68 2.25 1.82

2.63 2.01 1.69 1.37

75.4 57.8 48.5 39.2

113 86.8 72.9 59.0

76.3 58.3 49.0 39.7

114 87.4 73.5 59.6

L4×3×5/8 ×1/2 ×3/8 ×5/16 ×1/4

3.99 3.25 2.49 2.09 1.69

2.99 2.44 1.87 1.57 1.27

86.0 70.1 53.7 45.1 36.4

129 105 80.7 67.7 54.8

86.7 70.8 54.2 45.5 36.8

130 106 81.3 68.3 55.2

L31/2×31/2×1/2 ×7/16 ×3/8 ×5/16 ×1/4

3.25 2.89 2.50 2.10 1.70

2.44 2.17 1.88 1.58 1.28

70.1 62.3 53.9 45.3 36.6

105 93.6 81.0 68.0 55.1

70.8 62.9 54.5 45.8 37.1

106 94.4 81.8 68.7 55.7

L31/2×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4

3.02 2.67 2.32 1.95 1.58

2.27 2.00 1.74 1.46 1.19

65.1 57.6 50.0 42.0 34.1

97.8 86.5 75.2 63.2 51.2

65.8 58.0 50.5 42.3 34.5

98.7 87.0 75.7 63.5 51.8

L31/2×21/2×1/2 ×3/8 ×5/16 ×1/4

2.77 2.12 1.79 1.45

2.08 1.59 1.34 1.09

59.7 45.7 38.6 31.3

89.7 68.7 58.0 47.0

60.3 46.1 38.9 31.6

90.5 69.2 58.3 47.4

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.745Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:40 AM

Page 17

5–17

STEEL TENSION MEMBER SELECTION TABLES

Table 5-2 (continued)

Available Strength in Axial Tension

Fy = 36 ksi Fu = 58 ksi

Angles

L3-L2

Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

L3×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4 ×3/16

2.76 2.43 2.11 1.78 1.44 1.09

2.07 1.82 1.58 1.34 1.08 0.818

59.5 52.4 45.5 38.4 31.0 23.5

89.4 78.7 68.4 57.7 46.7 35.3

60.0 52.8 45.8 38.9 31.3 23.7

90.0 79.2 68.7 58.3 47.0 35.6

L3×21/2×1/2 ×7/16 ×3/8 ×5/16 ×1/4 ×3/16

2.50 2.22 1.93 1.63 1.32 1.00

1.88 1.67 1.45 1.22 0.990 0.750

53.9 47.9 41.6 35.1 28.5 21.6

81.0 71.9 62.5 52.8 42.8 32.4

54.5 48.4 42.1 35.4 28.7 21.8

81.8 72.6 63.1 53.1 43.1 32.6

L3×2×1/2 ×3/8 ×5/16 ×1/4 ×3/16

2.26 1.75 1.48 1.20 0.917

1.70 1.31 1.11 0.900 0.688

48.7 37.7 31.9 25.9 19.8

73.2 56.7 48.0 38.9 29.7

49.3 38.0 32.2 26.1 20.0

74.0 57.0 48.3 39.2 29.9

L21/2×21/2×1/2 ×3/8 ×5/16 ×1/4 ×3/16

2.26 1.73 1.46 1.19 0.901

1.70 1.30 1.10 0.893 0.676

48.7 37.3 31.5 25.7 19.4

73.2 56.1 47.3 38.6 29.2

49.3 37.7 31.9 25.9 19.6

74.0 56.6 47.9 38.8 29.4

L21/2×2×3/8 ×5/16 ×1/4 ×3/16

1.55 1.32 1.07 0.818

1.16 0.990 0.803 0.614

33.4 28.5 23.1 17.6

50.2 42.8 34.7 26.5

33.6 28.7 23.3 17.8

50.5 43.1 34.9 26.7

L21/2×11/2×1/4 ×3/16

0.947 0.724

0.710 0.543

20.4 15.6

30.7 23.5

20.6 15.7

30.9 23.6

L2×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

1.37 1.16 0.944 0.722 0.491

1.03 0.870 0.708 0.542 0.368

29.5 25.0 20.3 15.6 10.6

44.4 37.6 30.6 23.4 15.9

29.9 25.2 20.5 15.5 10.7

44.8 37.8 30.8 23.6 16.0

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.745Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:40 AM

Page 18

5–18

DESIGN OF TENSION MEMBERS

Table 5-3

Available Strength in Axial Tension WT22–WT20

Fy = 50 ksi Fu = 65 ksi

WT-Shapes Yielding

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

WT22×167.5 ×145 ×131 ×115

49.2 42.6 38.5 33.9

36.9 32.0 28.9 25.4

1470 1280 1150 1010

2210 1920 1730 1530

1200 1040 939 826

1800 1560 1410 1240

WT20×296.5h ×251.5h ×215.5h ×198.5h ×186h ×181h ×162 ×148.5 ×138.5 ×124.5 ×107.5 ×99.5

87.2 74.0 63.3 58.3 54.7 53.2 47.7 43.6 40.7 36.7 31.8 29.2

65.4 55.5 47.5 43.7 41.0 39.9 35.8 32.7 30.5 27.5 23.9 21.9

2610 2220 1900 1750 1640 1590 1430 1310 1220 1100 952 874

3920 3330 2850 2620 2460 2390 2150 1960 1830 1650 1430 1310

2130 1800 1540 1420 1330 1300 1160 1060 991 894 777 712

3190 2710 2320 2130 2000 1950 1750 1590 1490 1340 1170 1070

WT20×196h ×165.5h ×163.5h ×147 ×139 ×132 ×117.5 ×105.5 ×91.5 ×83.5 ×74.5

57.8 48.8 47.9 43.1 41.0 38.7 34.6 31.1 26.7 24.5 21.9

43.4 36.6 35.9 32.3 30.8 29.0 26.0 23.3 20.0 18.4 16.4

1730 1460 1430 1290 1230 1160 1040 931 799 734 656

2600 2200 2160 1940 1850 1740 1560 1400 1200 1100 986

1410 1190 1170 1050 1000 943 845 757 650 598 533

2120 1780 1750 1570 1500 1410 1270 1140 975 897 800

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

kips

h

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.923Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:40 AM

Page 19

5–19

STEEL TENSION MEMBER SELECTION TABLES

Table 5-3 (continued)

Available Strength in Axial Tension

Fy = 50 ksi Fu = 65 ksi

WT18-WT16.5

WT-Shapes Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

WT18×326h ×264.5h ×243.5h ×220.5h ×197.5h ×180.5h ×165 ×151 ×141 ×131 ×123.5 ×115.5

96.2 77.8 71.7 64.9 58.1 53.0 48.4 44.5 41.5 38.5 36.3 34.1

72.2 58.4 53.8 48.7 43.6 39.8 36.3 33.4 31.1 28.9 27.2 25.6

2880 2330 2150 1940 1740 1590 1450 1330 1240 1150 1090 1020

4330 3500 3230 2920 2610 2390 2180 2000 1870 1730 1630 1530

2350 1900 1750 1580 1420 1290 1180 1090 1010 939 884 832

3520 2850 2620 2370 2130 1940 1770 1630 1520 1410 1330 1250

WT18×128 ×116 ×105 ×97 ×91 ×85 ×80 ×75 ×67.5

37.6 34.0 30.9 28.5 26.8 25.0 23.5 22.1 19.9

28.2 25.5 23.2 21.4 20.1 18.8 17.6 16.6 14.9

1130 1020 925 853 802 749 704 662 596

1690 1530 1390 1280 1210 1130 1060 995 896

917 829 754 696 653 611 572 540 484

1370 1240 1130 1040 980 917 858 809 726

WT16.5×193.5h ×177h ×159 ×145.5 ×131.5 ×120.5 ×110.5 ×100.5

57.0 52.1 46.8 42.8 38.7 35.6 32.6 29.7

42.8 39.1 35.1 32.1 29.0 26.7 24.5 22.3

1710 1560 1400 1280 1160 1070 976 889

2570 2340 2110 1930 1740 1600 1470 1340

1390 1270 1140 1040 943 868 796 725

2090 1910 1710 1560 1410 1300 1190 1090

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

h

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.923Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 20

5–20

DESIGN OF TENSION MEMBERS

Table 5-3 (continued)

Available Strength in Axial Tension WT16.5-WT13.5

Fy = 50 ksi Fu = 65 ksi

WT-Shapes Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

24.7 22.5 20.7 19.1 17.4

18.5 16.9 15.5 14.3 13.1

740 674 620 572 521

1110 1010 932 860 783

601 549 504 465 426

902 824 756 697 639

WT15×195.5h ×178.5h ×163h ×146 ×130.5 ×117.5 ×105.5 ×95.5 ×86.5

57.6 52.5 48.0 43.0 38.5 34.7 31.1 28.0 25.4

43.2 39.4 36.0 32.3 28.9 26.0 23.3 21.0 19.1

1720 1570 1440 1290 1150 1040 931 838 760

2590 2360 2160 1940 1730 1560 1400 1260 1140

1400 1280 1170 1050 939 845 757 683 621

2110 1920 1760 1570 1410 1270 1140 1020 931

WT15×74 ×66 ×62 ×58 ×54 ×49.5 ×45

21.8 19.5 18.2 17.1 15.9 14.5 13.2

16.4 14.6 13.7 12.8 11.9 10.9 9.90

653 584 545 512 476 434 395

981 878 819 770 716 653 594

533 475 445 416 387 354 322

800 712 668 624 580 531 483

WT13.5×269.5h ×184h ×168h ×153.5h ×140.5 ×129 ×117.5 ×108.5 ×97 ×89 ×80.5 ×73

79.3 54.2 49.5 45.2 41.5 38.1 34.7 32.0 28.6 26.3 23.8 21.6

59.5 40.7 37.1 33.9 31.1 28.6 26.0 24.0 21.5 19.7 17.9 16.2

2370 1620 1480 1350 1240 1140 1040 958 856 787 713 647

3570 2440 2230 2030 1870 1710 1560 1440 1290 1180 1070 972

1930 1320 1210 1100 1010 930 845 780 699 640 582 527

2900 1980 1810 1650 1520 1390 1270 1170 1050 960 873 790

Shape

WT16.5×84.5 ×76 ×70.5 ×65 ×59

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

h

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.923Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 21

5–21

STEEL TENSION MEMBER SELECTION TABLES

Table 5-3 (continued)

Available Strength in Axial Tension

Fy = 50 ksi Fu = 65 ksi

WT13.5-WT10.5

WT-Shapes Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

18.9 16.8 15.0 13.8 12.4

14.2 12.6 11.3 10.4 9.30

566 503 449 413 371

851 756 675 621 558

462 410 367 338 302

692 614 551 507 453

WT12×185h ×167.5h ×153h ×139.5h ×125 ×114.5 ×103.5 ×96 ×88 ×81 ×73 ×65.5 ×58.5 ×52

54.5 49.1 44.9 41.0 36.8 33.6 30.3 28.2 25.8 23.9 21.5 19.3 17.2 15.3

40.9 36.8 33.7 30.8 27.6 25.2 22.7 21.2 19.4 17.9 16.1 14.5 12.9 11.5

1630 1470 1340 1230 1100 1010 907 844 772 716 644 578 515 458

2450 2210 2020 1850 1660 1510 1360 1270 1160 1080 968 869 774 689

1330 1200 1100 1000 897 819 738 689 631 582 523 471 419 374

1990 1790 1640 1500 1350 1230 1110 1030 946 873 785 707 629 561

WT12×51.5 ×47 ×42 ×38 ×34

15.1 13.8 12.4 11.2 10.0

11.3 10.4 9.30 8.40 7.50

452 413 371 335 299

680 621 558 504 450

367 338 302 273 244

551 507 453 410 366

6.83 6.08

273 243

410 365

222 198

333 296

886 802 731 647 581 536 488 446

1330 1210 1100 972 873 806 734 671

722 653 595 527 475 436 397 364

1080 980 892 790 712 653 595 546

Shape

WT13.5×64.5 ×57 ×51 ×47 ×42

WT12×31 ×27.5

9.11 8.10

WT10.5×100.5 ×91 ×83 ×73.5 ×66 ×61 ×55.5 ×50.5

29.6 26.8 24.4 21.6 19.4 17.9 16.3 14.9

22.2 20.1 18.3 16.2 14.6 13.4 12.2 11.2

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

h

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.923Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 22

5–22

DESIGN OF TENSION MEMBERS

Table 5-3 (continued)

Available Strength in Axial Tension WT10.5-WT9

Fy = 50 ksi Fu = 65 ksi

WT-Shapes Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

WT10.5×46.5 ×41.5 ×36.5 ×34 ×31 ×27.5 ×24

13.7 12.2 10.7 10.0 9.13 8.10 7.07

10.3 9.15 8.03 7.50 6.85 6.08 5.30

410 365 320 299 273 243 212

617 549 482 450 411 365 318

335 297 261 244 223 198 172

502 446 391 366 334 296 258

WT10.5×28.5 ×25 ×22

8.37 7.36 6.49

6.28 5.52 4.87

251 220 194

377 331 292

204 179 158

306 269 237

Shape

WT9×155.5h ×141.5h ×129h ×117h ×105.5 ×96 ×87.5 ×79 ×71.5 ×65 ×59.5 ×53 ×48.5 ×43 ×38

45.8 41.7 38.0 34.3 31.2 28.1 25.7 23.2 21.0 19.2 17.6 15.6 14.2 12.7 11.1

34.4 31.3 28.5 25.7 23.4 21.1 19.3 17.4 15.8 14.4 13.2 11.7 10.7 9.53 8.33

1370 1250 1140 1030 934 841 769 695 629 575 527 467 425 380 332

2060 1880 1710 1540 1400 1260 1160 1040 945 864 792 702 639 572 500

1120 1020 926 835 761 686 627 566 514 468 429 380 348 310 271

1680 1530 1390 1250 1140 1030 941 848 770 702 644 570 522 465 406

WT9×35.5 ×32.5 ×30 ×27.5 ×25

10.4 9.55 8.82 8.10 7.34

7.80 7.16 6.62 6.08 5.51

311 286 264 243 220

468 430 397 365 330

254 233 215 198 179

380 349 323 296 269

WT9×23 ×20 ×17.5

6.77 5.88 5.15

5.08 4.41 3.86

203 176 154

305 265 232

165 143 125

248 215 188

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

h

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.923Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 23

5–23

STEEL TENSION MEMBER SELECTION TABLES

Table 5-3 (continued)

Available Strength in Axial Tension

Fy = 50 ksi Fu = 65 ksi

WT8-WT7

WT-Shapes Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

WT8×50 ×44.5 ×38.5 ×33.5

14.7 13.1 11.3 9.81

11.0 9.83 8.48 7.36

440 392 338 294

662 590 509 441

358 319 276 239

536 479 413 359

WT8×28.5 ×25 ×22.5 ×20 ×18

8.39 7.37 6.63 5.89 5.29

6.29 5.53 4.97 4.42 3.97

251 221 199 176 158

378 332 298 265 238

204 180 162 144 129

307 270 242 215 194

WT8×15.5 ×13

4.56 3.84

3.42 2.88

137 115

205 173

111 93.6

167 140

3200 2930 2660 2420 2200 2000 1880 1750 1630 1510 1370 1250 1130 1020 928 850 775 701 638

4820 4400 4010 3640 3310 3010 2820 2630 2450 2260 2060 1870 1700 1540 1400 1280 1170 1050 959

Shape

WT7×365h ×332.5h ×302.5h ×275h ×250h ×227.5h ×213h ×199h ×185h ×171h ×155.5h ×141.5h ×128.5 ×116.5 ×105.5 ×96.5 ×88 ×79.5 ×72.5

107 97.8 89.0 80.9 73.5 66.9 62.7 58.4 54.4 50.3 45.7 41.6 37.8 34.2 31.0 28.4 25.9 23.4 21.3

80.3 73.4 66.8 60.7 55.1 50.2 47.0 43.8 40.8 37.7 34.3 31.2 28.4 25.7 23.3 21.3 19.4 17.6 16.0

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

h

2610 2390 2170 1970 1790 1630 1530 1420 1330 1230 1110 1010 923 835 757 692 631 572 520

3910 3580 3260 2960 2690 2450 2290 2140 1990 1840 1670 1520 1380 1250 1140 1040 946 858 780

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.923Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 24

5–24

DESIGN OF TENSION MEMBERS

Table 5-3 (continued)

Available Strength in Axial Tension WT7-WT6

Fy = 50 ksi Fu = 65 ksi

WT-Shapes Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

WT7×66 ×60 ×54.5 ×49.5 ×45

19.4 17.7 16.0 14.6 13.2

14.6 13.3 12.0 11.0 9.90

581 530 479 437 395

873 797 720 657 594

475 432 390 358 322

712 648 585 536 483

WT7×41 ×37 ×34 ×30.5

12.0 10.9 10.0 8.96

9.00 8.18 7.50 6.72

359 326 299 268

540 491 450 403

293 266 244 218

439 399 366 328

WT7×26.5 ×24 ×21.5

7.80 7.07 6.31

5.85 5.30 4.73

234 212 189

351 318 284

190 172 154

285 258 231

WT7×19 ×17 ×15

5.58 5.00 4.42

4.19 3.75 3.32

167 150 132

251 225 199

136 122 108

204 183 162

WT7×13 ×11

3.85 3.25

2.89 2.44

115 97.3

173 146

49.5 44.7 41.0 37.1 33.8 30.9 28.0 25.0 22.4 20.0 17.6 15.6 14.1 12.8 11.6 10.6 9.54

37.1 33.5 30.8 27.8 25.4 23.2 21.0 18.8 16.8 15.0 13.2 11.7 10.6 9.60 8.70 7.95 7.16

Shape

WT6×168h ×152.5h ×139.5h ×126h ×115h ×105 ×95 ×85 ×76 ×68 ×60 ×53 ×48 ×43.5 ×39.5 ×36 ×32.5 Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

1480 1340 1230 1110 1010 925 838 749 671 599 527 467 422 383 347 317 286

2230 2010 1850 1670 1520 1390 1260 1130 1010 900 792 702 635 576 522 477 429

h

93.9 79.3 1210 1090 1000 904 826 754 683 611 546 488 429 380 345 312 283 258 233

141 119 1810 1630 1500 1360 1240 1130 1020 917 819 731 644 570 517 468 424 388 349

Flange thickness is greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.923Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 25

5–25

STEEL TENSION MEMBER SELECTION TABLES

Table 5-3 (continued)

Available Strength in Axial Tension

Fy = 50 ksi Fu = 65 ksi

WT6-WT5

WT-Shapes

Shape

Gross Area, Ag

Ae = 0.75Ag

in.

2

Yielding kips

Rupture kips

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.

ASD

LRFD

ASD

LRFD

2

WT6×29 ×26.5

8.52 7.78

6.39 5.84

255 233

383 350

208 190

312 285

WT6×25 ×22.5 ×20

7.30 6.56 5.84

5.48 4.92 4.38

219 196 175

329 295 263

178 160 142

267 240 214

WT6×17.5 ×15 ×13

5.17 4.40 3.82

3.88 3.30 2.87

155 132 114

233 198 172

126 107 93.3

189 161 140

WT6×11 ×9.5 ×8 ×7

3.24 2.79 2.36 2.08

2.43 2.09 1.77 1.56

WT5×56 ×50 ×44 ×38.5 ×34 ×30 ×27 ×24.5

16.5 14.7 13.0 11.3 10.0 8.84 7.90 7.21

12.4 11.0 9.75 8.48 7.50 6.63 5.93 5.41

494 440 389 338 299 265 237 216

743 662 585 509 450 398 356 324

403 358 317 276 244 215 193 176

605 536 475 413 366 323 289 264

WT5×22.5 ×19.5 ×16.5

6.63 5.73 4.85

4.97 4.30 3.64

199 172 145

298 258 218

162 140 118

242 210 177

WT5×15 ×13 ×11

4.42 3.81 3.24

3.32 2.86 2.43

132 114 97.0

199 171 146

108 93.0 79.0

162 139 118

WT5×9.5 ×8.5 ×7.5 ×6

2.81 2.50 2.21 1.77

2.11 1.88 1.66 1.33

84.1 74.9 66.2 53.0

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

97.0 83.5 70.7 62.3

146 126 106 93.6

126 113 99.5 79.7

79.0 67.9 57.5 50.7

68.6 61.1 54.0 43.2

118 102 86.3 76.1

103 91.7 80.9 64.8

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.923Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 26

5–26

DESIGN OF TENSION MEMBERS

Table 5-3 (continued)

Available Strength in Axial Tension WT4

Fy = 50 ksi Fu = 65 ksi

WT-Shapes Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

WT4×33.5 ×29 ×24 ×20 ×17.5 ×15.5

9.84 8.54 7.05 5.87 5.14 4.56

7.38 6.41 5.29 4.40 3.86 3.42

295 256 211 176 154 137

443 384 317 264 231 205

240 208 172 143 125 111

360 312 258 215 188 167

WT4×14 ×12

4.12 3.54

3.09 2.66

123 106

185 159

100 86.5

151 130

WT4×10.5 ×9

3.08 2.63

2.31 1.97

92.2 78.7

139 118

75.1 64.0

113 96.0

WT4×7.5 ×6.5 ×5

2.22 1.92 1.48

1.67 1.44 1.11

66.5 57.5 44.3

54.3 46.8 36.1

81.4 70.2 54.1

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

99.9 86.4 66.6

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.923Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 27

5–27

STEEL TENSION MEMBER SELECTION TABLES

Table 5-4

Available Strength in Axial Tension

Fy = 46 ksi Fu = 58 ksi

Rectangular HSS

HSS20-HSS16

Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

HSS20×12×5/8 ×1/2 ×3/8 ×5/16

35.0 28.3 21.5 18.1

26.3 21.2 16.1 13.6

964 780 592 499

1450 1170 890 749

763 615 467 394

1140 922 700 592

HSS20×8×5/8 ×1/2 ×3/8 ×5/16

30.3 24.6 18.7 15.7

22.7 18.5 14.0 11.8

835 678 515 432

1250 1020 774 650

658 537 406 342

987 805 609 513

HSS20×4×1/2 ×3/8 ×5/16 ×1/4

20.9 16.0 13.4 10.8

15.7 12.0 10.1 8.10

576 441 369 297

865 662 555 447

455 348 293 235

683 522 439 352

HSS18×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4

25.7 20.9 16.0 13.4 10.8

19.3 15.7 12.0 10.1 8.10

708 576 441 369 297

1060 865 662 555 447

560 455 348 293 235

840 683 522 439 352

HSS16×12×5/8 ×1/2 ×3/8 ×5/16

30.3 24.6 18.7 15.7

22.7 18.5 14.0 11.8

835 678 515 432

1250 1020 774 650

658 537 406 342

987 805 609 513

HSS16×8×5/8 ×1/2 ×3/8 ×1/4

25.7 20.9 16.0 10.8

19.3 15.7 12.0 8.10

708 576 441 297

1060 865 662 447

560 455 348 235

840 683 522 352

HSS16×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

21.0 17.2 13.2 11.1 8.96 6.76

15.8 12.9 9.90 8.32 6.72 5.07

578 474 364 306 247 186

869 712 546 460 371 280

458 374 287 241 195 147

687 561 431 362 292 221

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Pn /Ωt ASD

φt Pn LRFD

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.952Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 28

5–28

DESIGN OF TENSION MEMBERS

Table 5-4 (continued)

Available Strength in Axial Tension HSS14-HSS12

Fy = 46 ksi Fu = 58 ksi

Rectangular HSS Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

HSS14×10×5/8 ×1/2 ×3/8 ×5/16 ×1/4

25.7 20.9 16.0 13.4 10.8

19.3 15.7 12.0 10.1 8.10

708 576 441 369 297

1060 865 662 555 447

560 455 348 293 235

840 683 522 439 352

HSS14×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

21.0 17.2 13.2 11.1 8.96 6.76

15.8 12.9 9.90 8.32 6.72 5.07

578 474 364 306 247 186

869 712 546 460 371 280

458 374 287 241 195 147

687 561 431 362 292 221

HSS14×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

18.7 15.3 11.8 9.92 8.03 6.06

14.0 11.5 8.85 7.44 6.02 4.55

515 421 325 273 221 167

774 633 489 411 332 251

406 334 257 216 175 132

609 500 385 324 262 198

HSS12×10×1/2 ×3/8 ×5/16 ×1/4

19.0 14.6 12.2 9.90

14.3 10.9 9.15 7.43

523 402 336 273

787 604 505 410

415 316 265 215

622 474 398 323

HSS12×8×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

21.0 17.2 13.2 11.1 8.96 6.76

15.8 12.9 9.90 8.32 6.72 5.07

578 474 364 306 247 186

869 712 546 460 371 280

458 374 287 241 195 147

687 561 431 362 292 221

HSS12×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

18.7 15.3 11.8 9.92 8.03 6.06

14.0 11.5 8.85 7.44 6.02 4.55

515 421 325 273 221 167

774 633 489 411 332 251

406 334 257 216 175 132

609 500 385 324 262 198

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.952Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 29

5–29

STEEL TENSION MEMBER SELECTION TABLES

Table 5-4 (continued)

Available Strength in Axial Tension

Fy = 46 ksi Fu = 58 ksi

Rectangular HSS

HSS12-HSS10

Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

HSS12×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

16.4 13.5 10.4 8.76 7.10 5.37

12.3 10.1 7.80 6.57 5.33 4.03

452 372 286 241 196 148

679 559 431 363 294 222

357 293 226 191 155 117

535 439 339 286 232 175

HSS12×31/2×3/8 ×5/16

10.0 8.46

7.50 6.34

275 233

414 350

218 184

326 276

HSS12×3×5/16 ×1/4 ×3/16

8.17 6.63 5.02

6.13 4.97 3.76

225 183 138

338 274 208

178 144 109

267 216 164

HSS12×2×5/16 ×1/4 ×3/16

7.59 6.17 4.67

5.69 4.63 3.50

209 170 129

314 255 193

165 134 102

248 201 152

HSS10×8×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

18.7 15.3 11.8 9.92 8.03 6.06

14.0 11.5 8.85 7.44 6.02 4.55

515 421 325 273 221 167

774 633 489 411 332 251

406 334 257 216 175 132

609 500 385 324 262 198

HSS10×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

16.4 13.5 10.4 8.76 7.10 5.37

12.3 10.1 7.80 6.57 5.33 4.03

452 372 286 241 196 148

679 559 431 363 294 222

357 293 226 191 155 117

535 439 339 286 232 175

HSS10×5×3/8 ×5/16 ×1/4 ×3/16

9.67 8.17 6.63 5.02

7.25 6.13 4.97 3.76

266 225 183 138

400 338 274 208

210 178 144 109

315 267 216 164

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.952Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC.

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 30

5–30

DESIGN OF TENSION MEMBERS

Table 5-4 (continued)

Available Strength in Axial Tension HSS10-HSS9

Fy = 46 ksi Fu = 58 ksi

Rectangular HSS Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

HSS10×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

14.0 11.6 8.97 7.59 6.17 4.67 3.16

10.5 8.70 6.73 5.69 4.63 3.50 2.37

386 320 247 209 170 129 87.0

580 480 371 314 255 193 131

305 252 195 165 134 102 68.7

457 378 293 248 201 152 103

HSS10×31/2×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

11.1 8.62 7.30 5.93 4.50 3.04

8.32 6.47 5.48 4.45 3.38 2.28

306 237 201 163 124 83.7

460 357 302 246 186 126

241 188 159 129 98.0 66.1

362 281 238 194 147 99.2

HSS10×3×3/8 ×5/16 ×1/4 ×3/16 ×1/8

8.27 7.01 5.70 4.32 2.93

6.20 5.26 4.27 3.24 2.20

228 193 157 119 80.7

342 290 236 179 121

180 153 124 94.0 63.8

270 229 186 141 95.7

HSS10×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

7.58 6.43 5.24 3.98 2.70

5.69 4.82 3.93 2.99 2.03

209 177 144 110 74.4

314 266 217 165 112

165 140 114 86.7 58.9

248 210 171 130 88.3

HSS9×7×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

16.4 13.5 10.4 8.76 7.10 5.37

12.3 10.1 7.80 6.57 5.33 4.03

452 372 286 241 196 148

679 559 431 363 294 222

357 293 226 191 155 117

535 439 339 286 232 175

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.952Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 31

5–31

STEEL TENSION MEMBER SELECTION TABLES

Table 5-4 (continued)

Available Strength in Axial Tension

Fy = 46 ksi Fu = 58 ksi

HSS9-HSS8

Rectangular HSS Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

HSS9×5×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

14.0 11.6 8.97 7.59 6.17 4.67

10.5 8.70 6.73 5.69 4.63 3.50

386 320 247 209 170 129

580 480 371 314 255 193

305 252 195 165 134 102

457 378 293 248 201 152

HSS9×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16

9.74 7.58 6.43 5.24 3.98

7.30 5.69 4.82 3.93 2.99

268 209 177 144 110

403 314 266 217 165

212 165 140 114 86.7

318 248 210 171 130

HSS8×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

14.0 11.6 8.97 7.59 6.17 4.67

10.5 8.70 6.73 5.69 4.63 3.50

386 320 247 209 170 129

580 480 371 314 255 193

305 252 195 165 134 102

457 378 293 248 201 152

HSS8×4×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

11.7 9.74 7.58 6.43 5.24 3.98 2.70

8.78 7.30 5.69 4.82 3.93 2.99 2.03

322 268 209 177 144 110 74.4

484 403 314 266 217 165 112

255 212 165 140 114 86.7 58.9

382 318 248 210 171 130 88.3

HSS8×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

8.81 6.88 5.85 4.77 3.63 2.46

6.61 5.16 4.39 3.58 2.72 1.85

243 190 161 131 100 67.8

365 285 242 197 150 102

192 150 127 104 78.9 53.7

288 224 191 156 118 80.5

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.952Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 32

5–32

DESIGN OF TENSION MEMBERS

Table 5-4 (continued)

Available Strength in Axial Tension HSS8-HSS6

Fy = 46 ksi Fu = 58 ksi

Rectangular HSS Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

HSS8×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

6.18 5.26 4.30 3.28 2.23

4.63 3.94 3.22 2.46 1.67

170 145 118 90.3 61.4

256 218 178 136 92.3

134 114 93.4 71.3 48.4

201 171 140 107 72.6

HSS7×5×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

9.74 7.58 6.43 5.24 3.98 2.70

7.30 5.69 4.82 3.93 2.99 2.03

268 209 177 144 110 74.4

403 314 266 217 165 112

212 165 140 114 86.7 58.9

318 248 210 171 130 88.3

HSS7×4×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

8.81 6.88 5.85 4.77 3.63 2.46

6.61 5.16 4.39 3.58 2.72 1.85

243 190 161 131 100 67.8

365 285 242 197 150 102

192 150 127 104 78.9 53.7

288 224 191 156 118 80.5

HSS7×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

7.88 6.18 5.26 4.30 3.28 2.23

5.91 4.63 3.94 3.22 2.46 1.67

217 170 145 118 90.3 61.4

326 256 218 178 136 92.3

171 134 114 93.4 71.3 48.4

257 201 171 140 107 72.6

HSS7×2×1/4 ×3/16 ×1/8

3.84 2.93 2.00

2.88 2.20 1.50

106 80.7 55.1

159 121 82.8

83.5 63.8 43.5

125 95.7 65.3

HSS6×5×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

8.81 6.88 5.85 4.77 3.63 2.46

6.61 5.16 4.39 3.58 2.72 1.85

243 190 161 131 100 67.8

365 285 242 197 150 102

192 150 127 104 78.9 53.7

288 224 191 156 118 80.5

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.952Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 33

5–33

STEEL TENSION MEMBER SELECTION TABLES

Table 5-4 (continued)

Available Strength in Axial Tension

Fy = 46 ksi Fu = 58 ksi

HSS6-HSS5

Rectangular HSS kips Yielding

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

HSS6×4×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

7.88 6.18 5.26 4.30 3.28 2.23

5.91 4.63 3.94 3.22 2.46 1.67

217 170 145 118 90.3 61.4

326 256 218 178 136 92.3

171 134 114 93.4 71.3 48.4

257 201 171 140 107 72.6

HSS6×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

6.95 5.48 4.68 3.84 2.93 2.00

5.21 4.11 3.51 2.88 2.20 1.50

191 151 129 106 80.7 55.1

288 227 194 159 121 82.8

151 119 102 83.5 63.8 43.5

227 179 153 125 95.7 65.3

HSS6×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

4.78 4.10 3.37 2.58 1.77

3.58 3.08 2.53 1.94 1.33

132 113 92.8 71.1 48.8

198 170 140 107 73.3

104 89.3 73.4 56.3 38.6

156 134 110 84.4 57.9

HSS5×4×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

6.95 5.48 4.68 3.84 2.93 2.00

5.21 4.11 3.51 2.88 2.20 1.50

191 151 129 106 80.7 55.1

288 227 194 159 121 82.8

151 119 102 83.5 63.8 43.5

227 179 153 125 95.7 65.3

HSS5×3×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

6.02 4.78 4.10 3.37 2.58 1.77

4.51 3.58 3.08 2.53 1.94 1.33

166 132 113 92.8 71.1 48.8

249 198 170 140 107 73.3

131 104 89.3 73.4 56.3 38.6

196 156 134 110 84.4 57.9

HSS5×21/2×1/4 ×3/16 ×1/8

3.14 2.41 1.65

2.36 1.81 1.24

86.5 66.4 45.4

130 99.8 68.3

68.4 52.5 36.0

103 78.7 53.9

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.952Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC.

AISC_PART 5:14th Ed.

1/20/11

7:41 AM

Page 34

5–34

DESIGN OF TENSION MEMBERS

Table 5-4 (continued)

Available Strength in Axial Tension HSS5-HSS31/2

Fy = 46 ksi Fu = 58 ksi

Rectangular HSS Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

HSS5×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

4.09 3.52 2.91 2.24 1.54

3.07 2.64 2.18 1.68 1.16

113 97.0 80.2 61.7 42.4

169 146 120 92.7 63.8

89.0 76.6 63.2 48.7 33.6

134 115 94.8 73.1 50.5

HSS4×3×3/8 ×5/16 ×1/4 ×3/16 ×1/8

4.09 3.52 2.91 2.24 1.54

3.07 2.64 2.18 1.68 1.16

113 97.0 80.2 61.7 42.4

169 146 120 92.7 63.8

89.0 76.6 63.2 48.7 33.6

134 115 94.8 73.1 50.5

HSS4×21/2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

3.74 3.23 2.67 2.06 1.42

2.81 2.42 2.00 1.55 1.07

103 89.0 73.5 56.7 39.1

155 134 111 85.3 58.8

81.5 70.2 58.0 45.0 31.0

122 105 87.0 67.4 46.5

HSS4×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

3.39 2.94 2.44 1.89 1.30

2.54 2.21 1.83 1.42 0.975

93.4 81.0 67.2 52.1 35.8

140 122 101 78.2 53.8

73.7 64.1 53.1 41.2 28.3

110 96.1 79.6 61.8 42.4

HSS31/2×21/2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

3.39 2.94 2.44 1.89 1.30

2.54 2.21 1.83 1.42 0.975

93.4 81.0 67.2 52.1 35.8

140 122 101 78.2 53.8

73.7 64.1 53.1 41.2 28.3

110 96.1 79.6 61.8 42.4

HSS31/2×2×1/4 ×3/16 ×1/8

2.21 1.71 1.19

1.66 1.28 0.892

60.9 47.1 32.8

91.5 70.8 49.3

48.1 37.1 25.9

72.2 55.7 38.8

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.952Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC.

AISC_PART 5:14th Ed.

1/20/11

7:42 AM

Page 35

5–35

STEEL TENSION MEMBER SELECTION TABLES

Table 5-4 (continued)

Available Strength in Axial Tension

Fy = 46 ksi Fu = 58 ksi

HSS3-HSS2

Rectangular HSS Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

in.2

in.2

HSS3×21/2×5/16 ×1/4 ×3/16 ×1/8

2.64 2.21 1.71 1.19

1.98 1.66 1.28 0.892

72.7 60.9 47.1 32.8

109 91.5 70.8 49.3

57.4 48.1 37.1 25.9

86.1 72.2 55.7 38.8

HSS3×2×5/16 ×1/4 ×3/16 ×1/8

2.35 1.97 1.54 1.07

1.76 1.48 1.16 0.803

64.7 54.3 42.4 29.5

97.3 81.6 63.8 44.3

51.0 42.9 33.6 23.3

76.6 64.4 50.5 34.9

HSS3×11/2×1/4 ×3/16 ×1/8

1.74 1.37 0.956

1.30 1.03 0.717

47.9 37.7 26.3

72.0 56.7 39.6

37.7 29.9 20.8

56.6 44.8 31.2

HSS3×1×3/16 ×1/8

1.19 0.840

0.892 0.630

32.8 23.1

49.3 34.8

25.9 18.3

38.8 27.4

HSS21/2×2×1/4 ×3/16 ×1/8

1.74 1.37 0.956

1.30 1.03 0.717

47.9 37.7 26.3

72.0 56.7 39.6

37.7 29.9 20.8

56.6 44.8 31.2

HSS21/2×11/2×1/4 ×3/16 ×1/8

1.51 1.19 0.840

1.13 0.892 0.630

41.6 32.8 23.1

62.5 49.3 34.8

32.8 25.9 18.3

49.2 38.8 27.4

HSS21/2×1×3/16 ×1/8

1.02 0.724

0.765 0.543

28.1 19.9

42.2 30.0

22.2 15.7

33.3 23.6

HSS21/4×2×3/16 ×1/8

1.28 0.898

0.960 0.674

35.3 24.7

53.0 37.2

27.8 19.5

41.8 29.3

HSS2×11/2×3/16 ×1/8

1.02 0.724

0.765 0.543

28.1 19.9

42.2 30.0

22.2 15.7

33.3 23.6

HSS2×1×3/16 ×1/8

0.845 0.608

0.634 0.456

23.3 16.7

35.0 25.2

18.4 13.2

27.6 19.8

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

ASD

LRFD

ASD

LRFD

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.952Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:42 AM

Page 36

5–36

DESIGN OF TENSION MEMBERS

Table 5-5

Available Strength in Axial Tension HSS16-HSS8

Fy = 46 ksi Fu = 58 ksi

Square HSS Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

in.2

in.2

HSS16×16×5/8 ×1/2 ×3/8 ×5/16

35.0 28.3 21.5 18.1

26.3 21.2 16.1 13.6

964 780 592 499

1450 1170 890 749

763 615 467 394

1140 922 700 592

HSS14×14×5/8 ×1/2 ×3/8 ×5/16

30.3 24.6 18.7 15.7

22.7 18.5 14.0 11.8

835 678 515 432

1250 1020 774 650

658 537 406 342

987 805 609 513

HSS12×12×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

25.7 20.9 16.0 13.4 10.8 8.15

19.3 15.7 12.0 10.1 8.10 6.11

708 576 441 369 297 224

1060 865 662 555 447 337

560 455 348 293 235 177

840 683 522 439 352 266

HSS10×10×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16

21.0 17.2 13.2 11.1 8.96 6.76

15.8 12.9 9.90 8.32 6.72 5.07

578 474 364 306 247 186

869 712 546 460 371 280

458 374 287 241 195 147

687 561 431 362 292 221

HSS9×9×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

18.7 15.3 11.8 9.92 8.03 6.06 4.09

14.0 11.5 8.85 7.44 6.02 4.55 3.07

515 421 325 273 221 167 113

774 633 489 411 332 251 169

406 334 257 216 175 132 89.0

609 500 385 324 262 198 134

HSS8×8×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

16.4 13.5 10.4 8.76 7.10 5.37 3.62

12.3 10.1 7.80 6.57 5.33 4.03 2.71

452 372 286 241 196 148 99.7

679 559 431 363 294 222 150

357 293 226 191 155 117 78.6

535 439 339 286 232 175 118

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

ASD

LRFD

ASD

LRFD

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.952Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:42 AM

Page 37

5–37

STEEL TENSION MEMBER SELECTION TABLES

Table 5-5 (continued)

Available Strength in Axial Tension

Fy = 46 ksi Fu = 58 ksi

HSS7-HSS41/2

Square HSS Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

HSS7×7×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

14.0 11.6 8.97 7.59 6.17 4.67 3.16

10.5 8.70 6.73 5.69 4.63 3.50 2.37

386 320 247 209 170 129 87.0

580 480 371 314 255 193 131

305 252 195 165 134 102 68.7

457 378 293 248 201 152 103

HSS6×6×5/8 ×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

11.7 9.74 7.58 6.43 5.24 3.98 2.70

8.78 7.30 5.69 4.82 3.93 2.99 2.03

322 268 209 177 144 110 74.4

484 403 314 266 217 165 112

255 212 165 140 114 86.7 58.9

382 318 248 210 171 130 88.3

HSS51/2×51/2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

6.88 5.85 4.77 3.63 2.46

5.16 4.39 3.58 2.72 1.85

190 161 131 100 67.8

285 242 197 150 102

150 127 104 78.9 53.7

224 191 156 118 80.5

HSS5×5×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

7.88 6.18 5.26 4.30 3.28 2.23

5.91 4.63 3.94 3.22 2.46 1.67

217 170 145 118 90.3 61.4

326 256 218 178 136 92.3

171 134 114 93.4 71.3 48.4

257 201 171 140 107 72.6

HSS41/2×41/2×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

6.95 5.48 4.68 3.84 2.93 2.00

5.21 4.11 3.51 2.88 2.20 1.50

191 151 129 106 80.7 55.1

288 227 194 159 121 82.8

151 119 102 83.5 63.8 43.5

227 179 153 125 95.7 65.3

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.952Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:42 AM

Page 38

5–38

DESIGN OF TENSION MEMBERS

Table 5-5 (continued)

Available Strength in Axial Tension HSS4-HSS2

Fy = 46 ksi Fu = 58 ksi

Square HSS Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

HSS4×4×1/2 ×3/8 ×5/16 ×1/4 ×3/16 ×1/8

6.02 4.78 4.10 3.37 2.58 1.77

4.51 3.58 3.08 2.53 1.94 1.33

166 132 113 92.8 71.1 48.8

249 198 170 140 107 73.3

131 104 89.3 73.4 56.3 38.6

196 156 134 110 84.4 57.9

HSS31/2×31/2×3/8 ×5/16 ×1/4 ×3/16 ×1/8

4.09 3.52 2.91 2.24 1.54

3.07 2.64 2.18 1.68 1.16

113 97.0 80.2 61.7 42.4

169 146 120 92.7 63.8

89.0 76.6 63.2 48.7 33.6

134 115 94.8 73.1 50.5

HSS3×3×3/8 ×5/16 ×1/4 ×3/16 ×1/8

3.39 2.94 2.44 1.89 1.30

2.54 2.21 1.83 1.42 0.975

93.4 81.0 67.2 52.1 35.8

140 122 101 78.2 53.8

73.7 64.1 53.1 41.2 28.3

110 96.1 79.6 61.8 42.4

HSS21/2×21/2×5/16 ×1/4 ×3/16 ×1/8

2.35 1.97 1.54 1.07

1.76 1.48 1.16 0.803

64.7 54.3 42.4 29.5

97.3 81.6 63.8 44.3

51.0 42.9 33.6 23.3

76.6 64.4 50.5 34.9

HSS21/4×21/4×1/4 ×3/16 ×1/8

1.74 1.37 0.956

1.30 1.03 0.717

47.9 37.7 26.3

72.0 56.7 39.6

37.7 29.9 20.8

56.6 44.8 31.2

HSS2×2×1/4 ×3/16 ×1/8

1.51 1.19 0.840

1.13 0.892 0.630

41.6 32.8 23.1

62.5 49.3 34.8

32.8 25.9 18.3

49.2 38.8 27.4

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.952Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:42 AM

Page 39

5–39

STEEL TENSION MEMBER SELECTION TABLES

Table 5-6

Available Strength in Axial Tension

Fy = 42 ksi Fu = 58 ksi

Round HSS Gross Area, Ag

Ae = 0.75Ag

in.2

in.2

HSS20×0.375

21.5

16.1

HSS18×0.500 ×0.375

25.6 19.4

HSS16×0.625 ×0.500 ×0.438 ×0.375 ×0.312 ×0.250 HSS14×0.625 ×0.500 ×0.375 ×0.312 ×0.250

Shape

HSS20-HSS10

Yielding kips

Rupture kips

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

ASD

LRFD

ASD

LRFD

541

813

467

700

19.2 14.6

644 488

968 733

557 423

835 635

28.1 22.7 19.9 17.2 14.4 11.5

21.1 17.0 14.9 12.9 10.8 8.63

707 571 500 433 362 289

1060 858 752 650 544 435

612 493 432 374 313 250

918 740 648 561 470 375

24.5 19.8 15.0 12.5 10.1

18.4 14.9 11.3 9.38 7.58

616 498 377 314 254

926 748 567 473 382

534 432 328 272 220

800 648 492 408 330

HSS12.750×0.500 ×0.375 ×0.250

17.9 13.6 9.16

13.4 10.2 6.87

450 342 230

677 514 346

389 296 199

583 444 299

HSS10.750×0.500 ×0.375 ×0.250

15.0 11.4 7.70

11.3 8.55 5.78

377 287 194

567 431 291

328 248 168

492 372 251

HSS10×0.625 ×0.500 ×0.375 ×0.312 ×0.250 ×0.188

17.2 13.9 10.6 8.88 7.15 5.37

12.9 10.4 7.95 6.66 5.36 4.03

433 350 267 223 180 135

650 525 401 336 270 203

374 302 231 193 155 117

561 452 346 290 233 175

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.869Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:42 AM

Page 40

5–40

DESIGN OF TENSION MEMBERS

Table 5-6 (continued)

Available Strength in Axial Tension HSS9.625HSS6.875

Round HSS Gross Area, Ag

Ae = 0.75Ag

in.2

in.2

HSS9.625×0.500 ×0.375 ×0.312 ×0.250 ×0.188

13.4 10.2 8.53 6.87 5.17

10.1 7.65 6.40 5.15 3.88

HSS8.625×0.625 ×0.500 ×0.375 ×0.322 ×0.250 ×0.188

14.7 11.9 9.07 7.85 6.14 4.62

HSS7.625×0.375 ×0.328

Shape

Fy = 42 ksi Fu = 58 ksi

Yielding kips

Rupture kips

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

ASD

LRFD

ASD

LRFD

337 257 215 173 130

507 386 322 260 195

293 222 186 149 113

439 333 278 224 169

11.0 8.92 6.80 5.89 4.60 3.47

370 299 228 197 154 116

556 450 343 297 232 175

319 259 197 171 133 101

479 388 296 256 200 151

7.98 7.01

5.99 5.26

201 176

302 265

174 153

261 229

HSS7.500×0.500 ×0.375 ×0.312 ×0.250 ×0.188

10.3 7.84 6.59 5.32 4.00

7.73 5.88 4.94 3.99 3.00

259 197 166 134 101

389 296 249 201 151

224 171 143 116 87.0

336 256 215 174 131

HSS7×0.500 ×0.375 ×0.312 ×0.250 ×0.188 ×0.125

9.55 7.29 6.13 4.95 3.73 2.51

7.16 5.47 4.60 3.71 2.80 1.88

240 183 154 124 93.8 63.1

361 276 232 187 141 94.9

208 159 133 108 81.2 54.5

311 238 200 161 122 81.8

HSS6.875×0.500 ×0.375 ×0.312 ×0.250 ×0.188

9.36 7.16 6.02 4.86 3.66

7.02 5.37 4.51 3.64 2.75

235 180 151 122 92.0

354 271 228 184 138

204 156 131 106 79.8

305 234 196 158 120

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.869Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:42 AM

Page 41

5–41

STEEL TENSION MEMBER SELECTION TABLES

Table 5-6 (continued)

Available Strength in Axial Tension

Fy = 42 ksi Fu = 58 ksi

HSS6.625HSS5

Round HSS Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

HSS6.625×0.500 ×0.432 ×0.375 ×0.312 ×0.280 ×0.250 ×0.188 ×0.125

9.00 7.86 6.88 5.79 5.20 4.68 3.53 2.37

6.75 5.90 5.16 4.34 3.90 3.51 2.65 1.78

226 198 173 146 131 118 88.8 59.6

340 297 260 219 197 177 133 89.6

196 171 150 126 113 102 76.9 51.6

294 257 224 189 170 153 115 77.4

HSS6.000×0.500 ×0.375 ×0.312 ×0.280 ×0.250 ×0.188 ×0.125

8.09 6.20 5.22 4.69 4.22 3.18 2.14

6.07 4.65 3.92 3.52 3.17 2.39 1.61

203 156 131 118 106 80.0 53.8

306 234 197 177 160 120 80.9

176 135 114 102 91.9 69.3 46.7

264 202 171 153 138 104 70.0

HSS5.563×0.500 ×0.375 ×0.258 ×0.188 ×0.134

7.45 5.72 4.01 2.95 2.12

5.59 4.29 3.01 2.21 1.59

187 144 101 74.2 53.3

282 216 152 112 80.1

162 124 87.3 64.1 46.1

243 187 131 96.1 69.2

HSS5.500×0.500 ×0.375 ×0.258

7.36 5.65 3.97

5.52 4.24 2.98

185 142 99.8

278 214 150

160 123 86.4

240 184 130

HSS5×0.500 ×0.375 ×0.312 ×0.258 ×0.250 ×0.188 ×0.125

6.62 5.10 4.30 3.59 3.49 2.64 1.78

4.97 3.82 3.22 2.69 2.62 1.98 1.34

166 128 108 90.3 87.8 66.4 44.8

250 193 163 136 132 99.8 67.3

144 111 93.4 78.0 76.0 57.4 38.9

216 166 140 117 114 86.1 58.3

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.869Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:42 AM

Page 42

5–42

DESIGN OF TENSION MEMBERS

Table 5-6 (continued)

Available Strength in Axial Tension HSS4.500HSS2.500

Fy = 42 ksi Fu = 58 ksi

Round HSS Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

HSS4.500×0.375 ×0.337 ×0.237 ×0.188 ×0.125

4.55 4.12 2.96 2.36 1.60

3.41 3.09 2.22 1.77 1.20

114 104 74.4 59.4 40.2

172 156 112 89.2 60.5

98.9 89.6 64.4 51.3 34.8

148 134 96.6 77.0 52.2

HSS4×0.313 ×0.250 ×0.237 ×0.226 ×0.220 ×0.188 ×0.125

3.39 2.76 2.61 2.50 2.44 2.09 1.42

2.54 2.07 1.96 1.88 1.83 1.57 1.07

85.3 69.4 65.6 62.9 61.4 52.6 35.7

128 104 98.7 94.5 92.2 79.0 53.7

73.7 60.0 56.8 54.5 53.1 45.5 31.0

110 90.0 85.3 81.8 79.6 68.3 46.5

HSS3.500×0.313 ×0.300 ×0.250 ×0.216 ×0.203 ×0.188 ×0.125

2.93 2.82 2.39 2.08 1.97 1.82 1.23

2.20 2.11 1.79 1.56 1.48 1.36 0.923

73.7 70.9 60.1 52.3 49.5 45.8 30.9

111 107 90.3 78.6 74.5 68.8 46.5

63.8 61.2 51.9 45.2 42.9 39.4 26.8

95.7 91.8 77.9 67.9 64.4 59.2 40.2

HSS3×0.250 ×0.216 ×0.203 ×0.188 ×0.152 ×0.134 ×0.125

2.03 1.77 1.67 1.54 1.27 1.12 1.05

1.52 1.33 1.25 1.16 0.953 0.840 0.788

51.1 44.5 42.0 38.7 31.9 28.2 26.4

76.7 66.9 63.1 58.2 48.0 42.3 39.7

44.1 38.6 36.3 33.6 27.6 24.4 22.9

66.1 57.9 54.4 50.5 41.5 36.5 34.3

HSS2.875×0.250 ×0.203 ×0.188 ×0.125

1.93 1.59 1.48 1.01

1.45 1.19 1.11 0.758

48.5 40.0 37.2 25.4

73.0 60.1 55.9 38.2

42.1 34.5 32.2 22.0

63.1 51.8 48.3 33.0

HSS2.500×0.250 ×0.188 ×0.125

1.66 1.27 0.869

1.25 0.953 0.652

41.7 31.9 21.9

62.7 48.0 32.8

36.3 27.6 18.9

54.4 41.5 28.4

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.869Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:42 AM

Page 43

5–43

STEEL TENSION MEMBER SELECTION TABLES

Table 5-6 (continued)

Available Strength in Axial Tension

Fy = 42 ksi Fu = 58 ksi

HSS2.375HSS1.660

Round HSS Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

HSS2.375×0.250 ×0.218 ×0.188 ×0.154 ×0.125

1.57 1.39 1.20 1.00 0.823

1.18 1.04 0.900 0.750 0.617

39.5 35.0 30.2 25.1 20.7

59.3 52.5 45.4 37.8 31.1

34.2 30.2 26.1 21.8 17.9

51.3 45.2 39.1 32.6 26.8

HSS1.900×0.188 ×0.145 ×0.120

0.943 0.749 0.624

0.707 0.562 0.468

23.7 18.8 15.7

35.6 28.3 23.6

20.5 16.3 13.6

30.8 24.4 20.4

HSS1.660×0.140

0.625

0.469

15.7

23.6

13.6

20.4

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.869Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:42 AM

Page 44

5–44

DESIGN OF TENSION MEMBERS

Table 5-7

Available Strength in Axial Tension PIPE12PIPE11/2

Fy = 35 ksi Fu = 60 ksi

Pipe Gross Area, Ag

Ae = 0.75Ag

in.2

in.2

Pipe 12 X-Strong Std

17.5 13.7

13.1 10.3

Pipe 10 X-Strong Std

15.1 11.5

Pipe 8 XX-Strong X-Strong Std

Shape

Yielding kips

Rupture kips

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

ASD

LRFD

ASD

LRFD

367 287

551 432

393 309

590 464

11.3 8.63

316 241

476 362

339 259

509 388

20.0 11.9 7.85

15.0 8.93 5.89

419 249 165

630 375 247

450 268 177

675 402 265

Pipe 6 XX-Strong X-Strong Std

14.7 7.83 5.20

11.0 5.87 3.90

308 164 109

463 247 164

330 176 117

495 264 176

Pipe 5 XX-Strong X-Strong Std

10.7 5.73 4.01

8.03 4.30 3.01

224 120 84.0

337 180 126

241 129 90.3

361 194 135

Pipe 4 XX-Strong X-Strong Std

7.66 4.14 2.96

5.75 3.11 2.22

161 86.8 62.0

241 130 93.2

173 93.3 66.6

259 140 99.9

Pipe 31/2 X-Strong Std

3.43 2.50

2.57 1.88

71.9 52.4

108 78.8

77.1 56.4

116 84.6

Pipe 3 XX-Strong X-Strong Std

5.17 2.83 2.07

3.88 2.12 1.55

108 59.3 43.4

163 89.1 65.2

116 63.6 46.5

175 95.4 69.8

Pipe 21/2 XX-Strong X-Strong Std

3.83 2.10 1.61

2.87 1.58 1.21

80.3 44.0 33.7

121 66.2 50.7

86.1 47.4 36.3

129 71.1 54.5

Pipe 2 XX-Strong X-Strong Std

2.51 1.40 1.02

1.88 1.05 0.765

52.6 29.3 21.4

79.1 44.1 32.1

56.4 31.5 23.0

84.6 47.3 34.4

Pipe 11/2 X-Strong Std

1.00 0.749

0.750 0.562

21.0 15.7

31.5 23.6

22.5 16.9

33.8 25.3

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.700Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:42 AM

Page 45

5–45

STEEL TENSION MEMBER SELECTION TABLES

Table 5-7 (continued)

Available Strength in Axial Tension

Fy = 35 ksi Fu = 60 ksi

PIPE11/4 PIPE1/2

Pipe

Shape

Gross Area, Ag

Ae = 0.75Ag

in.

2

Yielding kips

Rupture kips

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.

ASD

LRFD

ASD

LRFD

2

Pipe 11/4 X-Strong Std

0.837 0.625

0.628 0.469

17.5 13.1

26.4 19.7

18.8 14.1

28.3 21.1

Pipe 1 X-Strong Std

0.602 0.469

0.452 0.352

12.6 9.83

19.0 14.8

13.6 10.6

20.3 15.8

Pipe 3/4 X-Strong Std

0.407 0.312

0.305 0.234

8.53 6.54

12.8 9.83

9.15 7.02

13.7 10.5

Pipe 1/2 X-Strong Std

0.303 0.234

0.227 0.176

6.35 4.90

9.54 7.37

6.81 5.28

10.2 7.92

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.700Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 5:14th Ed.

1/20/11

7:42 AM

Page 46

5–46

DESIGN OF TENSION MEMBERS

Table 5-8

Available Strength in Axial Tension

2L8-2L6

Fy = 36 ksi Fu = 58 ksi

Double Angles Yielding kips

Gross Area, Ag

Ae = 0.75Ag

in.2

in.2

2L8×8×11/8 ×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2

33.6 30.2 26.6 23.0 19.4 17.5 15.7

25.2 22.7 20.0 17.3 14.6 13.1 11.8

724 651 573 496 418 377 338

2L8×6×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16

26.2 23.0 20.0 16.8 15.2 13.6 12.0

19.7 17.3 15.0 12.6 11.4 10.2 9.00

2L8×4×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16

22.2 19.6 17.0 14.3 13.0 11.6 10.2

2L7×4×3/4 ×5/8 ×1/2 ×7/16 ×3/8 2L6×6×1 ×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16 ×3/8 ×5/16

Shape

Rupture kips

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

ASD

LRFD

ASD

LRFD

1090 978 862 745 629 567 509

731 658 580 502 423 380 342

1100 987 870 753 635 570 513

565 496 431 362 328 293 259

849 745 648 544 492 441 389

571 502 435 365 331 296 261

857 753 653 548 496 444 392

16.7 14.7 12.8 10.7 9.75 8.70 7.65

479 423 366 308 280 250 220

719 635 551 463 421 376 330

484 426 371 310 283 252 222

726 639 557 465 424 378 333

15.5 13.0 10.5 9.26 8.00

11.6 9.75 7.88 6.95 6.00

334 280 226 200 172

502 421 340 300 259

336 283 229 202 174

505 424 343 302 261

22.0 19.5 16.9 14.3 12.9 11.5 10.2 8.76 7.34

16.5 14.6 12.7 10.7 9.68 8.63 7.65 6.57 5.51

474 420 364 308 278 248 220 189 158

713 632 548 463 418 373 330 284 238

479 423 368 310 281 250 222 191 160

718 635 552 465 421 375 333 286 240

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.745Ag .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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STEEL TENSION MEMBER SELECTION TABLES

Table 5-8 (continued)

Available Strength in Axial Tension

Fy = 36 ksi Fu = 58 ksi

2L6-2L5

Double Angles Gross Area, Ag

Ae = 0.75Ag

in.2

in.2

2L6×4×7/8 ×3/4 ×5/8 ×9/16 ×1/2 ×7/16 ×3/8 ×5/16

16.0 13.9 11.7 10.6 9.50 8.36 7.22 6.06

2L6×31/2×1/2 ×3/8 ×5/16

Shape

Yielding kips

Rupture kips

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

ASD

LRFD

ASD

LRFD

12.0 10.4 8.78 7.95 7.13 6.27 5.42 4.55

345 300 252 229 205 180 156 131

518 450 379 343 308 271 234 196

348 302 255 231 207 182 157 132

522 452 382 346 310 273 236 198

9.00 6.88 5.78

6.75 5.16 4.34

194 148 125

292 223 187

196 150 126

294 224 189

2L5×5×7/8 ×3/4 ×5/8 ×1/2 ×7/16 ×3/8 ×5/16

16.0 14.0 11.8 9.58 8.44 7.30 6.14

12.0 10.5 8.85 7.19 6.33 5.48 4.61

345 302 254 207 182 157 132

518 454 382 310 273 237 199

348 305 257 209 184 159 134

522 457 385 313 275 238 201

2L5×31/2×3/4 ×5/8 ×1/2 ×3/8 ×5/16 ×1/4

11.7 9.86 8.00 6.10 5.12 4.14

8.78 7.40 6.00 4.58 3.84 3.11

252 213 172 131 110 89.2

379 319 259 198 166 134

255 215 174 133 111 90.2

382 322 261 199 167 135

2L5×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4

7.50 6.62 5.72 4.82 3.88

5.63 4.97 4.29 3.62 2.91

162 143 123 104 83.6

243 214 185 156 126

163 144 124 105 84.4

245 216 187 157 127

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.745Ag .

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DESIGN OF TENSION MEMBERS

Table 5-8 (continued)

Available Strength in Axial Tension

2L4-2L31/2

Fy = 36 ksi Fu = 58 ksi

Double Angles Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

2L4×4×3/4 ×5/8 ×1/2 ×7/16 ×3/8 ×5/16 ×1/4

10.9 9.22 7.50 6.60 5.72 4.80 3.86

8.18 6.92 5.63 4.95 4.29 3.60 2.90

235 199 162 142 123 103 83.2

353 299 243 214 185 156 125

237 201 163 144 124 104 84.1

356 301 245 215 187 157 126

2L4×31/2×1/2 ×3/8 ×5/16 ×1/4

7.00 5.36 4.50 3.64

5.25 4.02 3.38 2.73

151 116 97.0 78.5

227 174 146 118

152 117 98.0 79.2

228 175 147 119

2L4×3×5/8 ×1/2 ×3/8 ×5/16 ×1/4

7.98 6.50 4.98 4.18 3.38

5.99 4.88 3.74 3.14 2.54

172 140 107 90.1 72.9

259 211 161 135 110

174 142 108 91.1 73.7

261 212 163 137 110

2L31/2×31/2×1/2 ×7/16 ×3/8 ×5/16 ×1/4

6.50 5.78 5.00 4.20 3.40

4.88 4.34 3.75 3.15 2.55

140 125 108 90.5 73.3

211 187 162 136 110

142 126 109 91.4 74.0

212 189 163 137 111

2L31/2×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4

6.04 5.34 4.64 3.90 3.16

4.53 4.01 3.48 2.93 2.37

130 115 100 84.1 68.1

196 173 150 126 102

131 116 101 85.0 68.7

197 174 151 127 103

2L31/2×21/2×1/2 ×3/8 ×5/16 ×1/4

5.54 4.24 3.58 2.90

4.16 3.18 2.69 2.18

119 91.4 77.2 62.5

179 137 116 94.0

121 92.2 78.0 63.2

181 138 117 94.8

Shape

Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.745Ag .

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STEEL TENSION MEMBER SELECTION TABLES

Table 5-8 (continued)

Available Strength in Axial Tension

Fy = 36 ksi Fu = 58 ksi

2L3-2L2

Double Angles Yielding kips

Rupture kips

Gross Area, Ag

Ae = 0.75Ag

Pn /Ωt

φt Pn

Pn /Ωt

φt Pn

in.2

in.2

ASD

LRFD

ASD

LRFD

2L3×3×1/2 ×7/16 ×3/8 ×5/16 ×1/4 ×3/16

5.52 4.86 4.22 3.56 2.88 2.18

4.14 3.65 3.17 2.67 2.16 1.64

119 105 91.0 76.7 62.1 47.0

179 157 137 115 93.3 70.6

120 106 91.9 77.4 62.6 47.6

180 159 138 116 94.0 71.3

2L3×21/2×1/2 ×7/16 ×3/8 ×5/16 ×1/4 ×3/16

5.00 4.44 3.86 3.26 2.64 2.00

3.75 3.33 2.90 2.45 1.98 1.50

108 95.7 83.2 70.3 56.9 43.1

162 144 125 106 85.5 64.8

109 96.6 84.1 71.1 57.4 43.5

163 145 126 107 86.1 65.3

2L3×2×1/2 ×3/8 ×5/16 ×1/4 ×3/16

4.52 3.50 2.96 2.40 1.83

3.39 2.63 2.22 1.80 1.37

97.4 75.4 63.8 51.7 39.4

146 113 95.9 77.8 59.3

98.3 76.3 64.4 52.2 39.7

147 114 96.6 78.3 59.6

2L21/2×21/2×1/2 ×3/8 ×5/16 ×1/4 ×3/16

4.52 3.46 2.92 2.38 1.80

3.39 2.60 2.19 1.79 1.35

97.4 74.6 62.9 51.3 38.8

146 112 94.6 77.1 58.3

98.3 75.4 63.5 51.9 39.2

147 113 95.3 77.9 58.7

2L21/2×2×3/8 ×5/16 ×1/4 ×3/16

3.10 2.64 2.14 1.64

2.33 1.98 1.61 1.23

66.8 56.9 46.1 35.4

100 85.5 69.3 53.1

67.6 57.4 46.7 35.7

101 86.1 70.0 53.5

2L21/2×11/2×1/4 ×3/16

1.89 1.45

1.42 1.09

40.7 31.3

61.2 47.0

41.2 31.6

61.8 47.4

2.74 2.32 1.89 1.44 0.982

2.06 1.74 1.42 1.08 0.737

59.1 50.0 40.7 31.0 21.2

88.8 75.2 61.2 46.7 31.8

59.7 50.5 41.2 31.3 21.4

89.6 75.7 61.8 47.0 32.1

Shape

2L2×2×3/8 ×5/16 ×1/4 ×3/16 ×1/8 Limit State

ASD

LRFD

Yielding

Ωt = 1.67

φ t = 0.90

Rupture

Ωt = 2.00

φ t = 0.75

Note: Tensile rupture on the effective net area will control over tensile yielding on the gross area unless the tension member is selected so that an end connection can be configured with Ae ≥ 0.745Ag .

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DESIGN OF TENSION MEMBERS

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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PART 6

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–2 COMPACT, NONCOMPACT AND SLENDER-ELEMENT SECTIONS . . . . . . . . . . . 6–2 MEMBERS SUBJECT TO COMBINED FLEXURE AND AXIAL COMPRESSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–2 MEMBERS SUBJECT TO COMBINED FLEXURE AND AXIAL TENSION . . . . . . 6–2 MEMBERS SUBJECT TO TORSION AND COMBINED TORSION, FLEXURE, SHEAR AND/OR AXIAL FORCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–2 MEMBERS WITH HOLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–2 COMPOSITE MEMBERS SUBJECT TO COMBINED FLEXURE AND AXIAL COMPRESSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–3 DESIGN TABLE DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–3 PART 6 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–6 STEEL BEAM-COLUMN SELECTION TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–7 Table 6-1. Combined Flexure and Axial Force, W-Shapes . . . . . . . . . . . . . . . . . . . . 6–7

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DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

SCOPE The specification requirements and other design considerations summarized in this Part apply to the design of members subject to combined forces. For the design of members subject to axial tension only, see Part 5. For the design of members subject to axial compression only, see Part 4. For the design of members subject to uniaxial flexure only, see Part 3.

COMPACT, NONCOMPACT AND SLENDER-ELEMENT SECTIONS Based upon the types of load transmitted by the member, the discussions of width-to-thickness ratios in Part 4 for compression members and Part 3 for flexural members apply to the design of members subject to combined forces. The values given in this Part already account for limitations due to width-to-thickness ratios.

MEMBERS SUBJECT TO COMBINED FLEXURE AND AXIAL COMPRESSION The interaction of the combined effects of the required strengths (axial compression and bending moment) must satisfy the unity check as follows: 1. For doubly and singly symmetric members, per AISC Specification Section H1.1 2 For unsymmetric and other members, per AISC Specification Section H2

MEMBERS SUBJECT TO COMBINED FLEXURE AND AXIAL TENSION The interaction of the combined effects of the required strengths (axial tension and bending moment) must satisfy the unity check as follows: 1. For doubly and singly symmetric members, per AISC Specification Section H1.2 2. For unsymmetric and other members, per AISC Specification Section H2

MEMBERS SUBJECT TO TORSION AND COMBINED TORSION, FLEXURE, SHEAR AND/OR AXIAL FORCE The interaction of the combined effects of the required strengths (torsion, bending moment, shear force and/or axial force) must satisfy the requirements of AISC Specification Section H3. See also AISC Design Guide 9, Torsional Analysis of Structural Steel Members.

MEMBERS WITH HOLES AISC Specification Section F13 provides provisions for potential impact of holes in shapes proportioned on the basis of flexural strength of the gross section. Additionally, AISC Specification Section H4 provides provisions applicable to rupture of flanges with holes subject to tension under combined axial force and major axis flexure. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COMPOSITE MEMBERS SUBJECT TO COMBINED FLEXURE AND AXIAL COMPRESSION For the design of composite members subject to combined flexure and axial compression, see AISC Specification Section I5.

DESIGN TABLE DISCUSSION Table 6-1. W-Shapes in Combined Flexure and Axial Force Steel W-shapes with Fy = 50 ksi (ASTM A992) and subject to combined axial force (tension or compression) and flexure may be checked for compliance with the provisions of Section H1.1 and H1.2 of the AISC Specification using values listed in Table 6-1 and the appropriate interaction equations provided in the following sections. Values p, bx, by, ty and tr presented in Table 6-1 are defined as follows. LRFD

ASD

Axial Compression

p =

1 , (kips)–1 φc Pn

p =

Ωc , (kips)–1 Pn

Strong Axis Bending

bx =

8 , (kip-ft)–1 9φbMnx

bx =

8Ωb , (kip-ft)–1 9Mnx

Weak Axis Bending

by =

8 , (kip-ft)–1 9φb Mny

by =

8Ωb , (kip-ft)–1 9Mny

Tension Yielding

ty =

1 , (kips)–1 φt Fy Ag

ty =

Ωt , (kips)–1 Fy Ag

Tension Rupture

tr =

1 , (kips)–1 φt Fu (0.75Ag)

tr =

Ωt , (kips)–1 Fu (0.75Ag)

Combined Flexure and Compression Equations H1-1a and H1-1b of the AISC Specification may be written as follows using the coefficients listed in Table 6-1 and defined above. When pPr ≥ 0.2: pPr + bx Mrx + by Mry ≤ 1.0

(6-1)

/2 pPr + 9/8 (bx Mrx + by Mry ) ≤ 1.0

(6-2)

When pPr < 0.2: 1

The designer may check acceptability of a given shape using the appropriate interaction equation from above. See Aminmansour (2000) for more information on this method, including an alternative approach for selection of a trial shape.

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DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Combined Flexure and Tension Equations H1-1a and H1-1b of the AISC Specification may be written as follows using the coefficients listed in Table 6-1 and defined above. When pPr ≥ 0.2: (ty or tr) Pr + bx Mrx + by Mry ≤ 1.0

(6-3)

/2 (ty or tr) Pr + 9/8 (bx Mrx + by Mry) ≤ 1.0

(6-4)

When pPr < 0.2: 1

The larger value of ty and tr should be used in the above equations. The designer may check acceptability of a given shape using the appropriate interaction equation from above along with variables tr, ty, bx and by. See Aminmansour (2006) for more information on this method. It is noted that the values for tr listed in Table 6-1 are based on the assumption that Ae = 0.75Ag. See Part 5 for more information on this assumption. When Ae > 0.75Ag, the tabulated values for tr are conservative. When Ae < 0.75Ag, tr must be calculated based upon the actual value of Ae.

General Considerations for Use of Values Listed in Table 6-1 The following remarks are offered for consideration in use of the values listed in Table 6-1. 1. Values of p, bx and by already account for section compactness and can be used directly. 2. Tabulated values of bx assume that Cb = 1.0. A procedure for determining bx when Cb > 1.0 follows. 3. Given that the limit state of lateral-torsional buckling does not apply to W-shapes bent about their weak axis, values of by are independent of unbraced length and Cb. 4. Values of bx equally apply to combined flexure and compression as well as combined flexure and tension. 5. Smaller values of variable p for a given KL and smaller values of bx for a given Lb indicate higher strength for the type of load in question. For example, a section with a smaller p at a certain KL is more effective in carrying axial compression than another section with a larger value of p at the same KL. Similarly, a section with a smaller bx is more effective for flexure at a given Lb than another section with a larger bx for the same Lb. This information may be used to select more efficient shapes when relatively large amounts of axial load or bending are present.

Determination of bx when Cb > 1.0

The tabulated values of bx assume that Cb = 1.0. These values may be modified in accordance with AISC Specification Sections F1 and H1.2. The following procedure may be used to account for Cb > 1.0. bx(Cb > 1.0) =

bx(Cb = 1.0) ≥ bxmin Cb

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DESIGN TABLE DISCUSSION

6–5

Values of bxmin are listed in Table 6-1 at Lb = 0 ft. See Aminmansour (2009) for more information on this method. Values for p, bx, by, ty and tr presented in Table 6-1 have been multiplied by 103. Thus, when used in the appropriate interaction equation they must be multiplied by 10–3 (0.001).

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DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

PART 6 REFERENCES Aminmansour, A. (2000), “A New Approach for Design of Steel Beam-Columns,” Engineering Journal, Vol. 37, No. 2, 2nd Quarter, pp. 41–72, AISC, Chicago, IL. Aminmansour, A. (2006), “New Method of Design for Combined Tension and Bending,” Engineering Journal, Vol. 43, No. 4, 4th Quarter, pp. 247–256, AISC, Chicago, IL. Aminmansour, A. (2009), “Optimum Flexural Design of Steel Members Utilizing Moment Gradient and Cb,” Engineering Journal, Vol. 46, No. 1, 1st Quarter, pp. 47–55, AISC, Chicago, IL. Seaburg, P.A. and Carter, C.J. (1997), Torsional Analysis of Structural Steel Members, Design Guide 9, AISC, Chicago, IL.

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STEEL BEAM-COLUMN SELECTION TABLES

6–7

Table 6-1

Combined Flexure and Axial Force

Fy = 50 ksi

W44

W-Shapes W44×

Shape

335c

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

290c

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

262c

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.346 0.230 0.220 0.146 0.417 0.278 0.253 0.168 0.474 0.316 0.281 0.187

11 12 13 14 15

0.378 0.384 0.392 0.402 0.412

0.251 0.256 0.261 0.267 0.274

0.220 0.220 0.222 0.225 0.229

0.146 0.146 0.148 0.150 0.152

0.454 0.462 0.470 0.480 0.490

0.302 0.307 0.313 0.319 0.326

0.253 0.253 0.255 0.259 0.264

0.168 0.168 0.170 0.173 0.175

0.516 0.524 0.533 0.544 0.555

0.343 0.349 0.355 0.362 0.369

0.281 0.281 0.284 0.289 0.294

0.187 0.187 0.189 0.192 0.196

16 17 18 19 20

0.423 0.435 0.449 0.463 0.479

0.281 0.290 0.299 0.308 0.319

0.232 0.236 0.240 0.244 0.248

0.155 0.157 0.160 0.162 0.165

0.501 0.514 0.527 0.542 0.559

0.333 0.342 0.351 0.361 0.372

0.268 0.273 0.277 0.282 0.287

0.178 0.181 0.184 0.188 0.191

0.568 0.582 0.597 0.613 0.632

0.378 0.387 0.397 0.408 0.420

0.299 0.304 0.310 0.316 0.322

0.199 0.203 0.206 0.210 0.214

22 24 26 28 30

0.515 0.558 0.608 0.668 0.738

0.343 0.371 0.405 0.444 0.491

0.256 0.266 0.275 0.286 0.297

0.171 0.177 0.183 0.190 0.198

0.597 0.643 0.702 0.77 0.851

0.397 0.428 0.467 0.512 0.567

0.298 0.309 0.321 0.335 0.349

0.198 0.206 0.214 0.223 0.232

0.674 0.724 0.785 0.859 0.950

0.448 0.482 0.522 0.571 0.632

0.335 0.348 0.363 0.379 0.397

0.223 0.232 0.242 0.252 0.264

32 34 36 38 40

0.822 0.923 1.03 1.15 1.28

0.547 0.614 0.689 0.767 0.850

0.310 0.323 0.338 0.354 0.377

0.206 0.215 0.225 0.235 0.251

0.948 1.06 1.19 1.33 1.47

0.631 0.708 0.794 0.885 0.980

0.365 0.382 0.401 0.429 0.464

0.243 0.254 0.267 0.286 0.309

1.06 1.19 1.34 1.49 1.65

0.705 0.793 0.889 0.990 1.10

0.417 0.438 0.465 0.507 0.549

0.277 0.292 0.310 0.337 0.365

42 44 46 48 50

1.41 1.55 1.69 1.84 2.00

0.937 1.03 1.12 1.22 1.33

0.404 0.431 0.459 0.486 0.514

0.269 0.287 0.305 0.323 0.342

1.62 1.78 1.95 2.12 2.30

1.08 1.19 1.30 1.41 1.53

0.499 0.534 0.570 0.605 0.641

0.332 0.355 0.379 0.403 0.426

1.82 2.00 2.18 2.37 2.58

1.21 1.33 1.45 1.58 1.71

0.592 0.635 0.679 0.722 0.766

0.394 0.423 0.452 0.481 0.510

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

c

–1

1.51 0.339 0.417

1.00 0.226 0.278

1.74 0.391 0.480

1.16 0.260 0.320

1.96 0.433 0.531

1.30 0.288 0.354

rx /ry

5.10

5.10

5.10

ry , in.

3.49

3.49

3.47

Shape is slender for compression with Fy = 50 ksi.

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DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W44-W40

W-Shapes W44×

Shape

p × 10 (kips) ASD 0

593h

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

W40×

230c, v

Design

Fy = 50 ksi

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10

3

–1

(kips) ASD

503h

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.557 0.370 0.324 0.215 0.192 0.128 0.129 0.0859 0.226 0.150 0.154 0.102

11 12 13 14 15

0.604 0.614 0.625 0.637 0.650

0.402 0.409 0.416 0.424 0.433

0.324 0.324 0.329 0.335 0.341

0.215 0.215 0.219 0.223 0.227

0.210 0.213 0.217 0.221 0.226

0.139 0.142 0.144 0.147 0.150

0.129 0.129 0.129 0.130 0.131

0.0859 0.0859 0.0859 0.0863 0.0870

0.247 0.252 0.257 0.262 0.268

0.165 0.168 0.171 0.174 0.178

0.154 0.154 0.154 0.155 0.156

0.102 0.102 0.102 0.103 0.104

16 17 18 19 20

0.665 0.681 0.698 0.718 0.739

0.442 0.453 0.465 0.478 0.492

0.347 0.354 0.360 0.367 0.375

0.231 0.235 0.240 0.244 0.249

0.231 0.237 0.243 0.250 0.257

0.154 0.158 0.162 0.166 0.171

0.132 0.133 0.134 0.135 0.136

0.0877 0.0884 0.0892 0.0899 0.0907

0.274 0.281 0.289 0.297 0.306

0.182 0.187 0.192 0.198 0.204

0.158 0.159 0.161 0.163 0.164

0.105 0.106 0.107 0.108 0.109

22 24 26 28 30

0.787 0.846 0.916 1.00 1.10

0.524 0.563 0.609 0.666 0.735

0.390 0.407 0.425 0.446 0.468

0.260 0.271 0.283 0.296 0.311

0.273 0.292 0.314 0.340 0.370

0.182 0.194 0.209 0.226 0.246

0.139 0.141 0.144 0.146 0.149

0.0923 0.0939 0.0956 0.0973 0.0991

0.326 0.350 0.377 0.410 0.448

0.217 0.233 0.251 0.273 0.298

0.168 0.171 0.175 0.179 0.183

0.112 0.114 0.117 0.119 0.122

32 34 36 38 40

1.23 1.39 1.56 1.73 1.92

0.820 0.924 1.04 1.15 1.28

0.492 0.519 0.568 0.621 0.674

0.327 0.346 0.378 0.413 0.449

0.405 0.446 0.494 0.551 0.610

0.269 0.297 0.329 0.366 0.406

0.152 0.155 0.158 0.161 0.164

0.101 0.103 0.105 0.107 0.109

0.492 0.544 0.606 0.675 0.748

0.327 0.362 0.403 0.449 0.498

0.187 0.192 0.197 0.201 0.207

0.125 0.128 0.131 0.134 0.138

42 44 46 48 50

2.12 2.33 2.54 2.77 3.00

1.41 1.55 1.69 1.84 2.00

0.729 0.784 0.840 0.897 0.954

0.485 0.522 0.559 0.597 0.634

0.673 0.738 0.807 0.879 0.953

0.448 0.491 0.537 0.585 0.634

0.168 0.171 0.175 0.179 0.183

0.112 0.114 0.116 0.119 0.122

0.825 0.906 0.990 1.08 1.17

0.549 0.603 0.659 0.717 0.778

0.212 0.218 0.224 0.230 0.237

0.141 0.145 0.149 0.153 0.158

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

2.27 0.493 0.605

1.51 0.328 0.403

0.741 0.192 0.236

0.493 0.128 0.157

0.904 0.226 0.277

0.602 0.150 0.185

rx /ry

5.10

4.47

4.52

ry , in.

3.43

3.80

3.72

Shape is slender for compression with Fy = 50 ksi. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. v Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:46 AM

Page 9

STEEL BEAM-COLUMN SELECTION TABLES

6–9

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W40

W-Shapes W40×

Shape

431h

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

397h

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

392h

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.263 0.175 0.182 0.121 0.285 0.190 0.198 0.132 0.288 0.192 0.208 0.139

11 12 13 14 15

0.289 0.295 0.301 0.307 0.314

0.193 0.196 0.200 0.204 0.209

0.182 0.182 0.182 0.184 0.186

0.121 0.121 0.121 0.122 0.124

0.314 0.320 0.327 0.334 0.341

0.209 0.213 0.217 0.222 0.227

0.198 0.198 0.198 0.201 0.203

0.132 0.132 0.132 0.133 0.135

0.346 0.358 0.372 0.387 0.404

0.230 0.238 0.247 0.258 0.269

0.213 0.217 0.220 0.223 0.227

0.142 0.144 0.146 0.148 0.151

16 17 18 19 20

0.322 0.330 0.340 0.350 0.361

0.214 0.220 0.226 0.233 0.240

0.188 0.190 0.193 0.195 0.197

0.125 0.127 0.128 0.130 0.131

0.350 0.359 0.369 0.380 0.392

0.233 0.239 0.246 0.253 0.261

0.205 0.208 0.211 0.213 0.216

0.137 0.138 0.140 0.142 0.144

0.424 0.446 0.470 0.497 0.527

0.282 0.296 0.313 0.331 0.351

0.230 0.234 0.238 0.241 0.245

0.153 0.156 0.158 0.161 0.163

22 24 26 28 30

0.386 0.415 0.449 0.489 0.536

0.257 0.276 0.299 0.325 0.356

0.202 0.207 0.212 0.218 0.224

0.134 0.138 0.141 0.145 0.149

0.419 0.451 0.488 0.532 0.584

0.279 0.300 0.325 0.354 0.388

0.221 0.227 0.234 0.240 0.247

0.147 0.151 0.155 0.160 0.164

0.598 0.687 0.801 0.929 1.07

0.398 0.457 0.533 0.618 0.710

0.254 0.263 0.273 0.283 0.295

0.169 0.175 0.181 0.188 0.196

32 34 36 38 40

0.591 0.656 0.734 0.818 0.906

0.393 0.436 0.488 0.544 0.603

0.230 0.236 0.243 0.251 0.259

0.153 0.157 0.162 0.167 0.172

0.644 0.715 0.801 0.892 0.989

0.429 0.476 0.533 0.594 0.658

0.255 0.262 0.271 0.280 0.289

0.169 0.175 0.180 0.186 0.192

1.21 1.37 1.54 1.71 1.90

0.807 0.911 1.02 1.14 1.26

0.307 0.320 0.335 0.351 0.372

0.204 0.213 0.223 0.233 0.248

42 44 46 48 50

0.999 1.10 1.20 1.30 1.42

0.665 0.729 0.797 0.868 0.942

0.267 0.276 0.285 0.295 0.308

0.178 0.184 0.190 0.197 0.205

1.09 1.20 1.31 1.42 1.55

0.725 0.796 0.870 0.947 1.03

0.299 0.310 0.322 0.338 0.356

0.199 2.09 0.206 2.29 0.214 0.225 0.237

1.39 1.53

0.394 0.262 0.415 0.276

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

1.09 0.263 0.323

0.723 0.175 0.215

1.19 0.285 0.351

0.790 0.190 0.234

1.71 0.288 0.354

1.14 0.192 0.236

rx /ry

4.55

4.56

6.10

ry , in.

3.65

3.64

2.64

h

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Heavy line indicates KL /ry equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:46 AM

6–10

Page 10

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W40

W-Shapes W40×

Shape

372h

p × 10 Design

(kips) ASD 0

362h

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10

3

–1

(kips) ASD

331h

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.304 0.202 0.212 0.141 0.315 0.210 0.217 0.145 0.342 0.227 0.249 0.166

11 12 13 14 15

0.335 0.341 0.348 0.356 0.365

0.223 0.227 0.232 0.237 0.243

0.212 0.212 0.213 0.215 0.218

0.141 0.141 0.142 0.143 0.145

0.348 0.354 0.361 0.369 0.378

0.231 0.236 0.240 0.246 0.252

0.217 0.217 0.218 0.221 0.224

0.145 0.145 0.145 0.147 0.149

0.415 0.430 0.448 0.467 0.489

0.276 0.286 0.298 0.311 0.326

0.257 0.262 0.266 0.271 0.276

0.171 0.174 0.177 0.180 0.184

16 17 18 19 20

0.374 0.384 0.395 0.407 0.420

0.249 0.255 0.263 0.271 0.280

0.221 0.224 0.227 0.230 0.233

0.147 0.149 0.151 0.153 0.155

0.388 0.398 0.410 0.422 0.436

0.258 0.265 0.273 0.281 0.290

0.227 0.230 0.233 0.236 0.239

0.151 0.153 0.155 0.157 0.159

0.514 0.542 0.573 0.608 0.647

0.342 0.361 0.381 0.404 0.430

0.281 0.287 0.292 0.298 0.304

0.187 0.191 0.194 0.198 0.202

22 24 26 28 30

0.450 0.485 0.526 0.574 0.631

0.299 0.323 0.350 0.382 0.420

0.240 0.246 0.254 0.261 0.270

0.159 0.164 0.169 0.174 0.179

0.467 0.503 0.546 0.596 0.655

0.311 0.335 0.363 0.396 0.436

0.246 0.253 0.261 0.269 0.278

0.164 0.168 0.174 0.179 0.185

0.739 0.856 1.00 1.16 1.34

0.492 0.570 0.668 0.774 0.889

0.317 0.331 0.346 0.362 0.381

0.211 0.220 0.230 0.241 0.253

32 34 36 38 40

0.698 0.777 0.871 0.970 1.08

0.464 0.517 0.579 0.646 0.715

0.278 0.288 0.298 0.308 0.320

0.185 0.191 0.198 0.205 0.213

0.724 0.806 0.904 1.01 1.12

0.482 0.536 0.601 0.670 0.742

0.287 0.297 0.307 0.319 0.331

0.191 0.197 0.204 0.212 0.220

1.52 1.72 1.92 2.14 2.38

1.01 1.14 1.28 1.43 1.58

0.401 0.425 0.456 0.488 0.519

0.267 0.283 0.304 0.324 0.345

42 44 46 48 50

1.19 1.30 1.42 1.55 1.68

0.789 0.866 0.946 1.03 1.12

0.332 0.345 0.365 0.385 0.405

0.221 0.230 0.243 0.256 0.270

1.23 1.35 1.48 1.61 1.74

0.818 0.898 0.982 1.07 1.16

0.344 0.358 0.380 0.401 0.422

0.229 2.62 0.238 0.253 0.267 0.281

1.74

0.550 0.366

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

1.29 0.304 0.373

0.856 0.202 0.249

1.32 0.315 0.387

0.878 0.210 0.258

2.10 0.342 0.420

1.40 0.227 0.280

rx /ry

4.58

4.58

6.19

ry , in.

3.60

3.60

2.57

h

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Heavy line indicates KL /ry equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:46 AM

Page 11

STEEL BEAM-COLUMN SELECTION TABLES

6–11

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W40

W-Shapes W40×

Shape

327h

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

3

–1

(kip-ft)

LRFD

297c

324

bx × 10

3

ASD

–1

LRFD

p × 10

bx × 10

3

(kips) ASD

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.348 0.232 0.253 0.168 0.350 0.233 0.244 0.162 0.386 0.257 0.268 0.178

11 12 13 14 15

0.422 0.437 0.455 0.475 0.497

0.281 0.291 0.303 0.316 0.331

0.261 0.265 0.270 0.275 0.280

0.174 0.177 0.180 0.183 0.186

0.387 0.394 0.403 0.412 0.422

0.258 0.262 0.268 0.274 0.281

0.244 0.244 0.245 0.249 0.252

0.162 0.162 0.163 0.165 0.168

0.424 0.432 0.441 0.451 0.462

0.282 0.287 0.293 0.300 0.308

0.268 0.268 0.270 0.274 0.278

0.178 0.178 0.179 0.182 0.185

16 17 18 19 20

0.522 0.550 0.581 0.616 0.656

0.347 0.366 0.387 0.410 0.436

0.285 0.290 0.296 0.302 0.308

0.190 0.193 0.197 0.201 0.205

0.433 0.444 0.457 0.471 0.487

0.288 0.296 0.304 0.314 0.324

0.256 0.259 0.263 0.267 0.271

0.170 0.173 0.175 0.178 0.180

0.474 0.488 0.502 0.518 0.535

0.316 0.325 0.334 0.345 0.356

0.282 0.286 0.291 0.295 0.300

0.188 0.190 0.193 0.197 0.200

22 24 26 28 30

0.749 0.866 1.01 1.18 1.35

0.498 0.576 0.675 0.783 0.899

0.321 0.335 0.350 0.367 0.385

0.213 0.223 0.233 0.244 0.256

0.522 0.563 0.611 0.667 0.734

0.347 0.374 0.406 0.444 0.488

0.279 0.288 0.298 0.308 0.319

0.186 0.192 0.198 0.205 0.212

0.575 0.621 0.675 0.739 0.815

0.382 0.413 0.449 0.492 0.542

0.310 0.321 0.332 0.344 0.357

0.206 0.213 0.221 0.229 0.238

32 34 36 38 40

1.54 1.73 1.95 2.17 2.40

1.02 1.15 1.29 1.44 1.60

0.406 0.430 0.462 0.494 0.526

0.270 0.286 0.307 0.329 0.350

0.813 0.907 1.02 1.13 1.25

0.541 0.603 0.676 0.754 0.835

0.330 0.343 0.357 0.371 0.387

0.220 0.228 0.237 0.247 0.258

0.904 1.01 1.13 1.26 1.40

0.602 0.674 0.755 0.841 0.932

0.372 0.387 0.404 0.422 0.446

0.247 0.257 0.269 0.281 0.297

42 44 46 48 50

2.65

1.76

0.557 0.371 1.38 1.52 1.66 1.81 1.96

0.921 1.01 1.10 1.20 1.30

0.408 0.435 0.461 0.488 0.514

0.272 0.289 0.307 0.324 0.342

1.54 1.70 1.85 2.02 2.19

1.03 1.13 1.23 1.34 1.46

0.478 0.509 0.541 0.573 0.605

0.318 0.339 0.360 0.381 0.403

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

2.12 0.348 0.428

1.41 0.232 0.285

1.49 0.350 0.430

0.992 0.233 0.287

1.66 0.383 0.470

1.10 0.255 0.313

rx /ry

6.20

4.58

4.60

ry , in.

2.58

3.58

3.54

Shape is slender for compression with Fy = 50 ksi. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:46 AM

6–12

Page 12

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W40

W-Shapes W40×

Shape

294

p × 10 Design

(kips) ASD 0

p × 10

3

–1

(kip-ft)

LRFD

277c

278

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

ASD

–1

LRFD

bx × 10

3

3

–1

(kips) ASD

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.387 0.258 0.281 0.187 0.406 0.270 0.299 0.199 0.425 0.283 0.285 0.190

11 12 13 14 15

0.471 0.489 0.509 0.532 0.558

0.314 0.325 0.339 0.354 0.371

0.291 0.296 0.302 0.308 0.314

0.194 0.197 0.201 0.205 0.209

0.496 0.515 0.537 0.562 0.589

0.330 0.343 0.357 0.374 0.392

0.312 0.318 0.324 0.331 0.338

0.207 0.211 0.216 0.220 0.225

0.462 0.470 0.479 0.488 0.498

0.308 0.313 0.318 0.325 0.332

0.285 0.285 0.287 0.291 0.295

0.190 0.190 0.191 0.193 0.196

16 17 18 19 20

0.586 0.619 0.655 0.695 0.740

0.390 0.412 0.436 0.463 0.493

0.321 0.328 0.335 0.342 0.350

0.214 0.218 0.223 0.228 0.233

0.620 0.655 0.694 0.738 0.788

0.413 0.436 0.462 0.491 0.524

0.345 0.352 0.360 0.369 0.377

0.229 0.234 0.240 0.245 0.251

0.510 0.522 0.536 0.551 0.569

0.339 0.347 0.357 0.367 0.379

0.300 0.304 0.309 0.314 0.320

0.199 0.203 0.206 0.209 0.213

22 24 26 28 30

0.848 0.985 1.16 1.34 1.54

0.564 0.655 0.769 0.892 1.02

0.366 0.384 0.404 0.426 0.451

0.244 0.256 0.269 0.284 0.300

0.905 1.06 1.24 1.44 1.65

0.602 0.702 0.824 0.956 1.10

0.396 0.416 0.439 0.464 0.493

0.263 0.277 0.292 0.309 0.328

0.610 0.658 0.714 0.780 0.858

0.406 0.438 0.475 0.519 0.571

0.330 0.342 0.355 0.368 0.382

0.220 0.228 0.236 0.245 0.254

32 34 36 38 40

1.75 1.98 2.22 2.47 2.73

1.16 1.31 1.47 1.64 1.82

0.482 0.521 0.561 0.601 0.640

0.320 0.347 0.373 0.400 0.426

1.88 2.12 2.38 2.65 2.93

1.25 1.41 1.58 1.76 1.95

0.535 0.580 0.624 0.669 0.714

0.356 0.386 0.415 0.445 0.475

0.950 1.06 1.19 1.32 1.47

0.632 0.705 0.791 0.881 0.976

0.398 0.415 0.434 0.454 0.484

0.265 0.276 0.289 0.302 0.322

42 44 46 48 50

3.02

2.01

0.679 0.452 3.23

2.15

0.758 0.504 1.62 1.78 1.94 2.11 2.29

1.08 1.18 1.29 1.41 1.53

0.519 0.555 0.590 0.625 0.661

0.345 0.369 0.393 0.416 0.440

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

2.38 0.387 0.476

1.58 0.258 0.317

2.56 0.406 0.498

1.70 0.270 0.332

1.75 0.410 0.503

1.16 0.273 0.336

rx /ry

6.24

6.27

4.58

ry , in.

2.55

2.52

3.58

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:46 AM

Page 13

STEEL BEAM-COLUMN SELECTION TABLES

6–13

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W40

W-Shapes W40×

Shape

p × 10

bx × 10

3

Design

(kips) ASD 0

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

249c

264

p × 10

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

(kips) ASD

235c

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.432 0.287 0.315 0.210 0.483 0.321 0.318 0.212 0.504 0.335 0.353 0.235

11 12 13 14 15

0.527 0.548 0.571 0.597 0.627

0.351 0.365 0.380 0.397 0.417

0.329 0.335 0.342 0.349 0.357

0.219 0.223 0.228 0.233 0.238

0.525 0.534 0.543 0.554 0.565

0.349 0.355 0.361 0.368 0.376

0.318 0.318 0.320 0.325 0.331

0.212 0.212 0.213 0.217 0.220

0.595 0.615 0.638 0.666 0.698

0.396 0.409 0.424 0.443 0.464

0.368 0.376 0.384 0.393 0.402

0.245 0.250 0.255 0.261 0.267

16 17 18 19 20

0.660 0.697 0.738 0.785 0.838

0.439 0.464 0.491 0.522 0.557

0.365 0.373 0.382 0.391 0.401

0.243 0.248 0.254 0.260 0.267

0.578 0.592 0.608 0.625 0.643

0.385 0.394 0.404 0.416 0.428

0.336 0.342 0.347 0.353 0.359

0.224 0.227 0.231 0.235 0.239

0.734 0.775 0.820 0.871 0.928

0.488 0.515 0.546 0.580 0.618

0.411 0.421 0.431 0.442 0.454

0.274 0.280 0.287 0.294 0.302

22 24 26 28 30

0.963 1.12 1.32 1.53 1.75

0.641 0.747 0.877 1.02 1.17

0.421 0.444 0.469 0.498 0.533

0.280 0.295 0.312 0.331 0.354

0.685 0.736 0.799 0.875 0.964

0.456 0.490 0.532 0.582 0.641

0.372 0.386 0.401 0.417 0.435

0.248 0.257 0.267 0.278 0.289

1.06 1.24 1.45 1.68 1.93

0.709 0.823 0.967 1.12 1.29

0.479 0.507 0.538 0.573 0.629

0.319 0.337 0.358 0.381 0.419

32 34 36 38 40

2.00 2.25 2.53 2.81 3.12

1.33 1.50 1.68 1.87 2.07

0.582 0.632 0.681 0.730 0.780

0.387 0.420 0.453 0.486 0.519

1.07 1.20 1.34 1.49 1.65

0.711 0.795 0.892 0.994 1.10

0.454 0.475 0.498 0.530 0.573

0.302 0.316 0.331 0.353 0.381

2.20 2.48 2.79 3.10 3.44

1.46 1.65 1.85 2.06 2.29

0.690 0.750 0.811 0.872 0.932

0.459 0.499 0.540 0.580 0.620

42 44 46 48 50

3.44

2.29

0.829 0.552 1.82 2.00 2.19 2.38 2.59

1.21 1.33 1.46 1.59 1.72

0.616 0.659 0.702 0.746 0.790

0.410 3.79 0.438 0.467 0.496 0.525

2.52

0.993 0.661

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

2.70 0.432 0.530

1.80 0.287 0.353

1.96 0.454 0.558

1.30 0.302 0.372

3.02 0.483 0.594

2.01 0.322 0.396

rx /ry

6.27

4.59

6.26

ry , in.

2.52

3.55

2.54

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:46 AM

6–14

Page 14

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W40

W-Shapes W40×

Shape

215c

p × 10 Design

(kips) ASD 0

211c

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

p × 10

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

–1

(kips) ASD

199c

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.578 0.385 0.370 0.246 0.578 0.385 0.393 0.262 0.629 0.419 0.410 0.273

11 12 13 14 15

0.627 0.637 0.648 0.661 0.674

0.417 0.424 0.431 0.440 0.448

0.370 0.370 0.373 0.379 0.385

0.246 0.246 0.248 0.252 0.256

0.681 0.704 0.729 0.759 0.792

0.453 0.468 0.485 0.505 0.527

0.412 0.422 0.432 0.442 0.453

0.274 0.281 0.287 0.294 0.301

0.685 0.696 0.708 0.722 0.738

0.456 0.463 0.471 0.481 0.491

0.410 0.410 0.416 0.423 0.431

0.273 0.273 0.277 0.282 0.287

16 17 18 19 20

0.689 0.705 0.723 0.742 0.764

0.458 0.469 0.481 0.494 0.508

0.392 0.399 0.406 0.413 0.421

0.261 0.265 0.270 0.275 0.280

0.830 0.873 0.924 0.983 1.05

0.552 0.581 0.615 0.654 0.698

0.464 0.476 0.489 0.503 0.517

0.309 0.317 0.325 0.334 0.344

0.754 0.773 0.793 0.815 0.840

0.502 0.514 0.528 0.543 0.559

0.439 0.447 0.455 0.464 0.473

0.292 0.297 0.303 0.309 0.315

22 24 26 28 30

0.812 0.870 0.939 1.02 1.12

0.540 0.579 0.625 0.680 0.746

0.437 0.455 0.474 0.495 0.517

0.291 0.303 0.315 0.329 0.344

1.21 1.41 1.66 1.92 2.20

0.803 0.938 1.10 1.28 1.47

0.548 0.582 0.622 0.679 0.753

0.364 0.388 0.414 0.452 0.501

0.896 0.963 1.04 1.14 1.26

0.596 0.640 0.694 0.759 0.838

0.493 0.514 0.537 0.562 0.590

0.328 0.342 0.357 0.374 0.393

32 34 36 38 40

1.24 1.39 1.56 1.74 1.93

0.827 0.926 1.04 1.16 1.28

0.542 0.569 0.605 0.660 0.715

0.361 0.379 0.403 0.439 0.476

2.51 2.83 3.17 3.54 3.92

1.67 1.88 2.11 2.35 2.61

0.827 0.902 0.978 1.05 1.13

0.550 0.600 0.650 0.701 0.751

1.41 1.58 1.77 1.98 2.19

0.935 1.05 1.18 1.32 1.46

0.621 0.655 0.716 0.782 0.849

0.413 0.436 0.476 0.520 0.565

42 44 46 48 50

2.12 2.33 2.55 2.77 3.01

1.41 1.55 1.69 1.85 2.00

0.771 0.828 0.885 0.942 1.00

0.513 0.551 0.589 0.627 0.665

2.41 2.65 2.90 3.15 3.42

1.61 1.76 1.93 2.10 2.28

0.918 0.987 1.06 1.13 1.20

0.610 0.657 0.703 0.750 0.797

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

2.28 0.526 0.646

1.52 0.350 0.431

3.39 0.538 0.661

2.26 0.358 0.440

2.60 0.568 0.698

1.73 0.378 0.465

rx /ry

4.58

6.29

4.64

ry , in.

3.54

2.51

3.45

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:46 AM

Page 15

STEEL BEAM-COLUMN SELECTION TABLES

6–15

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W40

W-Shapes W40×

Shape

183c

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

167c

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

149 c, v

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.702 0.467 0.460 0.306 0.767 0.510 0.514 0.342 0.883 0.587 0.596 0.396

11 12 13 14 15

0.823 0.850 0.880 0.914 0.953

0.548 0.565 0.585 0.608 0.634

0.485 0.497 0.509 0.522 0.536

0.323 0.330 0.339 0.348 0.357

0.907 0.937 0.973 1.01 1.06

0.603 0.624 0.647 0.674 0.705

0.547 0.562 0.577 0.593 0.610

0.364 0.374 0.384 0.395 0.406

1.05 1.09 1.14 1.19 1.25

0.701 0.727 0.756 0.790 0.828

0.644 0.663 0.682 0.703 0.725

0.429 0.441 0.454 0.468 0.483

16 17 18 19 20

0.997 1.05 1.10 1.17 1.24

0.663 0.696 0.734 0.777 0.826

0.551 0.567 0.583 0.600 0.619

0.367 0.377 0.388 0.399 0.412

1.11 1.17 1.24 1.32 1.41

0.739 0.779 0.825 0.878 0.938

0.628 0.647 0.668 0.689 0.712

0.418 0.431 0.444 0.459 0.474

1.31 1.39 1.48 1.58 1.70

0.873 0.925 0.984 1.05 1.13

0.749 0.774 0.801 0.830 0.861

0.498 0.515 0.533 0.552 0.573

22 24 26 28 30

1.43 1.67 1.96 2.27 2.61

0.948 1.11 1.30 1.51 1.74

0.659 0.705 0.763 0.859 0.957

0.439 0.469 0.507 0.571 0.636

1.64 1.94 2.28 2.65 3.04

1.09 1.29 1.52 1.76 2.02

0.763 0.822 0.919 1.04 1.16

0.508 0.547 0.611 0.690 0.771

2.02 2.40 2.82 3.27 3.75

1.34 1.60 1.88 2.18 2.50

0.930 1.03 1.18 1.33 1.49

0.619 0.683 0.783 0.887 0.993

32 34 36 38 40

2.97 3.35 3.76 4.19 4.64

1.98 2.23 2.50 2.79 3.09

1.06 1.16 1.26 1.36 1.46

0.702 0.769 0.837 0.905 0.973

3.45 3.90 4.37 4.87 5.40

2.30 2.59 2.91 3.24 3.59

1.28 1.41 1.53 1.66 1.79

0.853 0.937 1.02 1.11 1.19

4.27 4.82 5.41 6.02

2.84 3.21 3.60 4.01

1.66 1.82 1.99 2.16

1.10 1.21 1.33 1.44

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

4.03 0.627 0.770

2.68 0.417 0.513

4.69 0.677 0.832

3.12 0.451 0.555

5.74 0.763 0.937

3.82 0.507 0.624

rx /ry

6.31

6.38

6.55

ry , in.

2.49

2.40

2.29

Shape is slender for compression with Fy = 50 ksi. v Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:46 AM

6–16

Page 16

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W36

W-Shapes W36×

Shape

652h

p × 10 Design

(kips) ASD 0

529h

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10

3

–1

(kips) ASD

487h

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.174 0.116 0.122 0.0815 0.214 0.142 0.153 0.102 0.234 0.155 0.167 0.111

11 12 13 14 15

0.188 0.190 0.193 0.197 0.200

0.125 0.127 0.129 0.131 0.133

0.122 0.122 0.122 0.122 0.123

0.0815 0.0815 0.0815 0.0815 0.0817

0.232 0.235 0.239 0.244 0.248

0.154 0.157 0.159 0.162 0.165

0.153 0.153 0.153 0.153 0.154

0.102 0.102 0.102 0.102 0.102

0.253 0.257 0.262 0.266 0.272

0.169 0.171 0.174 0.177 0.181

0.167 0.167 0.167 0.167 0.169

0.111 0.111 0.111 0.111 0.112

16 17 18 19 20

0.204 0.208 0.213 0.218 0.223

0.136 0.139 0.142 0.145 0.149

0.124 0.124 0.125 0.126 0.127

0.0823 0.0828 0.0833 0.0839 0.0845

0.253 0.259 0.265 0.272 0.279

0.169 0.172 0.176 0.181 0.185

0.155 0.157 0.158 0.159 0.160

0.103 0.104 0.105 0.106 0.107

0.277 0.284 0.290 0.298 0.306

0.185 0.189 0.193 0.198 0.203

0.170 0.172 0.173 0.175 0.176

0.113 0.114 0.115 0.116 0.117

22 24 26 28 30

0.236 0.250 0.266 0.284 0.306

0.157 0.166 0.177 0.189 0.203

0.129 0.130 0.132 0.134 0.136

0.0856 0.0868 0.0880 0.0892 0.0905

0.294 0.313 0.334 0.359 0.387

0.196 0.208 0.222 0.239 0.258

0.163 0.166 0.169 0.172 0.175

0.109 0.110 0.112 0.114 0.117

0.323 0.344 0.368 0.395 0.427

0.215 0.229 0.245 0.263 0.284

0.180 0.183 0.187 0.190 0.194

0.120 0.122 0.124 0.127 0.129

32 34 36 38 40

0.330 0.359 0.392 0.430 0.475

0.220 0.239 0.261 0.286 0.316

0.138 0.140 0.142 0.144 0.147

0.0918 0.0932 0.0946 0.0960 0.0975

0.420 0.458 0.502 0.554 0.614

0.279 0.305 0.334 0.369 0.409

0.178 0.182 0.185 0.189 0.193

0.119 0.121 0.123 0.126 0.128

0.465 0.508 0.558 0.617 0.684

0.309 0.338 0.371 0.410 0.455

0.198 0.202 0.207 0.211 0.216

0.132 0.135 0.138 0.141 0.144

42 44 46 48 50

0.524 0.575 0.628 0.684 0.742

0.348 0.382 0.418 0.455 0.494

0.149 0.151 0.154 0.156 0.159

0.0990 0.101 0.102 0.104 0.106

0.677 0.743 0.812 0.884 0.960

0.450 0.494 0.540 0.588 0.638

0.197 0.201 0.205 0.210 0.215

0.131 0.134 0.137 0.140 0.143

0.754 0.827 0.904 0.984 1.07

0.501 0.550 0.601 0.655 0.711

0.221 0.226 0.232 0.237 0.243

0.147 0.150 0.154 0.158 0.162

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

h

–1

0.613 0.174 0.214

0.408 0.116 0.142

0.785 0.214 0.263

0.522 0.142 0.175

0.865 0.234 0.287

0.575 0.155 0.191

rx /ry

3.95

4.00

3.99

ry , in.

4.10

4.00

3.96

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:46 AM

Page 17

STEEL BEAM-COLUMN SELECTION TABLES

6–17

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W36

W-Shapes W36×

Shape

441h

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

395h

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

361h

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.257 0.171 0.187 0.124 0.288 0.192 0.208 0.139 0.315 0.210 0.230 0.153

11 12 13 14 15

0.279 0.284 0.288 0.294 0.300

0.186 0.189 0.192 0.196 0.199

0.187 0.187 0.187 0.187 0.189

0.124 0.124 0.124 0.124 0.125

0.313 0.318 0.324 0.330 0.337

0.208 0.212 0.216 0.220 0.224

0.208 0.208 0.208 0.209 0.211

0.139 0.139 0.139 0.139 0.141

0.343 0.349 0.355 0.362 0.370

0.228 0.232 0.236 0.241 0.246

0.230 0.230 0.230 0.231 0.234

0.153 0.153 0.153 0.154 0.155

16 17 18 19 20

0.306 0.313 0.321 0.329 0.338

0.204 0.208 0.213 0.219 0.225

0.190 0.192 0.194 0.196 0.198

0.127 0.128 0.129 0.130 0.132

0.344 0.352 0.361 0.371 0.381

0.229 0.234 0.240 0.247 0.253

0.213 0.216 0.218 0.221 0.223

0.142 0.144 0.145 0.147 0.148

0.378 0.387 0.397 0.407 0.419

0.251 0.257 0.264 0.271 0.279

0.236 0.239 0.242 0.245 0.248

0.157 0.159 0.161 0.163 0.165

22 24 26 28 30

0.358 0.381 0.408 0.440 0.476

0.238 0.254 0.272 0.293 0.317

0.202 0.206 0.211 0.215 0.220

0.135 0.137 0.140 0.143 0.147

0.404 0.431 0.462 0.498 0.540

0.269 0.287 0.307 0.331 0.359

0.228 0.234 0.239 0.245 0.251

0.152 0.155 0.159 0.163 0.167

0.444 0.474 0.509 0.550 0.597

0.296 0.316 0.339 0.366 0.397

0.254 0.260 0.267 0.274 0.282

0.169 0.173 0.178 0.183 0.188

32 34 36 38 40

0.518 0.567 0.624 0.693 0.767

0.345 0.377 0.415 0.461 0.511

0.225 0.231 0.236 0.242 0.248

0.150 0.153 0.157 0.161 0.165

0.589 0.646 0.713 0.792 0.878

0.392 0.430 0.474 0.527 0.584

0.258 0.265 0.272 0.280 0.288

0.172 0.176 0.181 0.186 0.191

0.652 0.716 0.791 0.880 0.976

0.434 0.477 0.526 0.586 0.649

0.290 0.299 0.308 0.317 0.327

0.193 0.199 0.205 0.211 0.218

42 44 46 48 50

0.846 0.928 1.01 1.10 1.20

0.563 0.618 0.675 0.735 0.798

0.255 0.261 0.269 0.276 0.284

0.169 0.174 0.179 0.184 0.189

0.968 1.06 1.16 1.26 1.37

0.644 0.707 0.772 0.841 0.913

0.296 0.305 0.315 0.325 0.336

0.197 0.203 0.210 0.216 0.224

1.08 1.18 1.29 1.40 1.52

0.716 0.785 0.858 0.935 1.01

0.338 0.350 0.362 0.376 0.395

0.225 0.233 0.241 0.250 0.263

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

h

–1

0.968 0.257 0.316

0.644 0.171 0.210

1.10 0.288 0.354

0.729 0.192 0.236

1.22 0.315 0.387

0.809 0.210 0.258

rx /ry

4.01

4.05

4.05

ry , in.

3.92

3.88

3.85

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:46 AM

6–18

Page 18

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W36

W-Shapes W36×

Shape

330

p × 10 Design

(kips) ASD 0

3

–1

(kip-ft)

LRFD

282c

302

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

ASD

–1

LRFD

p × 10

bx × 10

3

3

–1

(kips) ASD

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.345 0.229 0.253 0.168 0.375 0.250 0.278 0.185 0.404 0.269 0.299 0.199

11 12 13 14 15

0.376 0.382 0.389 0.397 0.405

0.250 0.254 0.259 0.264 0.270

0.253 0.253 0.253 0.254 0.257

0.168 0.168 0.168 0.169 0.171

0.410 0.416 0.424 0.432 0.441

0.272 0.277 0.282 0.288 0.294

0.278 0.278 0.278 0.280 0.284

0.185 0.185 0.185 0.186 0.189

0.440 0.447 0.456 0.465 0.475

0.293 0.298 0.303 0.309 0.316

0.299 0.299 0.299 0.302 0.306

0.199 0.199 0.199 0.201 0.203

16 17 18 19 20

0.414 0.424 0.435 0.447 0.459

0.276 0.282 0.289 0.297 0.306

0.260 0.264 0.267 0.270 0.274

0.173 0.175 0.178 0.180 0.182

0.451 0.462 0.474 0.487 0.501

0.300 0.308 0.315 0.324 0.333

0.287 0.291 0.295 0.299 0.303

0.191 0.194 0.196 0.199 0.202

0.486 0.497 0.510 0.524 0.539

0.323 0.331 0.339 0.349 0.359

0.310 0.314 0.319 0.323 0.328

0.206 0.209 0.212 0.215 0.218

22 24 26 28 30

0.488 0.521 0.560 0.605 0.658

0.325 0.347 0.373 0.403 0.438

0.281 0.289 0.297 0.306 0.315

0.187 0.192 0.198 0.204 0.210

0.532 0.569 0.611 0.661 0.718

0.354 0.378 0.407 0.440 0.478

0.312 0.321 0.331 0.341 0.352

0.208 0.214 0.220 0.227 0.234

0.573 0.613 0.660 0.714 0.777

0.382 0.408 0.439 0.475 0.517

0.338 0.348 0.359 0.371 0.384

0.225 0.232 0.239 0.247 0.255

32 34 36 38 40

0.719 0.790 0.874 0.973 1.08

0.478 0.526 0.581 0.648 0.717

0.325 0.335 0.346 0.358 0.371

0.216 0.223 0.230 0.238 0.247

0.786 0.864 0.956 1.07 1.18

0.523 0.575 0.636 0.709 0.785

0.364 0.376 0.389 0.404 0.419

0.242 0.250 0.259 0.269 0.279

0.850 0.936 1.04 1.16 1.28

0.566 0.623 0.690 0.769 0.852

0.397 0.412 0.428 0.444 0.463

0.264 0.274 0.284 0.296 0.308

42 44 46 48 50

1.19 1.30 1.43 1.55 1.69

0.791 0.868 0.949 1.03 1.12

0.384 0.399 0.417 0.441 0.465

0.256 0.265 0.277 0.293 0.309

1.30 1.43 1.56 1.70 1.84

0.866 0.950 1.04 1.13 1.23

0.436 0.456 0.484 0.513 0.541

0.290 0.303 0.322 0.341 0.360

1.41 1.55 1.69 1.84 2.00

0.939 1.03 1.13 1.23 1.33

0.482 0.514 0.547 0.580 0.612

0.321 0.342 0.364 0.386 0.407

Other Constants and Properties

by × 10 , (kip-ft) ty × 103, (kips)–1 tr × 103, (kips)–1 3

c

–1

1.34 0.345 0.423

0.894 0.229 0.282

1.48 0.375 0.461

0.984 0.250 0.307

1.60 0.403 0.495

1.06 0.268 0.330

rx /ry

4.05

4.03

4.05

ry , in.

3.83

3.82

3.80

Shape is slender for compression with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:47 AM

Page 19

STEEL BEAM-COLUMN SELECTION TABLES

6–19

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W36

W-Shapes W36×

Shape

262c

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

p × 10

3

–1

(kip-ft)

LRFD

247c

256

bx × 10

3

ASD

–1

LRFD

bx × 10

3

(kips) ASD

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.440 0.293 0.324 0.215 0.444 0.295 0.343 0.228 0.475 0.316 0.346 0.230

11 12 13 14 15

0.476 0.483 0.491 0.501 0.512

0.317 0.322 0.327 0.333 0.340

0.324 0.324 0.324 0.327 0.332

0.215 0.215 0.215 0.218 0.221

0.532 0.550 0.571 0.595 0.622

0.354 0.366 0.380 0.396 0.414

0.353 0.360 0.367 0.374 0.381

0.235 0.239 0.244 0.249 0.254

0.513 0.521 0.530 0.539 0.550

0.341 0.347 0.352 0.359 0.366

0.346 0.346 0.346 0.350 0.355

0.230 0.230 0.230 0.233 0.236

16 17 18 19 20

0.524 0.537 0.551 0.566 0.583

0.348 0.357 0.366 0.377 0.388

0.337 0.342 0.347 0.352 0.357

0.224 0.227 0.231 0.234 0.238

0.651 0.684 0.721 0.762 0.808

0.433 0.455 0.480 0.507 0.538

0.389 0.397 0.406 0.414 0.424

0.259 0.264 0.270 0.276 0.282

0.561 0.574 0.588 0.605 0.623

0.373 0.382 0.391 0.402 0.414

0.360 0.366 0.372 0.378 0.384

0.240 0.243 0.247 0.251 0.255

22 24 26 28 30

0.620 0.664 0.716 0.776 0.846

0.413 0.442 0.476 0.516 0.563

0.369 0.381 0.394 0.408 0.423

0.245 0.253 0.262 0.271 0.281

0.916 1.05 1.22 1.42 1.63

0.610 0.700 0.815 0.945 1.08

0.443 0.465 0.489 0.515 0.545

0.295 0.309 0.325 0.343 0.362

0.663 0.711 0.766 0.831 0.907

0.441 0.473 0.510 0.553 0.603

0.396 0.410 0.424 0.440 0.457

0.264 0.273 0.282 0.293 0.304

32 34 36 38 40

0.928 1.02 1.14 1.27 1.40

0.617 0.681 0.757 0.843 0.934

0.439 0.456 0.474 0.495 0.517

0.292 0.303 0.316 0.329 0.344

1.86 2.09 2.35 2.62 2.90

1.23 1.39 1.56 1.74 1.93

0.582 0.632 0.681 0.730 0.779

0.387 0.420 0.453 0.486 0.519

0.996 1.10 1.22 1.36 1.51

0.663 0.732 0.815 0.908 1.01

0.475 0.495 0.516 0.539 0.570

0.316 0.329 0.343 0.359 0.379

42 44 46 48 50

1.55 1.70 1.86 2.02 2.19

1.03 1.13 1.24 1.35 1.46

0.551 0.589 0.628 0.666 0.705

0.367 3.20 0.392 3.51 0.418 0.443 0.469

2.13 2.33

0.828 0.551 1.67 0.877 0.584 1.83 2.00 2.18 2.36

1.11 1.22 1.33 1.45 1.57

0.613 0.657 0.700 0.744 0.788

0.408 0.437 0.466 0.495 0.524

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

1.75 0.433 0.531

1.16 0.288 0.354

2.60 0.444 0.545

1.73 0.295 0.363

1.88 0.461 0.566

1.25 0.307 0.377

rx /ry

4.07

5.62

4.06

ry , in.

3.76

2.65

3.74

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:47 AM

6–20

Page 20

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W36

W-Shapes W36×

Shape

232c

p × 10 Design

(kips) ASD 0

231c

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

p × 10

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

–1

(kips) ASD

210c

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.498 0.331 0.381 0.253 0.511 0.340 0.370 0.246 0.555 0.369 0.428 0.285

11 12 13 14 15

0.591 0.613 0.637 0.663 0.694

0.393 0.408 0.424 0.441 0.461

0.394 0.402 0.410 0.419 0.427

0.262 0.267 0.273 0.278 0.284

0.553 0.561 0.570 0.581 0.592

0.368 0.373 0.379 0.386 0.394

0.370 0.370 0.370 0.375 0.381

0.246 0.246 0.246 0.249 0.253

0.653 0.678 0.705 0.736 0.770

0.435 0.451 0.469 0.489 0.512

0.445 0.454 0.465 0.475 0.486

0.296 0.302 0.309 0.316 0.323

16 17 18 19 20

0.727 0.765 0.807 0.855 0.907

0.484 0.509 0.537 0.569 0.604

0.437 0.447 0.457 0.468 0.479

0.291 0.297 0.304 0.311 0.319

0.604 0.618 0.633 0.649 0.667

0.402 0.411 0.421 0.432 0.444

0.387 0.393 0.399 0.406 0.412

0.257 0.261 0.266 0.270 0.274

0.809 0.852 0.901 0.955 1.02

0.538 0.567 0.599 0.635 0.676

0.498 0.510 0.523 0.536 0.550

0.331 0.339 0.348 0.357 0.366

22 24 26 28 30

1.03 1.19 1.39 1.61 1.85

0.687 0.791 0.923 1.07 1.23

0.503 0.530 0.559 0.592 0.631

0.335 0.352 0.372 0.394 0.420

0.709 0.761 0.821 0.892 0.975

0.472 0.506 0.546 0.594 0.649

0.426 0.442 0.458 0.476 0.494

0.284 0.294 0.305 0.316 0.329

1.16 1.34 1.57 1.82 2.09

0.772 0.893 1.05 1.21 1.39

0.580 0.614 0.653 0.696 0.765

0.386 0.409 0.434 0.463 0.509

32 34 36 38 40

2.10 2.37 2.66 2.96 3.28

1.40 1.58 1.77 1.97 2.18

0.691 0.751 0.812 0.872 0.932

0.460 0.500 0.540 0.580 0.620

1.07 1.19 1.32 1.47 1.63

0.713 0.789 0.880 0.981 1.09

0.515 0.537 0.562 0.588 0.631

0.343 0.357 0.374 0.391 0.420

2.38 2.69 3.01 3.36 3.72

1.58 1.79 2.00 2.23 2.48

0.841 0.917 0.993 1.07 1.15

0.559 0.610 0.661 0.712 0.763

42 44 46 48 50

3.62

2.41

0.992 0.660 1.80 1.98 2.16 2.35 2.55

1.20 1.31 1.44 1.56 1.70

0.680 0.729 0.778 0.828 0.878

0.452 4.10 0.485 0.518 0.551 0.584

2.73

1.220 0.814

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

2.92 0.491 0.603

1.94 0.327 0.402

2.02 0.490 0.602

1.35 0.326 0.401

3.33 0.540 0.663

2.22 0.359 0.442

rx /ry

5.65

4.07

5.66

ry , in.

2.62

3.71

2.58

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:47 AM

Page 21

STEEL BEAM-COLUMN SELECTION TABLES

6–21

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W36

W-Shapes W36×

Shape

194c

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

182c

bx × 10

3

p × 10

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

(kips) ASD

170c

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.618 0.411 0.464 0.309 0.669 0.445 0.496 0.330 0.732 0.487 0.533 0.355

11 12 13 14 15

0.725 0.749 0.775 0.806 0.841

0.483 0.498 0.516 0.536 0.560

0.485 0.496 0.507 0.519 0.532

0.322 0.330 0.337 0.345 0.354

0.783 0.808 0.837 0.869 0.905

0.521 0.538 0.557 0.578 0.602

0.519 0.531 0.544 0.557 0.571

0.345 0.353 0.362 0.371 0.380

0.856 0.883 0.913 0.948 0.988

0.569 0.587 0.608 0.631 0.657

0.559 0.573 0.587 0.602 0.617

0.372 0.381 0.390 0.400 0.411

16 17 18 19 20

0.884 0.932 0.986 1.05 1.11

0.588 0.620 0.656 0.696 0.741

0.545 0.559 0.574 0.589 0.606

0.363 0.372 0.382 0.392 0.403

0.947 0.995 1.05 1.12 1.19

0.630 0.662 0.701 0.744 0.792

0.586 0.601 0.618 0.635 0.653

0.390 0.400 0.411 0.422 0.435

1.03 1.08 1.14 1.21 1.29

0.687 0.721 0.760 0.805 0.858

0.634 0.651 0.670 0.689 0.710

0.422 0.433 0.445 0.458 0.472

22 24 26 28 30

1.28 1.48 1.73 2.01 2.31

0.848 0.984 1.15 1.34 1.54

0.641 0.681 0.726 0.786 0.873

0.427 0.453 0.483 0.523 0.581

1.36 1.58 1.86 2.16 2.47

0.908 1.05 1.24 1.43 1.65

0.693 0.738 0.789 0.868 0.966

0.461 0.491 0.525 0.577 0.642

1.48 1.72 2.02 2.35 2.69

0.985 1.15 1.35 1.56 1.79

0.755 0.806 0.864 0.966 1.08

0.502 0.536 0.575 0.643 0.717

32 34 36 38 40

2.63 2.96 3.32 3.70 4.10

1.75 1.97 2.21 2.46 2.73

0.961 1.05 1.14 1.23 1.32

0.639 0.699 0.758 0.818 0.878

2.81 3.18 3.56 3.97 4.40

1.87 2.11 2.37 2.64 2.93

1.07 1.17 1.27 1.37 1.47

0.709 0.775 0.843 0.911 0.979

3.07 3.46 3.88 4.32 4.79

2.04 2.30 2.58 2.88 3.19

1.19 1.31 1.42 1.54 1.66

0.792 0.869 0.946 1.02 1.10

42

4.52

3.01

1.41

0.938 4.85

3.23

1.57

1.05

5.28

3.51

1.77

1.18

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

3.65 0.586 0.720

2.43 0.390 0.480

3.93 0.623 0.765

2.61 0.415 0.510

4.25 0.668 0.821

2.83 0.444 0.547

rx /ry

5.70

5.69

5.73

ry , in.

2.56

2.55

2.53

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:47 AM

6–22

Page 22

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W36

W-Shapes W36×

Shape

160c

p × 10 Design

(kips) ASD 0

150c

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10

3

–1

(kips) ASD

135c, v

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.791 0.526 0.571 0.380 0.851 0.566 0.613 0.408 0.967 0.643 0.700 0.466

11 12 13 14 15

0.925 0.955 0.988 1.03 1.07

0.616 0.635 0.657 0.683 0.711

0.601 0.616 0.632 0.648 0.666

0.400 0.410 0.420 0.431 0.443

0.997 1.03 1.06 1.11 1.15

0.663 0.684 0.709 0.736 0.767

0.648 0.665 0.682 0.701 0.721

0.431 0.442 0.454 0.466 0.479

1.14 1.18 1.22 1.27 1.33

0.758 0.783 0.812 0.845 0.883

0.748 0.769 0.791 0.814 0.838

0.498 0.512 0.526 0.541 0.558

16 17 18 19 20

1.12 1.17 1.24 1.31 1.39

0.744 0.781 0.824 0.872 0.928

0.684 0.703 0.724 0.746 0.769

0.455 0.468 0.482 0.496 0.511

1.21 1.27 1.34 1.42 1.51

0.803 0.844 0.890 0.943 1.00

0.741 0.763 0.786 0.811 0.837

0.493 0.508 0.523 0.540 0.557

1.39 1.47 1.55 1.65 1.77

0.927 0.977 1.03 1.10 1.18

0.864 0.892 0.921 0.952 0.986

0.575 0.593 0.613 0.634 0.656

22 24 26 28 30

1.61 1.88 2.20 2.56 2.94

1.07 1.25 1.47 1.70 1.95

0.820 0.878 0.950 1.07 1.20

0.545 0.584 0.632 0.714 0.797

1.74 2.04 2.40 2.78 3.19

1.16 1.36 1.59 1.85 2.12

0.895 0.962 1.06 1.20 1.34

0.596 0.640 0.706 0.799 0.894

2.06 2.44 2.87 3.32 3.82

1.37 1.62 1.91 2.21 2.54

1.06 1.15 1.31 1.49 1.67

0.706 0.763 0.871 0.989 1.11

32 34 36 38 40

3.34 3.77 4.23 4.71 5.22

2.22 2.51 2.81 3.13 3.47

1.33 1.46 1.59 1.72 1.86

0.883 0.969 1.06 1.15 1.23

3.63 4.10 4.59 5.12 5.67

2.42 2.73 3.06 3.41 3.77

1.49 1.64 1.79 1.94 2.10

0.991 1.09 1.19 1.29 1.40

4.34 4.90 5.49 6.12

2.89 3.26 3.66 4.07

1.85 2.05 2.24 2.44

1.23 1.36 1.49 1.62

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

4.61 0.711 0.873

3.07 0.473 0.582

5.02 0.754 0.926

3.34 0.502 0.617

5.97 0.837 1.030

3.97 0.557 0.685

rx /ry

5.76

5.79

5.88

ry , in.

2.50

2.47

2.38

Shape is slender for compression with Fy = 50 ksi. v Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:47 AM

Page 23

STEEL BEAM-COLUMN SELECTION TABLES

6–23

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W33

W-Shapes W33×

Shape

387h

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

354h

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

318

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.293 0.195 0.228 0.152 0.321 0.214 0.251 0.167 0.356 0.237 0.281 0.187

11 12 13 14 15

0.320 0.326 0.332 0.339 0.346

0.213 0.217 0.221 0.225 0.230

0.228 0.228 0.228 0.230 0.232

0.152 0.152 0.152 0.153 0.155

0.352 0.358 0.365 0.372 0.380

0.234 0.238 0.243 0.248 0.253

0.251 0.251 0.251 0.253 0.256

0.167 0.167 0.167 0.168 0.170

0.391 0.398 0.406 0.414 0.423

0.260 0.265 0.270 0.276 0.282

0.281 0.281 0.281 0.283 0.287

0.187 0.187 0.187 0.189 0.191

16 17 18 19 20

0.354 0.363 0.372 0.383 0.394

0.236 0.241 0.248 0.255 0.262

0.235 0.237 0.239 0.242 0.244

0.156 0.158 0.159 0.161 0.163

0.389 0.399 0.410 0.421 0.434

0.259 0.266 0.273 0.280 0.289

0.259 0.261 0.264 0.267 0.270

0.172 0.174 0.176 0.178 0.180

0.434 0.445 0.457 0.470 0.484

0.288 0.296 0.304 0.313 0.322

0.290 0.294 0.297 0.301 0.305

0.193 0.195 0.198 0.200 0.203

22 24 26 28 30

0.419 0.449 0.483 0.524 0.571

0.279 0.299 0.322 0.348 0.380

0.250 0.255 0.261 0.267 0.273

0.166 0.170 0.174 0.178 0.182

0.462 0.495 0.534 0.579 0.632

0.308 0.330 0.355 0.386 0.421

0.277 0.283 0.290 0.298 0.305

0.184 0.189 0.193 0.198 0.203

0.516 0.554 0.598 0.649 0.710

0.343 0.368 0.398 0.432 0.472

0.313 0.321 0.330 0.339 0.349

0.208 0.214 0.220 0.226 0.232

32 34 36 38 40

0.626 0.690 0.766 0.854 0.946

0.416 0.459 0.510 0.568 0.629

0.280 0.287 0.294 0.302 0.310

0.186 0.191 0.196 0.201 0.206

0.694 0.767 0.854 0.951 1.05

0.462 0.510 0.568 0.633 0.701

0.313 0.322 0.331 0.340 0.351

0.208 0.214 0.220 0.227 0.233

0.780 0.863 0.963 1.07 1.19

0.519 0.574 0.641 0.714 0.791

0.359 0.370 0.382 0.395 0.408

0.239 0.246 0.254 0.263 0.271

42 44 46 48 50

1.04 1.14 1.25 1.36 1.48

0.694 0.762 0.832 0.906 0.984

0.318 0.327 0.337 0.347 0.358

0.212 0.218 0.224 0.231 0.238

1.16 1.28 1.39 1.52 1.65

0.773 0.848 0.927 1.01 1.10

0.361 0.373 0.385 0.398 0.412

0.240 0.248 0.256 0.265 0.274

1.31 1.44 1.57 1.71 1.86

0.872 0.957 1.05 1.14 1.24

0.422 0.438 0.454 0.477 0.502

0.281 0.291 0.302 0.318 0.334

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

rx /ry ry , in. h

1.14 0.293 0.360

0.760 0.195 0.240

1.26 0.321 0.394

0.841 0.214 0.263

1.43 0.356 0.438

0.948 0.237 0.292

3.87

3.88

3.91

3.77

3.74

3.71

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:47 AM

6–24

Page 24

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W33

W-Shapes W33×

Shape

291

p × 10 Design

(kips) ASD 0

3

–1

(kip-ft)

LRFD

241c

263

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

ASD

–1

LRFD

p × 10

bx × 10

3

3

–1

(kips) ASD

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.390 0.260 0.307 0.204 0.432 0.287 0.343 0.228 0.471 0.313 0.379 0.252

11 12 13 14 15

0.429 0.436 0.445 0.454 0.465

0.285 0.290 0.296 0.302 0.309

0.307 0.307 0.307 0.311 0.315

0.204 0.204 0.204 0.207 0.210

0.475 0.483 0.493 0.503 0.515

0.316 0.322 0.328 0.335 0.343

0.343 0.343 0.343 0.348 0.352

0.228 0.228 0.228 0.231 0.234

0.518 0.527 0.538 0.550 0.563

0.344 0.351 0.358 0.366 0.374

0.379 0.379 0.380 0.386 0.391

0.252 0.252 0.253 0.257 0.260

16 17 18 19 20

0.476 0.488 0.502 0.517 0.533

0.317 0.325 0.334 0.344 0.354

0.319 0.323 0.328 0.332 0.337

0.212 0.215 0.218 0.221 0.224

0.528 0.542 0.557 0.573 0.591

0.351 0.360 0.370 0.381 0.393

0.357 0.362 0.367 0.373 0.378

0.238 0.241 0.244 0.248 0.252

0.577 0.593 0.609 0.628 0.648

0.384 0.394 0.405 0.418 0.431

0.397 0.403 0.409 0.416 0.422

0.264 0.268 0.272 0.276 0.281

22 24 26 28 30

0.568 0.611 0.660 0.718 0.786

0.378 0.406 0.439 0.478 0.523

0.346 0.356 0.367 0.378 0.390

0.230 0.237 0.244 0.251 0.259

0.631 0.679 0.734 0.799 0.875

0.420 0.452 0.488 0.532 0.582

0.390 0.402 0.415 0.428 0.443

0.259 0.267 0.276 0.285 0.295

0.693 0.746 0.809 0.882 0.968

0.461 0.496 0.538 0.587 0.644

0.436 0.450 0.466 0.483 0.501

0.290 0.300 0.310 0.321 0.333

32 34 36 38 40

0.865 0.959 1.07 1.19 1.32

0.576 0.638 0.713 0.794 0.880

0.403 0.416 0.431 0.447 0.463

0.268 0.277 0.287 0.297 0.308

0.965 1.07 1.20 1.33 1.48

0.642 0.712 0.797 0.888 0.984

0.459 0.476 0.494 0.514 0.535

0.305 0.317 0.329 0.342 0.356

1.07 1.19 1.33 1.48 1.65

0.712 0.791 0.887 0.988 1.09

0.520 0.541 0.564 0.589 0.619

0.346 0.360 0.375 0.392 0.412

42 44 46 48 50

1.46 1.60 1.75 1.90 2.07

0.970 1.06 1.16 1.27 1.37

0.482 0.503 0.533 0.563 0.592

0.320 0.335 0.354 0.374 0.394

1.63 1.79 1.96 2.13 2.31

1.08 1.19 1.30 1.42 1.54

0.562 0.598 0.635 0.672 0.708

0.374 0.398 0.422 0.447 0.471

1.81 1.99 2.18 2.37 2.57

1.21 1.32 1.45 1.58 1.71

0.663 0.708 0.753 0.797 0.842

0.441 0.471 0.501 0.530 0.560

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

c

–1

1.58 0.390 0.479

1.05 0.260 0.320

1.76 0.432 0.530

1.17 0.287 0.353

1.96 0.470 0.577

1.30 0.313 0.385

rx /ry

3.91

3.91

3.90

ry , in.

3.68

3.66

3.62

Shape is slender for compression with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:47 AM

Page 25

STEEL BEAM-COLUMN SELECTION TABLES

6–25

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W33

W-Shapes W33×

Shape

221c

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

201c

bx × 10

3

p × 10

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

(kips) ASD

169c

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.522 0.347 0.416 0.277 0.588 0.391 0.461 0.307 0.720 0.479 0.566 0.377

11 12 13 14 15

0.568 0.578 0.588 0.600 0.615

0.378 0.384 0.391 0.399 0.409

0.416 0.416 0.418 0.424 0.431

0.277 0.277 0.278 0.282 0.286

0.640 0.651 0.663 0.676 0.690

0.426 0.433 0.441 0.450 0.459

0.461 0.461 0.464 0.471 0.479

0.307 0.307 0.309 0.314 0.319

0.851 0.880 0.913 0.950 0.992

0.566 0.586 0.607 0.632 0.660

0.595 0.608 0.623 0.638 0.654

0.396 0.405 0.415 0.425 0.435

16 17 18 19 20

0.630 0.648 0.666 0.687 0.709

0.419 0.431 0.443 0.457 0.472

0.437 0.444 0.451 0.459 0.467

0.291 0.296 0.300 0.305 0.310

0.706 0.724 0.743 0.764 0.788

0.470 0.482 0.494 0.508 0.524

0.487 0.495 0.504 0.512 0.522

0.324 0.329 0.335 0.341 0.347

1.04 1.10 1.16 1.24 1.32

0.692 0.731 0.775 0.825 0.881

0.671 0.689 0.708 0.728 0.749

0.447 0.458 0.471 0.484 0.498

22 24 26 28 30

0.760 0.819 0.889 0.970 1.07

0.505 0.545 0.591 0.646 0.710

0.483 0.500 0.519 0.539 0.560

0.321 0.333 0.345 0.358 0.373

0.845 0.912 0.991 1.08 1.19

0.562 0.607 0.659 0.721 0.794

0.541 0.561 0.584 0.608 0.634

0.360 0.374 0.388 0.404 0.422

1.52 1.78 2.09 2.43 2.79

1.01 1.19 1.39 1.62 1.85

0.794 0.846 0.905 0.999 1.11

0.528 0.563 0.602 0.664 0.737

32 34 36 38 40

1.18 1.32 1.48 1.64 1.82

0.786 0.876 0.982 1.09 1.21

0.584 0.609 0.637 0.667 0.719

0.388 0.405 0.424 0.444 0.478

1.32 1.48 1.66 1.85 2.05

0.880 0.984 1.10 1.23 1.36

0.663 0.694 0.728 0.782 0.846

0.441 0.462 0.484 0.520 0.563

3.17 3.58 4.01 4.47 4.95

2.11 2.38 2.67 2.98 3.30

1.21 1.33 1.44 1.55 1.66

0.810 0.883 0.957 1.03 1.10

42 44 46 48 50

2.01 2.20 2.41 2.62 2.85

1.34 1.47 1.60 1.75 1.89

0.772 0.825 0.879 0.932 0.986

0.514 0.549 0.585 0.620 0.656

2.26 2.48 2.71 2.95 3.20

1.50 1.65 1.80 1.96 2.13

0.910 0.975 1.04 1.11 1.17

0.606 0.649 0.692 0.736 0.780

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

2.17 0.511 0.628

1.45 0.340 0.419

2.42 0.565 0.694

1.61 0.376 0.463

4.22 0.675 0.829

2.81 0.449 0.553

rx /ry

3.93

3.93

5.48

ry , in.

3.59

3.56

2.50

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:47 AM

6–26

Page 26

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W33

W-Shapes W33×

Shape

152c

p × 10 Design

(kips) ASD 0

141c

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

p × 10

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

–1

(kips) ASD

130c

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.809 0.538 0.637 0.424 0.891 0.593 0.693 0.461 0.982 0.654 0.763 0.508

11 12 13 14 15

0.956 0.988 1.03 1.07 1.11

0.636 0.658 0.682 0.710 0.742

0.673 0.689 0.707 0.725 0.745

0.447 0.459 0.470 0.483 0.496

1.05 1.09 1.13 1.18 1.23

0.702 0.726 0.753 0.784 0.820

0.735 0.754 0.774 0.796 0.818

0.489 0.502 0.515 0.529 0.544

1.16 1.20 1.25 1.30 1.36

0.775 0.801 0.832 0.867 0.907

0.814 0.837 0.860 0.885 0.911

0.542 0.557 0.572 0.589 0.606

16 17 18 19 20

1.17 1.23 1.30 1.39 1.48

0.778 0.819 0.866 0.923 0.987

0.765 0.787 0.810 0.834 0.860

0.509 0.524 0.539 0.555 0.572

1.29 1.36 1.44 1.53 1.64

0.860 0.907 0.960 1.02 1.09

0.841 0.866 0.893 0.921 0.951

0.560 0.576 0.594 0.613 0.633

1.43 1.51 1.60 1.70 1.82

0.952 1.00 1.06 1.13 1.21

0.939 0.968 0.999 1.03 1.07

0.624 0.644 0.665 0.687 0.711

22 24 26 28 30

1.71 2.01 2.36 2.74 3.15

1.14 1.34 1.57 1.82 2.09

0.917 0.982 1.07 1.20 1.33

0.610 0.653 0.709 0.798 0.888

1.91 2.25 2.64 3.07 3.52

1.27 1.50 1.76 2.04 2.34

1.02 1.09 1.21 1.37 1.53

0.677 0.728 0.808 0.911 1.02

2.13 2.52 2.96 3.43 3.94

1.42 1.68 1.97 2.28 2.62

1.15 1.24 1.41 1.60 1.78

0.764 0.826 0.939 1.06 1.19

32 34 36 38 40

3.58 4.04 4.53 5.05 5.60

2.38 2.69 3.02 3.36 3.72

1.47 1.61 1.75 1.89 2.03

0.979 1.07 1.16 1.26 1.35

4.00 4.52 5.07 5.65 6.26

2.66 3.01 3.37 3.76 4.16

1.69 1.85 2.02 2.18 2.35

1.12 1.23 1.34 1.45 1.56

4.48 5.06 5.68 6.32

2.98 3.37 3.78 4.21

1.98 2.17 2.37 2.57

1.32 1.45 1.58 1.71

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

4.82 0.744 0.914

3.21 0.495 0.609

5.33 0.805 0.989

3.54 0.535 0.659

5.99 0.872 1.07

3.98 0.580 0.714

rx /ry

5.47

5.51

5.52

ry , in.

2.47

2.43

2.39

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:47 AM

Page 27

STEEL BEAM-COLUMN SELECTION TABLES

6–27

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W33-W30

W-Shapes W33×

Shape

p × 10 Design

(kips)

391h

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

W30×

118c, v 3

–1

(kip-ft) ASD

–1

LRFD

p × 10 (kips)

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips)

ASD

LRFD

0

1.11

0.738 0.858 0.571 0.290 0.193 0.246 0.163 0.318 0.212 0.270 0.180

11 12 13 14 15

1.32 1.37 1.42 1.48 1.56

0.879 0.910 0.946 0.988 1.03

0.926 0.952 0.980 1.01 1.04

0.616 0.634 0.652 0.672 0.693

0.319 0.325 0.331 0.339 0.346

0.212 0.216 0.221 0.225 0.230

0.246 0.246 0.246 0.248 0.250

0.163 0.163 0.164 0.165 0.166

0.350 0.357 0.364 0.372 0.380

0.233 0.237 0.242 0.247 0.253

0.270 0.270 0.270 0.273 0.276

0.180 0.180 0.180 0.182 0.183

16 17 18 19 20

1.64 1.73 1.84 1.96 2.11

1.09 1.15 1.22 1.31 1.40

1.08 1.11 1.15 1.19 1.24

0.716 0.740 0.765 0.793 0.822

0.355 0.364 0.374 0.385 0.397

0.236 0.242 0.249 0.256 0.264

0.252 0.255 0.257 0.259 0.262

0.168 0.169 0.171 0.172 0.174

0.390 0.400 0.412 0.424 0.437

0.259 0.266 0.274 0.282 0.291

0.278 0.281 0.284 0.287 0.290

0.185 0.187 0.189 0.191 0.193

22 24 26 28 30

2.48 2.95 3.47 4.02 4.62

1.65 1.97 2.31 2.68 3.07

1.34 1.48 1.70 1.92 2.16

0.888 0.984 1.13 1.28 1.44

0.424 0.456 0.493 0.536 0.587

0.282 0.303 0.328 0.357 0.391

0.267 0.272 0.277 0.282 0.288

0.177 0.181 0.184 0.188 0.192

0.467 0.503 0.544 0.593 0.650

0.311 0.334 0.362 0.395 0.433

0.296 0.302 0.308 0.315 0.322

0.197 0.201 0.205 0.210 0.215

32 34 36 38 40

5.25 5.93 6.65 7.41

3.49 3.95 4.42 4.93

2.40 2.64 2.89 3.14

1.59 1.76 1.92 2.09

0.647 0.717 0.802 0.893 0.990

0.430 0.477 0.533 0.594 0.658

0.294 0.300 0.307 0.314 0.321

0.196 0.200 0.204 0.209 0.213

0.718 0.797 0.892 0.994 1.10

0.478 0.530 0.594 0.662 0.733

0.330 0.338 0.346 0.355 0.364

0.220 0.225 0.230 0.236 0.242

1.09 1.20 1.31 1.43 1.55

0.726 0.797 0.871 0.948 1.03

0.328 0.336 0.344 0.353 0.362

0.218 0.224 0.229 0.235 0.241

1.21 1.33 1.46 1.59 1.72

0.808 0.887 0.969 1.06 1.15

0.373 0.383 0.394 0.405 0.417

0.248 0.255 0.262 0.270 0.278

42 44 46 48 50

ASD

357h

bx × 10

3

ASD

LRFD

ASD

LRFD

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

6.94 0.963 1.18

4.62 0.640 0.788

1.15 0.290 0.357

0.765 0.193 0.238

1.28 0.318 0.391

0.850 0.212 0.260

rx /ry

5.60

3.65

3.65

ry , in.

3.32

3.67

3.64

Shape is slender for compression with Fy = 50 ksi. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. v Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:47 AM

6–28

Page 28

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W30

W-Shapes W30×

Shape

326h

p × 10 Design

(kips) ASD 0

292

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10

3

–1

(kips) ASD

261

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.348 0.232 0.299 0.199 0.388 0.258 0.336 0.224 0.434 0.289 0.378 0.251

11 12 13 14 15

0.384 0.392 0.400 0.408 0.418

0.256 0.260 0.266 0.272 0.278

0.299 0.299 0.300 0.303 0.307

0.199 0.199 0.200 0.202 0.204

0.429 0.437 0.446 0.456 0.467

0.285 0.291 0.297 0.304 0.311

0.336 0.336 0.337 0.341 0.345

0.224 0.224 0.225 0.227 0.230

0.480 0.490 0.500 0.512 0.525

0.320 0.326 0.333 0.341 0.349

0.378 0.378 0.380 0.385 0.390

0.251 0.251 0.253 0.256 0.260

16 17 18 19 20

0.429 0.440 0.453 0.467 0.482

0.285 0.293 0.301 0.311 0.321

0.310 0.313 0.317 0.320 0.324

0.206 0.208 0.211 0.213 0.215

0.479 0.492 0.507 0.522 0.539

0.319 0.328 0.337 0.348 0.359

0.349 0.353 0.358 0.362 0.366

0.232 0.235 0.238 0.241 0.244

0.539 0.554 0.570 0.588 0.608

0.358 0.368 0.379 0.392 0.405

0.395 0.400 0.406 0.411 0.417

0.263 0.266 0.270 0.274 0.277

22 24 26 28 30

0.516 0.556 0.603 0.658 0.724

0.343 0.370 0.401 0.438 0.481

0.331 0.339 0.347 0.355 0.364

0.220 0.225 0.231 0.236 0.242

0.578 0.623 0.677 0.740 0.813

0.385 0.415 0.450 0.492 0.541

0.376 0.385 0.396 0.406 0.418

0.250 0.256 0.263 0.270 0.278

0.653 0.706 0.768 0.841 0.928

0.434 0.470 0.511 0.560 0.617

0.429 0.441 0.454 0.468 0.483

0.285 0.294 0.302 0.312 0.322

32 34 36 38 40

0.800 0.891 0.999 1.11 1.23

0.532 0.593 0.665 0.741 0.821

0.373 0.383 0.393 0.404 0.416

0.248 0.255 0.262 0.269 0.277

0.901 1.00 1.13 1.26 1.39

0.599 0.669 0.749 0.835 0.925

0.430 0.443 0.456 0.471 0.486

0.286 0.295 0.304 0.313 0.323

1.03 1.15 1.29 1.44 1.60

0.686 0.768 0.861 0.959 1.06

0.499 0.516 0.534 0.554 0.575

0.332 0.343 0.356 0.368 0.382

42 44 46 48 50

1.36 1.49 1.63 1.78 1.93

0.905 0.993 1.09 1.18 1.28

0.428 0.441 0.454 0.469 0.485

0.285 0.293 0.302 0.312 0.322

1.53 1.68 1.84 2.00 2.17

1.02 1.12 1.22 1.33 1.45

0.502 0.520 0.539 0.564 0.592

0.334 0.346 0.358 0.375 0.394

1.76 1.93 2.11 2.30 2.50

1.17 1.29 1.41 1.53 1.66

0.597 0.626 0.662 0.698 0.734

0.398 0.416 0.440 0.464 0.488

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

h

–1

1.41 0.348 0.428

0.941 0.232 0.285

1.60 0.388 0.477

1.06 0.258 0.318

1.82 0.434 0.533

1.21 0.289 0.355

rx /ry

3.67

3.69

3.71

ry , in.

3.60

3.58

3.53

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:47 AM

Page 29

STEEL BEAM-COLUMN SELECTION TABLES

6–29

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W30

W-Shapes W30×

Shape

235

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

3

–1

(kip-ft)

LRFD

191c

211

bx × 10

3

ASD

–1

LRFD

p × 10

bx × 10

3

(kips) ASD

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.482 0.321 0.421 0.280 0.536 0.357 0.474 0.316 0.604 0.402 0.528 0.351

11 12 13 14 15

0.534 0.545 0.557 0.570 0.584

0.356 0.363 0.370 0.379 0.389

0.421 0.421 0.424 0.430 0.436

0.280 0.280 0.282 0.286 0.290

0.595 0.607 0.620 0.635 0.651

0.396 0.404 0.413 0.423 0.433

0.474 0.474 0.479 0.486 0.493

0.316 0.316 0.319 0.323 0.328

0.663 0.676 0.691 0.707 0.726

0.441 0.450 0.460 0.471 0.483

0.528 0.528 0.534 0.543 0.551

0.351 0.351 0.355 0.361 0.367

16 17 18 19 20

0.600 0.617 0.636 0.656 0.678

0.399 0.411 0.423 0.437 0.451

0.442 0.448 0.455 0.461 0.468

0.294 0.298 0.302 0.307 0.311

0.669 0.688 0.709 0.732 0.758

0.445 0.458 0.472 0.487 0.504

0.501 0.509 0.517 0.525 0.533

0.333 0.338 0.344 0.349 0.355

0.746 0.768 0.792 0.818 0.846

0.496 0.511 0.527 0.544 0.563

0.560 0.570 0.579 0.589 0.599

0.373 0.379 0.385 0.392 0.399

22 24 26 28 30

0.729 0.788 0.859 0.942 1.04

0.485 0.525 0.571 0.627 0.692

0.483 0.498 0.514 0.531 0.550

0.321 0.331 0.342 0.354 0.366

0.815 0.882 0.962 1.06 1.17

0.542 0.587 0.640 0.702 0.777

0.551 0.570 0.591 0.613 0.636

0.367 0.379 0.393 0.408 0.423

0.911 0.988 1.08 1.19 1.31

0.606 0.657 0.718 0.789 0.874

0.621 0.644 0.669 0.696 0.726

0.413 0.429 0.445 0.463 0.483

32 34 36 38 40

1.16 1.30 1.45 1.62 1.80

0.769 0.863 0.968 1.08 1.19

0.570 0.591 0.614 0.639 0.666

0.379 0.393 0.409 0.425 0.443

1.30 1.46 1.64 1.83 2.02

0.864 0.971 1.09 1.21 1.34

0.662 0.690 0.720 0.753 0.802

0.440 0.459 0.479 0.501 0.533

1.47 1.65 1.85 2.06 2.28

0.975 1.10 1.23 1.37 1.52

0.758 0.793 0.831 0.889 0.957

0.504 0.527 0.553 0.591 0.637

42 44 46 48 50

1.98 2.17 2.37 2.59 2.81

1.32 1.45 1.58 1.72 1.87

0.704 0.748 0.792 0.837 0.881

0.468 0.498 0.527 0.557 0.586

2.23 2.44 2.67 2.91 3.16

1.48 1.63 1.78 1.94 2.10

0.858 0.914 0.970 1.03 1.08

0.571 0.608 0.645 0.683 0.720

2.52 2.76 3.02 3.29 3.57

1.67 1.84 2.01 2.19 2.37

1.03 1.10 1.16 1.23 1.30

0.683 0.729 0.775 0.821 0.867

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

c

–1

2.04 0.482 0.592

1.35 0.321 0.395

2.30 0.536 0.659

1.53 0.357 0.439

2.58 0.595 0.731

1.72 0.396 0.488

rx /ry

3.70

3.70

3.70

ry , in.

3.51

3.49

3.46

Shape is slender for compression with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:48 AM

6–30

Page 30

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W30

W-Shapes W30×

Shape

173c

p × 10 Design

(kips) ASD 0

148c

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

p × 10

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

–1

(kips) ASD

132c

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.678 0.451 0.587 0.391 0.801 0.533 0.713 0.474 0.917 0.610 0.815 0.542

11 12 13 14 15

0.745 0.758 0.773 0.790 0.809

0.495 0.505 0.515 0.526 0.538

0.587 0.587 0.596 0.606 0.616

0.391 0.391 0.396 0.403 0.410

0.986 1.03 1.08 1.14 1.21

0.656 0.684 0.718 0.758 0.804

0.765 0.784 0.804 0.826 0.849

0.509 0.522 0.535 0.550 0.565

1.13 1.18 1.23 1.30 1.37

0.751 0.783 0.819 0.862 0.915

0.882 0.906 0.931 0.958 0.987

0.587 0.603 0.620 0.638 0.657

16 17 18 19 20

0.829 0.852 0.878 0.908 0.941

0.552 0.567 0.584 0.604 0.626

0.626 0.637 0.649 0.660 0.673

0.417 0.424 0.432 0.439 0.447

1.29 1.38 1.48 1.59 1.72

0.856 0.915 0.982 1.06 1.15

0.873 0.898 0.925 0.954 0.984

0.581 0.598 0.616 0.635 0.655

1.47 1.57 1.69 1.82 1.98

0.975 1.04 1.12 1.21 1.32

1.02 1.05 1.08 1.12 1.16

0.677 0.699 0.721 0.746 0.772

22 24 26 28 30

1.01 1.10 1.21 1.33 1.48

0.675 0.733 0.802 0.884 0.982

0.698 0.726 0.756 0.789 0.825

0.465 0.483 0.503 0.525 0.549

2.05 2.43 2.86 3.31 3.80

1.36 1.62 1.90 2.20 2.53

1.05 1.13 1.25 1.39 1.53

0.700 0.751 0.828 0.923 1.02

2.36 2.81 3.30 3.82 4.39

1.57 1.87 2.19 2.54 2.92

1.25 1.36 1.54 1.72 1.91

0.831 0.904 1.02 1.15 1.27

32 34 36 38 40

1.65 1.86 2.09 2.32 2.57

1.10 1.24 1.39 1.55 1.71

0.864 0.906 0.964 1.05 1.13

0.575 4.33 0.603 4.89 0.641 5.48 0.696 0.751

2.88 3.25 3.64

1.67 1.82 1.96

1.11 1.21 1.30

4.99 5.64 6.32

3.32 3.75 4.21

2.09 2.28 2.47

1.39 1.52 1.64

42 44 46 48 50

2.84 3.12 3.41 3.71 4.02

1.89 2.07 2.27 2.47 2.68

1.21 1.30 1.38 1.47 1.55

0.807 0.863 0.919 0.976 1.03 Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

2.90 0.656 0.806

1.93 0.437 0.537

5.24 0.766 0.941

3.49 0.510 0.627

6.10 0.861 1.06

4.06 0.573 0.705

rx /ry

3.71

5.44

5.42

ry , in.

3.42

2.28

2.25

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:48 AM

Page 31

STEEL BEAM-COLUMN SELECTION TABLES

6–31

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W30

W-Shapes W30×

Shape

124c

p × 10 Design

(kips) ASD

p × 10

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

(kips) ASD

108c

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips)

ASD

LRFD

0.991 0.659 0.873 0.581 1.07

0.713 0.943 0.627 1.17

0.782 1.03

0.685

11 12 13 14 15

1.22 1.27 1.33 1.40 1.48

0.811 0.845 0.885 0.931 0.984

0.949 0.976 1.00 1.03 1.07

0.631 0.649 0.668 0.688 0.710

1.32 1.38 1.45 1.52 1.61

0.880 0.918 0.962 1.01 1.07

1.03 1.06 1.09 1.13 1.16

0.686 0.706 0.728 0.750 0.775

1.45 1.52 1.59 1.68 1.78

0.968 1.01 1.06 1.12 1.18

1.14 1.17 1.21 1.25 1.29

0.755 0.779 0.804 0.830 0.859

16 17 18 19 20

1.57 1.69 1.82 1.97 2.13

1.05 1.12 1.21 1.31 1.42

1.10 1.14 1.18 1.22 1.26

0.732 0.757 0.782 0.810 0.840

1.72 1.84 1.99 2.16 2.35

1.14 1.23 1.32 1.44 1.56

1.20 1.24 1.29 1.34 1.39

0.801 0.828 0.858 0.890 0.924

1.90 2.04 2.20 2.40 2.62

1.26 1.35 1.47 1.60 1.74

1.34 1.39 1.44 1.50 1.56

0.889 0.922 0.957 0.995 1.04

22 24 26 28 30

2.55 3.04 3.57 4.14 4.75

1.70 2.02 2.37 2.75 3.16

1.36 1.51 1.72 1.92 2.13

0.907 1.01 1.14 1.28 1.42

2.83 3.36 3.95 4.58 5.26

1.88 2.24 2.63 3.05 3.50

1.51 1.70 1.94 2.18 2.42

1.00 1.13 1.29 1.45 1.61

3.16 3.77 4.42 5.13 5.88

2.11 2.51 2.94 3.41 3.91

1.70 1.96 2.24 2.52 2.81

1.13 1.31 1.49 1.68 1.87

32 34 36

5.40 6.10 6.84

3.60 4.06 4.55

2.35 2.56 2.78

1.56 1.70 1.85

5.98 6.75 7.57

3.98 4.49 5.04

2.67 2.92 3.17

1.78 1.94 2.11

6.69 7.56

4.45 5.03

3.10 3.40

2.06 2.26

0

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

116c

bx × 10

3

ASD

LRFD

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

6.60 0.915 1.12

4.39 0.609 0.749

7.24 0.977 1.20

4.82 0.650 0.800

8.12 1.05 1.29

5.40 0.701 0.863

rx /ry

5.43

5.48

5.53

ry , in.

2.23

2.19

2.15

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:48 AM

6–32

Page 32

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W30-W27

W-Shapes W30×

Shape

W27×

99c

90c, v

p × 10

bx × 10

3

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

(kips)

3

–1

(kip-ft) ASD

–1

LRFD

p × 10

3

–1

(kips) ASD

539h

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips)

bx × 103

–1

(kip-ft)–1

ASD

LRFD

0

1.31

0.872 1.14

0.760 1.49

0.994 1.26

0.838 0.210 0.140 0.189 0.125

11 12 13 14 15

1.63 1.70 1.79 1.89 2.01

1.08 1.13 1.19 1.26 1.33

1.27 1.31 1.36 1.41 1.46

0.846 0.874 0.903 0.935 0.969

1.85 1.93 2.02 2.13 2.26

1.23 1.28 1.35 1.42 1.50

1.41 1.45 1.51 1.56 1.62

0.936 0.968 1.00 1.04 1.08

0.231 0.235 0.240 0.245 0.251

0.154 0.157 0.160 0.163 0.167

0.189 0.189 0.189 0.190 0.191

0.125 0.125 0.125 0.126 0.127

16 17 18 19 20

2.14 2.30 2.50 2.73 3.00

1.43 1.53 1.66 1.81 1.99

1.51 1.57 1.63 1.70 1.78

1.01 1.04 1.09 1.13 1.18

2.41 2.59 2.79 3.04 3.34

1.60 1.72 1.86 2.02 2.22

1.68 1.75 1.82 1.90 1.99

1.12 1.16 1.21 1.27 1.32

0.257 0.264 0.271 0.279 0.288

0.171 0.176 0.181 0.186 0.192

0.192 0.193 0.194 0.195 0.196

0.128 0.128 0.129 0.130 0.131

22 24 26 28 30

3.63 4.31 5.06 5.87 6.74

2.41 2.87 3.37 3.91 4.49

2.00 2.32 2.65 2.99 3.34

1.33 1.54 1.76 1.99 2.22

4.04 4.80 5.64 6.54 7.51

2.69 3.20 3.75 4.35 4.99

2.28 2.65 3.04 3.44 3.85

1.52 1.76 2.02 2.29 2.56

0.308 0.331 0.358 0.390 0.428

0.205 0.220 0.238 0.260 0.285

0.199 0.201 0.203 0.206 0.208

0.132 0.134 0.135 0.137 0.139

32 34 36 38 40

7.67 8.66

5.10 5.76

3.69 4.06

2.46 2.70

8.54 9.64

5.68 6.41

4.27 4.70

2.84 3.13

0.472 0.524 0.586 0.653 0.724

0.314 0.348 0.390 0.435 0.481

0.211 0.213 0.216 0.219 0.222

0.140 0.142 0.144 0.146 0.148

0.798 0.876 0.957 1.04 1.13

0.531 0.583 0.637 0.693 0.752

0.225 0.228 0.231 0.234 0.237

0.149 0.151 0.154 0.156 0.158

42 44 46 48 50

ASD

3

LRFD

ASD

LRFD

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

9.23 1.15 1.41

6.14 0.766 0.943

10.3 1.27 1.56

6.83 0.845 1.04

0.815 0.210 0.258

0.542 0.140 0.172

rx /ry

5.57

5.60

3.48

ry , in.

2.10

2.09

3.65

Shape is slender for compression with Fy = 50 ksi. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. v Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:48 AM

Page 33

STEEL BEAM-COLUMN SELECTION TABLES

6–33

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W27

W-Shapes W27×

Shape

368h

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

336h

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

307h

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.306 0.204 0.287 0.191 0.337 0.224 0.315 0.210 0.370 0.246 0.346 0.230

11 12 13 14 15

0.340 0.347 0.355 0.363 0.373

0.226 0.231 0.236 0.242 0.248

0.287 0.287 0.289 0.291 0.294

0.191 0.191 0.192 0.194 0.195

0.375 0.382 0.391 0.400 0.411

0.249 0.254 0.260 0.266 0.273

0.315 0.315 0.318 0.320 0.323

0.210 0.210 0.211 0.213 0.215

0.413 0.422 0.432 0.442 0.454

0.275 0.281 0.287 0.294 0.302

0.346 0.346 0.349 0.353 0.356

0.230 0.230 0.232 0.235 0.237

16 17 18 19 20

0.383 0.394 0.406 0.419 0.434

0.255 0.262 0.270 0.279 0.289

0.296 0.299 0.301 0.304 0.306

0.197 0.199 0.200 0.202 0.204

0.422 0.435 0.448 0.463 0.480

0.281 0.289 0.298 0.308 0.319

0.326 0.329 0.332 0.336 0.339

0.217 0.219 0.221 0.223 0.225

0.467 0.481 0.497 0.513 0.532

0.311 0.320 0.330 0.342 0.354

0.360 0.364 0.367 0.371 0.375

0.239 0.242 0.244 0.247 0.250

22 24 26 28 30

0.467 0.506 0.552 0.606 0.670

0.311 0.336 0.367 0.403 0.446

0.312 0.317 0.323 0.329 0.335

0.207 0.211 0.215 0.219 0.223

0.517 0.560 0.612 0.674 0.746

0.344 0.373 0.407 0.448 0.497

0.345 0.352 0.359 0.367 0.375

0.230 0.234 0.239 0.244 0.249

0.574 0.624 0.683 0.753 0.836

0.382 0.415 0.454 0.501 0.557

0.383 0.392 0.401 0.410 0.420

0.255 0.261 0.267 0.273 0.279

32 34 36 38 40

0.746 0.839 0.941 1.05 1.16

0.497 0.558 0.626 0.697 0.773

0.342 0.348 0.355 0.363 0.370

0.227 0.232 0.236 0.241 0.246

0.833 0.938 1.05 1.17 1.30

0.554 0.624 0.700 0.780 0.864

0.383 0.391 0.400 0.409 0.419

0.255 0.260 0.266 0.272 0.279

0.936 1.06 1.18 1.32 1.46

0.623 0.703 0.788 0.878 0.972

0.430 0.441 0.452 0.464 0.476

0.286 0.293 0.301 0.309 0.317

42 44 46 48 50

1.28 1.41 1.54 1.67 1.81

0.852 0.935 1.02 1.11 1.21

0.378 0.386 0.395 0.404 0.413

0.252 0.257 0.263 0.269 0.275

1.43 1.57 1.72 1.87 2.03

0.952 1.05 1.14 1.24 1.35

0.429 0.439 0.451 0.462 0.475

0.285 0.292 0.300 0.308 0.316

1.61 1.77 1.93 2.10 2.28

1.07 1.18 1.29 1.40 1.52

0.490 0.504 0.518 0.534 0.551

0.326 0.335 0.345 0.355 0.367

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

h

–1

1.28 0.306 0.376

0.850 0.204 0.251

1.41 0.337 0.414

0.941 0.224 0.276

1.57 0.370 0.455

1.04 0.246 0.303

rx /ry

3.51

3.51

3.52

ry , in.

3.48

3.45

3.41

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:48 AM

6–34

Page 34

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W27

W-Shapes W27×

Shape

281

p × 10 Design

(kips) ASD 0

258

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10

3

–1

(kips) ASD

235

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.402 0.267 0.381 0.253 0.439 0.292 0.418 0.278 0.481 0.320 0.461 0.307

11 12 13 14 15

0.449 0.459 0.469 0.481 0.494

0.299 0.305 0.312 0.320 0.329

0.381 0.381 0.385 0.389 0.393

0.253 0.253 0.256 0.259 0.262

0.491 0.502 0.514 0.527 0.541

0.327 0.334 0.342 0.351 0.360

0.418 0.419 0.424 0.429 0.434

0.278 0.279 0.282 0.285 0.289

0.540 0.552 0.565 0.580 0.596

0.359 0.367 0.376 0.386 0.396

0.461 0.463 0.469 0.475 0.481

0.307 0.308 0.312 0.316 0.320

16 17 18 19 20

0.508 0.524 0.541 0.559 0.580

0.338 0.348 0.360 0.372 0.386

0.397 0.402 0.406 0.411 0.416

0.264 0.267 0.270 0.273 0.277

0.557 0.575 0.594 0.615 0.637

0.371 0.382 0.395 0.409 0.424

0.439 0.444 0.450 0.455 0.461

0.292 0.296 0.299 0.303 0.307

0.614 0.633 0.655 0.678 0.704

0.408 0.421 0.436 0.451 0.468

0.487 0.494 0.500 0.507 0.514

0.324 0.328 0.333 0.337 0.342

22 24 26 28 30

0.626 0.681 0.747 0.824 0.917

0.417 0.453 0.497 0.548 0.610

0.426 0.436 0.447 0.458 0.470

0.283 0.290 0.297 0.305 0.313

0.689 0.751 0.824 0.912 1.02

0.459 0.500 0.549 0.607 0.676

0.473 0.485 0.498 0.512 0.527

0.315 0.323 0.332 0.341 0.351

0.762 0.832 0.914 1.01 1.13

0.507 0.553 0.608 0.674 0.753

0.529 0.544 0.560 0.578 0.596

0.352 0.362 0.373 0.384 0.397

32 34 36 38 40

1.03 1.16 1.30 1.45 1.61

0.683 0.772 0.865 0.964 1.07

0.482 0.496 0.510 0.524 0.540

0.321 0.330 0.339 0.349 0.359

1.14 1.29 1.45 1.61 1.78

0.760 0.858 0.962 1.07 1.19

0.543 0.559 0.577 0.596 0.616

0.361 0.372 0.384 0.396 0.410

1.27 1.44 1.61 1.80 1.99

0.848 0.957 1.07 1.20 1.33

0.616 0.637 0.660 0.684 0.710

0.410 0.424 0.439 0.455 0.472

42 44 46 48 50

1.77 1.94 2.12 2.31 2.51

1.18 1.29 1.41 1.54 1.67

0.557 0.574 0.593 0.614 0.639

0.370 0.382 0.395 0.408 0.425

1.97 2.16 2.36 2.57 2.79

1.31 1.44 1.57 1.71 1.85

0.637 0.660 0.685 0.721 0.756

0.424 0.439 0.456 0.479 0.503

2.20 2.41 2.63 2.87 3.11

1.46 1.60 1.75 1.91 2.07

0.738 0.776 0.818 0.861 0.904

0.491 0.516 0.544 0.573 0.601

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

1.73 0.402 0.494

1.15 0.267 0.329

1.91 0.439 0.539

1.27 0.292 0.359

2.12 0.481 0.591

1.41 0.320 0.394

rx /ry

3.54

3.54

3.54

ry , in.

3.39

3.36

3.33

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:48 AM

Page 35

STEEL BEAM-COLUMN SELECTION TABLES

6–35

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W27

W-Shapes W27×

Shape

217

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

194

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

178

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.523 0.348 0.501 0.333 0.585 0.389 0.565 0.376 0.636 0.423 0.625 0.416

11 12 13 14 15

0.587 0.600 0.614 0.630 0.648

0.390 0.399 0.409 0.419 0.431

0.501 0.503 0.510 0.517 0.524

0.333 0.335 0.339 0.344 0.348

0.658 0.673 0.689 0.708 0.728

0.438 0.448 0.459 0.471 0.484

0.565 0.568 0.576 0.584 0.593

0.376 0.378 0.383 0.389 0.395

0.718 0.734 0.753 0.773 0.796

0.478 0.489 0.501 0.515 0.530

0.625 0.630 0.640 0.650 0.661

0.416 0.419 0.426 0.432 0.439

16 17 18 19 20

0.667 0.689 0.712 0.738 0.766

0.444 0.458 0.474 0.491 0.510

0.531 0.538 0.546 0.554 0.562

0.353 0.358 0.363 0.369 0.374

0.750 0.775 0.802 0.831 0.863

0.499 0.516 0.533 0.553 0.574

0.602 0.612 0.621 0.631 0.641

0.401 0.407 0.413 0.420 0.427

0.821 0.849 0.879 0.912 0.948

0.546 0.565 0.585 0.607 0.631

0.671 0.683 0.694 0.706 0.718

0.447 0.454 0.462 0.470 0.478

22 24 26 28 30

0.830 0.906 0.997 1.11 1.23

0.552 0.603 0.663 0.735 0.822

0.579 0.597 0.617 0.637 0.660

0.385 0.398 0.410 0.424 0.439

0.937 1.02 1.13 1.25 1.40

0.623 0.682 0.751 0.834 0.934

0.663 0.686 0.711 0.737 0.766

0.441 0.456 0.473 0.490 0.509

1.03 1.13 1.25 1.39 1.56

0.686 0.752 0.830 0.925 1.04

0.745 0.773 0.803 0.836 0.871

0.495 0.514 0.534 0.556 0.580

32 34 36 38 40

1.39 1.57 1.76 1.96 2.18

0.927 1.05 1.17 1.31 1.45

0.683 0.709 0.736 0.766 0.798

0.455 0.471 0.490 0.509 0.531

1.59 1.79 2.01 2.24 2.48

1.06 1.19 1.34 1.49 1.65

0.797 0.830 0.867 0.906 0.968

0.530 0.552 0.577 0.603 0.644

1.77 2.00 2.24 2.49 2.76

1.18 1.33 1.49 1.66 1.84

0.910 0.952 1.00 1.07 1.15

0.606 0.634 0.665 0.713 0.765

42 44 46 48 50

2.40 2.63 2.88 3.13 3.40

1.60 1.75 1.91 2.09 2.26

0.842 0.892 0.942 0.992 1.04

0.560 0.593 0.627 0.660 0.693

2.73 3.00 3.28 3.57 3.88

1.82 2.00 2.18 2.38 2.58

1.03 1.10 1.16 1.22 1.29

0.687 0.729 0.771 0.813 0.855

3.05 3.34 3.66 3.98 4.32

2.03 2.23 2.43 2.65 2.87

1.23 1.31 1.38 1.46 1.54

0.817 0.869 0.920 0.972 1.02

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

2.31 0.523 0.642

1.54 0.348 0.428

2.62 0.585 0.718

1.74 0.389 0.479

2.92 0.636 0.781

1.94 0.423 0.521

rx /ry

3.55

3.56

3.57

ry , in.

3.32

3.29

3.25

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:48 AM

6–36

Page 36

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W27

W-Shapes W27×

Shape

161c

p × 10 Design

(kips) ASD 0

146 c

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

p × 10

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

–1

(kips) ASD

129c

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.704 0.468 0.692 0.460 0.792 0.527 0.768 0.511 0.910 0.606 0.902 0.600

11 12 13 14 15

0.793 0.811 0.832 0.855 0.881

0.527 0.540 0.554 0.569 0.586

0.692 0.698 0.710 0.722 0.735

0.460 0.465 0.472 0.480 0.489

0.883 0.901 0.922 0.946 0.974

0.587 0.600 0.614 0.629 0.648

0.768 0.777 0.791 0.805 0.819

0.511 0.517 0.526 0.535 0.545

1.15 1.21 1.27 1.35 1.44

0.763 0.802 0.846 0.897 0.955

0.976 1.00 1.03 1.06 1.09

0.649 0.666 0.684 0.703 0.723

16 17 18 19 20

0.909 0.939 0.973 1.01 1.05

0.604 0.625 0.647 0.672 0.699

0.747 0.761 0.775 0.789 0.804

0.497 0.506 0.515 0.525 0.535

1.01 1.04 1.08 1.12 1.17

0.669 0.692 0.718 0.746 0.776

0.835 0.850 0.867 0.884 0.901

0.555 0.566 0.577 0.588 0.600

1.53 1.65 1.78 1.92 2.09

1.02 1.10 1.18 1.28 1.39

1.12 1.15 1.19 1.23 1.27

0.744 0.767 0.791 0.816 0.843

22 24 26 28 30

1.14 1.25 1.39 1.55 1.74

0.761 0.835 0.924 1.03 1.16

0.835 0.869 0.906 0.946 0.990

0.556 0.578 0.603 0.630 0.659

1.27 1.40 1.55 1.73 1.95

0.846 0.930 1.03 1.15 1.30

0.939 0.980 1.02 1.07 1.13

0.625 0.652 0.681 0.714 0.750

2.51 2.99 3.51 4.07 4.67

1.67 1.99 2.33 2.71 3.11

1.36 1.46 1.64 1.82 2.00

0.903 0.973 1.09 1.21 1.33

32 34 36 38 40

1.98 2.23 2.50 2.79 3.09

1.31 1.48 1.66 1.85 2.05

1.04 1.09 1.17 1.27 1.36

0.691 0.726 0.781 0.844 0.907

2.22 2.50 2.81 3.13 3.47

1.48 1.67 1.87 2.08 2.31

1.19 1.27 1.38 1.50 1.61

0.789 5.31 0.843 6.00 0.919 6.73 0.995 1.07

3.54 3.99 4.47

2.18 2.36 2.54

1.45 1.57 1.69

42 44 46 48 50

3.40 3.73 4.08 4.44 4.82

2.26 2.48 2.72 2.96 3.21

1.46 1.55 1.65 1.74 1.84

0.970 1.03 1.10 1.16 1.22

3.82 4.19 4.58 4.99 5.41

2.54 2.79 3.05 3.32 3.60

1.73 1.84 1.96 2.07 2.19

1.15 1.23 1.30 1.38 1.46

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

3.27 0.702 0.862

2.17 0.467 0.575

3.65 0.773 0.950

2.43 0.514 0.633

6.19 0.884 1.09

4.12 0.588 0.724

rx /ry

3.56

3.59

5.07

ry , in.

3.23

3.20

2.21

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:48 AM

Page 37

STEEL BEAM-COLUMN SELECTION TABLES

6–37

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W27

W-Shapes W27×

Shape

114c

p × 10

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Design

(kips)

102c

bx × 10

3

p × 10

3

–1

(kip-ft) ASD

–1

LRFD

(kips) ASD

94c

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips)

ASD

LRFD

ASD

LRFD

0

1.05

0.696 1.04

0.691 1.21

0.804 1.17

0.777 1.34

ASD

LRFD

0.890 1.28

0.853

11 12 13 14 15

1.31 1.37 1.45 1.53 1.64

0.873 0.913 0.962 1.02 1.09

1.13 1.17 1.20 1.24 1.27

0.754 0.775 0.798 0.822 0.847

1.51 1.58 1.66 1.76 1.86

1.01 1.05 1.11 1.17 1.24

1.28 1.32 1.36 1.41 1.45

0.854 0.880 0.907 0.935 0.966

1.67 1.75 1.84 1.95 2.07

1.11 1.17 1.23 1.30 1.38

1.42 1.46 1.51 1.56 1.62

0.944 0.974 1.01 1.04 1.07

16 17 18 19 20

1.75 1.89 2.04 2.21 2.41

1.17 1.25 1.36 1.47 1.60

1.31 1.36 1.40 1.45 1.51

0.874 0.903 0.934 0.967 1.00

1.99 2.15 2.33 2.53 2.77

1.33 1.43 1.55 1.69 1.84

1.50 1.55 1.61 1.67 1.74

1.00 1.03 1.07 1.11 1.16

2.21 2.38 2.59 2.82 3.09

1.47 1.58 1.72 1.88 2.06

1.67 1.74 1.80 1.88 1.95

1.11 1.15 1.20 1.25 1.30

22 24 26 28 30

2.90 3.46 4.06 4.70 5.40

1.93 2.30 2.70 3.13 3.59

1.63 1.80 2.04 2.27 2.51

1.08 1.20 1.36 1.51 1.67

3.34 3.98 4.67 5.42 6.22

2.22 2.65 3.11 3.60 4.14

1.89 2.15 2.44 2.74 3.03

1.25 1.43 1.63 1.82 2.02

3.74 4.45 5.22 6.06 6.95

2.49 2.96 3.47 4.03 4.62

2.16 2.50 2.84 3.19 3.54

1.44 1.66 1.89 2.12 2.36

32 34 36

6.14 6.94 7.78

4.09 4.61 5.17

2.75 2.99 3.23

1.83 1.99 2.15

7.07 7.99

4.71 5.31

3.33 3.63

2.22 2.42

7.91 8.93

5.26 5.94

3.90 4.26

2.59 2.83

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

7.23 0.994 1.22

4.81 0.661 0.814

8.21 1.11 1.37

5.46 0.741 0.912

9.18 1.21 1.49

6.11 0.805 0.991

rx /ry

5.05

5.12

5.14

ry , in.

2.18

2.15

2.12

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:48 AM

6–38

Page 38

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W27-W24

W-Shapes W27×

Shape

370h

p × 10

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

W24×

84c

Design

Fy = 50 ksi

(kips)

3

–1

(kip-ft)

–1

p × 10

335h

bx × 10

3

3

–1

(kips)

(kip-ft) ASD

LRFD

p × 10 (kips) ASD

bx × 103

–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

0

1.53

1.02

1.46

0.971

0.306 0.204 0.315 0.210 0.340 0.226 0.349 0.232

11 12 13 14 15

1.92 2.02 2.12 2.25 2.39

1.28 1.34 1.41 1.49 1.59

1.63 1.69 1.75 1.81 1.88

1.09 1.12 1.16 1.20 1.25

0.345 0.353 0.362 0.372 0.382

0.230 0.235 0.241 0.247 0.254

0.315 0.316 0.319 0.321 0.323

0.210 0.210 0.212 0.213 0.215

0.384 0.393 0.403 0.414 0.426

0.255 0.261 0.268 0.276 0.284

0.349 0.351 0.354 0.357 0.359

0.232 0.233 0.235 0.237 0.239

16 17 18 19 20

2.56 2.76 3.00 3.28 3.62

1.70 1.84 1.99 2.18 2.41

1.95 2.03 2.11 2.21 2.31

1.30 1.35 1.41 1.47 1.53

0.394 0.407 0.422 0.437 0.454

0.262 0.271 0.280 0.291 0.302

0.326 0.328 0.330 0.333 0.335

0.217 0.218 0.220 0.221 0.223

0.440 0.455 0.471 0.489 0.509

0.293 0.303 0.314 0.325 0.338

0.362 0.365 0.368 0.371 0.375

0.241 0.243 0.245 0.247 0.249

22 24 26 28 30

4.38 5.21 6.12 7.10 8.15

2.91 3.47 4.07 4.72 5.42

2.64 3.06 3.49 3.93 4.38

1.76 2.04 2.32 2.62 2.92

0.494 0.540 0.596 0.663 0.743

0.328 0.359 0.397 0.441 0.495

0.340 0.346 0.351 0.357 0.363

0.226 0.230 0.234 0.237 0.241

0.554 0.608 0.672 0.750 0.843

0.368 0.404 0.447 0.499 0.561

0.381 0.388 0.395 0.402 0.409

0.254 0.258 0.263 0.267 0.272

32 34 36 38 40

9.27 10.5

6.17 6.96

4.84 5.31

3.22 3.53

0.842 0.950 1.07 1.19 1.32

0.560 0.632 0.709 0.790 0.875

0.369 0.375 0.381 0.388 0.395

0.245 0.249 0.254 0.258 0.263

0.957 1.08 1.21 1.35 1.49

0.636 0.718 0.806 0.897 0.994

0.417 0.425 0.433 0.442 0.451

0.277 0.283 0.288 0.294 0.300

1.45 1.59 1.74 1.89 2.05

0.965 1.06 1.16 1.26 1.37

0.402 0.409 0.417 0.425 0.433

0.267 0.272 0.277 0.283 0.288

1.65 1.81 1.98 2.15 2.34

1.10 1.20 1.32 1.43 1.55

0.460 0.470 0.480 0.491 0.502

0.306 0.313 0.319 0.326 0.334

42 44 46 48 50

LRFD

–1

3

LRFD

ASD

LRFD

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

10.7 1.35 1.66

7.14 0.900 1.11

1.33 0.306 0.376

0.888 0.204 0.251

1.50 0.340 0.417

1.00 0.226 0.278

rx /ry

5.17

3.39

3.41

ry , in.

2.07

3.27

3.23

Shape is slender for compression with Fy = 50 ksi. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:48 AM

Page 39

STEEL BEAM-COLUMN SELECTION TABLES

6–39

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W24

W-Shapes W24×

Shape

306h

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

279h

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

250

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.372 0.248 0.386 0.257 0.408 0.271 0.427 0.284 0.454 0.302 0.479 0.319

11 12 13 14 15

0.422 0.432 0.443 0.455 0.469

0.281 0.287 0.295 0.303 0.312

0.386 0.389 0.392 0.396 0.399

0.257 0.259 0.261 0.263 0.266

0.463 0.474 0.487 0.501 0.516

0.308 0.316 0.324 0.333 0.343

0.427 0.430 0.434 0.438 0.443

0.284 0.286 0.289 0.292 0.294

0.517 0.530 0.544 0.560 0.578

0.344 0.353 0.362 0.373 0.384

0.479 0.483 0.489 0.494 0.499

0.319 0.322 0.325 0.329 0.332

16 17 18 19 20

0.484 0.501 0.520 0.540 0.562

0.322 0.333 0.346 0.359 0.374

0.403 0.406 0.410 0.414 0.418

0.268 0.270 0.273 0.275 0.278

0.533 0.552 0.573 0.595 0.620

0.355 0.367 0.381 0.396 0.413

0.447 0.451 0.456 0.461 0.465

0.297 0.300 0.303 0.306 0.310

0.597 0.619 0.642 0.668 0.697

0.397 0.412 0.427 0.445 0.463

0.505 0.510 0.516 0.522 0.528

0.336 0.340 0.343 0.347 0.351

22 24 26 28 30

0.612 0.673 0.746 0.834 0.939

0.407 0.448 0.496 0.555 0.625

0.426 0.434 0.442 0.451 0.461

0.283 0.289 0.294 0.300 0.306

0.677 0.746 0.828 0.927 1.05

0.451 0.496 0.551 0.617 0.697

0.475 0.485 0.496 0.507 0.519

0.316 0.323 0.330 0.337 0.345

0.762 0.841 0.935 1.05 1.19

0.507 0.559 0.622 0.698 0.792

0.541 0.554 0.567 0.582 0.597

0.360 0.368 0.378 0.387 0.397

32 34 36 38 40

1.07 1.21 1.35 1.51 1.67

0.711 0.802 0.899 1.00 1.11

0.470 0.480 0.491 0.502 0.513

0.313 0.320 0.327 0.334 0.341

1.19 1.35 1.51 1.68 1.86

0.793 0.895 1.00 1.12 1.24

0.531 0.544 0.557 0.571 0.586

0.353 0.362 0.371 0.380 0.390

1.35 1.53 1.71 1.91 2.12

0.901 1.02 1.14 1.27 1.41

0.613 0.630 0.648 0.667 0.687

0.408 0.419 0.431 0.444 0.457

42 44 46 48 50

1.84 2.02 2.21 2.40 2.61

1.22 1.34 1.47 1.60 1.73

0.525 0.538 0.551 0.565 0.579

0.349 0.358 0.367 0.376 0.386

2.05 2.25 2.46 2.68 2.91

1.37 1.50 1.64 1.78 1.94

0.601 0.618 0.635 0.653 0.673

0.400 0.411 0.423 0.435 0.448

2.33 2.56 2.80 3.05 3.31

1.55 1.70 1.86 2.03 2.20

0.708 0.731 0.755 0.781 0.814

0.471 0.486 0.502 0.519 0.541

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

h

–1

1.66 0.372 0.457

1.11 0.248 0.305

1.85 0.408 0.501

1.23 0.271 0.334

2.08 0.454 0.558

1.39 0.302 0.372

rx /ry

3.41

3.41

3.41

ry , in.

3.20

3.17

3.14

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:49 AM

6–40

Page 40

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W24

W-Shapes W24×

Shape

229

p × 10 Design

(kips) ASD 0

207

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10

3

–1

(kips) ASD

192

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1

LRFD

ASD

LRFD

0.497 0.331 0.528 0.351 0.550 0.366 0.588 0.391 0.591 0.393 0.637 0.424

11 12 13 14 15

0.567 0.581 0.597 0.615 0.635

0.377 0.387 0.397 0.409 0.422

0.528 0.534 0.540 0.547 0.553

0.351 0.355 0.359 0.364 0.368

0.629 0.646 0.664 0.684 0.706

0.419 0.430 0.442 0.455 0.470

0.589 0.596 0.604 0.612 0.620

0.392 0.397 0.402 0.407 0.412

0.677 0.694 0.714 0.736 0.760

0.450 0.462 0.475 0.490 0.506

0.639 0.647 0.656 0.665 0.675

0.425 0.431 0.437 0.443 0.449

16 17 18 19 20

0.657 0.681 0.707 0.736 0.768

0.437 0.453 0.471 0.490 0.511

0.560 0.567 0.574 0.581 0.588

0.372 0.377 0.382 0.387 0.391

0.731 0.758 0.788 0.821 0.858

0.486 0.505 0.525 0.547 0.571

0.628 0.637 0.646 0.655 0.664

0.418 0.424 0.429 0.435 0.442

0.787 0.816 0.849 0.885 0.924

0.524 0.543 0.565 0.589 0.615

0.684 0.694 0.705 0.715 0.726

0.455 0.462 0.469 0.476 0.483

22 24 26 28 30

0.842 0.930 1.04 1.17 1.33

0.560 0.619 0.690 0.776 0.883

0.604 0.620 0.637 0.655 0.674

0.402 0.412 0.424 0.436 0.448

0.942 1.04 1.17 1.31 1.50

0.626 0.694 0.775 0.874 0.996

0.683 0.704 0.725 0.749 0.773

0.454 0.468 0.483 0.498 0.514

1.02 1.13 1.26 1.42 1.62

0.675 0.749 0.837 0.944 1.08

0.749 0.773 0.799 0.827 0.857

0.498 0.514 0.532 0.550 0.570

32 34 36 38 40

1.51 1.70 1.91 2.13 2.36

1.00 1.13 1.27 1.42 1.57

0.694 0.716 0.739 0.763 0.789

0.462 0.476 0.491 0.508 0.525

1.70 1.92 2.16 2.40 2.66

1.13 1.28 1.43 1.60 1.77

0.800 0.828 0.858 0.891 0.926

0.532 0.551 0.571 0.593 0.616

1.84 2.08 2.33 2.60 2.88

1.23 1.38 1.55 1.73 1.92

0.888 0.923 0.960 1.00 1.05

0.591 0.614 0.639 0.666 0.697

42 44 46 48 50

2.60 2.85 3.12 3.40 3.68

1.73 1.90 2.08 2.26 2.45

0.817 0.847 0.884 0.928 0.971

0.544 0.563 0.588 0.617 0.646

2.93 3.22 3.52 3.83 4.16

1.95 2.14 2.34 2.55 2.77

0.967 1.02 1.07 1.13 1.18

0.643 0.679 0.715 0.751 0.787

3.17 3.48 3.81 4.15 4.50

2.11 2.32 2.53 2.76 2.99

1.11 1.17 1.24 1.30 1.36

0.740 0.782 0.824 0.866 0.908

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

2.31 0.497 0.611

1.54 0.331 0.407

2.60 0.550 0.676

1.73 0.366 0.451

2.83 0.591 0.726

1.88 0.393 0.484

rx /ry

3.44

3.44

3.42

ry , in.

3.11

3.08

3.07

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:49 AM

Page 41

STEEL BEAM-COLUMN SELECTION TABLES

6–41

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W24

W-Shapes W24×

Shape

176

p × 10 Design

(kips) ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

162

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

146

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips) ASD

LRFD

ASD

LRFD

0.646 0.430 0.697 0.464 0.699 0.465 0.761 0.506 0.777 0.517 0.852 0.567

11 12 13 14 15

0.742 0.761 0.783 0.808 0.835

0.493 0.506 0.521 0.537 0.555

0.700 0.710 0.721 0.731 0.743

0.466 0.472 0.479 0.487 0.494

0.801 0.822 0.846 0.872 0.901

0.533 0.547 0.563 0.580 0.600

0.764 0.776 0.788 0.801 0.814

0.508 0.516 0.524 0.533 0.541

0.894 0.918 0.945 0.975 1.01

0.595 0.611 0.629 0.649 0.671

0.857 0.872 0.887 0.902 0.918

0.571 0.580 0.590 0.600 0.611

16 17 18 19 20

0.865 0.898 0.934 0.975 1.02

0.575 0.597 0.622 0.649 0.678

0.754 0.766 0.778 0.791 0.804

0.502 0.510 0.518 0.526 0.535

0.934 0.969 1.01 1.05 1.10

0.621 0.645 0.671 0.700 0.731

0.827 0.841 0.855 0.870 0.886

0.550 0.560 0.569 0.579 0.589

1.05 1.09 1.13 1.18 1.24

0.696 0.723 0.753 0.786 0.823

0.935 0.952 0.970 0.988 1.01

0.622 0.633 0.645 0.657 0.670

22 24 26 28 30

1.12 1.25 1.40 1.58 1.80

0.746 0.829 0.928 1.05 1.20

0.832 0.861 0.893 0.927 0.964

0.553 0.573 0.594 0.617 0.641

1.21 1.34 1.50 1.70 1.94

0.804 0.892 0.999 1.13 1.29

0.918 0.953 0.991 1.03 1.08

0.611 0.634 0.660 0.687 0.716

1.36 1.52 1.70 1.93 2.21

0.907 1.01 1.13 1.29 1.47

1.05 1.09 1.14 1.19 1.25

0.697 0.727 0.759 0.794 0.832

32 34 36 38 40

2.05 2.32 2.60 2.90 3.21

1.37 1.54 1.73 1.93 2.13

1.00 1.05 1.09 1.15 1.23

0.668 0.697 0.728 0.767 0.818

2.21 2.49 2.79 3.11 3.45

1.47 1.66 1.86 2.07 2.29

1.13 1.18 1.24 1.33 1.42

0.749 0.784 0.826 0.886 0.947

2.52 2.84 3.19 3.55 3.93

1.68 1.89 2.12 2.36 2.62

1.31 1.39 1.50 1.62 1.73

0.874 0.926 1.00 1.08 1.15

42 44 46 48 50

3.54 3.88 4.24 4.62 5.01

2.35 2.58 2.82 3.07 3.34

1.31 1.38 1.46 1.53 1.61

0.869 0.920 0.970 1.02 1.07

3.80 4.17 4.56 4.96 5.39

2.53 2.78 3.03 3.30 3.58

1.51 1.60 1.69 1.78 1.87

1.01 1.07 1.13 1.19 1.25

4.34 4.76 5.20 5.67 6.15

2.89 3.17 3.46 3.77 4.09

1.85 1.96 2.07 2.19 2.30

1.23 1.30 1.38 1.45 1.53

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

3.10 0.646 0.794

2.06 0.430 0.529

3.39 0.699 0.858

2.26 0.465 0.572

3.82 0.777 0.954

2.54 0.517 0.636

rx /ry

3.45

3.41

3.42

ry , in.

3.04

3.05

3.01

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:49 AM

6–42

Page 42

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W24

W-Shapes W24×

Shape

117c

131

p × 10

bx × 10

3

Design

(kips) ASD

p × 10

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

–1

(kips) ASD

104c

bx × 10

3

(kip-ft)

LRFD

–1

p × 10 (kips)

3

bx × 103

–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

0.865 0.576 0.963 0.641 0.994 0.661 1.09

0.725

1.14

0.759 1.23

0.820

11 12 13 14 15

1.00 1.03 1.06 1.09 1.13

0.665 0.684 0.704 0.727 0.753

0.972 0.989 1.01 1.03 1.05

0.646 0.658 0.670 0.683 0.696

1.13 1.16 1.19 1.23 1.28

0.752 0.771 0.794 0.820 0.850

1.10 1.12 1.15 1.17 1.19

0.733 0.748 0.762 0.778 0.794

1.30 1.33 1.37 1.41 1.45

0.862 0.884 0.908 0.936 0.966

1.25 1.28 1.30 1.33 1.36

0.832 0.849 0.867 0.886 0.905

16 17 18 19 20

1.17 1.22 1.27 1.33 1.39

0.781 0.813 0.848 0.886 0.928

1.07 1.09 1.11 1.13 1.16

0.710 0.724 0.739 0.754 0.770

1.33 1.38 1.44 1.51 1.58

0.882 0.919 0.959 1.00 1.05

1.22 1.24 1.27 1.30 1.33

0.810 0.828 0.846 0.865 0.885

1.50 1.56 1.63 1.70 1.79

1.00 1.04 1.08 1.13 1.19

1.39 1.42 1.46 1.49 1.53

0.925 0.946 0.969 0.992 1.02

22 24 26 28 30

1.54 1.72 1.94 2.21 2.53

1.03 1.14 1.29 1.47 1.68

1.21 1.26 1.33 1.39 1.47

0.804 0.841 0.882 0.928 0.977

1.75 1.96 2.21 2.53 2.90

1.16 1.30 1.47 1.68 1.93

1.39 1.46 1.54 1.63 1.73

0.927 0.974 1.03 1.08 1.15

1.99 2.23 2.52 2.89 3.32

1.32 1.48 1.68 1.92 2.21

1.61 1.69 1.79 1.90 2.06

1.07 1.13 1.19 1.27 1.37

32 34 36 38 40

2.88 3.25 3.65 4.06 4.50

1.92 2.16 2.43 2.70 3.00

1.56 1.70 1.84 1.99 2.13

1.04 1.13 1.23 1.32 1.42

3.30 3.72 4.18 4.65 5.16

2.20 2.48 2.78 3.10 3.43

1.89 2.07 2.25 2.43 2.62

1.26 1.38 1.50 1.62 1.74

3.77 4.26 4.78 5.32 5.90

2.51 2.83 3.18 3.54 3.92

2.29 2.51 2.74 2.97 3.20

1.52 1.67 1.82 1.98 2.13

42 44 46 48

4.96 5.45 5.95 6.48

3.30 3.62 3.96 4.31

2.28 2.42 2.57 2.71

1.52 1.61 1.71 1.80

5.68 6.24 6.82 7.42

3.78 4.15 4.54 4.94

2.80 2.98 3.17 3.35

1.86 1.99 2.11 2.23

6.50 7.13 7.80 8.49

4.33 4.75 5.19 5.65

3.44 3.67 3.91 4.14

2.29 2.44 2.60 2.76

0

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

4.37 0.865 1.06

2.91 0.576 0.709

4.99 0.971 1.19

3.32 0.646 0.795

5.71 1.09 1.34

3.80 0.724 0.891

rx /ry

3.43

3.44

3.47

ry , in.

2.97

2.94

2.91

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/17/12

10:01 AM

Page 43

STEEL BEAM-COLUMN SELECTION TABLES

6–43

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W24

W-Shapes W24×

Shape

103c

p × 10

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Design

(kips)

94c

bx × 10

3

–1

(kip-ft) ASD

bx × 10

3

–1

LRFD

84c

p × 10

3

(kips) ASD

3

–1

(kip-ft)

LRFD

–1

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips)

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1.13

0.753 1.27

0.847 1.26

0.840 1.40

0.933

1.46

0.968 1.59

1.06

11 12 13 14 15

1.52 1.62 1.73 1.86 2.00

1.01 1.08 1.15 1.23 1.33

1.42 1.46 1.51 1.55 1.61

0.944 0.972 1.00 1.03 1.07

1.67 1.78 1.90 2.04 2.21

1.11 1.18 1.26 1.36 1.47

1.57 1.62 1.68 1.73 1.79

1.05 1.08 1.12 1.15 1.19

1.92 2.03 2.17 2.33 2.52

1.28 1.35 1.44 1.55 1.68

1.80 1.87 1.93 2.00 2.08

1.20 1.24 1.28 1.33 1.38

16 17 18 19 20

2.18 2.38 2.61 2.88 3.19

1.45 1.58 1.74 1.92 2.12

1.66 1.72 1.78 1.85 1.92

1.10 1.14 1.19 1.23 1.28

2.40 2.62 2.88 3.18 3.53

1.60 1.74 1.92 2.12 2.35

1.86 1.93 2.01 2.09 2.17

1.24 1.28 1.33 1.39 1.45

2.75 3.01 3.32 3.68 4.08

1.83 2.00 2.21 2.45 2.71

2.16 2.25 2.34 2.45 2.56

1.44 1.49 1.56 1.63 1.70

22 24 26 28 30

3.86 4.60 5.40 6.26 7.19

2.57 3.06 3.59 4.16 4.78

2.09 2.37 2.65 2.94 3.22

1.39 1.58 1.77 1.95 2.14

4.27 5.08 5.96 6.92 7.94

2.84 3.38 3.97 4.60 5.28

2.43 2.76 3.10 3.44 3.79

1.61 1.84 2.06 2.29 2.52

4.94 5.88 6.90 8.00 9.18

3.28 3.91 4.59 5.32 6.11

2.95 3.37 3.80 4.24 4.67

1.96 2.24 2.53 2.82 3.11

32

8.18

5.44

3.50

2.33

9.03

6.01

4.13

2.75

6.95

5.11

3.40

10.4

ASD

LRFD

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

8.58 1.10 1.35

5.71 0.733 0.903

9.50 1.21 1.48

6.32 0.802 0.987

10.9 1.35 1.66

7.27 0.900 1.11

rx /ry

5.03

4.98

5.02

ry , in.

1.99

1.98

1.95

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:49 AM

6–44

Page 44

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W24

W-Shapes W24×

Shape

68c

76

p × 10

bx × 10

3

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

(kips)

–1

(kip-ft)

62c

p × 10

3

bx × 10

3

–1

3

–1

(kips)

(kip-ft)

–1

p × 10 (kips)

3

bx × 103

–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1.64

1.09

1.78

1.19

1.87

1.24

2.01

1.34

2.08

1.38

2.33

1.55

6 7 8 9 10

1.78 1.83 1.89 1.97 2.06

1.18 1.22 1.26 1.31 1.37

1.78 1.79 1.85 1.91 1.97

1.19 1.19 1.23 1.27 1.31

2.03 2.09 2.17 2.26 2.36

1.35 1.39 1.44 1.50 1.57

2.01 2.04 2.11 2.18 2.26

1.34 1.36 1.40 1.45 1.50

2.40 2.54 2.72 2.94 3.22

1.60 1.69 1.81 1.96 2.14

2.44 2.56 2.68 2.82 2.97

1.63 1.70 1.78 1.87 1.97

11 12 13 14 15

2.17 2.30 2.45 2.62 2.84

1.44 1.53 1.63 1.75 1.89

2.04 2.11 2.19 2.28 2.37

1.36 1.41 1.46 1.52 1.58

2.49 2.64 2.82 3.03 3.29

1.66 1.76 1.88 2.02 2.19

2.34 2.43 2.53 2.63 2.75

1.56 1.62 1.68 1.75 1.83

3.59 4.07 4.67 5.42 6.22

2.39 2.71 3.11 3.60 4.14

3.13 3.32 3.53 3.77 4.15

2.08 2.21 2.35 2.51 2.76

16 17 18 19 20

3.10 3.40 3.76 4.19 4.64

2.06 2.26 2.50 2.79 3.09

2.47 2.58 2.69 2.82 3.02

1.64 1.71 1.79 1.88 2.01

3.59 3.97 4.42 4.92 5.45

2.39 2.64 2.94 3.27 3.63

2.87 3.01 3.16 3.35 3.66

1.91 2.00 2.10 2.23 2.43

7.08 7.99 8.96 9.98 11.1

4.71 5.31 5.96 6.64 7.36

4.62 5.11 5.60 6.10 6.61

3.08 3.40 3.72 4.06 4.40

22 24 26 28 30

5.62 6.68 7.84 9.10 10.4

3.74 4.45 5.22 6.05 6.95

3.53 4.05 4.58 5.12 5.66

2.35 2.69 3.05 3.41 3.77

6.60 7.85 9.21 10.7 12.3

4.39 5.22 6.13 7.11 8.16

4.29 4.94 5.61 6.30 6.99

2.85 3.29 3.74 4.19 4.65

13.4

8.90

7.64

5.08

32

11.9

7.90

6.21

4.13

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

12.5 1.49 1.83

8.29 0.992 1.22

14.5 1.66 2.04

9.67 1.11 1.36

22.7 1.84 2.25

15.1 1.22 1.50

rx /ry

5.05

5.11

6.69

ry , in.

1.92

1.87

1.38

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:49 AM

Page 45

STEEL BEAM-COLUMN SELECTION TABLES

6–45

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W24-W21

W-Shapes W24×

Shape

p × 10 Design

(kips)

201

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

W21×

55c, v 3

–1

(kip-ft)

–1

p × 10 (kips)

182

bx × 10

3

3

–1

(kip-ft)

LRFD

bx × 103

–1

(kip-ft)–1

(kips)

ASD

LRFD

ASD

LRFD

ASD

2.42

1.61

2.66

1.77

0.563 0.375 0.672 0.447 0.623 0.415 0.748 0.498

6 7 8 9 10

2.80 2.97 3.18 3.45 3.79

1.87 1.98 2.11 2.29 2.52

2.82 2.95 3.10 3.27 3.46

1.87 1.96 2.07 2.18 2.30

0.587 0.596 0.606 0.618 0.632

0.391 0.397 0.403 0.411 0.421

0.672 0.672 0.672 0.672 0.672

0.447 0.447 0.447 0.447 0.447

0.650 0.660 0.672 0.685 0.700

0.432 0.439 0.447 0.456 0.466

0.748 0.748 0.748 0.748 0.748

0.498 0.498 0.498 0.498 0.498

11 12 13 14 15

4.23 4.80 5.57 6.46 7.41

2.81 3.19 3.70 4.29 4.93

3.67 3.91 4.18 4.51 5.08

2.44 2.60 2.78 3.00 3.38

0.648 0.665 0.685 0.706 0.730

0.431 0.443 0.455 0.470 0.486

0.675 0.682 0.690 0.698 0.706

0.449 0.454 0.459 0.464 0.470

0.718 0.737 0.759 0.784 0.811

0.478 0.491 0.505 0.521 0.539

0.752 0.761 0.771 0.780 0.790

0.500 0.507 0.513 0.519 0.526

16 17 18 19 20

8.43 9.52 10.7 11.9 13.2

5.61 6.33 7.10 7.91 8.77

5.68 6.29 6.91 7.55 8.20

3.78 4.18 4.60 5.02 5.46

0.757 0.786 0.819 0.854 0.894

0.504 0.523 0.545 0.568 0.595

0.714 0.723 0.731 0.740 0.749

0.475 0.481 0.487 0.492 0.498

0.841 0.874 0.910 0.951 0.995

0.559 0.581 0.606 0.632 0.662

0.801 0.811 0.822 0.833 0.844

0.533 0.540 0.547 0.554 0.562

22 24 26 28 30

15.9

9.52

6.34

0.985 1.10 1.23 1.39 1.59

0.655 0.729 0.818 0.926 1.06

0.768 0.788 0.809 0.831 0.854

0.511 0.524 0.538 0.553 0.568

1.10 1.22 1.37 1.56 1.79

0.730 0.813 0.914 1.04 1.19

0.868 0.893 0.919 0.947 0.977

0.577 0.594 0.612 0.630 0.650

1.81 2.05 2.30 2.56 2.83

1.21 1.36 1.53 1.70 1.89

0.878 0.904 0.932 0.961 0.993

0.584 0.602 0.620 0.640 0.660

2.03 2.30 2.57 2.87 3.18

1.35 1.53 1.71 1.91 2.11

1.01 1.04 1.08 1.12 1.16

0.671 0.694 0.718 0.744 0.772

32 34 36 38 40

ASD

p × 10

0

10.6

LRFD

–1

3

ASD

LRFD

ASD

LRFD

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

26.8 2.06 2.53

17.8 1.37 1.69

2.68 0.563 0.692

1.78 0.375 0.461

2.99 0.623 0.765

1.99 0.415 0.510

rx /ry

6.80

3.14

3.13

ry , in.

1.34

3.02

3.00

Shape is slender for compression with Fy = 50 ksi. v Shape does not meet the h /tw limit for shear in AISC Specification Section G2.1(a) with Fy = 50 ksi; therefore, φv = 0.90 and Ωv = 1.67. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:49 AM

6–46

Page 46

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W21

W-Shapes W21×

Shape

166

p × 10 Design

(kips) ASD

147

bx × 10

3

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10

3

–1

(kips) ASD

132

bx × 10

3

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10 (kips) ASD

3

bx × 103

–1

(kip-ft)–1 ASD

LRFD

0.684 0.455 0.825 0.549 0.773 0.514 0.955 0.635 0.861 0.573 1.07

0.712

6 7 8 9 10

0.714 0.725 0.738 0.753 0.770

0.475 0.482 0.491 0.501 0.512

0.825 0.825 0.825 0.825 0.825

0.549 0.549 0.549 0.549 0.549

0.808 0.820 0.835 0.853 0.873

0.537 0.546 0.556 0.567 0.581

0.955 0.955 0.955 0.955 0.955

0.635 0.635 0.635 0.635 0.635

0.900 0.914 0.931 0.951 0.973

0.599 0.608 0.620 0.633 0.647

1.07 1.07 1.07 1.07 1.07

0.712 0.712 0.712 0.712 0.712

11 12 13 14 15

0.789 0.811 0.835 0.862 0.892

0.525 0.540 0.556 0.574 0.594

0.829 0.841 0.852 0.864 0.876

0.552 0.559 0.567 0.575 0.583

0.895 0.920 0.949 0.980 1.02

0.596 0.612 0.631 0.652 0.675

0.963 0.978 0.993 1.01 1.02

0.641 0.651 0.661 0.671 0.682

0.999 1.03 1.06 1.09 1.13

0.664 0.683 0.705 0.728 0.755

1.08 1.10 1.12 1.14 1.16

0.719 0.731 0.743 0.756 0.769

16 17 18 19 20

0.925 0.962 1.00 1.05 1.10

0.616 0.640 0.667 0.697 0.729

0.888 0.901 0.914 0.927 0.941

0.591 0.599 0.608 0.617 0.626

1.05 1.10 1.14 1.20 1.25

0.701 0.730 0.761 0.796 0.835

1.04 1.06 1.08 1.09 1.11

0.693 0.704 0.716 0.728 0.740

1.18 1.23 1.28 1.34 1.41

0.784 0.816 0.852 0.892 0.935

1.18 1.20 1.22 1.24 1.26

0.782 0.796 0.811 0.826 0.841

22 24 26 28 30

1.21 1.35 1.52 1.72 1.98

0.805 0.897 1.01 1.15 1.31

0.970 1.00 1.03 1.07 1.11

0.645 0.666 0.688 0.711 0.736

1.39 1.55 1.75 2.00 2.29

0.924 1.03 1.17 1.33 1.53

1.15 1.19 1.24 1.29 1.34

0.767 0.795 0.825 0.858 0.894

1.56 1.74 1.97 2.25 2.59

1.04 1.16 1.31 1.50 1.72

1.31 1.37 1.43 1.49 1.56

0.874 0.910 0.948 0.990 1.04

32 34 36 38 40

2.25 2.54 2.85 3.17 3.51

1.50 1.69 1.89 2.11 2.34

1.15 1.19 1.24 1.29 1.34

0.763 0.792 0.823 0.857 0.895

2.61 2.95 3.30 3.68 4.08

1.74 1.96 2.20 2.45 2.71

1.40 1.47 1.54 1.64 1.75

0.933 0.975 1.02 1.09 1.16

2.95 3.32 3.73 4.15 4.60

1.96 2.21 2.48 2.76 3.06

1.63 1.72 1.85 1.98 2.12

1.09 1.14 1.23 1.32 1.41

0

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

LRFD

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

3.30 0.684 0.841

2.19 0.455 0.560

3.85 0.773 0.950

2.56 0.514 0.633

4.33 0.861 1.06

2.88 0.573 0.705

rx /ry

3.13

3.11

3.11

ry , in.

2.99

2.95

2.93

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:49 AM

Page 47

STEEL BEAM-COLUMN SELECTION TABLES

6–47

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W21

W-Shapes W21×

Shape

122

p × 10 Design

(kips) ASD

(kip-ft)

LRFD

ASD

–1

LRFD

p × 10

bx × 10

3

(kips) ASD

3

–1

(kip-ft)

LRFD

ASD

–1

LRFD

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips)

ASD

LRFD

0.930 0.619 1.16

0.772 1.02

0.682 1.28

0.850 1.13

0.754 1.41

0.937

6 7 8 9 10

0.973 0.988 1.01 1.03 1.05

0.647 0.658 0.670 0.684 0.700

1.16 1.16 1.16 1.16 1.16

0.772 0.772 0.772 0.772 0.772

1.07 1.09 1.11 1.13 1.16

0.713 0.725 0.739 0.754 0.773

1.28 1.28 1.28 1.28 1.28

0.850 0.850 0.850 0.850 0.850

1.18 1.20 1.22 1.24 1.27

0.785 0.797 0.810 0.826 0.846

1.41 1.41 1.41 1.41 1.41

0.937 0.937 0.937 0.937 0.937

11 12 13 14 15

1.08 1.11 1.15 1.19 1.23

0.719 0.739 0.763 0.789 0.817

1.17 1.19 1.22 1.24 1.26

0.781 0.795 0.809 0.823 0.838

1.19 1.23 1.27 1.31 1.36

0.793 0.816 0.842 0.871 0.903

1.29 1.32 1.34 1.37 1.40

0.861 0.877 0.894 0.911 0.929

1.31 1.34 1.39 1.43 1.49

0.869 0.894 0.923 0.955 0.990

1.43 1.46 1.49 1.52 1.55

0.951 0.969 0.989 1.01 1.03

16 17 18 19 20

1.28 1.33 1.39 1.45 1.52

0.849 0.884 0.924 0.967 1.01

1.28 1.31 1.33 1.36 1.39

0.854 0.870 0.887 0.905 0.923

1.41 1.47 1.54 1.61 1.69

0.939 0.979 1.02 1.07 1.12

1.42 1.45 1.48 1.51 1.55

0.947 0.966 0.986 1.01 1.03

1.55 1.61 1.69 1.77 1.86

1.03 1.07 1.12 1.18 1.23

1.58 1.61 1.65 1.69 1.72

1.05 1.07 1.10 1.12 1.15

22 24 26 28 30

1.69 1.89 2.14 2.45 2.82

1.13 1.26 1.43 1.63 1.87

1.45 1.51 1.58 1.65 1.74

0.961 1.00 1.05 1.10 1.16

1.88 2.11 2.39 2.74 3.14

1.25 1.40 1.59 1.82 2.09

1.62 1.69 1.78 1.87 1.97

1.08 1.13 1.18 1.24 1.31

2.06 2.32 2.63 3.02 3.46

1.37 1.54 1.75 2.01 2.30

1.81 1.90 2.00 2.11 2.24

1.20 1.26 1.33 1.41 1.49

32 34 36 38 40

3.20 3.62 4.06 4.52 5.01

2.13 2.41 2.70 3.01 3.33

1.83 1.97 2.12 2.28 2.44

1.22 1.31 1.41 1.52 1.62

3.58 4.04 4.53 5.05 5.59

2.38 2.69 3.01 3.36 3.72

2.12 2.31 2.50 2.69 2.88

1.41 1.53 1.66 1.79 1.91

3.94 4.45 4.99 5.56 6.16

2.62 2.96 3.32 3.70 4.10

2.46 2.69 2.92 3.14 3.37

1.64 1.79 1.94 2.09 2.24

0

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

3

–1

101c

111

bx × 10

3

ASD

LRFD

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

c

–1

4.71 0.930 1.14

3.14 0.619 0.762

5.22 1.02 1.26

3.48 0.682 0.839

5.77 1.12 1.38

3.84 0.746 0.918

rx /ry

3.11

3.12

3.12

ry , in.

2.92

2.90

2.89

Shape is slender for compression with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed.

2/4/11

8:49 AM

6–48

Page 48

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W21

W-Shapes W21×

Shape

83c

93

p × 10

bx × 10

3

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

(kips)

–1

(kip-ft) ASD

73c

p × 10

3

bx × 10

3

–1

3

–1

(kips)

(kip-ft) ASD

–1

p × 10 (kips)

3

bx × 103

–1

(kip-ft)–1

ASD

LRFD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

ASD

LRFD

0

1.22

0.814 1.61

1.07

1.38

0.916 1.82

1.21

1.62

1.08

2.07

1.38

6 7 8 9 10

1.37 1.42 1.49 1.57 1.67

0.910 0.948 0.993 1.05 1.11

1.61 1.63 1.68 1.73 1.78

1.07 1.09 1.12 1.15 1.18

1.53 1.60 1.67 1.77 1.87

1.02 1.06 1.11 1.17 1.25

1.82 1.85 1.90 1.96 2.02

1.21 1.23 1.26 1.30 1.34

1.78 1.85 1.93 2.02 2.14

1.19 1.23 1.28 1.35 1.43

2.07 2.11 2.18 2.25 2.32

1.38 1.40 1.45 1.49 1.55

11 12 13 14 15

1.78 1.91 2.07 2.25 2.46

1.19 1.27 1.38 1.50 1.64

1.83 1.89 1.95 2.01 2.08

1.22 1.25 1.29 1.34 1.38

2.00 2.15 2.33 2.53 2.78

1.33 1.43 1.55 1.69 1.85

2.09 2.16 2.23 2.31 2.40

1.39 1.43 1.48 1.54 1.60

2.29 2.47 2.67 2.92 3.20

1.52 1.64 1.78 1.94 2.13

2.40 2.49 2.58 2.68 2.79

1.60 1.66 1.72 1.79 1.86

16 17 18 19 20

2.71 3.01 3.36 3.74 4.15

1.80 2.00 2.23 2.49 2.76

2.15 2.23 2.32 2.41 2.51

1.43 1.48 1.54 1.60 1.67

3.06 3.40 3.80 4.23 4.69

2.04 2.26 2.53 2.82 3.12

2.49 2.59 2.70 2.82 2.95

1.66 1.72 1.80 1.88 1.96

3.54 3.93 4.41 4.91 5.44

2.35 2.62 2.93 3.27 3.62

2.91 3.04 3.18 3.33 3.58

1.94 2.02 2.11 2.22 2.38

22 24 26 28 30

5.02 5.97 7.01 8.13 9.33

3.34 3.97 4.66 5.41 6.21

2.77 3.12 3.46 3.81 4.16

1.84 2.07 2.30 2.54 2.77

5.67 6.75 7.93 9.19 10.6

3.78 4.49 5.27 6.12 7.02

3.37 3.81 4.25 4.69 5.13

2.24 2.53 2.83 3.12 3.41

6.58 7.83 9.19 10.7 12.2

4.38 5.21 6.12 7.09 8.14

4.13 4.68 5.24 5.81 6.37

2.75 3.12 3.49 3.86 4.24

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

10.3 1.22 1.50

6.83 0.814 1.00

11.7 1.37 1.68

7.77 0.911 1.12

13.4 1.55 1.91

8.91 1.03 1.27

rx /ry

4.73

4.74

4.77

ry , in.

1.84

1.83

1.81

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06A:14th Ed._

2/17/12

10:14 AM

Page 49

STEEL BEAM-COLUMN SELECTION TABLES

6–49

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W21

W-Shapes W21×

Shape

68c

62c

p × 10

bx × 10

3

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Design

(kips)

–1

(kip-ft)

57c

p × 10

3

bx × 10

3

–1

(kips)

3

–1

(kip-ft)

–1

3

p × 10

bx × 103

–1

(kip-ft)–1

(kips)

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1.77

1.18

2.23

1.48

1.98

1.31

2.47

1.65

2.18

1.45

2.76

1.84

6 7 8 9 10

1.95 2.02 2.10 2.21 2.33

1.30 1.34 1.40 1.47 1.55

2.23 2.27 2.35 2.43 2.51

1.48 1.51 1.56 1.62 1.67

2.18 2.26 2.35 2.47 2.61

1.45 1.50 1.56 1.64 1.74

2.47 2.54 2.62 2.71 2.81

1.65 1.69 1.74 1.81 1.87

2.56 2.73 2.94 3.21 3.56

1.71 1.82 1.96 2.14 2.37

2.91 3.04 3.19 3.35 3.53

1.94 2.03 2.12 2.23 2.35

11 12 13 14 15

2.48 2.67 2.89 3.16 3.47

1.65 1.77 1.92 2.10 2.31

2.61 2.70 2.81 2.93 3.05

1.73 1.80 1.87 1.95 2.03

2.78 2.98 3.22 3.53 3.89

1.85 1.98 2.14 2.35 2.59

2.92 3.04 3.16 3.30 3.44

1.94 2.02 2.10 2.19 2.29

4.02 4.60 5.32 6.17 7.08

2.68 3.06 3.54 4.10 4.71

3.73 3.95 4.20 4.48 4.94

2.48 2.63 2.79 2.98 3.29

16 17 18 19 20

3.84 4.27 4.79 5.34 5.91

2.55 2.84 3.19 3.55 3.93

3.19 3.34 3.50 3.72 4.03

2.12 2.22 2.33 2.48 2.68

4.31 4.83 5.41 6.03 6.68

2.87 3.21 3.60 4.01 4.45

3.61 3.78 3.98 4.33 4.70

2.40 2.52 2.65 2.88 3.13

8.06 9.10 10.2 11.4 12.6

5.36 6.05 6.79 7.56 8.38

5.47 6.01 6.55 7.10 7.65

3.64 4.00 4.36 4.72 5.09

22 24 26 28 30

7.16 8.52 9.99 11.6 13.3

4.76 5.67 6.65 7.71 8.85

4.66 5.31 5.95 6.60 7.26

3.10 3.53 3.96 4.39 4.83

8.09 9.63 11.3 13.1

5.38 6.40 7.52 8.72

5.46 6.24 7.02 7.81

3.63 4.15 4.67 5.20

15.2

8.76

5.83

10.1

Other Constants and Properties

by × 10 , (kip-ft) t y × 103, (kips)–1 t r × 103, (kips)–1 3

–1

14.6 1.67 2.05

9.71 1.11 1.37

16.4 1.83 2.24

10.9 1.21 1.49

24.1 2.00 2.46

16.0 1.33 1.64

rx /ry

4.78

4.82

6.19

ry , in.

1.80

1.77

1.35

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:51 AM

6–50

Page 50

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W21

W-Shapes W21×

Shape

55c

p×

50c

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

103

(kip-ft)–1

p×

48c, f

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

2.29

1.52

2.83

1.88

2.54

1.69

3.24

2.15

2.71

1.80

3.36

2.23

6 7 8 9 10

2.52 2.61 2.73 2.86 3.03

1.68 1.74 1.81 1.91 2.02

2.83 2.92 3.02 3.14 3.27

1.88 1.94 2.01 2.09 2.17

3.01 3.22 3.48 3.81 4.25

2.00 2.14 2.31 2.54 2.82

3.45 3.63 3.81 4.02 4.26

2.30 2.41 2.54 2.68 2.83

3.00 3.11 3.25 3.42 3.63

1.99 2.07 2.16 2.28 2.42

3.36 3.47 3.61 3.76 3.92

2.23 2.31 2.40 2.50 2.61

11 12 13 14 15

3.23 3.47 3.76 4.11 4.55

2.15 2.31 2.50 2.73 3.03

3.40 3.55 3.71 3.89 4.08

2.26 2.36 2.47 2.59 2.71

4.83 5.57 6.52 7.56 8.68

3.21 3.71 4.34 5.03 5.77

4.52 4.82 5.16 5.67 6.36

3.01 3.21 3.43 3.77 4.23

3.88 4.19 4.56 5.02 5.60

2.58 2.79 3.04 3.34 3.72

4.10 4.30 4.51 4.74 5.01

2.73 2.86 3.00 3.16 3.33

16 17 18 19 20

5.07 5.71 6.40 7.13 7.90

3.38 3.80 4.26 4.75 5.26

4.29 4.53 4.92 5.38 5.86

2.86 3.01 3.27 3.58 3.90

9.87 6.57 11.1 7.42 12.5 8.31 13.9 9.26 15.4 10.3

7.06 7.78 8.51 9.24 9.99

4.70 5.17 5.66 6.15 6.65

6.31 7.13 7.99 8.90 9.86

4.20 4.74 5.32 5.92 6.56

5.30 5.75 6.35 6.97 7.60

3.52 3.82 4.22 4.63 5.06

21 22 23 24 25

8.71 9.56 10.5 11.4 12.3

5.80 6.36 6.95 7.57 8.22

6.34 6.84 7.34 7.84 8.35

4.22 4.55 4.88 5.22 5.56

17.0

10.9 11.9 13.0 14.2 15.4

7.23 8.25 7.94 8.91 8.68 9.58 9.45 10.3 10.3 10.9

5.49 5.93 6.37 6.82 7.28

26 27 28

13.4 14.4 15.5

8.89 9.58 10.3

8.87 9.38 9.90

5.90 6.24 6.59

16.7 18.0

11.1 12.0

7.75 8.22

11.3

10.7

7.15

11.6 12.3

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

19.4 2.06 2.53

12.9 1.37 1.69

29.2 2.27 2.79

19.4 1.51 1.86

24.2 2.37 2.91

16.1 1.58 1.94

rx /ry

4.86

6.29

4.96

ry , in.

1.73

1.30

1.66

Shape is slender for compression with Fy = 50 ksi. f Shape does not meet compact limit for flexure with F = 50 ksi. y Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/17/12

10:30 AM

Page 51

STEEL BEAM-COLUMN SELECTION TABLES

6–51

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W21-W18

W-Shapes W21×

Shape

p×

311h

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

W18×

44c 103

(kip-ft)–1

p×

283h

bx ×

103

(kips)–1

103

(kip-ft)–1

LRFD

ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

0

2.97

1.98

3.73

2.48

0.365 0.243 0.473 0.314 0.401 0.267 0.527 0.351

ASD

LRFD

ASD

LRFD

6 7 8 9 10

3.53 3.78 4.09 4.50 5.03

2.35 2.51 2.72 3.00 3.35

4.03 4.24 4.48 4.75 5.05

2.68 2.82 2.98 3.16 3.36

0.381 0.387 0.394 0.402 0.412

0.253 0.257 0.262 0.268 0.274

0.473 0.473 0.473 0.473 0.473

0.314 0.314 0.314 0.314 0.314

0.419 0.426 0.434 0.443 0.454

0.279 0.284 0.289 0.295 0.302

0.527 0.527 0.527 0.527 0.527

0.351 0.351 0.351 0.351 0.351

11 12 13 14 15

5.74 6.68 7.84 9.10 10.4

3.82 4.45 5.22 6.05 6.95

5.39 5.79 6.25 7.11 7.99

3.59 3.85 4.16 4.73 5.32

0.422 0.434 0.447 0.462 0.479

0.281 0.289 0.298 0.308 0.319

0.474 0.477 0.480 0.483 0.486

0.315 0.317 0.319 0.321 0.323

0.466 0.480 0.495 0.512 0.530

0.310 0.319 0.329 0.340 0.353

0.530 0.533 0.537 0.540 0.544

0.352 0.355 0.357 0.359 0.362

16 17 18 19 20

11.9 13.4 15.0 16.8 18.6

7.91 8.90 8.93 9.83 10.0 10.8 11.1 11.8 12.4 12.7

5.92 6.54 7.18 7.82 8.47

0.497 0.517 0.540 0.564 0.592

0.331 0.344 0.359 0.375 0.394

0.489 0.492 0.495 0.498 0.501

0.325 0.327 0.329 0.331 0.333

0.551 0.574 0.600 0.628 0.659

0.367 0.382 0.399 0.418 0.439

0.548 0.551 0.555 0.559 0.563

0.364 0.367 0.369 0.372 0.374

22 24 26 28 30

0.655 0.732 0.826 0.942 1.08

0.436 0.487 0.550 0.627 0.720

0.507 0.514 0.521 0.528 0.535

0.338 0.342 0.347 0.351 0.356

0.732 0.821 0.929 1.06 1.22

0.487 0.546 0.618 0.708 0.813

0.571 0.579 0.588 0.596 0.605

0.380 0.385 0.391 0.397 0.403

32 34 36 38 40

1.23 1.39 1.56 1.74 1.92

0.819 0.924 1.04 1.15 1.28

0.542 0.550 0.557 0.565 0.573

0.361 0.366 0.371 0.376 0.382

1.39 1.57 1.76 1.96 2.17

0.925 1.04 1.17 1.30 1.45

0.614 0.624 0.634 0.644 0.654

0.409 0.415 0.422 0.428 0.435

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

35.0 2.57 3.16

23.3 1.71 2.10

1.72 0.365 0.448

1.15 0.243 0.299

1.93 0.401 0.493

1.28 0.267 0.328

rx /ry

6.40

2.96

2.96

ry , in.

1.26

2.95

2.91

Shape is slender for compression with Fy = 50 ksi. h Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:52 AM

6–52

Page 52

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W18

W-Shapes W18×

Shape

258h

p× ASD 0

234h

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

103

(kip-ft)–1

LRFD

ASD

LRFD

p×

(kips)–1 ASD

211

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

0.439 0.292 0.583 0.388 0.487 0.324 0.649 0.432 0.536 0.357 0.727 0.484

6 7 8 9 10

0.460 0.468 0.477 0.487 0.499

0.306 0.311 0.317 0.324 0.332

0.583 0.583 0.583 0.583 0.583

0.388 0.388 0.388 0.388 0.388

0.510 0.519 0.529 0.541 0.554

0.339 0.345 0.352 0.360 0.369

0.649 0.649 0.649 0.649 0.649

0.432 0.432 0.432 0.432 0.432

0.562 0.572 0.584 0.597 0.612

0.374 0.381 0.388 0.397 0.407

0.727 0.727 0.727 0.727 0.727

0.484 0.484 0.484 0.484 0.484

11 12 13 14 15

0.512 0.528 0.545 0.564 0.585

0.341 0.351 0.362 0.375 0.389

0.587 0.591 0.595 0.600 0.604

0.390 0.393 0.396 0.399 0.402

0.570 0.587 0.606 0.628 0.652

0.379 0.390 0.403 0.418 0.434

0.654 0.659 0.664 0.670 0.675

0.435 0.438 0.442 0.446 0.449

0.629 0.649 0.671 0.695 0.722

0.419 0.432 0.446 0.462 0.480

0.734 0.740 0.747 0.754 0.761

0.488 0.493 0.497 0.502 0.506

16 17 18 19 20

0.608 0.634 0.663 0.695 0.730

0.405 0.422 0.441 0.462 0.486

0.609 0.613 0.618 0.623 0.627

0.405 0.408 0.411 0.414 0.417

0.678 0.708 0.741 0.777 0.818

0.451 0.471 0.493 0.517 0.544

0.681 0.687 0.692 0.698 0.704

0.453 0.457 0.461 0.465 0.469

0.752 0.786 0.823 0.865 0.910

0.501 0.523 0.548 0.575 0.606

0.768 0.775 0.782 0.790 0.797

0.511 0.516 0.520 0.525 0.531

22 24 26 28 30

0.812 0.913 1.04 1.19 1.37

0.541 0.607 0.690 0.793 0.910

0.637 0.648 0.658 0.669 0.680

0.424 0.431 0.438 0.445 0.453

0.912 1.03 1.17 1.35 1.55

0.607 0.683 0.778 0.897 1.03

0.717 0.729 0.742 0.756 0.770

0.477 0.485 0.494 0.503 0.513

1.02 1.15 1.31 1.52 1.74

0.677 0.765 0.873 1.01 1.16

0.813 0.829 0.846 0.864 0.882

0.541 0.552 0.563 0.575 0.587

32 34 36 38 40

1.56 1.76 1.97 2.19 2.43

1.04 1.17 1.31 1.46 1.62

0.692 0.704 0.716 0.729 0.743

0.460 0.468 0.477 0.485 0.494

1.76 1.99 2.23 2.48 2.75

1.17 1.32 1.48 1.65 1.83

0.785 0.800 0.816 0.833 0.850

0.522 0.533 0.543 0.554 0.566

1.98 2.24 2.51 2.79 3.09

1.32 1.49 1.67 1.86 2.06

0.902 0.922 0.943 0.965 0.988

0.600 0.613 0.627 0.642 0.657

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

h

2.15 0.439 0.540

1.43 0.292 0.360

2.39 0.487 0.598

1.59 0.324 0.399

2.70 0.536 0.659

1.80 0.357 0.439

rx /ry

2.96

2.96

2.96

ry , in.

2.88

2.85

2.82

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:52 AM

Page 53

STEEL BEAM-COLUMN SELECTION TABLES

6–53

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W18

W-Shapes W18×

Shape

192

p×

(kips)–1

Design

ASD

103

(kip-ft)–1

LRFD

ASD

LRFD

p×

(kips)–1 ASD

158

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1 ASD

LRFD

0.594 0.395 0.806 0.536 0.650 0.432 0.895 0.596 0.721 0.480 1.00

0.666

6 7 8 9 10

0.624 0.635 0.648 0.663 0.680

0.415 0.423 0.431 0.441 0.453

0.806 0.806 0.806 0.806 0.807

0.536 0.536 0.536 0.536 0.537

0.683 0.695 0.710 0.727 0.746

0.454 0.463 0.472 0.484 0.496

0.895 0.895 0.895 0.895 0.898

0.596 0.596 0.596 0.596 0.597

0.759 0.773 0.789 0.808 0.830

0.505 0.514 0.525 0.538 0.552

1.00 1.00 1.00 1.00 1.00

0.666 0.666 0.666 0.666 0.668

11 12 13 14 15

0.700 0.722 0.747 0.775 0.806

0.466 0.480 0.497 0.515 0.536

0.815 0.823 0.831 0.840 0.848

0.542 0.548 0.553 0.559 0.564

0.768 0.793 0.821 0.852 0.887

0.511 0.528 0.546 0.567 0.590

0.907 0.917 0.927 0.938 0.948

0.604 0.610 0.617 0.624 0.631

0.855 0.883 0.914 0.950 0.989

0.569 0.587 0.608 0.632 0.658

1.02 1.03 1.04 1.05 1.07

0.676 0.685 0.693 0.702 0.710

16 17 18 19 20

0.840 0.879 0.921 0.968 1.02

0.559 0.585 0.613 0.644 0.679

0.857 0.866 0.875 0.884 0.894

0.570 0.576 0.582 0.588 0.595

0.926 0.969 1.02 1.07 1.13

0.616 0.645 0.677 0.712 0.752

0.959 0.970 0.981 0.993 1.00

0.638 0.645 0.653 0.661 0.669

1.03 1.08 1.14 1.20 1.26

0.687 0.720 0.756 0.796 0.841

1.08 1.10 1.11 1.12 1.14

0.719 0.729 0.738 0.748 0.758

22 24 26 28 30

1.14 1.30 1.48 1.72 1.97

0.761 0.862 0.987 1.14 1.31

0.913 0.934 0.955 0.978 1.00

0.608 0.621 0.636 0.651 0.666

1.27 1.44 1.65 1.92 2.20

0.844 0.958 1.10 1.28 1.47

1.03 1.06 1.08 1.11 1.14

0.685 0.702 0.720 0.739 0.759

1.42 1.62 1.86 2.16 2.48

0.946 1.08 1.24 1.44 1.65

1.17 1.20 1.24 1.28 1.32

0.779 0.801 0.824 0.849 0.875

32 34 36 38 40

2.24 2.53 2.84 3.16 3.50

1.49 1.68 1.89 2.10 2.33

1.03 1.05 1.08 1.11 1.14

0.683 0.700 0.718 0.737 0.757

2.51 2.83 3.17 3.53 3.91

1.67 1.88 2.11 2.35 2.60

1.17 1.21 1.24 1.28 1.32

0.780 0.803 0.827 0.852 0.878

2.82 3.19 3.57 3.98 4.41

1.88 2.12 2.38 2.65 2.93

1.36 1.40 1.45 1.50 1.56

0.903 0.933 0.965 0.999 1.04

0

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

175

bx ×

103

ASD

LRFD

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

2.99 0.594 0.730

1.99 0.395 0.487

3.36 0.650 0.798

2.24 0.432 0.532

3.76 0.721 0.886

2.50 0.480 0.591

rx /ry

2.97

2.97

2.96

ry , in.

2.79

2.76

2.74

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:52 AM

6–54

Page 54

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W18

W-Shapes W18×

Shape

143

p× ASD

130

bx ×

103

(kips)–1

Design

103

(kip-ft)–1

LRFD

ASD

LRFD

p×

(kips)–1 ASD

119

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

LRFD

ASD

LRFD

0.795 0.529 1.11

0.736 0.872 0.580 1.23

0.817 0.952 0.633

1.36

0.905

6 7 8 9 10

0.837 0.853 0.871 0.892 0.917

0.557 0.567 0.580 0.594 0.610

1.11 1.11 1.11 1.11 1.11

0.736 0.736 0.736 0.736 0.740

0.919 0.936 0.957 0.980 1.01

0.611 0.623 0.636 0.652 0.670

1.23 1.23 1.23 1.23 1.24

0.817 0.817 0.817 0.817 0.823

1.00 1.02 1.04 1.07 1.10

0.667 0.680 0.695 0.712 0.732

1.36 1.36 1.36 1.36 1.37

0.905 0.905 0.905 0.905 0.912

11 12 13 14 15

0.945 0.976 1.01 1.05 1.10

0.629 0.649 0.673 0.699 0.729

1.13 1.14 1.16 1.17 1.19

0.750 0.760 0.770 0.780 0.791

1.04 1.07 1.11 1.16 1.21

0.691 0.714 0.741 0.770 0.803

1.25 1.27 1.29 1.31 1.33

0.835 0.847 0.859 0.872 0.886

1.13 1.17 1.22 1.27 1.32

0.755 0.781 0.810 0.842 0.878

1.39 1.41 1.44 1.46 1.49

0.926 0.941 0.956 0.972 0.989

16 17 18 19 20

1.14 1.20 1.26 1.33 1.41

0.762 0.798 0.839 0.884 0.935

1.21 1.22 1.24 1.26 1.28

0.802 0.814 0.825 0.838 0.850

1.26 1.32 1.39 1.47 1.55

0.840 0.881 0.926 0.977 1.03

1.35 1.37 1.39 1.42 1.44

0.899 0.913 0.928 0.943 0.959

1.38 1.45 1.52 1.61 1.70

0.919 0.964 1.01 1.07 1.13

1.51 1.54 1.57 1.59 1.62

1.01 1.02 1.04 1.06 1.08

22 24 26 28 30

1.58 1.81 2.08 2.42 2.77

1.05 1.20 1.39 1.61 1.85

1.32 1.36 1.40 1.45 1.50

0.876 0.904 0.933 0.965 0.999

1.75 2.00 2.32 2.69 3.09

1.17 1.33 1.54 1.79 2.05

1.49 1.54 1.60 1.66 1.73

0.992 1.03 1.06 1.10 1.15

1.92 2.20 2.55 2.96 3.39

1.28 1.46 1.70 1.97 2.26

1.69 1.75 1.83 1.90 1.99

1.12 1.17 1.21 1.27 1.32

32 34 36 38 40

3.16 3.56 4.00 4.45 4.93

2.10 2.37 2.66 2.96 3.28

1.56 1.61 1.68 1.74 1.82

1.03 1.07 1.12 1.16 1.21

3.51 3.97 4.45 4.95 5.49

2.34 2.64 2.96 3.30 3.65

1.80 1.87 1.96 2.08 2.20

1.20 1.25 1.30 1.38 1.47

3.86 4.36 4.89 5.45 6.04

2.57 2.90 3.25 3.62 4.02

2.08 2.19 2.34 2.50 2.65

1.39 1.46 1.56 1.66 1.77

0

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

ASD

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 tr × 103, (kips)–1

4.17 0.795 0.977

2.78 0.529 0.651

4.64 0.872 1.07

3.09 0.580 0.714

5.16 0.952 1.17

3.43 0.633 0.779

rx /ry

2.97

2.97

2.94

ry , in.

2.72

2.70

2.69

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:52 AM

Page 55

STEEL BEAM-COLUMN SELECTION TABLES

6–55

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W18

W-Shapes W18×

Shape

106

p×

(kips)–1

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Design

97

bx ×

103

103

(kip-ft)–1 ASD

p×

86

bx ×

103

(kips)–1

103

(kip-ft)–1 ASD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

0

1.07

0.715 1.55

1.03

1.17

0.780 1.69

1.12

1.32

0.878 1.92

ASD

1.27

LRFD

6 7 8 9 10

1.13 1.16 1.18 1.21 1.25

0.754 0.769 0.786 0.806 0.829

1.55 1.55 1.55 1.55 1.56

1.03 1.03 1.03 1.03 1.04

1.24 1.26 1.29 1.32 1.36

0.823 0.839 0.858 0.880 0.906

1.69 1.69 1.69 1.69 1.71

1.12 1.12 1.12 1.12 1.14

1.39 1.42 1.46 1.49 1.54

0.928 0.946 0.968 0.994 1.02

1.92 1.92 1.92 1.92 1.94

1.27 1.27 1.27 1.27 1.29

11 12 13 14 15

1.29 1.33 1.38 1.44 1.50

0.856 0.885 0.919 0.957 0.999

1.59 1.62 1.65 1.68 1.71

1.06 1.08 1.10 1.12 1.14

1.41 1.45 1.51 1.57 1.64

0.935 0.968 1.00 1.05 1.09

1.74 1.77 1.81 1.84 1.88

1.16 1.18 1.20 1.23 1.25

1.59 1.64 1.71 1.78 1.86

1.06 1.09 1.14 1.18 1.24

1.98 2.02 2.06 2.11 2.15

1.32 1.35 1.37 1.40 1.43

16 17 18 19 20

1.57 1.65 1.74 1.84 1.95

1.05 1.10 1.16 1.22 1.30

1.74 1.78 1.81 1.85 1.89

1.16 1.18 1.21 1.23 1.26

1.72 1.81 1.90 2.01 2.13

1.14 1.20 1.27 1.34 1.42

1.92 1.96 2.00 2.04 2.09

1.28 1.30 1.33 1.36 1.39

1.95 2.05 2.16 2.29 2.43

1.30 1.36 1.44 1.52 1.61

2.20 2.25 2.31 2.36 2.42

1.47 1.50 1.53 1.57 1.61

22 24 26 28 30

2.21 2.53 2.94 3.41 3.92

1.47 1.68 1.96 2.27 2.61

1.97 2.06 2.15 2.26 2.38

1.31 1.37 1.43 1.50 1.58

2.42 2.78 3.24 3.75 4.31

1.61 1.85 2.15 2.50 2.87

2.18 2.29 2.41 2.54 2.68

1.45 1.52 1.60 1.69 1.78

2.76 3.17 3.70 4.29 4.93

1.83 2.11 2.46 2.86 3.28

2.54 2.68 2.84 3.01 3.29

1.69 1.79 1.89 2.00 2.19

32 34 36 38 40

4.46 5.03 5.64 6.29 6.97

2.97 3.35 3.75 4.18 4.63

2.51 2.72 2.92 3.12 3.32

1.67 1.81 1.94 2.08 2.21

4.90 5.53 6.20 6.91 7.66

3.26 3.68 4.13 4.60 5.10

2.91 3.15 3.38 3.62 3.86

1.93 2.09 2.25 2.41 2.57

5.61 6.33 7.10 7.91 8.76

3.73 4.21 4.72 5.26 5.83

3.59 3.90 4.21 4.51 4.82

2.39 2.60 2.80 3.00 3.21

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

5.89 1.07 1.32

3.92 0.715 0.879

6.44 1.17 1.44

4.29 0.780 0.960

7.36 1.32 1.62

4.90 0.878 1.08

rx /ry

2.95

2.95

2.95

ry , in.

2.66

2.65

2.63

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:52 AM

6–56

Page 56

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W18

W-Shapes W18×

Shape

76c

p×

71

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

p×

103

(kip-ft)–1

65

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1.52

1.01

2.19

1.45

1.60

1.06

2.44

1.62

1.75

1.16

2.68

1.78

6 7 8 9 10

1.59 1.62 1.66 1.70 1.75

1.06 1.08 1.10 1.13 1.16

2.19 2.19 2.19 2.19 2.22

1.45 1.45 1.45 1.45 1.48

1.82 1.91 2.02 2.15 2.30

1.21 1.27 1.34 1.43 1.53

2.44 2.51 2.59 2.67 2.76

1.62 1.67 1.72 1.78 1.83

2.00 2.09 2.21 2.36 2.53

1.33 1.39 1.47 1.57 1.68

2.68 2.76 2.85 2.95 3.05

1.78 1.84 1.90 1.96 2.03

11 12 13 14 15

1.81 1.87 1.94 2.03 2.12

1.20 1.24 1.29 1.35 1.41

2.27 2.32 2.37 2.43 2.49

1.51 1.54 1.58 1.62 1.65

2.48 2.70 2.96 3.26 3.63

1.65 1.80 1.97 2.17 2.41

2.85 2.95 3.05 3.17 3.29

1.90 1.96 2.03 2.11 2.19

2.73 2.97 3.26 3.60 4.01

1.82 1.98 2.17 2.40 2.67

3.15 3.27 3.39 3.53 3.67

2.10 2.18 2.26 2.35 2.44

16 17 18 19 20

2.22 2.34 2.47 2.62 2.78

1.48 1.56 1.64 1.74 1.85

2.55 2.61 2.68 2.75 2.82

1.69 1.74 1.78 1.83 1.88

4.06 4.58 5.14 5.73 6.34

2.70 3.05 3.42 3.81 4.22

3.42 3.57 3.72 3.89 4.12

2.28 2.37 2.48 2.59 2.74

4.50 5.08 5.69 6.34 7.02

2.99 3.38 3.79 4.22 4.67

3.83 4.00 4.19 4.43 4.76

2.55 2.66 2.79 2.95 3.17

22 24 26 28 30

3.16 3.65 4.26 4.94 5.68

2.11 2.43 2.84 3.29 3.78

2.98 3.16 3.36 3.67 4.06

1.98 2.10 2.24 2.44 2.70

7.68 9.14 10.7 12.4

5.11 6.08 7.13 8.27

4.69 5.25 5.82 6.38

3.12 3.50 3.87 4.25

8.50 10.1 11.9 13.8

5.66 6.73 7.90 9.16

5.44 6.11 6.79 7.46

3.62 4.07 4.51 4.96

32 34 36 38 40

6.46 7.29 8.17 9.11 10.1

4.30 4.85 5.44 6.06 6.71

4.45 4.85 5.24 5.64 6.04

2.96 3.22 3.49 3.75 4.02 Other Constants and Properties

× 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

8.44 1.50 1.84

5.62 0.997 1.23

14.4 1.60 1.96

9.60 1.06 1.31

15.8 1.75 2.15

10.5 1.16 1.43

rx /ry

2.96

4.41

4.43

ry , in.

2.61

1.70

1.69

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:52 AM

Page 57

STEEL BEAM-COLUMN SELECTION TABLES

6–57

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W18

W-Shapes W18×

Shape

60c

p×

bx ×

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

55c

103

p×

103

(kip-ft)–1

50c

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1.94

1.29

2.90

1.93

2.14

1.43

3.18

2.12

2.42

1.61

3.53

2.35

6 7 8 9 10

2.18 2.28 2.41 2.57 2.76

1.45 1.52 1.60 1.71 1.83

2.90 3.00 3.10 3.20 3.32

1.93 1.99 2.06 2.13 2.21

2.40 2.51 2.64 2.80 3.01

1.60 1.67 1.75 1.86 2.00

3.19 3.30 3.42 3.54 3.68

2.12 2.20 2.27 2.36 2.45

2.72 2.84 2.98 3.16 3.37

1.81 1.89 1.98 2.10 2.24

3.55 3.68 3.81 3.96 4.12

2.36 2.45 2.54 2.64 2.74

11 12 13 14 15

2.98 3.25 3.56 3.94 4.39

1.98 2.16 2.37 2.62 2.92

3.44 3.58 3.72 3.88 4.05

2.29 2.38 2.48 2.58 2.69

3.26 3.55 3.90 4.32 4.82

2.17 2.36 2.60 2.87 3.21

3.83 3.99 4.16 4.35 4.55

2.55 2.65 2.77 2.89 3.03

3.63 3.97 4.37 4.85 5.42

2.42 2.64 2.91 3.23 3.61

4.29 4.48 4.69 4.91 5.16

2.86 2.98 3.12 3.27 3.43

16 17 18 19 20

4.94 5.57 6.25 6.96 7.71

3.28 3.71 4.16 4.63 5.13

4.23 4.44 4.66 5.02 5.41

2.82 2.95 3.10 3.34 3.60

5.43 6.13 6.87 7.65 8.48

3.61 4.08 4.57 5.09 5.64

4.78 5.03 5.39 5.85 6.32

3.18 3.35 3.59 3.89 4.20

6.13 6.92 7.76 8.64 9.58

4.08 4.60 5.16 5.75 6.37

5.44 5.76 6.31 6.86 7.43

3.62 3.83 4.20 4.57 4.94

9.33 6.21 11.1 7.39 13.0 8.67 15.1 10.1

6.19 6.98 7.76 8.55

4.12 4.64 5.16 5.69

6.83 8.13 9.54

7.26 8.20 9.16

4.83 5.46 6.09

7.71 8.56 9.17 9.72 10.8 10.9

5.70 6.47 7.24

22 24 26 28

10.3 12.2 14.3

11.6 13.8 16.2

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

17.3 1.90 2.33

11.5 1.26 1.55

19.3 2.06 2.53

12.8 1.37 1.69

21.5 2.27 2.79

14.3 1.51 1.86

rx /ry

4.45

4.44

4.47

ry , in.

1.68

1.67

1.65

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B_14th Ed._ 20/02/12 3:21 PM Page 58

6–58

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W18

W-Shapes W18×

Shape

46c

p×

40c

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

p×

103

(kip-ft)–1

35c

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

2.65

1.76

3.93

2.61

3.15

2.10

4.54

3.02

3.71

2.47

5.36

3.56

6 7 8 9 10

3.19 3.42 3.72 4.13 4.66

2.12 2.28 2.48 2.75 3.10

4.19 4.39 4.61 4.85 5.12

2.79 2.92 3.07 3.23 3.41

3.79 4.06 4.41 4.87 5.45

2.52 2.70 2.94 3.24 3.63

4.88 5.13 5.40 5.71 6.05

3.25 3.41 3.59 3.80 4.03

4.49 4.83 5.27 5.85 6.61

2.99 3.21 3.51 3.89 4.40

5.84 6.17 6.54 6.96 7.43

3.89 4.11 4.35 4.63 4.94

11 12 13 14 15

5.32 6.15 7.21 8.36 9.60

3.54 4.09 4.80 5.56 6.38

5.43 5.77 6.16 6.69 7.45

3.61 3.84 4.10 4.45 4.95

6.24 7.25 8.51 9.87 11.3

4.15 4.82 5.66 6.56 7.54

6.44 6.88 7.38 8.30 9.27

4.28 7.63 4.58 9.00 4.91 10.6 5.52 12.2 6.17 14.1

5.08 7.97 5.99 8.60 7.03 9.67 8.15 11.0 9.36 12.3

5.30 5.72 6.43 7.29 8.17

16 17 18 19 20

10.9 12.3 13.8 15.4 17.1

7.26 8.21 8.20 8.98 9.19 9.75 10.2 10.5 11.3 11.3

5.46 5.97 6.49 7.01 7.53

12.9 14.5 16.3 18.2 20.1

8.57 9.68 10.9 12.1 13.4

10.3 11.3 12.3 13.3 14.4

21

18.8

12.5

8.05

22.2

14.8

15.4

12.1

6.83 7.50 8.17 8.85 9.54

16.0 18.1 20.2 22.6 25.0

10.6 12.0 13.5 15.0 16.6

13.6 15.0 16.4 17.9 19.3

9.07 10.0 10.9 11.9 12.8

10.2

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

30.5 2.47 3.04

20.3 1.65 2.03

35.6 2.83 3.48

23.7 1.88 2.32

44.2 3.24 3.98

29.4 2.16 2.66

rx /ry

5.62

5.68

5.77

ry , in.

1.29

1.27

1.22

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates Kl /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:52 AM

Page 59

STEEL BEAM-COLUMN SELECTION TABLES

6–59

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W16

W-Shapes W16×

Shape

100

p×

(kips)–1

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Design

89

bx ×

103

103

(kip-ft)–1

p×

77

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1.14

0.756

1.80

1.20

1.27

0.848

2.04

1.35

1.48 0.983

2.38

1.58

6 7 8 9 10

1.21 1.23 1.26 1.30 1.34

0.803 0.820 0.841 0.865 0.893

1.80 1.80 1.80 1.80 1.83

1.20 1.20 1.20 1.20 1.22

1.36 1.39 1.42 1.46 1.51

0.902 0.922 0.946 0.973 1.01

2.04 2.04 2.04 2.04 2.08

1.35 1.35 1.35 1.36 1.38

1.57 1.61 1.65 1.70 1.76

1.05 1.07 1.10 1.13 1.17

2.38 2.38 2.38 2.39 2.44

1.58 1.58 1.58 1.59 1.62

11 12 13 14 15

1.39 1.45 1.51 1.58 1.65

0.925 0.962 1.00 1.05 1.10

1.86 1.89 1.93 1.96 1.99

1.24 1.26 1.28 1.30 1.33

1.57 1.63 1.70 1.78 1.87

1.04 1.08 1.13 1.18 1.24

2.12 2.16 2.20 2.24 2.29

1.41 1.44 1.46 1.49 1.52

1.82 1.89 1.98 2.07 2.18

1.21 1.26 1.32 1.38 1.45

2.49 2.54 2.59 2.65 2.71

1.65 1.69 1.72 1.76 1.80

16 17 18 19 20

1.74 1.84 1.95 2.08 2.22

1.16 1.23 1.30 1.38 1.47

2.03 2.07 2.11 2.15 2.19

1.35 1.38 1.40 1.43 1.46

1.97 2.08 2.21 2.35 2.51

1.31 1.39 1.47 1.57 1.67

2.34 2.38 2.43 2.49 2.54

1.55 1.59 1.62 1.65 1.69

2.30 2.43 2.59 2.76 2.95

1.53 1.62 1.72 1.83 1.96

2.77 2.83 2.90 2.97 3.05

1.84 1.89 1.93 1.98 2.03

22 24 26 28 30

2.55 2.98 3.50 4.06 4.66

1.70 1.98 2.33 2.70 3.10

2.28 2.37 2.48 2.59 2.72

1.51 1.58 1.65 1.72 1.81

2.90 3.40 3.99 4.62 5.31

1.93 2.26 2.65 3.08 3.53

2.66 2.79 2.93 3.09 3.27

1.77 1.86 1.95 2.06 2.17

3.41 4.00 4.70 5.45 6.25

2.27 2.66 3.13 3.62 4.16

3.21 3.39 3.59 3.83 4.20

2.14 2.26 2.39 2.55 2.80

32 34 36 38 40

5.30 5.98 6.70 7.47 8.28

3.52 3.98 4.46 4.97 5.51

2.85 3.04 3.26 3.47 3.68

1.90 2.03 2.17 2.31 2.45

6.04 6.82 7.64 8.52 9.44

4.02 4.54 5.09 5.67 6.28

3.54 3.82 4.09 4.36 4.63

2.36 2.54 2.72 2.90 3.08

7.12 8.03 9.01 10.0 11.1

4.73 5.34 5.99 6.68 7.40

4.57 4.94 5.31 5.68 6.04

3.04 3.29 3.53 3.78 4.02

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

6.49 1.14 1.40

4.32 0.756 0.930

7.41 1.27 1.57

4.93 0.848 1.04

8.67 1.48 1.82

5.77 0.983 1.21

rx /ry

2.83

2.83

2.83

ry , in.

2.51

2.49

2.47

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:52 AM

6–60

Page 60

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W16

W-Shapes W16×

Shape

67c

p×

50c

57

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

p×

103

(kip-ft)–1

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1.71

1.14

2.74

1.82

1.99

1.32

3.39

2.26

2.30

1.53

3.87

2.58

6 7 8 9 10

1.81 1.86 1.90 1.96 2.03

1.21 1.23 1.27 1.31 1.35

2.74 2.74 2.74 2.76 2.82

1.82 1.82 1.82 1.84 1.88

2.31 2.43 2.59 2.77 3.00

1.53 1.62 1.72 1.85 2.00

3.43 3.54 3.65 3.78 3.91

2.28 2.35 2.43 2.51 2.60

2.64 2.79 2.97 3.18 3.45

1.76 1.85 1.97 2.12 2.29

3.92 4.06 4.21 4.36 4.53

2.61 2.70 2.80 2.90 3.02

11 12 13 14 15

2.10 2.19 2.29 2.40 2.52

1.40 1.46 1.52 1.59 1.68

2.88 2.95 3.02 3.09 3.17

1.92 1.96 2.01 2.06 2.11

3.27 3.59 3.98 4.45 5.02

2.18 2.39 2.65 2.96 3.34

4.05 4.20 4.37 4.55 4.74

2.70 2.80 2.91 3.03 3.15

3.76 4.14 4.59 5.14 5.80

2.50 2.75 3.06 3.42 3.86

4.72 4.91 5.13 5.37 5.63

3.14 3.27 3.41 3.57 3.74

16 17 18 19 20

2.66 2.82 2.99 3.19 3.42

1.77 1.87 1.99 2.12 2.27

3.25 3.33 3.42 3.51 3.61

2.16 2.22 2.27 2.34 2.40

5.70 6.44 7.22 8.04 8.91

3.79 4.28 4.80 5.35 5.93

4.95 5.18 5.43 5.81 6.23

3.29 3.45 3.61 3.86 4.14

6.60 7.45 8.35 9.31 10.3

4.39 4.96 5.56 6.19 6.86

5.91 6.23 6.74 7.28 7.83

3.93 4.14 4.48 4.85 5.21

22 24 26 28 30

3.96 4.65 5.46 6.33 7.27

2.63 3.10 3.63 4.21 4.84

3.83 4.07 4.34 4.82 5.31

2.55 2.71 2.89 3.21 3.53

7.17 8.54 10.0

7.07 7.90 8.74

4.70 5.26 5.82

12.5 14.8 17.4

8.30 8.93 9.88 10.0 11.6 11.1

5.94 6.67 7.40

32 34 36 38 40

8.27 9.34 10.5 11.7 12.9

5.50 6.21 6.96 7.76 8.60

5.80 6.29 6.77 7.26 7.75

3.86 4.18 4.51 4.83 5.15

10.8 12.8 15.1

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

10.0 1.70 2.09

6.68 1.13 1.40

18.9 1.99 2.44

12.5 1.32 1.63

21.9 2.27 2.79

14.5 1.51 1.86

rx /ry

2.83

4.20

4.20

ry , in.

2.46

1.60

1.59

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:52 AM

Page 61

STEEL BEAM-COLUMN SELECTION TABLES

6–61

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W16

W-Shapes W16×

Shape

45c

p×

bx ×

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

40 c

103

p×

103

(kip-ft)–1

36c

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

2.61

1.73

4.33

2.88

3.03

2.02

4.88

3.25

3.42

2.28

5.57

3.70

6 7 8 9 10

2.97 3.12 3.31 3.55 3.85

1.98 2.08 2.20 2.36 2.56

4.40 4.56 4.74 4.92 5.13

2.93 3.03 3.15 3.28 3.41

3.44 3.61 3.81 4.06 4.37

2.29 2.40 2.54 2.70 2.91

4.96 5.16 5.36 5.59 5.83

3.30 3.43 3.57 3.72 3.88

3.91 4.10 4.35 4.65 5.03

2.60 2.73 2.89 3.10 3.34

5.71 5.94 6.20 6.48 6.78

3.80 3.95 4.12 4.31 4.51

11 12 13 14 15

4.21 4.65 5.17 5.80 6.58

2.80 3.09 3.44 3.86 4.37

5.35 5.59 5.86 6.15 6.47

3.56 3.72 3.90 4.09 4.30

4.75 5.24 5.83 6.54 7.41

3.16 3.48 3.88 4.35 4.93

6.10 6.39 6.72 7.07 7.47

4.06 4.25 4.47 4.71 4.97

5.49 6.07 6.81 7.70 8.80

3.65 4.04 4.53 5.12 5.86

7.12 7.49 7.90 8.36 8.88

4.74 4.98 5.26 5.56 5.91

16 17 18 19 20

7.48 8.45 9.47 10.5 11.7

4.98 5.62 6.30 7.02 7.78

6.82 7.36 8.03 8.70 9.37

4.54 4.90 5.34 5.79 6.23

8.43 9.52 10.7 11.9 13.2

5.61 7.96 6.33 8.76 7.10 9.58 7.91 10.4 8.77 11.2

5.30 5.83 6.38 6.93 7.48

10.0 11.3 12.7 14.1 15.6

6.66 7.52 8.43 9.40 10.4

9.79 10.8 11.9 12.9 14.0

6.51 7.19 7.89 8.59 9.31

21 22 23 24 25

12.9 14.1 15.5 16.8 18.3

8.57 9.41 10.3 11.2 12.2

10.0 10.7 11.4 12.1 12.8

6.68 7.14 7.59 8.04 8.50

14.5 15.9 17.4 19.0 20.6

9.66 10.6 11.6 12.6 13.7

12.1 12.9 13.8 14.6 15.5

8.04 8.61 9.17 9.74 10.3

17.3 18.9 20.7 22.5 24.4

11.5 12.6 13.8 15.0 16.3

15.1 16.2 17.3 18.4 19.5

26

19.8

13.1

13.5

8.95

22.3

14.8

16.4

10.9

10.0 10.8 11.5 12.2 13.0

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

24.6 2.51 3.08

16.3 1.67 2.06

28.1 2.83 3.48

18.7 1.88 2.32

33.0 3.15 3.87

21.9 2.10 2.58

rx /ry

4.24

4.22

4.28

ry , in.

1.57

1.57

1.52

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:52 AM

6–62

Page 62

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W16

W-Shapes W16×

Shape

31c

p×

26c, v

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

103

p×

bx × 103

(kips)–1

(kip-ft)–1

103

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

4.09

2.72

6.60

4.39

5.06

3.37

ASD 8.06

LRFD 5.36

6 7 8 9 10

5.08 5.52 6.10 6.87 7.89

3.38 3.67 4.06 4.57 5.25

7.28 7.71 8.19 8.74 9.37

4.85 5.13 5.45 5.82 6.23

6.33 6.91 7.68 8.70 10.1

4.21 4.60 5.11 5.79 6.72

9.07 9.66 10.3 11.1 12.0

6.03 6.43 6.87 7.39 7.99

11 12 13 14 15

9.28 11.0 13.0 15.0 17.2

6.17 7.34 8.62 10.0 11.5

10.1 11.1 12.6 14.2 15.8

6.71 7.35 8.39 9.45 10.5

12.0 14.3 16.8 19.5 22.4

8.01 9.53 11.2 13.0 14.9

13.1 15.0 17.2 19.5 21.9

8.69 10.0 11.5 13.0 14.6

16 17 18 19

19.6 22.2 24.8 27.7

13.1 14.7 16.5 18.4

17.5 19.2 20.9 22.6

11.6 12.8 13.9 15.0

25.5 28.7 32.2

16.9 19.1 21.4

24.3 26.7 29.2

16.2 17.8 19.4

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

50.7 3.66 4.49

33.7 2.43 3.00

65.0 4.35 5.34

43.3 2.89 3.56

rx /ry

5.48

5.59

ry , in.

1.17

1.12

Shape is slender for compression with Fy = 50 ksi. v Shape does not meet the h /t limit for shear in AISC Specification Section G2.1(a) with F = 50 ksi; therefore, φ = 0.90 and w y v Ωv = 1.67. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:52 AM

Page 63

STEEL BEAM-COLUMN SELECTION TABLES

6–63

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W14

W-Shapes W14×

Shape

730h

p×

(kips)–1

Design

ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

665h

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

p×

(kips)–1 ASD

605h

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

0.155 0.103 0.215 0.143 0.170 0.113 0.241 0.160 0.188 0.125 0.270 0.180

11 12 13 14 15

0.165 0.166 0.168 0.171 0.173

0.110 0.111 0.112 0.114 0.115

0.215 0.215 0.215 0.215 0.215

0.143 0.143 0.143 0.143 0.143

0.181 0.183 0.185 0.188 0.190

0.120 0.122 0.123 0.125 0.127

0.241 0.241 0.241 0.241 0.241

0.160 0.160 0.160 0.160 0.160

0.200 0.202 0.204 0.207 0.210

0.133 0.134 0.136 0.138 0.140

0.270 0.270 0.270 0.270 0.270

0.180 0.180 0.180 0.180 0.180

16 17 18 19 20

0.176 0.178 0.181 0.185 0.188

0.117 0.119 0.121 0.123 0.125

0.215 0.215 0.215 0.216 0.216

0.143 0.143 0.143 0.143 0.144

0.193 0.197 0.200 0.204 0.208

0.129 0.131 0.133 0.135 0.138

0.241 0.241 0.242 0.242 0.242

0.160 0.160 0.161 0.161 0.161

0.214 0.217 0.221 0.225 0.230

0.142 0.145 0.147 0.150 0.153

0.270 0.270 0.271 0.272 0.272

0.180 0.180 0.180 0.181 0.181

22 24 26 28 30

0.196 0.205 0.215 0.226 0.239

0.130 0.136 0.143 0.150 0.159

0.217 0.217 0.218 0.219 0.220

0.144 0.145 0.145 0.146 0.146

0.216 0.226 0.238 0.251 0.266

0.144 0.151 0.158 0.167 0.177

0.243 0.244 0.245 0.246 0.247

0.162 0.163 0.163 0.164 0.164

0.240 0.252 0.265 0.280 0.297

0.160 0.167 0.176 0.186 0.197

0.273 0.274 0.276 0.277 0.278

0.182 0.183 0.183 0.184 0.185

32 34 36 38 40

0.254 0.270 0.289 0.310 0.334

0.169 0.180 0.192 0.206 0.222

0.221 0.221 0.222 0.223 0.224

0.147 0.147 0.148 0.148 0.149

0.282 0.301 0.323 0.347 0.375

0.188 0.201 0.215 0.231 0.250

0.248 0.249 0.250 0.251 0.252

0.165 0.166 0.166 0.167 0.168

0.316 0.338 0.363 0.391 0.423

0.210 0.225 0.241 0.260 0.282

0.279 0.280 0.282 0.283 0.284

0.186 0.187 0.187 0.188 0.189

42 44 46 48 50

0.361 0.392 0.429 0.467 0.506

0.240 0.261 0.285 0.311 0.337

0.225 0.226 0.226 0.227 0.228

0.150 0.150 0.151 0.151 0.152

0.407 0.443 0.485 0.528 0.573

0.271 0.295 0.322 0.351 0.381

0.253 0.254 0.255 0.256 0.257

0.168 0.169 0.170 0.171 0.171

0.460 0.503 0.550 0.599 0.650

0.306 0.335 0.366 0.399 0.432

0.285 0.287 0.288 0.289 0.290

0.190 0.191 0.191 0.192 0.193

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

h

0.437 0.155 0.191

0.290 0.103 0.127

0.488 0.170 0.209

0.325 0.113 0.140

0.546 0.188 0.230

0.364 0.125 0.154

rx /ry

1.74

1.73

1.71

ry , in.

4.69

4.62

4.55

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:53 AM

6–64

Page 64

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W14

W-Shapes W14×

Shape

550h

p× ASD 0

500h

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

103

(kip-ft)–1

LRFD

ASD

LRFD

p×

(kips)–1 ASD

455h

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

0.206 0.137 0.302 0.201 0.227 0.151 0.339 0.226 0.249 0.166 0.381 0.253

11 12 13 14 15

0.220 0.222 0.225 0.228 0.232

0.146 0.148 0.150 0.152 0.154

0.302 0.302 0.302 0.302 0.302

0.201 0.201 0.201 0.201 0.201

0.242 0.245 0.249 0.252 0.256

0.161 0.163 0.166 0.168 0.171

0.339 0.339 0.339 0.339 0.339

0.226 0.226 0.226 0.226 0.226

0.266 0.270 0.273 0.278 0.282

0.177 0.179 0.182 0.185 0.188

0.381 0.381 0.381 0.381 0.381

0.253 0.253 0.253 0.253 0.253

16 17 18 19 20

0.236 0.240 0.244 0.249 0.254

0.157 0.160 0.162 0.166 0.169

0.302 0.303 0.303 0.304 0.305

0.201 0.201 0.202 0.202 0.203

0.261 0.265 0.270 0.276 0.282

0.173 0.177 0.180 0.183 0.187

0.340 0.340 0.341 0.342 0.343

0.226 0.227 0.227 0.228 0.228

0.287 0.292 0.298 0.304 0.310

0.191 0.194 0.198 0.202 0.207

0.381 0.382 0.383 0.384 0.385

0.254 0.254 0.255 0.256 0.256

22 24 26 28 30

0.265 0.279 0.293 0.310 0.330

0.177 0.185 0.195 0.207 0.219

0.306 0.308 0.309 0.310 0.312

0.204 0.205 0.206 0.207 0.208

0.295 0.309 0.327 0.346 0.368

0.196 0.206 0.217 0.230 0.245

0.345 0.346 0.348 0.350 0.352

0.229 0.230 0.232 0.233 0.234

0.325 0.342 0.361 0.383 0.408

0.216 0.227 0.240 0.255 0.272

0.387 0.389 0.392 0.394 0.396

0.258 0.259 0.261 0.262 0.263

32 34 36 38 40

0.352 0.377 0.406 0.438 0.475

0.234 0.251 0.270 0.292 0.316

0.313 0.315 0.316 0.318 0.319

0.209 0.209 0.210 0.211 0.213

0.394 0.422 0.455 0.493 0.536

0.262 0.281 0.303 0.328 0.357

0.353 0.355 0.357 0.359 0.361

0.235 0.236 0.238 0.239 0.240

0.437 0.470 0.508 0.551 0.600

0.291 0.313 0.338 0.366 0.399

0.398 0.400 0.403 0.405 0.407

0.265 0.266 0.268 0.269 0.271

42 44 46 48 50

0.518 0.568 0.621 0.676 0.733

0.345 0.378 0.413 0.450 0.488

0.321 0.322 0.324 0.326 0.327

0.214 0.215 0.216 0.217 0.218

0.586 0.643 0.703 0.765 0.830

0.390 0.428 0.468 0.509 0.552

0.363 0.365 0.367 0.369 0.371

0.241 0.243 0.244 0.245 0.247

0.657 0.721 0.789 0.859 0.932

0.437 0.480 0.525 0.571 0.620

0.409 0.412 0.414 0.417 0.419

0.272 0.274 0.276 0.277 0.279

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

h

0.611 0.206 0.253

0.407 0.137 0.169

0.683 0.227 0.279

0.454 0.151 0.186

0.761 0.249 0.306

0.506 0.166 0.204

rx /ry

1.70

1.69

1.67

ry , in.

4.49

4.43

4.38

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:53 AM

Page 65

STEEL BEAM-COLUMN SELECTION TABLES

6–65

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W14

W-Shapes W14×

Shape

426h

p×

(kips)–1

Design

ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

398h

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

p×

(kips)–1 ASD

370h

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

0.267 0.178 0.410 0.273 0.285 0.190 0.445 0.296 0.306 0.204 0.484 0.322

11 12 13 14 15

0.286 0.290 0.294 0.298 0.303

0.190 0.193 0.195 0.198 0.202

0.410 0.410 0.410 0.410 0.410

0.273 0.273 0.273 0.273 0.273

0.306 0.310 0.314 0.319 0.324

0.203 0.206 0.209 0.212 0.216

0.445 0.445 0.445 0.445 0.445

0.296 0.296 0.296 0.296 0.296

0.329 0.333 0.338 0.343 0.349

0.219 0.222 0.225 0.228 0.232

0.484 0.484 0.484 0.484 0.484

0.322 0.322 0.322 0.322 0.322

16 17 18 19 20

0.308 0.314 0.320 0.327 0.334

0.205 0.209 0.213 0.218 0.222

0.411 0.412 0.413 0.414 0.415

0.273 0.274 0.275 0.276 0.276

0.330 0.336 0.343 0.350 0.358

0.220 0.224 0.228 0.233 0.238

0.446 0.447 0.449 0.450 0.451

0.297 0.298 0.298 0.299 0.300

0.355 0.362 0.369 0.377 0.386

0.236 0.241 0.246 0.251 0.257

0.485 0.487 0.489 0.490 0.492

0.323 0.324 0.325 0.326 0.327

22 24 26 28 30

0.350 0.369 0.390 0.414 0.442

0.233 0.245 0.259 0.276 0.294

0.418 0.420 0.423 0.425 0.428

0.278 0.280 0.281 0.283 0.285

0.376 0.396 0.419 0.445 0.475

0.250 0.263 0.279 0.296 0.316

0.454 0.457 0.460 0.462 0.465

0.302 0.304 0.306 0.308 0.310

0.405 0.427 0.453 0.482 0.515

0.270 0.284 0.301 0.321 0.343

0.495 0.498 0.501 0.505 0.508

0.329 0.331 0.334 0.336 0.338

32 34 36 38 40

0.474 0.510 0.551 0.599 0.654

0.315 0.339 0.367 0.399 0.435

0.430 0.433 0.435 0.438 0.441

0.286 0.288 0.290 0.291 0.293

0.510 0.550 0.595 0.647 0.707

0.339 0.366 0.396 0.431 0.470

0.468 0.471 0.474 0.477 0.480

0.312 0.314 0.316 0.318 0.320

0.554 0.597 0.648 0.705 0.772

0.368 0.397 0.431 0.469 0.514

0.512 0.515 0.519 0.522 0.526

0.340 0.343 0.345 0.347 0.350

42 44 46 48 50

0.718 0.788 0.861 0.938 1.02

0.478 0.524 0.573 0.624 0.677

0.443 0.446 0.449 0.452 0.454

0.295 0.297 0.299 0.300 0.302

0.778 0.853 0.933 1.02 1.10

0.517 0.568 0.621 0.676 0.733

0.484 0.487 0.490 0.493 0.496

0.322 0.324 0.326 0.328 0.330

0.850 0.933 1.02 1.11 1.21

0.566 0.621 0.679 0.739 0.802

0.529 0.533 0.537 0.541 0.545

0.352 0.355 0.357 0.360 0.362

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

h

0.821 0.267 0.328

0.546 0.178 0.219

0.886 0.285 0.351

0.590 0.190 0.234

0.963 0.306 0.376

0.641 0.204 0.251

rx /ry

1.67

1.66

1.66

ry , in.

4.34

4.31

4.27

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:53 AM

6–66

Page 66

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W14

W-Shapes W14×

Shape

342h

p× ASD 0

311h

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

103

(kip-ft)–1

LRFD

ASD

LRFD

p×

(kips)–1 ASD

283h

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

0.331 0.220 0.530 0.353 0.365 0.243 0.591 0.393 0.401 0.267 0.657 0.437

11 12 13 14 15

0.355 0.360 0.365 0.371 0.377

0.236 0.239 0.243 0.247 0.251

0.530 0.530 0.530 0.530 0.530

0.353 0.353 0.353 0.353 0.353

0.393 0.398 0.404 0.411 0.418

0.261 0.265 0.269 0.273 0.278

0.591 0.591 0.591 0.591 0.591

0.393 0.393 0.393 0.393 0.393

0.431 0.437 0.444 0.451 0.459

0.287 0.291 0.296 0.300 0.306

0.657 0.657 0.657 0.657 0.658

0.437 0.437 0.437 0.437 0.438

16 17 18 19 20

0.384 0.392 0.400 0.409 0.418

0.256 0.261 0.266 0.272 0.278

0.532 0.534 0.536 0.538 0.539

0.354 0.355 0.356 0.358 0.359

0.426 0.434 0.443 0.453 0.464

0.283 0.289 0.295 0.302 0.309

0.593 0.596 0.598 0.600 0.602

0.395 0.396 0.398 0.399 0.401

0.468 0.478 0.488 0.499 0.511

0.312 0.318 0.325 0.332 0.340

0.661 0.663 0.666 0.669 0.672

0.440 0.441 0.443 0.445 0.447

22 24 26 28 30

0.439 0.463 0.491 0.523 0.560

0.292 0.308 0.327 0.348 0.373

0.543 0.547 0.551 0.555 0.559

0.361 0.364 0.367 0.369 0.372

0.488 0.515 0.547 0.583 0.625

0.325 0.343 0.364 0.388 0.416

0.607 0.612 0.617 0.621 0.626

0.404 0.407 0.410 0.413 0.417

0.537 0.568 0.604 0.645 0.691

0.358 0.378 0.402 0.429 0.460

0.677 0.683 0.689 0.695 0.701

0.451 0.455 0.458 0.462 0.466

32 34 36 38 40

0.602 0.651 0.706 0.770 0.844

0.401 0.433 0.470 0.513 0.562

0.563 0.567 0.571 0.575 0.580

0.374 0.377 0.380 0.383 0.386

0.673 0.729 0.792 0.865 0.951

0.448 0.485 0.527 0.576 0.633

0.631 0.636 0.641 0.647 0.652

0.420 0.423 0.427 0.430 0.434

0.745 0.807 0.879 0.961 1.06

0.496 0.537 0.585 0.640 0.704

0.707 0.713 0.720 0.726 0.733

0.471 0.475 0.479 0.483 0.488

42 44 46 48 50

0.931 1.02 1.12 1.22 1.32

0.619 0.680 0.743 0.809 0.878

0.584 0.588 0.593 0.597 0.602

0.389 0.391 0.394 0.397 0.401

1.05 1.15 1.26 1.37 1.49

0.697 0.765 0.837 0.911 0.988

0.657 0.663 0.669 0.674 0.680

0.437 0.441 0.445 0.449 0.452

1.17 1.28 1.40 1.52 1.65

0.776 0.852 0.931 1.01 1.10

0.740 0.747 0.754 0.761 0.768

0.492 0.497 0.501 0.506 0.511

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

h

1.05 0.331 0.406

0.701 0.220 0.271

1.17 0.365 0.449

0.780 0.243 0.299

1.30 0.401 0.493

0.865 0.267 0.328

rx /ry

1.65

1.64

1.63

ry , in.

4.24

4.20

4.17

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:53 AM

Page 67

STEEL BEAM-COLUMN SELECTION TABLES

6–67

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W14

W-Shapes W14×

Shape

257

p×

(kips)–1

Design

ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

233

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

p×

(kips)–1 ASD

211

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

0.442 0.294 0.732 0.487 0.488 0.324 0.817 0.544 0.539 0.358 0.914 0.608

11 12 13 14 15

0.476 0.483 0.490 0.499 0.508

0.317 0.321 0.326 0.332 0.338

0.732 0.732 0.732 0.732 0.733

0.487 0.487 0.487 0.487 0.488

0.526 0.534 0.542 0.551 0.561

0.350 0.355 0.361 0.367 0.374

0.817 0.817 0.817 0.817 0.819

0.544 0.544 0.544 0.544 0.545

0.582 0.590 0.600 0.610 0.622

0.387 0.393 0.399 0.406 0.414

0.914 0.914 0.914 0.914 0.917

0.608 0.608 0.608 0.608 0.610

16 17 18 19 20

0.517 0.528 0.540 0.552 0.566

0.344 0.351 0.359 0.367 0.376

0.736 0.740 0.743 0.746 0.750

0.490 0.492 0.494 0.497 0.499

0.572 0.584 0.597 0.611 0.626

0.381 0.389 0.397 0.407 0.417

0.823 0.827 0.832 0.836 0.840

0.548 0.551 0.553 0.556 0.559

0.634 0.647 0.662 0.678 0.695

0.422 0.431 0.440 0.451 0.462

0.922 0.927 0.932 0.937 0.942

0.613 0.617 0.620 0.623 0.627

22 24 26 28 30

0.596 0.630 0.671 0.717 0.770

0.396 0.419 0.446 0.477 0.512

0.757 0.764 0.771 0.778 0.786

0.503 0.508 0.513 0.518 0.523

0.660 0.699 0.745 0.797 0.857

0.439 0.465 0.495 0.530 0.570

0.849 0.857 0.866 0.876 0.885

0.565 0.571 0.576 0.583 0.589

0.733 0.777 0.828 0.887 0.955

0.488 0.517 0.551 0.590 0.635

0.953 0.964 0.975 0.987 0.998

0.634 0.641 0.649 0.656 0.664

32 34 36 38 40

0.831 0.902 0.983 1.08 1.19

0.553 0.600 0.654 0.717 0.791

0.794 0.801 0.809 0.818 0.826

0.528 0.533 0.539 0.544 0.549

0.926 1.01 1.10 1.20 1.33

0.616 0.669 0.731 0.801 0.886

0.895 0.904 0.914 0.925 0.935

0.595 0.602 0.608 0.615 0.622

1.03 1.12 1.23 1.35 1.49

0.687 0.747 0.817 0.897 0.993

1.01 1.02 1.04 1.05 1.06

0.672 0.680 0.689 0.697 0.706

42 44 46 48 50

1.31 1.44 1.57 1.71 1.86

0.872 0.957 1.05 1.14 1.24

0.834 0.843 0.852 0.861 0.870

0.555 0.561 0.567 0.573 0.579

1.47 1.61 1.76 1.92 2.08

0.976 1.07 1.17 1.28 1.38

0.946 0.957 0.968 0.979 0.991

0.629 0.637 0.644 0.652 0.659

1.65 1.81 1.97 2.15 2.33

1.09 1.20 1.31 1.43 1.55

1.08 1.09 1.10 1.12 1.13

0.715 0.725 0.734 0.744 0.754

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

1.45 0.442 0.543

0.964 0.294 0.362

1.61 0.488 0.599

1.07 0.324 0.399

1.80 0.539 0.662

1.20 0.358 0.441

rx /ry

1.62

1.62

1.61

ry , in.

4.13

4.10

4.07

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:53 AM

6–68

Page 68

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W14

W-Shapes W14×

Shape

193

p× ASD

176

bx ×

103

(kips)–1

Design

103

(kip-ft)–1

LRFD

ASD

LRFD

p×

(kips)–1 ASD

159

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1 ASD

LRFD

0.588 0.391 1.00

0.668 0.645 0.429 1.11

0.741 0.715 0.476 1.24

0.826

11 12 13 14 15

0.636 0.645 0.655 0.667 0.679

0.423 0.429 0.436 0.444 0.452

1.00 1.00 1.00 1.00 1.01

0.668 0.668 0.668 0.668 0.670

0.698 0.708 0.720 0.733 0.747

0.464 0.471 0.479 0.487 0.497

1.11 1.11 1.11 1.11 1.12

0.741 0.741 0.741 0.741 0.745

0.774 0.786 0.799 0.814 0.829

0.515 0.523 0.532 0.541 0.552

1.24 1.24 1.24 1.24 1.25

0.826 0.826 0.826 0.826 0.831

16 17 18 19 20

0.693 0.708 0.724 0.741 0.760

0.461 0.471 0.482 0.493 0.506

1.01 1.02 1.03 1.03 1.04

0.675 0.679 0.683 0.687 0.691

0.762 0.778 0.796 0.816 0.837

0.507 0.518 0.530 0.543 0.557

1.13 1.13 1.14 1.15 1.16

0.750 0.755 0.760 0.765 0.770

0.846 0.865 0.885 0.907 0.931

0.563 0.576 0.589 0.603 0.619

1.26 1.27 1.28 1.29 1.30

0.837 0.843 0.850 0.856 0.863

22 24 26 28 30

0.802 0.851 0.908 0.973 1.05

0.534 0.566 0.604 0.647 0.697

1.05 1.07 1.08 1.09 1.11

0.700 0.709 0.718 0.727 0.737

0.884 0.938 1.00 1.07 1.16

0.588 0.624 0.666 0.715 0.771

1.17 1.19 1.21 1.22 1.24

0.781 0.791 0.803 0.814 0.826

0.983 1.04 1.12 1.20 1.29

0.654 0.695 0.742 0.797 0.860

1.32 1.34 1.36 1.38 1.40

0.876 0.889 0.904 0.918 0.933

32 34 36 38 40

1.13 1.23 1.35 1.49 1.65

0.755 0.822 0.899 0.989 1.09

1.12 1.14 1.15 1.17 1.19

0.747 0.757 0.767 0.778 0.789

1.26 1.37 1.50 1.65 1.83

0.836 0.911 0.998 1.10 1.22

1.26 1.28 1.30 1.32 1.34

0.838 0.851 0.864 0.877 0.891

1.40 1.53 1.68 1.85 2.05

0.934 1.02 1.12 1.23 1.36

1.43 1.45 1.47 1.50 1.53

0.949 0.965 0.981 0.998 1.02

42 44 46 48 50

1.81 1.99 2.18 2.37 2.57

1.21 1.32 1.45 1.58 1.71

1.20 1.22 1.24 1.26 1.28

0.800 0.812 0.824 0.836 0.848

2.02 2.22 2.42 2.64 2.86

1.34 1.47 1.61 1.75 1.90

1.36 1.38 1.41 1.43 1.45

0.905 0.920 0.935 0.951 0.967

2.26 2.48 2.71 2.95 3.21

1.50 1.65 1.81 1.97 2.13

1.56 1.58 1.61 1.64 1.68

1.03 1.05 1.07 1.09 1.12

0

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

ASD

LRFD

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

1.98 0.588 0.722

1.32 0.391 0.482

2.19 0.645 0.792

1.45 0.429 0.528

2.44 0.715 0.878

1.62 0.476 0.586

rx /ry

1.60

1.60

1.60

ry , in.

4.05

4.02

4.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:53 AM

Page 69

STEEL BEAM-COLUMN SELECTION TABLES

6–69

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W14

W-Shapes W14×

Shape

145

p×

(kips)–1

Design

ASD

103

(kip-ft)–1

LRFD

ASD

LRFD

p×

(kips)–1 ASD

120

bx ×

103

103

(kip-ft)–1

LRFD

ASD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

LRFD

ASD

0.782 0.520 1.37

0.912 0.861 0.573 1.52

1.01

0.946 0.630 1.68

1.12

11 12 13 14 15

0.848 0.861 0.875 0.891 0.908

0.564 0.573 0.582 0.593 0.604

1.37 1.37 1.37 1.37 1.38

0.912 0.912 0.912 0.912 0.919

0.942 0.958 0.976 0.996 1.02

0.627 0.638 0.650 0.663 0.677

1.52 1.52 1.52 1.53 1.55

1.01 1.01 1.01 1.02 1.03

1.04 1.05 1.07 1.10 1.12

0.690 0.702 0.715 0.730 0.746

1.68 1.68 1.68 1.69 1.71

1.12 1.12 1.12 1.13 1.14

16 17 18 19 20

0.927 0.948 0.970 0.994 1.02

0.617 0.631 0.645 0.662 0.679

1.39 1.40 1.41 1.43 1.44

0.926 0.933 0.941 0.949 0.956

1.04 1.07 1.10 1.13 1.16

0.693 0.710 0.729 0.749 0.771

1.56 1.57 1.59 1.60 1.62

1.04 1.05 1.06 1.07 1.08

1.15 1.18 1.21 1.24 1.28

0.763 0.783 0.803 0.826 0.851

1.73 1.74 1.76 1.78 1.80

1.15 1.16 1.17 1.18 1.20

22 24 26 28 30

1.08 1.15 1.23 1.32 1.42

0.718 0.763 0.816 0.876 0.947

1.46 1.49 1.51 1.54 1.57

0.973 0.989 1.01 1.02 1.04

1.23 1.32 1.42 1.54 1.68

0.821 0.880 0.948 1.03 1.12

1.65 1.68 1.71 1.75 1.79

1.10 1.12 1.14 1.16 1.19

1.36 1.46 1.57 1.71 1.86

0.906 0.971 1.05 1.14 1.24

1.84 1.88 1.92 1.96 2.00

1.22 1.25 1.28 1.30 1.33

32 34 36 38 40

1.54 1.69 1.85 2.05 2.27

1.03 1.12 1.23 1.36 1.51

1.60 1.63 1.66 1.69 1.72

1.06 1.08 1.10 1.12 1.15

1.85 2.04 2.26 2.52 2.79

1.23 1.35 1.51 1.68 1.86

1.82 1.86 1.90 1.95 1.99

1.21 1.24 1.27 1.29 1.32

2.05 2.26 2.51 2.80 3.10

1.36 1.50 1.67 1.86 2.07

2.05 2.10 2.15 2.21 2.27

1.37 1.40 1.43 1.47 1.51

42 44 46 48 50

2.50 2.74 3.00 3.26 3.54

1.66 1.82 1.99 2.17 2.36

1.76 1.79 1.83 1.87 1.91

1.17 1.19 1.22 1.24 1.27

3.08 3.38 3.70 4.02 4.37

2.05 2.25 2.46 2.68 2.91

2.04 2.09 2.14 2.19 2.25

1.36 1.39 1.42 1.46 1.50

3.42 3.76 4.11 4.47 4.85

2.28 2.50 2.73 2.97 3.23

2.33 2.39 2.46 2.53 2.60

1.55 1.59 1.63 1.68 1.73

0

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

132

bx ×

103

LRFD

ASD

LRFD

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

2.68 0.782 0.961

1.78 0.520 0.641

3.15 0.861 1.06

2.10 0.573 0.705

3.49 0.946 1.16

2.32 0.630 0.775

rx /ry

1.59

1.67

1.67

ry , in.

3.98

3.76

3.74

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:53 AM

6–70

Page 70

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W14

W-Shapes W14×

Shape

99f

109

p×

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

103

(kip-ft)–1 ASD

p×

90f

bx ×

103

(kips)–1

103

(kip-ft)–1 ASD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

0

1.04

0.694 1.86

1.23

1.15

0.764 2.07

1.38

1.26

0.839 2.33

ASD

1.55

LRFD

11 12 13 14 15

1.14 1.16 1.19 1.21 1.24

0.761 0.774 0.789 0.805 0.823

1.86 1.86 1.86 1.87 1.89

1.23 1.23 1.23 1.25 1.26

1.26 1.28 1.31 1.33 1.36

0.838 0.853 0.869 0.887 0.907

2.07 2.07 2.07 2.08 2.10

1.38 1.38 1.38 1.38 1.40

1.38 1.41 1.44 1.47 1.50

0.920 0.937 0.955 0.975 0.997

2.33 2.33 2.33 2.33 2.33

1.55 1.55 1.55 1.55 1.55

16 17 18 19 20

1.27 1.30 1.33 1.37 1.41

0.843 0.864 0.887 0.913 0.940

1.91 1.93 1.95 1.98 2.00

1.27 1.29 1.30 1.31 1.33

1.40 1.43 1.47 1.51 1.56

0.929 0.953 0.978 1.01 1.04

2.13 2.15 2.18 2.21 2.23

1.42 1.43 1.45 1.47 1.49

1.53 1.57 1.62 1.66 1.71

1.02 1.05 1.08 1.11 1.14

2.35 2.38 2.42 2.45 2.48

1.57 1.59 1.61 1.63 1.65

22 24 26 28 30

1.51 1.61 1.74 1.89 2.06

1.00 1.07 1.16 1.26 1.37

2.04 2.09 2.14 2.20 2.25

1.36 1.39 1.43 1.46 1.50

1.66 1.78 1.92 2.09 2.28

1.11 1.19 1.28 1.39 1.52

2.29 2.35 2.41 2.48 2.55

1.52 1.56 1.60 1.65 1.69

1.83 1.96 2.12 2.30 2.52

1.22 1.31 1.41 1.53 1.68

2.55 2.62 2.70 2.78 2.87

1.70 1.74 1.80 1.85 1.91

32 34 36 38 40

2.27 2.50 2.79 3.11 3.44

1.51 1.67 1.86 2.07 2.29

2.31 2.37 2.44 2.51 2.58

1.54 1.58 1.62 1.67 1.72

2.51 2.78 3.10 3.45 3.83

1.67 1.85 2.06 2.30 2.55

2.62 2.70 2.78 2.87 2.96

1.74 1.80 1.85 1.91 1.97

2.77 3.07 3.42 3.81 4.23

1.84 2.04 2.28 2.54 2.81

2.96 3.06 3.16 3.27 3.39

1.97 2.03 2.10 2.18 2.26

42 44 46 48 50

3.80 4.17 4.55 4.96 5.38

2.53 2.77 3.03 3.30 3.58

2.66 2.74 2.82 2.92 3.05

1.77 1.82 1.88 1.94 2.03

4.22 4.63 5.06 5.51 5.98

2.81 3.08 3.37 3.67 3.98

3.06 3.17 3.31 3.48 3.66

2.04 2.11 2.20 2.32 2.43

4.66 5.11 5.59 6.08 6.60

3.10 3.40 3.72 4.05 4.39

3.52 3.72 3.94 4.15 4.36

2.34 2.48 2.62 2.76 2.90

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

f

3.84 1.04 1.28

2.56 0.694 0.855

4.29 1.15 1.41

2.85 0.764 0.940

4.90 1.26 1.55

3.26 0.839 1.03

rx /ry

1.67

1.66

1.66

ry , in.

3.73

3.71

3.70

Shape does not meet compact limit for flexure with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:53 AM

Page 71

STEEL BEAM-COLUMN SELECTION TABLES

6–71

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W14

W-Shapes W14×

Shape

82

p×

bx ×

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

74

103

103

(kip-ft)–1 ASD

p×

68

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1.39

0.926 2.56

1.71

1.53

1.02

2.83

1.88

1.67

1.11

3.10

2.06

6 7 8 9 10

1.48 1.51 1.55 1.60 1.65

0.985 1.01 1.03 1.06 1.10

2.56 2.56 2.56 2.57 2.61

1.71 1.71 1.71 1.71 1.74

1.63 1.67 1.71 1.76 1.82

1.08 1.11 1.14 1.17 1.21

2.83 2.83 2.83 2.84 2.89

1.88 1.88 1.88 1.89 1.92

1.78 1.82 1.87 1.92 1.99

1.18 1.21 1.24 1.28 1.32

3.10 3.10 3.10 3.12 3.17

2.06 2.06 2.06 2.07 2.11

11 12 13 14 15

1.71 1.78 1.86 1.95 2.05

1.14 1.18 1.24 1.30 1.36

2.66 2.70 2.74 2.79 2.84

1.77 1.80 1.83 1.86 1.89

1.88 1.96 2.05 2.14 2.25

1.25 1.30 1.36 1.43 1.50

2.94 2.99 3.05 3.10 3.16

1.96 1.99 2.03 2.06 2.10

2.06 2.15 2.24 2.35 2.47

1.37 1.43 1.49 1.56 1.64

3.23 3.30 3.36 3.43 3.50

2.15 2.19 2.24 2.28 2.33

16 17 18 19 20

2.16 2.28 2.42 2.58 2.76

1.44 1.52 1.61 1.72 1.84

2.89 2.94 2.99 3.05 3.11

1.92 1.96 1.99 2.03 2.07

2.37 2.51 2.67 2.84 3.04

1.58 1.67 1.78 1.89 2.02

3.22 3.29 3.35 3.42 3.49

2.14 2.19 2.23 2.28 2.32

2.61 2.76 2.93 3.13 3.35

1.73 1.84 1.95 2.08 2.23

3.57 3.65 3.73 3.81 3.90

2.38 2.43 2.48 2.53 2.59

22 24 26 28 30

3.19 3.74 4.39 5.09 5.84

2.12 2.49 2.92 3.39 3.89

3.23 3.36 3.51 3.66 3.83

2.15 2.24 2.33 2.44 2.55

3.51 4.12 4.83 5.60 6.43

2.33 2.74 3.21 3.73 4.28

3.65 3.81 3.99 4.20 4.42

2.43 2.54 2.66 2.79 2.94

3.88 4.56 5.35 6.21 7.12

2.58 3.03 3.56 4.13 4.74

4.08 4.29 4.51 4.77 5.10

2.72 2.85 3.00 3.17 3.39

32 34 36 38 40

6.65 7.50 8.41 9.37 10.4

4.42 4.99 5.60 6.24 6.91

4.02 4.26 4.56 4.85 5.14

2.67 2.84 3.03 3.22 3.42

7.32 8.26 9.26 10.3 11.4

4.87 5.50 6.16 6.86 7.61

4.72 5.07 5.43 5.78 6.14

3.14 3.38 3.61 3.85 4.08

8.11 9.15 10.3 11.4 12.7

5.39 6.09 6.83 7.60 8.43

5.53 5.96 6.38 6.81 7.23

3.68 3.96 4.25 4.53 4.81

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

7.95 1.39 1.71

5.29 0.926 1.14

8.80 1.53 1.88

5.85 1.02 1.25

9.65 1.67 2.05

6.42 1.11 1.37

rx /ry

2.44

2.44

2.44

ry , in.

2.48

2.48

2.46

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:53 AM

6–72

Page 72

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W14

W-Shapes W14×

Shape

61

p×

53

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

p×

103

(kip-ft)–1

48

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1.87

1.24

3.49

2.32

2.14

1.42

4.09

2.72

2.37

1.58

4.54

3.02

6 7 8 9 10

1.99 2.03 2.09 2.15 2.22

1.32 1.35 1.39 1.43 1.48

3.49 3.49 3.49 3.52 3.59

2.32 2.32 2.32 2.34 2.39

2.37 2.46 2.57 2.70 2.85

1.58 1.64 1.71 1.80 1.90

4.09 4.11 4.21 4.32 4.44

2.72 2.74 2.80 2.88 2.95

2.63 2.73 2.85 2.99 3.16

1.75 1.82 1.90 1.99 2.10

4.54 4.57 4.70 4.83 4.96

3.02 3.04 3.13 3.21 3.30

11 12 13 14 15

2.31 2.40 2.51 2.63 2.77

1.54 1.60 1.67 1.75 1.84

3.66 3.74 3.82 3.90 3.99

2.44 2.49 2.54 2.59 2.65

3.02 3.23 3.47 3.75 4.07

2.01 2.15 2.31 2.49 2.71

4.56 4.68 4.81 4.96 5.11

3.03 3.11 3.20 3.30 3.40

3.36 3.59 3.86 4.17 4.53

2.23 2.39 2.57 2.77 3.02

5.11 5.26 5.43 5.60 5.79

3.40 3.50 3.61 3.73 3.85

16 17 18 19 20

2.92 3.10 3.29 3.51 3.76

1.95 2.06 2.19 2.34 2.50

4.08 4.17 4.27 4.38 4.49

2.71 2.78 2.84 2.91 2.98

4.45 4.89 5.40 6.01 6.66

2.96 3.25 3.59 4.00 4.43

5.26 5.43 5.61 5.81 6.01

3.50 3.62 3.74 3.86 4.00

4.96 5.45 6.03 6.72 7.45

3.30 3.63 4.01 4.47 4.96

5.98 6.20 6.42 6.67 6.94

3.98 4.12 4.27 4.44 4.61

22 24 26 28 30

4.36 5.14 6.03 6.99 8.02

2.90 3.42 4.01 4.65 5.34

4.72 4.99 5.28 5.66 6.20

3.14 3.32 3.51 3.77 4.13

8.06 9.60 11.3 13.1 15.0

5.36 6.38 7.49 8.69 9.98

6.47 7.22 7.99 8.76 9.53

4.31 4.80 5.32 5.83 6.34

9.01 6.00 7.69 10.7 7.14 8.64 12.6 8.38 9.59 14.6 9.72 10.5 16.8 11.2 11.5

5.12 5.75 6.38 7.01 7.65

32 34 36 38 40

9.13 10.3 11.6 12.9 14.3

6.07 6.86 7.69 8.57 9.49

6.74 7.27 7.81 8.34 8.87

4.48 4.84 5.20 5.55 5.90

17.1

11.3

10.3

6.85

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

10.9 1.87 2.29

7.23 1.24 1.53

16.2 2.14 2.63

10.8 1.42 1.75

18.2 2.37 2.91

12.1 1.58 1.94

rx /ry

2.44

3.07

3.06

ry , in.

2.45

1.92

1.91

Note: Heavy line indicates KL /ry equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:53 AM

Page 73

STEEL BEAM-COLUMN SELECTION TABLES

6–73

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W14

W-Shapes W14×

Shape

43c

p×

bx ×

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

38c

103

p×

103

(kip-ft)–1

34c

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

2.68

1.78

5.12

3.41

3.06

2.04

5.79

3.85

3.50

2.33

6.53

4.34

6 7 8 9 10

2.95 3.06 3.20 3.37 3.56

1.96 2.04 2.13 2.24 2.37

5.12 5.17 5.31 5.47 5.64

3.41 3.44 3.54 3.64 3.75

3.51 3.70 3.95 4.25 4.62

2.34 2.46 2.63 2.83 3.08

5.90 6.12 6.36 6.61 6.89

3.93 4.07 4.23 4.40 4.58

4.02 4.23 4.49 4.81 5.24

2.67 2.81 2.99 3.20 3.48

6.67 6.94 7.22 7.53 7.87

4.44 4.61 4.80 5.01 5.23

11 12 13 14 15

3.79 4.05 4.36 4.72 5.15

2.52 2.70 2.90 3.14 3.42

5.82 6.01 6.21 6.42 6.66

3.87 4.00 4.13 4.27 4.43

5.07 5.61 6.25 7.04 8.01

3.37 3.73 4.16 4.68 5.33

7.19 7.52 7.88 8.27 8.71

4.78 5.00 5.24 5.50 5.80

5.76 6.38 7.14 8.07 9.21

3.83 8.24 4.25 8.64 4.75 9.09 5.37 9.58 6.13 10.1

5.48 5.75 6.05 6.37 6.74

16 17 18 19 20

5.64 6.21 6.90 7.68 8.51

3.75 4.13 4.59 5.11 5.66

6.90 7.17 7.46 7.78 8.12

4.59 4.77 4.97 5.17 5.40

9.11 10.3 11.5 12.9 14.2

6.06 9.20 6.85 9.99 7.68 10.9 8.55 11.8 9.48 12.6

6.12 6.65 7.23 7.82 8.41

10.5 11.8 13.3 14.8 16.4

6.97 7.87 8.82 9.83 10.9

11.0 12.0 13.1 14.2 15.3

7.29 8.01 8.73 9.47 10.2

21 22 23 24 25

9.39 10.3 11.3 12.3 13.3

6.25 8.71 6.85 9.31 7.49 9.90 8.16 10.5 8.85 11.1

5.80 6.19 6.59 6.99 7.39

15.7 17.2 18.8 20.5 22.3

9.00 9.60 10.2 10.8 11.4

18.0 19.8 21.6 23.6 25.6

12.0 13.2 14.4 15.7 17.0

16.5 17.6 18.7 19.8 21.0

11.0 11.7 12.4 13.2 13.9

26 27 28 29 30

14.4 15.5 16.7 17.9 19.2

9.57 10.3 11.1 11.9 12.7

11.7 12.3 12.9 13.5 14.1

10.4 11.5 12.5 13.6 14.8

13.5 14.4 15.3 16.2 17.1

7.78 8.18 8.58 8.98 9.37 Other Constants and Properties

× 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

20.6 2.65 3.26

13.7 1.76 2.17

29.4 2.98 3.66

19.6 1.98 2.44

33.6 3.34 4.10

22.4 2.22 2.74

rx /ry

3.08

3.79

3.81

ry , in.

1.89

1.55

1.53

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:54 AM

6–74

Page 74

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W14

W-Shapes W14×

Shape

30c

p×

26c

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

p×

103

(kip-ft)–1

22c

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

4.02

2.68

7.53

5.01

4.73

3.15

8.86

5.90

5.82

3.87 10.7

6 7 8 9 10

4.63 4.89 5.20 5.59 6.07

3.08 3.25 3.46 3.72 4.04

7.76 8.09 8.44 8.83 9.26

5.16 6.18 5.38 6.85 5.62 7.75 5.88 9.02 6.16 10.7

4.11 4.56 5.16 6.00 7.13

10.0 10.7 11.4 12.3 13.2

11 12 13 14 15

6.70 7.47 8.41 9.56 11.0

4.46 4.97 5.60 6.36 7.30

9.74 10.3 10.8 11.5 12.3

8.60 10.2 12.0 13.9 16.0

14.4 16.5 18.7 20.9 23.2

9.56 11.0 12.4 13.9 15.4

16.5 19.7 23.1 26.8 30.7

16 17 18 19 20

12.5 14.1 15.8 17.6 19.5

8.31 9.38 10.5 11.7 13.0

13.7 15.1 16.5 18.0 19.4

9.12 27.3 10.0 30.9 11.0 34.6 12.0 12.9

18.2 20.5 23.0

25.5 27.8 30.1

17.0 18.5 20.0

34.9 39.4

21 22 23 24

21.5 23.6 25.8 28.1

14.3 15.7 17.2 18.7

20.9 22.4 23.9 25.4

13.9 14.9 15.9 16.9

6.48 6.83 7.21 7.65 8.20

12.9 15.4 18.1 20.9 24.0

6.67 7.65 7.10 8.52 7.59 9.70 8.15 11.3 8.80 13.6

5.09 5.67 6.45 7.54 9.08

ASD

LRFD 7.14

12.4 13.3 14.3 15.5 16.9

8.24 8.83 9.51 10.3 11.2

11.0 13.1 15.3 17.8 20.4

19.2 22.3 25.4 28.5 31.8

12.8 14.8 16.9 19.0 21.2

23.2 26.2

35.1 38.4

23.3 25.6

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

39.6 3.77 4.64

26.4 2.51 3.09

64.3 4.34 5.33

42.8 2.89 3.56

81.2 5.15 6.32

54.0 3.42 4.21

rx /ry

3.85

5.23

5.33

ry , in.

1.49

1.08

1.04

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:54 AM

Page 75

STEEL BEAM-COLUMN SELECTION TABLES

6–75

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W12

W-Shapes W12×

Shape

336h

p×

(kips)–1

Design

ASD

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

0

305h

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

p×

(kips)–1 ASD

279h

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

0.338 0.225 0.591 0.393 0.373 0.248 0.663 0.441 0.408 0.271 0.741 0.493

6 7 8 9 10

0.349 0.352 0.357 0.363 0.369

0.232 0.235 0.238 0.241 0.245

0.591 0.591 0.591 0.591 0.591

0.393 0.393 0.393 0.393 0.393

0.385 0.390 0.395 0.401 0.408

0.256 0.259 0.263 0.267 0.272

0.663 0.663 0.663 0.663 0.663

0.441 0.441 0.441 0.441 0.441

0.422 0.427 0.433 0.439 0.447

0.280 0.284 0.288 0.292 0.298

0.741 0.741 0.741 0.741 0.741

0.493 0.493 0.493 0.493 0.493

11 12 13 14 15

0.375 0.383 0.391 0.401 0.411

0.250 0.255 0.260 0.267 0.274

0.591 0.591 0.592 0.594 0.596

0.393 0.393 0.394 0.395 0.397

0.416 0.425 0.435 0.445 0.457

0.277 0.283 0.289 0.296 0.304

0.663 0.663 0.666 0.668 0.670

0.441 0.441 0.443 0.444 0.446

0.456 0.466 0.477 0.489 0.502

0.303 0.310 0.317 0.325 0.334

0.741 0.741 0.744 0.746 0.749

0.493 0.493 0.495 0.497 0.499

16 17 18 19 20

0.422 0.435 0.448 0.463 0.479

0.281 0.289 0.298 0.308 0.319

0.598 0.600 0.602 0.604 0.606

0.398 0.399 0.400 0.402 0.403

0.470 0.484 0.500 0.516 0.535

0.313 0.322 0.332 0.344 0.356

0.673 0.675 0.677 0.680 0.682

0.448 0.449 0.451 0.452 0.454

0.516 0.532 0.550 0.569 0.590

0.344 0.354 0.366 0.378 0.392

0.752 0.755 0.758 0.761 0.764

0.500 0.502 0.504 0.506 0.508

22 24 26 28 30

0.516 0.559 0.610 0.670 0.742

0.343 0.372 0.406 0.446 0.494

0.610 0.614 0.618 0.622 0.626

0.406 0.408 0.411 0.414 0.417

0.577 0.627 0.686 0.756 0.839

0.384 0.417 0.456 0.503 0.558

0.687 0.692 0.697 0.702 0.708

0.457 0.461 0.464 0.467 0.471

0.637 0.693 0.760 0.840 0.935

0.424 0.461 0.506 0.559 0.622

0.770 0.776 0.782 0.788 0.795

0.512 0.516 0.520 0.524 0.529

32 34 36 38 40

0.827 0.930 1.04 1.16 1.29

0.550 0.619 0.694 0.773 0.856

0.630 0.635 0.639 0.644 0.648

0.419 0.422 0.425 0.428 0.431

0.938 1.06 1.19 1.32 1.46

0.624 0.704 0.789 0.879 0.974

0.713 0.718 0.724 0.729 0.735

0.474 0.478 0.481 0.485 0.489

1.05 1.18 1.33 1.48 1.64

0.698 0.788 0.883 0.984 1.09

0.801 0.808 0.814 0.821 0.828

0.533 0.537 0.542 0.546 0.551

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

h

1.30 0.338 0.415

0.865 0.225 0.277

1.46 0.373 0.458

0.971 0.248 0.306

1.62 0.408 0.501

1.08 0.271 0.334

rx /ry

1.85

1.84

1.82

ry , in.

3.47

3.42

3.38

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:54 AM

6–76

Page 76

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W12

W-Shapes W12×

Shape

252h

p× ASD

230h

bx ×

103

(kips)–1

Design

103

(kip-ft)–1

LRFD

ASD

LRFD

p×

(kips)–1 ASD

210

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1 ASD

LRFD

0.451 0.300 0.832 0.554 0.493 0.328 0.923 0.614 0.540 0.360 1.02

0.681

6 7 8 9 10

0.466 0.472 0.479 0.487 0.495

0.310 0.314 0.319 0.324 0.330

0.832 0.832 0.832 0.832 0.832

0.554 0.554 0.554 0.554 0.554

0.511 0.517 0.525 0.533 0.543

0.340 0.344 0.349 0.355 0.361

0.923 0.923 0.923 0.923 0.923

0.614 0.614 0.614 0.614 0.614

0.560 0.567 0.575 0.585 0.596

0.372 0.377 0.383 0.389 0.397

1.02 1.02 1.02 1.02 1.02

0.681 0.681 0.681 0.681 0.681

11 12 13 14 15

0.505 0.516 0.529 0.542 0.557

0.336 0.344 0.352 0.361 0.371

0.832 0.833 0.837 0.840 0.844

0.554 0.554 0.557 0.559 0.561

0.554 0.567 0.580 0.596 0.612

0.369 0.377 0.386 0.396 0.407

0.923 0.924 0.928 0.933 0.937

0.614 0.615 0.618 0.621 0.623

0.608 0.622 0.638 0.655 0.674

0.405 0.414 0.424 0.436 0.448

1.02 1.03 1.03 1.04 1.04

0.681 0.683 0.686 0.689 0.693

16 17 18 19 20

0.574 0.592 0.612 0.634 0.657

0.382 0.394 0.407 0.422 0.437

0.847 0.851 0.854 0.858 0.862

0.564 0.566 0.568 0.571 0.573

0.631 0.651 0.674 0.698 0.725

0.420 0.433 0.448 0.464 0.482

0.941 0.946 0.950 0.954 0.959

0.626 0.629 0.632 0.635 0.638

0.694 0.717 0.742 0.769 0.799

0.462 0.477 0.494 0.512 0.532

1.05 1.05 1.06 1.06 1.07

0.696 0.700 0.703 0.707 0.710

22 24 26 28 30

0.712 0.776 0.853 0.945 1.05

0.474 0.516 0.568 0.629 0.701

0.869 0.877 0.884 0.892 0.900

0.578 0.583 0.588 0.594 0.599

0.786 0.858 0.945 1.05 1.17

0.523 0.571 0.629 0.697 0.780

0.968 0.977 0.986 0.996 1.01

0.644 0.650 0.656 0.663 0.669

0.868 0.950 1.05 1.16 1.30

0.577 0.632 0.697 0.775 0.868

1.08 1.09 1.10 1.11 1.13

0.718 0.725 0.733 0.741 0.749

32 34 36 38 40

1.19 1.34 1.50 1.67 1.85

0.790 0.891 0.999 1.11 1.23

0.908 0.916 0.925 0.933 0.942

0.604 0.610 0.615 0.621 0.627

1.32 1.49 1.67 1.87 2.07

0.880 0.993 1.11 1.24 1.37

1.02 1.03 1.04 1.05 1.06

0.676 0.682 0.689 0.696 0.704

1.48 1.67 1.87 2.08 2.31

0.982 1.11 1.24 1.38 1.53

1.14 1.15 1.16 1.18 1.19

0.757 0.765 0.774 0.782 0.791

0

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

ASD

LRFD

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

h

1.82 0.451 0.554

1.21 0.300 0.369

2.01 0.493 0.606

1.34 0.328 0.404

2.24 0.540 0.664

1.49 0.360 0.443

rx /ry

1.81

1.80

1.80

ry , in.

3.34

3.31

3.28

Flange thickness greater than 2 in. Special requirements may apply per AISC Specification Section A3.1c.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:54 AM

Page 77

STEEL BEAM-COLUMN SELECTION TABLES

6–77

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W12

W-Shapes W12×

Shape

190

p×

(kips)–1

Design

ASD

103

(kip-ft)–1

LRFD

ASD

LRFD

p×

(kips)–1 ASD

152

bx ×

103

103

(kip-ft)–1

LRFD

ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1 ASD

LRFD

0.596 0.397 1.15

0.762 0.668 0.444 1.30

0.862 0.747 0.497 1.47

0.975

6 7 8 9 10

0.618 0.626 0.636 0.647 0.659

0.411 0.417 0.423 0.430 0.438

1.15 1.15 1.15 1.15 1.15

0.762 0.762 0.762 0.762 0.762

0.693 0.702 0.713 0.725 0.739

0.461 0.467 0.474 0.483 0.492

1.30 1.30 1.30 1.30 1.30

0.862 0.862 0.862 0.862 0.862

0.776 0.786 0.798 0.813 0.829

0.516 0.523 0.531 0.541 0.551

1.47 1.47 1.47 1.47 1.47

0.975 0.975 0.975 0.975 0.975

11 12 13 14 15

0.673 0.688 0.706 0.725 0.746

0.448 0.458 0.470 0.482 0.497

1.15 1.15 1.16 1.16 1.17

0.762 0.764 0.768 0.773 0.777

0.755 0.773 0.793 0.815 0.839

0.503 0.514 0.528 0.542 0.559

1.30 1.30 1.31 1.32 1.32

0.862 0.865 0.870 0.876 0.881

0.847 0.867 0.890 0.915 0.943

0.563 0.577 0.592 0.609 0.627

1.47 1.47 1.48 1.49 1.50

0.975 0.980 0.987 0.994 1.00

16 17 18 19 20

0.770 0.796 0.824 0.855 0.889

0.512 0.529 0.548 0.569 0.591

1.17 1.18 1.19 1.19 1.20

0.781 0.786 0.790 0.794 0.799

0.866 0.896 0.928 0.964 1.00

0.576 0.596 0.618 0.641 0.667

1.33 1.34 1.35 1.36 1.37

0.887 0.892 0.898 0.903 0.909

0.974 1.01 1.04 1.09 1.13

0.648 0.670 0.695 0.722 0.752

1.51 1.52 1.54 1.55 1.56

1.01 1.01 1.02 1.03 1.04

22 24 26 28 30

0.966 1.06 1.17 1.30 1.46

0.643 0.705 0.778 0.867 0.973

1.21 1.23 1.24 1.26 1.27

0.808 0.817 0.827 0.837 0.847

1.09 1.20 1.33 1.48 1.67

0.727 0.798 0.883 0.985 1.11

1.38 1.40 1.42 1.44 1.46

0.921 0.932 0.945 0.957 0.970

1.23 1.36 1.50 1.68 1.90

0.820 0.902 1.00 1.12 1.26

1.58 1.60 1.63 1.65 1.68

1.05 1.07 1.08 1.10 1.12

32 34 36 38 40

1.66 1.87 2.10 2.34 2.59

1.10 1.25 1.40 1.56 1.72

1.29 1.30 1.32 1.34 1.35

0.857 0.867 0.878 0.889 0.900

1.89 2.14 2.39 2.67 2.96

1.26 1.42 1.59 1.78 1.97

1.48 1.50 1.52 1.54 1.56

0.983 0.997 1.01 1.03 1.04

2.16 2.43 2.73 3.04 3.37

1.43 1.62 1.82 2.02 2.24

1.70 1.73 1.76 1.79 1.82

1.13 1.15 1.17 1.19 1.21

0

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

170

bx ×

103

ASD

LRFD

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

2.49 0.596 0.733

1.66 0.397 0.488

2.83 0.668 0.821

1.88 0.444 0.547

3.21 0.747 0.918

2.14 0.497 0.612

rx /ry

1.79

1.78

1.77

ry , in.

3.25

3.22

3.19

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:54 AM

6–78

Page 78

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W12

W-Shapes W12×

Shape

136

p× ASD

120

bx ×

103

(kips)–1

Design

103

(kip-ft)–1

LRFD

ASD

p×

106

bx ×

103

(kips)–1

103

(kip-ft)–1

LRFD

ASD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

LRFD

ASD

LRFD

ASD

LRFD

0.837 0.557 1.66

1.11

0.949 0.631 1.92

1.27

1.07

0.712 2.17

1.45

6 7 8 9 10

0.869 0.881 0.896 0.912 0.930

0.578 0.586 0.596 0.607 0.619

1.66 1.66 1.66 1.66 1.66

1.11 1.11 1.11 1.11 1.11

0.986 1.00 1.02 1.04 1.06

0.656 0.665 0.676 0.689 0.703

1.92 1.92 1.92 1.92 1.92

1.27 1.27 1.27 1.27 1.27

1.11 1.13 1.15 1.17 1.19

0.741 0.751 0.764 0.778 0.794

2.17 2.17 2.17 2.17 2.17

1.45 1.45 1.45 1.45 1.45

11 12 13 14 15

0.951 0.974 1.00 1.03 1.06

0.633 0.648 0.666 0.685 0.706

1.66 1.68 1.69 1.70 1.71

1.11 1.11 1.12 1.13 1.14

1.08 1.11 1.14 1.17 1.21

0.719 0.737 0.757 0.779 0.804

1.92 1.93 1.95 1.96 1.98

1.27 1.28 1.30 1.31 1.32

1.22 1.25 1.29 1.33 1.37

0.813 0.833 0.856 0.882 0.910

2.17 2.19 2.22 2.24 2.26

1.45 1.46 1.47 1.49 1.50

16 17 18 19 20

1.10 1.14 1.18 1.22 1.28

0.730 0.755 0.784 0.815 0.849

1.73 1.74 1.76 1.77 1.78

1.15 1.16 1.17 1.18 1.19

1.25 1.29 1.34 1.40 1.46

0.831 0.861 0.894 0.931 0.970

2.00 2.02 2.04 2.05 2.07

1.33 1.34 1.35 1.37 1.38

1.41 1.47 1.52 1.59 1.65

0.941 0.976 1.01 1.06 1.10

2.28 2.31 2.33 2.35 2.38

1.52 1.53 1.55 1.57 1.58

22 24 26 28 30

1.39 1.54 1.71 1.91 2.16

0.928 1.02 1.14 1.27 1.44

1.81 1.84 1.87 1.91 1.94

1.21 1.23 1.25 1.27 1.29

1.60 1.76 1.96 2.20 2.50

1.06 1.17 1.31 1.47 1.66

2.11 2.15 2.19 2.24 2.28

1.41 1.43 1.46 1.49 1.52

1.81 2.00 2.23 2.51 2.86

1.21 1.33 1.49 1.67 1.90

2.43 2.48 2.54 2.60 2.66

1.62 1.65 1.69 1.73 1.77

32 34 36 38 40

2.46 2.78 3.12 3.47 3.85

1.64 1.85 2.07 2.31 2.56

1.97 2.01 2.05 2.09 2.13

1.31 1.34 1.36 1.39 1.41

2.84 3.21 3.60 4.01 4.44

1.89 2.14 2.40 2.67 2.96

2.33 2.38 2.43 2.48 2.54

1.55 1.58 1.62 1.65 1.69

3.25 3.67 4.11 4.58 5.08

2.16 2.44 2.74 3.05 3.38

2.72 2.79 2.86 2.93 3.01

1.81 1.86 1.90 1.95 2.00

0

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

ASD

LRFD

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

3.64 0.837 1.03

2.42 0.557 0.685

4.17 0.949 1.17

2.78 0.631 0.777

4.74 1.07 1.31

3.16 0.712 0.877

rx /ry

1.77

1.76

1.76

ry , in.

3.16

3.13

3.11

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:54 AM

Page 79

STEEL BEAM-COLUMN SELECTION TABLES

6–79

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W12

W-Shapes W12×

Shape

96

p×

bx ×

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

87

103

103

(kip-ft)–1 ASD

p×

79

bx ×

103

(kips)–1

103

(kip-ft)–1 ASD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

0

1.18

0.788 2.42

1.61

1.30

0.868 2.70

1.80

1.44

0.958 2.99

ASD

1.99

LRFD

6 7 8 9 10

1.23 1.25 1.27 1.30 1.32

0.820 0.832 0.846 0.862 0.880

2.42 2.42 2.42 2.42 2.42

1.61 1.61 1.61 1.61 1.61

1.36 1.38 1.40 1.43 1.46

0.904 0.917 0.932 0.950 0.971

2.70 2.70 2.70 2.70 2.70

1.80 1.80 1.80 1.80 1.80

1.50 1.52 1.55 1.58 1.61

0.998 1.01 1.03 1.05 1.07

2.99 2.99 2.99 2.99 2.99

1.99 1.99 1.99 1.99 1.99

11 12 13 14 15

1.35 1.39 1.43 1.47 1.52

0.901 0.924 0.949 0.978 1.01

2.43 2.45 2.48 2.50 2.53

1.61 1.63 1.65 1.67 1.68

1.49 1.53 1.58 1.62 1.68

0.994 1.02 1.05 1.08 1.12

2.70 2.74 2.77 2.80 2.84

1.80 1.82 1.84 1.86 1.89

1.65 1.69 1.74 1.80 1.86

1.10 1.13 1.16 1.20 1.24

3.00 3.04 3.08 3.12 3.16

2.00 2.02 2.05 2.08 2.11

16 17 18 19 20

1.57 1.63 1.69 1.76 1.84

1.05 1.08 1.13 1.17 1.22

2.56 2.59 2.62 2.65 2.68

1.70 1.72 1.74 1.76 1.78

1.74 1.80 1.87 1.95 2.04

1.16 1.20 1.25 1.30 1.36

2.87 2.91 2.94 2.98 3.02

1.91 1.93 1.96 1.98 2.01

1.92 2.00 2.08 2.17 2.26

1.28 1.33 1.38 1.44 1.51

3.21 3.25 3.30 3.34 3.39

2.13 2.16 2.19 2.22 2.26

22 24 26 28 30

2.02 2.24 2.50 2.81 3.20

1.34 1.49 1.66 1.87 2.13

2.74 2.81 2.88 2.95 3.03

1.83 1.87 1.92 1.97 2.02

2.24 2.48 2.78 3.13 3.57

1.49 1.65 1.85 2.08 2.38

3.10 3.19 3.28 3.37 3.47

2.06 2.12 2.18 2.24 2.31

2.49 2.76 3.09 3.50 4.00

1.66 1.84 2.06 2.33 2.66

3.49 3.60 3.71 3.84 3.96

2.32 2.40 2.47 2.55 2.64

32 34 36 38 40

3.64 4.11 4.61 5.14 5.69

2.42 2.74 3.07 3.42 3.79

3.11 3.20 3.29 3.39 3.49

2.07 2.13 2.19 2.26 2.32

4.07 4.59 5.15 5.73 6.35

2.71 3.05 3.42 3.81 4.23

3.58 3.69 3.81 3.94 4.08

2.38 2.46 2.54 2.62 2.72

4.55 5.13 5.75 6.41 7.10

3.02 3.41 3.83 4.26 4.73

4.10 4.25 4.41 4.58 4.78

2.73 2.83 2.93 3.05 3.18

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

5.28 1.18 1.45

3.51 0.788 0.970

5.90 1.30 1.60

3.92 0.868 1.07

6.56 1.44 1.77

4.37 0.958 1.18

rx /ry

1.76

1.75

1.75

ry , in.

3.09

3.07

3.05

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:54 AM

6–80

Page 80

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W12

W-Shapes W12×

Shape

65 f

72

p×

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

103

(kip-ft)–1

p×

58

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1.58

1.05

3.30

2.19

1.75

1.16

3.75

2.50

1.96

1.31

4.12

2.74

6 7 8 9 10

1.65 1.67 1.70 1.74 1.77

1.10 1.11 1.13 1.16 1.18

3.30 3.30 3.30 3.30 3.30

2.19 2.19 2.19 2.19 2.19

1.82 1.85 1.88 1.92 1.96

1.21 1.23 1.25 1.28 1.31

3.75 3.75 3.75 3.75 3.75

2.50 2.50 2.50 2.50 2.50

2.09 2.13 2.19 2.25 2.32

1.39 1.42 1.45 1.50 1.54

4.12 4.12 4.12 4.13 4.21

2.74 2.74 2.74 2.75 2.80

11 12 13 14 15

1.82 1.87 1.92 1.98 2.05

1.21 1.24 1.28 1.32 1.36

3.31 3.36 3.40 3.45 3.50

2.20 2.23 2.27 2.30 2.33

2.01 2.06 2.13 2.19 2.27

1.34 1.37 1.41 1.46 1.51

3.75 3.75 3.81 3.87 3.93

2.50 2.50 2.54 2.58 2.62

2.41 2.50 2.61 2.73 2.86

1.60 1.66 1.73 1.81 1.90

4.28 4.36 4.45 4.53 4.62

2.85 2.90 2.96 3.02 3.07

16 17 18 19 20

2.12 2.20 2.29 2.39 2.50

1.41 1.46 1.52 1.59 1.66

3.56 3.61 3.67 3.72 3.78

2.37 2.40 2.44 2.48 2.52

2.35 2.44 2.54 2.65 2.77

1.56 1.62 1.69 1.77 1.85

4.00 4.06 4.13 4.20 4.27

2.66 2.70 2.75 2.80 2.84

3.01 3.18 3.38 3.59 3.83

2.01 2.12 2.25 2.39 2.55

4.71 4.81 4.91 5.01 5.12

3.14 3.20 3.27 3.34 3.41

22 24 26 28 30

2.75 3.05 3.42 3.87 4.42

1.83 2.03 2.28 2.57 2.94

3.91 4.04 4.18 4.33 4.49

2.60 2.69 2.78 2.88 2.99

3.06 3.40 3.82 4.32 4.95

2.03 2.26 2.54 2.88 3.29

4.43 4.59 4.77 4.96 5.17

2.95 3.06 3.17 3.30 3.44

4.41 5.15 6.05 7.01 8.05

2.94 3.43 4.02 4.67 5.36

5.36 5.61 5.90 6.21 6.57

3.56 3.74 3.92 4.13 4.37

32 34 36 38 40

5.03 5.68 6.37 7.09 7.86

3.35 3.78 4.24 4.72 5.23

4.67 4.86 5.06 5.32 5.66

3.10 3.23 3.37 3.54 3.76

5.63 6.36 7.13 7.94 8.80

3.75 4.23 4.74 5.28 5.85

5.39 5.64 5.97 6.39 6.81

3.59 3.75 3.98 4.25 4.53

9.16 10.3 11.6 12.9 14.3

6.09 6.88 7.71 8.59 9.52

7.12 7.66 8.21 8.75 9.29

4.74 5.10 5.46 5.82 6.18

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

f

7.24 1.58 1.94

4.82 1.05 1.30

8.31 1.75 2.15

5.53 1.16 1.43

11.0 1.96 2.41

7.29 1.31 1.61

rx /ry

1.75

1.75

2.10

ry , in.

3.04

3.02

2.51

Shape does not meet compact limit for flexure with Fy = 50 ksi.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:54 AM

Page 81

STEEL BEAM-COLUMN SELECTION TABLES

6–81

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W12

W-Shapes W12×

Shape

53

p×

bx ×

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

50

103

p×

103

(kip-ft)–1

45

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

2.14

1.42

4.57

3.04

2.29

1.52

4.96

3.30

2.55

1.70

5.55

3.69

6 7 8 9 10

2.28 2.33 2.39 2.46 2.54

1.52 1.55 1.59 1.64 1.69

4.57 4.57 4.57 4.59 4.68

3.04 3.04 3.04 3.06 3.12

2.52 2.62 2.73 2.86 3.01

1.68 1.74 1.81 1.90 2.00

4.96 4.96 5.08 5.19 5.32

3.30 3.30 3.38 3.46 3.54

2.82 2.92 3.04 3.19 3.36

1.87 1.94 2.03 2.12 2.24

5.55 5.56 5.70 5.84 6.00

3.69 3.70 3.79 3.89 3.99

11 12 13 14 15

2.63 2.74 2.86 2.99 3.15

1.75 1.82 1.90 1.99 2.09

4.77 4.87 4.97 5.07 5.18

3.18 3.24 3.31 3.38 3.45

3.19 3.39 3.64 3.91 4.24

2.12 2.26 2.42 2.60 2.82

5.45 5.58 5.73 5.88 6.04

3.62 3.72 3.81 3.91 4.02

3.56 3.80 4.07 4.39 4.75

2.37 2.53 2.71 2.92 3.16

6.15 6.32 6.50 6.69 6.88

4.09 4.21 4.32 4.45 4.58

16 17 18 19 20

3.32 3.51 3.73 3.97 4.25

2.21 2.34 2.48 2.64 2.83

5.29 5.41 5.53 5.66 5.80

3.52 3.60 3.68 3.77 3.86

4.61 5.05 5.56 6.17 6.83

3.07 3.36 3.70 4.10 4.55

6.20 6.38 6.57 6.77 6.98

4.13 4.25 4.37 4.50 4.64

5.18 5.68 6.25 6.94 7.69

3.45 3.78 4.16 4.62 5.12

7.09 7.32 7.56 7.81 8.08

4.72 4.87 5.03 5.20 5.38

22 24 26 28 30

4.90 5.75 6.75 7.83 8.99

3.26 3.83 4.49 5.21 5.98

6.09 6.41 6.77 7.16 7.81

4.05 4.26 4.50 4.77 5.20

8.27 5.50 7.45 9.84 6.55 8.01 11.5 7.68 8.84 13.4 8.91 9.67 15.4 10.2 10.5

4.95 5.33 5.88 6.44 6.99

9.31 6.19 8.69 11.1 7.37 9.66 13.0 8.65 10.7 15.1 10.0 11.7 17.3 11.5 12.8

5.78 6.43 7.11 7.80 8.48

6.80 8.48 7.68 9.15 8.61 9.81 9.59 10.5 10.6 11.1

5.64 6.09 6.53 6.97 7.41

17.5

7.53

19.7

9.16

32 34 36 38 40

10.2 11.5 12.9 14.4 16.0

11.6

11.3

13.1

13.8

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

12.2 2.14 2.63

8.15 1.42 1.75

16.7 2.29 2.81

11.1 1.52 1.87

18.8 2.55 3.13

12.5 1.70 2.09

rx /ry

2.11

2.64

2.64

ry , in.

2.48

1.96

1.95

Note: Heavy line indicates KL /ry equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:54 AM

6–82

Page 82

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W12

W-Shapes W12×

Shape

35c

40

p×

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

p×

103

(kip-ft)–1

30c

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

2.85

1.90

6.25

4.16

3.25

2.17

6.96

4.63

3.94

2.62

8.27

5.50

6 7 8 9 10

3.16 3.27 3.41 3.58 3.78

2.10 2.18 2.27 2.38 2.51

6.25 6.27 6.44 6.62 6.80

4.16 4.17 4.29 4.40 4.53

3.80 4.03 4.31 4.65 5.05

2.53 2.68 2.87 3.09 3.36

7.09 7.34 7.61 7.90 8.22

4.72 4.89 5.07 5.26 5.47

4.54 4.79 5.10 5.50 5.99

3.02 3.19 3.39 3.66 3.99

8.46 8.79 9.14 9.53 9.94

5.63 5.85 6.08 6.34 6.62

11 12 13 14 15

4.00 4.27 4.58 4.94 5.36

2.66 2.84 3.05 3.29 3.56

7.00 7.21 7.43 7.66 7.91

4.66 4.79 4.94 5.10 5.26

5.55 6.15 6.87 7.74 8.82

3.69 8.56 4.09 8.93 4.57 9.33 5.15 9.77 5.87 10.3

5.69 6.60 5.94 7.32 6.21 8.21 6.50 9.28 6.82 10.6

4.39 4.87 5.46 6.18 7.06

10.4 10.9 11.5 12.1 12.7

6.92 7.25 7.62 8.02 8.48

16 17 18 19 20

5.84 6.41 7.07 7.85 8.70

3.89 4.26 4.70 5.23 5.79

8.18 8.46 8.77 9.10 9.45

5.44 5.63 5.83 6.05 6.29

12.1 13.6 15.3 17.0 18.9

8.04 9.07 10.2 11.3 12.6

13.7 15.0 16.4 17.7 19.0

9.13 10.0 10.9 11.8 12.7

22.8 27.2

15.2 18.1

21.7 24.4

14.5 16.3

10.0 11.3 12.7 14.2 15.7

22 24 26 28 30

10.5 12.5 14.7 17.1 19.6

7.01 8.34 9.79 11.3 13.0

10.5 11.8 13.1 14.4 15.7

6.96 19.0 7.83 22.6 8.69 9.56 10.4

32

22.3

14.8

16.9

11.3

6.68 7.54 8.45 9.42 10.4

10.8 11.5 12.5 13.4 14.4

12.6 15.0

16.3 18.3

7.18 7.66 8.30 8.94 9.59 10.9 12.2

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

21.2 2.85 3.51

14.1 1.90 2.34

31.0 3.24 3.98

20.6 2.16 2.66

37.3 3.80 4.67

24.8 2.53 3.11

rx /ry

2.64

3.41

3.43

ry , in.

1.94

1.54

1.52

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200.

c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:54 AM

Page 83

STEEL BEAM-COLUMN SELECTION TABLES

6–83

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W12

W-Shapes W12×

Shape

26c

p×

bx ×

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

22c

103

p×

103

(kip-ft)–1

19c

bx ×

103

(kips)–1

103

(kip-ft)–1

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

0

4.66

3.10

9.58

6.37

5.42

3.60 12.2

8.09

6.52

4.34 14.4

1 2 3 4 5

4.67 4.73 4.82 4.95 5.13

3.11 3.14 3.21 3.29 3.41

9.58 9.58 9.58 9.58 9.58

6.37 6.37 6.37 6.37 6.37

5.48 5.68 6.03 6.58 7.43

3.65 3.78 4.01 4.38 4.95

12.2 12.2 12.2 13.0 14.0

8.09 8.09 8.09 8.65 9.28

6.60 6.84 7.28 7.95 8.97

4.39 4.55 4.84 5.29 5.97

14.4 14.4 14.5 15.6 16.9

9.60 9.60 9.66 10.4 11.2

6 7 8 9 10

5.36 5.64 6.00 6.43 6.97

3.56 3.75 3.99 4.28 4.64

9.83 10.2 10.7 11.2 11.7

6.54 6.81 7.11 7.43 7.79

8.73 5.81 10.6 7.03 13.2 8.75 16.7 11.1 20.6 13.7

15.1 16.4 17.9 19.8 23.0

10.0 10.9 11.9 13.1 15.3

10.5 12.9 16.3 20.6 25.5

6.99 8.56 10.8 13.7 16.9

18.4 20.2 22.3 25.7 30.4

12.2 13.4 14.9 17.1 20.2

11 12 13 14 15

7.64 8.49 9.53 10.8 12.4

5.08 5.65 6.34 7.18 8.22

12.3 12.9 13.6 14.4 15.4

8.17 8.60 9.08 9.61 10.3

24.9 29.6 34.7 40.3

26.5 30.0 33.5 37.1

17.6 20.0 22.3 24.7

30.8 36.7 43.0

20.5 24.4 28.6

35.2 40.1 45.1

23.4 26.7 30.0

16 17 18 19 20

14.1 15.9 17.8 19.8 22.0

9.36 10.6 11.8 13.2 14.6

17.1 18.8 20.6 22.3 24.1

11.4 12.5 13.7 14.9 16.0

21 22 23 24 25

24.2 26.6 29.1 31.6 34.3

16.1 17.7 19.3 21.0 22.8

25.9 27.7 29.5 31.3 33.1

17.2 18.4 19.6 20.8 22.0

16.5 19.7 23.1 26.8

ASD

103

ASD

LRFD 9.60

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

43.6 4.37 5.36

29.0 2.90 3.58

97.3 5.15 6.33

64.8 3.43 4.22

120 6.00 7.37

79.5 3.99 4.91

rx /ry

3.42

5.79

5.86

ry , in.

1.51

0.848

0.822

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:54 AM

6–84

Page 84

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W12

W-Shapes W12×

Shape

16c

p×

14c, v

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

103

p×

bx × 103

(kips)–1

(kip-ft)–1

103

(kip-ft)–1

ASD

LRFD

LRFD

ASD

LRFD

0

7.98

5.31

17.7

ASD

11.8

9.39

6.24

20.5

ASD

13.6

LRFD

1 2 3 4 5

8.08 8.39 8.97 9.87 11.3

5.38 5.59 5.96 6.57 7.49

17.7 17.7 18.1 19.6 21.4

11.8 11.8 12.0 13.1 14.3

9.50 9.88 10.5 11.6 13.3

6.32 6.57 7.02 7.73 8.83

20.5 20.5 21.0 22.9 25.1

13.6 13.6 14.0 15.2 16.7

6 7 8 9 10

13.4 16.8 21.8 27.6 34.0

8.91 11.2 14.5 18.3 22.6

23.6 26.3 29.6 36.1 42.9

15.7 17.5 19.7 24.0 28.5

15.8 19.9 26.0 32.9 40.6

10.5 13.3 17.3 21.9 27.0

27.8 31.2 36.4 44.6 53.3

18.5 20.7 24.2 29.7 35.5

11 12

41.2 49.0

27.4 32.6

50.0 57.2

33.3 38.1

49.1 58.5

32.7 38.9

62.4 71.8

41.5 47.8

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

158 7.09 8.71

105 4.72 5.81

188 8.03 9.86

125 5.34 6.57

rx /ry

6.04

6.14

ry , in.

0.773

0.753

Shape is slender for compression with Fy = 50 ksi. v Shape does not meet the h /t limit for shear in AISC Specification Section G2.1(a) with F = 50 ksi; therefore, φ = 0.90 and w y v Ωv = 1.67. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:55 AM

Page 85

STEEL BEAM-COLUMN SELECTION TABLES

6–85

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W10

W-Shapes W10×

Shape

112

p×

(kips)–1

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Design

100

bx ×

103

103

(kip-ft)–1 ASD

p×

88

bx ×

103

(kips)–1

103

(kip-ft)–1 ASD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

0

1.02

0.675 2.42

1.61

1.14

0.758 2.74

1.82

1.28

0.855 3.15

ASD

2.10

LRFD

6 7 8 9 10

1.07 1.09 1.12 1.14 1.18

0.712 0.726 0.742 0.761 0.782

2.42 2.42 2.42 2.42 2.43

1.61 1.61 1.61 1.61 1.62

1.20 1.23 1.25 1.29 1.32

0.800 0.816 0.835 0.856 0.881

2.74 2.74 2.74 2.74 2.75

1.82 1.82 1.82 1.82 1.83

1.36 1.38 1.42 1.45 1.50

0.903 0.921 0.942 0.967 0.995

3.15 3.15 3.15 3.15 3.17

2.10 2.10 2.10 2.10 2.11

11 12 13 14 15

1.21 1.25 1.30 1.35 1.41

0.807 0.834 0.865 0.900 0.939

2.45 2.47 2.49 2.51 2.53

1.63 1.64 1.66 1.67 1.68

1.37 1.41 1.47 1.53 1.60

0.909 0.941 0.977 1.02 1.06

2.78 2.80 2.82 2.85 2.87

1.85 1.86 1.88 1.90 1.91

1.54 1.60 1.66 1.73 1.81

1.03 1.06 1.11 1.15 1.20

3.20 3.23 3.27 3.30 3.33

2.13 2.15 2.17 2.19 2.22

16 17 18 19 20

1.48 1.55 1.63 1.72 1.82

0.983 1.03 1.09 1.15 1.21

2.55 2.56 2.59 2.61 2.63

1.69 1.71 1.72 1.73 1.75

1.67 1.76 1.85 1.96 2.08

1.11 1.17 1.23 1.30 1.38

2.90 2.92 2.95 2.98 3.00

1.93 1.94 1.96 1.98 2.00

1.90 1.99 2.10 2.23 2.36

1.26 1.33 1.40 1.48 1.57

3.36 3.40 3.43 3.47 3.50

2.24 2.26 2.28 2.31 2.33

22 24 26 28 30

2.06 2.36 2.74 3.18 3.65

1.37 1.57 1.82 2.11 2.43

2.67 2.71 2.76 2.80 2.85

1.78 1.80 1.83 1.87 1.90

2.36 2.70 3.15 3.65 4.19

1.57 1.80 2.09 2.43 2.79

3.06 3.11 3.17 3.23 3.30

2.03 2.07 2.11 2.15 2.19

2.68 3.09 3.60 4.18 4.79

1.79 2.05 2.40 2.78 3.19

3.58 3.65 3.73 3.82 3.90

2.38 2.43 2.48 2.54 2.60

32 34 36 38 40

4.15 4.69 5.25 5.85 6.49

2.76 3.12 3.50 3.90 4.32

2.90 2.95 3.01 3.06 3.12

1.93 1.97 2.00 2.04 2.08

4.77 5.38 6.03 6.72 7.45

3.17 3.58 4.01 4.47 4.96

3.36 3.43 3.50 3.58 3.66

2.24 2.28 2.33 2.38 2.43

5.46 6.16 6.90 7.69 8.52

3.63 4.10 4.59 5.12 5.67

4.00 4.09 4.19 4.30 4.41

2.66 2.72 2.79 2.86 2.94

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

5.15 1.02 1.25

3.43 0.675 0.831

5.84 1.14 1.40

3.89 0.758 0.933

6.71 1.28 1.58

4.46 0.855 1.05

rx /ry

1.74

1.74

1.73

ry , in.

2.68

2.65

2.63

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:55 AM

6–86

Page 86

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W10

W-Shapes W10×

Shape

77

p×

68

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

103

(kip-ft)–1

p×

60

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1.47

0.979

3.65

2.43

1.68

1.12

4.18

2.78

1.89

1.26

4.78

3.18

6 7 8 9 10

1.56 1.59 1.63 1.67 1.72

1.04 1.06 1.08 1.11 1.14

3.65 3.65 3.65 3.65 3.68

2.43 2.43 2.43 2.43 2.45

1.78 1.81 1.86 1.91 1.96

1.18 1.21 1.23 1.27 1.31

4.18 4.18 4.18 4.18 4.22

2.78 2.78 2.78 2.78 2.81

2.00 2.04 2.09 2.15 2.21

1.33 1.36 1.39 1.43 1.47

4.78 4.78 4.78 4.78 4.84

3.18 3.18 3.18 3.18 3.22

11 12 13 14 15

1.78 1.84 1.91 2.00 2.09

1.18 1.23 1.27 1.33 1.39

3.72 3.76 3.80 3.85 3.89

2.48 2.50 2.53 2.56 2.59

2.03 2.10 2.19 2.28 2.39

1.35 1.40 1.46 1.52 1.59

4.27 4.32 4.38 4.44 4.49

2.84 2.88 2.91 2.95 2.99

2.29 2.37 2.47 2.58 2.70

1.52 1.58 1.64 1.72 1.80

4.90 4.97 5.04 5.12 5.19

3.26 3.31 3.36 3.41 3.46

16 17 18 19 20

2.19 2.31 2.44 2.58 2.74

1.46 1.54 1.62 1.72 1.83

3.94 3.98 4.03 4.08 4.13

2.62 2.65 2.68 2.71 2.74

2.51 2.64 2.79 2.96 3.14

1.67 1.76 1.86 1.97 2.09

4.55 4.61 4.67 4.74 4.80

3.03 3.07 3.11 3.15 3.20

2.84 2.99 3.16 3.36 3.57

1.89 1.99 2.10 2.23 2.38

5.27 5.35 5.43 5.52 5.61

3.51 3.56 3.62 3.67 3.73

22 24 26 28 30

3.13 3.61 4.22 4.89 5.62

2.08 2.40 2.81 3.26 3.74

4.23 4.33 4.45 4.56 4.69

2.81 2.88 2.96 3.04 3.12

3.59 4.15 4.85 5.63 6.46

2.39 2.76 3.23 3.74 4.30

4.94 5.08 5.24 5.40 5.57

3.29 3.38 3.49 3.59 3.71

4.08 4.73 5.54 6.42 7.38

2.72 3.14 3.69 4.27 4.91

5.79 5.99 6.20 6.43 6.67

3.85 3.99 4.13 4.28 4.44

32 34 36 38 40

6.39 7.22 8.09 9.02 9.99

4.25 4.80 5.38 6.00 6.65

4.82 4.96 5.11 5.26 5.43

3.21 3.30 3.40 3.50 3.61

7.35 8.30 9.30 10.4 11.5

4.89 5.52 6.19 6.90 7.64

5.76 5.96 6.17 6.40 6.64

3.83 3.96 4.10 4.26 4.42

8.39 9.47 10.6 11.8 13.1

5.58 6.30 7.07 7.87 8.72

6.94 7.22 7.53 7.96 8.43

4.61 4.80 5.01 5.30 5.61

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

7.76 1.47 1.81

5.16 0.979 1.20

8.88 1.68 2.06

5.91 1.12 1.37

10.2 1.89 2.32

6.77 1.26 1.55

rx /ry

1.73

1.71

1.71

ry , in.

2.60

2.59

2.57

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:55 AM

Page 87

STEEL BEAM-COLUMN SELECTION TABLES

6–87

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W10

W-Shapes W10×

Shape

54

p×

bx ×

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

49

103

p×

103

(kip-ft)–1

45

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

2.11

1.41

5.35

3.56

2.32

1.54

5.90

3.92

2.51

1.67

6.49

4.32

6 7 8 9 10

2.24 2.29 2.34 2.41 2.48

1.49 1.52 1.56 1.60 1.65

5.35 5.35 5.35 5.35 5.43

3.56 3.56 3.56 3.56 3.61

2.46 2.51 2.57 2.65 2.73

1.64 1.67 1.71 1.76 1.82

5.90 5.90 5.90 5.90 6.00

3.92 3.92 3.92 3.93 3.99

2.76 2.85 2.97 3.10 3.26

1.84 1.90 1.97 2.06 2.17

6.49 6.49 6.60 6.73 6.87

4.32 4.32 4.39 4.48 4.57

11 12 13 14 15

2.57 2.66 2.77 2.90 3.03

1.71 1.77 1.85 1.93 2.02

5.51 5.60 5.69 5.78 5.88

3.67 3.72 3.78 3.85 3.91

2.83 2.93 3.06 3.19 3.35

1.88 1.95 2.03 2.12 2.23

6.10 6.20 6.31 6.42 6.54

4.06 4.13 4.20 4.27 4.35

3.44 3.65 3.90 4.19 4.51

2.29 2.43 2.60 2.78 3.00

7.00 7.15 7.30 7.46 7.63

4.66 4.76 4.86 4.96 5.07

16 17 18 19 20

3.19 3.36 3.56 3.78 4.02

2.12 2.24 2.37 2.51 2.67

5.97 6.08 6.18 6.29 6.40

3.97 4.04 4.11 4.19 4.26

3.52 3.72 3.94 4.18 4.46

2.34 2.47 2.62 2.78 2.96

6.66 6.78 6.91 7.04 7.18

4.43 4.51 4.60 4.69 4.78

4.89 5.33 5.84 6.44 7.13

3.26 3.55 3.89 4.28 4.75

7.80 7.98 8.17 8.37 8.58

5.19 5.31 5.44 5.57 5.71

22 24 26 28 30

4.60 5.33 6.25 7.25 8.33

3.06 3.55 4.16 4.83 5.54

6.64 6.90 7.18 7.48 7.81

4.42 4.59 4.78 4.98 5.20

5.11 5.94 6.97 8.08 9.28

3.40 3.95 4.64 5.38 6.17

7.48 7.80 8.15 8.53 8.95

4.98 5.19 5.42 5.68 5.96

8.63 5.74 9.03 10.3 6.83 9.53 12.1 8.02 10.1 14.0 9.30 10.9 16.0 10.7 11.7

6.01 6.34 6.71 7.22 7.82

32 34 36 38 40

9.47 10.7 12.0 13.4 14.8

6.30 7.12 7.98 8.89 9.85

8.17 8.60 9.19 9.77 10.4

5.43 5.72 6.11 6.50 6.89

7.03 7.93 8.89 9.91 11.0

9.47 10.2 10.9 11.6 12.3

6.30 6.77 7.24 7.71 8.18

18.3

8.41

10.6 11.9 13.4 14.9 16.5

12.1

12.6

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

11.4 2.11 2.60

7.57 1.41 1.73

12.6 2.32 2.85

8.38 1.54 1.90

17.6 2.51 3.08

11.7 1.67 2.06

rx /ry

1.71

1.71

2.15

ry , in.

2.56

2.54

2.01

Note: Heavy line indicates KL /ry equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:55 AM

6–88

Page 88

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W10

W-Shapes W10×

Shape

39

p×

33

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

p×

103

(kip-ft)–1

30

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

2.90

1.93

7.61

5.06

3.44

2.29

9.18

6.11

3.78

2.51

9.73

6.48

6 7 8 9 10

3.20 3.31 3.45 3.61 3.80

2.13 2.20 2.29 2.40 2.53

7.61 7.61 7.78 7.96 8.14

5.06 5.07 5.18 5.29 5.41

3.80 3.95 4.11 4.31 4.55

2.53 2.62 2.74 2.87 3.03

9.18 9.22 9.45 9.70 9.96

6.11 6.13 6.29 6.45 6.62

4.62 4.97 5.41 5.95 6.62

3.08 3.31 3.60 3.96 4.41

10.1 10.5 10.9 11.3 11.8

6.74 6.99 7.25 7.53 7.84

11 12 13 14 15

4.02 4.28 4.57 4.92 5.31

2.67 2.84 3.04 3.27 3.54

8.33 8.53 8.74 8.96 9.19

5.54 5.67 5.81 5.96 6.12

4.83 5.15 5.52 5.95 6.45

3.21 3.42 3.67 3.96 4.29

10.2 10.5 10.8 11.2 11.5

6.81 7.45 7.00 8.47 7.20 9.76 7.42 11.3 7.65 13.0

4.96 5.64 6.49 7.53 8.64

12.3 12.8 13.4 14.1 14.8

8.17 8.54 8.93 9.37 9.85

16 17 18 19 20

5.78 6.31 6.93 7.67 8.50

3.84 9.44 4.20 9.70 4.61 9.97 5.10 10.3 5.66 10.6

6.28 7.04 6.45 7.72 6.63 8.51 6.82 9.46 7.03 10.5

4.68 5.14 5.67 6.30 6.98

11.9 12.3 12.7 13.1 13.6

7.89 8.15 8.43 8.73 9.05

9.83 11.1 12.4 13.9 15.4

15.6 16.8 18.1 19.4 20.7

10.4 11.2 12.1 12.9 13.8

18.6

23.2

15.4

14.8 16.7 18.7 20.8 23.1

22 24 26 28 30

10.3 12.2 14.4 16.7 19.1

6.84 8.14 9.56 11.1 12.7

11.2 12.0 13.2 14.4 15.6

7.47 7.98 8.77 9.58 10.4

12.7 15.1 17.7 20.6 23.6

8.44 10.0 11.8 13.7 15.7

14.8 16.5 18.3 20.1 21.9

9.82 27.9 11.0 12.2 13.4 14.5

32

21.8

14.5

16.8

11.2

26.8

17.9

23.6

15.7

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

20.7 2.90 3.57

13.8 1.93 2.38

25.4 3.44 4.23

16.9 2.29 2.82

40.3 3.78 4.64

26.8 2.51 3.09

rx /ry

2.16

2.16

3.20

ry , in.

1.98

1.94

1.37

Note: Heavy line indicates KL /ry equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:55 AM

Page 89

STEEL BEAM-COLUMN SELECTION TABLES

6–89

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W10

W-Shapes W10×

Shape

p×

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

22c

26

p×

103

(kip-ft)–1 ASD

19

bx ×

103

(kips)–1

103

(kip-ft)–1 ASD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

0

4.39

2.92 11.4

7.57

5.19

3.45 13.7

9.12

5.94

3.95 16.5

11.0

1 2 3 4 5

4.41 4.49 4.62 4.81 5.06

2.94 2.99 3.07 3.20 3.37

11.4 11.4 11.4 11.4 11.5

7.57 7.57 7.57 7.57 7.63

5.22 5.30 5.44 5.66 5.97

3.47 3.53 3.62 3.77 3.97

13.7 13.7 13.7 13.7 13.9

9.12 9.12 9.12 9.12 9.23

6.03 6.28 6.73 7.41 8.39

4.01 4.18 4.48 4.93 5.58

16.5 16.5 16.5 17.4 18.6

11.0 11.0 11.0 11.6 12.4

6 7 8 9 10

5.39 5.80 6.32 6.96 7.76

3.58 3.86 4.20 4.63 5.16

11.9 12.4 12.9 13.5 14.1

7.93 8.25 8.59 8.97 9.38

6.38 6.89 7.53 8.33 9.33

4.24 4.58 5.01 5.55 6.21

14.5 15.1 15.9 16.7 17.6

9.64 10.1 10.6 11.1 11.7

9.76 6.49 11.7 7.77 14.4 9.55 18.1 12.0 22.3 14.8

19.9 21.4 23.2 25.3 28.2

13.2 14.3 15.4 16.8 18.8

11 12 13 14 15

8.74 5.81 9.96 6.63 11.5 7.65 13.3 8.88 15.3 10.2

14.8 15.5 16.4 17.3 18.4

9.84 10.3 10.9 11.5 12.2

10.6 12.1 14.1 16.4 18.8

7.04 8.07 9.38 10.9 12.5

18.5 19.6 20.9 22.5 25.0

12.3 13.1 13.9 15.0 16.6

27.0 32.1 37.7 43.7

32.3 36.4 40.5 44.6

21.5 24.2 26.9 29.7

16 17 18 19 20

17.4 19.7 22.1 24.6 27.2

11.6 13.1 14.7 16.3 18.1

20.1 21.8 23.6 25.3 27.0

13.4 14.5 15.7 16.8 18.0

21.4 24.1 27.0 30.1 33.4

14.2 16.0 18.0 20.0 22.2

27.4 29.9 32.4 34.9 37.4

18.2 19.9 21.6 23.2 24.9

21 22

30.0 32.9

20.0 21.9

28.7 30.5

19.1 20.3

36.8 40.4

24.5 26.9

39.9 42.4

26.5 28.2

18.0 21.4 25.1 29.1

ASD

LRFD

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

47.5 4.39 5.39

31.6 2.92 3.59

58.4 5.15 6.32

38.9 3.42 4.21

106 5.94 7.30

70.8 3.95 4.87

rx /ry

3.20

3.21

4.74

ry , in.

1.36

1.33

0.874

Shape is slender for compression with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:55 AM

6–90

Page 90

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W10

W-Shapes W10×

Shape

17c

p×

15c

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

103

(kip-ft)–1 ASD

p×

12c, f

bx ×

103

(kips)–1

103

(kip-ft)–1 ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

LRFD

ASD

LRFD

LRFD

ASD

0

6.77

4.50 19.1

12.7

7.77

5.17 22.3

14.8

10.3

ASD

6.87

28.5

19.0

LRFD

1 2 3 4 5

6.85 7.11 7.64 8.47 9.68

4.56 4.73 5.09 5.64 6.44

19.1 19.1 19.1 20.4 21.9

12.7 12.7 12.7 13.6 14.5

7.87 8.19 8.76 9.79 11.3

5.24 5.45 5.83 6.51 7.53

22.3 22.3 22.5 24.2 26.1

14.8 14.8 15.0 16.1 17.4

10.5 10.9 11.6 12.8 14.6

6.96 28.5 7.24 28.5 7.74 28.8 8.52 31.1 9.73 33.9

19.0 19.0 19.1 20.7 22.6

6 7 8 9 10

11.4 13.8 17.2 21.8 26.9

7.57 9.17 11.4 14.5 17.9

23.6 25.6 28.0 30.9 36.0

15.7 17.0 18.6 20.6 23.9

13.5 16.6 21.2 26.8 33.1

8.98 11.1 14.1 17.8 22.0

28.4 31.2 34.5 39.6 46.8

18.9 20.7 22.9 26.4 31.1

17.5 21.8 28.1 35.6 43.9

11.6 14.5 18.7 23.7 29.2

37.3 41.3 46.4 56.5 67.2

24.8 27.5 30.9 37.6 44.7

11 12 13 14

32.5 38.7 45.4 52.7

21.6 25.8 30.2 35.1

41.4 46.8 52.3 57.8

27.5 31.2 34.8 38.5

40.1 47.7 56.0

26.7 31.7 37.2

54.0 61.4 68.8

35.9 40.9 45.8

53.1 63.2 74.2

35.4 42.1 49.4

78.3 89.6 101

52.1 59.6 67.3

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

127 6.69 8.22

84.7 4.45 5.48

155 7.57 9.30

103 5.04 6.20

207 9.44 11.6

138 6.28 7.73

rx /ry

4.79

4.88

4.97

ry , in.

0.845

0.810

0.785

Shape is slender for compression with Fy = 50 ksi. f Shape does not meet compact limit for flexure with F = 50 ksi. y Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:55 AM

Page 91

STEEL BEAM-COLUMN SELECTION TABLES

6–91

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W8

W-Shapes W8×

Shape

67

p×

bx ×

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

58

103

p×

103

(kip-ft)–1

48

bx ×

103

(kips)–1

103

(kip-ft)–1

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

1.70

1.13

5.08

3.38

1.95

1.30

5.96

3.96

2.37

1.58

7.27

4.84

6 7 8 9 10

1.84 1.90 1.97 2.05 2.14

1.23 1.27 1.31 1.36 1.43

5.08 5.08 5.11 5.16 5.21

3.38 3.38 3.40 3.43 3.47

2.13 2.20 2.28 2.37 2.48

1.42 1.46 1.51 1.58 1.65

5.96 5.96 6.00 6.07 6.14

3.96 3.96 3.99 4.04 4.08

2.59 2.67 2.77 2.88 3.02

1.72 1.78 1.84 1.92 2.01

7.27 7.27 7.34 7.44 7.55

4.84 4.84 4.88 4.95 5.02

11 12 13 14 15

2.25 2.38 2.52 2.68 2.87

1.50 1.58 1.68 1.79 1.91

5.27 5.32 5.38 5.43 5.49

3.50 3.54 3.58 3.61 3.65

2.61 2.75 2.92 3.12 3.34

1.73 1.83 1.95 2.08 2.22

6.21 6.29 6.36 6.44 6.52

4.13 4.18 4.23 4.29 4.34

3.18 3.36 3.57 3.82 4.10

2.12 2.24 2.38 2.54 2.73

7.65 7.77 7.88 8.00 8.12

5.09 5.17 5.24 5.32 5.41

16 17 18 19 20

3.09 3.34 3.62 3.95 4.33

2.05 2.22 2.41 2.63 2.88

5.55 5.61 5.67 5.74 5.80

3.69 3.73 3.77 3.82 3.86

3.60 3.89 4.23 4.62 5.08

2.39 2.59 2.82 3.08 3.38

6.61 6.69 6.78 6.87 6.96

4.40 4.45 4.51 4.57 4.63

4.42 4.79 5.21 5.70 6.28

2.94 3.18 3.47 3.79 4.18

8.25 8.38 8.52 8.66 8.80

5.49 5.58 5.67 5.76 5.85

22 24 26 28 30

5.24 6.23 7.31 8.48 9.74

3.48 4.15 4.87 5.64 6.48

5.93 6.07 6.22 6.38 6.54

3.95 4.04 4.14 4.24 4.35

6.15 7.32 8.59 9.96 11.4

4.09 4.87 5.71 6.63 7.61

7.15 7.35 7.57 7.79 8.03

4.76 4.89 5.03 5.19 5.35

7.60 9.05 10.6 12.3 14.1

5.06 9.10 6.02 9.43 7.06 9.77 8.19 10.1 9.40 10.6

6.06 6.27 6.50 6.75 7.02

7.37 8.32

6.71 6.89

4.46 4.58

13.0 14.7

8.66 9.77

8.29 8.56

5.52 5.70

16.1 18.2

32 34

11.1 12.5

10.7 12.1

11.0 11.5

7.31 7.63

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

10.9 1.70 2.08

7.25 1.13 1.39

12.8 1.95 2.40

8.50 1.30 1.60

15.6 2.37 2.91

10.4 1.58 1.94

rx /ry

1.75

1.74

1.74

ry , in.

2.12

2.10

2.08

Note: Heavy line indicates KL /ry equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:55 AM

6–92

Page 92

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W8

W-Shapes W8×

Shape

40

p×

35

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

103

p×

bx × 103

(kips)–1

(kip-ft)–1

103

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

2.85

1.90

8.95

5.96

3.24

2.16

10.3

6.83

6 7 8 9 10

3.13 3.23 3.36 3.50 3.68

2.08 2.15 2.23 2.33 2.45

8.95 8.95 9.07 9.22 9.38

5.96 5.96 6.03 6.14 6.24

3.56 3.68 3.82 3.99 4.19

2.37 2.45 2.54 2.65 2.79

10.3 10.3 10.4 10.6 10.8

6.83 6.83 6.94 7.07 7.21

11 12 13 14 15

3.88 4.11 4.38 4.69 5.04

2.58 2.73 2.91 3.12 3.36

9.55 9.72 9.90 10.1 10.3

6.35 6.47 6.59 6.71 6.84

4.42 4.68 4.99 5.35 5.76

2.94 3.12 3.32 3.56 3.83

11.1 11.3 11.5 11.8 12.0

7.36 7.51 7.67 7.83 8.00

16 17 18 19 20

5.46 5.93 6.48 7.12 7.87

3.63 3.95 4.31 4.73 5.24

10.5 10.7 10.9 11.1 11.4

6.97 7.11 7.25 7.40 7.55

6.24 6.79 7.42 8.16 9.03

4.15 4.51 4.94 5.43 6.01

12.3 12.6 12.9 13.2 13.5

8.18 8.37 8.56 8.77 8.99

22 24 26 28 30

9.52 11.3 13.3 15.4 17.7

6.34 7.54 8.85 10.3 11.8

11.8 12.4 13.0 13.6 14.4

7.88 8.24 8.64 9.07 9.57

10.9 13.0 15.3 17.7 20.3

7.27 8.65 10.2 11.8 13.5

14.2 15.0 15.8 17.0 18.4

9.45 9.97 10.5 11.3 12.3

32 34

20.1 22.7

13.4 15.1

15.4 16.5

23.1

15.4

19.8

13.2

10.3 11.0

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

19.3 2.85 3.51

12.8 1.90 2.34

22.1 3.24 3.98

14.7 2.16 2.66

rx /ry

1.73

1.73

ry , in.

2.04

2.03

Note: Heavy line indicates KL /ry equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:55 AM

Page 93

STEEL BEAM-COLUMN SELECTION TABLES

6–93

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W8

W-Shapes W8×

Shape

31f

p×

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

bx ×

(kips)–1

Design

28

103

103

p×

bx × 103

(kips)–1

(kip-ft)–1

103

(kip-ft)–1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

0

3.66

2.43

11.7

7.80

4.05

2.69

13.1

8.71

6 7 8 9 10

4.01 4.15 4.32 4.51 4.74

2.67 2.76 2.87 3.00 3.15

11.7 11.7 11.9 12.2 12.5

7.80 7.80 7.94 8.11 8.29

4.68 4.93 5.23 5.60 6.05

3.11 3.28 3.48 3.73 4.02

13.2 13.5 13.9 14.2 14.6

8.77 9.00 9.23 9.48 9.74

11 12 13 14 15

5.00 5.30 5.66 6.07 6.54

3.33 3.53 3.76 4.04 4.35

12.7 13.0 13.3 13.7 14.0

8.48 8.67 8.88 9.09 9.32

6.58 7.21 7.98 8.89 9.98

4.38 4.80 5.31 5.91 6.64

15.0 15.5 15.9 16.4 17.0

10.0 10.3 10.6 10.9 11.3

16 17 18 19 20

7.08 7.71 8.44 9.29 10.3

4.71 5.13 5.62 6.18 6.84

14.4 14.7 15.1 15.6 16.0

9.56 9.81 10.1 10.3 10.6

11.3 12.8 14.3 16.0 17.7

7.54 8.51 9.54 10.6 11.8

17.5 18.1 18.7 19.4 20.2

11.7 12.0 12.5 12.9 13.4

22 24 26 28 30

12.4 14.8 17.4 20.2 23.1

8.28 9.86 11.6 13.4 15.4

17.0 18.0 19.6 21.4 23.3

11.3 12.0 13.1 14.3 15.5

21.4 25.5 29.9

14.2 17.0 19.9

22.1 24.5 26.9

14.7 16.3 17.9

32

26.3

17.5

25.1

16.7

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

25.3 3.66 4.49

16.8 2.43 3.00

35.3 4.05 4.97

23.5 2.69 3.32

rx /ry

1.72

2.13

ry , in.

2.02

1.62

Shape does not meet compact limit for flexure with Fy = 50 ksi. Note: Heavy line indicates KL /ry equal to or greater than 200. f

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:55 AM

6–94

Page 94

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

Table 6-1 (continued)

Combined Flexure and Axial Force W8

W-Shapes W8×

Shape

24

p×

21

bx ×

103

(kips)–1

Design

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

Fy = 50 ksi

p×

103

(kip-ft)–1 ASD

18

bx ×

103

(kips)–1

103

(kip-ft)–1 ASD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

0

4.72

3.14 15.4

10.3

5.42

3.61 17.5

11.6

6.35

4.22 21.0

ASD

13.9

LRFD

1 2 3 4 5

4.74 4.79 4.89 5.03 5.22

3.15 3.19 3.26 3.35 3.47

15.4 15.4 15.4 15.4 15.4

10.3 10.3 10.3 10.3 10.3

5.46 5.57 5.76 6.03 6.40

3.63 3.70 3.83 4.01 4.26

17.5 17.5 17.5 17.5 17.8

11.6 11.6 11.6 11.6 11.9

6.39 6.53 6.76 7.10 7.56

4.25 4.34 4.50 4.72 5.03

21.0 21.0 21.0 21.0 21.5

13.9 13.9 13.9 13.9 14.3

6 7 8 9 10

5.46 5.76 6.12 6.56 7.08

3.63 3.83 4.07 4.36 4.71

15.6 16.0 16.5 17.0 17.5

10.4 10.6 11.0 11.3 11.7

6.88 7.50 8.29 9.28 10.5

4.58 4.99 5.51 6.17 7.00

18.5 19.2 20.0 20.9 21.9

12.3 12.8 13.3 13.9 14.5

8.16 8.93 9.91 11.2 12.7

5.43 5.94 6.60 7.42 8.47

22.5 23.5 24.6 25.9 27.3

15.0 15.6 16.4 17.2 18.1

11 12 13 14 15

7.71 8.47 9.37 10.5 11.8

5.13 5.63 6.24 6.96 7.83

18.1 18.7 19.3 20.0 20.8

12.0 12.4 12.9 13.3 13.8

12.1 14.1 16.6 19.2 22.0

8.05 9.39 11.0 12.8 14.7

22.9 24.1 25.3 26.7 28.5

15.2 16.0 16.8 17.8 18.9

14.7 17.3 20.3 23.6 27.1

9.81 11.5 13.5 15.7 18.0

28.8 30.5 32.5 35.3 38.8

19.2 20.3 21.6 23.5 25.8

16 17 18 19 20

13.4 15.1 16.9 18.8 20.9

8.89 10.0 11.3 12.5 13.9

21.6 22.5 23.4 24.5 26.1

14.4 14.9 15.6 16.3 17.4

25.1 28.3 31.7 35.4 39.2

16.7 18.8 21.1 23.5 26.1

30.9 33.4 35.9 38.3 40.7

20.6 22.2 23.9 25.5 27.1

30.8 34.8 39.0 43.5 48.2

20.5 23.1 26.0 28.9 32.0

42.4 45.9 49.4 52.9 56.4

28.2 30.5 32.9 35.2 37.5

21 22 23 24 25

23.0 25.3 27.6 30.1 32.6

15.3 16.8 18.4 20.0 21.7

27.8 29.4 31.0 32.6 34.2

18.5 19.6 20.6 21.7 22.8

43.2

28.7

43.2

28.7

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

41.6 4.72 5.79

27.7 3.14 3.86

62.6 5.42 6.66

41.7 3.61 4.44

76.5 6.35 7.80

50.9 4.22 5.20

rx /ry

2.12

2.77

2.79

ry , in.

1.61

1.26

1.23

Note: Heavy line indicates KL /ry equal to or greater than 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

2/4/11

8:55 AM

Page 95

STEEL BEAM-COLUMN SELECTION TABLES

6–95

Table 6-1 (continued)

Combined Flexure and Axial Force

Fy = 50 ksi

W8

W-Shapes W8×

Shape

15

p×

Effective length, KL (ft), with respect to least radius of gyration, ry , or Unbraced Length, Lb (ft), for X-X axis bending

bx ×

(kips)–1

Design

10 c, f

13

103

103

(kip-ft)–1 ASD

p×

bx ×

103

(kips)–1

103

(kip-ft)–1 ASD

LRFD

103

p×

bx × 103

(kips)–1

(kip-ft)–1

ASD

LRFD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

0

7.52

5.01 26.2

17.4

8.70

5.79 31.3

20.8

11.7

ASD

7.78

40.6

27.0

1 2 3 4 5

7.63 7.95 8.51 9.37 10.6

5.07 5.29 5.66 6.23 7.05

26.2 26.2 26.2 27.6 29.4

17.4 17.4 17.4 18.4 19.5

8.83 9.23 9.94 11.0 12.6

5.87 6.14 6.61 7.34 8.38

31.3 31.3 31.3 33.4 35.7

20.8 20.8 20.8 22.2 23.8

11.8 12.3 13.1 14.3 16.4

7.88 8.18 8.71 9.55 10.9

40.6 40.6 40.6 43.2 46.7

27.0 27.0 27.0 28.8 31.1

6 7 8 9 10

12.3 14.7 18.1 22.8 28.1

8.20 9.80 12.0 15.2 18.7

31.3 33.6 36.2 39.3 42.9

20.8 22.4 24.1 26.1 28.6

14.8 18.0 22.5 28.4 35.1

9.86 12.0 14.9 18.9 23.4

38.5 41.7 45.4 50.0 57.4

25.6 27.7 30.2 33.2 38.2

19.3 23.4 29.3 37.1 45.8

12.8 15.6 19.5 24.7 30.4

50.8 55.7 61.6 71.3 84.3

33.8 37.0 41.0 47.4 56.1

11 12 13 14

34.0 40.5 47.5 55.1

22.6 26.9 31.6 36.7

48.9 54.9 60.9 66.9

32.5 36.5 40.5 44.5

42.5 50.6 59.3 68.8

28.3 33.6 39.5 45.8

65.8 74.3 82.7 91.2

43.8 49.4 55.0 60.7

55.4 65.9 77.3 89.7

36.8 43.8 51.5 59.7

97.6 111 125 139

64.9 73.9 83.0 92.2

Other Constants and Properties × 103, (kip-ft)–1

by t y × 103, (kips)–1 t r × 103, (kips)–1

133 7.52 9.24

88.8 5.01 6.16

166 8.70 10.7

110 5.79 7.12

218 11.3 13.9

145 7.51 9.24

rx /ry

3.76

3.81

3.83

ry , in.

0.876

0.843

0.841

Shape is slender for compression with Fy = 50 ksi. f Shape does not meet compact limit for flexure with F = 50 ksi. y Note: Heavy line indicates KL /ry equal to or greater than 200. c

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 06B:14th Ed.

6–96

2/4/11

8:55 AM

Page 96

DESIGN OF MEMBERS SUBJECT TO COMBINED FORCES

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A:14th Ed.

4/1/11

8:53 AM

Page 1

7–1

PART 7 DESIGN CONSIDERATIONS FOR BOLTS

SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–3 GENERAL REQUIREMENTS FOR BOLTED JOINTS . . . . . . . . . . . . . . . . . . . . . . . . 7–3 Fastener Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–3 Proper Selection of Bolt Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–3 Washer Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–4 Nut Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–4 Bolted Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–4 PROPER SPECIFICATION OF JOINT TYPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–4 Snug-Tightened Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–4 Pretensioned Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–5 Slip-Critical Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–5 DESIGN REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–5 Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–5 Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–6 Combined Shear and Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–6 Bearing Strength at Bolt Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–6 Slip Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–6 ECCENTRICALLY LOADED BOLT GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–6 Eccentricity in the Plane of the Faying Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–6 Instantaneous Center of Rotation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–6 Elastic Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–8 Eccentricity Normal to the Plane of the Faying Surface . . . . . . . . . . . . . . . . . . . . . 7–10 Case I—Neutral Axis Not at Center of Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . 7–10 Case II—Neutral Axis at Center of Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–12 SPECIAL CONSIDERATIONS FOR HOLLOW STRUCTURAL SECTIONS . . . . . 7–13 Through-Bolting to HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–13 Blind Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–13 Flow-Drilling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–13 Threaded Studs to HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–14 Nailing to HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–15

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A:14th Ed.

7–2

2/24/11

8:32 AM

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DESIGN CONSIDERATIONS FOR BOLTS

Screwing to HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–15 Connection Shear per Screw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–15 OTHER SPECIFICATION REQUIREMENTS AND DESIGN CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–16 Placement of Bolt Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–16 Bolts in Combination with Welds or Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–16 Galvanizing High-Strength Bolts and Nuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–16 Reuse of Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–16 Fatigue Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–16 Entering and Tightening Clearances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–17 Fully Threaded ASTM A325 Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–17 ASTM A307 Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–17 ASTM A449 Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–17 DESIGN TABLE DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–17 PART 7 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–21 DESIGN TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–22 Table 7-1. Available Shear Strength of Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–22 Table 7-2. Available Tensile Strength of Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–23 Table 7-3. Slip-Critical Connections, Available Shear Strength . . . . . . . . . . . . . . . . 7–24 Tables 7-4 and 7-5. Available Bearing Strength at Bolt Holes . . . . . . . . . . . . . . . . . 7–26 Tables 7-6 through 7-13. Coefficients C for Eccentrically Loaded Bolt Groups . . . 7–30 Table 7-14. Dimensions of High-Strength Fasteners . . . . . . . . . . . . . . . . . . . . . . . . 7–78 Tables 7-15 and 7-16. Entering and Tightening Clearance . . . . . . . . . . . . . . . . . . . 7–79 Table 7-17. Threading Dimensions for High-Strength and Non-High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–81 Table 7-18. Weights of High-Strength Fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–82 Table 7-19. Dimensions of Non-High-Strength Fasteners . . . . . . . . . . . . . . . . . . . . 7–83 Tables 7-20, 7-21 and 7-22. Weights of Non-High-Strength Fasteners . . . . . . . . . . 7–85

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SCOPE The specification requirements and other design considerations summarized in this Part apply to the design of bolts in steel-to-steel structural connections. Additional guidance on bolt design is available in AISC Design Guide 17, High Strength Bolts—A Primer for Structural Engineers, (Kulak, 2002). For the design of steel-to-concrete anchorage, see Part 14. For the design of connection elements, see Part 9. For the design of simple shear, moment, bracing and other connections, see Parts 10 through 15.

GENERAL REQUIREMENTS FOR BOLTED JOINTS Fastener Components The applicable material specifications for fastener components are as given in Part 2. For convenience in referencing and consistent with AISC Specification Section J3.1, ASTM A325 and F1852 bolts have been labelled Group A bolts, and ASTM A490 and F2280 bolts have been labelled Group B bolts. Material and storage requirements for fastener components are as given in AISC Specification Section A3.3 and RCSC Specification Section 2. The compatibility of ASTM A563 nuts and F436 washers with ASTM A325, F1852, A490 and F2280 bolts is as given in RCSC Specification Table 2.1. These products are given identifying marks, as illustrated in RCSC Specification Figure C-2.1. Alternative-design fasteners and alternative washertype indicating devices are permitted, subject to the requirements in RCSC Specification Sections 2.8 and 2.6.2, respectively. Mixing grades of fasteners raises inventory and quality control issues associated with the use of multiple fastener grades. When both Group A and Group B bolts are used on a project, different diameters can be specified for each to help ensure that the Group B bolts are installed in the proper location. Regardless of the bolt type selected, the typical sizes of 3/ 4-in., 7/8-in., 1-in. and 11/8-in. diameter are usually preferred. Diameters above 1 in. require special consideration for availability as well as installation, when pretensioned installation is required. Special equipment may be required to pretension large-diameter Group B bolts.

Proper Selection of Bolt Length Per RCSC Specification Section 2.3.2, adequate thread engagement is developed when the end of the bolt is at least flush with or projects beyond the face of the nut. To provide for this, the ordered length of Group A and Group B bolts should be calculated as the grip (see Figure 7-1) plus the nominal thickness of washers and/or direct-tension indicators, if used, plus the allowance from Table 7-14, with the total rounded to the next higher increment of 1 /4 in. up to a 5-in. length and the next higher 1/2 in. over a 5-in. length. Note that bolts longer than 5 in. are generally available only in 1/2-in. increments, except by special arrangement with the manufacturer or vendor. While longer lengths may be ordered, an 8-in. length is generally the maximum stock length available. Requirements for a minimum stick-through greater than zero are discouraged because of the risk of jamming the nut on the thread runout, particularly in the bolt length range available only in 1/2-in. increments. See Carter (1996) for further information.

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Washer Requirements Requirements for the use of ASTM F436 washers and/or plate washers are given in RCSC Specification Section 6.

Nut Requirements The compatibility of ASTM A563 nuts with Group A and Group B bolts is as given in RCSC Specification Table 2.1.

Bolted Parts The requirements for connected plies, faying surfaces, bolt holes and burrs are given in AISC Specification Sections J3.2 and M2.5, and RCSC Specification Section 3. Spacing and edge distance requirements are given in AISC Specification Sections J3.3, J3.4 and J3.5.

PROPER SPECIFICATION OF JOINT TYPE When Group A or Group B high-strength bolts are to be used, the joint type must be specified as snug-tightened, pretensioned or slip-critical, per AISC Specification Section J3.1.

Snug-Tightened Joints Snug-tightened joints simplify design, installation and inspection and should be specified whenever pretensioned joints and slip-critical joints are not required. The applicability is summarized and design requirements, installation requirements and inspection requirements are stipulated for snug-tightened joints per RCSC Specification Section 4.1. Faying surfaces in snug-tightened joints must meet the requirements in RCSC Specification Sections 3.2 and 3.2.1, but not those for slip-critical joints in RCSC Specification Section 3.2.2. Note that there is generally no need to limit the actual level of pretension provided in snug-tightened joints, per RCSC Specification Section 9.1.

Specification

Fig. 7-1. Grip and other parameters for bolt length selection. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Pretensioned Joints When pretension is required but slip-resistance is not of concern, a pretensioned joint should be specified. The applicability is summarized and design requirements, installation requirements and inspection requirements are stipulated for pretensioned joints per RCSC Specification Section 4.2. Additionally, pretensioned joints are required by default in some cases per AISC Specification Section J1.10. Faying surfaces in pretensioned joints must meet the requirements in RCSC Specification Sections 3.2 and 3.2.1, but not those for slipcritical joints in RCSC Specification Section 3.2.2.

Slip-Critical Joints The applicability of slip critical joints is summarized and design requirements, installation requirements, and inspection requirements are stipulated in RCSC Specification Section 4.3, except as modified by AISC Specification Sections J3.8 and J3.9. Faying surfaces in slipcritical joints must meet the requirements in RCSC Specification Sections 3.2 and 3.2.2. RCSC defines a faying surface as “the plane of contact between two plies of a joint.” Note that the surfaces under the bolt head, washer and/or nut are not faying surfaces. Subject to the requirements in RCSC Specification Section 4.3, slip-critical joints are rarely required in building design. Slip-critical joints are appreciably more expensive because of the associated costs of faying surface preparation and installation and inspection requirements. When slip-resistance is required and the steel is painted, the fabricator should be consulted to determine the most economical approach to providing the necessary slip resistance. Special paint systems that are rated for slip resistance can be specified. Alternatively, a paint system that is not rated for slip resistance can be used with the faying surfaces masked.

DESIGN REQUIREMENTS Design requirements are found in the AISC Specification as follows. In each case, the available strength determined in accordance with these provisions must equal or exceed the required strength. These requirements are derived from those in the RCSC Specification.

Shear Available shear strength is determined as given in RCSC Specification Section 5.1 and AISC Specification Section J3.6, with consideration of the presence of fillers or shims, per RCSC Specification Section 5.1 and AISC Specification Section J5. The nominal shear strengths given in Table J3.2 have been reduced by approximately 10% from statistical results of tests to account for uneven force distributions associated with end loading and other effects normally neglected in the design process. When the length of a bolted joint measured parallel to the line of force exceeds 38 in., a 16.7% strength reduction may be applicable, per AISC Specification Table J3.2 footnote a. The force that can be resisted by a snug-tightened or pretensioned high-strength bolt may also be limited by the bearing strength at the bolt hole per AISC Specification Section J3.10. The effective strength of an individual bolt may be taken as the lesser of the shear strength per Section J3.6 or the bearing strength at the bolt hole per Section J3.10. The strength of the bolt group may be taken as the sum of the effective strengths of the individual fasteners. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Tension Available tensile strength is determined as given in RCSC Specification Section 5.1 and AISC Specification Section J3.6, with consideration of the effects of prying action, if any. Prying action is a phenomenon (in bolted construction only) whereby the deformation of a fitting under a tensile force increases the tensile force in the bolt. While the effect of prying action is relevant to the design of the bolts, it is primarily a function of the strength and stiffness of the connection elements. Prying action is addressed in Part 9.

Combined Shear and Tension Available strength for combined shear and tension in bearing-type connections is determined as given in RCSC Specification Section 5.2 and AISC Specification Section J3.7.

Bearing Strength at Bolt Holes Available bearing strength at bolt holes is determined as given in RCSC Specification Section 5.3 and AISC Specification Section J3.10.

Slip Resistance The available strength of slip-critical connections is determined in accordance with AISC Specification Section J3.8. The available strength, φRn or Rn /Ω, is determined by applying the resistance factor or safety factor appropriate for the hole type used.

ECCENTRICALLY LOADED BOLT GROUPS Eccentricity in the Plane of the Faying Surface When eccentricity occurs in the plane of the faying surface, the bolts must be designed to resist the combined effect of the direct shear, Pu or Pa, and the additional shear from the induced moment, Pu e or Pa e. Two analysis methods for this type of eccentricity are the instantaneous center of rotation method and the elastic method. The instantaneous center of rotation method is more accurate, but generally requires the use of tabulated values or an iterative solution. The elastic method is simplified, but may be excessively conservative because it neglects the ductility of the bolt group and the potential for load redistribution.

Instantaneous Center of Rotation Method Eccentricity produces both a rotation and a translation of one connection element with respect to the other. The combined effect of this rotation and translation is equivalent to a rotation about a point defined as the instantaneous center of rotation (IC), as illustrated in Figure 7-2(a). The location of the IC depends upon the geometry of the bolt group as well as the direction and point of application of the load. The load-deformation relationship for one bolt is illustrated in Figure 7-3, where R = Rult (1 ⫺ e⫺10Δ ) 0.55

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where R = nominal shear strength of one bolt at a deformation Δ, kips Rult = ultimate shear strength of one bolt, kips Δ = total deformation, including shear, bearing and bending deformation in the bolt and bearing deformation of the connection elements, in. e = 2.718…, base of the natural logarithm The nominal shear strength of the bolt most remote from the IC can be determined by applying a maximum deformation, Δmax, to that bolt. The load-deformation relationship is based upon data obtained experimentally for 3/ 4-in.-diameter ASTM A325 bolts, where Rult = 74 kips, and Δ max = 0.34 in. The nominal shear strengths of the other bolts in the joint can be determined by applying a deformation Δ that varies linearly with distance from the IC. The nominal shear strength of the bolt group is, then, the sum of the individual strengths of all bolts.

(a) Instantaneous center of rotation (IC)

(b) Forces on bolts in group for case of θ = 0° for simplicity Fig. 7-2. Illustration for instantaneous center of rotation method.

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The individual resistance of each bolt is assumed to act on a line perpendicular to a ray passing through the IC and the centroid of that bolt, as illustrated in Figure 7-2(b). If the correct location of the IC has been selected, the three equations of in-plane static equilibrium (ΣFx = 0, ΣFy = 0, and ΣM = 0) will be satisfied. For further information, see Crawford and Kulak (1968).

Elastic Method For a force applied as illustrated in Figure 7-4, the eccentric force, Pu or Pa , is resolved into a direct shear, Pu or Pa , acting through the center of gravity (CG) of the bolt group and a moment, Pu e or Pa e, where e is the eccentricity. Each bolt is then assumed to resist an equal share of the direct shear and a share of the eccentric moment proportional to its distance from the CG. The resultant vectorial sum of these forces is the required strength for the bolt, ru or ra.

Fig. 7-3. Load-deformation relationship for one 3/4-in.-diameter ASTM A325 bolt in single shear.

Fig. 7-4. Illustration for elastic method. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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The shear per bolt due to the concentric force, Pu or Pa , is rpu or rpa, where LRFD rpu =

ASD

Pu n

rpa =

(7-2a)

Pa n

(7-2b)

and n is the number of bolts. To determine the resultant forces on each bolt when Pu or Pa is applied at an angle θ with respect to the vertical, rpu or rpa must be resolved into horizontal component, rpxu or rpxa, and vertical component, rpyu or rpya, where rpxu = rpu sinθ (LRFD) rpxa = rpa sinθ (ASD) rpyu = rpu cosθ (LRFD) rpya = rpa cosθ (ASD)

(7-3a) (7-3b) (7-4a) (7-4b)

The shear on the bolt most remote from the CG due to the moment, Pu e or Pa e, is rmu or rma, where LRFD rmu =

ASD

Puec Ip

rma =

(7-5a)

Paec Ip

(7-5b)

where c = radial distance from CG to center of bolt most remote from CG, in. Ip = Ix + Iy = polar moment of inertia of the bolt group, in.4 per in.2 To determine the resultant force on the most highly stressed bolt, rmu or rma must be resolved into horizontal component rmxu or rmxa and vertical component rmyu or rmya, where LRFD

ASD

rmxu =

Puecy Ip

(7-6a)

rmxa =

Paecy Ip

(7-6b)

rmyu =

Puecx Ip

(7-7a)

rmya =

Paecx Ip

(7-7b)

In the above equations, cx and cy are the horizontal and vertical components of the diagonal distance c. Thus, the required strength per bolt is ru or ra, where LRFD ru =

ASD

(rpxu + rmxu )2 + (rpyu + rmyu )2

(7-8a)

ra =

(rpxa + rmxa )2 + (rpya + rmya )2

For further information, see Higgins (1971). AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Eccentricity Normal to the Plane of the Faying Surface Eccentricity normal to the plane of the faying surface produces tension above and compression below the neutral axis for a bracket connection as shown in Figure 7-5. The eccentric force, Pu or Pa , is resolved into a direct shear, Pu or Pa , acting at the faying surface of the joint and a moment normal to the plane of the faying surface, Pu e or Pa e, where e is the eccentricity. Each bolt is then assumed to resist an equal share of the concentric force, Pu or Pa , and the moment is resisted by tension in the bolts above the neutral axis and compression below the neutral axis. Two design approaches for this type of eccentricity are available: Case I, in which the neutral axis is not taken at the center of gravity (CG), and Case II, in which the neutral axis is taken at the CG.

Case I—Neutral Axis Not at Center of Gravity The shear per bolt due to the concentric force, ruv or rav, is determined as LRFD ruv =

Pu n

ASD (7-9a)

rav =

Pa n

(7-9b)

where n is the number of bolts in the connection. A trial position for the neutral axis can be selected at one-sixth of the total bracket depth, measured upward from the bottom (line X-X in Figure 7-6(a)). To provide for reasonable proportions and to account for the bending stiffness of the connection elements, the effective width of the compression block, beff , should be taken as beff = 8tf ≤ bf

Fig. 7-5. Tee bracket subject to eccentric loading normal to the plane of the faying surface. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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where tf = lesser connection element thickness, in. bf = connection element width, in. This effective width is valid for bracket flanges made from W-shapes, S-shapes, welded plates and angles. Where the bracket flange thickness is not constant, the average flange thickness should be used. The assumed location of the neutral axis can be evaluated by checking static equilibrium assuming an elastic stress distribution. Equating the moment of the bolt area above the neutral axis with the moment of the compression block area below the neutral axis, (ΣAb)y = beff d (d/2)

(7-11)

where ΣAb = sum of the areas of all bolts above the neutral axis, in.2 y = distance from line X-X to the CG of the bolt group above the neutral axis, in. d = depth of compression block, in. The value of d may then be adjusted until a reasonable equality exists. Once the neutral axis has been located, the tensile force per bolt, rut or rat , as illustrated in Figure 7-6(b), may be determined as LRFD ⎛ P ec ⎞ rut = ⎜ u ⎟ Ab ⎝ Ix ⎠

ASD (7-12a)

⎛ P ec ⎞ rat = ⎜ a ⎟ Ab ⎝ Ix ⎠

(7-12b)

where c = distance from neutral axis to the most remote bolt in the group, in. Ix = combined moment of inertia of the bolt group and compression block about the neutral axis, in.4

(a) Initial approximation of location of NA

(b) Force diagram with final location of NA

Fig. 7-6. Location of neutral axis (NA) for out-of-plane eccentric loading using Case I. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Bolts above the neutral axis are subjected to the shear force, the tensile force, and the effect of prying action (see Part 9); bolts below the neutral axis are subjected to the shear force, ruv or rav, only.

Case II—Neutral Axis at Center of Gravity This method provides a more direct, but also a more conservative result. As for Case I, the shear force per bolt, ruv or rav , due to the concentric force, Pu or Pa , is determined as LRFD ruv =

Pu n

ASD (7-13a)

rav =

Pa n

(7-13b)

where n is the number of bolts in the connection. The neutral axis is assumed to be located at the CG of the bolt group as illustrated in Figure 7-7. The bolts above the neutral axis are in tension and the bolts below the neutral axis are said to be in “compression.” To obtain a more accurate result, a plastic stress distribution is assumed; this assumption is justified because this method is still more conservative than Case I. Accordingly, the tensile force in each bolt above the neutral axis, rut or rat, due to the moment, Pu e or Pa e, is determined as LRFD rut =

Pu e n ′d m

ASD (7-14a)

rat =

Pa e n ′d m

(7-14b)

Fig. 7-7. Location of neutral axis (NA) for out-of-plane eccentric loading using Case II. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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where n′ = number of bolts above the neutral axis dm = moment arm between resultant tensile force and resultant compressive force, in. Bolts above the neutral axis are subjected to the shear force, the tensile force, and the effect of prying action (see Part 9); bolts below the neutral axis are subjected to the shear force, ruv or rav , only.

SPECIAL CONSIDERATIONS FOR HOLLOW STRUCTURAL SECTIONS Through-Bolting to HSS Long bolts that extend through the entire HSS are satisfactory for shear connections that do not require a pretensioned installation. The flexibility of the walls of the HSS precludes installation of pretensioned bolts. Standard structural bolts may be used, although ASTM A449 bolts may be required for longer lengths. The bolts are designed for static shear and the only limit-state involving the HSS is bolt bearing. The available bearing strength is determined as φRn or Rn /Ω, where Rn = 1.8nFy dtdesign φ = 0.75

(7-15)

Ω = 2.00

where n = number of fasteners d = fastener diameter, in. = specified minimum yield strength of HSS, ksi Fy tdesign = design wall thickness of HSS, in.

Blind Bolts Special fasteners are available that eliminate the need for access to install a nut (Korol et al, 1993; Henderson, 1996). The shank of the fastener is inserted through holes in the parts to be connected until the head bears on the outer ply (see Figure 7-8). In some cases, a special wrench is used on the open side to keep the outer part of the shank from rotating and simultaneously turn the threaded part of the shank. A wedge or other mechanism on the blind side causes the fixed part of the shank to expand and form a contact with the inside of the HSS. Some fasteners contain a break-off mechanism when the fastener is pretensioned. Recent versions of these fasteners meet the requirements for a pretensioned ASTM A325 bolt (Henderson, 1996) and could be used in slip-critical or tension conditions. HSS limit states are bolt bearing in shear, tear-out of the bolt in tension, and wall distortion. Manufacturers’ literature must be consulted to determine the available strength of blind bolts.

Flow-Drilling Flow-drilling is a process that can be used to produce a threaded hole in an HSS to permit blind bolting when the inside of the HSS is inaccessible (Sherman, 1995; Henderson, 1996). The process is to force a hole through the HSS with a carbide conical tool rotating at sufficient speed to produce high rapid heating, which softens the material in a local area. The material AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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that is displaced as the tool is forced through the plate forms a truncated hollow cone (bushing) on the inner surface and a small upset on the outer surface. Tools can be obtained with a milling collar so that the material on the outer surface is removed, producing a flat surface allowing parts to be brought in close contact. A cold-formed tap is then used to roll a thread into the hole without any chips or removal of material. The resulting threaded hole has the approximate dimensions and hardness of a heavy hex nut. Shear and tension strengths of ASTM A325 bolts can be developed for certain combinations of bolt size and HSS thickness (see Figure 7-9). Drilling equipment with suitable rotational speed, torque and thrust is required, but with small sizes and thicknesses, field installation with conventional tools is possible. The bolts are designed with the normal criteria and the HSS limit states are bolt bearing in shear and distortion of the HSS wall in tension. HSS strength is not affected by the process except for the reduction in area due to the holes.

Threaded Studs to HSS Threaded studs are available in 3/ 8-in. to 7/ 8-in. diameters and can be shop- or field-welded to an HSS with a stud-welding gun. The connection is similar to a bolted connection with an

Fig. 7-8. Two types of blind bolts.

HSS Thickness (in.) 3/16 1/4 5/16 3/8

BOLT DIAMETER (in.) 1/2

5/8

X X

X X X

3/4

7/8

X X X

X X

1

/2

Fig. 7-9. HSS thickness and bolt diameter combinations. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1

X X

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external nut. The strength of the stud in tension or shear is based on manufacturer’s recommendations and tests. The HSS limit state is distortion of the wall. When using threaded studs, countersunk holes must be used in the attached element to clear the weld fillet at the base of the stud.

Nailing to HSS Power-driven nails that are installed with a power-actuated gun are satisfactory for pure shear connections where the combined thickness of the attachment and the HSS does not exceed 1/2 in. This system was tested as splices between telescoping round HSS loaded with an axial force (Packer, 1996). The shear resistance of the fasteners is taken as the number of nails times the shear strength of a single nail and ignores any secondary contribution from a dimpling effect between the materials. The limit state for the HSS is shear-bearing. See Packer (1996).

Screwing to HSS Self-tapping screws with or without self-drilling points are available for connecting materials with combined thicknesses up to 1/2 in. The screws have diameters from 0.08 in. to 0.25 in. The limit-states for connections in the AISI North American Specification for the Design of Cold-Formed Steel Structural Members (AISI, 2007) are associated with bearing failure of the material or pull-out of the screw either in direct tension or after tilting occurs in a shear load. Failure of the screws themselves is prevented by requiring that the product be 25% stronger than the available shear or tension strength of the material. Edge distances and spacing of screws should not be less than 3 times the screw diameter, d. For attaching material with thickness t1 and ultimate strength Fu1 to an HSS with thickness t and strength Fu, the available strength, φPn or Pn /Ω, is determined as follows, with φ = 0.50 and Ω = 3.00.

Connection Shear per Screw For t/t1 ≤ 1, Pn is the smallest of 1 ⎫ ⎧ 3 2 Fu ⎪ ⎪ 4.2 t d ⎪ ⎪ ⎨ 2.7 t1dFu1 ⎬ ⎪ ⎪ 2.7 tdF u ⎪ ⎪ ⎭ ⎩

(7-16)

⎧2.7 t1dFu1 ⎫ ⎬ ⎨ ⎩ 2.7 tdFu ⎭

(7-17)

( )

For t/t1 ≥ 2.5, Pn is the smaller of

For 1 < t/t1 < 2.5, Pn is determined by linear interpolation between the above two cases. Connection tension per screw, Pn , is the smaller of ⎧0.85tc dFu ⎫ ⎬ ⎨ ⎩1.5t1d w Fu1 ⎭ AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(7-18)

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DESIGN CONSIDERATIONS FOR BOLTS

where tc = lesser of the depth of penetration and the HSS thickness, in. dw = larger of the screw head or washer diameter, and shall not be taken larger than 1/2 in., in.

OTHER SPECIFICATION REQUIREMENTS AND DESIGN CONSIDERATIONS The following other specification requirements and design considerations apply to the design of bolts:

Placement of Bolt Groups For the required placement of bolt groups at the ends of axially loaded members, see AISC Specification Section J1.7.

Bolts in Combination with Welds or Rivets For bolts used in combination with welds or rivets, see AISC Specification Section J1.8 or J1.9, respectively.

Galvanizing High-Strength Bolts and Nuts Galvanizing of high-strength bolts is permitted as follows: 1. By the hot-dip or mechanical process for ASTM A325 Type 1 high-strength bolts, per ASTM A325 Section 4.3 2. By the mechanical process only for ASTM F1852 twist-off-type tension-control bolt assemblies, per ASTM F1852 Section 6.3 3. By the hot-dip or mechanical process for ASTM A449 bolts, per ASTM A449 Section 5.1 Nuts for ASTM A325 and F1852 bolts must be galvanized by the same process as the bolt with which they are used. See RCSC Specification Table 2.1 for compatible nut grade and finish requirements for ASTM A325 and F1852 bolts, and ASTM A563 for compatible nut grade and finish requirements for ASTM A449 bolts. Group B bolts are not permitted to be galvanized, per ASTM A490 Section 5.4 and ASTM F2280 Section 6.6. See also RCSC Specification Commentary Section 2.3 where it discusses that ASTM A490 bolts and F2280 twist-off-type tension-control bolt assemblies are permitted to be coated using a method compliant with ASTM F1136.

Reuse of Bolts The reuse of high-strength bolts is limited, per RCSC Specification Section 2.3.3. See also Bowman and Betancourt (1991) and AISC Design Guide 17, Section 8.6 (Kulak, 2002).

Fatigue Applications For applications involving fatigue, see RCSC Specification Sections 4.2, 4.3 and 5.5, and AISC Specification Appendix 3.

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Entering and Tightening Clearances Clearances must be provided for the entering and tightening of the bolts with an impact wrench. The clearance requirements for conventional high-strength bolts (ASTM A325 and A490) are as given in Table 7-15. When high-strength tension-control bolts (ASTM F1852 and F2280) are specified, the clearance requirements are as given in Table 7-16.

Fully Threaded ASTM A325 Bolts ASTM A325 bolts with length equal to or less than four times the nominal bolt diameter may be ordered as fully threaded with the designation ASTM A325T. Fully threaded ASTM A325T bolts are not for use in bearing-type X connections since it would be impossible to exclude the threads from the shear plane. While this supplementary provision exists for ASTM A325 bolts, there is no similar supplementary provision made in ASTM A490 for full-length threading.

ASTM A307 Bolts Limitations are provided on the use of ASTM A307 bolts, per AISC Specification Sections J1.8 and J1.10. ASTM A307 bolts are available with both hex and square heads in diameters from 1/4 in. to 4 in. in Grade A for general applications and Grade B for cast-iron-flanged piping joints. ASTM A563 Grade A nuts are recommended for use with ASTM A307 bolts. Other suitable grades are listed in ASTM A563 Table X1.1.

ASTM A449 Bolts Limitations are provided on the use of ASTM A449 bolts, per AISC Specification Sections A3.3 and J3.1.

DESIGN TABLE DISCUSSION Table 7-1. Available Shear Strength of Bolts The available bolt shear strengths of various grades and sizes of bolts are summarized in Table 7-1.

Table 7-2. Available Tensile Strength of Bolts The available bolt tensile strengths of various grades and sizes of bolts are summarized in Table 7-2.

Table 7-3. Available Resistance to Slip The available slip resistances of various grades and sizes of bolts are summarized in Table 7-3.

Tables 7-4 and 7-5. Available Bearing Strength at Bolt Holes The available bearing strength at bolt holes is tabulated for various spacings and edge distances in Tables 7-4 and 7-5, respectively. Note that these tables may be applied to bolts with countersunk heads, by subtracting one-half the depth of the countersink from the material

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DESIGN CONSIDERATIONS FOR BOLTS

thickness, t. As illustrated in Figure 7-10, this is equivalent to subtracting db /4 from the material thickness, t.

Tables 7-6 through 7-13. Coefficients C for Eccentrically Loaded Bolt Groups Tables 7-6 through 7-13 employ the instantaneous center of rotation method for the bolt patterns and eccentric conditions indicated, and inclined loads at 0°, 15°, 30°, 45°, 60° and 75°. The tabulated non-dimensional coefficient, C, represents the number of bolts that are effective in resisting the eccentric shear force. In the following discussion, rn is the least nominal strength of one bolt determined from the limit states of bolt shear strength, bearing strength at bolt holes, and slip resistance (if the connection is to be slip-critical).

When Analyzing a Known Bolt Group Geometry For any of the bolt group geometries shown, the available strength of the eccentrically loaded bolt group, φRn or Rn /Ω, is determined as Rn = C × rn φ = 0.75

(7-19)

Ω = 2.00

When Selecting a Bolt Group The available strength must be greater than or equal to the required strength, Pu or Pa . Thus, by dividing the required strength, Pu or Pa , by φrn or rn /Ω, the minimum coefficient, C, is obtained. The bolt group can then be selected from the table corresponding to the appropriate load angle, at the appropriate eccentricity, ex, for which the coefficient is of that magnitude or greater. These tables may be used with any bolt diameter and are conservative when used with Group B bolts (see Kulak, 1975). Linear interpolation within a given table between adjacent values of ex is permitted. Although this procedure is based on bearing connections,

Fig. 7-10. Effective bearing-thickness for bolts with countersunk heads. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN TABLE DISCUSSION

both load tests and analytical studies indicate that it may be conservatively extended to slip-critical connections (Kulak, 1975). A convergence criterion of 1% was employed for the tabulated iterative solutions. Straight-line interpolation between values for loads at different angles may be significantly unconservative. Either a direct analysis should be performed or the values for the next lower angle increment in the tables should be used for design. For bolt group patterns not treated in these tables, a direct analysis is required if the instantaneous center of rotation method is to be used. In some cases, it is necessary to calculate the pure moment strength of a bolt group for purposes of linear interpolation. For these cases, the value of C⬘ has been provided for a load angle of 0°. This moment strength of the bolt group is based on the instantaneous center of rotation method and, since a moment-only condition is assumed, the instantaneous center of rotation coincides with the center of gravity of the bolt group. In this case, the strength is: Mmax = C′rn

(7-20)

where

C′

⎛ 10 l Δ ⎞ ⎡ ⎛ − ⎜ i max ⎟ ⎞ = ∑ ⎢li ⎜ 1 − e ⎝ lmax ⎠ ⎟ ⎢ ⎝ ⎠ ⎣

0.55

⎤ ⎥ , in. ⎥ ⎦

(7-21)

li = distance from the center of gravity of the bolt group to the ith bolt, in. Δmax = maximum deformation on the bolt farthest from the center of gravity = 0.34 in. lmax = distance from the center of gravity of the bolt group to the center of the farthest bolt, in.

Table 7-14. Dimensions of High-Strength Fasteners Dimensions of ASTM A325 and A490 bolts, A563 nuts, and F436 washers are given and illustrated in Table 7-14.

Table 7-15 and 16. Entering and Tightening Clearances Clearance is required for entering and tightening bolts with an impact wrench. The required clearances are given for conventional high-strength bolts and twist-off-type tension-control bolt assemblies in Tables 7-15 and 7-16, respectively.

Table 7-17. Threading Dimensions for High-Strength and Non-High-Strength Bolts Data regarding the characteristics of the threading dimensions of high-strength and nonhigh-strength bolts is provided in Table 7-17.

Table 7-18. Weights of High-Strength Fasteners Weights of conventional ASTM A325 and A490 bolts, A563 nuts, and F436 washers are given in Table 7-18. For dimensions and weights of tension-control ASTM F1852 and F2280 bolts, refer to manufacturers’ literature or the Industrial Fasteners Institute (IFI). For dimensions of ASTM A449 bolts, refer to Table 7-19.

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Table 7-19. Dimensions of Non-High-Strength Fasteners Typical non-high-strength bolt head and nut dimensions are given in Table 7-19. Thread lengths listed in this table may be calculated for non-high-strength bolts as 2d + 1/4 in. for bolts up to 6 in. long and 2d + 1/2 in. for bolts over 6 in. long, where d is the bolt diameter. Note that these thread lengths are longer than those given previously for high-strength bolts in Table 7-14. Threading dimensions are given in Table 7-17.

Tables 7-20, 7-21 and 7-22. Weights of Non-High-Strength Fasteners Weights of non-high-strength bolts are given in Tables 7-20, 7-21 and 7-22.

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PART 7 REFERENCES

PART 7 REFERENCES American Iron and Steel Institute (2007), North American Specification for the Design of Cold-Formed Steel Structural Members, AISI, Washington, DC. Bowman, M.D. and Betancourt, M. (1991), “Reuse of A325 and A490 High-Strength Bolts,” Engineering Journal, Vol. 28, No. 3, 3rd Quarter, pp. 110–118, AISC, Chicago, IL. Carter, C.J. (1996), “Specifying Bolt Length for High-Strength Bolts,” Engineering Journal, Vol. 33, No. 2, 2nd Quarter, pp. 43–53, AISC, Chicago, IL. Crawford, S.F and Kulak, G.L. (1968), “Behavior of Eccentrically Loaded Bolted Connections,” Studies in Structural Engineering, No. 4, Department of Civil Engineering, Nova Scotia Technical College, Halifax, Nova Scotia. Henderson, J.E. (1996), “Bending, Bolting and Nailing of Hollow Structural Sections,” Proceedings International Conference on Tubular Structures, pp. 150–161, American Welding Society. Higgins, T.R. (1971), “Treatment of Eccentrically Loaded Connections in the AISC Manual,” Engineering Journal, Vol. 8, No. 2, April, pp. 52–54, AISC, Chicago, IL. Korol, R.M., Ghobarah, A. and Mourad, S. (1993), “Blind Bolting W-Shape Beams to HSS Columns,” Journal of Structural Engineering, ASCE, Vol.119, No.12, pp. 3,463–3,481. Kulak, G.L. (1975), Eccentrically Loaded Slip-Resistant Connections,” Engineering Journal, Vol. 12, No. 2, 2nd Quarter, pp. 52–55, AISC, Chicago, IL. Kulak, G.L. (2002), High-Strength Bolts—A Primer for Structural Engineers, Design Guide 17, AISC, Chicago, IL. Packer, J.A. (1996), “Nailed Tubular Connections under Axial Loading,” Journal of Structural Engineering, ASCE, Vol. 122, No. 8, pp. 867–872. Sherman, D.R. (1995), “Simple Framing Connections to HSS Columns,” Proceedings National Steel Construction Conference, AISC, pp. 30-1 to 30-16.

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Table 7-1

Available Shear Strength of Bolts, kips Nominal Bolt Diameter, d , in.

5/8

3/4

7/8

1

Nominal Bolt Area, in.2

0.307

0.442

0.601

0.785

ASTM Desig.

Fnv /Ω (ksi)

φFnv (ksi)

ASD

LRFD

N

27.0

40.5

X

34.0

51.0

N

34.0

51.0

X

42.0

63.0

–

13.5

20.3

Thread Cond.

Group A

Group B A307

Loading S D S D S D S D S D

rn /Ω

φrn

rn /Ω

φrn

rn /Ω

φrn

rn /Ω

φrn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

8.29 16.6 10.4 20.9 10.4 20.9 12.9 25.8 4.14 8.29

12.4 24.9 15.7 31.3 15.7 31.3 19.3 38.7 6.23 12.5

11.9 23.9 15.0 30.1 15.0 30.1 18.6 37.1 5.97 11.9

17.9 35.8 22.5 45.1 22.5 45.1 27.8 55.7 8.97 17.9

16.2 32.5 20.4 40.9 20.4 40.9 25.2 50.5 8.11 16.2

24.3 48.7 30.7 61.3 30.7 61.3 37.9 75.7 12.2 24.4

21.2 42.4 26.7 53.4 26.7 53.4 33.0 65.9 10.6 21.2

31.8 63.6 40.0 80.1 40.0 80.1 49.5 98.9 15.9 31.9

11/8

11/4

13/8

11/2

0.994

1.23

1.48

1.77

Nominal Bolt Diameter, d , in. Nominal Bolt Area,

in.2

Fnv /Ω (ksi)

φFnv (ksi)

ASD

LRFD

N

27.0

40.5

X

34.0

51.0

N

34.0

51.0

X

42.0

63.0

A307

–

13.5

20.3

ASD

LRFD

Ω = 2.00

φ = 0.75

ASTM Desig.

Group A

Group B

Thread Cond.

Loading S D S D S D S D S D

rn /Ω

φrn

rn /Ω

φrn

rn /Ω

φrn

rn /Ω

φrn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

59.9 47.8 120 95.6 75.5 60.2 151 120 75.5 60.2 151 120 93.2 74.3 186 149 30.0 23.9 60.1 47.8

71.7 143 90.3 181 90.3 181 112 223 35.9 71.9

26.8 40.3 33.2 49.8 40.0 53.7 80.5 66.4 99.6 79.9 33.8 50.7 41.8 62.7 50.3 67.6 101 83.6 125 101 33.8 50.7 41.8 62.7 50.3 67.6 101 83.6 125 101 41.7 62.6 51.7 77.5 62.2 83.5 125 103 155 124 13.4 20.2 16.6 25.0 20.0 26.8 40.4 33.2 49.9 40.0

For end loaded connections greater than 38 in., see AISC Specification Table J3.2 footnote b.

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Table 7-2

Available Tensile Strength of Bolts, kips Nominal Bolt Diameter, d , in.

5/8

3/4

7/8

1

Nominal Bolt Area, in.2

0.307

0.442

0.601

0.785

ASTM Desig. Group A Group B A307

Fnt /Ω (ksi)

φFnt (ksi)

rn /Ω

φrn

rn /Ω

φrn

rn /Ω

φrn

rn /Ω

φrn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

45.0 56.5 22.5

67.5 84.8 33.8

13.8 17.3 6.90

20.7 26.0 10.4

19.9 25.0 9.94

29.8 37.4 14.9

27.1 34.0 13.5

40.6 51.0 20.3

35.3 44.4 17.7

53.0 66.6 26.5

Nominal Bolt Diameter, d , in.

11/8

11/4

13/8

11/2

Nominal Bolt Area, in.2

0.994

1.23

1.48

1.77

φFnt (ksi)

ASTM Desig.

Fnt /Ω (ksi) ASD

LRFD

ASD

LRFD

ASD

Group A Group B A307

45.0 56.5 22.5

67.5 84.8 33.8

44.7 56.2 22.4

67.1 84.2 33.5

55.2 69.3 27.6

ASD

LRFD

Ω = 2.00

φ = 0.75

rn /Ω

φrn

rn /Ω

φrn LRFD 82.8 104 41.4

rn /Ω ASD 66.8 83.9 33.4

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

φrn LRFD 100 126 50.1

rn /Ω ASD 79.5 99.8 39.8

φrn LRFD 119 150 59.6

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Group A

Table 7-3

Bolts

Slip-Critical Connections Available Shear Strength, kips (Class A Faying Surface, μ = 0.30) Group A Bolts Nominal Bolt Diameter, d , in. 5/8

3/4

7/8

1

Minimum Group A Bolt Pretension, kips Hole Type

STD/SSLT OVS/SSLP LSL

Loading

S D S D S D

19

28

39

51

rn /Ω

φrn

rn /Ω

φrn

rn /Ω

φrn

rn /Ω

φrn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

6.44 12.9 5.47 10.9 4.51 9.02

6.33 12.7 5.39 10.8 4.44 8.87

9.49 19.0 8.07 16.1 6.64 13.3

8.81 17.6 7.51 15.0 6.18 12.4

13.2 26.4 11.2 22.5 9.25 18.5

11.5 23.1 9.82 19.6 8.08 16.2

17.3 34.6 14.7 29.4 12.1 24.2

4.29 8.59 3.66 7.32 3.01 6.02

Nominal Bolt Diameter, d , in. 11/8

11/4

13/8

11/2

Minimum Group A Bolt Pretension, kips Hole Type

STD/SSLT OVS/SSLP LSL

Loading

S D S D S D

56

71

85

φrn

rn /Ω

φrn

rn /Ω

φrn

rn /Ω

φrn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

12.7 25.3 10.8 21.6 8.87 17.7

19.0 38.0 16.1 32.3 13.3 26.6

16.0 32.1 13.7 27.4 11.2 22.5

24.1 48.1 20.5 40.9 16.8 33.7

19.2 38.4 16.4 32.7 13.5 26.9

28.8 57.6 24.5 49.0 20.2 40.3

23.3 46.6 19.8 39.7 16.3 32.6

34.9 69.8 29.7 59.4 24.4 48.9

STD = standard hole OVS = oversized hole SSLT = short-slotted hole transverse to the line of force SSLP = short-slotted hole parallel to the line of force LSL = long-slotted hole transverse or parallel to the line of force Hole Type

103

rn /Ω

ASD

LRFD

STD and SSLT

Ω = 1.50

φ = 1.00

OVS and SSLP

Ω = 1.76

φ = 0.85

LSL

Ω = 2.14

φ = 0.70

S = single shear D = double shear

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers. See AISC Specification Sections J3.8 and J5 for provisions when fillers are present. For Class B faying surfaces, multiply the tabulated available strength by 1.67.

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Table 7-3 (continued)

Group B

Slip-Critical Connections

Bolts

Available Shear Strength, kips (Class A Faying Surface, μ = 0.30) Group B Bolts Nominal Bolt Diameter, d , in. 5/8

3/4

7/8

1

Minimum Group B Bolt Pretension, kips Hole Type

STD/SSLT OVS/SSLP LSL

Loading

S D S D S D

24

35

49

64

rn /Ω

φrn

rn /Ω

φrn

rn /Ω

φrn

rn /Ω

φrn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

5.42 10.8 4.62 9.25 3.80 7.60

8.14 16.3 6.92 13.8 5.70 11.4

7.91 15.8 6.74 13.5 5.54 11.1

11.9 23.7 10.1 20.2 8.31 16.6

11.1 22.1 9.44 18.9 7.76 15.5

16.6 33.2 14.1 28.2 11.6 23.3

14.5 28.9 12.3 24.7 10.1 20.3

21.7 43.4 18.4 36.9 15.2 30.4

Nominal Bolt Diameter, d , in. 11/8

11/4

13/8

11/2

Minimum Group B Bolt Pretension, kips Hole Type

STD/SSLT OVS/SSLP LSL

Loading

S D S D S D

80

102

121

φrn

rn /Ω

φrn

rn /Ω

φrn

rn /Ω

φrn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

18.1 36.2 15.4 30.8 12.7 25.3

27.1 54.2 23.1 46.1 19.0 38.0

23.1 46.1 19.6 39.3 16.2 32.3

34.6 69.2 29.4 58.8 24.2 48.4

27.3 54.7 23.3 46.6 19.2 38.3

41.0 82.0 34.9 69.7 28.7 57.4

33.4 66.9 28.5 57.0 23.4 46.9

STD = standard hole OVS = oversized hole SSLT = short-slotted hole transverse to the line of force SSLP = short-slotted hole parallel to the line of force LSL = long-slotted hole transverse or parallel to the line of force Hole Type

148

rn /Ω

ASD

LRFD

STD and SSLT

Ω = 1.50

φ = 1.00

OVS and SSLP

Ω = 1.76

φ = 0.85

LSL

Ω = 2.14

φ = 0.70

50.2 100 42.6 85.3 35.1 70.2

S = single shear D = double shear

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers. See AISC Specification Sections J3.8 and J5 for provisions when fillers are present. For Class B faying surfaces, multiply the tabulated available strength by 1.67.

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Table 7-4

Available Bearing Strength at Bolt Holes Based on Bolt Spacing kips/in. thickness Nominal Bolt Diameter, d , in. Hole Type

STD SSLT

Bolt Spacing, s, in.

φrn

rn /Ω

7/8

rn /Ω

φrn

1

rn /Ω

φrn

rn /Ω

φrn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

3 in.

34.1 38.2 43.5 48.8 27.6 30.9 43.5 48.8 29.7 33.3 43.5 48.8 3.62 4.06 43.5 48.8 28.4 31.8 36.3 40.6

51.1 57.3 65.3 73.1 41.3 46.3 65.3 73.1 44.6 50.0 65.3 73.1 5.44 6.09 65.3 73.1 42.6 47.7 54.4 60.9

41.3 46.3 52.2 58.5 34.8 39.0 52.2 58.5 37.0 41.4 52.2 58.5 4.35 4.88 39.2 43.9 34.4 38.6 43.5 48.8

62.0 69.5 78.3 87.8 52.2 58.5 78.3 87.8 55.5 62.2 78.3 87.8 6.53 7.31 58.7 65.8 51.7 57.9 65.3 73.1

48.6 54.4 60.9 68.3 42.1 47.1 60.9 68.3 44.2 49.6 60.9 68.3 5.08 5.69 28.3 31.7 40.5 45.4 50.8 56.9

72.9 81.7 91.4 102 63.1 70.7 91.4 102 66.3 74.3 91.4 102 7.61 8.53 42.4 47.5 60.7 68.0 76.1 85.3

55.8 62.6 67.4 75.6 47.1 52.8 58.7 65.8 49.3 55.3 60.9 68.3 5.80 6.50 17.4 19.5 46.5 52.1 56.2 63.0

83.7 93.8 101 113 70.7 79.2 88.1 98.7 74.0 82.9 91.4 102 8.70 9.75 26.1 29.3 69.8 78.2 84.3 94.5

s ≥ s full

58 65

43.5 48.8

65.3 73.1

52.2 58.5

78.3 87.8

60.9 68.3

91.4 102

69.6 78.0

104 117

36.3 40.6

54.4 60.9

43.5 48.8

65.3 73.1

50.8 56.9

76.1 85.3

58.0 65.0

2 2/3 db 3 in. 2 2/3 db 3 in. 2 2/3 db

OVS 3 in. 2 2/3 db LSLP 3 in. 2 2/3 db LSLT

58 65 STD, SSLT, Spacing for full LSLT bearing strength OVS s full a, in. SSLP LSLP Minimum Spacinga = 2 2/3d , in. LSLT

3/4

58 65 58 65 58 65 58 65 58 65 58 65 58 65 58 65 58 65 58 65

SSLP

STD, SSLT, SSLP, OVS, LSLP

Fu, ksi

5/8

s ≥ s full

87.0 97.5

1 15/16

2 5/16

211/16

31/16

2 1/16 2 1/8 2 13/16 1 11/16

2 7/16 2 1/2 3 3/8 2

2 13/16 2 7/8 3 15/16 2 5/16

3 1/4 3 5/16 4 1/2 211/16

STD = standard hole SSLT = short-slotted hole oriented transverse to the line of force SSLP = short-slotted hole oriented parallel to the line of force OVS = oversized hole LSLP = long-slotted hole oriented parallel to the line of force LSLT = long-slotted hole oriented transverse to the line of force ASD

LRFD

Ω = 2.00

φ = 0.75

Note: Spacing indicated is from the center of the hole or slot to the center of the adjacent hole or slot in the line of force. Hole deformation is considered. When hole deformation is not considered, see AISC Specification Section J3.10. a Decimal value has been rounded to the nearest sixteenth of an inch.

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DESIGN TABLES

Table 7-4 (continued)

Available Bearing Strength at Bolt Holes Based on Bolt Spacing kips/in. thickness Nominal Bolt Diameter, d , in. Hole Type

STD SSLT

Bolt Spacing, s, in.

φrn

φrn

rn /Ω

1 3/8 φrn

rn /Ω

1 1/2 φrn

rn /Ω

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

3 in.

63.1 70.7 63.1 70.7 52.2 58.5 52.2 58.5 54.4 60.9 54.4 60.9 6.53 7.31 6.53 7.31 52.6 58.9 52.6 58.9

94.6 106 94.6 106 78.3 87.8 78.3 87.8 81.6 91.4 81.6 91.4 9.79 11.0 9.79 11.0 78.8 88.4 78.8 88.4

70.3 78.8 — — 59.5 66.6 — — 61.6 69.1 — — 7.25 8.13 — — 58.6 65.7 — —

105 118 — — 89.2 99.9 — — 92.4 104 — — 10.9 12.2 — — 87.9 98.5 — —

77.6 86.9 — — 66.7 74.8 — — 68.9 77.2 — — 7.98 8.94 — — 64.6 72.4 — —

116 130 — — 100 112 — — 103 116 — — 12.0 13.4 — — 97.0 109 — —

84.8 95.1 — — 74.0 82.9 — — 76.1 85.3 — — 8.70 9.75 — — 70.7 79.2 — —

127 143 — — 111 124 — — 114 128 — — 13.1 14.6 — — 106 119 — —

s ≥ s full

58 65

78.3 87.8

117 132

87.0 97.5

131 146

95.7 107

144 161

65.3 73.1

97.9 110

72.5 81.3

109 122

79.8 89.4

120 134

2 2/3 db 3 in. 2 2/3 db 3 in. 2 2/3 db

OVS 3 in. 2 2/3 db LSLP 3 in. 2 2/3 db LSLT

58 65 STD, SSLT, Spacing for full LSLT bearing strength OVS s full a, in. SSLP LSLP Minimum Spacinga = 2 2/3d , in. LSLT

rn /Ω

1 1/4

58 65 58 65 58 65 58 65 58 65 58 65 58 65 58 65 58 65 58 65

SSLP

STD, SSLT, SSLP, OVS, LSLP

Fu, ksi

1 1/8

s ≥ s full

104 117

157 176

87.0 97.5

131 146

3 7/16

3 13/16

4 3/16

4 9/16

3 11/16 3 3/4 5 1/16 3

4 1/16 4 1/8 5 5/8 3 5/16

4 7/16 4 1/2 6 3/16 3 11/16

4 13/16 4 7/8 6 3/4 4

STD = standard hole SSLT = short-slotted hole oriented transverse to the line of force SSLP = short-slotted hole oriented parallel to the line of force OVS = oversized hole LSLP = long-slotted hole oriented parallel to the line of force LSLT = long-slotted hole oriented transverse to the line of force ASD

LRFD

Ω = 2.00

φ = 0.75

— indicates spacing less than minimum spacing required per AISC Specification Section J3.3. Note: Spacing indicated is from the center of the hole or slot to the center of the adjacent hole or slot in the line of force. Hole deformation is considered. When hole deformation is not considered, see AISC Specification Section J3.10. a Decimal value has been rounded to the nearest sixteenth of an inch.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A_14th Ed._February 12, 2013 12/02/13 9:05 AM Page 28

7–28

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-5

Available Bearing Strength at Bolt Holes Based on Edge Distance kips/in. thickness Nominal Bolt Diameter, d , in. Hole Type

STD SSLT

Edge Distance Le , in.

1 1/4 2 1 1/4

SSLP 2 1 1/4 OVS 2 1 1/4 LSLP 2 1 1/4 LSLT 2 STD, SSLT, SSLP, OVS, Le ≥ Le full LSLP LSLT

Le ≥ Le full

Edge distance for full bearing strength Le ≥ Le full a, in.

Fu, ksi

5/8

3/4

rn /Ω

φrn

7/8

rn /Ω

φrn

1

rn /Ω

φrn

rn /Ω

φrn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

58 65 58 65 58 65 58 65 58 65 58 65 58 65 58 65 58 65 58 65

31.5 35.3 43.5 48.8 28.3 31.7 43.5 48.8 29.4 32.9 43.5 48.8 16.3 18.3 42.4 47.5 26.3 29.5 36.3 40.6

47.3 53.0 65.3 73.1 42.4 47.5 65.3 73.1 44.0 49.4 65.3 73.1 24.5 27.4 63.6 71.3 39.4 44.2 54.4 60.9

29.4 32.9 52.2 58.5 26.1 29.3 52.2 58.5 27.2 30.5 52.2 58.5 10.9 12.2 37.0 41.4 24.5 27.4 43.5 48.8

44.0 49.4 78.3 87.8 39.2 43.9 78.3 87.8 40.8 45.7 78.3 87.8 16.3 18.3 55.5 62.2 36.7 41.1 65.3 73.1

27.2 30.5 53.3 59.7 23.9 26.8 50.0 56.1 25.0 28.0 51.1 57.3 5.44 6.09 31.5 35.3 22.7 25.4 44.4 49.8

40.8 45.7 79.9 89.6 35.9 40.2 75.0 84.1 37.5 42.0 76.7 85.9 8.16 9.14 47.3 53.0 34.0 38.1 66.6 74.6

25.0 28.0 51.1 57.3 20.7 23.2 46.8 52.4 21.8 24.4 47.9 53.6 — — 26.1 29.3 20.8 23.4 42.6 47.7

37.5 42.0 76.7 85.9 31.0 34.7 70.1 78.6 32.6 36.6 71.8 80.4 — — 39.2 43.9 31.3 35.0 63.9 71.6

58 65

43.5 48.8

65.3 73.1

52.2 58.5

78.3 87.8

60.9 68.3

91.4 102

69.6 78.0

58 65 STD, SSLT, LSLT OVS SSLP LSLP

36.3 40.6

54.4 60.9

43.5 48.8

65.3 73.1

50.8 56.9

76.1 85.3

58.0 65.0

104 117 87.0 97.5

1 5/8

1 15/16

2 1/4

2 9/16

1 11/16 1 11/16 2 1/16

2 2 2 7/16

2 5/16 2 5/16 2 7/8

2 5/8 2 11/16 3 1/4

STD = standard hole SSLT = short-slotted hole oriented transverse to the line of force SSLP = short-slotted hole oriented parallel to the line of force OVS = oversized hole LSLP = long-slotted hole oriented parallel to the line of force LSLT = long-slotted hole oriented transverse to the line of force ASD

LRFD

Ω = 2.00

φ = 0.75

— indicates spacing less than minimum spacing required per AISC Specification Section J3.3. Note: Edge distance indicated is from the center of the hole or slot to the edge of the element in the line of force. Hole deformation is considered. When hole deformation is not considered, see AISC Specification Section J3.10. a Decimal value has been rounded to the nearest sixteenth of an inch.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A_14th Ed._February 12, 2013 12/02/13 9:07 AM Page 29

DESIGN TABLES

7–29

Table 7-5 (continued)

Available Bearing Strength at Bolt Holes Based on Edge Distance kips/in. thickness Nominal Bolt Diameter, d , in. Hole Type

STD SSLT

Edge Distance Le, in.

1 1/4 2 1 1/4

SSLP 2 1 1/4 OVS 2 1 1/4 LSLP 2 1 1/4 LSLT 2 STD, SSLT, SSLP, OVS, Le ≥ Le full LSLP LSLT

Le ≥ Le full

Edge distance for full bearing strength Le ≥ Le full a, in.

Fu, ksi

1 1/8

rn /Ω

φrn

1 1/4

rn /Ω

φrn

1 3/8

rn /Ω

φrn

1 1/2

rn /Ω

φrn

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

58 65 58 65 58 65 58 65 58 65 58 65 58 65 58 65 58 65 58 65

22.8 25.6 48.9 54.8 17.4 19.5 43.5 48.8 18.5 20.7 44.6 50.0 — — 20.7 23.2 19.0 21.3 40.8 45.7

34.3 38.4 73.4 82.3 26.1 29.3 65.3 73.1 27.7 31.1 66.9 75.0 — — 31.0 34.7 28.5 32.0 61.2 68.6

20.7 23.2 46.8 52.4 15.2 17.1 41.3 46.3 16.3 18.3 42.4 47.5 — — 15.2 17.1 17.2 19.3 39.0 43.7

31.0 34.7 70.1 78.6 22.8 25.6 62.0 69.5 24.5 27.4 63.6 71.3 — — 22.8 25.6 25.8 28.9 58.5 65.5

18.5 20.7 44.6 50.0 13.1 14.6 39.2 43.9 14.1 15.8 40.2 45.1 — — 9.79 11.0 15.4 17.3 37.2 41.6

27.7 31.1 66.9 75.0 19.6 21.9 58.7 65.8 21.2 23.8 60.4 67.6 — — 14.7 16.5 23.1 25.9 55.7 62.5

16.3 18.3 42.4 47.5 10.9 12.2 37.0 41.4 12.0 13.4 38.1 42.7 — — 4.35 4.88 13.6 15.2 35.3 39.6

24.5 27.4 63.6 71.3 16.3 18.3 55.5 62.2 17.9 20.1 57.1 64.0 — — 6.53 7.31 20.4 22.9 53.0 59.4

58 65

78.3 87.8

117 132

87.0 97.5

131 146

95.7 107

144 161

58 65 STD, SSLT, LSLT OVS SSLP LSLP

65.3 73.1

97.9 110

72.5 81.3

109 122

79.8 89.4

120 134

104 117 87.0 97.5

157 176 131 146

2 7/8

3 3/16

3 1/2

3 13/16

3 3 3 11/16

3 5/16 3 5/16 4 1/16

3 5/8 3 5/8 4 1/2

3 15/16 3 15/16 4 7/8

STD = standard hole SSLT = short-slotted hole oriented transverse to the line of force SSLP = short-slotted hole oriented parallel to the line of force OVS = oversized hole LSLP = long-slotted hole oriented parallel to the line of force LSLT = long-slotted hole oriented transverse to the line of force ASD

LRFD

Ω = 2.00

φ = 0.75

— indicates spacing less than minimum spacing required per AISC Specification Section J3.3. Note: Edge distance indicated is from the center of the hole or slot to the edge of the element in the line of force. Hole deformation is considered. When hole deformation is not considered, see AISC Specification Section J3.10. a Decimal value has been rounded to the nearest sixteenth of an inch.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 30

7–30

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-6

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0° where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 C ⬘, in. 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 C ⬘, in.

2

3

4

5

6

7

1.18 0.88 0.69 0.56 0.48 0.41 0.36 0.32 0.29 0.24 0.21 0.18 0.16 0.15 0.12 0.11 0.09 0.08 2.94 1.63 1.39 1.18 1.01 0.88 0.77 0.69 0.62 0.56 0.48 0.41 0.36 0.32 0.29 0.24 0.21 0.18 0.16 5.89

2.23 1.75 1.40 1.15 0.97 0.83 0.73 0.65 0.59 0.49 0.42 0.37 0.33 0.29 0.25 0.21 0.18 0.16 5.89 2.71 2.48 2.23 1.98 1.75 1.56 1.40 1.26 1.15 0.97 0.83 0.73 0.65 0.59 0.49 0.42 0.37 0.33 11.8

3.32 2.81 2.36 2.01 1.73 1.51 1.34 1.21 1.09 0.92 0.79 0.70 0.62 0.56 0.47 0.40 0.35 0.31 11.3 3.75 3.56 3.32 3.07 2.81 2.58 2.36 2.17 2.01 1.73 1.51 1.34 1.21 1.09 0.92 0.79 0.70 0.62 22.5

4.39 3.90 3.40 2.96 2.59 2.28 2.04 1.83 1.66 1.40 1.21 1.06 0.95 0.85 0.71 0.61 0.54 0.48 17.1 4.77 4.60 4.39 4.15 3.90 3.64 3.40 3.17 2.96 2.59 2.28 2.04 1.83 1.66 1.40 1.21 1.06 0.95 34.3

5.45 4.98 4.47 3.98 3.55 3.17 2.85 2.59 2.36 2.00 1.74 1.53 1.37 1.24 1.03 0.89 0.78 0.69 25.1 5.77 5.63 5.45 5.23 4.98 4.73 4.47 4.22 3.98 3.55 3.17 2.85 2.59 2.36 2.00 1.74 1.53 1.37 50.2

6.48 6.06 5.56 5.05 4.57 4.13 3.75 3.42 3.14 2.68 2.33 2.06 1.84 1.67 1.40 1.20 1.05 0.94 33.8 6.77 6.65 6.48 6.28 6.06 5.81 5.56 5.30 5.05 4.57 4.13 3.75 3.42 3.14 2.68 2.33 2.06 1.84 67.6

8

9

10

11

12

7.51 8.52 9.53 10.5 11.5 7.12 8.17 9.21 10.2 11.3 6.64 7.72 8.78 9.84 10.9 6.13 7.22 8.30 9.38 10.4 5.63 6.70 7.79 8.87 9.96 5.15 6.20 7.28 8.36 9.44 4.72 5.73 6.78 7.85 8.93 4.34 5.31 6.32 7.36 8.42 4.00 4.92 5.89 6.90 7.94 3.44 4.27 5.15 6.09 7.06 3.01 3.75 4.55 5.41 6.31 2.67 3.33 4.06 4.85 5.68 2.39 3.00 3.66 4.38 5.15 2.16 2.72 3.33 3.99 4.70 1.82 2.29 2.81 3.37 3.99 1.57 1.97 2.42 2.92 3.45 1.37 1.73 2.13 2.57 3.04 1.22 1.54 1.90 2.29 2.72 44.4 55.9 69.2 83.5 100 7.76 8.75 9.74 10.7 11.7 7.65 8.66 9.66 10.7 11.6 7.51 8.52 9.53 10.5 11.5 7.33 8.36 9.38 10.4 11.4 7.12 8.17 9.21 10.2 11.3 6.89 7.95 9.00 10.1 11.1 6.64 7.72 8.78 9.84 10.9 6.39 7.47 8.55 9.61 10.7 6.13 7.22 8.30 9.38 10.4 5.63 6.70 7.79 8.87 9.96 5.15 6.20 7.28 8.36 9.44 4.72 5.73 6.78 7.85 8.93 4.34 5.31 6.32 7.36 8.42 4.00 4.92 5.89 6.90 7.94 3.44 4.27 5.15 6.09 7.06 3.01 3.75 4.55 5.41 6.31 2.67 3.33 4.06 4.85 5.68 2.39 3.00 3.66 4.38 5.15 88.8 112 138 167 199

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 31

7–31

DESIGN TABLES

Table 7-6 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15° where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 2

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

1.15 0.86 0.67 0.55 0.47 0.41 0.36 0.32 0.29 0.24 0.21 0.19 0.17 0.15 0.12 0.11 0.09 0.08 1.61 1.36 1.15 0.98 0.86 0.75 0.67 0.61 0.55 0.47 0.41 0.36 0.32 0.29 0.24 0.21 0.19 0.17

3

4

5

6

7

8

9

10

2.20 1.76 1.42 1.17 0.99 0.86 0.75 0.67 0.61 0.51 0.43 0.38 0.34 0.30 0.25 0.22 0.19 0.17 2.69 2.45 2.20 1.96 1.76 1.57 1.42 1.29 1.17 0.99 0.86 0.75 0.67 0.61 0.51 0.43 0.38 0.34

3.28 2.78 2.35 2.00 1.73 1.52 1.35 1.22 1.10 0.93 0.81 0.71 0.63 0.57 0.48 0.41 0.36 0.32 3.72 3.52 3.28 3.03 2.78 2.55 2.35 2.16 2.00 1.73 1.52 1.35 1.22 1.10 0.93 0.81 0.71 0.63

4.34 3.85 3.36 2.94 2.58 2.30 2.06 1.86 1.69 1.43 1.24 1.09 0.97 0.88 0.73 0.63 0.55 0.49 4.74 4.56 4.34 4.10 3.85 3.60 3.36 3.14 2.94 2.58 2.30 2.06 1.86 1.69 1.43 1.24 1.09 0.97

5.39 4.92 4.41 3.94 3.52 3.16 2.86 2.60 2.38 2.03 1.76 1.56 1.39 1.26 1.06 0.91 0.80 0.71 5.74 5.59 5.39 5.16 4.92 4.66 4.41 4.17 3.94 3.52 3.16 2.86 2.60 2.38 2.03 1.76 1.56 1.39

6.42 5.98 5.48 4.98 4.52 4.11 3.74 3.43 3.16 2.71 2.37 2.10 1.88 1.70 1.43 1.23 1.08 0.96 6.74 6.60 6.42 6.21 5.98 5.73 5.48 5.23 4.98 4.52 4.11 3.74 3.43 3.16 2.71 2.37 2.10 1.88

7.45 7.03 6.55 6.04 5.55 5.10 4.69 4.32 4.00 3.46 3.04 2.70 2.43 2.20 1.86 1.60 1.41 1.26 7.73 7.61 7.45 7.25 7.03 6.80 6.55 6.30 6.04 5.55 5.10 4.69 4.32 4.00 3.46 3.04 2.70 2.43

8.46 8.08 7.61 7.11 6.61 6.13 5.68 5.27 4.90 4.28 3.78 3.37 3.04 2.76 2.33 2.02 1.77 1.58 8.73 8.61 8.46 8.28 8.08 7.85 7.61 7.36 7.11 6.61 6.13 5.68 5.27 4.90 4.28 3.78 3.37 3.04

9.47 9.11 8.67 8.18 7.67 7.18 6.70 6.26 5.85 5.15 4.57 4.09 3.70 3.37 2.86 2.47 2.18 1.95 9.71 9.61 9.47 9.30 9.11 8.90 8.67 8.43 8.18 7.67 7.18 6.70 6.26 5.85 5.15 4.57 4.09 3.70

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11

12

10.5 10.1 9.72 9.24 8.74 8.24 7.74 7.28 6.84 6.06 5.41 4.87 4.42 4.03 3.43 2.97 2.62 2.34 10.7 10.6 10.5 10.3 10.1 9.94 9.72 9.49 9.24 8.74 8.24 7.74 7.28 6.84 6.06 5.41 4.87 4.42

11.5 11.2 10.8 10.3 9.81 9.30 8.80 8.31 7.85 7.01 6.30 5.69 5.18 4.74 4.04 3.51 3.10 2.78 11.7 11.6 11.5 11.3 11.2 11.0 10.8 10.5 10.3 9.81 9.30 8.80 8.31 7.85 7.01 6.30 5.69 5.18

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 32

7–32

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-6 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30° where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 2

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

1.14 0.86 0.69 0.57 0.49 0.43 0.38 0.34 0.31 0.26 0.23 0.20 0.18 0.16 0.14 0.12 0.10 0.09 1.59 1.34 1.14 0.98 0.86 0.77 0.69 0.63 0.57 0.49 0.43 0.38 0.34 0.31 0.26 0.23 0.20 0.18

3

4

5

6

7

8

9

10

2.20 1.80 1.50 1.27 1.09 0.95 0.83 0.75 0.67 0.56 0.48 0.42 0.38 0.34 0.28 0.24 0.21 0.19 2.66 2.43 2.20 1.99 1.80 1.64 1.50 1.37 1.27 1.09 0.95 0.83 0.75 0.67 0.56 0.48 0.42 0.38

3.25 2.79 2.40 2.08 1.82 1.61 1.44 1.30 1.19 1.01 0.87 0.77 0.69 0.62 0.52 0.45 0.40 0.35 3.69 3.48 3.25 3.02 2.79 2.59 2.40 2.23 2.08 1.82 1.61 1.44 1.30 1.19 1.01 0.87 0.77 0.69

4.30 3.83 3.39 3.00 2.68 2.40 2.17 1.98 1.82 1.55 1.35 1.20 1.07 0.97 0.81 0.70 0.61 0.55 4.70 4.52 4.30 4.06 3.83 3.60 3.39 3.19 3.00 2.68 2.40 2.17 1.98 1.82 1.55 1.35 1.20 1.07

5.33 4.87 4.41 3.98 3.60 3.27 2.98 2.74 2.52 2.17 1.90 1.69 1.52 1.37 1.16 1.00 0.88 0.78 5.71 5.54 5.33 5.11 4.87 4.64 4.41 4.19 3.98 3.60 3.27 2.98 2.74 2.52 2.17 1.90 1.69 1.52

6.36 5.92 5.45 4.99 4.57 4.20 3.86 3.57 3.31 2.87 2.53 2.26 2.04 1.85 1.57 1.36 1.19 1.07 6.70 6.55 6.36 6.14 5.92 5.68 5.45 5.22 4.99 4.57 4.20 3.86 3.57 3.31 2.87 2.53 2.26 2.04

7.38 6.96 6.49 6.02 5.58 5.17 4.79 4.46 4.15 3.64 3.23 2.89 2.62 2.38 2.02 1.75 1.54 1.38 7.70 7.55 7.38 7.17 6.96 6.73 6.49 6.26 6.02 5.58 5.17 4.79 4.46 4.15 3.64 3.23 2.89 2.62

8.39 7.99 7.53 7.06 6.60 6.17 5.76 5.39 5.05 4.46 3.98 3.58 3.25 2.97 2.53 2.20 1.94 1.74 8.69 8.56 8.39 8.20 7.99 7.77 7.53 7.30 7.06 6.60 6.17 5.76 5.39 5.05 4.46 3.98 3.58 3.25

9.40 9.02 8.57 8.11 7.64 7.18 6.75 6.35 5.98 5.33 4.78 4.33 3.94 3.61 3.09 2.69 2.38 2.13 9.68 9.55 9.40 9.22 9.02 8.80 8.57 8.34 8.11 7.64 7.18 6.75 6.35 5.98 5.33 4.78 4.33 3.94

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11

12

10.4 10.0 9.61 9.15 8.68 8.21 7.77 7.34 6.95 6.24 5.63 5.11 4.67 4.30 3.69 3.22 2.85 2.56 10.7 10.6 10.4 10.2 10.0 9.83 9.61 9.38 9.15 8.68 8.21 7.77 7.34 6.95 6.24 5.63 5.11 4.67

11.4 11.1 10.6 10.2 9.72 9.25 8.79 8.35 7.93 7.17 6.51 5.94 5.45 5.02 4.33 3.79 3.37 3.03 11.7 11.5 11.4 11.2 11.1 10.9 10.6 10.4 10.2 9.72 9.25 8.79 8.35 7.93 7.17 6.51 5.94 5.45

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 33

7–33

DESIGN TABLES

Table 7-6 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45° where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 2

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

1.17 0.92 0.75 0.64 0.55 0.49 0.44 0.40 0.36 0.31 0.27 0.24 0.21 0.19 0.16 0.14 0.12 0.11 1.57 1.35 1.17 1.03 0.92 0.83 0.75 0.69 0.64 0.55 0.49 0.44 0.40 0.36 0.31 0.27 0.24 0.21

3

4

5

6

7

8

9

10

2.23 1.89 1.63 1.42 1.25 1.11 0.99 0.90 0.81 0.68 0.59 0.52 0.46 0.41 0.35 0.30 0.26 0.23 2.64 2.43 2.23 2.05 1.89 1.75 1.63 1.52 1.42 1.25 1.11 0.99 0.90 0.81 0.68 0.59 0.52 0.46

3.26 2.87 2.54 2.25 2.01 1.81 1.64 1.49 1.37 1.17 1.03 0.91 0.82 0.74 0.63 0.54 0.48 0.43 3.66 3.46 3.26 3.06 2.87 2.70 2.54 2.39 2.25 2.01 1.81 1.64 1.49 1.37 1.17 1.03 0.91 0.82

4.28 3.87 3.50 3.17 2.88 2.63 2.41 2.22 2.06 1.79 1.58 1.41 1.27 1.16 0.98 0.85 0.75 0.67 4.67 4.48 4.28 4.07 3.87 3.68 3.50 3.33 3.17 2.88 2.63 2.41 2.22 2.06 1.79 1.58 1.41 1.27

5.29 4.88 4.49 4.13 3.80 3.51 3.25 3.02 2.82 2.47 2.20 1.97 1.78 1.62 1.38 1.19 1.05 0.94 5.67 5.49 5.29 5.09 4.88 4.68 4.49 4.30 4.13 3.80 3.51 3.25 3.02 2.82 2.47 2.20 1.97 1.78

6.30 5.90 5.49 5.11 4.76 4.43 4.14 3.87 3.63 3.22 2.88 2.60 2.36 2.16 1.85 1.61 1.43 1.28 6.66 6.49 6.30 6.10 5.90 5.69 5.49 5.30 5.11 4.76 4.43 4.14 3.87 3.63 3.22 2.88 2.60 2.36

7.31 6.91 6.51 6.11 5.73 5.38 5.06 4.77 4.50 4.02 3.62 3.29 3.00 2.76 2.37 2.08 1.84 1.65 7.66 7.50 7.31 7.12 6.91 6.71 6.51 6.30 6.11 5.73 5.38 5.06 4.77 4.50 4.02 3.62 3.29 3.00

8.32 7.93 7.52 7.11 6.73 6.36 6.01 5.69 5.39 4.87 4.41 4.03 3.70 3.41 2.94 2.58 2.30 2.07 8.65 8.49 8.32 8.13 7.93 7.72 7.52 7.31 7.11 6.73 6.36 6.01 5.69 5.39 4.87 4.41 4.03 3.70

9.32 8.94 8.53 8.12 7.73 7.34 6.98 6.64 6.32 5.74 5.24 4.81 4.43 4.10 3.56 3.14 2.80 2.53 9.64 9.49 9.32 9.13 8.94 8.74 8.53 8.33 8.12 7.73 7.34 6.98 6.64 6.32 5.74 5.24 4.81 4.43

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11

12

10.3 9.95 9.55 9.14 8.73 8.34 7.96 7.61 7.27 6.65 6.11 5.63 5.21 4.84 4.22 3.73 3.34 3.02 10.6 10.5 10.3 10.1 9.95 9.75 9.55 9.34 9.14 8.73 8.34 7.96 7.61 7.27 6.65 6.11 5.63 5.21

11.3 11.0 10.6 10.2 9.74 9.34 8.96 8.58 8.23 7.58 6.99 6.48 6.02 5.61 4.92 4.37 3.92 3.55 11.6 11.5 11.3 11.1 11.0 10.8 10.6 10.4 10.2 9.74 9.34 8.96 8.58 8.23 7.58 6.99 6.48 6.02

AISC_Part 7A:14th Ed.

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8:33 AM

Page 34

7–34

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-6 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60° where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 2

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

1.27 1.05 0.89 0.77 0.68 0.61 0.56 0.51 0.47 0.40 0.35 0.32 0.29 0.26 0.22 0.19 0.17 0.15 1.60 1.42 1.27 1.15 1.05 0.96 0.89 0.83 0.77 0.68 0.61 0.56 0.51 0.47 0.40 0.35 0.32 0.29

3

4

5

6

7

8

9

10

2.32 2.05 1.83 1.65 1.49 1.37 1.26 1.16 1.07 0.93 0.81 0.72 0.65 0.58 0.49 0.42 0.37 0.33 2.65 2.48 2.32 2.18 2.05 1.93 1.83 1.73 1.65 1.49 1.37 1.26 1.16 1.07 0.93 0.81 0.72 0.65

3.32 3.02 2.77 2.54 2.34 2.17 2.01 1.87 1.74 1.52 1.35 1.21 1.09 1.00 0.85 0.74 0.65 0.59 3.65 3.48 3.32 3.17 3.02 2.89 2.77 2.65 2.54 2.34 2.17 2.01 1.87 1.74 1.52 1.35 1.21 1.09

4.31 4.00 3.72 3.47 3.24 3.03 2.83 2.66 2.50 2.22 2.00 1.81 1.66 1.53 1.32 1.15 1.02 0.92 4.64 4.48 4.31 4.15 4.00 3.86 3.72 3.59 3.47 3.24 3.03 2.83 2.66 2.50 2.22 2.00 1.81 1.66

5.30 4.98 4.69 4.41 4.16 3.93 3.71 3.51 3.32 3.00 2.73 2.49 2.30 2.12 1.84 1.61 1.43 1.29 5.64 5.47 5.30 5.14 4.98 4.83 4.69 4.55 4.41 4.16 3.93 3.71 3.51 3.32 3.00 2.73 2.49 2.30

6.30 5.97 5.66 5.37 5.10 4.85 4.61 4.39 4.19 3.82 3.50 3.23 2.98 2.77 2.41 2.13 1.91 1.72 6.63 6.46 6.30 6.13 5.97 5.81 5.66 5.51 5.37 5.10 4.85 4.61 4.39 4.19 3.82 3.50 3.23 2.98

7.29 6.96 6.64 6.34 6.06 5.79 5.54 5.30 5.08 4.67 4.32 4.00 3.72 3.47 3.05 2.71 2.44 2.21 7.62 7.45 7.29 7.12 6.96 6.80 6.64 6.49 6.34 6.06 5.79 5.54 5.30 5.08 4.67 4.32 4.00 3.72

8.27 7.94 7.62 7.32 7.02 6.74 6.48 6.23 5.99 5.55 5.16 4.81 4.50 4.21 3.73 3.34 3.02 2.74 8.61 8.44 8.27 8.11 7.94 7.78 7.62 7.47 7.32 7.02 6.74 6.48 6.23 5.99 5.55 5.16 4.81 4.50

9.27 8.94 8.61 8.29 7.99 7.71 7.43 7.17 6.92 6.45 6.03 5.65 5.31 4.99 4.45 4.00 3.63 3.31 9.60 9.44 9.27 9.10 8.94 8.77 8.61 8.45 8.29 7.99 7.71 7.43 7.17 6.92 6.45 6.03 5.65 5.31

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11

12

10.3 9.93 9.60 9.28 8.97 8.67 8.39 8.12 7.86 7.37 6.92 6.51 6.14 5.80 5.21 4.70 4.28 3.92 10.6 10.4 10.3 10.1 9.93 9.76 9.60 9.43 9.28 8.97 8.67 8.39 8.12 7.86 7.37 6.92 6.51 6.14

11.3 10.9 10.6 10.3 9.95 9.64 9.35 9.07 8.81 8.30 7.83 7.40 7.00 6.63 5.99 5.44 4.97 4.57 11.6 11.4 11.3 11.1 10.9 10.8 10.6 10.4 10.3 9.95 9.64 9.35 9.07 8.81 8.30 7.83 7.40 7.00

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 35

7–35

DESIGN TABLES

Table 7-6 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75° where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 2

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

1.49 1.32 1.18 1.07 0.98 0.90 0.84 0.78 0.73 0.65 0.58 0.53 0.48 0.44 0.38 0.34 0.30 0.27 1.71 1.60 1.49 1.40 1.32 1.25 1.18 1.13 1.07 0.98 0.90 0.84 0.78 0.73 0.65 0.58 0.53 0.48

3

4

5

6

7

8

9

10

2.51 2.33 2.18 2.04 1.92 1.82 1.72 1.63 1.55 1.41 1.30 1.20 1.11 1.03 0.89 0.79 0.70 0.62 2.72 2.61 2.51 2.42 2.33 2.25 2.18 2.11 2.04 1.92 1.82 1.72 1.63 1.55 1.41 1.30 1.20 1.11

3.49 3.30 3.14 2.99 2.85 2.73 2.62 2.51 2.41 2.23 2.06 1.92 1.78 1.66 1.46 1.29 1.16 1.05 3.70 3.59 3.49 3.39 3.30 3.22 3.14 3.06 2.99 2.85 2.73 2.62 2.51 2.41 2.23 2.06 1.92 1.78

4.46 4.27 4.09 3.93 3.79 3.65 3.52 3.40 3.29 3.08 2.88 2.70 2.53 2.38 2.12 1.90 1.73 1.58 4.69 4.57 4.46 4.37 4.27 4.18 4.09 4.01 3.93 3.79 3.65 3.52 3.40 3.29 3.08 2.88 2.70 2.53

5.44 5.24 5.05 4.88 4.73 4.58 4.44 4.31 4.19 3.95 3.73 3.52 3.33 3.16 2.85 2.59 2.38 2.19 5.67 5.55 5.44 5.34 5.24 5.14 5.05 4.97 4.88 4.73 4.58 4.44 4.31 4.19 3.95 3.73 3.52 3.33

6.42 6.21 6.01 5.84 5.67 5.52 5.37 5.23 5.10 4.84 4.60 4.38 4.17 3.97 3.63 3.33 3.08 2.85 6.66 6.53 6.42 6.31 6.21 6.11 6.01 5.92 5.84 5.67 5.52 5.37 5.23 5.10 4.84 4.60 4.38 4.17

7.40 7.18 6.98 6.79 6.62 6.46 6.30 6.16 6.02 5.75 5.50 5.26 5.03 4.82 4.44 4.11 3.81 3.55 7.64 7.52 7.40 7.29 7.18 7.07 6.98 6.88 6.79 6.62 6.46 6.30 6.16 6.02 5.75 5.50 5.26 5.03

8.38 8.15 7.95 7.75 7.57 7.40 7.24 7.09 6.94 6.66 6.40 6.15 5.91 5.69 5.27 4.91 4.58 4.28 8.79 8.50 8.38 8.26 8.15 8.05 7.95 7.85 7.75 7.57 7.40 7.24 7.09 6.94 6.66 6.40 6.15 5.91

9.36 9.13 8.92 8.72 8.53 8.36 8.19 8.03 7.88 7.59 7.31 7.05 6.80 6.56 6.13 5.73 5.37 5.05 9.78 9.48 9.36 9.24 9.13 9.01 8.92 8.81 8.72 8.53 8.36 8.19 8.03 7.88 7.59 7.31 7.05 6.80

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11

12

10.3 10.1 9.89 9.68 9.49 9.31 9.14 8.97 8.81 8.51 8.23 7.96 7.70 7.45 6.99 6.57 6.19 5.84 10.8 10.5 10.3 10.2 10.1 10.0 9.89 9.78 9.68 9.49 9.31 9.14 8.97 8.81 8.51 8.23 7.96 7.70

11.3 11.1 10.9 10.7 10.5 10.3 10.1 9.92 9.76 9.45 9.16 8.88 8.61 8.35 7.87 7.43 7.02 6.65 11.7 11.5 11.3 11.2 11.1 11.0 10.9 10.8 10.7 10.5 10.3 10.1 9.92 9.76 9.45 9.16 8.88 8.61

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 36

7–36

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-7

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 1

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 C ⬘, in. 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 C ⬘, in.

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

0.84 0.65 0.54 0.45 0.39 0.35 0.31 0.28 0.26 0.22 0.19 0.17 0.15 0.14 0.12 0.10 0.09 0.08 2.94 0.84 0.65 0.54 0.45 0.39 0.35 0.31 0.28 0.26 0.22 0.19 0.17 0.15 0.14 0.12 0.10 0.09 0.08 2.94

2

3

2.54 4.48 2.03 3.68 1.67 3.06 1.42 2.59 1.22 2.25 1.08 1.99 0.96 1.78 0.86 1.60 0.78 1.46 0.66 1.24 0.57 1.08 0.51 0.95 0.45 0.85 0.41 0.77 0.34 0.65 0.29 0.56 0.26 0.49 0.23 0.43 8.33 15.8 3.24 5.39 2.79 4.93 2.41 4.44 2.10 3.97 1.85 3.55 1.64 3.18 1.47 2.87 1.34 2.61 1.22 2.39 1.04 2.04 0.90 1.77 0.80 1.57 0.71 1.41 0.64 1.28 0.54 1.07 0.46 0.93 0.41 0.81 0.36 0.73 13.2 26.5

4

5

6

6.59 8.72 10.8 5.67 7.77 9.91 4.86 6.84 8.93 4.21 6.01 8.00 3.69 5.32 7.17 3.27 4.74 6.46 2.93 4.27 5.86 2.65 3.87 5.34 2.42 3.53 4.90 2.06 3.01 4.19 1.78 2.62 3.66 1.57 2.32 3.24 1.41 2.07 2.90 1.27 1.88 2.63 1.07 1.58 2.21 0.92 1.36 1.90 0.80 1.19 1.67 0.72 1.06 1.49 26.0 38.7 54.2 7.47 9.51 11.5 7.08 9.17 11.2 6.60 8.75 10.9 6.11 8.27 10.4 5.62 7.77 9.93 5.17 7.27 9.43 4.75 6.79 8.92 4.39 6.34 8.43 4.06 5.92 7.96 3.52 5.20 7.10 3.09 4.61 6.36 2.75 4.12 5.74 2.48 3.72 5.21 2.25 3.38 4.77 1.90 2.86 4.06 1.64 2.47 3.52 1.44 2.18 3.11 1.29 1.94 2.78 47.0 71.4 103

7

8

9

10

11

12

12.9 12.1 11.1 10.1 9.16 8.33 7.60 6.97 6.42 5.51 4.82 4.27 3.83 3.48 2.93 2.53 2.22 1.98 72.2 13.5 13.3 12.9 12.5 12.1 11.6 11.1 10.6 10.1 9.12 8.27 7.52 6.87 6.31 5.40 4.70 4.16 3.72 138

15.0 14.2 13.2 12.2 11.2 10.3 9.50 8.75 8.10 7.01 6.15 5.47 4.92 4.47 3.77 3.25 2.86 2.55 93.1 15.5 15.3 15.0 14.6 14.2 13.7 13.3 12.7 12.2 11.2 10.3 9.44 8.68 8.02 6.91 6.05 5.37 4.81 180

17.0 16.3 15.4 14.4 13.4 12.4 11.5 10.7 9.91 8.63 7.61 6.79 6.11 5.55 4.69 4.05 3.57 3.18 117 17.5 17.3 17.0 16.7 16.3 15.9 15.4 14.9 14.4 13.4 12.4 11.5 10.6 9.85 8.55 7.52 6.69 6.02 226

19.0 18.3 17.5 16.5 15.5 14.5 13.6 12.7 11.8 10.4 9.19 8.23 7.43 6.76 5.72 4.95 4.36 3.90 143 19.5 19.3 19.1 18.7 18.4 18.0 17.5 17.1 16.6 15.5 14.5 13.5 12.6 11.8 10.3 9.12 8.15 7.34 279

21.0 20.4 19.6 18.7 17.7 16.7 15.7 14.7 13.8 12.2 10.9 9.78 8.85 8.07 6.85 5.93 5.23 4.67 172 21.5 21.3 21.1 20.8 20.4 20.1 19.6 19.2 18.7 17.7 16.7 15.7 14.7 13.8 12.2 10.8 9.71 8.78 337

23.0 22.5 21.7 20.8 19.8 18.8 17.8 16.8 15.9 14.2 12.7 11.4 10.4 9.48 8.06 7.00 6.18 5.52 204 23.4 23.3 23.1 22.8 22.5 22.1 21.7 21.3 20.9 19.9 18.9 17.8 16.8 15.9 14.1 12.6 11.4 10.3 400

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 37

7–37

DESIGN TABLES

Table 7-7 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

0.87 0.68 0.55 0.47 0.41 0.36 0.32 0.29 0.27 0.23 0.20 0.17 0.16 0.14 0.12 0.10 0.09 0.08 0.87 0.68 0.55 0.47 0.41 0.36 0.32 0.29 0.27 0.23 0.20 0.17 0.16 0.14 0.12 0.10 0.09 0.08

2.54 2.04 1.69 1.44 1.25 1.10 0.98 0.88 0.81 0.68 0.59 0.52 0.47 0.42 0.35 0.30 0.27 0.24 3.21 2.76 2.38 2.07 1.83 1.63 1.47 1.34 1.23 1.05 0.91 0.81 0.72 0.66 0.55 0.48 0.42 0.37

4.47 3.71 3.11 2.66 2.31 2.04 1.83 1.65 1.51 1.28 1.11 0.98 0.88 0.79 0.67 0.57 0.50 0.45 5.35 4.88 4.40 3.96 3.56 3.22 2.92 2.66 2.45 2.09 1.83 1.62 1.45 1.32 1.11 0.96 0.84 0.75

6.54 5.63 4.85 4.21 3.70 3.29 2.96 2.68 2.45 2.09 1.82 1.61 1.44 1.31 1.10 0.94 0.83 0.74 7.42 7.00 6.53 6.04 5.56 5.12 4.73 4.37 4.05 3.53 3.11 2.78 2.50 2.28 1.93 1.67 1.47 1.32

8.63 7.69 6.79 6.00 5.34 4.79 4.32 3.94 3.61 3.08 2.69 2.38 2.13 1.93 1.62 1.40 1.23 1.10 9.45 9.09 8.65 8.17 7.67 7.19 6.72 6.29 5.90 5.21 4.64 4.17 3.77 3.45 2.93 2.54 2.24 2.00

10.7 9.80 8.84 7.94 7.15 6.46 5.87 5.37 4.93 4.24 3.71 3.29 2.96 2.68 2.26 1.95 1.72 1.53 11.5 11.1 10.7 10.3 9.80 9.30 8.81 8.33 7.88 7.06 6.35 5.75 5.24 4.80 4.10 3.57 3.16 2.83

12.8 11.9 10.9 9.98 9.09 8.30 7.60 6.99 6.45 5.58 4.90 4.36 3.92 3.56 3.00 2.60 2.28 2.04 13.5 13.2 12.8 12.4 11.9 11.4 10.9 10.4 9.95 9.04 8.22 7.51 6.88 6.34 5.46 4.78 4.24 3.80

14.8 14.0 13.1 12.1 11.1 10.2 9.45 8.74 8.11 7.05 6.21 5.54 4.99 4.54 3.84 3.32 2.93 2.61 15.5 15.2 14.9 14.5 14.0 13.6 13.1 12.6 12.1 11.1 10.2 9.38 8.66 8.02 6.95 6.11 5.44 4.89

16.9 16.1 15.2 14.2 13.2 12.3 11.4 10.6 9.88 8.66 7.67 6.86 6.20 5.65 4.79 4.15 3.66 3.27 17.4 17.2 16.9 16.5 16.1 15.7 15.2 14.7 14.2 13.2 12.2 11.4 10.5 9.82 8.57 7.58 6.77 6.10

18.9 18.2 17.3 16.3 15.3 14.3 13.4 12.6 11.8 10.4 9.23 8.29 7.51 6.85 5.82 5.05 4.46 3.98 19.4 19.2 18.9 18.6 18.2 17.8 17.3 16.8 16.3 15.3 14.3 13.4 12.5 11.7 10.3 9.15 8.21 7.42

20.9 20.2 19.4 18.4 17.4 16.4 15.5 14.6 13.7 12.2 10.9 9.83 8.93 8.17 6.96 6.05 5.34 4.78 21.4 21.2 20.9 20.6 20.3 19.9 19.4 18.9 18.5 17.5 16.5 15.5 14.5 13.7 12.1 10.8 9.75 8.85

22.9 22.3 21.5 20.5 19.6 18.6 17.6 16.6 15.7 14.1 12.7 11.5 10.4 9.57 8.17 7.12 6.29 5.64 23.4 23.2 22.9 22.6 22.3 21.9 21.5 21.0 20.6 19.6 18.6 17.6 16.6 15.7 14.0 12.6 11.4 10.4

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 38

7–38

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-7 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

0.97 0.75 0.62 0.52 0.45 0.40 0.36 0.32 0.30 0.25 0.22 0.19 0.17 0.16 0.13 0.12 0.10 0.09 0.97 0.75 0.62 0.52 0.45 0.40 0.36 0.32 0.30 0.25 0.22 0.19 0.17 0.16 0.13 0.12 0.10 0.09

2.60 2.12 1.78 1.53 1.34 1.19 1.07 0.97 0.88 0.75 0.65 0.58 0.52 0.47 0.39 0.34 0.30 0.26 3.20 2.75 2.39 2.10 1.87 1.69 1.53 1.40 1.29 1.12 0.98 0.87 0.79 0.71 0.60 0.52 0.46 0.41

4.52 3.83 3.29 2.85 2.51 2.23 2.00 1.81 1.66 1.41 1.23 1.08 0.97 0.88 0.74 0.64 0.56 0.50 5.31 4.86 4.42 4.02 3.67 3.36 3.08 2.84 2.63 2.28 2.00 1.78 1.60 1.45 1.23 1.06 0.93 0.83

6.54 5.71 4.99 4.39 3.89 3.48 3.15 2.87 2.64 2.27 1.98 1.76 1.58 1.43 1.21 1.04 0.92 0.82 7.37 6.95 6.49 6.04 5.61 5.21 4.84 4.51 4.21 3.70 3.29 2.95 2.68 2.45 2.08 1.82 1.61 1.44

8.59 7.71 6.88 6.16 5.54 5.01 4.57 4.19 3.87 3.34 2.93 2.60 2.34 2.12 1.79 1.55 1.36 1.21 9.39 9.01 8.57 8.11 7.66 7.21 6.79 6.40 6.04 5.39 4.86 4.40 4.02 3.70 3.17 2.77 2.45 2.20

10.6 9.75 8.87 8.06 7.33 6.70 6.14 5.66 5.24 4.54 3.99 3.56 3.21 2.92 2.48 2.14 1.89 1.69 11.4 11.1 10.6 10.2 9.73 9.27 8.82 8.39 7.98 7.23 6.57 6.01 5.52 5.09 4.39 3.85 3.42 3.08

12.7 11.8 10.9 10.0 9.23 8.51 7.86 7.28 6.77 5.92 5.24 4.69 4.24 3.87 3.29 2.85 2.51 2.25 13.4 13.1 12.7 12.3 11.8 11.4 10.9 10.4 9.99 9.16 8.41 7.75 7.17 6.65 5.79 5.11 4.56 4.12

14.7 13.9 13.0 12.1 11.2 10.4 9.68 9.02 8.43 7.43 6.61 5.94 5.38 4.92 4.18 3.63 3.21 2.87 15.4 15.1 14.7 14.3 13.9 13.4 13.0 12.5 12.0 11.2 10.3 9.6 8.9 8.3 7.3 6.5 5.8 5.3

16.7 15.9 15.1 14.1 13.2 12.4 11.6 10.9 10.2 9.04 8.09 7.30 6.64 6.08 5.19 4.52 4.00 3.59 17.4 17.1 16.8 16.4 16.0 15.5 15.1 14.6 14.1 13.2 12.3 11.5 10.8 10.1 8.95 7.99 7.20 6.53

18.8 18.0 17.1 16.2 15.3 14.4 13.6 12.8 12.0 10.8 9.67 8.77 8.0 7.3 6.3 5.5 4.9 4.4 19.4 19.1 18.8 18.4 18.0 17.6 17.1 16.7 16.2 15.3 14.4 13.5 12.7 12.0 10.7 9.59 8.68 7.91

20.8 20.0 19.2 18.3 17.3 16.4 15.6 14.7 13.9 12.5 11.4 10.3 9.45 8.70 7.48 6.54 5.81 5.22 21.3 21.1 20.8 20.4 20.1 19.6 19.2 18.7 18.3 17.3 16.4 15.5 14.7 13.9 12.5 11.3 10.3 9.37

22.8 22.1 21.3 20.4 19.4 18.5 17.6 16.7 15.9 14.4 13.1 12.0 11.0 10.1 8.75 7.68 6.83 6.15 23.3 23.1 22.8 22.5 22.1 21.7 21.3 20.8 20.4 19.4 18.5 17.6 16.7 15.9 14.4 13.0 11.9 10.9

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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8:33 AM

Page 39

7–39

DESIGN TABLES

Table 7-7 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.17 0.92 0.75 0.64 0.55 0.49 0.44 0.40 0.36 0.31 0.27 0.24 0.21 0.19 0.16 0.14 0.12 0.11 1.17 0.92 0.75 0.64 0.55 0.49 0.44 0.40 0.36 0.31 0.27 0.24 0.21 0.19 0.16 0.14 0.12 0.11

2.79 2.32 1.99 1.74 1.54 1.38 1.25 1.14 1.05 0.90 0.78 0.69 0.62 0.56 0.48 0.41 0.36 0.32 3.24 2.84 2.51 2.24 2.03 1.85 1.70 1.57 1.46 1.28 1.13 1.01 0.92 0.84 0.72 0.62 0.55 0.49

4.67 4.06 3.57 3.17 2.84 2.57 2.33 2.13 1.96 1.68 1.47 1.31 1.17 1.06 0.90 0.77 0.68 0.61 5.30 4.90 4.52 4.17 3.86 3.59 3.35 3.13 2.94 2.60 2.32 2.09 1.90 1.73 1.47 1.28 1.13 1.01

6.62 5.92 5.31 4.78 4.33 3.93 3.60 3.31 3.06 2.65 2.33 2.08 1.88 1.71 1.45 1.26 1.11 0.99 7.32 6.93 6.53 6.15 5.78 5.45 5.13 4.85 4.58 4.11 3.71 3.36 3.07 2.83 2.43 2.13 1.90 1.71

8.61 7.86 7.16 6.53 5.98 5.49 5.06 4.69 4.36 3.83 3.40 3.05 2.76 2.52 2.14 1.86 1.64 1.47 9.33 8.96 8.56 8.15 7.76 7.39 7.03 6.70 6.38 5.81 5.31 4.88 4.50 4.18 3.64 3.22 2.88 2.61

10.6 9.83 9.09 8.39 7.76 7.20 6.70 6.25 5.85 5.17 4.61 4.16 3.77 3.45 2.94 2.56 2.27 2.03 11.3 11.0 10.6 10.2 9.77 9.38 9.00 8.63 8.28 7.64 7.06 6.55 6.09 5.69 5.00 4.45 3.99 3.62

12.6 11.8 11.1 10.3 9.63 9.00 8.43 7.91 7.44 6.63 5.95 5.38 4.91 4.51 3.87 3.38 3.00 2.70 13.3 13.0 12.6 12.2 11.8 11.4 11.0 10.6 10.2 9.54 8.89 8.31 7.78 7.31 6.48 5.80 5.24 4.77

14.6 13.9 13.1 12.3 11.6 10.9 10.3 9.67 9.14 8.20 7.41 6.74 6.18 5.69 4.91 4.30 3.82 3.44 15.3 15.0 14.6 14.2 13.8 13.4 13.0 12.6 12.2 11.5 10.8 10.2 9.56 9.02 8.08 7.28 6.62 6.05

16.6 15.9 15.1 14.3 13.5 12.8 12.1 11.5 10.9 9.86 8.97 8.20 7.55 6.97 6.04 5.30 4.73 4.26 17.3 17.0 16.6 16.2 15.8 15.4 15.0 14.6 14.2 13.5 12.7 12.0 11.4 10.8 9.76 8.86 8.09 7.43

18.6 17.9 17.1 16.3 15.5 14.8 14.0 13.4 12.7 11.6 10.6 9.75 9.00 8.34 7.26 6.41 5.73 5.17 19.3 19.0 18.6 18.3 17.9 17.5 17.1 16.7 16.3 15.5 14.7 14.0 13.3 12.7 11.5 10.5 9.65 8.90

20.6 19.9 19.1 18.3 17.5 16.7 16.0 15.3 14.6 13.4 12.3 11.4 10.5 9.80 8.57 7.59 6.80 6.15 21.3 21.0 20.6 20.3 19.9 19.5 19.1 18.7 18.3 17.5 16.7 15.9 15.2 14.6 13.3 12.2 11.3 10.4

22.6 21.9 21.1 20.3 19.5 18.7 18.0 17.2 16.5 15.2 14.1 13.1 12.1 11.3 9.95 8.85 7.94 7.20 23.2 23.0 22.6 22.3 21.9 21.5 21.1 20.7 20.3 19.5 18.7 17.9 17.2 16.5 15.2 14.0 13.0 12.1

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 40

7–40

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-7 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.51 1.24 1.04 0.89 0.77 0.68 0.61 0.56 0.51 0.43 0.38 0.34 0.30 0.27 0.23 0.20 0.18 0.16 1.51 1.24 1.04 0.89 0.77 0.68 0.61 0.56 0.51 0.43 0.38 0.34 0.30 0.27 0.23 0.20 0.18 0.16

3.17 2.76 2.43 2.16 1.95 1.77 1.62 1.49 1.38 1.20 1.06 0.95 0.85 0.78 0.66 0.57 0.50 0.45 3.39 3.08 2.80 2.57 2.37 2.19 2.04 1.91 1.80 1.60 1.44 1.31 1.20 1.10 0.95 0.84 0.74 0.67

4.97 4.47 4.04 3.70 3.40 3.13 2.90 2.70 2.52 2.21 1.96 1.76 1.60 1.46 1.24 1.07 0.95 0.85 5.36 5.04 4.73 4.45 4.20 3.98 3.77 3.59 3.42 3.11 2.85 2.63 2.43 2.26 1.97 1.73 1.54 1.39

6.85 6.30 5.81 5.39 5.01 4.67 4.37 4.09 3.84 3.40 3.05 2.75 2.51 2.30 1.97 1.72 1.52 1.37 7.33 7.01 6.69 6.39 6.11 5.85 5.61 5.38 5.17 4.78 4.43 4.12 3.84 3.58 3.15 2.80 2.52 2.28

8.77 8.19 7.65 7.17 6.73 6.33 5.96 5.62 5.31 4.76 4.30 3.92 3.59 3.32 2.87 2.52 2.24 2.02 9.31 8.98 8.66 8.35 8.05 7.76 7.49 7.24 7.00 6.54 6.13 5.74 5.40 5.08 4.53 4.08 3.71 3.39

10.7 10.1 9.53 9.01 8.52 8.07 7.65 7.26 6.89 6.25 5.71 5.24 4.84 4.48 3.90 3.44 3.07 2.77 11.3 11.0 10.6 10.3 10.0 9.70 9.41 9.13 8.87 8.37 7.91 7.48 7.08 6.71 6.06 5.52 5.05 4.65

12.7 12.0 11.5 10.9 10.4 9.88 9.42 8.98 8.58 7.85 7.23 6.68 6.19 5.76 5.04 4.47 4.01 3.63 13.3 12.9 12.6 12.3 12.0 11.7 11.4 11.1 10.8 10.2 9.74 9.27 8.84 8.43 7.69 7.06 6.51 6.02

14.6 14.0 13.4 12.8 12.3 11.7 11.2 10.8 10.3 9.53 8.83 8.20 7.64 7.14 6.29 5.61 5.06 4.59 15.2 14.9 14.6 14.3 13.9 13.6 13.3 13.0 12.7 12.1 11.6 11.1 10.7 10.2 9.39 8.68 8.05 7.49

16.6 16.0 15.3 14.7 14.2 13.6 13.1 12.6 12.1 11.3 10.5 9.79 9.16 8.60 7.64 6.85 6.20 5.65 17.2 16.9 16.6 16.2 15.9 15.6 15.3 15.0 14.7 14.1 13.5 13.0 12.5 12.0 11.2 10.4 9.66 9.03

18.6 17.9 17.3 16.7 16.1 15.5 15.0 14.5 14.0 13.0 12.2 11.5 10.8 10.1 9.06 8.17 7.41 6.77 19.2 18.9 18.6 18.2 17.9 17.6 17.2 16.9 16.6 16.0 15.4 14.9 14.4 13.9 12.9 12.1 11.3 10.7

20.6 19.9 19.3 18.6 18.0 17.4 16.9 16.3 15.8 14.9 14.0 13.2 12.4 11.7 10.6 9.55 8.70 7.98 21.2 20.9 20.5 20.2 19.9 19.5 19.2 18.9 18.6 18.0 17.4 16.8 16.3 15.7 14.8 13.9 13.1 12.3

22.5 21.9 21.2 20.6 20.0 19.4 18.8 18.2 17.7 16.7 15.8 14.9 14.1 13.4 12.1 11.0 10.1 9.26 23.2 22.8 22.5 22.2 21.8 21.5 21.2 20.9 20.5 19.9 19.3 18.7 18.2 17.6 16.6 15.7 14.8 14.0

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 41

7–41

DESIGN TABLES

Table 7-7 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.84 1.71 1.57 1.44 1.31 1.20 1.10 1.01 0.93 0.81 0.71 0.63 0.57 0.52 0.44 0.38 0.34 0.30 1.84 1.71 1.57 1.44 1.31 1.20 1.10 1.01 0.93 0.81 0.71 0.63 0.57 0.52 0.44 0.38 0.34 0.30

3.63 3.41 3.19 2.98 2.79 2.61 2.45 2.31 2.18 1.95 1.77 1.61 1.48 1.36 1.18 1.04 0.92 0.83 3.66 3.49 3.32 3.16 3.02 2.88 2.75 2.63 2.52 2.32 2.15 2.00 1.87 1.75 1.55 1.40 1.27 1.16

5.44 5.17 4.90 4.65 4.41 4.19 3.99 3.81 3.63 3.33 3.06 2.83 2.63 2.45 2.15 1.91 1.71 1.55 5.55 5.36 5.18 5.01 4.84 4.69 4.54 4.40 4.27 4.03 3.82 3.62 3.44 3.28 2.98 2.74 2.52 2.33

7.29 6.97 6.67 6.39 6.12 5.88 5.65 5.43 5.23 4.86 4.53 4.23 3.96 3.72 3.30 2.95 2.67 2.43 7.48 7.27 7.08 6.89 6.72 6.55 6.39 6.24 6.09 5.82 5.57 5.35 5.14 4.94 4.57 4.24 3.95 3.68

9.17 8.82 8.50 8.19 7.90 7.62 7.37 7.14 6.91 6.49 6.11 5.75 5.42 5.12 4.60 4.16 3.78 3.47 9.42 9.20 9.00 8.81 8.62 8.44 8.27 8.11 7.95 7.66 7.38 7.13 6.90 6.67 6.24 5.85 5.49 5.16

11.1 10.7 10.4 10.0 9.71 9.42 9.14 8.89 8.65 8.19 7.76 7.36 6.98 6.63 6.02 5.49 5.04 4.65 11.4 11.2 10.9 10.7 10.5 10.4 10.2 10.0 9.83 9.52 9.22 8.95 8.69 8.45 7.98 7.54 7.13 6.75

13.0 12.6 12.2 11.9 11.6 11.3 11.0 10.7 10.4 9.94 9.47 9.03 8.61 8.23 7.53 6.93 6.41 5.94 13.3 13.1 12.9 12.7 12.5 12.3 12.1 11.9 11.7 11.4 11.1 10.8 10.5 10.3 9.75 9.28 8.83 8.41

14.9 14.5 14.1 13.8 13.4 13.1 12.8 12.5 12.2 11.7 11.2 10.8 10.3 9.88 9.12 8.45 7.86 7.32 15.3 15.1 14.8 14.6 14.4 14.2 14.0 13.8 13.6 13.3 13.0 12.7 12.4 12.1 11.6 11.1 10.6 10.1

16.9 16.4 16.0 15.7 15.3 15.0 14.7 14.3 14.1 13.5 13.0 12.5 12.0 11.6 10.8 10.0 9.37 8.78 17.6 17.0 16.8 16.6 16.3 16.1 15.9 15.7 15.6 15.2 14.9 14.5 14.2 13.9 13.4 12.9 12.4 11.9

18.8 18.4 18.0 17.6 17.2 16.9 16.5 16.2 15.9 15.3 14.8 14.3 13.8 13.3 12.4 11.7 10.9 10.3 19.6 19.0 18.7 18.5 18.3 18.1 17.9 17.7 17.5 17.1 16.7 16.4 16.1 15.8 15.2 14.7 14.1 13.7

20.8 20.3 19.9 19.5 19.1 18.8 18.4 18.1 17.8 17.2 16.6 16.1 15.6 15.1 14.2 13.3 12.6 11.9 21.5 21.0 20.7 20.5 20.2 20.0 19.8 19.6 19.4 19.0 18.7 18.3 18.0 17.7 17.1 16.5 16.0 15.4

22.7 22.3 21.8 21.4 21.0 20.7 20.3 20.0 19.6 19.0 18.4 17.9 17.4 16.9 15.9 15.0 14.2 13.5 23.5 22.9 22.7 22.4 22.2 22.0 21.8 21.5 21.3 20.9 20.6 20.2 19.9 19.5 18.9 18.3 17.8 17.3

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

8:33 AM

Page 42

7–42

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-8

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 1

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 C ⬘, in. 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 C ⬘, in.

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1.14 0.94 0.80 0.70 0.62 0.55 0.50 0.46 0.42 0.37 0.32 0.29 0.26 0.24 0.20 0.18 0.16 0.14 5.40 1.14 0.94 0.80 0.70 0.62 0.55 0.50 0.46 0.42 0.37 0.32 0.29 0.26 0.24 0.20 0.18 0.16 0.14 5.40

2

3

2.75 4.59 2.32 3.92 1.99 3.39 1.74 2.96 1.54 2.62 1.38 2.36 1.25 2.14 1.14 1.96 1.04 1.80 0.90 1.55 0.79 1.36 0.70 1.21 0.63 1.09 0.57 0.99 0.48 0.84 0.42 0.73 0.37 0.64 0.33 0.57 12.3 21.2 3.25 5.37 2.86 4.93 2.52 4.47 2.24 4.04 2.00 3.65 1.80 3.31 1.64 3.02 1.50 2.77 1.38 2.56 1.19 2.21 1.04 1.95 0.93 1.74 0.84 1.57 0.76 1.43 0.64 1.21 0.55 1.05 0.49 0.93 0.43 0.83 16.0 30.6

4

5

6

6.61 8.69 10.8 5.80 7.82 9.90 5.10 6.98 9.00 4.51 6.24 8.15 4.03 5.60 7.39 3.63 5.07 6.72 3.30 4.61 6.15 3.01 4.22 5.66 2.78 3.89 5.23 2.39 3.36 4.53 2.10 2.96 3.99 1.87 2.64 3.55 1.68 2.37 3.20 1.53 2.16 2.91 1.29 1.83 2.46 1.11 1.58 2.13 0.98 1.39 1.88 0.88 1.24 1.68 32.3 45.8 61.8 7.45 9.49 11.5 7.05 9.14 11.2 6.59 8.72 10.8 6.12 8.25 10.4 5.66 7.77 9.91 5.23 7.29 9.42 4.84 6.83 8.93 4.49 6.39 8.45 4.18 5.99 7.99 3.65 5.29 7.16 3.24 4.72 6.44 2.90 4.24 5.83 2.62 3.84 5.31 2.39 3.50 4.87 2.02 2.98 4.16 1.76 2.59 3.63 1.55 2.29 3.21 1.38 2.05 2.88 51.0 76.2 107

7

8

9

10

11

12

12.9 12.0 11.1 10.2 9.30 8.53 7.84 7.23 6.70 5.82 5.13 4.58 4.14 3.77 3.19 2.77 2.44 2.18 80.3 13.5 13.2 12.9 12.5 12.1 11.6 11.1 10.6 10.1 9.15 8.32 7.59 6.95 6.39 5.49 4.80 4.25 3.81 143

14.9 14.1 13.2 12.3 11.3 10.5 9.67 8.97 8.34 7.28 6.44 5.76 5.21 4.75 4.03 3.49 3.08 2.75 102 15.5 15.3 15.0 14.6 14.2 13.7 13.2 12.7 12.2 11.2 10.3 9.48 8.74 8.08 6.99 6.13 5.45 4.90 185

17.0 16.2 15.3 14.4 13.4 12.5 11.6 10.8 10.1 8.87 7.87 7.05 6.38 5.82 4.94 4.29 3.79 3.39 125 17.5 17.3 17.0 16.7 16.3 15.8 15.4 14.9 14.4 13.4 12.4 11.5 10.7 9.89 8.61 7.59 6.77 6.09 232

19.0 18.3 17.4 16.5 15.5 14.6 13.6 12.8 12.0 10.6 9.42 8.47 7.68 7.02 5.97 5.19 4.58 4.10 152 19.5 19.3 19.0 18.7 18.4 17.9 17.5 17.0 16.5 15.5 14.5 13.6 12.6 11.8 10.4 9.18 8.21 7.41 284

21.0 20.4 19.6 18.6 17.7 16.7 15.7 14.8 13.9 12.4 11.1 9.99 9.08 8.30 7.07 6.15 5.44 4.87 181 21.4 21.3 21.0 20.8 20.4 20.0 19.6 19.2 18.7 17.7 16.7 15.7 14.7 13.8 12.2 10.9 9.76 8.83 342

23.0 22.4 21.7 20.8 19.8 18.8 17.8 16.9 15.9 14.3 12.8 11.6 10.6 9.69 8.28 7.21 6.38 5.72 213 23.4 23.3 23.1 22.8 22.5 22.1 21.7 21.3 20.8 19.8 18.8 17.8 16.8 15.9 14.1 12.7 11.4 10.4 406

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 43

7–43

DESIGN TABLES

Table 7-8 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.18 0.97 0.83 0.72 0.64 0.57 0.52 0.48 0.44 0.38 0.33 0.30 0.27 0.25 0.21 0.18 0.16 0.14 1.18 0.97 0.83 0.72 0.64 0.57 0.52 0.48 0.44 0.38 0.33 0.30 0.27 0.25 0.21 0.18 0.16 0.14

2.78 2.34 2.02 1.77 1.57 1.41 1.28 1.17 1.07 0.93 0.81 0.72 0.65 0.59 0.50 0.43 0.38 0.34 3.24 2.85 2.51 2.23 2.00 1.81 1.65 1.52 1.40 1.21 1.07 0.95 0.86 0.78 0.66 0.57 0.50 0.45

4.61 3.97 3.45 3.03 2.70 2.43 2.20 2.01 1.85 1.60 1.40 1.25 1.13 1.02 0.87 0.75 0.66 0.59 5.34 4.90 4.45 4.05 3.68 3.36 3.08 2.83 2.62 2.27 2.00 1.79 1.62 1.47 1.25 1.08 0.95 0.85

6.59 5.80 5.11 4.54 4.06 3.66 3.34 3.06 2.82 2.44 2.15 1.91 1.72 1.57 1.33 1.15 1.01 0.90 7.40 6.99 6.53 6.07 5.62 5.20 4.82 4.48 4.18 3.66 3.25 2.92 2.65 2.42 2.06 1.79 1.58 1.42

8.64 7.78 6.97 6.26 5.65 5.13 4.68 4.30 3.98 3.44 3.03 2.70 2.44 2.22 1.88 1.63 1.43 1.28 9.43 9.07 8.63 8.16 7.69 7.22 6.78 6.36 5.98 5.31 4.76 4.29 3.90 3.58 3.05 2.66 2.35 2.11

10.7 9.83 8.94 8.12 7.39 6.74 6.18 5.70 5.27 4.58 4.05 3.62 3.27 2.98 2.53 2.19 1.93 1.73 11.5 11.1 10.7 10.3 9.80 9.31 8.83 8.37 7.93 7.13 6.44 5.85 5.34 4.91 4.21 3.68 3.26 2.93

12.8 11.9 11.0 10.1 9.27 8.52 7.86 7.27 6.76 5.90 5.22 4.68 4.23 3.86 3.27 2.84 2.50 2.24 13.5 13.2 12.8 12.4 11.9 11.4 10.9 10.5 9.97 9.08 8.28 7.58 6.97 6.43 5.55 4.87 4.33 3.90

14.8 14.0 13.1 12.1 11.2 10.4 9.65 8.97 8.36 7.34 6.51 5.84 5.28 4.83 4.11 3.57 3.15 2.82 15.4 15.2 14.8 14.5 14.0 13.5 13.1 12.6 12.1 11.1 10.2 9.43 8.72 8.09 7.03 6.19 5.52 4.97

16.8 16.1 15.2 14.2 13.3 12.4 11.6 10.8 10.1 8.91 7.94 7.14 6.48 5.93 5.05 4.39 3.88 3.48 17.4 17.2 16.9 16.5 16.1 15.7 15.2 14.7 14.2 13.2 12.3 11.4 10.6 9.87 8.64 7.65 6.84 6.18

18.9 18.1 17.3 16.3 15.4 14.4 13.5 12.7 11.9 10.6 9.47 8.54 7.77 7.11 6.07 5.29 4.68 4.19 19.4 19.2 18.9 18.6 18.2 17.7 17.3 16.8 16.3 15.3 14.3 13.4 12.5 11.7 10.4 9.22 8.27 7.49

20.9 20.2 19.3 18.4 17.5 16.5 15.6 14.7 13.8 12.4 11.1 10.1 9.16 8.40 7.19 6.28 5.56 4.99 21.4 21.2 20.9 20.6 20.2 19.8 19.4 18.9 18.4 17.4 16.4 15.5 14.6 13.7 12.2 10.9 9.81 8.91

22.9 22.2 21.4 20.5 19.6 18.6 17.6 16.7 15.8 14.2 12.8 11.7 10.7 9.78 8.39 7.33 6.50 5.84 23.4 23.2 22.9 22.6 22.3 21.9 21.5 21.0 20.6 19.6 18.6 17.6 16.6 15.7 14.1 12.6 11.4 10.4

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 44

7–44

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-8 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.30 1.08 0.92 0.80 0.71 0.64 0.58 0.53 0.49 0.42 0.37 0.33 0.30 0.27 0.23 0.20 0.18 0.16 1.30 1.08 0.92 0.80 0.71 0.64 0.58 0.53 0.49 0.42 0.37 0.33 0.30 0.27 0.23 0.20 0.18 0.16

2.90 2.47 2.14 1.89 1.69 1.53 1.39 1.28 1.18 1.02 0.90 0.80 0.72 0.66 0.56 0.48 0.43 0.38 3.27 2.89 2.56 2.29 2.08 1.89 1.74 1.61 1.49 1.30 1.15 1.03 0.93 0.85 0.72 0.63 0.55 0.50

4.72 4.13 3.64 3.24 2.91 2.63 2.40 2.20 2.03 1.76 1.55 1.38 1.25 1.13 0.96 0.83 0.73 0.66 5.33 4.91 4.50 4.13 3.80 3.51 3.25 3.02 2.81 2.47 2.19 1.96 1.78 1.62 1.38 1.20 1.06 0.95

6.66 5.94 5.30 4.76 4.29 3.90 3.57 3.29 3.04 2.65 2.34 2.09 1.89 1.73 1.46 1.27 1.12 1.00 7.36 6.96 6.53 6.10 5.69 5.31 4.96 4.64 4.35 3.85 3.44 3.11 2.83 2.60 2.23 1.95 1.73 1.55

8.65 7.86 7.12 6.46 5.88 5.38 4.95 4.58 4.26 3.72 3.29 2.95 2.67 2.43 2.07 1.79 1.58 1.42 9.38 9.01 8.58 8.14 7.70 7.27 6.86 6.49 6.13 5.51 4.98 4.54 4.16 3.83 3.30 2.89 2.57 2.31

10.7 9.85 9.04 8.29 7.61 7.01 6.49 6.02 5.61 4.92 4.37 3.92 3.55 3.25 2.77 2.41 2.13 1.91 11.4 11.0 10.6 10.2 9.75 9.30 8.86 8.44 8.04 7.31 6.67 6.12 5.63 5.21 4.51 3.96 3.53 3.18

12.7 11.9 11.0 10.2 9.45 8.76 8.14 7.59 7.09 6.25 5.58 5.03 4.57 4.19 3.57 3.11 2.76 2.47 13.4 13.1 12.7 12.3 11.8 11.4 10.9 10.5 10.0 9.22 8.49 7.83 7.26 6.74 5.89 5.21 4.67 4.22

14.7 13.9 13.0 12.2 11.4 10.6 9.92 9.29 8.72 7.73 6.93 6.26 5.70 5.23 4.47 3.90 3.46 3.10 15.4 15.1 14.7 14.3 13.9 13.4 13.0 12.5 12.1 11.2 10.4 9.66 9.00 8.41 7.40 6.59 5.92 5.36

16.7 16.0 15.1 14.2 13.4 12.5 11.8 11.1 10.4 9.31 8.38 7.59 6.93 6.36 5.47 4.78 4.25 3.81 17.4 17.1 16.8 16.4 15.9 15.5 15.0 14.6 14.1 13.2 12.4 11.6 10.8 10.2 9.02 8.07 7.28 6.61

18.7 18.0 17.1 16.3 15.4 14.5 13.7 12.9 12.2 11.0 9.93 9.03 8.27 7.62 6.56 5.75 5.11 4.59 19.3 19.1 18.8 18.4 18.0 17.6 17.1 16.7 16.2 15.3 14.4 13.5 12.8 12.0 10.7 9.66 8.75 7.98

20.8 20.0 19.2 18.3 17.4 16.5 15.7 14.9 14.1 12.8 11.6 10.6 9.70 8.95 7.73 6.78 6.04 5.44 21.3 21.1 20.8 20.4 20.0 19.6 19.2 18.7 18.3 17.3 16.4 15.6 14.7 13.9 12.5 11.3 10.3 9.43

22.8 22.1 21.2 20.4 19.5 18.6 17.7 16.8 16.0 14.6 13.3 12.2 11.2 10.4 8.99 7.91 7.06 6.36 23.3 23.1 22.8 22.5 22.1 21.7 21.3 20.8 20.4 19.4 18.5 17.6 16.7 15.9 14.4 13.1 12.0 11.0

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 45

7–45

DESIGN TABLES

Table 7-8 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.53 1.30 1.11 0.98 0.87 0.78 0.71 0.65 0.60 0.52 0.45 0.41 0.37 0.33 0.28 0.25 0.22 0.20 1.53 1.30 1.11 0.98 0.87 0.78 0.71 0.65 0.60 0.52 0.45 0.41 0.37 0.33 0.28 0.25 0.22 0.20

3.18 2.76 2.43 2.17 1.95 1.78 1.63 1.50 1.39 1.22 1.08 0.96 0.87 0.79 0.68 0.59 0.52 0.46 3.39 3.04 2.74 2.49 2.28 2.10 1.94 1.81 1.69 1.50 1.34 1.21 1.10 1.01 0.86 0.75 0.67 0.60

4.96 4.42 3.97 3.60 3.28 3.01 2.77 2.57 2.39 2.08 1.85 1.65 1.50 1.37 1.16 1.01 0.89 0.80 5.36 4.99 4.64 4.31 4.02 3.76 3.53 3.32 3.13 2.80 2.52 2.29 2.09 1.92 1.64 1.44 1.27 1.14

6.84 6.22 5.67 5.19 4.77 4.40 4.07 3.78 3.52 3.09 2.75 2.48 2.25 2.06 1.76 1.53 1.35 1.21 7.35 6.98 6.60 6.24 5.89 5.57 5.28 5.00 4.74 4.29 3.89 3.55 3.26 3.01 2.61 2.30 2.05 1.85

8.77 8.09 7.46 6.89 6.37 5.91 5.50 5.13 4.81 4.26 3.82 3.45 3.14 2.88 2.47 2.15 1.91 1.71 9.35 8.98 8.60 8.21 7.84 7.48 7.13 6.81 6.50 5.94 5.45 5.02 4.65 4.33 3.79 3.36 3.02 2.73

10.7 10.0 9.32 8.68 8.09 7.56 7.07 6.64 6.25 5.58 5.02 4.55 4.16 3.82 3.28 2.87 2.55 2.29 11.3 11.0 10.6 10.2 9.82 9.44 9.07 8.71 8.37 7.74 7.17 6.67 6.22 5.82 5.13 4.58 4.12 3.74

12.7 12.0 11.2 10.6 9.90 9.31 8.76 8.26 7.81 7.01 6.34 5.77 5.29 4.87 4.21 3.69 3.29 2.96 13.3 13.0 12.6 12.2 11.8 11.4 11.0 10.7 10.3 9.61 8.98 8.41 7.89 7.42 6.60 5.92 5.35 4.88

14.7 14.0 13.2 12.5 11.8 11.1 10.5 9.97 9.45 8.54 7.76 7.09 6.53 6.04 5.23 4.61 4.11 3.70 15.3 15.0 14.6 14.2 13.8 13.4 13.0 12.7 12.3 11.5 10.9 10.2 9.65 9.11 8.17 7.38 6.72 6.15

16.7 15.9 15.2 14.4 13.7 13.0 12.4 11.8 11.2 10.2 9.28 8.53 7.87 7.30 6.35 5.61 5.01 4.53 17.3 17.0 16.6 16.3 15.9 15.5 15.1 14.7 14.3 13.5 12.8 12.1 11.5 10.9 9.84 8.95 8.18 7.52

18.7 17.9 17.2 16.4 15.6 14.9 14.2 13.6 13.0 11.9 10.9 10.1 9.30 8.65 7.55 6.69 6.00 5.43 19.3 19.0 18.6 18.3 17.9 17.5 17.1 16.7 16.3 15.5 14.7 14.0 13.4 12.7 11.6 10.6 9.73 8.98

20.7 19.9 19.2 18.4 17.6 16.9 16.2 15.5 14.8 13.6 12.6 11.6 10.8 10.1 8.85 7.87 7.07 6.40 21.3 21.0 20.6 20.3 19.9 19.5 19.1 18.7 18.3 17.5 16.7 16.0 15.3 14.6 13.4 12.3 11.4 10.5

22.6 21.9 21.2 20.4 19.6 18.8 18.1 17.4 16.7 15.4 14.3 13.3 12.4 11.6 10.2 9.11 8.20 7.44 23.2 22.9 22.6 22.3 21.9 21.5 21.1 20.7 20.3 19.5 18.7 17.9 17.2 16.5 15.2 14.1 13.0 12.1

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 46

7–46

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-8 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.78 1.62 1.45 1.31 1.18 1.07 0.98 0.90 0.83 0.72 0.64 0.57 0.52 0.47 0.40 0.35 0.31 0.28 1.78 1.62 1.45 1.31 1.18 1.07 0.98 0.90 0.83 0.72 0.64 0.57 0.52 0.47 0.40 0.35 0.31 0.28

3.55 3.26 2.97 2.71 2.48 2.28 2.11 1.97 1.84 1.62 1.45 1.31 1.19 1.09 0.93 0.82 0.72 0.65 3.59 3.35 3.11 2.89 2.70 2.52 2.36 2.23 2.10 1.89 1.71 1.57 1.44 1.33 1.16 1.02 0.91 0.82

5.34 4.95 4.57 4.23 3.93 3.66 3.43 3.22 3.03 2.70 2.43 2.21 2.02 1.85 1.59 1.39 1.24 1.11 5.48 5.20 4.93 4.66 4.42 4.19 3.99 3.81 3.64 3.34 3.08 2.85 2.65 2.47 2.17 1.92 1.72 1.56

7.17 6.71 6.27 5.86 5.50 5.18 4.88 4.61 4.37 3.93 3.56 3.24 2.98 2.75 2.37 2.08 1.86 1.67 7.41 7.12 6.82 6.53 6.26 6.01 5.77 5.55 5.35 4.97 4.63 4.32 4.04 3.79 3.36 3.00 2.71 2.46

9.04 8.53 8.04 7.58 7.16 6.79 6.45 6.12 5.82 5.28 4.81 4.42 4.07 3.77 3.28 2.90 2.59 2.34 9.36 9.06 8.75 8.45 8.16 7.88 7.62 7.37 7.13 6.70 6.29 5.92 5.58 5.26 4.71 4.26 3.88 3.55

10.9 10.4 9.86 9.36 8.90 8.48 8.09 7.72 7.37 6.73 6.19 5.71 5.29 4.93 4.32 3.83 3.43 3.11 11.3 11.0 10.7 10.4 10.1 9.79 9.51 9.24 8.98 8.49 8.04 7.62 7.22 6.86 6.21 5.67 5.20 4.80

12.9 12.3 11.7 11.2 10.7 10.2 9.80 9.39 9.00 8.28 7.66 7.11 6.63 6.19 5.46 4.86 4.37 3.97 13.3 13.0 12.7 12.3 12.0 11.7 11.4 11.1 10.9 10.3 9.85 9.39 8.95 8.55 7.82 7.19 6.64 6.16

14.8 14.2 13.6 13.1 12.5 12.0 11.6 11.1 10.7 9.91 9.22 8.60 8.05 7.55 6.69 5.99 5.41 4.93 15.3 15.0 14.6 14.3 14.0 13.7 13.4 13.1 12.8 12.2 11.7 11.2 10.7 10.3 9.50 8.80 8.17 7.61

16.7 16.1 15.5 15.0 14.4 13.9 13.4 12.9 12.5 11.6 10.9 10.2 9.55 8.98 8.01 7.21 6.54 5.98 17.2 16.9 16.6 16.3 15.9 15.6 15.3 15.0 14.7 14.1 13.6 13.1 12.6 12.1 11.2 10.5 9.77 9.14

18.7 18.1 17.5 16.9 16.3 15.7 15.2 14.7 14.2 13.4 12.5 11.8 11.1 10.5 9.41 8.51 7.75 7.10 19.2 18.9 18.6 18.2 17.9 17.6 17.3 17.0 16.7 16.1 15.5 15.0 14.4 13.9 13.0 12.2 11.4 10.7

20.6 20.0 19.4 18.8 18.2 17.6 17.1 16.6 16.1 15.1 14.3 13.5 12.7 12.1 10.9 9.88 9.02 8.29 21.2 20.9 20.6 20.2 19.9 19.6 19.2 18.9 18.6 18.0 17.4 16.9 16.3 15.8 14.8 14.0 13.1 12.4

22.6 22.0 21.4 20.7 20.1 19.5 19.0 18.4 17.9 16.9 16.0 15.2 14.4 13.7 12.4 11.3 10.4 9.55 23.2 22.9 22.5 22.2 21.9 21.5 21.2 20.9 20.6 19.9 19.3 18.8 18.2 17.7 16.7 15.8 14.9 14.1

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7A:14th Ed.

2/24/11

8:33 AM

Page 47

7–47

DESIGN TABLES

Table 7-8 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.92 1.87 1.82 1.75 1.68 1.60 1.52 1.45 1.38 1.25 1.13 1.03 0.95 0.87 0.75 0.66 0.59 0.53 1.92 1.87 1.82 1.75 1.68 1.60 1.52 1.45 1.38 1.25 1.13 1.03 0.95 0.87 0.75 0.66 0.59 0.53

3.82 3.72 3.60 3.47 3.33 3.19 3.06 2.93 2.80 2.57 2.36 2.18 2.02 1.88 1.65 1.46 1.31 1.19 3.80 3.70 3.59 3.48 3.36 3.24 3.13 3.02 2.91 2.72 2.54 2.38 2.24 2.11 1.88 1.70 1.55 1.42

5.70 5.54 5.37 5.18 5.00 4.81 4.63 4.46 4.29 3.98 3.70 3.45 3.23 3.03 2.69 2.42 2.18 1.99 5.69 5.55 5.40 5.26 5.11 4.97 4.84 4.71 4.58 4.34 4.13 3.92 3.74 3.57 3.27 3.00 2.77 2.57

7.57 7.36 7.14 6.92 6.69 6.47 6.26 6.05 5.85 5.48 5.15 4.85 4.57 4.32 3.87 3.50 3.19 2.92 7.59 7.42 7.25 7.09 6.93 6.77 6.62 6.47 6.33 6.07 5.82 5.59 5.38 5.17 4.80 4.47 4.17 3.90

9.45 9.19 8.94 8.68 8.42 8.17 7.93 7.70 7.48 7.07 6.69 6.34 6.01 5.71 5.17 4.71 4.32 3.98 9.51 9.32 9.14 8.96 8.78 8.62 8.45 8.29 8.14 7.85 7.57 7.32 7.09 6.87 6.44 6.06 5.70 5.37

11.3 11.1 10.8 10.5 10.2 9.92 9.66 9.41 9.16 8.71 8.29 7.90 7.54 7.19 6.57 6.03 5.56 5.15 11.5 11.2 11.1 10.9 10.7 10.5 10.3 10.2 9.98 9.67 9.38 9.10 8.85 8.61 8.15 7.72 7.31 6.93

13.2 12.9 12.6 12.3 12.0 11.7 11.4 11.2 10.9 10.4 9.96 9.53 9.13 8.75 8.05 7.44 6.90 6.42 13.4 13.2 13.0 12.8 12.6 12.4 12.2 12.0 11.9 11.5 11.2 10.9 10.7 10.4 9.90 9.43 8.99 8.57

15.2 14.8 14.5 14.1 13.8 13.5 13.2 12.9 12.6 12.1 11.7 11.2 10.8 10.4 9.60 8.93 8.32 7.78 15.4 15.1 14.9 14.7 14.5 14.3 14.1 13.9 13.7 13.4 13.1 12.8 12.5 12.2 11.7 11.2 10.7 10.3

17.1 16.7 16.3 16.0 15.7 15.3 15.0 14.7 14.4 13.9 13.4 12.9 12.5 12.0 11.2 10.5 9.81 9.21 17.6 17.1 16.9 16.6 16.4 16.2 16.0 15.8 15.6 15.3 15.0 14.6 14.3 14.0 13.5 13.0 12.5 12.0

19.0 18.6 18.2 17.9 17.5 17.2 16.9 16.5 16.2 15.7 15.2 14.7 14.2 13.7 12.9 12.1 11.4 10.7 19.6 19.0 18.8 18.6 18.4 18.1 17.9 17.7 17.6 17.2 16.8 16.5 16.2 15.9 15.3 14.8 14.3 13.8

20.9 20.5 20.1 19.8 19.4 19.1 18.7 18.4 18.1 17.5 16.9 16.4 15.9 15.4 14.5 13.7 12.9 12.2 21.5 21.0 20.8 20.5 20.3 20.1 19.9 19.7 19.5 19.1 18.7 18.4 18.1 17.7 17.1 16.6 16.1 15.5

22.9 22.5 22.1 21.7 21.3 20.9 20.6 20.3 19.9 19.3 18.7 18.2 17.7 17.2 16.2 15.4 14.6 13.8 23.5 23.0 22.7 22.5 22.2 22.0 21.8 21.6 21.4 21.0 20.6 20.3 19.9 19.6 19.0 18.4 17.9 17.3

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:35 AM

Page 48

7–48

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-9

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 1

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 C ⬘, in. 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 C ⬘, in.

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1.31 1.12 0.98 0.87 0.79 0.71 0.65 0.60 0.56 0.49 0.44 0.39 0.36 0.33 0.28 0.25 0.22 0.20 7.85 1.31 1.12 0.98 0.87 0.79 0.71 0.65 0.60 0.56 0.49 0.44 0.39 0.36 0.33 0.28 0.25 0.22 0.20 7.85

2

3

2.91 4.71 2.54 4.14 2.24 3.66 1.99 3.27 1.80 2.95 1.63 2.68 1.49 2.46 1.38 2.27 1.28 2.11 1.11 1.84 0.99 1.64 0.89 1.47 0.80 1.33 0.73 1.22 0.63 1.04 0.55 0.91 0.48 0.80 0.43 0.72 16.8 27.3 3.28 5.35 2.93 4.94 2.63 4.52 2.37 4.13 2.15 3.78 1.97 3.47 1.81 3.19 1.67 2.95 1.55 2.75 1.35 2.40 1.20 2.14 1.08 1.92 0.97 1.75 0.89 1.60 0.76 1.37 0.66 1.19 0.58 1.05 0.52 0.95 19.6 35.6

4

5

6

6.66 8.69 10.8 5.95 7.90 9.93 5.33 7.15 9.10 4.80 6.48 8.33 4.35 5.90 7.63 3.97 5.40 7.02 3.65 4.97 6.48 3.37 4.59 6.01 3.13 4.27 5.59 2.73 3.73 4.90 2.42 3.31 4.36 2.17 2.98 3.91 1.97 2.70 3.55 1.80 2.47 3.25 1.53 2.10 2.77 1.33 1.83 2.41 1.18 1.62 2.13 1.06 1.45 1.91 39.9 54.6 71.5 7.42 9.47 11.5 7.03 9.12 11.2 6.59 8.70 10.8 6.15 8.25 10.4 5.72 7.78 9.90 5.32 7.33 9.43 4.95 6.89 8.95 4.62 6.48 8.49 4.33 6.10 8.05 3.82 5.43 7.25 3.41 4.86 6.56 3.07 4.40 5.96 2.79 4.00 5.46 2.56 3.67 5.02 2.18 3.14 4.32 1.90 2.75 3.78 1.68 2.44 3.35 1.51 2.19 3.01 56.6 82.5 114

7

8

9

10

11

12

12.8 12.0 11.1 10.3 9.49 8.77 8.13 7.55 7.04 6.19 5.50 4.95 4.50 4.12 3.51 3.06 2.71 2.43 90.9 13.5 13.2 12.9 12.5 12.0 11.6 11.1 10.6 10.1 9.21 8.40 7.69 7.06 6.52 5.62 4.93 4.38 3.94 150

14.9 14.1 13.2 12.3 11.5 10.7 9.91 9.24 8.64 7.63 6.80 6.13 5.57 5.10 4.35 3.79 3.36 3.01 113 15.5 15.3 14.9 14.6 14.1 13.7 13.2 12.7 12.2 11.3 10.4 9.56 8.83 8.18 7.11 6.26 5.58 5.02 192

16.9 16.2 15.3 14.4 13.5 12.6 11.8 11.1 10.4 9.18 8.20 7.40 6.73 6.17 5.28 4.60 4.08 3.66 137 17.5 17.3 17.0 16.6 16.2 15.8 15.4 14.9 14.4 13.4 12.4 11.5 10.7 9.97 8.71 7.70 6.88 6.21 239

18.9 18.2 17.4 16.5 15.6 14.6 13.8 13.0 12.2 10.9 9.73 8.80 8.02 7.35 6.30 5.50 4.87 4.37 164 19.5 19.3 19.0 18.7 18.3 17.9 17.5 17.0 16.5 15.5 14.5 13.6 12.7 11.9 10.4 9.27 8.31 7.52 292

21.0 20.3 19.5 18.6 17.7 16.7 15.8 14.9 14.1 12.6 11.4 10.3 9.39 8.62 7.39 6.46 5.73 5.15 194 21.4 21.3 21.0 20.7 20.4 20.0 19.6 19.1 18.7 17.7 16.7 15.7 14.7 13.9 12.3 11.0 9.85 8.93 350

23.0 22.4 21.6 20.7 19.8 18.8 17.9 17.0 16.1 14.5 13.1 11.9 10.9 9.99 8.59 7.51 6.67 5.99 226 23.4 23.3 23.0 22.8 22.4 22.1 21.7 21.3 20.8 19.8 18.8 17.8 16.8 15.9 14.2 12.7 11.5 10.4 414

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:35 AM

Page 49

DESIGN TABLES

7–49

Table 7-9 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.35 1.16 1.02 0.90 0.81 0.74 0.68 0.63 0.58 0.51 0.45 0.41 0.37 0.34 0.29 0.25 0.23 0.20 1.35 1.16 1.02 0.90 0.81 0.74 0.68 0.63 0.58 0.51 0.45 0.41 0.37 0.34 0.29 0.25 0.23 0.20

2.96 2.58 2.28 2.03 1.84 1.67 1.53 1.42 1.31 1.15 1.02 0.91 0.83 0.76 0.65 0.56 0.50 0.45 3.29 2.94 2.64 2.38 2.17 1.99 1.83 1.69 1.58 1.38 1.23 1.10 1.00 0.92 0.78 0.68 0.60 0.54

4.75 4.20 3.73 3.35 3.03 2.76 2.53 2.34 2.17 1.90 1.69 1.51 1.37 1.26 1.07 0.93 0.83 0.74 5.33 4.93 4.52 4.15 3.82 3.52 3.25 3.02 2.81 2.47 2.20 1.98 1.80 1.65 1.41 1.23 1.09 0.97

6.67 5.98 5.37 4.85 4.40 4.02 3.70 3.43 3.19 2.79 2.48 2.23 2.02 1.85 1.58 1.37 1.22 1.09 7.39 6.99 6.55 6.12 5.70 5.31 4.95 4.63 4.34 3.84 3.44 3.11 2.83 2.60 2.23 1.95 1.73 1.55

8.67 7.90 7.17 6.53 5.96 5.48 5.05 4.68 4.36 3.82 3.40 3.05 2.77 2.54 2.16 1.89 1.67 1.50 9.42 9.05 8.63 8.18 7.72 7.28 6.86 6.46 6.10 5.45 4.91 4.46 4.08 3.75 3.22 2.82 2.50 2.25

10.7 9.89 9.08 8.34 7.66 7.06 6.53 6.07 5.66 4.97 4.43 3.99 3.63 3.32 2.84 2.47 2.19 1.96 11.4 11.1 10.7 10.3 9.80 9.33 8.87 8.43 8.00 7.23 6.56 5.99 5.49 5.06 4.36 3.83 3.41 3.07

12.7 11.9 11.1 10.3 9.48 8.79 8.17 7.61 7.12 6.28 5.61 5.05 4.60 4.21 3.60 3.14 2.78 2.49 13.4 13.1 12.8 12.4 11.9 11.4 11.0 10.5 10.0 9.15 8.38 7.69 7.09 6.56 5.70 5.02 4.47 4.03

14.8 14.0 13.1 12.2 11.4 10.6 9.91 9.27 8.69 7.69 6.88 6.21 5.66 5.19 4.45 3.88 3.44 3.09 15.4 15.2 14.8 14.4 14.0 13.5 13.1 12.6 12.1 11.2 10.3 9.52 8.82 8.20 7.15 6.32 5.64 5.09

16.8 16.0 15.2 14.3 13.4 12.6 11.8 11.0 10.4 9.23 8.29 7.50 6.84 6.28 5.39 4.71 4.18 3.75 17.4 17.2 16.9 16.5 16.1 15.6 15.2 14.7 14.2 13.2 12.3 11.5 10.7 9.96 8.74 7.76 6.96 6.30

18.8 18.1 17.3 16.3 15.4 14.5 13.7 12.9 12.2 10.9 9.79 8.88 8.11 7.45 6.40 5.61 4.98 4.47 19.4 19.2 18.9 18.5 18.2 17.7 17.3 16.8 16.3 15.3 14.4 13.5 12.6 11.8 10.4 9.31 8.38 7.60

20.9 20.2 19.3 18.4 17.5 16.6 15.7 14.8 14.0 12.6 11.4 10.4 9.48 8.73 7.52 6.59 5.86 5.27 21.4 21.2 20.9 20.6 20.2 19.8 19.4 18.9 18.4 17.4 16.5 15.5 14.6 13.8 12.2 11.0 9.90 9.01

22.9 22.2 21.4 20.5 19.6 18.6 17.7 16.8 16.0 14.4 13.1 11.9 11.0 10.1 8.71 7.64 6.80 6.12 23.4 23.2 22.9 22.6 22.3 21.9 21.5 21.0 20.5 19.6 18.6 17.6 16.6 15.7 14.1 12.7 11.5 10.5

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:35 AM

Page 50

7–50

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-9 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.49 1.29 1.13 1.00 0.90 0.82 0.75 0.70 0.65 0.57 0.50 0.45 0.41 0.38 0.32 0.28 0.25 0.23 1.49 1.29 1.13 1.00 0.90 0.82 0.75 0.70 0.65 0.57 0.50 0.45 0.41 0.38 0.32 0.28 0.25 0.23

3.12 2.74 2.43 2.18 1.98 1.81 1.67 1.55 1.44 1.26 1.12 1.01 0.92 0.84 0.72 0.63 0.56 0.50 3.36 3.02 2.73 2.48 2.27 2.09 1.93 1.80 1.68 1.49 1.33 1.20 1.09 1.00 0.86 0.75 0.67 0.60

4.91 4.39 3.95 3.58 3.26 2.99 2.76 2.56 2.38 2.09 1.86 1.67 1.52 1.39 1.19 1.04 0.92 0.83 5.36 4.97 4.60 4.26 3.96 3.68 3.43 3.21 3.01 2.67 2.39 2.16 1.97 1.81 1.55 1.35 1.20 1.08

6.80 6.16 5.60 5.10 4.67 4.30 3.97 3.69 3.44 3.03 2.71 2.44 2.22 2.03 1.74 1.52 1.35 1.21 7.37 6.99 6.58 6.18 5.80 5.44 5.11 4.81 4.53 4.05 3.65 3.31 3.03 2.80 2.41 2.12 1.89 1.70

8.75 8.04 7.37 6.77 6.23 5.76 5.35 4.98 4.66 4.13 3.69 3.33 3.03 2.78 2.38 2.08 1.84 1.66 9.38 9.01 8.61 8.18 7.76 7.36 6.97 6.61 6.27 5.67 5.15 4.71 4.34 4.01 3.48 3.06 2.73 2.46

10.7 9.98 9.24 8.55 7.93 7.37 6.87 6.42 6.02 5.34 4.78 4.33 3.95 3.62 3.11 2.72 2.41 2.17 11.4 11.0 10.7 10.2 9.79 9.35 8.93 8.53 8.14 7.43 6.81 6.27 5.79 5.37 4.68 4.13 3.69 3.34

12.7 12.0 11.2 10.4 9.72 9.08 8.49 7.96 7.49 6.66 5.99 5.44 4.97 4.57 3.93 3.44 3.06 2.75 13.4 13.1 12.7 12.3 11.8 11.4 11.0 10.5 10.1 9.31 8.60 7.96 7.39 6.89 6.04 5.36 4.81 4.36

14.7 14.0 13.2 12.4 11.6 10.9 10.2 9.62 9.07 8.12 7.33 6.66 6.10 5.62 4.84 4.24 3.77 3.40 15.4 15.1 14.7 14.3 13.9 13.5 13.0 12.6 12.1 11.3 10.5 9.76 9.12 8.53 7.53 6.72 6.05 5.50

16.7 16.0 15.2 14.3 13.5 12.8 12.0 11.4 10.8 9.67 8.75 7.98 7.32 6.75 5.83 5.13 4.57 4.11 17.4 17.1 16.7 16.4 15.9 15.5 15.1 14.6 14.2 13.3 12.4 11.7 10.9 10.3 9.14 8.19 7.40 6.74

18.7 18.0 17.2 16.3 15.5 14.7 13.9 13.2 12.5 11.3 10.3 9.39 8.64 7.98 6.92 6.09 5.43 4.89 19.3 19.1 18.8 18.4 18.0 17.6 17.1 16.7 16.2 15.3 14.4 13.6 12.8 12.1 10.8 9.76 8.86 8.09

20.8 20.0 19.2 18.4 17.5 16.7 15.9 15.1 14.4 13.0 11.9 10.9 10.1 9.30 8.08 7.12 6.36 5.74 21.3 21.1 20.8 20.4 20.0 19.6 19.2 18.7 18.3 17.4 16.5 15.6 14.8 14.0 12.6 11.4 10.4 9.53

22.7 22.1 21.3 20.4 19.5 18.7 17.8 17.0 16.2 14.8 13.6 12.5 11.5 10.7 9.32 8.24 7.37 6.66 23.3 23.1 22.8 22.4 22.1 21.7 21.2 20.8 20.4 19.4 18.5 17.6 16.8 15.9 14.5 13.2 12.0 11.1

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:35 AM

Page 51

DESIGN TABLES

7–51

Table 7-9 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.70 1.51 1.35 1.21 1.10 1.00 0.92 0.85 0.79 0.69 0.61 0.55 0.50 0.46 0.40 0.35 0.31 0.28 1.70 1.51 1.35 1.21 1.10 1.00 0.92 0.85 0.79 0.69 0.61 0.55 0.50 0.46 0.40 0.35 0.31 0.28

3.43 3.09 2.78 2.52 2.30 2.12 1.96 1.82 1.70 1.50 1.34 1.21 1.11 1.02 0.87 0.76 0.68 0.61 3.52 3.23 2.96 2.72 2.51 2.33 2.18 2.04 1.92 1.71 1.55 1.41 1.29 1.19 1.03 0.90 0.80 0.72

5.22 4.76 4.34 3.97 3.67 3.40 3.17 2.96 2.78 2.46 2.21 2.00 1.82 1.67 1.43 1.26 1.12 1.00 5.44 5.11 4.79 4.48 4.20 3.96 3.73 3.53 3.35 3.02 2.75 2.51 2.31 2.13 1.84 1.62 1.44 1.30

7.06 6.52 6.01 5.57 5.17 4.82 4.51 4.23 3.97 3.54 3.18 2.88 2.64 2.42 2.09 1.83 1.63 1.46 7.40 7.06 6.70 6.36 6.03 5.73 5.45 5.19 4.94 4.50 4.12 3.78 3.49 3.24 2.82 2.50 2.24 2.02

8.95 8.35 7.78 7.25 6.78 6.35 5.96 5.60 5.28 4.73 4.27 3.89 3.56 3.29 2.84 2.49 2.22 2.00 9.37 9.03 8.67 8.30 7.94 7.60 7.27 6.96 6.67 6.13 5.65 5.22 4.85 4.53 3.99 3.56 3.20 2.90

10.9 10.2 9.60 9.01 8.47 7.97 7.51 7.08 6.70 6.04 5.48 5.01 4.60 4.25 3.68 3.24 2.89 2.60 11.4 11.0 10.7 10.3 9.90 9.53 9.17 8.83 8.50 7.88 7.33 6.83 6.39 6.00 5.32 4.76 4.30 3.92

12.8 12.2 11.5 10.8 10.2 9.67 9.15 8.68 8.24 7.46 6.80 6.23 5.74 5.31 4.62 4.07 3.64 3.29 13.3 13.0 12.7 12.3 11.9 11.5 11.1 10.8 10.4 9.73 9.11 8.55 8.04 7.57 6.76 6.09 5.52 5.04

14.8 14.1 13.4 12.7 12.1 11.5 10.9 10.4 9.86 8.97 8.21 7.54 6.97 6.47 5.65 5.00 4.47 4.04 15.3 15.0 14.6 14.3 13.9 13.5 13.1 12.7 12.4 11.6 11.0 10.3 9.77 9.25 8.32 7.53 6.86 6.30

16.8 16.1 15.3 14.6 13.9 13.3 12.7 12.1 11.5 10.6 9.70 8.95 8.30 7.73 6.77 6.00 5.38 4.87 17.3 17.0 16.6 16.3 15.9 15.5 15.1 14.7 14.3 13.6 12.9 12.2 11.6 11.0 9.97 9.08 8.32 7.66

18.7 18.0 17.3 16.6 15.9 15.2 14.5 13.9 13.3 12.2 11.3 10.4 9.71 9.06 7.96 7.08 6.37 5.78 19.3 19.0 18.6 18.3 17.9 17.5 17.1 16.7 16.3 15.5 14.8 14.1 13.4 12.8 11.7 10.7 9.85 9.10

20.7 20.0 19.3 18.5 17.8 17.1 16.4 15.7 15.1 14.0 12.9 12.0 11.2 10.5 9.23 8.24 7.43 6.75 21.3 21.0 20.6 20.3 19.9 19.5 19.1 18.7 18.3 17.5 16.8 16.0 15.3 14.7 13.5 12.4 11.5 10.6

22.7 22.0 21.3 20.5 19.8 19.0 18.3 17.6 17.0 15.7 14.6 13.6 12.7 11.9 10.6 9.47 8.56 7.79 23.2 22.9 22.6 22.3 21.9 21.5 21.1 20.7 20.3 19.5 18.8 18.0 17.3 16.6 15.3 14.2 13.1 12.2

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:35 AM

Page 52

7–52

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-9 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.86 1.77 1.66 1.54 1.43 1.33 1.24 1.16 1.08 0.96 0.86 0.77 0.70 0.65 0.56 0.49 0.43 0.39 1.86 1.77 1.66 1.54 1.43 1.33 1.24 1.16 1.08 0.96 0.86 0.77 0.70 0.65 0.56 0.49 0.43 0.39

3.71 3.52 3.31 3.10 2.90 2.71 2.54 2.38 2.24 2.00 1.81 1.64 1.51 1.39 1.20 1.06 0.94 0.85 3.72 3.55 3.36 3.17 2.99 2.82 2.67 2.52 2.40 2.17 1.98 1.82 1.69 1.57 1.37 1.22 1.09 0.99

5.56 5.29 4.99 4.70 4.41 4.15 3.92 3.70 3.51 3.17 2.88 2.64 2.43 2.25 1.95 1.72 1.54 1.39 5.59 5.37 5.14 4.90 4.67 4.46 4.26 4.08 3.91 3.61 3.35 3.11 2.91 2.72 2.41 2.15 1.94 1.76

7.41 7.07 6.70 6.34 6.00 5.68 5.39 5.12 4.88 4.44 4.07 3.74 3.46 3.21 2.80 2.48 2.22 2.01 7.50 7.25 6.98 6.72 6.46 6.21 5.98 5.76 5.56 5.20 4.87 4.57 4.30 4.05 3.61 3.25 2.94 2.69

9.28 8.88 8.45 8.04 7.64 7.27 6.94 6.63 6.34 5.82 5.36 4.95 4.59 4.28 3.76 3.34 3.00 2.72 9.43 9.16 8.88 8.59 8.31 8.05 7.79 7.55 7.32 6.90 6.51 6.15 5.81 5.50 4.96 4.49 4.10 3.77

11.2 10.7 10.3 9.79 9.35 8.94 8.56 8.22 7.89 7.28 6.73 6.25 5.83 5.45 4.81 4.29 3.87 3.52 11.4 11.1 10.8 10.5 10.2 9.92 9.65 9.39 9.14 8.66 8.23 7.81 7.43 7.07 6.43 5.88 5.41 5.00

13.1 12.6 12.1 11.6 11.1 10.7 10.3 9.86 9.49 8.81 8.19 7.64 7.15 6.71 5.96 5.34 4.83 4.40 13.3 13.0 12.7 12.4 12.1 11.8 11.5 11.3 11.0 10.5 10.0 9.56 9.13 8.73 8.00 7.38 6.83 6.35

15.0 14.5 13.9 13.4 12.9 12.4 12.0 11.6 11.2 10.4 9.72 9.11 8.56 8.06 7.19 6.47 5.87 5.36 15.3 15.0 14.7 14.4 14.1 13.8 13.5 13.2 12.9 12.4 11.8 11.4 10.9 10.5 9.67 8.97 8.34 7.78

16.9 16.4 15.8 15.3 14.7 14.2 13.8 13.3 12.9 12.1 11.3 10.7 10.0 9.48 8.50 7.68 6.99 6.41 17.3 17.0 16.7 16.3 16.0 15.7 15.4 15.1 14.8 14.2 13.7 13.2 12.7 12.2 11.4 10.6 9.92 9.30

18.8 18.3 17.7 17.1 16.6 16.1 15.6 15.1 14.6 13.8 13.0 12.2 11.6 11.0 9.88 8.97 8.19 7.53 19.2 18.9 18.6 18.3 18.0 17.7 17.3 17.0 16.7 16.1 15.6 15.1 14.5 14.1 13.2 12.3 11.6 10.9

20.8 20.2 19.6 19.0 18.5 17.9 17.4 16.9 16.4 15.5 14.7 13.9 13.2 12.5 11.3 10.3 9.46 8.71 21.2 20.9 20.6 20.3 19.9 19.6 19.3 19.0 18.7 18.1 17.5 16.9 16.4 15.9 15.0 14.1 13.3 12.5

22.7 22.1 21.6 21.0 20.4 19.8 19.3 18.7 18.2 17.3 16.4 15.6 14.8 14.1 12.8 11.7 10.8 9.96 23.2 22.9 22.6 22.2 21.9 21.6 21.3 20.9 20.6 20.0 19.4 18.9 18.3 17.8 16.8 15.9 15.0 14.2

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:35 AM

Page 53

DESIGN TABLES

7–53

Table 7-9 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.94 1.92 1.89 1.85 1.81 1.76 1.71 1.66 1.61 1.51 1.41 1.31 1.23 1.15 1.01 0.90 0.81 0.73 1.94 1.92 1.89 1.85 1.81 1.76 1.71 1.66 1.61 1.51 1.41 1.31 1.23 1.15 1.01 0.90 0.81 0.73

3.87 3.82 3.75 3.67 3.59 3.50 3.40 3.30 3.20 3.01 2.82 2.65 2.48 2.34 2.08 1.87 1.69 1.54 3.86 3.80 3.74 3.66 3.58 3.49 3.40 3.31 3.22 3.05 2.88 2.73 2.58 2.45 2.21 2.01 1.84 1.70

5.79 5.70 5.60 5.48 5.35 5.22 5.08 4.94 4.80 4.53 4.27 4.03 3.80 3.60 3.23 2.93 2.67 2.45 5.77 5.68 5.57 5.46 5.35 5.23 5.12 5.00 4.89 4.67 4.46 4.26 4.08 3.90 3.59 3.32 3.08 2.87

7.70 7.58 7.43 7.28 7.11 6.94 6.76 6.59 6.42 6.08 5.76 5.47 5.19 4.93 4.48 4.08 3.75 3.45 7.68 7.55 7.42 7.29 7.15 7.01 6.88 6.74 6.61 6.36 6.12 5.89 5.68 5.47 5.10 4.77 4.47 4.19

9.61 9.45 9.26 9.07 8.87 8.67 8.46 8.26 8.06 7.67 7.31 6.96 6.64 6.34 5.80 5.33 4.91 4.55 9.60 9.45 9.29 9.14 8.98 8.83 8.68 8.53 8.38 8.10 7.84 7.59 7.35 7.13 6.71 6.32 5.97 5.64

11.5 11.3 11.1 10.9 10.6 10.4 10.2 9.96 9.73 9.30 8.90 8.52 8.16 7.82 7.20 6.65 6.17 5.74 11.5 11.4 11.2 11.0 10.8 10.7 10.5 10.4 10.2 9.89 9.61 9.33 9.08 8.84 8.38 7.96 7.56 7.19

13.4 13.2 12.9 12.7 12.4 12.2 11.9 11.7 11.4 11.0 10.5 10.1 9.73 9.36 8.67 8.06 7.51 7.01 13.5 13.3 13.1 12.9 12.7 12.5 12.4 12.2 12.0 11.7 11.4 11.1 10.8 10.6 10.1 9.65 9.21 8.80

15.3 15.1 14.8 14.5 14.2 14.0 13.7 13.4 13.2 12.7 12.2 11.8 11.3 10.9 10.2 9.52 8.91 8.36 15.4 15.2 15.0 14.8 14.6 14.4 14.3 14.1 13.9 13.6 13.3 12.9 12.7 12.4 11.9 11.4 10.9 10.5

17.3 17.0 16.7 16.4 16.1 15.8 15.5 15.2 14.9 14.4 13.9 13.4 13.0 12.6 11.8 11.0 10.4 9.77 17.6 17.2 16.9 16.7 16.5 16.3 16.2 16.0 15.8 15.4 15.1 14.8 14.5 14.2 13.6 13.1 12.7 12.2

19.2 18.9 18.5 18.2 17.9 17.6 17.3 17.0 16.7 16.2 15.6 15.2 14.7 14.2 13.4 12.6 11.9 11.2 19.6 19.1 18.9 18.7 18.5 18.3 18.1 17.9 17.7 17.3 17.0 16.6 16.3 16.0 15.5 14.9 14.4 13.9

21.1 20.8 20.4 20.1 19.8 19.4 19.1 18.8 18.5 17.9 17.4 16.9 16.4 15.9 15.0 14.2 13.5 12.8 21.5 21.1 20.8 20.6 20.4 20.2 20.0 19.8 19.6 19.2 18.9 18.5 18.2 17.9 17.3 16.7 16.2 15.7

23.0 22.7 22.3 22.0 21.6 21.3 21.0 20.6 20.3 19.7 19.2 18.6 18.1 17.7 16.7 15.9 15.1 14.3 23.5 23.0 22.8 22.6 22.3 22.1 21.9 21.7 21.5 21.1 20.8 20.4 20.1 19.7 19.1 18.5 18.0 17.5

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:35 AM

Page 54

7–54

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-10

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 1

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 C ⬘, in. 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 C ⬘, in.

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1.71 1.42 1.21 1.05 0.92 0.81 0.72 0.64 0.58 0.49 0.42 0.37 0.33 0.29 0.24 0.21 0.18 0.16 5.89 1.71 1.42 1.21 1.05 0.92 0.81 0.72 0.64 0.58 0.49 0.42 0.37 0.33 0.29 0.24 0.21 0.18 0.16 5.89

2

3

4.07 6.81 3.40 5.79 2.90 4.97 2.51 4.34 2.21 3.85 1.96 3.44 1.76 3.11 1.60 2.83 1.46 2.59 1.24 2.21 1.08 1.92 0.95 1.70 0.85 1.52 0.77 1.37 0.64 1.15 0.55 0.99 0.49 0.87 0.43 0.77 15.8 28.0 4.85 8.04 4.24 7.36 3.72 6.66 3.29 6.00 2.93 5.41 2.63 4.90 2.38 4.46 2.17 4.09 2.00 3.78 1.71 3.27 1.49 2.87 1.32 2.55 1.19 2.30 1.08 2.09 0.91 1.76 0.78 1.52 0.69 1.33 0.61 1.19 22.4 43.3

4

5

9.86 13.0 8.61 11.7 7.53 10.4 6.64 9.24 5.91 8.27 5.31 7.46 4.80 6.78 4.38 6.20 4.02 5.71 3.44 4.91 3.00 4.30 2.66 3.82 2.39 3.43 2.16 3.11 1.82 2.62 1.57 2.26 1.38 1.98 1.23 1.77 44.7 64.3 11.2 14.2 10.6 13.7 9.86 13.1 9.14 12.4 8.44 11.6 7.79 10.9 7.20 10.2 6.67 9.54 6.20 8.94 5.41 7.88 4.78 7.01 4.28 6.29 3.86 5.70 3.51 5.20 2.97 4.42 2.57 3.84 2.27 3.39 2.03 3.03 74.4 112

6

7

8

9

10

11

12

16.1 14.8 13.4 12.1 11.0 9.95 9.09 8.34 7.70 6.65 5.83 5.19 4.67 4.24 3.57 3.08 2.71 2.42 88.5 17.3 16.8 16.2 15.6 14.9 14.1 13.4 12.6 12.0 10.7 9.61 8.69 7.91 7.25 6.19 5.39 4.77 4.27 158

19.3 18.0 16.6 15.2 13.9 12.7 11.6 10.7 9.91 8.59 7.57 6.75 6.08 5.53 4.67 4.04 3.55 3.17 116 20.3 19.9 19.4 18.7 18.1 17.3 16.6 15.8 15.1 13.7 12.4 11.3 10.4 9.54 8.19 7.14 6.33 5.67 212

22.3 21.1 19.8 18.3 16.9 15.6 14.4 13.3 12.4 10.8 9.53 8.51 7.68 6.99 5.92 5.12 4.51 4.03 148 23.2 22.9 22.4 21.9 21.2 20.6 19.8 19.1 18.3 16.8 15.4 14.2 13.1 12.1 10.4 9.15 8.13 7.30 275

25.4 24.3 23.0 21.5 20.0 18.6 17.3 16.1 15.0 13.2 11.7 10.5 9.45 8.61 7.30 6.33 5.58 4.99 183 26.2 25.9 25.5 25.0 24.4 23.7 23.0 22.3 21.6 20.0 18.6 17.2 15.9 14.8 12.9 11.4 10.1 9.10 345

28.5 27.4 26.1 24.7 23.2 21.8 20.4 19.1 17.9 15.7 14.0 12.6 11.4 10.4 8.84 7.67 6.77 6.05 223 29.2 28.9 28.5 28.1 27.5 26.9 26.2 25.5 24.8 23.3 21.8 20.3 18.9 17.7 15.5 13.7 12.3 11.1 424

31.5 30.5 29.3 27.9 26.4 25.0 23.5 22.1 20.8 18.5 16.5 14.9 13.5 12.3 10.5 9.13 8.06 7.21 267 32.2 31.9 31.6 31.1 30.6 30.0 29.4 28.7 28.0 26.5 25.0 23.5 22.0 20.7 18.3 16.3 14.6 13.2 510

34.5 33.6 32.5 31.1 29.7 28.2 26.7 25.2 23.8 21.3 19.2 17.3 15.8 14.4 12.3 10.7 9.47 8.48 315 35.1 34.9 34.6 34.2 33.7 33.2 32.6 31.9 31.2 29.8 28.2 26.7 25.2 23.8 21.2 19.0 17.1 15.5 606

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:35 AM

Page 55

DESIGN TABLES

7–55

Table 7-10 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.77 1.47 1.25 1.08 0.94 0.83 0.74 0.66 0.60 0.50 0.43 0.38 0.34 0.30 0.25 0.22 0.19 0.17 1.77 1.47 1.25 1.08 0.94 0.83 0.74 0.66 0.60 0.50 0.43 0.38 0.34 0.30 0.25 0.22 0.19 0.17

4.10 3.45 2.95 2.57 2.26 2.01 1.81 1.64 1.50 1.28 1.11 0.98 0.88 0.79 0.67 0.57 0.50 0.45 4.83 4.22 3.71 3.28 2.94 2.65 2.40 2.20 2.02 1.74 1.52 1.35 1.22 1.10 0.93 0.80 0.71 0.63

6.84 5.86 5.07 4.44 3.93 3.52 3.18 2.90 2.65 2.27 1.98 1.75 1.57 1.42 1.19 1.02 0.90 0.80 7.98 7.31 6.64 6.01 5.45 4.97 4.55 4.18 3.86 3.34 2.94 2.62 2.36 2.14 1.81 1.56 1.37 1.23

9.82 8.61 7.55 6.67 5.96 5.37 4.87 4.45 4.10 3.52 3.08 2.73 2.45 2.22 1.87 1.61 1.42 1.26 11.1 10.5 9.77 9.06 8.38 7.75 7.17 6.66 6.20 5.43 4.82 4.32 3.91 3.57 3.03 2.63 2.32 2.08

12.9 11.6 10.4 9.26 8.33 7.55 6.88 6.31 5.81 5.01 4.40 3.91 3.52 3.19 2.69 2.32 2.04 1.82 14.1 13.6 12.9 12.2 11.5 10.8 10.1 9.49 8.92 7.91 7.07 6.38 5.79 5.30 4.52 3.93 3.47 3.11

16.0 14.7 13.3 12.1 11.0 9.97 9.13 8.40 7.77 6.74 5.93 5.29 4.77 4.33 3.66 3.17 2.79 2.49 17.2 16.7 16.1 15.4 14.7 13.9 13.2 12.5 11.9 10.6 9.60 8.71 7.95 7.31 6.26 5.47 4.85 4.35

19.1 17.8 16.4 15.1 13.8 12.7 11.7 10.8 9.99 8.71 7.69 6.87 6.20 5.65 4.78 4.14 3.65 3.26 20.2 19.7 19.2 18.5 17.8 17.1 16.4 15.6 14.9 13.6 12.4 11.3 10.4 9.60 8.28 7.26 6.45 5.80

22.2 20.9 19.5 18.1 16.8 15.5 14.4 13.3 12.4 10.9 9.62 8.62 7.80 7.12 6.04 5.24 4.62 4.13 23.2 22.8 22.3 21.7 21.0 20.3 19.6 18.8 18.1 16.6 15.3 14.1 13.0 12.1 10.5 9.24 8.23 7.41

25.2 24.1 22.7 21.3 19.8 18.5 17.2 16.1 15.0 13.2 11.8 10.6 9.59 8.76 7.45 6.47 5.72 5.11 26.1 25.8 25.3 24.8 24.1 23.5 22.7 22.0 21.3 19.8 18.4 17.0 15.8 14.8 12.9 11.4 10.2 9.23

28.3 27.2 25.8 24.4 23.0 21.5 20.2 18.9 17.8 15.8 14.1 12.7 11.5 10.5 8.99 7.82 6.92 6.20 29.1 28.8 28.3 27.8 27.2 26.6 25.9 25.2 24.5 23.0 21.5 20.1 18.8 17.6 15.5 13.8 12.4 11.2

31.3 30.3 29.0 27.6 26.1 24.7 23.2 21.9 20.7 18.4 16.5 15.0 13.6 12.5 10.7 9.31 8.24 7.38 32.1 31.8 31.4 30.9 30.3 29.7 29.1 28.4 27.6 26.1 24.6 23.2 21.8 20.5 18.2 16.3 14.7 13.3

34.3 33.3 32.1 30.7 29.3 27.8 26.4 25.0 23.6 21.2 19.1 17.4 15.9 14.6 12.5 10.9 9.66 8.66 35.0 34.8 34.4 33.9 33.4 32.8 32.2 31.5 30.8 29.3 27.8 26.3 24.9 23.5 21.1 18.9 17.1 15.6

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 56

7–56

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-10 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

1.94 1.61 1.37 1.19 1.04 0.92 0.82 0.74 0.67 0.56 0.48 0.42 0.38 0.34 0.28 0.24 0.21 0.19 1.94 1.61 1.37 1.19 1.04 0.92 0.82 0.74 0.67 0.56 0.48 0.42 0.38 0.34 0.28 0.24 0.21 0.19

4.26 3.63 3.15 2.77 2.45 2.19 1.98 1.80 1.65 1.41 1.23 1.08 0.97 0.88 0.74 0.64 0.56 0.50 4.86 4.27 3.78 3.39 3.06 2.78 2.54 2.34 2.16 1.87 1.65 1.47 1.33 1.21 1.02 0.88 0.78 0.70

6.99 6.09 5.35 4.74 4.23 3.81 3.45 3.16 2.90 2.49 2.18 1.93 1.73 1.57 1.32 1.14 1.00 0.89 7.96 7.32 6.70 6.14 5.64 5.19 4.80 4.45 4.14 3.61 3.20 2.86 2.58 2.35 2.00 1.73 1.52 1.36

9.90 8.80 7.83 7.00 6.30 5.71 5.22 4.79 4.42 3.82 3.36 2.99 2.69 2.44 2.06 1.78 1.57 1.40 11.0 10.4 9.75 9.10 8.48 7.91 7.38 6.90 6.46 5.71 5.10 4.60 4.19 3.84 3.29 2.86 2.54 2.27

12.9 11.7 10.6 9.54 8.67 7.92 7.27 6.71 6.22 5.41 4.78 4.26 3.85 3.50 2.96 2.56 2.26 2.02 14.1 13.5 12.9 12.2 11.5 10.9 10.3 9.67 9.14 8.20 7.41 6.74 6.17 5.68 4.89 4.28 3.80 3.41

16.0 14.7 13.5 12.3 11.3 10.4 9.58 8.88 8.26 7.22 6.40 5.73 5.18 4.73 4.01 3.48 3.07 2.75 17.1 16.6 15.9 15.3 14.6 13.9 13.3 12.6 12.0 10.9 9.95 9.12 8.39 7.75 6.71 5.90 5.25 4.73

19.0 17.7 16.5 15.2 14.1 13.0 12.1 11.2 10.5 9.23 8.22 7.40 6.71 6.14 5.22 4.54 4.01 3.59 20.1 19.6 19.0 18.4 17.7 17.0 16.3 15.7 15.0 13.8 12.7 11.7 10.8 10.1 8.78 7.77 6.95 6.28

22.0 20.8 19.5 18.2 17.0 15.8 14.8 13.8 12.9 11.5 10.3 9.25 8.41 7.70 6.58 5.73 5.07 4.54 23.1 22.6 22.1 21.5 20.8 20.1 19.4 18.7 18.1 16.8 15.6 14.5 13.5 12.6 11.1 9.83 8.83 8.00

25.1 23.9 22.6 21.2 19.9 18.7 17.6 16.5 15.5 13.8 12.4 11.3 10.3 9.42 8.08 7.05 6.25 5.61 26.0 25.6 25.1 24.5 23.9 23.2 22.6 21.9 21.2 19.8 18.5 17.3 16.2 15.2 13.5 12.1 10.9 9.88

28.1 27.0 25.7 24.3 23.0 21.7 20.5 19.3 18.2 16.4 14.8 13.4 12.3 11.3 9.72 8.51 7.55 6.78 29.0 28.6 28.1 27.6 27.0 26.3 25.7 25.0 24.3 22.9 21.5 20.3 19.1 18.0 16.1 14.5 13.1 11.9

31.1 30.0 28.7 27.4 26.0 24.7 23.4 22.2 21.1 19.0 17.2 15.7 14.4 13.3 11.5 10.1 8.96 8.06 32.0 31.6 31.1 30.6 30.1 29.4 28.8 28.1 27.4 26.0 24.6 23.3 22.0 20.9 18.8 17.0 15.4 14.1

34.1 33.1 31.8 30.5 29.1 27.8 26.4 25.2 24.0 21.8 19.8 18.2 16.7 15.4 13.4 11.8 10.5 9.44 35.0 34.6 34.2 33.7 33.1 32.5 31.9 31.2 30.5 29.1 27.7 26.4 25.0 23.8 21.6 19.6 17.9 16.4

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 57

DESIGN TABLES

7–57

Table 7-10 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

2.23 1.89 1.63 1.42 1.25 1.11 0.99 0.90 0.81 0.68 0.59 0.52 0.46 0.41 0.35 0.30 0.26 0.23 2.23 1.89 1.63 1.42 1.25 1.11 0.99 0.90 0.81 0.68 0.59 0.52 0.46 0.41 0.35 0.30 0.26 0.23

4.67 4.06 3.57 3.17 2.84 2.57 2.33 2.13 1.96 1.68 1.47 1.31 1.17 1.06 0.90 0.77 0.68 0.61 5.02 4.50 4.05 3.68 3.36 3.09 2.86 2.65 2.47 2.16 1.92 1.72 1.56 1.43 1.22 1.06 0.94 0.84

7.33 6.50 5.84 5.27 4.78 4.36 3.99 3.68 3.40 2.95 2.59 2.31 2.08 1.89 1.60 1.38 1.22 1.08 8.01 7.44 6.89 6.40 5.96 5.57 5.22 4.90 4.61 4.11 3.69 3.34 3.04 2.79 2.38 2.08 1.84 1.65

10.2 9.19 8.36 7.63 6.99 6.42 5.92 5.49 5.10 4.46 3.95 3.54 3.20 2.92 2.48 2.15 1.90 1.69 11.0 10.4 9.86 9.30 8.78 8.29 7.84 7.43 7.04 6.35 5.76 5.25 4.82 4.44 3.84 3.37 3.00 2.71

13.1 12.0 11.1 10.2 9.40 8.70 8.09 7.54 7.05 6.22 5.55 4.99 4.54 4.15 3.54 3.08 2.72 2.44 14.0 13.5 12.9 12.3 11.7 11.2 10.6 10.2 9.69 8.85 8.11 7.47 6.91 6.43 5.62 4.98 4.46 4.04

16.0 14.9 13.9 12.9 12.0 11.2 10.5 9.80 9.21 8.19 7.35 6.65 6.06 5.56 4.76 4.16 3.68 3.30 17.0 16.5 15.9 15.3 14.7 14.1 13.6 13.0 12.5 11.6 10.7 9.94 9.26 8.66 7.64 6.81 6.12 5.56

19.0 17.9 16.8 15.7 14.7 13.8 13.0 12.2 11.6 10.4 9.34 8.49 7.77 7.15 6.15 5.39 4.79 4.30 20.0 19.5 18.9 18.3 17.7 17.1 16.5 16.0 15.4 14.4 13.4 12.6 11.8 11.1 9.84 8.82 7.97 7.27

22.0 20.9 19.7 18.6 17.6 16.6 15.7 14.8 14.0 12.7 11.5 10.5 9.64 8.90 7.70 6.77 6.03 5.42 23.0 22.5 21.9 21.3 20.7 20.1 19.5 19.0 18.4 17.3 16.2 15.3 14.4 13.6 12.2 11.0 10.0 9.18

25.0 23.9 22.7 21.5 20.4 19.4 18.4 17.5 16.6 15.1 13.8 12.7 11.7 10.8 9.39 8.28 7.39 6.66 25.9 25.5 24.9 24.4 23.8 23.2 22.6 22.0 21.4 20.2 19.1 18.1 17.2 16.3 14.7 13.4 12.2 11.2

28.0 26.9 25.7 24.5 23.4 22.3 21.2 20.3 19.3 17.7 16.2 14.9 13.8 12.8 11.2 9.91 8.87 8.02 28.9 28.4 27.9 27.4 26.8 26.2 25.6 25.0 24.4 23.2 22.1 21.0 20.0 19.0 17.3 15.8 14.6 13.4

31.0 29.9 28.7 27.5 26.3 25.2 24.1 23.1 22.1 20.3 18.7 17.3 16.1 15.0 13.1 11.7 10.5 9.49 31.9 31.4 30.9 30.4 29.8 29.2 28.6 28.0 27.4 26.2 25.0 23.9 22.9 21.9 20.0 18.4 17.0 15.7

33.9 32.9 31.7 30.5 29.3 28.2 27.0 26.0 24.9 23.0 21.3 19.8 18.5 17.2 15.2 13.5 12.2 11.1 34.8 34.4 33.9 33.4 32.8 32.3 31.7 31.1 30.4 29.2 28.0 26.9 25.8 24.7 22.8 21.1 19.5 18.1

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 58

7–58

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-10 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

2.59 2.32 2.07 1.84 1.65 1.49 1.35 1.23 1.12 0.95 0.83 0.73 0.65 0.59 0.49 0.42 0.37 0.33 2.59 2.32 2.07 1.84 1.65 1.49 1.35 1.23 1.12 0.95 0.83 0.73 0.65 0.59 0.49 0.42 0.37 0.33

5.21 4.73 4.29 3.90 3.56 3.27 3.01 2.78 2.58 2.25 1.98 1.77 1.60 1.46 1.24 1.07 0.95 0.85 5.32 4.94 4.57 4.25 3.95 3.69 3.46 3.25 3.06 2.73 2.46 2.23 2.04 1.88 1.63 1.43 1.27 1.15

7.88 7.27 6.69 6.18 5.73 5.32 4.95 4.63 4.34 3.84 3.43 3.09 2.81 2.57 2.20 1.91 1.69 1.51 8.17 7.73 7.31 6.91 6.55 6.22 5.92 5.64 5.39 4.92 4.52 4.18 3.87 3.60 3.15 2.79 2.49 2.25

10.6 9.91 9.23 8.63 8.08 7.59 7.13 6.71 6.33 5.67 5.11 4.64 4.24 3.90 3.35 2.93 2.60 2.34 11.1 10.6 10.2 9.73 9.32 8.94 8.58 8.25 7.94 7.37 6.85 6.39 5.97 5.59 4.94 4.41 3.97 3.61

13.4 12.7 11.9 11.2 10.6 10.0 9.48 8.98 8.52 7.70 7.00 6.40 5.89 5.44 4.72 4.15 3.70 3.34 14.0 13.5 13.1 12.6 12.2 11.8 11.4 11.0 10.6 9.97 9.36 8.80 8.28 7.81 6.99 6.31 5.74 5.26

16.3 15.5 14.6 13.9 13.2 12.6 12.0 11.4 10.9 9.91 9.08 8.36 7.73 7.19 6.27 5.55 4.97 4.49 17.0 16.5 16.0 15.5 15.1 14.6 14.2 13.8 13.4 12.7 12.0 11.4 10.8 10.2 9.25 8.44 7.74 7.13

19.2 18.3 17.5 16.6 15.9 15.2 14.5 13.9 13.3 12.3 11.3 10.5 9.74 9.09 7.99 7.10 6.38 5.79 19.9 19.4 19.0 18.5 18.0 17.5 17.1 16.7 16.3 15.5 14.7 14.0 13.4 12.8 11.7 10.7 9.90 9.17

22.1 21.2 20.3 19.5 18.7 17.9 17.2 16.5 15.9 14.7 13.7 12.7 11.9 11.1 9.85 8.81 7.95 7.23 22.9 22.4 21.9 21.4 20.9 20.5 20.0 19.6 19.1 18.3 17.5 16.8 16.1 15.4 14.2 13.1 12.2 11.4

25.0 24.1 23.2 22.3 21.5 20.7 19.9 19.2 18.5 17.3 16.1 15.1 14.2 13.3 11.9 10.7 9.65 8.81 25.8 25.4 24.9 24.4 23.9 23.4 22.9 22.5 22.0 21.2 20.3 19.6 18.8 18.1 16.8 15.7 14.6 13.7

28.0 27.0 26.1 25.2 24.3 23.5 22.7 22.0 21.2 19.9 18.7 17.5 16.5 15.6 14.0 12.6 11.5 10.5 28.8 28.3 27.8 27.4 26.9 26.4 25.9 25.4 24.9 24.1 23.2 22.4 21.6 20.9 19.5 18.2 17.1 16.1

30.9 30.0 29.0 28.1 27.2 26.3 25.5 24.7 24.0 22.6 21.3 20.1 19.0 17.9 16.2 14.7 13.4 12.3 31.8 31.3 30.8 30.3 29.8 29.3 28.8 28.4 27.9 27.0 26.1 25.3 24.4 23.7 22.2 20.9 19.7 18.6

33.9 32.9 32.0 31.0 30.1 29.2 28.4 27.6 26.8 25.3 23.9 22.6 21.5 20.4 18.5 16.8 15.4 14.2 34.7 34.3 33.8 33.3 32.8 32.3 31.8 31.3 30.8 29.9 29.0 28.1 27.3 26.5 25.0 23.6 22.3 21.1

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 59

DESIGN TABLES

7–59

Table 7-10 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

2.86 2.77 2.66 2.53 2.40 2.26 2.13 2.00 1.89 1.67 1.49 1.34 1.21 1.10 0.93 0.80 0.71 0.63 2.86 2.77 2.66 2.53 2.40 2.26 2.13 2.00 1.89 1.67 1.49 1.34 1.21 1.10 0.93 0.80 0.71 0.63

5.68 5.49 5.27 5.04 4.81 4.57 4.35 4.13 3.93 3.57 3.25 2.97 2.73 2.53 2.19 1.93 1.72 1.55 5.66 5.49 5.30 5.10 4.91 4.72 4.54 4.37 4.21 3.90 3.63 3.39 3.17 2.98 2.65 2.38 2.16 1.97

8.47 8.19 7.89 7.58 7.27 6.97 6.69 6.41 6.15 5.67 5.25 4.87 4.54 4.24 3.75 3.34 3.01 2.74 8.48 8.25 8.02 7.79 7.56 7.34 7.14 6.94 6.75 6.39 6.06 5.75 5.47 5.22 4.76 4.37 4.03 3.73

11.3 10.9 10.5 10.2 9.81 9.47 9.13 8.82 8.51 7.95 7.44 6.98 6.56 6.18 5.52 4.97 4.51 4.12 11.3 11.1 10.8 10.6 10.3 10.1 9.83 9.61 9.40 9.00 8.63 8.29 7.96 7.66 7.10 6.60 6.15 5.75

14.1 13.7 13.2 12.8 12.4 12.0 11.7 11.3 11.0 10.4 9.77 9.23 8.74 8.28 7.48 6.79 6.20 5.70 14.2 13.9 13.6 13.4 13.1 12.9 12.6 12.4 12.1 11.7 11.3 10.9 10.6 10.2 9.57 8.99 8.45 7.96

16.9 16.4 16.0 15.5 15.1 14.7 14.3 13.9 13.5 12.9 12.2 11.6 11.1 10.5 9.59 8.78 8.08 7.47 17.1 16.8 16.5 16.2 15.9 15.7 15.4 15.2 14.9 14.4 14.0 13.6 13.2 12.9 12.2 11.5 10.9 10.3

19.8 19.2 18.8 18.3 17.8 17.4 16.9 16.5 16.1 15.4 14.7 14.1 13.5 12.9 11.8 10.9 10.1 9.40 20.1 19.7 19.4 19.1 18.8 18.5 18.3 18.0 17.7 17.2 16.8 16.3 15.9 15.5 14.8 14.1 13.4 12.8

22.6 22.1 21.6 21.0 20.6 20.1 19.6 19.2 18.8 18.0 17.3 16.6 16.0 15.3 14.2 13.2 12.3 11.5 23.0 22.7 22.3 22.0 21.7 21.4 21.1 20.8 20.6 20.0 19.6 19.1 18.7 18.2 17.5 16.7 16.0 15.3

25.5 24.9 24.4 23.9 23.3 22.9 22.4 21.9 21.5 20.7 19.9 19.2 18.5 17.8 16.6 15.5 14.5 13.6 26.4 25.6 25.2 24.9 24.6 24.3 24.0 23.7 23.4 22.9 22.4 21.9 21.4 21.0 20.2 19.4 18.7 17.9

28.4 27.8 27.2 26.7 26.2 25.6 25.1 24.7 24.2 23.4 22.6 21.8 21.1 20.4 19.1 17.9 16.8 15.9 29.3 28.5 28.2 27.8 27.5 27.2 26.9 26.6 26.3 25.7 25.2 24.7 24.2 23.8 22.9 22.1 21.3 20.6

31.3 30.7 30.1 29.5 29.0 28.4 27.9 27.4 27.0 26.1 25.3 24.5 23.7 23.0 21.6 20.4 19.2 18.2 32.3 31.5 31.1 30.8 30.4 30.1 29.8 29.5 29.2 28.6 28.1 27.5 27.0 26.6 25.7 24.8 24.0 23.3

34.2 33.6 33.0 32.4 31.8 31.3 30.7 30.2 29.8 28.8 28.0 27.2 26.4 25.6 24.2 22.9 21.7 20.6 35.2 34.4 34.0 33.7 33.3 33.0 32.7 32.4 32.1 31.5 30.9 30.4 29.9 29.4 28.5 27.6 26.8 26.0

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 60

7–60

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-11

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 1

3

6

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

2

3

2 2.15 4.55 7.17 3 1.91 4.06 6.43 4 1.71 3.65 5.80 5 1.55 3.31 5.27 6 1.42 3.02 4.82 7 1.31 2.77 4.44 8 1.21 2.56 4.10 9 1.12 2.38 3.81 10 1.05 2.21 3.55 12 0.92 1.94 3.12 14 0.81 1.72 2.77 16 0.72 1.53 2.48 18 0.64 1.38 2.25 20 0.58 1.26 2.05 24 0.49 1.06 1.73 28 0.42 0.92 1.50 32 0.37 0.81 1.32 36 0.33 0.72 1.18 C ⬘, in. 11.8 26.5 43.3 2 2.15 4.94 7.98 3 1.91 4.48 7.39 4 1.71 4.07 6.81 5 1.55 3.71 6.27 6 1.42 3.40 5.79 7 1.31 3.13 5.35 8 1.21 2.90 4.97 9 1.12 2.69 4.64 10 1.05 2.51 4.34 12 0.92 2.21 3.85 14 0.81 1.96 3.44 16 0.72 1.76 3.11 18 0.64 1.60 2.83 20 0.58 1.46 2.59 24 0.49 1.24 2.21 28 0.42 1.08 1.92 32 0.37 0.95 1.70 36 0.33 0.85 1.52 C ⬘, in. 11.8 31.6 56.1

4

5

10.0 13.0 9.06 11.9 8.23 10.9 7.51 9.97 6.88 9.16 6.34 8.46 5.87 7.85 5.46 7.31 5.09 6.84 4.48 6.03 3.99 5.38 3.58 4.84 3.25 4.40 2.96 4.02 2.52 3.42 2.19 2.97 1.93 2.63 1.72 2.35 63.7 86.8 11.1 14.2 10.5 13.6 9.86 13.0 9.22 12.3 8.61 11.7 8.05 11.0 7.53 10.4 7.07 9.78 6.64 9.24 5.91 8.27 5.31 7.46 4.80 6.78 4.38 6.20 4.02 5.71 3.44 4.91 3.00 4.30 2.66 3.82 2.39 3.43 89.4 129

6

7

8

9

10

11

12

16.0 14.9 13.7 12.7 11.7 10.8 10.1 9.39 8.79 7.78 6.95 6.27 5.70 5.21 4.45 3.87 3.42 3.06 114 17.2 16.7 16.1 15.5 14.8 14.1 13.4 12.8 12.1 11.0 9.95 9.09 8.34 7.70 6.65 5.83 5.19 4.67 177

19.1 17.9 16.7 15.5 14.4 13.4 12.5 11.7 10.9 9.70 8.69 7.85 7.15 6.55 5.60 4.88 4.32 3.87 144 20.2 19.8 19.3 18.6 18.0 17.3 16.6 15.9 15.2 13.9 12.7 11.6 10.7 9.91 8.59 7.57 6.75 6.08 232

22.2 21.0 19.8 18.5 17.3 16.1 15.1 14.1 13.3 11.8 10.6 9.60 8.75 8.03 6.88 6.00 5.32 4.77 178 23.2 22.8 22.3 21.8 21.1 20.5 19.8 19.0 18.3 16.9 15.6 14.4 13.3 12.4 10.8 9.53 8.51 7.68 296

25.3 24.1 22.9 21.5 20.3 19.0 17.9 16.8 15.8 14.1 12.7 11.5 10.5 9.65 8.29 7.24 6.42 5.76 216 26.2 25.8 25.4 24.9 24.3 23.6 23.0 22.2 21.5 20.0 18.6 17.3 16.1 15.0 13.2 11.7 10.5 9.45 366

28.3 27.2 26.0 24.7 23.3 22.0 20.7 19.6 18.5 16.6 14.9 13.6 12.4 11.4 9.82 8.59 7.62 6.84 257 29.2 28.9 28.5 28.0 27.4 26.8 26.1 25.4 24.7 23.2 21.8 20.4 19.1 17.9 15.7 14.0 12.6 11.4 446

31.4 30.3 29.1 27.8 26.4 25.1 23.7 22.5 21.3 19.1 17.3 15.8 14.4 13.3 11.5 10.1 8.93 8.02 302 32.1 31.9 31.5 31.0 30.5 29.9 29.3 28.6 27.9 26.4 25.0 23.5 22.1 20.8 18.5 16.5 14.9 13.5 533

34.4 33.4 32.3 31.0 29.6 28.2 26.8 25.5 24.2 21.9 19.9 18.1 16.6 15.3 13.2 11.6 10.3 9.29 352 35.1 34.8 34.5 34.1 33.6 33.1 32.5 31.8 31.1 29.7 28.2 26.7 25.2 23.8 21.3 19.2 17.3 15.8 629

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 61

DESIGN TABLES

7–61

Table 7-11 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

2.22 1.97 1.77 1.61 1.47 1.35 1.25 1.16 1.08 0.94 0.83 0.74 0.66 0.60 0.50 0.43 0.38 0.34 2.22 1.97 1.77 1.61 1.47 1.35 1.25 1.16 1.08 0.94 0.83 0.74 0.66 0.60 0.50 0.43 0.38 0.34

4.62 4.13 3.72 3.38 3.10 2.85 2.63 2.44 2.28 2.00 1.77 1.58 1.43 1.30 1.10 0.95 0.84 0.75 4.97 4.50 4.10 3.75 3.45 3.18 2.95 2.75 2.57 2.26 2.01 1.81 1.64 1.50 1.28 1.11 0.98 0.88

7.25 6.53 5.91 5.39 4.93 4.54 4.21 3.91 3.65 3.20 2.85 2.56 2.31 2.11 1.79 1.55 1.37 1.22 7.97 7.40 6.84 6.32 5.86 5.44 5.07 4.73 4.44 3.93 3.52 3.18 2.90 2.65 2.27 1.98 1.75 1.57

10.1 9.13 8.31 7.60 6.98 6.45 5.98 5.57 5.21 4.59 4.09 3.68 3.34 3.05 2.59 2.25 1.99 1.78 11.0 10.5 9.82 9.20 8.61 8.06 7.55 7.09 6.67 5.96 5.37 4.87 4.45 4.10 3.52 3.08 2.73 2.45

13.0 11.9 10.9 10.1 9.28 8.59 7.98 7.45 6.97 6.16 5.50 4.96 4.51 4.13 3.52 3.06 2.70 2.42 14.1 13.5 12.9 12.3 11.6 11.0 10.4 9.78 9.26 8.33 7.55 6.88 6.31 5.81 5.01 4.40 3.91 3.52

16.0 14.9 13.7 12.7 11.8 10.9 10.2 9.51 8.92 7.91 7.08 6.40 5.83 5.34 4.56 3.98 3.52 3.15 17.1 16.6 16.0 15.4 14.7 14.0 13.3 12.7 12.1 11.0 9.97 9.13 8.40 7.77 6.74 5.93 5.29 4.77

19.0 17.9 16.7 15.5 14.4 13.5 12.6 11.8 11.1 9.84 8.84 8.00 7.30 6.70 5.74 5.01 4.43 3.98 20.1 19.7 19.1 18.5 17.8 17.1 16.4 15.7 15.1 13.8 12.7 11.7 10.8 9.99 8.71 7.69 6.87 6.20

22.1 20.9 19.7 18.4 17.2 16.1 15.1 14.2 13.4 11.9 10.8 9.75 8.91 8.19 7.03 6.15 5.45 4.89 23.1 22.7 22.2 21.6 20.9 20.3 19.5 18.8 18.1 16.8 15.5 14.4 13.3 12.4 10.9 9.62 8.62 7.80

25.1 24.0 22.7 21.4 20.2 19.0 17.8 16.8 15.9 14.2 12.8 11.7 10.7 9.82 8.45 7.40 6.57 5.90 26.1 25.7 25.2 24.7 24.1 23.4 22.7 22.0 21.3 19.8 18.5 17.2 16.1 15.0 13.2 11.8 10.6 9.59

28.2 27.1 25.8 24.5 23.2 21.9 20.7 19.5 18.5 16.6 15.0 13.7 12.6 11.6 10.0 8.77 7.79 7.01 29.1 28.7 28.3 27.8 27.2 26.5 25.8 25.1 24.4 23.0 21.5 20.2 18.9 17.8 15.8 14.1 12.7 11.5

31.2 30.1 28.9 27.6 26.2 24.9 23.6 22.4 21.2 19.2 17.4 15.9 14.6 13.5 11.7 10.2 9.12 8.20 32.1 31.7 31.3 30.8 30.3 29.6 29.0 28.3 27.6 26.1 24.7 23.2 21.9 20.7 18.4 16.5 15.0 13.6

34.2 33.2 32.0 30.7 29.3 27.9 26.6 25.3 24.1 21.9 19.9 18.2 16.8 15.5 13.4 11.8 10.5 9.49 35.0 34.7 34.3 33.9 33.3 32.7 32.1 31.4 30.7 29.3 27.8 26.4 25.0 23.6 21.2 19.1 17.4 15.9

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 62

7–62

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-11 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

2.40 2.15 1.94 1.76 1.61 1.49 1.37 1.28 1.19 1.04 0.92 0.82 0.74 0.67 0.56 0.48 0.42 0.38 2.40 2.15 1.94 1.76 1.61 1.49 1.37 1.28 1.19 1.04 0.92 0.82 0.74 0.67 0.56 0.48 0.42 0.38

4.89 4.40 3.99 3.65 3.35 3.10 2.87 2.67 2.49 2.19 1.95 1.75 1.58 1.44 1.22 1.06 0.93 0.83 5.11 4.66 4.26 3.92 3.63 3.38 3.15 2.95 2.77 2.45 2.19 1.98 1.80 1.65 1.41 1.23 1.08 0.97

7.53 6.84 6.24 5.74 5.29 4.90 4.55 4.24 3.97 3.50 3.12 2.81 2.55 2.33 1.98 1.72 1.52 1.36 8.05 7.51 6.99 6.52 6.09 5.70 5.35 5.03 4.74 4.23 3.81 3.45 3.16 2.90 2.49 2.18 1.93 1.73

10.3 9.45 8.69 8.02 7.42 6.89 6.42 6.00 5.63 4.98 4.46 4.03 3.66 3.35 2.86 2.49 2.20 1.97 11.1 10.5 9.90 9.34 8.80 8.30 7.83 7.40 7.00 6.30 5.71 5.22 4.79 4.42 3.82 3.36 2.99 2.69

13.2 12.2 11.3 10.5 9.72 9.06 8.47 7.94 7.47 6.64 5.97 5.40 4.92 4.52 3.87 3.37 2.99 2.68 14.1 13.5 12.9 12.3 11.7 11.1 10.6 10.0 9.54 8.67 7.92 7.27 6.71 6.22 5.41 4.78 4.26 3.85

16.1 15.1 14.0 13.1 12.2 11.4 10.7 10.1 9.49 8.48 7.64 6.93 6.33 5.82 5.00 4.37 3.88 3.48 17.1 16.5 16.0 15.3 14.7 14.1 13.5 12.9 12.3 11.3 10.4 9.58 8.88 8.26 7.22 6.40 5.73 5.18

19.1 18.0 16.9 15.8 14.8 13.9 13.1 12.4 11.7 10.5 9.46 8.61 7.89 7.27 6.26 5.48 4.87 4.38 20.1 19.6 19.0 18.4 17.7 17.1 16.5 15.8 15.2 14.1 13.0 12.1 11.2 10.5 9.23 8.22 7.40 6.71

22.1 21.0 19.8 18.7 17.6 16.6 15.6 14.8 14.0 12.6 11.4 10.4 9.59 8.85 7.65 6.71 5.97 5.38 23.0 22.6 22.0 21.5 20.8 20.2 19.5 18.8 18.2 17.0 15.8 14.8 13.8 12.9 11.5 10.3 9.25 8.41

25.1 24.0 22.8 21.6 20.4 19.3 18.3 17.4 16.5 14.9 13.6 12.4 11.4 10.6 9.16 8.06 7.18 6.47 26.0 25.6 25.1 24.5 23.9 23.2 22.6 21.9 21.2 19.9 18.7 17.6 16.5 15.5 13.8 12.4 11.3 10.3

28.1 27.0 25.8 24.6 23.4 22.2 21.1 20.0 19.1 17.3 15.8 14.5 13.4 12.4 10.8 9.51 8.49 7.66 29.0 28.6 28.1 27.6 27.0 26.3 25.7 25.0 24.3 23.0 21.7 20.5 19.3 18.2 16.4 14.8 13.4 12.3

31.1 30.0 28.8 27.6 26.3 25.1 23.9 22.8 21.8 19.9 18.2 16.7 15.5 14.4 12.5 11.1 9.91 8.95 32.0 31.6 31.1 30.6 30.0 29.4 28.7 28.1 27.4 26.0 24.7 23.4 22.2 21.1 19.0 17.2 15.7 14.4

34.1 33.0 31.9 30.6 29.3 28.1 26.9 25.7 24.6 22.5 20.7 19.1 17.7 16.4 14.4 12.8 11.4 10.3 34.9 34.6 34.1 33.6 33.1 32.5 31.8 31.2 30.5 29.1 27.8 26.4 25.2 24.0 21.8 19.8 18.2 16.7

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 63

DESIGN TABLES

7–63

Table 7-11 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

2.64 2.43 2.23 2.05 1.89 1.75 1.63 1.52 1.42 1.25 1.11 0.99 0.90 0.81 0.68 0.59 0.52 0.46 2.64 2.43 2.23 2.05 1.89 1.75 1.63 1.52 1.42 1.25 1.11 0.99 0.90 0.81 0.68 0.59 0.52 0.46

5.30 4.90 4.52 4.17 3.86 3.59 3.35 3.13 2.94 2.60 2.32 2.09 1.90 1.73 1.47 1.28 1.13 1.01 5.38 5.02 4.67 4.34 4.06 3.80 3.57 3.36 3.17 2.84 2.57 2.33 2.13 1.96 1.68 1.47 1.31 1.17

8.01 7.44 6.89 6.40 5.96 5.57 5.22 4.90 4.61 4.11 3.69 3.34 3.04 2.79 2.38 2.08 1.84 1.65 8.22 7.78 7.33 6.90 6.50 6.16 5.84 5.54 5.27 4.78 4.36 3.99 3.68 3.40 2.95 2.59 2.31 2.08

10.8 10.1 9.38 8.75 8.20 7.70 7.25 6.83 6.45 5.78 5.21 4.74 4.33 3.98 3.42 2.99 2.65 2.38 11.1 10.7 10.2 9.66 9.19 8.76 8.36 7.99 7.63 6.99 6.42 5.92 5.49 5.10 4.46 3.95 3.54 3.20

13.6 12.8 12.0 11.2 10.6 9.99 9.43 8.91 8.44 7.60 6.90 6.29 5.77 5.33 4.60 4.03 3.59 3.23 14.1 13.6 13.1 12.5 12.0 11.5 11.1 10.6 10.2 9.40 8.70 8.09 7.54 7.05 6.22 5.55 4.99 4.54

16.4 15.6 14.7 13.9 13.1 12.4 11.7 11.1 10.6 9.58 8.73 8.00 7.36 6.81 5.91 5.20 4.63 4.17 17.0 16.6 16.0 15.5 14.9 14.4 13.9 13.4 12.9 12.0 11.2 10.5 9.80 9.21 8.19 7.35 6.65 6.06

19.3 18.4 17.5 16.6 15.7 14.9 14.2 13.5 12.8 11.7 10.7 9.85 9.10 8.44 7.35 6.49 5.80 5.23 20.0 19.5 19.0 18.4 17.9 17.3 16.8 16.2 15.7 14.7 13.8 13.0 12.2 11.6 10.4 9.34 8.49 7.77

22.3 21.3 20.3 19.3 18.4 17.5 16.7 15.9 15.2 14.0 12.8 11.8 11.0 10.2 8.91 7.90 7.07 6.40 23.0 22.5 22.0 21.4 20.9 20.3 19.7 19.2 18.6 17.6 16.6 15.7 14.8 14.0 12.7 11.5 10.5 9.64

25.2 24.2 23.2 22.2 21.2 20.2 19.3 18.5 17.7 16.3 15.0 13.9 12.9 12.1 10.6 9.42 8.46 7.67 25.9 25.5 25.0 24.4 23.9 23.3 22.7 22.1 21.5 20.4 19.4 18.4 17.5 16.6 15.1 13.8 12.7 11.7

28.1 27.1 26.1 25.0 24.0 23.0 22.1 21.2 20.3 18.8 17.4 16.1 15.0 14.1 12.4 11.1 9.95 9.04 28.9 28.5 28.0 27.4 26.9 26.3 25.7 25.1 24.5 23.4 22.3 21.2 20.3 19.3 17.7 16.2 14.9 13.8

31.1 30.1 29.0 27.9 26.9 25.8 24.8 23.9 23.0 21.3 19.8 18.5 17.3 16.2 14.3 12.8 11.6 10.5 31.9 31.4 31.0 30.4 29.9 29.3 28.7 28.1 27.5 26.3 25.2 24.1 23.1 22.1 20.3 18.7 17.3 16.1

34.0 33.1 32.0 30.9 29.8 28.7 27.7 26.7 25.7 23.9 22.3 20.9 19.5 18.4 16.3 14.6 13.3 12.1 34.8 34.4 33.9 33.4 32.9 32.3 31.7 31.1 30.5 29.3 28.2 27.0 26.0 24.9 23.0 21.3 19.8 18.5

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 64

7–64

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-11 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

2.83 2.72 2.59 2.46 2.32 2.19 2.07 1.95 1.84 1.65 1.49 1.35 1.23 1.12 0.95 0.83 0.73 0.65 2.83 2.72 2.59 2.46 2.32 2.19 2.07 1.95 1.84 1.65 1.49 1.35 1.23 1.12 0.95 0.83 0.73 0.65

5.64 5.43 5.18 4.92 4.66 4.41 4.17 3.95 3.74 3.38 3.06 2.79 2.55 2.35 2.02 1.76 1.56 1.40 5.64 5.44 5.21 4.97 4.73 4.51 4.29 4.09 3.90 3.56 3.27 3.01 2.78 2.58 2.25 1.98 1.77 1.60

8.45 8.13 7.77 7.40 7.03 6.68 6.35 6.04 5.75 5.22 4.76 4.37 4.02 3.72 3.22 2.84 2.53 2.27 8.47 8.19 7.88 7.57 7.27 6.97 6.69 6.43 6.18 5.73 5.32 4.95 4.63 4.34 3.84 3.43 3.09 2.81

11.3 10.8 10.4 9.92 9.46 9.02 8.61 8.22 7.86 7.19 6.61 6.09 5.64 5.24 4.57 4.04 3.61 3.26 11.3 11.0 10.6 10.3 9.91 9.56 9.23 8.92 8.63 8.08 7.59 7.13 6.71 6.33 5.67 5.11 4.64 4.24

14.1 13.6 13.0 12.5 12.0 11.4 11.0 10.5 10.1 9.28 8.58 7.95 7.39 6.90 6.06 5.39 4.84 4.38 14.2 13.8 13.4 13.1 12.7 12.3 11.9 11.5 11.2 10.6 10.0 9.48 8.98 8.52 7.70 7.00 6.40 5.89

16.9 16.3 15.7 15.1 14.5 13.9 13.4 12.9 12.4 11.5 10.7 9.93 9.28 8.69 7.68 6.86 6.19 5.62 17.1 16.7 16.3 15.9 15.5 15.0 14.6 14.3 13.9 13.2 12.6 12.0 11.4 10.9 9.91 9.08 8.36 7.73

19.8 19.1 18.5 17.8 17.1 16.5 15.9 15.3 14.8 13.8 12.9 12.0 11.3 10.6 9.43 8.47 7.66 6.98 20.0 19.6 19.2 18.8 18.3 17.9 17.5 17.0 16.6 15.9 15.2 14.5 13.9 13.3 12.3 11.3 10.5 9.74

22.6 21.9 21.2 20.5 19.8 19.1 18.4 17.8 17.3 16.2 15.2 14.2 13.4 12.6 11.3 10.2 9.26 8.46 23.0 22.6 22.1 21.7 21.2 20.8 20.3 19.9 19.5 18.7 17.9 17.2 16.5 15.9 14.7 13.7 12.7 11.9

25.5 24.8 24.0 23.2 22.5 21.8 21.1 20.4 19.8 18.6 17.5 16.5 15.6 14.8 13.3 12.0 11.0 10.1 25.9 25.5 25.0 24.6 24.1 23.7 23.2 22.8 22.3 21.5 20.7 19.9 19.2 18.5 17.3 16.1 15.1 14.2

28.4 27.6 26.8 26.0 25.2 24.5 23.7 23.0 22.4 21.1 20.0 18.9 17.9 17.0 15.4 14.0 12.8 11.7 28.9 28.4 28.0 27.5 27.0 26.6 26.1 25.6 25.2 24.3 23.5 22.7 22.0 21.2 19.9 18.7 17.5 16.5

31.3 30.5 29.7 28.9 28.0 27.2 26.5 25.7 25.0 23.7 22.5 21.3 20.3 19.3 17.5 16.0 14.7 13.5 31.8 31.4 30.9 30.4 30.0 29.5 29.0 28.6 28.1 27.2 26.3 25.5 24.7 24.0 22.6 21.3 20.1 19.0

34.2 33.4 32.5 31.7 30.8 30.0 29.2 28.5 27.7 26.3 25.0 23.8 22.7 21.7 19.8 18.1 16.7 15.4 34.8 34.3 33.9 33.4 32.9 32.4 32.0 31.5 31.0 30.1 29.2 28.4 27.6 26.8 25.3 23.9 22.6 21.5

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 65

DESIGN TABLES

7–65

Table 7-11 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

2.92 2.89 2.86 2.82 2.77 2.72 2.66 2.60 2.53 2.40 2.26 2.13 2.00 1.89 1.67 1.49 1.34 1.21 2.92 2.89 2.86 2.82 2.77 2.72 2.66 2.60 2.53 2.40 2.26 2.13 2.00 1.89 1.67 1.49 1.34 1.21

5.83 5.77 5.70 5.61 5.51 5.40 5.29 5.16 5.04 4.78 4.52 4.27 4.03 3.81 3.41 3.06 2.77 2.52 5.82 5.76 5.68 5.59 5.49 5.39 5.27 5.16 5.04 4.81 4.57 4.35 4.13 3.93 3.57 3.25 2.97 2.73

8.73 8.63 8.51 8.38 8.23 8.06 7.89 7.71 7.53 7.16 6.80 6.45 6.12 5.80 5.24 4.75 4.33 3.97 8.71 8.60 8.47 8.34 8.19 8.04 7.89 7.74 7.58 7.27 6.97 6.69 6.41 6.15 5.67 5.25 4.87 4.54

11.6 11.5 11.3 11.1 10.9 10.7 10.5 10.3 10.0 9.57 9.12 8.68 8.27 7.88 7.18 6.56 6.02 5.56 11.6 11.4 11.3 11.1 10.9 10.7 10.5 10.4 10.2 9.81 9.47 9.13 8.82 8.51 7.95 7.44 6.98 6.56

14.5 14.3 14.1 13.9 13.6 13.4 13.1 12.8 12.6 12.0 11.5 11.0 10.5 10.1 9.22 8.49 7.84 7.27 14.5 14.3 14.1 13.9 13.7 13.4 13.2 13.0 12.8 12.4 12.0 11.7 11.3 11.0 10.4 9.77 9.23 8.74

17.4 17.2 16.9 16.6 16.3 16.0 15.7 15.4 15.1 14.5 13.9 13.3 12.8 12.3 11.4 10.5 9.77 9.10 17.4 17.1 16.9 16.7 16.4 16.2 16.0 15.8 15.5 15.1 14.7 14.3 13.9 13.5 12.9 12.2 11.6 11.1

20.3 20.0 19.7 19.4 19.0 18.7 18.3 18.0 17.7 17.0 16.4 15.8 15.2 14.6 13.6 12.6 11.8 11.1 20.3 20.0 19.8 19.5 19.2 19.0 18.8 18.5 18.3 17.8 17.4 16.9 16.5 16.1 15.4 14.7 14.1 13.5

23.1 22.8 22.5 22.1 21.8 21.4 21.0 20.6 20.3 19.6 18.9 18.2 17.6 17.0 15.9 14.9 13.9 13.1 23.5 22.9 22.6 22.4 22.1 21.8 21.6 21.3 21.0 20.6 20.1 19.6 19.2 18.8 18.0 17.3 16.6 16.0

26.0 25.7 25.3 24.9 24.5 24.1 23.7 23.3 22.9 22.1 21.4 20.7 20.1 19.4 18.2 17.1 16.1 15.2 26.4 25.8 25.5 25.2 24.9 24.6 24.4 24.1 23.9 23.3 22.9 22.4 21.9 21.5 20.7 19.9 19.2 18.5

28.9 28.5 28.1 27.7 27.2 26.8 26.4 26.0 25.6 24.8 24.0 23.3 22.6 21.9 20.7 19.5 18.4 17.4 29.3 28.7 28.4 28.1 27.8 27.5 27.2 27.0 26.7 26.2 25.6 25.1 24.7 24.2 23.4 22.6 21.8 21.1

31.8 31.4 30.9 30.5 30.0 29.6 29.1 28.7 28.3 27.4 26.6 25.9 25.1 24.4 23.1 21.9 20.7 19.7 32.3 31.7 31.3 31.0 30.7 30.4 30.1 29.8 29.5 29.0 28.4 27.9 27.4 27.0 26.1 25.3 24.5 23.7

34.7 34.2 33.7 33.3 32.8 32.3 31.9 31.4 31.0 30.1 29.3 28.5 27.7 27.0 25.6 24.3 23.1 22.0 35.2 34.6 34.2 33.9 33.6 33.3 33.0 32.7 32.4 31.8 31.3 30.7 30.2 29.8 28.8 28.0 27.2 26.4

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 66

7–66

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-12

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 1

3

6

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

2

3

4

5

2 2.60 5.70 9.24 13.2 17.3 3 2.23 4.92 8.05 11.7 15.6 4 1.94 4.30 7.09 10.4 14.0 5 1.69 3.79 6.30 9.29 12.6 6 1.49 3.37 5.65 8.37 11.5 7 1.32 3.03 5.10 7.59 10.4 8 1.18 2.74 4.63 6.92 9.56 9 1.07 2.50 4.24 6.35 8.81 10 0.98 2.29 3.89 5.86 8.15 12 0.83 1.96 3.34 5.06 7.06 14 0.73 1.72 2.92 4.44 6.21 16 0.65 1.52 2.59 3.95 5.54 18 0.58 1.37 2.33 3.55 4.99 20 0.53 1.24 2.11 3.23 4.53 24 0.44 1.04 1.78 2.72 3.83 28 0.38 0.90 1.54 2.35 3.31 32 0.34 0.79 1.36 2.07 2.91 36 0.30 0.71 1.21 1.85 2.60 C ⬘, in. 11.3 26.0 44.7 68.1 96.0 2 2.60 6.48 10.7 14.8 18.9 3 2.23 5.75 9.79 14.0 18.2 4 1.94 5.12 8.91 13.1 17.4 5 1.69 4.58 8.10 12.2 16.4 6 1.49 4.13 7.37 11.3 15.5 7 1.32 3.74 6.74 10.5 14.5 8 1.18 3.41 6.20 9.73 13.6 9 1.07 3.13 5.73 9.05 12.8 10 0.98 2.89 5.31 8.45 12.0 12 0.83 2.50 4.63 7.43 10.7 14 0.73 2.19 4.09 6.60 9.53 16 0.65 1.95 3.65 5.93 8.59 18 0.58 1.76 3.29 5.37 7.81 20 0.53 1.60 2.99 4.90 7.15 24 0.44 1.35 2.53 4.16 6.10 28 0.38 1.17 2.19 3.61 5.31 32 0.34 1.03 1.93 3.19 4.69 36 0.30 0.92 1.72 2.85 4.20 C ⬘, in. 11.3 33.7 63.7 106 156

6

7

8

9

10

11

12

21.4 19.7 18.0 16.4 14.9 13.7 12.6 11.6 10.8 9.37 8.27 7.39 6.67 6.07 5.14 4.45 3.92 3.50 129 23.0 22.3 21.6 20.7 19.7 18.8 17.8 16.9 16.0 14.3 12.9 11.7 10.7 9.85 8.44 7.37 6.53 5.85 219

25.6 23.9 22.1 20.3 18.7 17.2 15.9 14.7 13.7 12.0 10.6 9.48 8.57 7.81 6.62 5.73 5.05 4.51 167 27.0 26.4 25.7 24.9 24.0 23.1 22.1 21.1 20.1 18.3 16.7 15.2 14.0 12.9 11.1 9.69 8.61 7.73 291

29.7 28.1 26.3 24.4 22.6 21.0 19.5 18.1 16.9 14.8 13.2 11.8 10.7 9.77 8.30 7.20 6.35 5.68 210 31.0 30.5 29.9 29.1 28.3 27.3 26.4 25.4 24.4 22.4 20.6 19.0 17.5 16.2 14.0 12.3 11.0 9.89 375

33.8 32.3 30.5 28.6 26.7 24.9 23.3 21.7 20.3 17.9 16.0 14.4 13.1 11.9 10.2 8.82 7.79 6.96 258 34.9 34.5 33.9 33.2 32.5 31.6 30.6 29.7 28.7 26.7 24.7 22.9 21.3 19.8 17.3 15.2 13.6 12.3 469

37.8 36.4 34.7 32.9 30.9 29.0 27.3 25.6 24.0 21.3 19.1 17.2 15.6 14.3 12.2 10.6 9.38 8.39 312 38.9 38.5 38.0 37.4 36.6 35.8 34.9 34.0 33.0 31.0 29.0 27.1 25.3 23.6 20.8 18.4 16.5 14.9 574

41.9 40.6 38.9 37.1 35.2 33.2 31.4 29.6 27.9 24.9 22.3 20.2 18.4 16.9 14.4 12.6 11.1 9.95 371 42.9 42.5 42.0 41.4 40.8 40.0 39.1 38.2 37.3 35.3 33.3 31.3 29.4 27.6 24.4 21.8 19.6 17.7 690

45.9 44.7 43.1 41.4 39.4 37.5 35.5 33.7 31.9 28.6 25.8 23.4 21.4 19.6 16.8 14.7 13.0 11.6 435 46.8 46.5 46.1 45.5 44.9 44.1 43.3 42.5 41.5 39.6 37.6 35.5 33.6 31.7 28.3 25.3 22.9 20.8 817

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 67

DESIGN TABLES

7–67

Table 7-12 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 1

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

2.68 2.30 1.99 1.74 1.53 1.36 1.22 1.11 1.01 0.86 0.75 0.67 0.60 0.54 0.46 0.40 0.35 0.31 2.68 2.30 1.99 1.74 1.53 1.36 1.22 1.11 1.01 0.86 0.75 0.67 0.60 0.54 0.46 0.40 0.35 0.31

2

3

5.77 9.31 5.00 8.17 4.38 7.22 3.88 6.43 3.45 5.77 3.10 5.21 2.81 4.74 2.57 4.34 2.36 4.00 2.02 3.44 1.77 3.01 1.57 2.68 1.41 2.40 1.28 2.18 1.08 1.84 0.93 1.59 0.82 1.40 0.73 1.25 6.48 10.6 5.75 9.75 5.13 8.91 4.61 8.14 4.17 7.45 3.79 6.84 3.46 6.30 3.19 5.83 2.94 5.42 2.55 4.73 2.24 4.18 2.00 3.74 1.80 3.38 1.64 3.08 1.39 2.60 1.20 2.26 1.06 1.99 0.94 1.78

4

5

6

7

8

9

10

11

12

13.2 11.7 10.4 9.37 8.47 7.71 7.05 6.48 5.98 5.18 4.55 4.05 3.65 3.32 2.80 2.43 2.14 1.91 14.7 13.9 13.0 12.1 11.2 10.4 9.71 9.05 8.47 7.47 6.66 6.00 5.45 4.98 4.25 3.69 3.26 2.92

17.2 15.6 14.1 12.7 11.6 10.6 9.70 8.95 8.29 7.21 6.36 5.67 5.12 4.66 3.94 3.41 3.00 2.68 18.8 18.1 17.2 16.3 15.3 14.4 13.6 12.8 12.0 10.7 9.62 8.71 7.94 7.28 6.23 5.43 4.81 4.31

21.3 19.6 17.9 16.4 15.0 13.7 12.7 11.7 10.9 9.52 8.43 7.54 6.81 6.21 5.26 4.56 4.03 3.60 22.9 22.2 21.4 20.5 19.5 18.6 17.6 16.7 15.9 14.3 12.9 11.8 10.8 9.92 8.54 7.48 6.65 5.97

25.4 23.7 21.9 20.2 18.6 17.2 15.9 14.8 13.8 12.1 10.8 9.66 8.74 7.98 6.78 5.89 5.19 4.65 26.9 26.3 25.5 24.7 23.7 22.8 21.8 20.9 19.9 18.2 16.6 15.2 14.0 13.0 11.2 9.85 8.77 7.89

29.5 27.8 26.0 24.2 22.5 20.9 19.5 18.1 17.0 15.0 13.3 12.0 10.9 9.95 8.47 7.37 6.51 5.83 30.9 30.3 29.6 28.8 27.9 27.0 26.0 25.1 24.1 22.2 20.5 18.9 17.5 16.2 14.1 12.5 11.1 10.0

33.6 32.0 30.2 28.3 26.5 24.8 23.2 21.7 20.4 18.1 16.1 14.6 13.3 12.1 10.4 9.02 7.98 7.15 34.8 34.3 33.7 33.0 32.1 31.2 30.3 29.3 28.3 26.4 24.5 22.8 21.2 19.8 17.3 15.4 13.8 12.5

37.6 36.1 34.4 32.5 30.6 28.8 27.1 25.5 24.0 21.4 19.2 17.3 15.8 14.5 12.4 10.8 9.59 8.59 38.8 38.3 37.7 37.1 36.3 35.4 34.5 33.5 32.6 30.6 28.6 26.8 25.1 23.5 20.8 18.5 16.6 15.1

41.7 40.2 38.5 36.7 34.8 32.9 31.1 29.4 27.7 24.9 22.4 20.3 18.6 17.1 14.6 12.8 11.3 10.2 42.8 42.3 41.8 41.1 40.4 39.6 38.7 37.8 36.8 34.8 32.8 30.9 29.1 27.4 24.4 21.8 19.7 17.9

45.7 44.3 42.7 40.9 39.0 37.1 35.2 33.4 31.6 28.5 25.8 23.5 21.5 19.8 17.0 14.9 13.2 11.9 46.7 46.3 45.8 45.2 44.5 43.7 42.9 42.0 41.0 39.1 37.1 35.1 33.2 31.4 28.1 25.3 22.9 20.9

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 68

7–68

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-12 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 1

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

2.90 2.50 2.18 1.91 1.69 1.51 1.36 1.23 1.13 0.96 0.84 0.74 0.67 0.61 0.51 0.44 0.39 0.35 2.90 2.50 2.18 1.91 1.69 1.51 1.36 1.23 1.13 0.96 0.84 0.74 0.67 0.61 0.51 0.44 0.39 0.35

2

3

6.06 9.59 5.31 8.52 4.70 7.62 4.18 6.85 3.75 6.19 3.38 5.63 3.07 5.14 2.81 4.73 2.59 4.37 2.23 3.78 1.95 3.32 1.73 2.96 1.56 2.66 1.42 2.42 1.20 2.04 1.03 1.77 0.91 1.56 0.81 1.39 6.59 10.6 5.88 9.83 5.30 9.05 4.81 8.35 4.38 7.72 4.01 7.15 3.69 6.64 3.41 6.19 3.16 5.79 2.76 5.09 2.44 4.54 2.18 4.08 1.97 3.70 1.80 3.38 1.53 2.87 1.32 2.49 1.17 2.20 1.05 1.97

4

5

6

7

8

9

10

11

12

13.4 12.1 10.9 9.86 8.98 8.21 7.55 6.97 6.46 5.62 4.96 4.43 4.00 3.65 3.09 2.68 2.36 2.11 14.7 13.9 13.0 12.2 11.4 10.7 10.0 9.41 8.85 7.88 7.08 6.41 5.85 5.37 4.61 4.02 3.57 3.21

17.3 15.8 14.4 13.2 12.1 11.1 10.3 9.54 8.88 7.78 6.90 6.19 5.60 5.11 4.34 3.77 3.32 2.97 18.7 18.0 17.1 16.3 15.4 14.6 13.8 13.0 12.4 11.1 10.1 9.21 8.45 7.80 6.74 5.91 5.26 4.73

21.3 19.7 18.2 16.8 15.5 14.3 13.3 12.4 11.6 10.2 9.08 8.17 7.41 6.77 5.77 5.01 4.43 3.97 22.7 22.0 21.2 20.4 19.5 18.6 17.7 16.9 16.1 14.7 13.4 12.3 11.4 10.5 9.16 8.07 7.20 6.49

25.3 23.7 22.1 20.5 19.1 17.8 16.6 15.5 14.5 12.9 11.5 10.4 9.46 8.67 7.41 6.46 5.71 5.12 26.7 26.1 25.3 24.5 23.6 22.7 21.8 20.9 20.1 18.5 17.0 15.7 14.6 13.6 11.9 10.5 9.45 8.55

29.4 27.8 26.1 24.4 22.9 21.4 20.0 18.8 17.7 15.8 14.2 12.9 11.7 10.8 9.22 8.05 7.14 6.40 30.7 30.1 29.4 28.6 27.7 26.8 25.9 25.0 24.1 22.4 20.8 19.4 18.1 16.9 14.9 13.3 11.9 10.8

33.4 31.8 30.1 28.4 26.8 25.2 23.7 22.3 21.1 18.9 17.1 15.5 14.2 13.1 11.2 9.83 8.72 7.84 34.7 34.1 33.5 32.7 31.8 31.0 30.0 29.1 28.2 26.4 24.7 23.2 21.7 20.4 18.1 16.2 14.6 13.3

37.4 35.9 34.2 32.5 30.7 29.1 27.5 26.0 24.7 22.2 20.1 18.4 16.8 15.5 13.4 11.8 10.5 9.41 38.7 38.1 37.5 36.8 35.9 35.1 34.2 33.3 32.4 30.5 28.8 27.1 25.5 24.1 21.5 19.4 17.6 16.0

41.4 40.0 38.3 36.6 34.8 33.1 31.4 29.8 28.3 25.7 23.4 21.4 19.7 18.2 15.7 13.9 12.3 11.1 42.6 42.1 41.5 40.8 40.0 39.2 38.3 37.4 36.5 34.6 32.8 31.1 29.4 27.9 25.1 22.7 20.7 18.9

45.4 44.0 42.4 40.7 38.9 37.1 35.4 33.7 32.2 29.3 26.8 24.6 22.7 21.0 18.2 16.1 14.4 13.0 46.6 46.1 45.5 44.9 44.1 43.3 42.4 41.6 40.6 38.8 36.9 35.1 33.4 31.8 28.8 26.2 23.9 22.0

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 69

DESIGN TABLES

7–69

Table 7-12 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 1

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

3.26 2.87 2.54 2.25 2.01 1.81 1.64 1.49 1.37 1.17 1.03 0.91 0.82 0.74 0.63 0.54 0.48 0.43 3.26 2.87 2.54 2.25 2.01 1.81 1.64 1.49 1.37 1.17 1.03 0.91 0.82 0.74 0.63 0.54 0.48 0.43

2

3

6.62 10.2 5.92 9.19 5.31 8.36 4.78 7.63 4.33 6.99 3.93 6.42 3.60 5.92 3.31 5.49 3.06 5.10 2.65 4.46 2.33 3.95 2.08 3.54 1.88 3.20 1.71 2.92 1.45 2.48 1.26 2.15 1.11 1.90 0.99 1.69 6.89 10.8 6.28 10.1 5.74 9.38 5.27 8.75 4.85 8.20 4.49 7.70 4.16 7.25 3.87 6.83 3.62 6.45 3.19 5.78 2.84 5.21 2.56 4.74 2.33 4.33 2.13 3.98 1.82 3.42 1.59 2.99 1.41 2.65 1.26 2.38

4

5

6

7

8

9

10

11

12

13.9 12.7 11.7 10.8 9.94 9.20 8.55 7.96 7.44 6.55 5.83 5.24 4.75 4.35 3.71 3.23 2.86 2.56 14.7 14.0 13.3 12.6 11.9 11.3 10.7 10.2 9.65 8.75 7.97 7.30 6.72 6.21 5.38 4.74 4.22 3.81

17.7 16.4 15.2 14.1 13.1 12.2 11.4 10.7 10.1 8.93 8.00 7.23 6.59 6.04 5.18 4.52 4.00 3.59 18.7 18.0 17.2 16.5 15.7 15.0 14.4 13.7 13.1 12.0 11.1 10.2 9.48 8.83 7.74 6.87 6.17 5.59

21.5 20.2 18.8 17.6 16.5 15.5 14.6 13.7 12.9 11.6 10.4 9.47 8.66 7.96 6.84 5.99 5.31 4.77 22.7 22.0 21.2 20.4 19.7 18.9 18.2 17.5 16.8 15.6 14.5 13.5 12.6 11.8 10.4 9.30 8.38 7.62

25.5 24.0 22.6 21.3 20.1 18.9 17.9 16.9 16.0 14.4 13.1 11.9 10.9 10.1 8.71 7.65 6.81 6.13 26.6 26.0 25.2 24.5 23.7 22.9 22.1 21.4 20.7 19.3 18.1 16.9 15.9 15.0 13.3 12.0 10.8 9.89

29.4 28.0 26.5 25.1 23.8 22.5 21.3 20.3 19.2 17.5 15.9 14.6 13.4 12.4 10.8 9.50 8.48 7.64 30.6 30.0 29.2 28.5 27.7 26.9 26.1 25.3 24.6 23.1 21.8 20.5 19.4 18.3 16.5 14.9 13.6 12.4

33.4 31.9 30.4 29.0 27.5 26.2 24.9 23.8 22.7 20.7 18.9 17.4 16.1 15.0 13.0 11.5 10.3 9.30 34.6 33.9 33.2 32.5 31.7 30.9 30.1 29.3 28.5 27.0 25.6 24.3 23.0 21.8 19.8 18.0 16.5 15.2

37.3 35.9 34.4 32.9 31.4 30.0 28.6 27.4 26.2 24.0 22.1 20.4 18.9 17.6 15.4 13.7 12.3 11.1 38.5 37.9 37.2 36.5 35.7 34.9 34.1 33.3 32.5 31.0 29.5 28.1 26.7 25.5 23.2 21.3 19.5 18.0

41.3 39.9 38.4 36.8 35.3 33.8 32.4 31.1 29.8 27.5 25.4 23.6 21.9 20.5 18.0 16.0 14.4 13.1 42.5 41.9 41.2 40.5 39.7 39.0 38.2 37.4 36.6 35.0 33.4 32.0 30.6 29.2 26.8 24.7 22.8 21.1

45.3 43.9 42.4 40.8 39.3 37.7 36.3 34.9 33.6 31.1 28.8 26.8 25.0 23.5 20.7 18.5 16.7 15.2 46.5 45.9 45.2 44.5 43.8 43.0 42.2 41.4 40.6 39.0 37.4 35.9 34.4 33.1 30.5 28.2 26.1 24.3

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 70

7–70

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-12 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

3.63 3.38 3.10 2.84 2.60 2.38 2.19 2.02 1.87 1.62 1.43 1.27 1.15 1.04 0.88 0.76 0.67 0.60 3.63 3.38 3.10 2.84 2.60 2.38 2.19 2.02 1.87 1.62 1.43 1.27 1.15 1.04 0.88 0.76 0.67 0.60

7.25 6.77 6.27 5.80 5.36 4.96 4.60 4.28 3.99 3.51 3.12 2.81 2.56 2.34 2.00 1.74 1.54 1.38 7.29 6.88 6.46 6.06 5.69 5.34 5.03 4.74 4.47 4.01 3.63 3.31 3.04 2.81 2.44 2.15 1.91 1.73

10.9 10.2 9.55 8.92 8.33 7.79 7.30 6.85 6.45 5.75 5.18 4.70 4.29 3.95 3.39 2.96 2.63 2.36 11.1 10.6 10.0 9.55 9.09 8.66 8.27 7.90 7.55 6.93 6.38 5.91 5.49 5.12 4.49 3.99 3.58 3.24

14.6 13.8 13.0 12.2 11.5 10.8 10.2 9.68 9.17 8.27 7.50 6.85 6.28 5.80 5.01 4.39 3.91 3.52 14.9 14.3 13.8 13.2 12.7 12.2 11.7 11.3 10.9 10.1 9.46 8.84 8.28 7.77 6.90 6.18 5.58 5.08

18.3 17.4 16.5 15.6 14.8 14.1 13.4 12.7 12.1 11.0 10.1 9.23 8.52 7.89 6.87 6.07 5.43 4.91 18.8 18.2 17.6 17.0 16.4 15.9 15.4 14.9 14.4 13.6 12.8 12.0 11.3 10.7 9.62 8.70 7.93 7.27

22.1 21.1 20.1 19.1 18.2 17.4 16.6 15.9 15.2 13.9 12.8 11.9 11.0 10.2 8.98 7.97 7.15 6.48 22.7 22.1 21.5 20.9 20.3 19.7 19.1 18.6 18.1 17.1 16.2 15.4 14.6 13.9 12.6 11.5 10.6 9.76

25.9 24.8 23.7 22.7 21.7 20.9 20.0 19.2 18.4 17.0 15.8 14.7 13.7 12.8 11.3 10.1 9.06 8.22 26.6 26.0 25.4 24.7 24.1 23.5 22.9 22.4 21.8 20.8 19.8 18.9 18.0 17.2 15.8 14.5 13.4 12.5

29.7 28.6 27.5 26.4 25.4 24.4 23.5 22.6 21.8 20.3 18.9 17.6 16.5 15.5 13.8 12.3 11.2 10.2 30.5 29.9 29.3 28.7 28.0 27.4 26.8 26.2 25.6 24.5 23.5 22.5 21.6 20.7 19.1 17.7 16.5 15.4

33.6 32.4 31.3 30.1 29.1 28.0 27.1 26.1 25.3 23.6 22.1 20.7 19.5 18.4 16.4 14.8 13.4 12.3 34.5 33.9 33.2 32.6 31.9 31.3 30.7 30.1 29.5 28.3 27.3 26.2 25.2 24.3 22.6 21.1 19.7 18.4

37.5 36.3 35.1 33.9 32.8 31.7 30.7 29.7 28.8 27.0 25.4 24.0 22.6 21.4 19.2 17.4 15.8 14.5 38.4 37.8 37.2 36.5 35.9 35.2 34.6 34.0 33.4 32.2 31.0 30.0 28.9 28.0 26.1 24.5 23.0 21.6

41.4 40.2 38.9 37.8 36.6 35.5 34.4 33.4 32.4 30.6 28.9 27.3 25.8 24.5 22.1 20.1 18.4 16.9 42.4 41.8 41.1 40.4 39.8 39.2 38.5 37.9 37.3 36.0 34.9 33.8 32.7 31.7 29.8 28.0 26.4 24.9

45.3 44.1 42.8 41.6 40.4 39.3 38.2 37.1 36.1 34.1 32.4 30.7 29.1 27.7 25.2 23.0 21.1 19.4 46.3 45.7 45.1 44.4 43.8 43.1 42.4 41.8 41.2 39.9 38.7 37.6 36.5 35.4 33.4 31.6 29.9 28.3

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 71

DESIGN TABLES

7–71

Table 7-12 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

3.86 3.79 3.70 3.59 3.47 3.34 3.20 3.07 2.94 2.68 2.45 2.24 2.06 1.90 1.63 1.43 1.27 1.14 3.86 3.79 3.70 3.59 3.47 3.34 3.20 3.07 2.94 2.68 2.45 2.24 2.06 1.90 1.63 1.43 1.27 1.14

7.69 7.53 7.34 7.13 6.89 6.65 6.40 6.16 5.91 5.45 5.03 4.65 4.31 4.01 3.51 3.11 2.79 2.53 7.67 7.51 7.32 7.12 6.92 6.70 6.49 6.28 6.08 5.69 5.33 4.99 4.69 4.42 3.95 3.57 3.25 2.98

11.5 11.2 11.0 10.6 10.3 9.98 9.64 9.31 8.98 8.36 7.79 7.28 6.81 6.40 5.69 5.11 4.62 4.22 11.5 11.2 11.0 10.7 10.4 10.2 9.92 9.66 9.42 8.95 8.51 8.10 7.72 7.36 6.74 6.21 5.74 5.33

15.3 14.9 14.6 14.2 13.8 13.4 12.9 12.6 12.2 11.4 10.7 10.1 9.55 9.03 8.13 7.36 6.71 6.15 15.3 15.0 14.7 14.4 14.1 13.8 13.5 13.2 12.9 12.4 11.9 11.4 11.0 10.6 9.83 9.16 8.56 8.02

19.1 18.6 18.2 17.7 17.2 16.8 16.3 15.9 15.4 14.6 13.8 13.1 12.5 11.9 10.8 9.83 9.02 8.31 19.1 18.8 18.4 18.1 17.7 17.4 17.1 16.8 16.5 15.9 15.4 14.9 14.4 13.9 13.1 12.3 11.6 11.0

22.9 22.4 21.8 21.3 20.8 20.3 19.8 19.3 18.8 17.9 17.1 16.3 15.5 14.8 13.6 12.5 11.5 10.7 23.0 22.6 22.2 21.8 21.5 21.1 20.8 20.5 20.2 19.5 19.0 18.4 17.9 17.4 16.5 15.6 14.8 14.1

26.7 26.1 25.5 24.9 24.4 23.8 23.3 22.8 22.2 21.3 20.4 19.5 18.7 18.0 16.6 15.3 14.2 13.3 26.9 26.4 26.0 25.6 25.3 24.9 24.5 24.2 23.9 23.2 22.6 22.0 21.5 21.0 20.0 19.0 18.2 17.3

30.5 29.9 29.2 28.6 28.0 27.4 26.8 26.3 25.7 24.7 23.8 22.9 22.0 21.2 19.7 18.3 17.1 16.0 30.8 30.3 29.9 29.5 29.1 28.7 28.3 28.0 27.6 26.9 26.3 25.7 25.1 24.6 23.5 22.5 21.6 20.7

34.3 33.6 33.0 32.3 31.7 31.1 30.4 29.9 29.3 28.2 27.2 26.3 25.4 24.5 22.8 21.4 20.0 18.8 35.2 34.2 33.8 33.3 32.9 32.5 32.1 31.8 31.4 30.7 30.0 29.4 28.8 28.2 27.1 26.1 25.1 24.1

38.2 37.4 36.7 36.1 35.4 34.7 34.1 33.5 32.9 31.8 30.7 29.7 28.8 27.9 26.1 24.6 23.1 21.8 39.1 38.1 37.7 37.2 36.8 36.4 36.0 35.6 35.2 34.5 33.8 33.1 32.5 31.9 30.7 29.7 28.6 27.6

42.0 41.3 40.5 39.8 39.1 38.4 37.8 37.1 36.5 35.4 34.3 33.2 32.2 31.3 29.5 27.8 26.3 24.9 43.0 42.1 41.6 41.1 40.7 40.2 39.8 39.4 39.0 38.3 37.6 36.9 36.2 35.6 34.4 33.3 32.2 31.2

45.9 45.1 44.3 43.6 42.9 42.2 41.5 40.8 40.2 39.0 37.9 36.8 35.8 34.8 32.9 31.1 29.5 28.0 47.0 46.0 45.5 45.0 44.6 44.1 43.7 43.3 42.9 42.1 41.4 40.7 40.0 39.3 38.1 36.9 35.9 34.8

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 72

7–72

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-13

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 1

3

6

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

2

3

4

5

2 2.82 5.98 9.46 13.3 17.3 3 2.50 5.31 8.43 12.0 15.7 4 2.23 4.74 7.58 10.8 14.3 5 2.01 4.27 6.86 9.82 13.1 6 1.81 3.86 6.24 8.96 12.0 7 1.64 3.52 5.70 8.22 11.1 8 1.49 3.22 5.24 7.57 10.2 9 1.36 2.96 4.83 7.01 9.48 10 1.25 2.73 4.47 6.51 8.83 12 1.07 2.37 3.89 5.68 7.74 14 0.94 2.08 3.42 5.02 6.86 16 0.83 1.86 3.05 4.49 6.15 18 0.75 1.67 2.75 4.06 5.56 20 0.68 1.52 2.50 3.70 5.07 24 0.58 1.29 2.12 3.14 4.30 28 0.50 1.12 1.84 2.72 3.73 32 0.44 0.98 1.62 2.40 3.30 36 0.40 0.88 1.45 2.15 2.95 C ⬘, in. 15.0 32.8 54.2 79.9 110 2 2.82 6.54 10.6 14.8 18.9 3 2.50 5.90 9.81 14.0 18.1 4 2.23 5.33 9.01 13.1 17.3 5 2.01 4.84 8.27 12.2 16.4 6 1.81 4.42 7.60 11.4 15.5 7 1.64 4.05 7.02 10.6 14.6 8 1.49 3.73 6.51 9.94 13.7 9 1.36 3.45 6.06 9.30 13.0 10 1.25 3.20 5.66 8.72 12.2 12 1.07 2.80 4.98 7.73 10.9 14 0.94 2.47 4.43 6.92 9.81 16 0.83 2.21 3.98 6.25 8.90 18 0.75 2.00 3.60 5.68 8.13 20 0.68 1.82 3.29 5.21 7.47 24 0.58 1.55 2.79 4.45 6.40 28 0.50 1.34 2.42 3.87 5.59 32 0.44 1.18 2.14 3.43 4.95 36 0.40 1.06 1.92 3.07 4.44 C ⬘, in. 15.0 39.4 71.8 115 167

6

7

8

9

10

21.3 19.7 18.2 16.7 15.4 14.2 13.2 12.3 11.4 10.1 8.95 8.04 7.29 6.65 5.66 4.92 4.34 3.89 145 22.9 22.3 21.5 20.6 19.7 18.8 17.8 16.9 16.1 14.5 13.2 12.0 11.0 10.1 8.72 7.64 6.79 6.10 230

25.5 23.8 22.2 20.5 19.0 17.6 16.4 15.3 14.3 12.6 11.3 10.2 9.22 8.43 7.18 6.24 5.51 4.94 184 26.9 26.4 25.7 24.8 24.0 23.0 22.0 21.1 20.2 18.4 16.8 15.4 14.2 13.1 11.3 9.96 8.87 7.98 304

29.6 28.0 26.3 24.5 22.9 21.3 19.9 18.6 17.5 15.5 13.8 12.5 11.4 10.4 8.88 7.73 6.84 6.13 229 30.9 30.4 29.8 29.0 28.2 27.3 26.3 25.3 24.4 22.5 20.7 19.1 17.7 16.4 14.3 12.6 11.2 10.1 388

33.7 32.2 30.4 28.6 26.9 25.2 23.6 22.1 20.8 18.5 16.6 15.0 13.7 12.6 10.8 9.37 8.29 7.43 279 34.9 34.5 33.9 33.2 32.4 31.5 30.6 29.6 28.6 26.7 24.8 23.0 21.4 20.0 17.5 15.5 13.8 12.5 483

37.7 36.3 34.6 32.8 31.0 29.2 27.5 25.9 24.4 21.8 19.6 17.8 16.3 14.9 12.8 11.2 9.90 8.88 333 38.9 38.5 37.9 37.3 36.6 35.7 34.8 33.9 32.9 30.9 29.0 27.1 25.3 23.7 20.9 18.6 16.7 15.1 588

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11

12

41.8 45.8 40.4 44.6 38.8 43.0 37.0 41.3 35.2 39.4 33.3 37.5 31.5 35.6 29.8 33.8 28.2 32.1 25.3 29.0 22.8 26.2 20.7 23.9 19.0 21.9 17.5 20.2 15.0 17.4 13.1 15.2 11.6 13.5 10.4 12.1 393 458 42.8 46.8 42.5 46.5 42.0 46.0 41.4 45.5 40.7 44.8 39.9 44.1 39.1 43.3 38.2 42.4 37.2 41.5 35.2 39.5 33.2 37.5 31.3 35.5 29.4 33.6 27.7 31.7 24.5 28.3 21.9 25.5 19.7 23.0 17.9 20.9 705 832

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 73

DESIGN TABLES

7–73

Table 7-13 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 1

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

2.91 2.57 2.30 2.06 1.86 1.69 1.53 1.40 1.29 1.11 0.97 0.86 0.78 0.71 0.60 0.52 0.46 0.41 2.91 2.57 2.30 2.06 1.86 1.69 1.53 1.40 1.29 1.11 0.97 0.86 0.78 0.71 0.60 0.52 0.46 0.41

2

3

6.06 9.56 5.40 8.57 4.84 7.72 4.37 6.99 3.96 6.37 3.61 5.83 3.31 5.36 3.04 4.95 2.81 4.59 2.44 4.00 2.15 3.52 1.92 3.15 1.73 2.84 1.57 2.59 1.33 2.19 1.15 1.90 1.02 1.68 0.91 1.50 6.57 10.6 5.93 9.81 5.37 9.04 4.89 8.33 4.48 7.70 4.12 7.13 3.80 6.62 3.52 6.17 3.27 5.77 2.86 5.09 2.54 4.53 2.27 4.08 2.06 3.70 1.88 3.38 1.59 2.88 1.38 2.50 1.22 2.21 1.09 1.98

4

5

6

7

8

9

10

11

12

13.3 12.0 10.9 9.93 9.09 8.36 7.72 7.15 6.65 5.82 5.15 4.61 4.17 3.80 3.23 2.80 2.48 2.22 14.7 13.9 13.0 12.2 11.4 10.6 9.95 9.32 8.76 7.80 7.00 6.34 5.78 5.30 4.54 3.96 3.51 3.15

17.2 15.8 14.4 13.2 12.1 11.2 10.4 9.64 9.0 7.9 7.0 6.3 5.7 5.2 4.4 3.9 3.4 3.0 18.8 18.0 17.2 16.3 15.4 14.5 13.7 12.9 12.2 11.0 9.92 9.02 8.26 7.60 6.54 5.72 5.08 4.56

21.3 19.7 18.2 16.7 15.5 14.3 13.3 12.4 11.6 10.2 9.12 8.21 7.45 6.81 5.80 5.05 4.46 4.00 22.8 22.1 21.3 20.5 19.5 18.6 17.7 16.8 16.0 14.5 13.2 12.0 11.1 10.2 8.84 7.77 6.92 6.23

25.3 23.7 22.1 20.5 19.0 17.7 16.5 15.4 14.5 12.8 11.5 10.3 9.41 8.61 7.36 6.41 5.67 5.08 26.8 26.2 25.5 24.6 23.7 22.8 21.8 20.9 20.0 18.3 16.8 15.4 14.2 13.2 11.5 10.1 9.03 8.15

29.4 27.8 26.1 24.4 22.8 21.3 19.9 18.7 17.6 15.6 14.0 12.7 11.6 10.6 9.07 7.91 7.01 6.29 30.8 30.3 29.6 28.8 27.9 27.0 26.0 25.1 24.1 22.3 20.6 19.0 17.7 16.4 14.4 12.7 11.4 10.3

33.5 31.9 30.2 28.5 26.7 25.1 23.6 22.2 20.9 18.7 16.8 15.2 13.9 12.8 11.0 9.59 8.50 7.63 34.8 34.3 33.6 32.9 32.1 31.2 30.2 29.3 28.3 26.4 24.6 22.9 21.3 19.9 17.5 15.6 14.0 12.7

37.5 36.1 34.3 32.6 30.8 29.0 27.4 25.8 24.4 21.9 19.8 18.0 16.5 15.2 13.0 11.4 10.1 9.09 38.8 38.3 37.7 37.0 36.2 35.4 34.4 33.5 32.5 30.6 28.7 26.9 25.2 23.6 20.9 18.7 16.8 15.3

41.6 40.2 38.5 36.7 34.9 33.1 31.3 29.7 28.1 25.3 22.9 20.9 19.2 17.7 15.3 13.4 11.9 10.7 42.7 42.3 41.7 41.1 40.3 39.5 38.6 37.7 36.8 34.8 32.8 30.9 29.1 27.5 24.5 22.0 19.9 18.1

45.6 44.3 42.6 40.9 39.0 37.2 35.3 33.6 31.9 28.9 26.3 24.0 22.1 20.4 17.6 15.5 13.8 12.4 46.7 46.3 45.8 45.1 44.4 43.7 42.8 41.9 41.0 39.0 37.1 35.1 33.2 31.4 28.2 25.4 23.1 21.1

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 74

7–74

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-13 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 1

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

3.14 2.79 2.50 2.25 2.04 1.85 1.69 1.55 1.43 1.23 1.08 0.96 0.87 0.79 0.67 0.58 0.51 0.46 3.14 2.79 2.50 2.25 2.04 1.85 1.69 1.55 1.43 1.23 1.08 0.96 0.87 0.79 0.67 0.58 0.51 0.46

2

3

6.41 9.91 5.75 8.95 5.19 8.16 4.71 7.45 4.29 6.83 3.93 6.28 3.61 5.80 3.33 5.38 3.08 5.00 2.68 4.37 2.36 3.88 2.11 3.47 1.91 3.14 1.74 2.86 1.48 2.43 1.28 2.11 1.13 1.87 1.01 1.67 6.75 10.7 6.12 9.94 5.58 9.23 5.13 8.58 4.73 8.00 4.38 7.47 4.06 6.98 3.78 6.55 3.53 6.15 3.10 5.47 2.76 4.90 2.48 4.43 2.25 4.04 2.06 3.70 1.76 3.17 1.53 2.76 1.35 2.45 1.21 2.19

4

5

6

7

8

9

10

11

12

13.6 12.4 11.4 10.5 9.65 8.92 8.27 7.70 7.19 6.32 5.62 5.05 4.57 4.18 3.56 3.10 2.74 2.45 14.7 13.9 13.1 12.4 11.6 10.9 10.3 9.72 9.18 8.25 7.46 6.79 6.22 5.72 4.93 4.32 3.84 3.46

17.5 16.1 14.9 13.7 12.7 11.8 11.0 10.3 9.64 8.52 7.61 6.86 6.24 5.71 4.88 4.25 3.76 3.37 18.7 18.0 17.2 16.3 15.5 14.7 14.0 13.3 12.6 11.4 10.4 9.55 8.79 8.14 7.06 6.22 5.54 5.00

21.4 20.0 18.5 17.2 16.0 15.0 14.0 13.1 12.3 11.0 9.83 8.89 8.10 7.43 6.36 5.55 4.92 4.41 22.7 22.0 21.2 20.4 19.5 18.7 17.9 17.1 16.3 14.9 13.7 12.6 11.7 10.9 9.48 8.38 7.50 6.77

25.4 23.9 22.4 20.9 19.6 18.3 17.2 16.2 15.3 13.6 12.3 11.1 10.2 9.35 8.03 7.02 6.23 5.60 26.7 26.1 25.3 24.5 23.6 22.7 21.9 21.0 20.2 18.6 17.2 16.0 14.9 13.9 12.2 10.8 9.73 8.82

29.4 27.9 26.3 24.7 23.3 21.9 20.6 19.4 18.4 16.5 14.9 13.6 12.4 11.5 9.87 8.65 7.69 6.91 30.7 30.1 29.4 28.6 27.7 26.8 25.9 25.1 24.2 22.5 21.0 19.6 18.3 17.1 15.2 13.5 12.2 11.1

33.4 31.9 30.3 28.6 27.1 25.6 24.2 22.9 21.7 19.6 17.8 16.2 14.9 13.8 11.9 10.4 9.29 8.36 34.7 34.1 33.4 32.7 31.8 31.0 30.1 29.2 28.3 26.5 24.9 23.3 21.9 20.6 18.3 16.5 14.9 13.6

37.4 35.9 34.3 32.6 31.0 29.4 27.9 26.5 25.2 22.8 20.8 19.0 17.5 16.2 14.1 12.4 11.0 9.95 38.6 38.1 37.5 36.7 35.9 35.1 34.2 33.3 32.4 30.6 28.8 27.2 25.7 24.2 21.7 19.6 17.8 16.3

41.4 40.0 38.4 36.7 35.0 33.3 31.7 30.2 28.8 26.2 24.0 22.0 20.3 18.9 16.4 14.5 12.9 11.7 42.6 42.1 41.5 40.8 40.0 39.2 38.3 37.4 36.5 34.7 32.9 31.2 29.5 28.0 25.3 22.9 20.9 19.1

45.4 44.0 42.4 40.7 39.0 37.3 35.6 34.0 32.5 29.8 27.3 25.2 23.3 21.6 18.9 16.7 14.9 13.5 46.6 46.1 45.5 44.8 44.1 43.3 42.4 41.5 40.6 38.8 37.0 35.2 33.5 31.9 28.9 26.3 24.1 22.2

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 75

DESIGN TABLES

7–75

Table 7-13 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in. 1

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

3.46 3.15 2.87 2.61 2.39 2.19 2.01 1.86 1.72 1.49 1.32 1.17 1.06 0.96 0.82 0.71 0.63 0.56 3.46 3.15 2.87 2.61 2.39 2.19 2.01 1.86 1.72 1.49 1.32 1.17 1.06 0.96 0.82 0.71 0.63 0.56

2

3

6.96 10.5 6.38 9.73 5.84 8.97 5.36 8.30 4.93 7.69 4.55 7.15 4.21 6.66 3.90 6.21 3.63 5.82 3.18 5.14 2.82 4.59 2.53 4.14 2.29 3.76 2.10 3.44 1.79 2.94 1.56 2.56 1.38 2.26 1.23 2.03 7.09 10.9 6.58 10.3 6.09 9.65 5.66 9.07 5.26 8.54 4.91 8.07 4.59 7.63 4.30 7.23 4.04 6.85 3.59 6.19 3.22 5.62 2.91 5.13 2.66 4.71 2.44 4.35 2.10 3.76 1.83 3.30 1.63 2.94 1.46 2.64

4

5

6

7

8

9

10

11

12

14.2 13.2 12.3 11.4 10.7 9.98 9.34 8.76 8.24 7.33 6.58 5.95 5.43 4.98 4.26 3.73 3.31 2.97 14.8 14.1 13.4 12.8 12.1 11.6 11.0 10.5 10.0 9.14 8.38 7.71 7.12 6.61 5.76 5.08 4.54 4.11

18.0 16.8 15.7 14.7 13.9 13.0 12.2 11.5 10.9 9.76 8.81 8.00 7.32 6.74 5.81 5.09 4.52 4.06 18.7 18.1 17.3 16.6 15.9 15.3 14.6 14.0 13.4 12.4 11.4 10.6 9.87 9.22 8.11 7.22 6.50 5.90

21.8 20.6 19.3 18.2 17.2 16.2 15.3 14.5 13.8 12.4 11.3 10.3 9.44 8.71 7.53 6.61 5.89 5.30 22.7 22.0 21.3 20.6 19.8 19.1 18.4 17.7 17.1 15.9 14.8 13.8 12.9 12.1 10.8 9.64 8.71 7.93

25.7 24.4 23.1 21.8 20.7 19.6 18.6 17.7 16.8 15.2 13.9 12.7 11.7 10.9 9.43 8.31 7.42 6.69 26.7 26.0 25.3 24.5 23.8 23.0 22.3 21.5 20.8 19.5 18.3 17.2 16.2 15.3 13.7 12.3 11.2 10.2

29.6 28.2 26.9 25.5 24.3 23.1 22.0 21.0 20.0 18.3 16.7 15.4 14.2 13.2 11.5 10.2 9.11 8.23 30.6 30.0 29.3 28.5 27.8 27.0 26.2 25.5 24.7 23.3 22.0 20.8 19.6 18.6 16.7 15.2 13.9 12.7

33.5 32.1 30.7 29.3 28.0 26.7 25.5 24.4 23.3 21.4 19.7 18.2 16.9 15.7 13.8 12.2 11.0 9.91 34.6 33.9 33.3 32.5 31.8 31.0 30.2 29.4 28.6 27.2 25.8 24.4 23.2 22.1 20.0 18.3 16.7 15.4

37.4 36.1 34.6 33.2 31.8 30.4 29.2 27.9 26.8 24.7 22.8 21.2 19.7 18.4 16.2 14.4 12.9 11.7 38.5 37.9 37.3 36.5 35.8 35.0 34.2 33.4 32.6 31.1 29.6 28.2 26.9 25.7 23.4 21.5 19.8 18.3

41.4 40.0 38.6 37.1 35.6 34.2 32.9 31.6 30.4 28.1 26.1 24.3 22.7 21.2 18.7 16.7 15.1 13.7 42.5 41.9 41.2 40.5 39.8 39.0 38.2 37.4 36.6 35.1 33.5 32.1 30.7 29.4 27.0 24.9 23.0 21.3

45.3 44.0 42.5 41.0 39.5 38.1 36.7 35.3 34.0 31.6 29.5 27.5 25.7 24.2 21.4 19.2 17.3 15.8 46.5 45.9 45.2 44.5 43.8 43.0 42.2 41.4 40.6 39.1 37.5 36.0 34.6 33.2 30.6 28.4 26.3 24.5

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 76

7–76

DESIGN CONSIDERATIONS FOR BOLTS

Table 7-13 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

3.74 3.57 3.38 3.17 2.97 2.78 2.60 2.44 2.28 2.02 1.80 1.62 1.47 1.34 1.15 1.00 0.88 0.79 3.74 3.57 3.38 3.17 2.97 2.78 2.60 2.44 2.28 2.02 1.80 1.62 1.47 1.34 1.15 1.00 0.88 0.79

7.46 7.12 6.75 6.36 5.99 5.63 5.29 4.98 4.69 4.18 3.76 3.40 3.10 2.85 2.45 2.15 1.91 1.72 7.47 7.16 6.82 6.47 6.14 5.82 5.52 5.24 4.98 4.51 4.10 3.76 3.46 3.21 2.79 2.47 2.21 2.00

11.2 10.7 10.2 9.61 9.09 8.59 8.13 7.69 7.28 6.56 5.95 5.43 4.99 4.61 3.99 3.51 3.13 2.81 11.2 10.8 10.4 9.94 9.52 9.11 8.73 8.37 8.03 7.41 6.86 6.37 5.94 5.56 4.91 4.38 3.95 3.58

14.9 14.3 13.6 12.9 12.3 11.7 11.1 10.6 10.1 9.16 8.38 7.70 7.11 6.59 5.73 5.06 4.52 4.08 15.0 14.6 14.1 13.6 13.1 12.6 12.1 11.7 11.3 10.6 9.91 9.29 8.74 8.23 7.34 6.61 5.99 5.46

18.6 17.9 17.1 16.4 15.6 14.9 14.2 13.6 13.0 11.9 11.0 10.2 9.42 8.76 7.67 6.80 6.11 5.53 18.9 18.4 17.8 17.3 16.7 16.2 15.7 15.2 14.8 14.0 13.2 12.4 11.8 11.2 10.1 9.13 8.33 7.65

22.4 21.6 20.7 19.8 19.0 18.2 17.5 16.8 16.1 14.9 13.8 12.8 11.9 11.1 9.82 8.76 7.89 7.16 22.8 22.2 21.7 21.1 20.5 19.9 19.4 18.9 18.4 17.5 16.6 15.8 15.0 14.3 13.0 11.9 11.0 10.1

26.2 25.3 24.3 23.4 22.5 21.6 20.8 20.1 19.3 18.0 16.7 15.6 14.6 13.7 12.2 10.9 9.83 8.95 26.7 26.1 25.5 24.9 24.3 23.7 23.2 22.6 22.1 21.1 20.1 19.2 18.4 17.6 16.2 14.9 13.8 12.8

30.0 29.0 28.0 27.0 26.1 25.1 24.3 23.4 22.7 21.2 19.8 18.6 17.4 16.4 14.6 13.2 11.9 10.9 30.6 30.0 29.4 28.8 28.2 27.6 27.0 26.4 25.8 24.8 23.8 22.8 21.9 21.0 19.5 18.1 16.8 15.7

33.9 32.8 31.8 30.7 29.7 28.7 27.8 26.9 26.1 24.5 23.0 21.6 20.4 19.3 17.3 15.6 14.2 13.0 34.5 33.9 33.3 32.7 32.1 31.5 30.8 30.2 29.7 28.5 27.5 26.5 25.5 24.6 22.9 21.4 20.0 18.7

37.7 36.7 35.6 34.5 33.4 32.3 31.4 30.4 29.5 27.8 26.3 24.8 23.5 22.2 20.1 18.2 16.6 15.3 38.5 37.9 37.3 36.6 36.0 35.3 34.7 34.1 33.5 32.3 31.2 30.2 29.2 28.2 26.4 24.7 23.2 21.9

41.6 40.5 39.4 38.2 37.1 36.0 35.0 34.0 33.1 31.3 29.6 28.1 26.7 25.3 23.0 20.9 19.2 17.7 42.4 41.8 41.2 40.5 39.9 39.3 38.6 38.0 37.4 36.2 35.0 33.9 32.9 31.9 30.0 28.2 26.6 25.1

45.5 44.4 43.2 42.0 40.9 39.8 38.7 37.7 36.7 34.8 33.1 31.4 29.9 28.5 26.0 23.8 21.8 20.2 46.4 45.8 45.1 44.5 43.8 43.2 42.5 41.9 41.3 40.1 38.9 37.7 36.6 35.6 33.6 31.8 30.1 28.5

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 7B:14th Ed.

2/24/11

8:36 AM

Page 77

DESIGN TABLES

7–77

Table 7-13 (continued)

Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75° Available strength of a bolt group, φRn or Rn /Ω, is determined with

Rn = C × rn or LRFD

ASD

P C min = u φrn

C min =

ΩPa rn

Number of Bolts in One Vertical Row, n

s, in. ex , in.

3

6

2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36

where P = required force, Pu or Pa, kips rn = nominal strength per bolt, kips e = eccentricity of P with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry) ex = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below

1

2

3

4

5

6

7

8

9

10

11

12

3.89 3.84 3.79 3.72 3.65 3.56 3.47 3.37 3.27 3.07 2.87 2.68 2.50 2.34 2.06 1.82 1.63 1.48 3.89 3.84 3.79 3.72 3.65 3.56 3.47 3.37 3.27 3.07 2.87 2.68 2.50 2.34 2.06 1.82 1.63 1.48

7.75 7.66 7.54 7.40 7.25 7.08 6.90 6.71 6.52 6.14 5.76 5.40 5.07 4.76 4.23 3.78 3.41 3.11 7.74 7.64 7.52 7.38 7.23 7.07 6.90 6.73 6.56 6.21 5.88 5.57 5.27 4.99 4.50 4.08 3.73 3.43

11.6 11.5 11.3 11.1 10.8 10.6 10.3 10.0 9.77 9.23 8.71 8.22 7.76 7.33 6.57 5.94 5.41 4.95 11.6 11.4 11.2 11.0 10.8 10.6 10.4 10.1 9.92 9.48 9.07 8.67 8.29 7.94 7.29 6.73 6.25 5.82

15.5 15.2 15.0 14.7 14.4 14.1 13.7 13.4 13.1 12.4 11.8 11.1 10.6 10.0 9.10 8.30 7.61 7.01 15.4 15.2 14.9 14.7 14.4 14.2 13.9 13.6 13.4 12.9 12.4 11.9 11.5 11.1 10.3 9.67 9.06 8.51

19.3 19.0 18.7 18.3 17.9 17.6 17.2 16.8 16.4 15.6 14.9 14.2 13.5 12.9 11.8 10.9 10.0 9.26 19.3 19.0 18.7 18.4 18.1 17.8 17.5 17.2 16.9 16.4 15.9 15.4 14.9 14.4 13.6 12.8 12.1 11.4

23.1 22.7 22.4 21.9 21.5 21.1 20.6 20.2 19.8 18.9 18.1 17.3 16.6 15.9 14.7 13.5 12.6 11.7 23.1 22.8 22.5 22.1 21.8 21.5 21.2 20.8 20.5 19.9 19.4 18.8 18.3 17.8 16.9 16.1 15.3 14.5

26.9 26.5 26.1 25.6 25.1 24.6 24.1 23.7 23.2 22.3 21.4 20.5 19.7 19.0 17.6 16.4 15.3 14.3 27.0 26.6 26.3 25.9 25.6 25.2 24.9 24.5 24.2 23.6 23.0 22.4 21.9 21.3 20.4 19.4 18.6 17.8

30.8 30.3 29.8 29.3 28.7 28.2 27.7 27.2 26.7 25.7 24.7 23.8 23.0 22.2 20.7 19.3 18.1 17.0 30.9 30.5 30.1 29.7 29.3 29.0 28.6 28.3 27.9 27.3 26.6 26.0 25.5 24.9 23.9 22.9 22.0 21.1

34.6 34.1 33.5 32.9 32.4 31.8 31.3 30.7 30.2 29.1 28.1 27.2 26.3 25.5 23.9 22.4 21.0 19.8 35.2 34.4 34.0 33.6 33.2 32.8 32.4 32.0 31.7 31.0 30.3 29.7 29.1 28.5 27.4 26.4 25.4 24.5

38.5 37.9 37.3 36.7 36.1 35.5 34.9 34.3 33.7 32.6 31.6 30.6 29.7 28.8 27.1 25.5 24.1 22.8 39.1 38.3 37.8 37.4 37.0 36.6 36.2 35.8 35.5 34.7 34.1 33.4 32.8 32.2 31.0 30.0 29.0 28.0

42.3 41.7 41.0 40.4 39.8 39.1 38.5 37.9 37.3 36.2 35.1 34.1 33.1 32.2 30.4 28.7 27.2 25.8 43.0 42.2 41.7 41.3 40.8 40.4 40.0 39.6 39.3 38.5 37.8 37.1 36.5 35.8 34.7 33.6 32.5 31.5

46.2 45.5 44.8 44.1 43.5 42.8 42.2 41.6 41.0 39.8 38.7 37.6 36.6 35.6 33.8 32.0 30.4 28.9 47.0 46.1 45.6 45.2 44.7 44.3 43.9 43.5 43.1 42.3 41.6 40.9 40.2 39.6 38.3 37.2 36.1 35.1

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN CONSIDERATIONS FOR BOLTS

Table 7-14

Dimensions of High-Strength Fasteners, in.

Nominal Bolt Diameter, in

F436 Square or Rect. Washers b,d

F436 Circular Washersb

A563 Nutsa

A325 and A490 Boltsa

Measurement Width Across Flats, F Height, H Thread Length Bolt Length = Grip + Washer Thickness + → Width Across Flats, W Height, H Nom. Outside Diameter, OD Nom. Inside Diameter, ID Thckns., Min. T Max. Min. Edge Distance, E c Min. Side Dimension, A Mean Thickness, T Taper in Thickness Min. Edge Distance, E c

1/2

5/8

3/4

7/8

1

11/8

11/4

13/8

11/2

78

/

11/16

11/4

1 7/16

15/8

113/16

2

2 3/16

2 3/8

5/16

25/64

15/32

35/64

39/64

11/16

25/32

27/32

15/16

1

11/4

13/8

11/2

13/4

2

2

21/4

21/4

11/16

7/8

1

11/8

11/4

11/2

15/8

1 3/4

17/8

78

/

11/16

11/4

17/16

15/8

113/16

2

2 3/16

23/8

31/64

39/64

47/64

55/64

63/64

17/64

17/32

111/32

115/32

11/16

15/16

115/32

13/4

2

21/4

21/2

23/4

3

17 32

/

11 16

/

13 16 /

15 16 /

11/8

11/4

13/8

11/2

15/8

0.097 0.177

0.122 0.177

0.122 0.177

0.136 0.177

0.136 0.177

0.136 0.177

0.136 0.177

0.136 0.177

0.136 0.177

7

/16

9 16 /

21 32

/

25 32 /

78

/

1

13/32

17/32

15/16

13/4

13/4

13/4

13/4

13/4

21/4

21/4

21/4

21/4

5 16 /

5 16 /

5 16 /

5 16 /

5 16 /

5 16 /

5 16 /

5 16 /

5 16 /

2:12

2:12

2:12

2:12

2:12

2:12

2:12

2:12

2:12

7/16

9 16 /

21 32

25 32 /

78

1

13/32

17/32

15/16

/

/

a

Tolerances as specified in ASME B18.2.6 ASTM F436 washer tolerances, in.: Nominal outside diameter Nominal diameter of hole Flatness: max. deviation from straight-edge placed on cut side shall not exceed Concentricity: center of hole to outside diameter (full indicator runout) Burr shall not project above immediately adjacent washer surface more than c For clipped washers only d For use with American standard beams (S) and channels (C) b

−1/32; +1/32 −0; +1/32 0.010 0.030 0.010

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DESIGN TABLES

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Table 7-15

Entering and Tightening Clearance, in. Conventional ASTM A325 and A490 Bolts Aligned Bolts

C3

Nominal Socket Bolt Dia. Dia. 5/8 3/4 7/8 1 11/8 11/4 13/8 11/2

13/4 21/4 21/2 25/8 27/8 31/8 31/4 31/2

H1

H2

C1

25/64

11/4 13/8 11/2 15/8 17/8 2 21/8 21/4

1 11/4 13/8 17/16 19/16 111/16 13/4 17/8

15/32 35/64 39/64 11/16 25/32 27/32 15/16

C2

Circular Clipped

11/16

11/16

3/4

3/4

7/8 15/16 11/16

11/8 11/4 15/16

7/8 1 11/8 11/4 13/8 11/2

9/16 11/16 13/16 7/8 1 11/8 11/4 15/16

Staggered Bolts Stagger P, in. Nominal Bolt Diameter, in.

F

5/8

1 11/8 11/4 13/8 11/2 15/8 13/4 17/8 2 2 1/8 2 1/4 2 3/8 2 1/2 2 5/8 2 3/4 2 7/8 3 3 1/8 3 1/4 3 3/8 3 1/2 3 5/8 3 3/4 37/8 4

15/8 11/2 11/2 17/16 11/4 11/4 13/16 11/8 1 13/16

3/4

115/16 17/8 113/16 13/4 111/16 19/16 11/2 13/8 11/4 11/8 7/8

7/8

23/16 21/8 21/16 2 115/16 113/16 111/16 19/16 11/2 13/8 13/16 15/16

Notes: H1 = height of head H2 = maximum shank extension* C1 = clearance for tightening C2 = clearance for entering

1

25/16 25/16 21/4 23/16 21/8 2 17/8 13/4 15/8 11/2 13/8 13/16 7/8

11/8

29/16 29/16 21/2 27/16 23/8 21/4 21/8 2 115/16 17/8 13/4 15/8 11/2 11/4 15/16

11/4

13/8

213/16 23/4 23/4 211/16 25/8 21/2 27/16 25/16 21/8 21/16 2 17/8 13/4 15/8 13/8 11/16

3 3 215/16 215/16 27/8 213/16 23/4 27/8 21/2 23/8 21/4 21/8 2 115/16 13/4 19/16 15/16

11/2

33/4 31/4 33/16 33/16 31/8 31/16 3 27/8 213/16 211/16 21/2 23/8 21/4 21/8 2 17/8 111/16 13/8

C3 = clearance for fillet* P = bolt stagger F = clearance for tightening staggered bolts * Based on the use of one ASTM F436 washer

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN CONSIDERATIONS FOR BOLTS

Table 7-16

Entering and Tightening Clearance, in. Tension Control ASTM F1852 and F2280 Bolts Aligned Bolts Nominal Bolt Dia.

Tools

C3 H1

H2

C1

C2

Circular Clipped

4 1/4-in. Diameter Critical

Large Tools 3/4 7/8

1/2 9/16

1

5/8

3/4 7/8

1/2 9/16

1

5/8

5/8

7/16

3/4

1/2

7/8

9/16

5/8

7/16

3/4

1/2

7/8

9/16

Small Tools

7/8 13/8 21/8 11/2 21/8 1 13/4 21/8 11/8 2 3/4-in. Diameter Critical

3/4

7/8 13/8 13/8 11/2 13/8 1 13/4 13/8 11/8 3 1/8-in. Diameter Critical

3/4

11/4 13/8 11/2

13/16 15/8 7/8 15/8 15/8 1 2 1/8-in. Diameter Critical

11/4 13/8 11/2

11/8 11/8 11/8

7/8

1

7/8

1 11/16 3/4 7/8

13/16

11/16

7/8

3/4

1

7/8

— — —

— — —

— — —

— — —

Staggered Bolts Stagger P, in. Nominal Bolt Diameter, in.

F

5/8

11/4

113/16

13/8 11/2 15/8 13/4 17/8 2 2 1/8 2 1/4 2 3/8 2 1/2 2 5/8 2 3/4 2 7/8 3 3 3/8

13/4 111/16 19/16 11/2 17/16 15/16 11/4 13/16 11/8 1

3/4

7/8

1

21/16 2 1 7/8 113/16 13/4 15/8 19/16 11/2 13/8 15/16 13/16 11/8

21/4 23/16 21/16 2 17/8 13/4 111/16 19/16 11/2 13/8 15/16 13/16 11/8

27/16 23/8 21/4 23/16 21/8 2 115/16 17/8 13/4 111/16 19/16 11/2 13/8 15/16 15/16

Notes: H1 = height of head C3 = clearance for fillet* H2 = maximum shank extension* P = bolt stagger C1 = clearance for tightening F = clearance for tightening staggered bolts C2 = clearance for entering * Based on one standard hardened washer

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN TABLES

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Table 7-17

Threading Dimensions for High-Strength and Non-High-Strength Bolts

Diameter Bolt Diameter d , in. 1/4 3/8 1/2 5/8 3/4 7/8 1 11/8 11/4 13/8 11/2 13/4 2 21/4 21/2 2 3/4 3 3 1/4 3 1/2 3 3/4 4

Area

Min. Root K, in.

Gross Bolt Area, in.2

Min. Root Area, in.2

Net Tensile Areaa, in.2

Threads per inch, n b

0.196 0.307 0.417 0.527 0.642 0.755 0.865 0.970 1.10 1.19 1.32 1.53 1.76 2.01 2.23 2.48 2.73 2.98 3.23 3.48 3.73

0.0490 0.110 0.196 0.307 0.442 0.601 0.785 0.994 1.23 1.49 1.77 2.41 3.14 3.98 4.91 5.94 7.07 8.30 9.62 11.0 12.6

0.0301 0.0742 0.136 0.218 0.323 0.447 0.587 0.740 0.942 1.12 1.37 1.85 2.43 3.17 3.90 4.83 5.85 6.97 8.19 9.51 10.9

0.0320 0.0780 0.142 0.226 0.334 0.462 0.606 0.763 0.969 1.16 1.41 1.90 2.50 3.25 4.00 4.93 5.97 7.10 8.33 9.66 11.1

20 16 13 11 10 9 8 7 7 6 6 5 4.5 4.5 4 4 4 4 4 4 4

冢

冣

0.9743 2 Net tensile area = 0.7854 × d − ᎏᎏ n b For diameters listed, thread series is UNC (coarse). For larger diameters, thread series is 4UN. c 2A denotes Class 2A fit applicable to external threads; 2B denotes corresponding Class 2B fit for internal threads. a

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN CONSIDERATIONS FOR BOLTS

Table 7-18

Weights of High-Strength Fasteners, pounds per 100 count Nominal Bolt Diameter, in.

100, Conventional A325 or A490 Bolts with A563 Nuts

Bolt Length, in.

1/2

5/8

3/4

7/8

1

11/8

11/4

13/8

11/2

1 11/4 11/2 13/4

16.5 17.8 19.2 20.5

29.4 31.1 33.1 35.3

47.0 49.6 52.2 55.3

— 74.4 78.0 81.9

— 104 109 114

— — 148 154

— — 197 205

— — — 261

— — — 333

2 2 1/4 2 1/2 2 3/4

21.9 23.3 24.7 26.1

37.4 39.8 41.7 43.9

58.4 61.6 64.7 67.8

86.1 90.3 94.6 98.8

119 124 130 135

160 167 174 181

212 220 229 237

270 279 290 300

344 355 366 379

3 3 1/4 3 1/2 3 3/4

27.4 28.8 30.2 31.6

46.1 48.2 50.4 52.5

70.9 74.0 77.1 80.2

103 107 111 116

141 146 151 157

188 195 202 209

246 255 263 272

310 321 332 342

391 403 416 428

4 4 1/4 4 1/2 4 3/4

33.0 34.3 35.7 37.1

54.7 56.9 59.0 61.2

83.3 86.4 89.5 92.7

120 124 128 133

162 168 173 179

216 223 230 237

280 289 298 306

353 363 374 384

441 453 465 478

5 5 1/4 5 1/2 5 3/4

38.5 39.9 41.2 42.6

63.3 65.5 67.7 69.8

95.8 98.9 102 105

137 141 146 150

184 190 196 201

244 251 258 265

315 324 332 341

395 405 416 426

490 503 515 527

6 6 1/4 6 1/2 6 3/4

44.0 — — —

71.9 74.1 76.3 78.5

108 111 114 118

154 158 163 167

207 212 218 223

272 279 286 293

349 358 367 375

437 447 458 468

540 552 565 577

7 71/4 71/2 7 3/4

— — — —

80.6 82.8 84.9 87.1

121 124 127 130

171 175 179 183

229 234 240 246

300 307 314 321

384 392 401 410

479 489 500 510

589 602 614 626

8 8 1/4 8 1/2 8 3/4

— — — —

89.2 — — —

133 — — —

187 192 196 —

251 257 262 —

328 335 342 —

418 427 435 444

521 531 542 552

639 651 664 676

—

—

—

—

—

—

453

563

689

12.4

16.9

22.1

28.0

34.4

42.5

49.7

11.3

13.8

16.8

20.0

34.0

31.6

31.2

32.9

9 Per inch add’tl. Add 100, F436 Circular Washers 100, F436 Square Washers

5.50

8.60

2.10

3.60

23.1

22.4

4.80 21.0

7.00 20.2

9.40 19.2

This table conforms to weight standards adopted by the Industrial Fasteners Institute (IFI), updated for washer weights.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN TABLES

7–83

Table 7-19

Dimensions of Non-High-Strength Fasteners, in.

Square

Hex

Heavy Hex

Countersunk

Bolts Dia d , in.

F, in. C, in. H, in. 1/4

3/8

1/2

3/8

9/16

13/16

1/2

3/4

5

15/16

/8 /4 7/8

Bolts

3

1 1 1/8 1 1/4 1 3/8 1 1/2 1 3/4 2 2 1/4 2 1/2 2 3/4 3 3 1/4 3 1/2 3 3/4 4

1 1/8 15/16 1 1/2 111/16 1 7/8 21/16 2 1/4 —

3/16 1/4

1 1/16 5/16 1 5/16 7/16 1 9/16 1/2 5/8 1 7/8 11/16 2 1/8 3/4 2 3/8 7/8 2 5/8 15 15 2 /16 /16 3 3/16 1 — —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

—

—

—

F, in. C, in. H, in. F, in. C, in. H, in. C, in. H, in. 7/16

1/2

3/16

9/16

5/8

1/4

– –

– –

– –

3/4

7/8

3/8

7/8

7/16

11/16

1 1/8 1 5/16

1 5/16 1 1/2

1/2

1 1/4 17/16

1 1/2 1 11/16 1 7/8 2 1/16 2 1/4 2 5/8 3 3 3/8 3 3/4 4 1/8 4 1/2 4 7/8 5 1/4 5 5/8 6

1 1/16 1 3/4 1 15/16 3/4 7/8 2 3/16 3 15/16 2 /8 5 2 /8 1 3 13/16 7 3 /16 13/8 3 7/8 11/2 5 4 /16 111/16 4 3/4 113/16 3 5 /16 2 5 5/8 23/16 1 6 /16 25/16 6 1/2 21/2 15 6 /16 211/16

1 5/8 113/16 2 2 3/16 2 3/8 2 3/4 3 1/8 3 1/2 3 7/8 4 1/4 4 5/8 —

1 11/4 17/16 111/16 17/8 21/16 25/16 21/2 23/4 33/16 35/8 41/16 41/2 415/16 55/16 —

3/8

1 1/16

— —

— —

—

—

15/16

9/16

1/2 11/16

1/8 3/16

Min, Thrd. Length, in.

L≤ 6 in.

L> 6 in.

3/4

1 1 1/4

1 1/4 1 1/2 1 3/4 2

1 1/2 1 3/4 2 2 1/4 2 1/2 2 3/4 3 3 1/4 3 1/2 4

1

7/8 1 1 /8

1/4

7/16 1/2 9/16

1 3/8 1 9/16

3/8

11/16

1/2

1 1 3/16

1 13/16 2 1/16 2 1/4 2 1/2 2 11/16 —

—

3 1/4 3 3/4

1 3/8 1 1/2

— —

— —

4 1/4 4 3/4

4 1/2 5

1 11/16 1 13/16

— —

— —

5 1/4 5 3/4

5 1/2 6

2 —

— —

— —

6 6

6 1/2 7

— —

— —

— —

6 6

7 1/2 8

—

—

—

6

8 1/2

3/4 7/8 15/16

5/16 7/16

9/16 5/8 11/16 3/4

Notes: For high-strength bolt and nut dimensions, refer to Table 7-14. Square, hex and heavy hex bolt dimensions, rounded to nearest 1/16 in., are in accordance with ANSI B18.2.1. Countersunk bolt dimensions, rounded to the nearest 1/16 in., are in accordance with ANSI 18.5. Minimum thread length = 2d + 1/4 in. for bolts up to 6 in. long, and 2d + 1/2 in. for bolts longer than 6 in.

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2 1/4 2 1/2 2 3/4 3

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DESIGN CONSIDERATIONS FOR BOLTS

Table 7-19 (continued)

Dimensions of Non-High-Strength Fasteners, in.

Nut Size, in.

Hex

W, in.

C, in.

N, in.

C, in.

N, in.

W, in.

7/16

5/8

1/4

7/16

1/2

3/16

1/2

3/8

5/8

7/8

5/16

9/16

5/8

1/4

11/16

1/2

4/5

7/16

3/4

7/8

3/8

7/8

1 1 1/8 1 5/16 1 1/2 1 11/16 1 7/8 2 1/16 2 1/4 —

1 1/8 1 7/16 1 9/16 1 7/8 2 1/8 2 3/8 2 5/8 2 15/16 3 3/16 —

9/16

15/16

1 1/16

7/16

1 1/16

1 5/16 1 1/2

1/2

3/4

1 1/8 1 5/16

1 1/4 1 7/16

7/8 1 1 1/8 1 1/4 1 5/16 —

1 1/2 1 11/16 1 7/8 2 1/16 2 1/4 —

11/16 1 3/4 1 15/16 3/4 7/8 2 3/16 3 15/16 2 /8 5 2 /8 1 — —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

—

—

/8 /4 7/8 3

1 1 1/8 1 1/4 1 3/8 1 1/2 13/4 2 2 1/4 2 1/2 2 3/4 3 3 1/4 3 1/2 3 3/4 4

W, in.

C, in.

N, in.

1/2

9/16

1

3/8

11/16

13/16

1/4 3/8

1/2

1 5/8 1 13/16 2 2 3/16 2 3/8 —

1 1/4 1 1/2 1 3/4 2 1/16 2 5/16 2 9/16 2 13/16 3 1/8 3 3/8 —

1 11/8 11/4 13/8 11/2 —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

1 5/8 1 13/16 2 2 3/16 2 3/8 2 3/4 3 1/8 3 1/2 3 7/8 4 1/4 4 5/8 5

— —

— —

— —

— —

— —

— —

— —

5 3/8 5 3/4

—

—

—

—

—

—

—

6 1/8

9/16

C, in.

Heavy Hex

1/4

11/16

W, in.

Heavy Square

1/4

5

Nuts

Square

11/16

N, in.

5/8 3/4 7/8

7/8 1 1 /16

1 1/4 1 7/16

Notes: For high-strength bolt and nut dimensions, refer to Table 7-14. Square, hex and heavy hex bolt dimensions, rounded to nearest 1/16 in., are in accordance with ANSI B18.2.1. Countersunk bolt dimensions, rounded to the nearest 1/16 in., are in accordance with ANSI 18.5. Minimum thread length = 2d + 1/4 in. for bolts up to 6 in. long, and 2d + 1/2 in. for bolts longer than 6 in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 1 1/4 1 7/16 1 11/16 1 7/8 2 1/16 2 5/16 2 1/2 2 3/4 3 3/16 3 5/8 4 1/16 4 1/2 4 15/16 5 5/16 5 3/4 6 3/16 6 5/8 7 1/16

1/2 5/8 3/4 7/8

1 1 1/8 1 1/4 1 3/8 1 1/2 1 3/4 2 2 3/16 2 7/16 2 11/16 2 15/16 3 3/16 3 7/16 3 11/16 3 15/16

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Table 7-20

Weights of Non-High-Strength Fasteners, pounds Nominal Bolt Diameter, in.

100 Square Bolts with Hexagonal Nuts*

Bolt Length, in. 1 1 1/4 1 1/2 1 3/4 2 2 1/4 2 1/2 2 3/4 3 3 1/4 3 1/2 3 3/4 4 4 1/4 4 1/2 4 3/4 5 5 1/4 5 1/2 5 3/4 6 6 1/4 6 1/2 6 3/4 7 7 1/4 7 1/2 7 3/4 8 8 1/2 9 9 1/2 10 10 1/2 11 11 1/2 12 12 1/2 13 13 1/2 14 14 1/2 15 15 1/2 16 Per inch add’tl. Add

1/4

3/8

1/2

5/8

3/4

7/8

1

2.38 2.71 3.05 3.39 3.73 4.06 4.40 4.74 5.07 5.41 5.75 6.09 6.42 6.76 7.10 7.43 7.77 8.11 8.44 8.78 9.12 9.37 9.71 10.1 10.4 10.7 11.0 11.4 11.7 — — — — — — — — — — — — — — — —

6.11 6.71 7.47 8.23 8.99 9.75 10.5 11.3 12.0 12.8 13.5 14.3 15.1 15.8 16.6 17.3 18.1 18.9 19.6 20.4 21.1 21.7 22.5 23.3 24.0 24.8 25.5 26.3 27.0 28.6 30.1 31.6 66.1 34.6 36.2 37.7 39.2 — — — — — — — —

13.0 14.0 15.1 16.5 17.8 19.1 20.5 21.8 23.2 24.5 25.9 27.2 28.6 29.9 31.3 32.6 33.9 35.3 36.6 38.0 39.3 40.4 41.8 43.1 44.4 45.8 47.1 48.5 49.8 52.5 55.2 57.9 60.6 63.3 66.0 68.7 71.3 74.0 76.7 79.4 82.1 84.8 87.5 90.2 92.9

24.1 25.8 27.6 29.3 31.4 33.5 35.6 37.7 39.8 41.9 44.0 46.1 48.2 50.3 52.3 54.4 56.5 58.6 60.7 62.8 64.9 66.7 68.7 70.8 72.9 75.0 77.1 79.2 81.3 85.5 89.7 93.9 98.1 102 106 110 115 119 123 127 131 135 140 144 148

38.9 41.5 44.0 46.5 49.1 52.1 55.1 58.2 61.2 64.2 67.2 70.2 73.3 76.3 79.3 82.3 85.3 88.4 91.4 94.4 97.4 100 103 106 109 112 115 118 121 127 133 139 145 151 157 163 170 176 182 188 194 200 206 212 218

— — 67.3 70.8 74.4 77.9 82.0 86.1 90.2 94.4 98.5 103 107 111 115 119 123 127 131 136 140 143 147 151 156 160 164 168 172 180 189 197 205 213 221 230 238 246 254 263 271 279 287 296 304

— — 95.1 99.7 104 109 114 119 124 129 135 140 145 151 156 162 167 172 178 183 188 193 198 204 209 214 220 225 231 241 252 263 274 284 295 306 316 327 338 349 359 370 381 392 402

1.3

3.0

5.4

8.4

12.1

16.5

21.4

11/8

11/4

— — — — 143 149 155 161 168 174 181 188 195 202 208 215 222 229 236 242 249 255 262 269 275 282 289 296 303 316 330 343 357 371 384 398 411 425 439 452 466 479 493 507 520

— — — — — — 206 213 221 229 237 246 254 262 271 279 288 296 304 313 321 329 337 345 354 362 371 379 387 404 421 438 454 471 488 505 522 538 556 572 589 605 622 639 656

27.2

33.6

Notes: For weight of high-strength fasteners, see Table 7-19. This table conforms to weight standards adopted by the Industrial Fasteners Institute (IFI). *Square bolt per ANSI B 18.2.1, hexagonal nut per ANSI B18.2.2. For other non-high-strength fasteners, refer to Tables 7-21 and 7-22.

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Table 7-21

Weight Adjustments for Combinations of Non-High-Strength Fasteners Other than Tabulated in Table 7-20 Add or Subtr.

100, Hex Bolts

100, Square Bolts with Hexagonal Nuts*

Square Bolts With

Combinations of 100 Square Nuts Heavy Square Nuts Heavy Hex Nuts Square Nuts Hex Nuts Heavy Square Nuts Heavy Hex Nuts Heavy Square Nuts Heavy Hex Nuts

+ + + + – + + + +

Nominal Bolt Diameter, in. 1/4

3/8

1/2

5/8

3/4

7/8

1

11/8

11/4

0.1 0.6 0.4 0.1 0.0 0.6 0.4 — —

1.0 2.1 1.5 0.6 0.4 1.7 1.1 — —

2.0 4.1 2.8 1.1 0.9 3.2 1.9 4.7 3.4

3.4 7.0 4.6 1.4 2.0 5.0 2.6 7.3 4.9

3.5 11.6 7.6 0.2 3.3 8.3 4.3 11.3 7.3

5.5 17.2 10.7 0.5 5.0 12.2 5.7 16.5 10.0

8.0 23.2 14.2 -0.2 8.2 15.0 6.0 20.7 11.7

12.2 32.1 18.9 -0.1 12.3 19.8 6.6 27.0 13.8

16.3 41.2 24.3 -1.7 18.0 23.2 6.3 33.6 16.7

Notes: For weights of high-strength fasteners, see Table 7-18. This table conforms to weight standards adopted by the Industrial Fasteners Institute (IFI). *Add or subtract value in this table to or from the value in Table 7-20.

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Table 7-22

Weights of Non-High-Strength Bolts of Diameter Greater than 11/4 in., pounds Nominal Bolt Diameter, in.

Heads of:

Weight of 100 Each

13/8

Square Bolts 105 Hex Bolts 84.0 Heavy Hex Bolts 95.0 One Linear Inch, Unthreaded Shank 42.0 One Linear Inch, Threaded Shank 35.0 Square Nuts 94.5 Heavy Square Nuts 125 Heavy Hex Nuts 102

11/2 130 112 124 50.0

13/4

2

21/4

21/2

23/4

3

— 178 195

— 259 280

— 369 397

— 508 541

— 680 720

— 900 950

89.0 113

139

168

200

120 — — 564

147 — — 738

178 — — 950

68.2

42.5 57.4 75.5 97.4 122 — — — 161 — — — 131 204 299 419

– Indicates that the bolt size is not available

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

31/4

31/2

33/4

4

— — — — 1120 1390 1730 2130 — — — — 235

272

313

356

210 246 284 325 — — — — — — — — 1190 1530 1810 2180

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AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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8–1

PART 8 DESIGN CONSIDERATIONS FOR WELDS SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–3 GENERAL REQUIREMENTS FOR WELDED JOINTS . . . . . . . . . . . . . . . . . . . . . . . 8–3 Consumables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–3 Thermal Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–3 Air-Arc Gouging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–3 Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–4 Visual Testing (VT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–4 Penetrant Testing (PT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–4 Magnetic-Particle Testing (MT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–5 Ultrasonic Testing (UT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–6 Radiographic Testing (RT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–7 PROPER SPECIFICATION OF JOINT TYPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–7 Selection of Weld Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–7 Weld Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–8 Available Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–8 Effect of Load Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–9 CONCENTRICALLY LOADED WELD GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–9 ECCENTRICALLY LOADED WELD GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–9 Eccentricity in the Plane of the Faying Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–9 Instantaneous Center of Rotation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–9 Elastic Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–12 Eccentricity Normal to the Plane of the Faying Surface . . . . . . . . . . . . . . . . . . . . . 8–14 OTHER SPECIFICATION REQUIREMENTS AND DESIGN CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–15 Special Requirements for Heavy Shapes and Plates . . . . . . . . . . . . . . . . . . . . . . . . . 8–15 Placement of Weld Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–15 Welds in Combination with Bolts or Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–15 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–15 One-Sided Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–15 Welding Considerations and Appurtenances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–15 Clearance Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–15 Excessive Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–17 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Minimum Shelf Dimensions for Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–17 Beam Copes and Weld Access Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–18 Corner Clips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–18 Backing Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–19 Spacer Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–19 Weld Tabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–19 Tack Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–21 Lamellar Tearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–21 Prior Qualification of Welding Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–21 Painting Welded Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–22 WELDING CONSIDERATIONS FOR HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–23 HSS Welding Requirements in AWS D1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–24 Clause 2, Part D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–25 Clause 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–25 Clause 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–25 Clause 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–26 Clause 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–26 Weld Sizing for Uneven Distribution of Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–26 Detailing Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–27 DESIGN TABLE DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–27 PART 8 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–32 DESIGN TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–33 Table 8-1. Coefficients, C, for Concentrically Loaded Weld Group Elements . . . . 8–33 Table 8-2. Prequalified Welded Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–34 Table 8-3. Electrode Strength Coefficient, C1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–65 Table 8-4. Coefficients, C, for Eccentrically Loaded Weld Groups . . . . . . . . . . . . . 8–66 Table 8-5. Coefficients, C, for Eccentrically Loaded Weld Groups . . . . . . . . . . . . . 8–72 Table 8-6. Coefficients, C, for Eccentrically Loaded Weld Groups . . . . . . . . . . . . . 8–78 Table 8-7. Coefficients, C, for Eccentrically Loaded Weld Groups . . . . . . . . . . . . . 8–84 Table 8-8. Coefficients, C, for Eccentrically Loaded Weld Groups . . . . . . . . . . . . . 8–90 Table 8-9. Coefficients, C, for Eccentrically Loaded Weld Groups . . . . . . . . . . . . . 8–96 Table 8-10. Coefficients, C, for Eccentrically Loaded Weld Groups . . . . . . . . . . . 8–102 Table 8-10a. Coefficients, C, for Eccentrically Loaded Weld Groups . . . . . . . . . . 8–108 Table 8-11. Coefficients, C, for Eccentrically Loaded Weld Groups . . . . . . . . . . . 8–113 Table 8-11a. Coefficients, C, for Eccentrically Loaded Weld Groups . . . . . . . . . . 8–119 Tables 8-12. Approximate Number of Passes for Welds . . . . . . . . . . . . . . . . . . . . 8–124 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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GENERAL REQUIREMENTS FOR WELDED JOINTS

8–3

SCOPE The specification requirements and other design considerations summarized in this Part apply to the design of welded joints. For the design of connecting elements, see Part 9. For the design of simple shear, moment, bracing and other connections, see Parts 10 through 15.

GENERAL REQUIREMENTS FOR WELDED JOINTS The requirements for welded construction are given in AISC Specification Section M2.4, which requires the use of AWS D1.1, except as modified in AISC Specification Section J2. For further information see also Blodgett et al. (1997). Welding in structural steel is performed in compliance with written welding procedure specifications (WPS). WPS are qualified by test or prequalified in AWS D1.1. WPS are used to control base metal, consumables, joint geometry, electrical and other essential variables for welded joints.

Consumables Requirements for welding consumables are given in AISC Specification Sections A3.5, J2.6 and J2.7. Permissible filler metal strengths are shown in Table J2.5, based on matching filler metals shown in AWS D1.1 Table 3.1. Filler metal notch-toughness requirements are given in AISC Specification Section J2.6. Low-hydrogen electrodes for shielded metal arc welding (SMAW) are required, as shown in AWS D1.1 Table 3.1. Low-hydrogen SMAW electrodes have a limited exposure time and rod ovens are necessary near the point of use for storage. Requirements for the manufacture, classification and packing of consumables are given in AWS A5.x specifications. Consumables vary based upon their welding process. SMAW, or “stick” welding, is a manual process. Submerged arc welding (SAW) is a semiautomatic or automatic process. Consumables are classified as an electrode flux combination because the weld metal properties are dependant on both the electrode and the flux. SAW is suitable for long straight or circumferential welds but the work must be performed in horizontal or flat positions. Flux-cored arc welding (FCAW) uses wire electrode that contains flux in the center. FCAW electrodes are provided for use with a gas shield or self shield. Gas for shielding is argon, carbon dioxide or a combination of the two. Gas metal arc welding (GMAW) uses wire electrodes that are solid or have a metal core. GMAW is performed with gas shielding.

Thermal Cutting Oxygen-fuel gas cutting can be used to cut almost any commercially available plate thickness. If the plate being cut contains large discontinuities or nonmetallic inclusions, turbulence may be created in the cutting stream, resulting in notches or gouges in the edge of the cut. Plasma-arc cutting is much faster and less susceptible to the effects of discontinuities or nonmetallic inclusions, but leaves a slight taper in the cut as it descends and can be used only up to about 11/2-in. thickness.

Air-Arc Gouging In this method, a carbon arc is used to melt a nugget-shaped area of the base metal, which is blown away with a jet of compressed air. Air-arc gouging can be used to remove weld AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN CONSIDERATIONS FOR WELDS

defects, gouge the weld root to sound weld metal, form a U groove on one side of a square butt joint, and for similar operations.

Inspection The five most commonly used methods for welding inspection are discussed following and in the Guide for the Nondestructive Examination of Welds (AWS B1.10) (AWS, 1992). Chapter N of the AISC Specification contains requirements for nondestructive examination (NDE) of welds. The general contractor or owner must arrange for this. This work must be scheduled to minimize interruption of the fabricator and erector. See AISC Specification Section N5.2.The designer may specify in the contract documents the types of weld inspection required as well as the extent and application of each type of inspection differing from the requirements of Chapter N. In the absence of instructions for weld inspection, the fabricator or erector is only responsible for those weld discontinuities found by visual inspection (see AWS D1.1). Welds may have defects that cannot be rejected based on AWS criteria. Stipulation of various NDE methods has the effect of selecting acceptance criteria and therefore has a related effect on costs. Weld repairs which may be difficult to perform and which may potentially damage other aspects of the connection are best referred to the engineer of record to determine the necessity of the correction with due consideration of fitness for purpose. Visual inspection is the most commonly required inspection process. The designer must realize that more stringent requirements for inspection can needlessly add significant cost to the project and should specify them only in those instances where they are essential to the integrity of the structure.

Visual Testing (VT) Visual inspection provides the most economical way to check weld quality and is the most commonly used method. Joints are scrutinized prior to the commencement of welding to check fit-up, preparation bevels, gaps, alignment and other variables. After the joint is welded, it is then visually inspected in accordance with AWS D1.1. If a discontinuity is suspected, the weld is either repaired or other inspection methods are used to validate the integrity of the weld. In most cases, timely visual inspection by an experienced inspector is sufficient and offers the most practical and effective inspection alternative to other, more costly methods.

Penetrant Testing (PT) This test uses a red dye penetrant applied to the work from a pressure spray can. The dye penetrates any crack or crevice open to the surface. Excess dye is removed and white developer is sprayed on. Dye seeps out of the crack, producing a red image on the white developer (See Figure 8-1). Penetrant testing (PT) can be used to detect tight cracks as long as they are open to the surface. However, only surface cracks are detectable. Furthermore, deep weld ripples and scratches may give a false indication when PT is used. Dye penetrant examination tends to be messy and slow, but can be helpful when determining the extent of a defect found by visual inspection. This is especially true when a defect is being removed by gouging or grinding for the repair of a weld to assure that the defect is completely removed. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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8–5

Magnetic-Particle Testing (MT) A magnetizing current is introduced with a yoke or contact prods into the weldment to be inspected, as sketched in Figure 8-2 (prods shown). This induces a magnetic field in the work, which will be distorted by any cracks, seams, inclusions, etc. located on or near (within approximately 0.1 in. of) the surface. A dry magnetic powder blown lightly on the surface by a rubber squirt bulb will be picked up at such discontinuities making a distinct mark. The magnetically held particles show the location, size, and shape of the discontinuity. The method will indicate surface cracks that might be difficult for liquid penetrant to enter and subsurface cracks to about 0.1-in. depth, with proper magnetization. Records may be kept by picking up the powder pattern with clear plastic tape. Cleanup is easy, but demagnetizing, if necessary, may not be. If the magnetizing prod is lifted from the work while the current is still on, an arc strike which could lead to cracking could result. If arc strikes occur, they should be ground out. Magnetic particle examination can be useful when a defect is suspected from visual inspection or when the absence of cracking in areas of high restraint must be confirmed. Relatively smooth surfaces are required for MT and it is reasonably economical. Where delayed cracking is suspected, the nondestructive examination may have to be performed after a cooling time—typically 48 hours.

Fig. 8-1. Schematic illustration of penetrant testing (PT).

Fig. 8-2. Schematic illustration of magnetic particle testing (MT). AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Ultrasonic Testing (UT) The ultrasonic inspection process is analogous to sonar. A short pulse of high-frequency sound is broadcast from a crystal into a metal, after which the crystal waits to receive reflections from the far end of the metal member and from any voids encountered on the way through. The technique is called pulse echo. The sound beam is produced by a piezoelectric transducer energized by an electric current which causes the crystal to vibrate and transmit through a liquid couplant into the metal. Any reflections are displayed as pips on a cathode ray tube (CRT) grid whose horizontal scale represents distance through the metal. The vertical scale represents the strength (or area) of the reflecting surface. The system is shown schematically in Figure 8-3. The accuracy of ultrasonic inspection is highly dependent upon the skill and training of the operator and frequent calibration of the instrument. There is a “dead” area beneath most transducers that makes it difficult to inspect members less than 5/16 in. in thickness. Austenitic stainless steels and extremely coarse-grained steels, e.g., electroslag welds, are difficult to inspect; but on structural carbon and low-alloy steels, the process can detect flat discontinuities (favorably oriented for reflection) smaller than 1/64 in. The crystal, which is 3 /8 in. to 1 in. in size, can be readily moved about to check many orientations and can project the beam into the metal at angles of 90°, 70°, 60° and 45°. With the latter three angles,

Fig. 8-3. Variations in UT reflections caused by defects at the boundary. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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the beam can be bounced around inside the metal, producing echoes from any discontinuity on the way. For more information see Krautkramer (1990) and Institute of Welding (1972). Ultrasonic testing (UT) is a more versatile, rapid and economical inspection method than radiography, but it does not provide a permanent record like the X-ray negative. The operator, instead, makes a written record of discontinuity indications appearing on his CRT. Certain joint geometry limits the use of the ultrasonic method. Ultrasonic examination has limited applicability in some applications, such as HSS fabrication. Relatively thin sections and variations in joint geometry can lead to difficulties in interpreting the signals, although technicians with specific experience on weldments similar to those to be examined may be able to decipher UT readings in some instances. Similarly, UT is usually not suitable for use with fillet welds and smaller partial-joint-penetration (PJP) groove welds. Complete-joint-penetration (CJP) groove welds with and without backing bars also give readings that are subject to differing interpretations. Ultrasonic examination may be specified to validate the integrity of CJP groove welds that are subject to tension. Ultrasonic examination has largely replaced radiographic examination for the inspection of critical CJP groove welds in building construction. New technology called phased array is in development and in use in some applications. Phased array is a computer controlled ultrasonic examination capable of providing an informative display. AWSD1.1 provisions for acceptance criteria have not been adopted for this method at this time.

Radiographic Testing (RT) Radiographic testing (RT) is basically an X-ray film process. To be detected by radiography, a crack must be oriented roughly parallel to the impinging radiation beam, and occupy about 11/2% of the metal thickness along that beam. There are problems with radiographs of fillets, tee and corner joints, however, because the radiation beam must penetrate varying thicknesses. Precautions for avoiding radiation hazards interfere with shop work, and equipment and film costs make it the most expensive inspection method. Ultrasonic systems have gradually supplemented and even supplanted radiography. Radiographic examination has very limited applicability in some applications, such as for HSS fabrication, because of the irregular shape of common joints and the resulting variations in thickness of material as projected onto film. RT can be used successfully for butt splices, but can only provide limited information about the condition of fusion at backing bars near the root corners. The general inability to place either the radiation source or the film inside the HSS means that exposures must usually be taken through both the front and back faces of the section with the film attached to the outside of the back face. Several such shots progressing around the member are needed to examine the complete joint.

PROPER SPECIFICATION OF JOINT TYPE Selection of Weld Type The most common weld types are fillet and groove welds. Fillet welds are normally more economical than groove welds and generally should be used in applications for which groove welds are not required. Additionally, fillet welds around the inside of holes or slots require less weld metal than plug or slot welds of the same size, even though the diameters of holes and widths of slots for fillet welds must be larger to accommodate the necessary tilt of the electrode. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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PJP groove welds are more economical than CJP groove welds. When groove welds are required, bevel and V groove welds, which can be flame-cut, are usually more economical than J and U groove welds, which must be air-arc gouged or planed. Also, double-bevel, double-V, double-J, and double-U welds are typically more economical than welds of the same type with single-sided preparation because they use less weld metal, particularly as the thickness of the connection element(s) being welded increases. The symmetry also results in less rotational distortion strain. However, in thinner connection elements, the savings in weld-metal volume may not offset the additional cost of double edge preparation, weld-root cleaning, and repositioning. As a general rule of thumb, double-sided joint preparation is normally less expensive than single-sided preparation above 1-in. thickness.

Weld Symbols For guidance on the proper use of weld symbols, refer to Table 8-2. More extensive information on weld symbols may be found in AWS A2.4, Standard Symbols for Welding, Brazing, and Nondestructive Examination (AWS, 2007).

Available Strength The available strength of a welded joint is determined in accordance with AISC Specification Section J2.4 and Table J2.5. The calculation of the available strength of a longitudinally loaded fillet weld can be simplified from that given in AISC Specification Table J2.5. For a fillet weld less than or equal to 100 times the weld size in length, the available shear strength, φRn or Rn/Ω, may be calculated as follows:

⎛ 2⎞⎛ D⎞ ⎜ ⎟l ⎝ 2 ⎟⎠ ⎝ 16 ⎠

Rn = 0.60 FEXX ⎜

φ = 0.75

(8-1)

Ω = 2.00

where l = length, in. D = weld size in sixteenths of an inch For FEXX = 70 ksi: LRFD

ASD

φRn = 1.392Dl

(8-2a)

Rn = 0.928Dl Ω

(8-2b)

When the fillet weld is not longitudinally loaded, the alternative provisions in AISC Specification Section J2.4(a) may be used to take advantage of the increased strength due to load angle. The maximum strength increase will be for a transversely loaded fillet weld, which is 50% stronger than the same fillet weld longitudinally loaded.

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Effect of Load Angle When designing fillet welds, the increased strength due to loading angle may be accounted for by multiplying the available strength of the weld by the following expression, as given in AISC Specification Equation J2-5: (1.0 + 0.50sin1.5 θ) where θ = angle of loading measured from the weld longitudinal axis, degrees For transversely loaded welds, θ = 90°. This accounts for a 50% increase in weld strength over a longitudinally loaded weld. However, this increased weld strength is accompanied by a decrease in ductility. For a single line weld, the decreased ductility is inconsequential for most applications. However, for weld groups composed of welds loaded at various angles, this change in ductility means that the designer must consider load-deformation compatibility.

CONCENTRICALLY LOADED WELD GROUPS The load-deformation curves shown in Figure 8-5 highlight the need for consideration of deformation compatibility, since the transversely loaded weld will fracture before the longitudinally loaded weld obtains its full strength. A simplified procedure for determining the available strength of concentrically loaded fillet weld groups is discussed later in Part 8 using Table 8-1. In lieu of using this procedure, it is permitted to sum the capacities of individual weld elements, neglecting load-deformation compatibility, when no increase in strength due to the loading angle is assumed.

ECCENTRICALLY LOADED WELD GROUPS Eccentricity in the Plane of the Faying Surface Eccentricity in the plane of the faying surface produces additional shear. The welds must be designed to resist the combined effect of the direct shear, Pu or Pa, and the additional shear from the induced moment, Pu e or Pa e. Two methods of analysis for this type of eccentricity are the instantaneous center of rotation method and the elastic method. The instantaneous center of rotation method is more accurate, but generally requires the use of tabulated values or an iterative solution. The elastic method is simplified, but may be excessively conservative because it neglects the ductility of the weld group and the potential load increase.

Instantaneous Center of Rotation Method Eccentricity produces both a rotation and a translation of one connection element with respect to the other. The combined effect of this rotation and translation is equivalent to a rotation about a point defined as the instantaneous center of rotation (IC) as illustrated in Figure 8-4(a). The location of the IC depends upon the geometry of the weld group as well as the direction and point of application of the load.

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The load deformation relationship for a unit length segment of the weld, as illustrated in Figure 8-5, is an approximation of the equation by Lesik and Kennedy (1990). The nominal shear strength of the weld element, Fnwi , is limited by the deformation, Δui, of the weld segment that first reaches its limit, where Fnwi = 0.60FEXX (1.0 + 0.50 sin1.5 θi ) [pi (1.9 − 0.9pi)]0.3

(a) Instantaneous center of rotation (IC)

(b) Forces on weld elements Fig. 8-4. Instantaneous center of rotation method.

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where Fnwi FEXX θi pi Δi Δucr Δui w

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= nominal shear strength of the weld segment at a deformation, Δ, ksi = weld electrode strength, ksi = load angle measured relative to the weld longitudinal axis, degrees = ratio of element deformation, Δi, to its deformation at the maximum stress, Δmi = deformation of the element taken as the critical deformation, Δucr, proportioned by the ratio of the IC to element distance to the IC to critical element distance, in. = ultimate deformation of the critical element, Δui, of the element with the minimum Δui /(IC to element distance), in. = 1.087w(θi + 6)-0.65 ≤ 0.17w, in. (8-4) = weld leg size, in.

Unlike the load-deformation relationship for bolts, the strength deformation of welds is dependent upon the angle, θi, that the resultant elemental force makes with the axis of the weld element. Load-deformation curves in Figure 8-5 for values of weld element shear strength, P, relative to Po = 0.60FEXX for values of θi = 0º, 15º, 30º, 45º, 60º, 75º and 90º are shown. For further information, see AISC Specification Section J2.4 and its commentary. The nominal strengths of the other unit-length weld segments in the joint can be determined by applying a deformation, Δ, that varies linearly with the distance from the IC. The nominal shear strength of the weld group is, then, the sum of the individual strengths of all weld segments. Because of the nonlinear nature of the requisite iterative solution, for sufficient accuracy, a minimum of 20 weld elements for the longest line segment is generally recommended.

Fig. 8-5. Fillet weld strength as a function of load angle, θ.

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The individual resistance of each weld segment is assumed to act on a line perpendicular to a ray passing through the IC and the centroid of that weld segment, as illustrated in Figure 8-4(b). If the correct location of the instantaneous center has been selected, the three equations of in-plane static equilibrium, ΣFx Awei = 0, ΣFy Awei = 0, and ΣM = 0, will be satisfied, where Awei is the effective weld area. For further information, see Crawford and Kulak (1968) and Butler et al. (1972).

Elastic Method For a force applied as illustrated in Figure 8-4, the eccentric force, Pu or Pa, is resolved into a force, Pu or Pa, acting through the center of gravity (CG) of the weld group and a moment, Pu e or Pa e, where e is the eccentricity. Each weld element is then assumed to resist an equal share of the direct shear, Pu or Pa, and a share of the eccentric moment, Pu e or Pa e, proportional to its distance from the CG. The resultant vectorial sum of these forces, ru or ra, is the required strength for the weld. The shear per linear inch of weld due to the concentric force, rpu or rpa, is determined as LRFD rpu =

ASD

Pu l

(8-5a)

rpa =

Pa l

(8-5b)

where l = total length of the weld in the weld group, in. To determine the resultant shear per linear inch of weld, rpu or rpa must be resolved into horizontal components, rpux or rpax, and vertical components, rpuy or rpay, where rpux rpax rpuy rpay

= rpusinθ (LRFD) = rpasinθ (ASD) = rpucosθ (LRFD) = rpacosθ (ASD)

(8-6a) (8-6b) (8-7a) (8-7b)

The shear per linear inch of weld due to the moment, Pu e or Pa e, is rmu or rma, where LRFD rmu =

ASD

Puec Ip

(8-8a)

rma =

Paec Ip

(8-8b)

where c = radial distance from CG to point in weld group most remote from CG, in. Ip = Ix + Iy = polar moment of inertia of the weld group, in.4 per in. Refer to Figure 8-6. For section moduli and torsional constants of various welds treated as line elements, refer to Table 5 in Section 7 of Blodgett (1966).

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⎛ π 2⎞ I xo = ⎜ − ⎟ R3 ⎝ 4 π⎠ 2 ⎛ π 2⎞ I x = ⎜ − ⎟ R3 + l ( d y ) ⎝ 4 π⎠

⎛ π 2⎞ I yo = ⎜ − ⎟ R3 ⎝ 4 π⎠ ⎛ π 2⎞ 2 I y = ⎜ − ⎟ R3 + l ( d x ) ⎝ 4 π⎠ Fig. 8-6. Moments of inertia of various weld segments.

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To determine the resultant force on the most highly stressed weld element, rmu or rma must be resolved into horizontal component rmux or rmax and vertical component rmuy or rmay, where LRFD

ASD

rmux =

Puecy Ip

(8-9a)

rmax =

Paecy Ip

(8-9b)

rmuy =

Puecx Ip

(8-10a)

rmay =

Paecx Ip

(8-10b)

In the above equations, cx and cy are the horizontal and vertical components of the radial distance c at the point where ru or ra is a maximum. The point in the weld group where the stress is highest will usually be at a corner, or a termination, or where the element is farthest from the center of gravity. Thus, the resultant force, ru or ra, is determined as LRFD ru =

ASD

(rpux + rmux )2 + (rpuy + rmuy )2

(8-11a) ra =

(rpax + rmax )2 + (rpay + rmay )2

(8-11b)

which should be compared against the available strength, found in AISC Specification Table J2.5. For further information, see Higgins (1971).

Eccentricity Normal to the Plane of the Faying Surface Eccentricity normal to the plane of the faying surface produces tension above and compression below the neutral axis, as illustrated in Figure 8-7 for a bracket connection. The eccentric force, Pu or Pa, is resolved into a direct shear, Pu or Pa, acting at the faying surface

Fig. 8-7. Welds subject to eccentricity normal to the plane of the faying surface. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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of the joint and a moment normal to the plane of the faying surface, Pu e or Pa e, where e is the eccentricity. Each unit-length segment of weld is then assumed to resist an equal share of the concentric force, Pu or Pa, and the moment is resisted by tension in the welds above the neutral axis and compression below the neutral axis. In contrast to bolts, where the interaction of shear and tension must be considered, for welds, shear and tension can be combined vectorially into a resultant shear. Thus, the solution of a weld loaded eccentrically normal to the plane of the faying surface is similar to that discussed previously for welds loaded eccentrically in the plane of the faying surface.

OTHER SPECIFICATION REQUIREMENTS AND DESIGN CONSIDERATIONS The following other specification requirements and design considerations apply to the design of welded joints.

Special Requirements for Heavy Shapes and Plates For CJP groove welded joints in heavy shapes with a flange thickness exceeding 2 in. or built-up sections consisting of plates with a thickness exceeding 2 in., see AISC Specification Sections A3.1c and Section A3.1d.

Placement of Weld Groups For the required placement of weld groups at the ends of axially loaded members, see AISC Specification Section J1.7.

Welds in Combination with Bolts or Rivets For welds used in combination with bolts or rivets, see AISC Specification Section J1.8.

Fatigue For applications involving fatigue, see AISC Specification Appendix 3.

One-Sided Fillet Welds When lateral deformation is not otherwise prevented, a severe notch can result at locations of one-sided welds. For the fillet-welded joint illustrated in Figure 8-8, the unwelded side has no strength in tension and a notch may form from the unwelded side. Using one fillet weld on each side will eliminate this condition. This is also true with PJP groove welds.

Welding Considerations and Appurtenances Clearance Requirements Clearances are required to allow the welder to make proper welds. Ample room must be provided so that the welder or welding operator may manipulate the electrode and observe the weld as it is being deposited. In the SMAW process, the preferred position of the electrode when welding in the horizontal position is in a plane forming 30° with the vertical side of the fillet weld being made. However, this angle, shown as angle x in Figure 8-9, may be varied somewhat to avoid AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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contact with some projecting part of the work. A simple rule to provide adequate clearance for the electrode in horizontal fillet welding is that the clear distance to a projecting element should be at least one-half the distance y in Figure 8-9(b). A special case of minimum clearance for welding with a straight electrode is illustrated in Figure 8-10. The 20° angle is the minimum that will allow satisfactory welding along the bottom of the angle and therefore governs the setback with respect to the end of the beam. If a 1/2-in. setback and 3/8-in. electrode diameter were used, the clearance between the angle and the beam flange could be no less than 11/4 in. for an angle with a leg dimension, w, of 3 in., nor less than 15/8 in. with a w of 4 in. When it is not possible to provide

Fig. 8-8. Notch effect at one-sided weld.

Fig. 8-9. Clearances for SMAW welding.

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this clearance, the end of the angle may be cut as noted by the optional cut in Figure 8-10 to allow the necessary angle. However, this secondary cut will increase the cost of fabricating the connection.

Excessive Welding The specification of over or excessive welding will increase the amount of heat input into the parts joined and thereby add to distortion in the joint. Distortion of the joint is caused by three fundamental dimensional changes that occur during and after welding: 1. Transverse shrinkage that occurs perpendicular to the weld line, 2. Longitudinal shrinkage that occurs parallel to the weld line, and 3. Angular change that consists of rotation around the weld line. If these dimensional changes alter the joint so that it is no longer within fabrication tolerances, the joint may need to be repaired with additional heating to bring the joint back to within fabrication tolerances. This added work will result in expensive repair costs which could have been avoided with appropriately sized welds. Over-specification of weld size also increases the cost of welding for no structural benefit.

Minimum Shelf Dimensions for Fillet Welds The recommended minimum shelf dimensions for normal size SMAW fillet welds are summarized in Figure 8-11. SAW fillet welds would require a greater shelf dimension to contain

Fig. 8-10. Clearances for SMAW welding.

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the flux, although auxiliary material can be clamped to the member to provide for this. The dimension b illustrated in Figure 8-12 must be sufficient to accommodate the combined dimensional variations of the angle length, cope depth, beam depth and weld size.

Beam Copes and Weld Access Holes Requirements for beam copes and weld access holes are given in AISC Specification Sections J1.6 and M2.2. Weld access holes, as illustrated in Figure 8-13, are used to permit down-hand welding to the beam bottom flange, as well as the placement of a continuous backing bar under the beam top flange. Weld access holes also help to mitigate the effects of weld shrinkage strains and prevent the intersection or close juncture of welds in orthogonal directions. Weld access holes should not be filled with weld metal because doing so may result in a state of triaxial stress under loading.

Corner Clips Corners of stiffeners and similar elements that fit into a corner should be clipped generously to avoid the lack of fusion that would likely result in that corner. In general, a 3/4-in. clip will be adequate, although this dimension can be adjusted to suit conditions, such as when the fillet radius is larger or smaller than that for which a 3/4-in. clip is appropriate. For further information, see Butler et al. (1972) and Blodgett (1980).

Fig. 8-11. Recommended minimum shelf dimensions for SMAW fillet welds.

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Backing Bars Backing bars, illustrated in Figure 8-13, should be of approved weldable material as specified in AWS D1.1 Section 5.2.2.2. Per AWS D1.1, backing bars on groove-welded joints are usually continuous or fully spliced to avoid stress concentrations or discontinuities and should be thoroughly fused with the weld metal. Backing bar removal is addressed in AISC Specification Section J2.6 and AWS D1.1.

Spacer Bars Spacer bars, illustrated in Figure 8-13, must be of the same material specification as the base metal, per AWS D1.1 Section 5.2.2.3. This can create a procurement problem, since small tonnage requirements may make them difficult to obtain in the specified ASTM designation.

Weld Tabs To obtain a fully welded cross section, the termination at either end of the joint must be of sound weld metal. Weld tabs, illustrated in Figure 8-13, should be of approved weldable material as specified in AWS D1.1 Section 5.2.2.1. Two configurations of weld tabs are illustrated in Figure 8-14, including flat-type weld tabs, which are normally used with bevel and V groove welds, and contour-type weld tabs, which are normally used with J and U

Fig. 8-12. Illustration of shelf dimensions for fillet welding.

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groove welds. Weld-tab removal is addressed in AWS D1.1. Frequently, the backing bar can be extended to serve as the weld tab. Some welds performed in the horizontal position require shelf bars. Shelf bars will be left in place unless they are required to be removed by the engineer.

Fig. 8-13. Illustration of backing bars, spacer bars, weld tabs and other fittings for welding.

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Tack Welds Tack welds placed as shown in Figure 8-15(a) should be avoided as they may cause notches. An improved detail is as shown in Figure 8-15(b), with the tack welds placed where they will be consumed in the final welded joint.

Lamellar Tearing Figures 8-16 and 8-17 illustrate preferred welded joint selection and connection configurations for avoiding susceptibility to lamellar tearing. Refer to the discussion “Avoiding Lamellar Tearing” in Part 2.

Prior Qualification of Welding Procedures Evidence of prior qualification of welding procedures, welders, welding operators or tackers may be accepted at the discretion of the owner’s designated representative for design,

Fig. 8-14. Illustration of weld tabs.

(a) Susceptible Detail

(b) Improved Detail

Fig. 8-15. Backing bar tack welding.

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resulting in significant cost savings. Fabricators that participate in the AISC Quality Certification Program have the experience and documentation necessary to assure that such prior qualifications could be accepted. For more information about the AISC Quality Certification Program, visit www.aisc.org.

Painting Welded Connections Paint is normally omitted in areas to be field-welded, per AISC Specification Section M3.5. Note that this requirement does not generally apply to shop-assembled connections, because painting is normally done after the welds are made. When required, the small paint-free

(a)

(b)

(c)

Fig. 8-16. Susceptible and improved details to reduce the incidence of lamellar tearing.

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areas can generally be identified with a general note (e.g., “no paint on OSL of connection angles,” where OSL stands for outstanding leg).

WELDING CONSIDERATIONS FOR HSS Flare welds are more common in HSS because of the increasing likelihood that the HSS corner is a part of the welded joint. A common flare bevel configuration which occurs when equal width sections are joined is illustrated in Figure 8-18. The easiest arrangement for welding occurs with equal wall thickness sections. However, when the corner radius increases due to wall thickness or manufacturing tolerances, the root gap may need to be adjusted by profile shaping, building out with weld metal, or by use of backing. See Figures 8-18 and 8-19.

Fig. 8-17. Susceptible and improved details to avoid intersecting welds with high restraint.

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HSS Welding Requirements in AWS D1.1 AWS uses the terminology “tubular” for all hollow members including pipe, hollow structural sections, and fabricated box sections. The following sections in AWS D1.1 apply to welded HSS-to-HSS connections:

Fig. 8-18. Flare bevel weld, equal width HSS weld joint.

Fig. 8-19. Welding methods accounting for the HSS corner radius.

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Clause 2, Part D As explained in AWS D1.1 Commentary Section C-2.21, “In commonly used types of tubular connections, the weld itself may not be the factor limiting the capacity of the joint. Such limitations as local failure (punching shear), general collapse of the main member, and lamellar tearing are discussed because they are not adequately covered in other codes.” Because of these various failure modes, the design of HSS-to-HSS connections must be part of the member sizing process. The members selected must be capable of transmitting the required strength or adequate reinforcement must be shown on the design documents. Differences in the relative stiffness across HSS walls loaded normal to their surface can make the load transfer highly nonuniform. To prevent progressive failure and to ensure ductile behavior of the joint, minimum welds must be provided in T-, Y- and K-connections to transmit the factored load in the branch or web member. For normal building applications, fillet welds and PJP welds can be used. While Part D deals primarily with HSS-to-HSS connections, some of these provisions are applicable to welded attachments that deliver a load normal to the wall of a tubular member.

Clause 3 AWS D1.1 Figure 3.2 shows prequalified fillet weld details for tubular joints that differ from details for nontubular skewed T-joints. These details will provide the minimum weld strength needed to ensure ductile joint behavior. AWS Figure 3.3 shows the joint detail and the effective throat for a flare-bevel and flareV PJP groove weld that is commonly used for welding connection material to the face of an HSS. Groove welded joint details for HSS are designed to accommodate both the geometry of the section and the lack of access to the back side of the joint. AWS Figure 3.5 shows various PJP groove welded HSS joint details and AWS Figures 3.6, 3.8, 3.9 and 3.10 show CJP groove welded HSS joint details. The joint preparation and weld sizing are complex and critical to obtain a sound weld. These details also provide the weld strength needed to ensure ductile joint behavior.

Clause 4 AWS D1.1 Clause 4, Qualification, covers the requirements for qualification testing of welding procedure specifications (WPS, see p. 8-3) and performance testing of the welder’s ability to produce sound welds. HSS connections may not always meet the requirements for a prequalified WPS because of unique geometry, connection access or for other reasons. This section also gives the requirements for a procedure qualification record (PQR), which is the basis for qualifying a WPS. The performance testing of welders and welding operators considers process, material thickness, position, nontubular or tubular joint access. AWS D1.1 Tables 4.1 through 4.4 list the required qualifications needed for each type of joint. Most welders are qualified for a particular process and position-in-plate (nontubular) joints. These qualifications will allow the welder to make similar fillet, PJP groove and backed CJP welds in tubular members. However, certain types of tubular connections, such as unbacked T-, Y- and K-connections, require special welder certifications because the lack of access to the back of the joint, the position of the connection, and the access to the connection require special skill to produce a sound connection.

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Clause 5 Clause 5, Fabrication, covers the requirements for the preparation, assembly and workmanship of welded steel structures. AWS Table 5.5, Tubular Root Opening Tolerances, gives the acceptable fitup for unbacked groove welds. AWS Table 5.8, Minimum Fillet Weld Size, and Section 2.25.1.3 give the minimum weld pass size based on material thickness and process.

Clause 6 Clause 6, Inspection, contains all of the requirements for the inspector’s qualifications and responsibilities, acceptance criteria for discontinuities, and procedures for NDE. AWS D1.1 considers fabrication/erection inspection and testing a separate function from verification inspection and testing. Fabrication/erection inspection and testing is usually the responsibility of the contractor and is performed as appropriate prior to assembly, during assembly, during welding, and after welding to ensure the requirements of the contract documents are met. Verification inspection and testing are the prerogatives of the owner. The extent of NDE and verification inspection must be specified in the contract documents. The inspection covers WPS qualification, equipment, welder qualification, joint preparation, joint fitup, welding techniques, and weld size length and location. It is especially important when inspecting HSS-to-HSS joints that joint preparation and fitup be checked prior to welding. In addition to inspecting the above items, AWS requires all welds to be visually inspected for conformance to the standards in AWS Table 6.1, Visual Acceptance Criteria. Four types of nondestructive testing can be used to supplement visual inspection. They are penetrant testing, magnetic particle testing, radiographic testing, and ultrasonic testing. The AWS ultrasonic testing (UT) acceptance criteria for non-HSS type groove welds starts at 5/16-in.-thick material. The procedures for HSS T-, Y- and K- connections have a minimum applicable thickness of 1/2 in., and diameter of 123/4 in. AWS does, however, make provision for qualifying UT procedures for smaller size applications. It is possible to UT portions of butt-type splices with backing bars using the non-HSS criteria, however, the corners of rectangular HSS cannot be inspected. AWS D1.1 makes provision for using alternate acceptance criteria based upon an evaluation of suitability for service using past experience, experimental evidence or engineering analysis. This can be especially important when deciding if and how to make any repairs.

Weld Sizing for Uneven Distribution of Loads The connection strength for a member welded normal to an HSS wall is a function of the geometric parameters of the connected members and is often less than the full strength of the member. When limited by geometry, the available strength cannot be increased by increasing the weld strength. Due to the varying relative flexibility of the HSS wall loaded normal to its surface and the axial stiffness of the connected member, the transfer of load along the weld line is highly nonuniform. To prevent progressive failure, or “unzipping” of the weld, it is important to provide adequate welds to maintain ductile behavior of the joint. Welds that satisfy this ductility requirement can be proportioned for the required strength using an effective width criteria similar to that used for checking the axial strength of the

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branch member or plate. For effective weld length of HSS-to-HSS connections, refer to AISC Specification Section K4. An alternative to the effective length procedure is the use of the prequalified fillet and PJP groove weld details in AWS D1.1 that are sized to ensure ductile behavior. In addition, fillet welds with an effective throat of 1.1 times the thickness of the branch member can be used. Either of these two alternatives will, in most cases, be conservative.

Detailing Considerations 1. Butt joints will require a groove weld detail. Where possible the joint should be a prequalified PJP groove weld sized for actual load or a CJP groove weld with steel backing. 2. T-, Y- and K-connections should, where possible, use either fillet welds or PJP groove welds sized for the design forces and checked for the minimum size needed to ensure ductile joint behavior. Where CJP welds are required, joint details using steel backing should be used whenever possible. For a detailed discussion of various types of backing and the advantages of using backing, see Post (1990).

DESIGN TABLE DISCUSSION Table 8-1. Coefficients, C, for Concentrically Loaded Weld Group Elements Concentrically loaded fillet weld groups must consider the effect of loading angle and deformation compatibility on weld strength. By multiplying the appropriate values of C from Table 8-1 by the available strength of each weld element, an effective strength is determined for each weld element. The available strength of the weld group can be determined by summing the effective strengths of all of the elements in a weld group. It should be noted that this table is to be entered at the largest load angle on any weld in the weld group. For the weld group shown in Figure 8-20, this is calculated as: LRFD φRw = 1.392 D

ASD (8-12a)

Rw /Ω = 0.928 D

× ⎡⎣1.5 (1) + 1.29 (1.41) + 0.825 (1) ⎤⎦ = 5.77 D

(8-12b)

× ⎡⎣1.5 (1) + 1.29 (1.41) + 0.825 (1) ⎤⎦ = 3.85 D

Table 8-2. Prequalified Welded Joints The prequalified welded joints details given in AWS D1.1 and Table 8-2 provide joint geometries, such as root openings, angles and clearances (see Figures 8-21 and 8-22) that will permit the deposition of sound weld material. Prequalified welded joints are not, in themselves, adequate consideration of welded design details and the other provisions in AWS D1.1 must be satisfied as they are referenced in AISC Specification Section J2. The design and detailing for successful welded construction requires consideration of factors which include, but are not limited to, the magnitude, type and distribution of forces to be

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transmitted, access, restraint against weld shrinkage, thickness of connected materials, residual stress, and distortion. AWS D1.1 has provisions for material that is thinner than is normally considered applicable for structural applications. See AWS D1.1 and D1.3 for welding requirements and limits applicable to these materials in lieu of provisions such as AISC Specification Table J2.3. The designations such as B-L1a, B-U2 and B-P3 are those used in AWS D1.1. Note that lowercase letters (e.g., a, b, c, etc.) are often used to differentiate between joints that would otherwise have the same joint designation. These prequalified welded joints are limited to those made by the SMAW, SAW, GMAW (except short circuit transfer), and FCAW procedures. Small deviations from dimensions, angles of grooves, and variation in depth of groove joints are permissible within the tolerances given. In general, all fillet welds are prequalified, provided they conform to the requirements in AWS D1.1. Groove welds are classified using the conventions indicated in the tables. Welded joints other than those prequalified by AWS may be qualified, provided they are tested and qualified in accordance with AWS D1.1.

Table 8-3. Electrode Strength Coefficient, C1 Electrode strength coefficients, C1, which can be used to adjust the tabulated values of Tables 8-4 through 8-11 for electrodes other than E70XX, are given in Table 8-3. Note that this coefficient includes an additional reduction factor of 0.90 for E80 and E90 electrodes and 0.85 for E100 and E110; this accounts for the uncertainty of extrapolation to these higher-strength electrodes.

Tables 8-4 through 8-11. Coefficients, C, for Eccentrically Loaded Weld Groups Tables 8-4 through 8-11 employ the instantaneous center of rotation method in accordance with AISC Specification Section J2.4 for the weld patterns and eccentric conditions indicated and inclined loads at 0°, 15°, 30°, 45°, 60° and 75°. The tabulated nondimensional coefficient, C, represents the effective strength of the weld group in resisting the eccentric shear force.

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When Analyzing a Known Weld Group Geometry For any of the weld group geometries shown, the available strength, φRn or Rn /Ω, of the eccentrically loaded weld group is determined by Rn = CC1Dl φ = 0.75

Ω = 2.00

where C = tabular value C1 = electrode coefficient from Table 8-3 D = number of sixteenths-of-an-inch in the weld size l = length of the reference weld, in.

Fig. 8-21. Fillet weld nomenclature. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Fig. 8-22. Groove weld nomenclature.

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In developing these tables, the instantaneous center of rotation method was used, with a convergence criterion of less than 1/2% and considering deformation compatibility of adjacent weld elements. The first row in each table (a = 0) gives the available strength of a concentrically loaded weld group in accordance with AISC Specification Section J2.4. Linear interpolation within a given table between adjacent a and k values is permitted. Straight-line interpolation between values for loads at different angles may be significantly unconservative. Either a rational analysis should be performed or the values for the next lower angle increment in the tables should be used for design. For weld group patterns not treated in these tables, a rational analysis is required.

Table 8-12. Approximate Number of Passes for Welds Table 8-12 lists the approximate number of passes required for various welds. The actual number of passes can vary depending on the welding position and process used. The table can be used as a guide in selecting economical welds because the labor required will be roughly proportional to the number of passes. Longer single-pass welds will generally be more economical than shorter multi-pass welds because the number of passes, and therefore the cost, required to deposit the larger multi-pass weld increases faster than the strength of the weld.

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PART 8 REFERENCES AWS (1992), Guide for the Nondestructive Inspection of Welds, AWSB1.10, American Welding Society, Miami, FL. AWS (2007), Standard Symbols for Welding, Brazing, and Nondestructive Examination, American Welding Society, Miami, FL. Blodgett, O.W. (1966), Design of Welded Structures, James F. Lincoln Arc Welding Foundation, Cleveland, OH. Blodgett, O.W. (1980), “Detailing to Achieve Practical Welded Fabrication,” Engineering Journal, AISC, Vol. 17, No. 4, 4th Quarter, pp. 106–119, Chicago, IL. Blodgett, O.W., Funderburk, R.S. and Miller, D.K. (1997), Fabricator’s and Erector’s Guide to Welded Steel Construction, James F. Lincoln Arc Welding Foundation, Cleveland, OH. Butler, L.J., Pal, S. and Kulak, G.L. (1972), Eccentrically Loaded Welded Connections,” Journal of the Structural Division, ASCE, Vol. 98, No. ST5, May, pp. 989–1005, Reston, VA. Crawford, S.F and Kulak, G.L. (1968), “Behavior of Eccentrically Loaded Bolted Connections,” Studies in Structural Engineering, No. 4, Department of Civil Engineering, Nova Scotia Technical College, Halifax, Nova Scotia. Higgins, T.R. (1971), “Treatment of Eccentrically Loaded Connections in the AISC Manual,” Engineering Journal, AISC, Vol. 8, No. 2, April, pp. 52-54, Chicago, IL. Institute of Welding (1972), Procedures and Recommendations for the Ultrasonic Testing of Butt Welds, London, England. Kaufmann, J.A., Pense, A.W. and Stout, R.D. (1981), “An Evaluation of Factors Significant to Lamellar Tearing,” Welding Journal Research Supplement, AWS, Vol. 60, No. 3, March, Miami, FL. Krautkramer, J. (1990), Ultrasonic Testing of Materials, 4th Ed., Springer-Verlag, Berlin, West Germany. Lesik, D.F. and Kennedy, D.J.L. (1990), “Ultimate Strength of Fillet-Welded Connections Loaded in Plane,” Canadian Journal of Civil Engineering, National Research Council of Canada, Vol. 17, No. 1, Ottawa, Canada. Post, J.W. (1990), “Box-Tube Connections: Choices of Joint Details and Their Influence on Costs,” National Steel Construction Conference Proceedings, AISC, Chicago, IL.

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Table 8-1

Coefficients, C, for Concentrically Loaded Weld Group Elements Load angle on weld element, degrees 0 15 30 45 60 75 90

Largest load angle on any weld group element, degrees 90 0.825 1.02 1.16 1.29 1.40 1.48 1.50

75

60

45

30

15

0

0.849 1.04 1.17 1.30 1.40 1.47

0.876 1.05 1.18 1.29 1.39

0.909 1.07 1.17 1.26

0.948 1.06 1.10

0.994 0.883

1.00

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Table 8-2

Prequalified Welded Joints Symbols for Joint Types B C T

butt joint corner joint T-joint

BC butt or corner joint TC T- or corner joint BTC butt, T- or corner joint Symbols for Base Metal Thickness and Penetration

L U P

limited thickness, complete-joint-penetration unlimited thickness, complete-joint-penetration partial-joint-penetration Symbols for Weld Types

1 2 3 4 5

square-groove 6 single-U-groove single-V-groove 7 double-U-groove double-V-groove 8 single-J-groove single-bevel-groove 9 double-J-groove double-bevel-groove 10 flare-bevel-groove Symbols for Welding Processes if not Shielded Metal Arc Welding (SMAW):

S G F

submerged arc welding (SAW) gas metal arc welding (GMAW) flux cored arc welding (FCAW)

F H V OH

flat horizontal vertical overhead

Symbols for Welding Positions

Symbols for Joint Designation The lower case letters (e.g., a, b, c, d, etc.) are used to differentiate between joints that would otherwise have the same joint designation. Symbols for Dimensions R α, β f r S, S1, S2 E, E1, E2

Root opening Groove angles Root face J- or U-groove radius PJP groove weld depth of groove PJP groove weld sizes corresponding to S, S1, S2, respectively

1 2 3 4 5 6 7

Not prequalified for gas metal arc welding (GMAW) using short circuiting transfer nor GTAW. Refer to AWS D1.1 Annex A. Joint is welded from one side only. Cyclic load application limits these joints to the horizontal welding position. Refer to AWS D1.1 Section 2.18.2. Backgouge root to sound metal before welding second side. SMAW joints may be used for prequalified GMAW (except GMAW-S) and FCAW. Minimum effective throat thickness (E) as shown in AISC Specification Table J2.3; S as specified on drawings. If fillet welds are used in buildings to reinforce groove welds in corner and T-joints, they shall be equal to 1/4 T1, but need not exceed 3/8 in. Groove welds in corner and T-joints of cyclically loaded structures shall be reinforced with fillet welds equal to 1/4 T1, but need not exceed 3/8 in. Double-groove welds may have grooves of unequal depth, but the depth of the shallower groove shall be no less than one-fourth of the thickness of the thinner part joined. Double-groove welds may have grooves of unequal depth, provided these conform to the limitations of Note 6. Also, the effective throat thickness (E) applies individually to each groove. The orientation of the two members in the joints may vary from 135° to 180° for butt joints, or 45° to 135° for corner joints, or 45° to 90° for T-joints. For corner joints, the outside groove preparation may be in either or both members, provided the basic groove configuration is not changed and adequate edge distance is maintained to support the welding operations without excessive edge melting. Effective throat thickness (E) is based on joints welded flush.

Notes to Prequalified Welded Joints

8 9 10 11

12

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Table 8-2 (continued)

Prequalified Welded Joints

Dimensions of fillet welds must be shown on both the arrow side and the other side.

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Table 8-2 (continued)

FILLET

Prequalified Welded Joints Fillet Welds

Notes: 1. (En), (E’n) = Effective throat thickness dependant on magnitude of root opening (Rn). Refer to AWS D1.1 Section 5.22.1. Subscript n represents 1, 2, 3, 4, or 5. 2. t = thickness of thinner part. 3. Not prequalified for gas metal arc welding (GMAW) using short circuit transfer nor GTAW. Refer to AWS D1.1 Annex A for GMAW-S. 4. Figure D. Apply Z loss dimension of AWS D1.1 Table 2.2 to determine effective throat thickness. 5. Figure D. Not prequlaified for angles under 30°. For welder qualifications see AWS D1.1 Table 4.8. 6. Angles under 60° are permissible, however, if the weld is considered to be a partial-joint-penetration groove weld.

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CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Square-groove weld (1) Butt joint (B) Corner joint (C)

Welding Process

SMAW FCAW GMAW

Joint Designation

Groove Preparation

Base Metal Thickness (U = unlimited)

B-L1a

1/4

C-L1a

1/4

B-L1a-GF

3/8

Tolerances

Allowed Welding Positions

Gas Shielding for FCAW

Notes

T1

T2

Root Opening

max

—

R = T1

+1/16, –0

+1/4, –1/16

All

—

5, 10

U

R = T1

+1/16,

–0

+1/4, –1/16

All

—

5, 10

R = T1

+1/16,

–0

+1/4,

All

Not Required

1, 10

Allowed Welding Positions

Gas Shielding for FCAW

Notes

max max

—

As Detailed As Fit-Up (see 3.13.1) (see 3.13.1)

–1/16

Square-groove weld (1) Butt joint (B)

Welding Process

Joint Designation

Groove Preparation

Base Metal Thickness (U = unlimited) T2

T1

Tolerances Root Opening T

As Detailed As Fit-Up (see 3.13.1) (see 3.13.1)

SMAW

B-L1b

1/4

max

—

R = ᎏ1 2

+1/16, –0

+1/16, –1/8

All

—

4, 5, 10

GMAW FCAW

B-L1b-GF

3/8

max

—

R = 0 to 1/8

+1/16, –0

+1/16, –1/8

All

Not Required

1, 4, 10

SAW

B-L1-S

3/8

max

—

R=0

±0

+1/16, –0

F

—

10

SAW

B-L1a-S

5/8

max

—

R=0

±0

+1/16, –0

F

—

4, 10

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

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CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Square-groove weld (1) T-joint (T) Corner joint (C)

Welding Process

Joint Designation

Groove Preparation

Base Metal Thickness (U = unlimited) T1

T2

Tolerances Root Opening

As Detailed As Fit-Up (see 3.13.1) (see 3.13.1)

T

Allowed Welding Positions

Gas Shielding for FCAW

Notes

SMAW

TC-L1b

1/4

max

U

R = ᎏ1 2

+1/16, –0

+1/16, –1/8

All

—

4, 5, 7

GMAW FCAW

TC-L1-GF

3/8

max

U

R = 0 to 1/8

+1/16, –0

+1/16, –1/8

All

Not Required

1, 4, 7

SAW

TC-L1-S

3/8

max

U

R=0

±0

+1/16, –0

F

—

4, 7

Tolerances

Single-V-groove weld (2) Butt joint (B)

Welding Process

SMAW

GMAW FCAW

Joint Designation

B-U2a

B-U2a-GF

Base Metal Thickness (U = unlimited) T1

T2

U

—

U

—

Groove Preparation

As Detailed (see 3.13.1)

As Fit-Up (see 3.13.1)

R = +1/16, –0

+1/4, –1/16

α = +10°, –0°

+10°, –5°

Allowed Welding Positions

Gas Shielding for FCAW

Notes

Root Opening

Groove Angle

R = 1/4

α = 45°

All

—

5, 10

R = 3/8

α = 30°

F, V, OH

5, 10

R = 1/2

α = 20°

F, V, OH

— – —

R = 3/16

α = 30°

F, V, OH

Required

1, 10

R = 3/8

α = 30°

F, V, OH

Not req.

1, 10

R = 1/4

α = 45°

F, V, OH

Not req.

1, 10

5, 10

SAW

B-L2a-S

2 max

—

R = 1/4

α = 30°

F

—

10

SAW

B-U2-S

U

—

R = 5/8

α = 20°

F

—

10

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

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CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances

Single-V-groove weld (2) Corner joint (C)

Welding Process

Joint Designation

As Detailed (see 3.13.1)

Base Metal Thickness (U = unlimited) T1

SMAW

GMAW FCAW

C-U2a

C-U2a-GF

T2

U

U

U

U

Groove Preparation

As Fit-Up (see 3.13.1)

R = +1/16, –0

+1/4, –1/16

α = +10°, –0°

+10°, –5°

Allowed Welding Positions

Gas Shielding for FCAW

Notes

Root Opening

Groove Angle

R = 1/4

α = 45°

All

—

5, 10

3/8

α = 30°

F, V, OH

5, 10

R = 1/2

α = 20°

F, V, OH

— – —

R = 3/16

α = 30°

F, V, OH

Required

1

R = 3/8

α = 30°

F, V, OH

Not req.

1, 10

R = 1/4

α = 45°

F, V, OH

Not req.

1, 10

1/4

α = 30°

F

—

10

α = 20°

F

—

10

R=

SAW

C-L2a-S

2 max

U

R=

SAW

C-U2-S

U

U

R = 5/8

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

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CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Single-V-groove weld (2) Butt joint (B)

Base Metal Thickness (U = unlimited) Welding Process

Joint Designation T1

T2

Groove Preparation Tolerances Root Opening As Detailed As Fit-Up Root Face (see 3.13.1) (see 3.13.1) Groove Angle

Allowed Welding Positions

Gas Shielding for FCAW

Notes

SMAW

B-U2

U

—

R = 0 to 1/8 +1/16, –0 +1/16, –1/8 f = 0 to 1/8 +1/16, –0 Not Limited α = 60° + 10°, –0° +10°, –5°

All

—

4, 5, 10

GMAW FCAW

B-U2-GF

U

—

R = 0 to 1/8 +1/16, –0 +1/16, –1/8 f = 0 to 1/8 +1/16, –0 Not Limited α = 60° + 10°, –0° +10°, –5°

All

Not Required

1, 4, 10

Over 1/2 to 1

—

R=0 f = 1/4 max α = 60°

Over 1 to 11/2

—

R = ±0 +1/16, –0 R=0 ± 1/16 f = +0, –f f = 1/2 max α = +10°, –0° +10°, –5° α = 60°

F

—

4, 10

Over 11/2 to 2

—

R=0 f = 5/8 max α = 60°

SAW

B-L2c-S

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 8A:14th Ed.

2/24/11

8:24 AM

Page 41

8–41

DESIGN TABLES

CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Single-V-groove weld (2) Corner joint (C)

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited) T1

T2

Groove Preparation Root Tolerances Opening As Detailed As Fit-Up Root Face Groove Angle (see 3.13.1) (see 3.13.1)

Allowed Welding Positions

Gas Shielding for FCAW

Notes

SMAW

C-U2

U

U

R = 0 to 1/8 +1/16, –0 +1/16, –1/8 f = 0 to 1/8 +1/16, –0 Not Limited α = 60° + 10°, –0° +10°, –5°

All

—

4, 5, 7, 10

GMAW FCAW

C-U2-GF

U

U

R = 0 to 1/8 +1/16, –0 +1/16, –1/8 f = 0 to 1/8 +1/16, –0 Not Limited α = 60° + 10°, –0° +10°, –5°

All

Not Required

1, 4, 7, 10

SAW

C-U2b-S

U

U

R = 0 to 1/8 f = 1/4 max α = 60°

F

—

4, 7, 10

±0 +0, –1/4 +10°, –0°

+1/16, –0 ±1/16 +10°, –5°

Tolerances

Double-V-groove weld (3) Butt joint (B)

As Detailed (see 3.13.1)

As Fit-Up (see 3.13.1)

R = ±0

+1/4, –0

f = ±0

+1/16, –0

α = +10°, –0°

+10°, –5°

SAW

±0

+1/16, –0

SMAW

±0

Spacer

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited) T2

T1

SMAW

SAW

B-U3a

B-U3a-S

U Spacer = 1/8 × R

—

U Spacer = 1/4 × R

—

Groove Preparation

1/8,

Allowed Welding Positions

Gas Shielding for FCAW

Root Opening

Root Face

Groove Angle

R = 1/4

f = 0 to 1/8

α = 45°

All

—

3/8

1/8

α = 30°

F, V, OH

—

R = 1/2

f = 0 to 1/8

α = 20°

F, V, OH

—

R = 5/8

f = 0 to 1/4

α = 20°

F

—

R=

f = 0 to

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

–0

Notes

4, 5, 8, 10

4, 8, 10

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DESIGN CONSIDERATIONS FOR WELDS

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Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds For B-U3c-S only

Double-V-groove weld (3) Butt joint (B)

T1

S1

Over

to

2

21/2

13/8

21/2

3

13/4

3

35/8

21/8

35/8

4

23/8

4

43/4

23/4

43/4

51/2

31/4

51/2

61/4

33/4

For T1 > or T1≤ 2 S1 = 2/3 (T1– 1/4) 61/4

Welding Process

SMAW GMAW FCAW

SAW

Joint Designation

Base Metal Thickness (U = unlimited) T1

T2

U

—

B-U3b B-U3-GF

B-U3c-S

U

Groove Preparation Tolerances Root Opening As Detailed As Fit-Up Root Face Groove Angle (see 3.13.1) (see 3.13.1)

R = 0 to 1/8

+1/16, –0

+1/16, –1/8

f = 0 to 1/8

+1/16, –0

Not limited

α = β = 60° +10°, –0°

+10°, –5°

+1/16, –0

+1/16, –0

R=0 f = 1/4 min +1/4, –0 — α = β = 60° +10°, –0°

+1/4, –0 +10°, –5°

Allowed Welding Positions

Gas Shielding for FCAW

Notes

All

—

4, 5, 8, 10

All

F

To find S1 see table above: S2 = T1 – (S1+f)

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Not required 1, 4, 8, 10

—

4, 8, 10

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DESIGN TABLES

CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances

Single-bevel-groove weld (4) Butt joint (B)

Welding Process

SMAW

GMAW FCAW

SAW

Joint Designation

As Detailed (see 3.13.1)

Base Metal Thickness (U = unlimited)

B-U4a

B-U4a-GF

T1

T2

U

—

U

B-U4a-S

U

—

U

SMAW

GMAW FCAW

SAW

Joint Designation

TC-U4a

TC-U4a-GF

TC-U4a-S

R = +1/16, –0

+1/4, –1/16

α = +10°, –0°

+10°, –5°

Root Opening

Groove Angle

Allowed Welding Positions

R = 1/4

α = 45°

All

—

3, 5, 10

3/8

α = 30°

All

—

3, 5, 10

R = 3/16

α = 30°

All

Required

1, 3, 10

R = 1/4

α = 45°

All

Not req.

1, 3, 10

R = 3/8

α = 30°

F, H

Not req.

1, 3, 10

R = 3/8

α = 30°

R = 1/4

α = 45°

F

—

3, 10

Groove Preparation

R=

Gas Shielding for FCAW

Notes

Tolerances

Single-bevel-groove weld (4) T-joint (T) Corner joint (C)

Welding Process

As Fit-Up (see 3.13.1)

As Detailed (see 3.13.1)

Base Metal Thickness (U = unlimited) T1

T2

U

U

U

U

U

U

Groove Preparation

As Fit-Up (see 3.13.1)

R = +1/16, –0

+1/4, –1/16

α = +10°, –0°

+10°, –5°

Allowed Welding Positions

Gas Shielding for FCAW

Notes

Root Opening

Groove Angle

R = 1/4

α = 45°

All

—

5, 7, 10, 11

3/8

α = 30°

F, V, OH

5, 7, 10, 11

R = 3/16

α = 30°

All

— – Required

R = 3/8

α = 30°

F

Not req.

1, 7, 10, 11

R = 1/4

α = 45°

All

Not req.

1, 7, 10, 11

R = 3/8

α = 30°

R = 1/4

α = 45°

F

—

7, 10, 11

R=

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1, 7, 10, 11

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DESIGN CONSIDERATIONS FOR WELDS

CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Single-bevel-groove weld (4) Butt joint (B)

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited) T1

T2

SMAW

B-U4b

U

—

GMAW FCAW

B-U4b-GF

U

—

SAW

U

B-U4b-S

U

Groove Preparation Tolerances Root Opening As Detailed As Fit-Up Root Face Groove Angle (see 3.13.1) (see 3.13.1) R = 0 to 1/8 +1/16, –0 f = 0 to 1/8 +1/16, –0 α = 45° + 10°, –0° R=0 f = 1/4 max α = 60°

+1/16, –1/8 Not Limited +10°, –5°

Allowed Welding Positions

Gas Shielding for FCAW

Notes

All

—

3, 4, 5, 10

All

Not Required 1, 3, 4, 10

+1/4,

–0 ±1/16 10°, –5°

±0 +0, –1/8 + 10°, –0°

F

—

3, 4, 10

Allowed Welding Positions

Gas Shielding for FCAW

Notes

All

—

All

Not Required

F

—

Single-bevel-groove weld (4) T-joint (T) Corner joint (C)

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited) T1

T2

SMAW

TC-U4b

U

U

GMAW FCAW

TC-U4b-GF

U

U

SAW

TC-U4b-S

U

U

Groove Preparation Tolerances Root Opening Root Face As Detailed As Fit-Up Groove Angle (see 3.13.1) (see 3.13.1) R = 0 to 1/8 +1/16, –0 f = 0 to 1/8 +1/16, –0 α = 45° + 10°, –0° R=0 f = 1/4 max α = 60°

±0 +0, –1/8 + 10°, –0°

+1/16, –1/8 Not Limited +10°, –5° +1/4,

–0 ±1/16 10°, –5°

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4, 5, 7, 10, 11 1, 4, 7, 10, 11 4, 7, 10, 11

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DESIGN TABLES

CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances

Double-bevel-groove weld (5) Butt joint (B) T-joint (T) Corner joint (C)

Spacer

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited)

B-U5b

Groove Preparation

As Detailed (see 3.13.1)

As Fit-Up (see 3.13.1)

R = ±0

+1/4, –0

f = +1/16, –0

± 1/16

α = +10°, –0°

+10°, –5°

+1/16, –0

+1/8, –0

Allowed Welding Positions

Gas Shielding for FCAW

Notes

3, 4, 5, 8, 10

T1

T2

Root Opening

Root Face

Groove Angle

U Spacer =

U

R = 1/4

f = 0 to 1/8

α = 45°

All

—

R = 1/4

f = 0 to 1/8

α = 45°

All

—

R = 3/8

f = 0 to 1/8

α = 30°

F, OH

—

Allowed Welding Positions

Gas Shielding for FCAW

Notes

All

—

3, 4, 5, 8, 10

All

Not Required

1, 3, 4, 8, 10

1/8×R

SMAW U Spacer = 1/4×R

TC-U5a

U

4, 5, 7, 8, 10, 11 4, 5, 7, 8, 10, 11

Double-bevel-groove weld Butt joint (B)

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited) T1

T2

Groove Preparation Root Tolerances Opening As Detailed As Fit-Up Root Face Groove Angle (see 3.13.1) (see 3.13.1) R = 0 to 1/8

SMAW

B-U5a

U

—

+1/16, –0

+1/16, –1/8

+1/16,

–0

Not limited

+10° α+β 0° β = 0° to 15°

+10° α+β –5°

f = 0 to

1/8

α = 45°

R = 0 to 1/8 GMAW FCAW

B-U5-GF

U

—

f = 0 to

1/8

α = 45°

+1/16, –0

+1/16, –1/8

+1/16,

Not limited

–0

α+β=

β = 0° to 15° + 10°, –0°

α+β= + 10°, –5°

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AISC_Part 8A:14th Ed.

2/24/11

8:25 AM

Page 46

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DESIGN CONSIDERATIONS FOR WELDS

CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Double-bevel-groove weld (5) T-joint (T) Corner joint (C)

Welding Process

SMAW

Joint Designation

TC-U5b

Base Metal Thickness (U = unlimited) T1

T2

U

U

GMAW FCAW

TC-U5-GF

U

U

SAW

TC-U5-S

U

U

Groove Preparation Root Tolerances Opening Root Face As Detailed As Fit-Up Groove Angle (see 3.13.1) (see 3.13.1) R = 0 to 1/8

+1/16, –0

+1/16, –1/8

f = 0 to 1/8

+1/16, –0

Not limited

α = 45°

+10°, –0

+10°, –5°

R=0 1/4 max

f= α = 60°

±0

+1/16, –0

+0, –3/16

±1/16

+10°, –0°

+10°, –5°

Allowed Welding Positions

Gas Shielding for FCAW

All

—

All

Not Required

F

—

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Notes

4, 5, 7, 8, 10, 11 1, 4, 7, 8, 10, 11 4, 7, 8, 10, 11

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DESIGN TABLES

CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances

Single-U-groove weld (6) Butt joint (B) Corner joint (C)

Welding Process

Joint Designation

B-U6

As Detailed (see 3.13.1)

Base Metal Thickness (U = unlimited) T1

T2

U

U

Groove Preparation

As Fit-Up (see 3.13.1)

R = +1/16, –0

+1/16, –1/8

α = +10°, –0°

+10°, –5°

f = ±1/16

Not Limited

r = +1/8, –0

+1/8, –0

Allowed Welding Positions

Gas Shielding for FCAW

Notes

R = 0 to 1/8 α = 45° f = 1/8 r = 1/4

All

—

4, 5, 10

R = 0 to 1/8 α = 20° f = 1/8 r = 1/4

F, OH

—

4, 5, 10

R = 0 to 1/8 α = 45° f = 1/8 r = 1/4

All

—

4, 5, 7, 10

R = 0 to 1/8 α = 20° f = 1/8 r = 1/4

F, OH

—

4, 5, 7, 10

Root Opening

Groove Angle

Root Face

Bevel Radius

SMAW C-U6

GMAW FCAW

U

U

B-U6-GF

U

U

R = 0 to 1/8 α = 20° f = 1/8 r = 1/4

All

Not req.

1, 4, 10

C-U6-GF

U

U

R = 0 to 1/8 α = 20° f = 1/8 r = 1/4

All

Not req.

1, 4, 7, 10

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 8A:14th Ed.

2/24/11

8:25 AM

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DESIGN CONSIDERATIONS FOR WELDS

CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances

Double-U-groove weld (7) Butt joint (B)

As Detailed (see 3.13.1)

As Fit-Up (see 3.13.1)

For B-U7 and B-U7-GF R = +1/16, –0

1/16,

–1/8

α = +10°, –0°

+10°, –5°

f = ± 1/16, –0

Not Limited

r = +1/4, –0

±1/16

For B-U7-S

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited) T1

SMAW

B-U7

U

T2

Groove Preparation

R = ±0

+1/16, –0

f = +0, +1/4

±1/16

Allowed Welding Positions

Gas Shielding for FCAW

Notes

R = 0 to 1/8 α = 45° f = 1/8 r = 1/4

All

—

4, 5, 8, 10

R = 0 to 1/8 α = 20° f = 1/8 r = 1/4

F, OH

—

4, 5, 8, 10

R = 0 to 1/8 α = 20° f = 1/8 r = 1/4

All

Not req.

1, 4, 10, 8

f = 1/4 r = 1/4 max

F

—

4, 8, 10

Root Opening

Groove Angle

Root Face

Bevel Radius

—

GMAW FCAW

B-U7-GF

U

—

SAW

B-U7-S

U

—

R=0

α = 20°

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 8A:14th Ed.

2/24/11

8:25 AM

Page 49

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DESIGN TABLES

CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances

Single-J-groove weld (8) Butt joint (B)

As Detailed (see 3.13.1)

As Fit-Up (see 3.13.1)

B-U8 and B-U8-GF R = +1/16, –0

+1/16, –1/8

α = +10°, –0°

+10°, –5°

f = +1/8, –0

Not Limited

r = +1/4, –0

±1/16 B-U8-S

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited) T1

T2

Groove Preparation Root Opening

Groove Angle

Root Face

Bevel Radius

R = ±0

+1/4, –0

α = +10°, –0°

+10°, –5°

f = +0, –1/8

±1/16

r = +1/4, –0

±1/16

Allowed Welding Positions

Gas Shielding for FCAW

Notes

SMAW

B-U8

U

—

R = 0 to 1/8 α = 45° f = 1/8 r = 3/8

All

—

3, 4, 5, 10

GMAW FCAW

B-U8-GF

U

—

R = 0 to 1/8 α = 30° f = 1/8 r = 3/8

All

Not req.

1, 3, 4, 10

SAW

B-U8-S

U

U

F

—

3, 4, 10

R=0

1 α = 45° f = /4 r = 3/8 max

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 8A:14th Ed.

2/24/11

8:25 AM

Page 50

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DESIGN CONSIDERATIONS FOR WELDS

CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances

Single-J-groove weld (8) T-joint (T) Corner joint (C)

As Detailed (see 3.13.1)

As Fit-Up (see 3.13.1)

TC-U8a and TC-U8a-GF R = +1/16, –0

1/16,

–1/8

α = +10°, –0°

+10°, –5°

f = +1/16, –0

Not Limited

r = +1/4, –0

±1/16

TC-U8a-S

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited) T1

SMAW

TC-U8a

U

T2

Groove Preparation

R = ±0

+1/4, –0

α = +10°, –0°

+10°, –5°

f = +0, –1/8

±1/16

r = +1/4, –0

±1/16

Allowed Welding Positions

Gas Shielding for FCAW

Notes

R = 0 to 1/8 α = 45° f = 1/8 r = 3/8

All

—

4, 5, 7, 10, 11

R = 0 to 1/8 α = 30° f = 1/8 r = 3/8

F, OH

—

4, 5, 7, 10, 11

R = 0 to 1/8 α = 30° f = 1/8 r = 3/8

All

Not req.

1, 4, 7, 10, 11

F

—

4, 7, 10, 11

Root Opening

Groove Angle

Root Face

Bevel Radius

U

GMAW FCAW

TC-U8a-GF

U

U

SAW

TC-U8a-S

U

U

R=0

1 α = 45° f = /4 r = 3/8 max

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 8A:14th Ed.

2/24/11

8:25 AM

Page 51

8–51

DESIGN TABLES

CJP

Table 8-2 (continued)

Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances

Double-J-groove weld (9) Butt joint (B)

Welding Process

Joint Designation

As Detailed (see 3.13.1)

Base Metal Thickness (U = unlimited) T1

T2

Groove Preparation Root Opening

Groove Angle

Root Face

Bevel Radius

As Fit-Up (see 3.13.1)

R = +1/16, –0

+1/16, –1/8

α = +10°, –0°

+10°, –5°

f = +1/16, –0

Not Limited

r = +1/8, –0

±1/16

Allowed Welding Positions

Gas Shielding for FCAW

Notes

SMAW

B-U9

U

—

R = 0 to 1/8 α = 45° f = 1/8 r = 3/8

All

—

3, 4, 5, 8, 10

GMAW FCAW

B-U9-GF

U

—

R = 0 to 1/8 α = 30° f = 1/8 r = 3/8

All

Not req.

1, 3, 4, 8, 10

Tolerances

Double-J-groove weld (9) T-joint (T) Corner joint (C)

Welding Process

Joint Designation

As Detailed (see 3.13.1)

Base Metal Thickness (U = unlimited) T1

SMAW

GMAW FCAW

TC-U9a

TC-U9a-GF

U

U

T2

Groove Preparation

As Fit-Up (see 3.13.1)

R = +1/16, –0

+1/16, –1/8

α = +10°, –0°

+10°, –5°

f = +1/16, –0

Not Limited

r = 1/8, –0

±1/16

Allowed Welding Positions

Gas Shielding for FCAW

Notes

R = 0 to 1/8 α = 45° f = 1/8 r = 3/8

All

—

4, 5, 7, 8, 10, 11

R = 0 to 1/8 α = 30° f = 1/8 r = 3/8

F, OH

—

4, 5, 7, 8, 11

R = 0 to 1/8 α = 30° f = 1/8 r = 3/8

All

Not req.

1, 4, 7, 8, 10, 11

Root Opening

Groove Angle

Root Face

Bevel Radius

U

U

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 8A:14th Ed.

2/24/11

8:25 AM

Page 52

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DESIGN CONSIDERATIONS FOR WELDS

PJP

Table 8-2 (continued)

Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Square-groove weld (1) Butt joint (B)

Welding Process

Joint Designation

B-P1a SMAW

Groove Preparation

Base Metal Thickness (U = unlimited) T1

T2

Root Opening

1/8

—

R = 0 to 1/16

1/4

B-P1c

Tolerances

max

—

As Detailed As Fit-Up (see 3.12.3) (see 3.12.3)

T1 R=

2

min

+1/16, –0 +1/16, –0

±1/16 ±1/16

Allowed Welding Positions

Weld Size (E)

Notes

All

T1 –1/32

2, 5

All

T1 2

2, 5

Square-groove weld (1) Butt joint (B)

E1 + E2 must not exceed 3T1 4

Welding Process

SMAW

Joint Designation

B-P1b

Groove Preparation

Base Metal Thickness (U = unlimited)

1/4

Tolerances

T1

T2

Root Opening

max

—

R=

T1 2

As Detailed As Fit-Up (see 3.12.3) (see 3.12.3) +1/16, –0

±1/16

Allowed Welding Positions

All

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Total Weld Size (E1 + E2) 3T1 4

Notes

5

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DESIGN TABLES

PJP

Table 8-2 (continued)

Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Single-V-groove weld (2) Butt joint (B) Corner joint (C)

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited) T1

SMAW

GMAW FCAW

SAW

BC-P2

BC-P2-GF

BC-P2-S

1/4

1/4

7/16

min

min

min

Groove Preparation Tolerances

T2

Root Opening Root Face Groove Angle

R=0

–0, +1/16

+1/8, –1/16

U

f = 1/32 min

±1/16

α = 60°

+U, –0 +10°, –0°

+ 10°, –5°

R=0

–0, +1/16

+1/8, –1/16

f = 1/8 min

±1/16

α = 60°

+U, –0 +10°, –0°

+ 10°, –5°

R=0

±0

+1/16, –0

f = 1/4 min

+U, –0 +10°, –0°

+ 10°, –5°

U

U

α = 60°

As Detailed As Fit-Up (see 3.12.3) (see 3.12.3)

±1/16

Allowed Welding Positions

Weld Size (E)

Notes

All

S

2, 5, 6, 10

All

S

1, 2, 6, 10

F

S

2, 6, 10

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8–54

DESIGN CONSIDERATIONS FOR WELDS

PJP

Table 8-2 (continued)

Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Double-V-groove weld (3) Butt joint (B)

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited) T2

T1

SMAW

GMAW FCAW

SAW

B-P3

B-P3-GF

B-P3-S

1/2

1/2

3/4

min

min

min

—

—

—

Groove Preparation Root Tolerances Opening As Detailed As Fit-Up Root Face Groove Angle (see 3.12.3) (see 3.12.3) R=0

+1/16, –0

+1/8, –1/16

1/8

±1/16

α = 60°

+U, –0 +10°, –0°

+ 10°, –5°

R=0

+1/16, –0

+1/8, –1/16

1/8

±1/16

α = 60°

+U, –0 +10°, –0°

+ 10°, –5°

R=0

±0

+1/16, –0

1/4

+U, –0 +10°, –0°

±1/16

f=

f=

f=

min

min

min

α = 60°

Allowed Welding Positions

Total Weld Size (E1 + E2)

Notes

All

S1 + S2

5, 6, 9, 10

All

S1 + S2

1, 6, 9, 10

F

S1 + S2

6, 9, 10

+ 10°, –5°

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Page 55

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DESIGN TABLES

PJP

Table 8-2 (continued)

Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Single-bevel-groove weld (4) Butt joint (B) T-joint (T) Corner joint (C)

Welding Process

SMAW

GMAW FCAW

SAW

Joint Designation

Base Metal Thickness (U = unlimited) T1

T2

U

U

BTC-P4

BTC-P4-GF

TC-P4-S

1/4

7/16

min

min

U

U

Groove Preparation Root Tolerances Opening Root Face As Detailed As Fit-Up Groove Angle (see 3.12.3) (see 3.12.3) R=0

+1/16, –0

+1/8, –1/16

f = 1/8 min

±1/16

α = 45°

+U, –0 +10°, –0°

+ 10°, –5°

R=0

+1/16, –0

+1/8, –1/16

α = 45°

+U, –0 +10°, –0°

±1/16 + 10°, –5°

R=0

±0

+1/16, –0

f = 1/4 min

+U, –0 +10°, –0°

±1/16

f = 1/8 min

α = 60°

Allowed Welding Positions

Total Weld Size (E)

Notes

All

S–1/8

2, 5, 6, 7, 10, 11

F, H

S

V, OH

S–1/8

F

S

+ 10°, –5°

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

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1, 2, 6, 7, 10, 11

2, 6, 7, 10, 11

AISC_Part 8A:14th Ed.

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DESIGN CONSIDERATIONS FOR WELDS

PJP

Table 8-2 (continued)

Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Double-bevel-groove weld (5) Butt joint (B) T-joint (T) Corner joint (C)

Welding Process

SMAW

GMAW FCAW

SAW

Joint Designation

BTC-P5

BTC-P5-GF

TC-P5-S

Base Metal Thickness (U = unlimited) T1

T2

5/16 min

U

1/2

3/4

min

min

U

U

Groove Preparation Root Tolerances Opening Root Face As Detailed As Fit-Up Groove Angle (see 3.12.3) (see 3.12.3) R=0

+1/16, –0

+1/8, –1/16

f = 1/8 min

±1/16

α = 45°

+U, –0 +10°, –0°

+ 10°, –5°

R=0

+1/16, –0

+1/8, –1/16

α = 45°

+U, –0 +10°, –0°

±1/16 + 10°, –5°

R=0

±0

+1/16, –0

f = 1/4 min

+U, –0 +10°, –0°

±1/16

f = 1/8 min

α = 60°

Allowed Welding Positions

All

F, H V, OH

F

+ 10°, –5°

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Total Weld Size (E1 + E2)

S1 + S2 –1/4

Notes

5, 6, 7, 9, 10, 11

S1 + S2 S1 + S2

1, 6, 7, 9, 10, 11

–1/4 S1 + S2

6, 7, 9, 10, 11

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DESIGN TABLES

PJP

Table 8-2 (continued)

Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Single-U-groove weld (6) Butt joint (B) Corner joint (C)

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited) T2

T1

SMAW

GMAW FCAW

SAW

BC-P6

BC-P6-GF

BC-P6-S

1/4 min

1/4

7/16

min

min

U

U

U

Groove Preparation Root Opening Tolerances Root Face Bevel Radius As Detailed As Fit-Up Groove Angle (see 3.12.3) (see 3.12.3)

R=0

+1/16, –0

+1/8, –1/16

f = 1/32 min

+U, –0

±1/16

r = 1/4

+1/4, –0

±1/16

α = 45°

+10°, –0°

+ 10°, –5°

R=0

+1/16, –0

+1/8, –1/16

f = 1/8 min

+U, –0

±1/16

r = 1/4

+1/4, –0

±1/16

α = 20°

+10°, –0°

+ 10°, –5°

R=0

±0

+1/16, –0°

f = 1/4 min

+U, –0

±1/16

r = 1/4

+1/4, –0

±1/16

α = 20°

+10°, –0°

+ 10°, –5°

Allowed Welding Positions

Total Weld Size (E)

Notes

All

S

2, 5, 6, 10

All

S

1, 2, 6, 10

F

S

2, 6, 10

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DESIGN CONSIDERATIONS FOR WELDS

PJP

Table 8-2 (continued)

Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Double-U-groove weld (7) Butt joint (B)

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited) T2

T1

SMAW

GMAW FCAW

SAW

B-P7

B-P7-GF

B-P7-S

1/2

1/2

3/4

min

min

min

—

—

—

Groove Preparation Root Opening Tolerances Root Face Bevel Radius As Detailed As Fit-Up Groove Angle (see 3.12.3) (see 3.12.3)

R=0

+1/16, –0

+1/8, –1/16

f = 1/8 min

+U, –0

±1/16

r = 1/4

+1/4, –0

±1/16

α = 45°

+10°, –0°

+ 10°, –5°

R=0

+1/16, –0

+1/8, –1/16

f = 1/8 min

+U, –0

±1/16

r = 1/4

+1/4, –0

±1/16

α = 20°

+10°, –0°

+ 10°, –5°

R=0

±0

+1/16, –0°

f = 1/4 min

+U, –0

±1/16

r = 1/4

+1/4, –0

±1/16

α = 20°

+10°, –0°

+ 10°, –5°

Allowed Welding Positions

Total Weld Size (E1 + E2)

Notes

All

S1 + S2

5, 6, 9, 10

All

S1 + S2

1, 6, 9, 10

F

S1 + S2

6, 9,10

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DESIGN TABLES

PJP

Table 8-2 (continued)

Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Single-J-groove weld (8) Butt joint (B) T-joint (T) Corner joint (C)

*αoc **αic

= Outside corner groove angle. = Inside corner groove angle.

Welding Process

Joint Designation

Base Metal Thickness (U = unlimited) T2

T1

Groove Preparation Root Opening Tolerances Root Face As Detailed As Fit-Up Bevel Radius Groove Angle (see 3.12.3) (see 3.12.3) R=0

B-P8

1/4 min

U

SMAW

f=

r=

B-P8-GF

1/4 min

1/4 min

U

U

GMAW FCAW

B-P8-S

1/4 min

7/16 min

U

U

SAW 7/16 min

U

+U, –0

±1/16

+1/4,

±1/16

–0

+10°, –5°

R=0

+1/16, –0

+1/8, –1/16

+U, –0

±1/16

+1/4,

±1/16

1/8 min

r=

3/8

–0

αoc = 30°*

+10°, –0°

+10°, –5°

αic = 45°**

+10°, –0°

+10°, –5°

R=0

+1/16, –0

+1/8, –1/16

+U, –0

±1/16

+1/4,

±1/16

f=

1/8 min

r=

3/8

–0

α = 30°

+10°, –0°

+10°, –5°

R=0

+1/16, –0

+1/8, –1/16

+U, –0

±1/16

+1/4,

±1/16

1/8 min

r=

3/8

–0

αoc = 30°*

+10°, –0°

+10°, –5°

αic = 45°**

+10°, –0°

+10°, –5°

R=0

±0

+1/16, –0

+U, –0

±1/16

+1/4,

±1/16

f=

1/4 min

r=

1/2

–0

α = 20°

+10°, –0°

+10°, –5°

R=0

±0

+1/16, –0

+U, –0

±1/16

+1/4,

±1/16

f= TC-P8-S

+1/8, –1/16

+10°, –0°

f= TC-P8-GF

3/8

+1/16, –0

α = 30° f= TC-P8

1/8 min

1/4 min

r=

1/2

–0

αoc = 20°*

+10°, –0°

+10°, –5°

αic = 45°**

+10°, –0°

+10°, –5°

Allowed Welding Positions

Total Weld Size (E)

All

S

All

S

All

S

All

S

F

S

F

S

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Notes

5, 6, 7, 10, 11

5, 6, 7, 10, 11

1, 6, 7, 10, 11

1, 6, 7, 10, 11

6, 7, 10, 11

6, 7, 10, 11

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DESIGN CONSIDERATIONS FOR WELDS

PJP

Table 8-2 (continued)

Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Double-J-groove weld (9) Butt joint (B) T-joint (T) Corner joint (C)

*αoc **αic

= Outside corner groove angle. = Inside corner groove angle.

Welding Process

Joint Designation

B-P9

Base Metal Thickness (U = unlimited) T2

T1

1/2

min

U

SMAW

Groove Preparation Root Opening Tolerances Root Face As Detailed As Fit-Up Bevel Radius Groove Angle (see 3.12.3) (see 3.12.3) R=0

+1/16, –0

+1/8, –1/16

1/8

+U, –0

±1/16

r = 3/8

+1/4, –0

±1/16

α = 30°

+10°, –0°

+10°, –5°

R=0

+1/16, –0

+1/8, –1/16

1/8

+U, –0

±1/16

+1/4,

±1/16

f=

f= TC-P9

B-P9-GF

1/2

1/2

min

min

U

U

GMAW FCAW

r=

TC-P9-GF

B-P9-S

3/4

min

min

U

U

SAW 3/4

min

U

–0

+10°, –0°

+10°, –5°

αic = 45°**

+10°, –0°

+10°, –5°

R=0

+1/16, –0

+1/8, –1/16

1/8

+U, –0

±1/16

r = 3/8

+1/4, –0

±1/16

α = 30°

+10°, –0°

+10°, –5°

R=0

±0

+1/16, –0

1/8

+U, –0

±1/16

+1/4,

±1/16

f=

r=

min

min

3/8

–0

αoc = 30°*

+10°, –0°

+10°, –5°

αic = 45°**

+10°, –0°

+10°, –5°

R=0

±0

+1/16, –0

1/4

+U, –0

±1/16

+1/4,

±1/16

f=

r=

min

1/2

–0

α = 20°

+10°, –0°

+10°, –5°

R=0

±0

+1/16, –0

1/4

+U, –0

±1/16

+1/4,

±1/16

f= TC-P9-S

min

3/8

αoc = 30°*

f= 1/2

min

r=

min

1/2

–0

αoc = 20°*

+10°, –0°

+10°, –5°

αic = 45°**

+10°, –0°

+10°, –5°

Allowed Welding Positions

Total Weld Size (E1 + E2)

All

S1 + S2

5, 6, 7, 9, 10, 11

5, 6, 7, All

S1 + S2

9, 10, 11

1, 6, 7, All

S1 + S2

9, 10, 11

1, 6, 7, All

S1 + S2

9, 10, 11

F

S1 + S2

F

S1 + S2

Reprinted from AWS D1.1 with permission from the American Welding Society (AWS)

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Notes

6, 7, 9, 10, 11

6, 7, 9, 10, 11

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DESIGN TABLES

FLARE

Table 8-2 (continued)

Prequalified Welded Joints Flare-Bevel Groove Welds Flare-bevel-groove weld (10) Butt joint (B) T-joint (T) Corner joint (C)

Welding Process

SMAW FCAW-S

Joint Designation

BTC-P10

Base Metal Thickness (U = unlimited) T1

3/16

min

T2

U

T3

T1 min

Groove Preparation Root Opening Root Face Bend Radius*

GMAW BTC-P10-GF FCAW-G

min

U

T1 min

R=0

+1/16, –0

+1/8, –1/16

+U, –0

+U, –1/16

SAW

B-P10-S

min

N/A

3T1

+U, –0

+U, –0

R=0

+1/16, –0

+1/8, –1/16

f = 3/16 min

+U, –0

+U, –1/16

C=

1/2

As Detailed As Fit-Up (see 3.12.3) (see 3.12.3)

f = 3/16 min C=

3/16

Tolerances

2

3T1 2

min

min

+U, –0

+U, –0

R=0

±0

+1/16, –0°

1/2

f = 1/2 min

+U, –0

+U, –1/16

min

3T1

+U, –0

+U, –0

C=

2

min

Allowed Welding Positions

All

All

F

Total Weld Size (E)

5T1 8

5T1 4

5T1 8

Notes

5, 7, 10, 12

1, 7, 10, 12

7, 10, 12

* For cold formed (A500) rectangular tubes, C dimension is not limited. See the following: Effective Weld Size of Flare-Bevel-Groove Welded Joints. Tests have been performed on cold formed ASTM A 500 material exhibiting a "C" dimension as small as T1 with a nominal radius of 2t. As the radius increases, the "C" dimension also increases. The corner curvature may not be a quadrant of a circle tangent to the sides. The corner dimension, "C," may be less than the radius of the corner.

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DESIGN CONSIDERATIONS FOR WELDS

Table 8-2 (continued)

TUBE

Prequalified Welded Joints PJP T-, Y- and K-Tubular Connections

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DESIGN TABLES

Table 8-2 (continued)

TUBE

Prequalified Welded Joints PJP T-, Y- and K-Tubular Connections

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Page 64

DESIGN CONSIDERATIONS FOR WELDS

Table 8-2 (continued)

TUBE

Prequalified Welded Joints PJP T-, Y- and K-Tubular Connections

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DESIGN TABLES

Table 8-3

Electrode Strength Coefficient, C1 Electrode

FEXX (ksi)

C1

E60 E70 E80 E90 E100 E110

60 70 80 90 100 110

0.857 1.00 1.03 1.16 1.21 1.34

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DESIGN CONSIDERATIONS FOR WELDS

Table 8-4

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 0° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

3.71 3.72 3.67 3.51 3.31

3.71 3.72 3.66 3.51 3.31

3.71 3.72 3.65 3.50 3.31

3.71 3.71 3.64 3.49 3.30

3.71 3.70 3.62 3.47 3.29

3.71 3.69 3.60 3.46 3.28

3.71 3.67 3.58 3.44 3.28

3.71 3.65 3.56 3.42 3.27

3.71 3.63 3.54 3.41 3.26

3.71 3.61 3.52 3.39 3.25

3.71 3.59 3.50 3.38 3.25

3.71 3.55 3.46 3.35 3.23

3.71 3.52 3.43 3.32 3.21

3.71 3.48 3.39 3.30 3.20

3.71 3.44 3.36 3.27 3.18

3.71 3.43 3.33 3.25 3.16

0.30 0.40 0.50 0.60 0.70

3.09 2.66 2.30 2.00 1.76

3.09 2.67 2.30 2.00 1.77

3.10 2.68 2.32 2.03 1.79

3.10 2.70 2.36 2.07 1.84

3.10 2.73 2.40 2.12 1.90

3.10 2.75 2.44 2.18 1.96

3.11 2.77 2.48 2.23 2.02

3.11 2.80 2.52 2.28 2.07

3.11 2.81 2.55 2.32 2.12

3.11 2.83 2.58 2.36 2.16

3.11 2.84 2.60 2.39 2.20

3.11 2.87 2.65 2.45 2.27

3.10 2.88 2.68 2.49 2.33

3.09 2.89 2.70 2.53 2.38

3.08 2.90 2.72 2.56 2.41

3.07 2.90 2.73 2.58 2.45

0.80 0.90 1.0 1.2 1.4

1.57 1.41 1.28 1.08 0.928

1.57 1.42 1.29 1.08 0.936

1.60 1.45 1.32 1.12 0.966

1.65 1.50 1.37 1.16 1.01

1.71 1.56 1.43 1.22 1.07

1.78 1.62 1.49 1.28 1.13

1.84 1.69 1.56 1.35 1.19

1.90 1.75 1.62 1.41 1.24

1.95 1.80 1.67 1.46 1.30

2.00 1.85 1.72 1.51 1.35

2.04 1.90 1.77 1.56 1.40

2.12 1.98 1.86 1.65 1.49

2.18 2.05 1.93 1.73 1.57

2.24 2.11 2.00 1.80 1.64

2.28 2.16 2.05 1.86 1.70

2.32 2.20 2.10 1.91 1.75

1.6 1.8 2.0 2.2 2.4

0.815 0.727 0.655 0.597 0.547

0.823 0.734 0.663 0.604 0.554

0.852 0.761 0.688 0.627 0.576

0.894 0.800 0.724 0.661 0.608

0.945 0.848 0.768 0.702 0.646

1.00 0.899 0.817 0.747 0.689

1.06 0.953 0.867 0.794 0.733

1.11 1.00 0.916 0.841 0.777

1.16 1.05 0.964 0.887 0.821

1.21 1.10 1.01 0.931 0.864

1.26 1.15 1.06 0.975 0.905

1.35 1.24 1.14 1.06 0.983

1.43 1.31 1.22 1.13 1.06

1.50 1.38 1.28 1.20 1.12

1.56 1.45 1.35 1.26 1.18

1.62 1.50 1.40 1.31 1.24

2.6 2.8 3.0

0.506 0.512 0.533 0.562 0.598 0.638 0.680 0.722 0.764 0.805 0.845 0.920 0.990 1.05 1.11 1.17 0.470 0.476 0.495 0.523 0.557 0.595 0.634 0.674 0.714 0.753 0.791 0.864 0.932 0.994 1.05 1.10 0.439 0.445 0.463 0.489 0.521 0.557 0.594 0.632 0.670 0.708 0.745 0.815 0.880 0.940 0.996 1.05

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:28 AM

Page 67

DESIGN TABLES

8–67

Table 8-4 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 15° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

3.96 3.79 3.68 3.51 3.31

3.96 3.79 3.68 3.51 3.31

3.96 3.78 3.67 3.51 3.31

3.96 3.78 3.66 3.50 3.31

3.96 3.77 3.65 3.50 3.31

3.96 3.76 3.64 3.49 3.32

3.96 3.75 3.63 3.49 3.32

3.96 3.74 3.62 3.48 3.32

3.96 3.73 3.61 3.48 3.33

3.96 3.72 3.61 3.47 3.33

3.96 3.71 3.60 3.47 3.33

3.96 3.69 3.58 3.46 3.34

3.96 3.67 3.57 3.46 3.34

3.96 3.65 3.55 3.45 3.34

3.96 3.64 3.54 3.44 3.34

3.96 3.62 3.53 3.43 3.34

0.30 0.40 0.50 0.60 0.70

3.09 2.68 2.32 2.03 1.79

3.09 2.68 2.32 2.03 1.80

3.10 2.69 2.35 2.06 1.82

3.11 2.72 2.38 2.10 1.87

3.13 2.75 2.43 2.16 1.93

3.14 2.79 2.48 2.22 2.00

3.15 2.82 2.53 2.27 2.06

3.16 2.85 2.57 2.33 2.12

3.17 2.88 2.61 2.38 2.18

3.18 2.90 2.65 2.42 2.23

3.19 2.93 2.68 2.46 2.27

3.21 2.96 2.74 2.54 2.36

3.22 3.00 2.79 2.60 2.42

3.23 3.02 2.83 2.65 2.48

3.24 3.04 2.86 2.69 2.53

3.24 3.06 2.89 2.72 2.58

0.80 0.90 1.0 1.2 1.4

1.60 1.44 1.31 1.10 0.954

1.60 1.45 1.32 1.11 0.961

1.63 1.48 1.35 1.14 0.993

1.68 1.53 1.40 1.19 1.04

1.75 1.59 1.46 1.25 1.10

1.81 1.66 1.53 1.32 1.16

1.88 1.73 1.60 1.38 1.22

1.94 1.79 1.66 1.45 1.28

2.00 1.85 1.72 1.51 1.34

2.06 1.91 1.78 1.56 1.39

2.11 1.96 1.83 1.62 1.45

2.20 2.05 1.93 1.72 1.54

2.27 2.14 2.01 1.80 1.63

2.34 2.21 2.09 1.88 1.71

2.39 2.27 2.15 1.95 1.78

2.44 2.32 2.21 2.01 1.84

1.6 1.8 2.0 2.2 2.4

0.839 0.748 0.675 0.615 0.565

0.847 0.756 0.683 0.622 0.572

0.876 0.783 0.708 0.646 0.594

0.919 0.824 0.746 0.681 0.626

0.972 0.872 0.791 0.723 0.666

1.03 0.926 0.841 0.770 0.710

1.09 0.981 0.893 0.819 0.756

1.15 1.04 0.945 0.868 0.802

1.20 1.09 0.995 0.916 0.848

1.25 1.14 1.04 0.963 0.893

1.31 1.19 1.09 1.01 0.937

1.40 1.28 1.18 1.10 1.02

1.49 1.37 1.26 1.18 1.10

1.57 1.45 1.34 1.25 1.17

1.64 1.52 1.41 1.32 1.24

1.70 1.58 1.47 1.38 1.30

2.6 2.8 3.0

0.522 0.529 0.550 0.580 0.617 0.658 0.702 0.746 0.789 0.832 0.874 0.954 1.03 1.10 1.16 1.22 0.485 0.491 0.511 0.540 0.575 0.614 0.655 0.697 0.738 0.779 0.819 0.896 0.969 1.04 1.10 1.16 0.453 0.459 0.478 0.505 0.538 0.574 0.614 0.653 0.693 0.732 0.771 0.845 0.915 0.980 1.04 1.10

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:28 AM

Page 68

8–68

DESIGN CONSIDERATIONS FOR WELDS

Table 8-4 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 30° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

4.37 4.05 3.83 3.64 3.43

4.37 4.05 3.83 3.64 3.43

4.37 4.05 3.83 3.64 3.43

4.37 4.05 3.84 3.65 3.45

4.37 4.06 3.84 3.65 3.46

4.37 4.06 3.84 3.66 3.48

4.37 4.07 3.85 3.67 3.50

4.37 4.08 3.85 3.68 3.51

4.37 4.08 3.86 3.69 3.53

4.37 4.08 3.87 3.70 3.54

4.37 4.08 3.87 3.71 3.56

4.37 4.08 3.89 3.72 3.58

4.37 4.08 3.91 3.74 3.60

4.37 4.08 3.92 3.76 3.62

4.37 4.07 3.92 3.77 3.64

4.37 4.06 3.93 3.79 3.66

0.30 0.40 0.50 0.60 0.70

3.22 2.81 2.46 2.17 1.93

3.22 2.81 2.46 2.17 1.93

3.23 2.83 2.49 2.20 1.96

3.24 2.86 2.53 2.25 2.02

3.27 2.90 2.58 2.31 2.08

3.30 2.94 2.64 2.37 2.15

3.32 2.99 2.69 2.44 2.22

3.35 3.03 2.75 2.50 2.29

3.37 3.07 2.80 2.56 2.36

3.39 3.11 2.85 2.62 2.42

3.41 3.14 2.89 2.67 2.47

3.45 3.19 2.96 2.75 2.57

3.48 3.24 3.02 2.83 2.65

3.50 3.28 3.08 2.89 2.72

3.52 3.31 3.12 2.94 2.78

3.54 3.34 3.16 2.99 2.84

0.80 0.90 1.0 1.2 1.4

1.73 1.57 1.43 1.21 1.05

1.74 1.57 1.44 1.22 1.06

1.77 1.61 1.47 1.25 1.09

1.82 1.66 1.52 1.31 1.14

1.89 1.73 1.59 1.37 1.20

1.96 1.80 1.66 1.44 1.27

2.03 1.88 1.74 1.51 1.34

2.11 1.95 1.81 1.59 1.41

2.18 2.02 1.88 1.65 1.47

2.24 2.08 1.95 1.72 1.53

2.30 2.14 2.01 1.78 1.59

2.40 2.25 2.12 1.89 1.71

2.49 2.34 2.22 1.99 1.81

2.57 2.43 2.30 2.08 1.90

2.64 2.50 2.38 2.16 1.98

2.69 2.56 2.44 2.23 2.05

1.6 1.8 2.0 2.2 2.4

0.926 0.827 0.747 0.681 0.626

0.934 0.835 0.755 0.689 0.634

0.966 0.865 0.783 0.715 0.658

1.01 0.909 0.824 0.754 0.694

1.07 0.962 0.874 0.800 0.737

1.13 1.02 0.929 0.852 0.786

1.20 1.08 0.987 0.906 0.837

1.26 1.14 1.04 0.961 0.889

1.33 1.20 1.10 1.01 0.940

1.39 1.26 1.16 1.07 0.990

1.44 1.32 1.21 1.12 1.04

1.55 1.42 1.31 1.22 1.13

1.65 1.52 1.41 1.31 1.22

1.74 1.61 1.49 1.39 1.30

1.82 1.69 1.57 1.47 1.38

1.90 1.76 1.64 1.54 1.45

2.6 2.8 3.0

0.579 0.586 0.609 0.643 0.684 0.729 0.778 0.827 0.875 0.924 0.971 1.06 1.15 1.23 1.30 1.37 0.538 0.545 0.567 0.599 0.637 0.680 0.726 0.773 0.819 0.865 0.910 0.997 1.08 1.16 1.23 1.30 0.503 0.510 0.530 0.560 0.596 0.637 0.681 0.725 0.769 0.813 0.856 0.940 1.02 1.09 1.16 1.23

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:28 AM

Page 69

DESIGN TABLES

8–69

Table 8-4 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 45° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

4.82 4.49 4.18 3.92 3.70

4.82 4.49 4.18 3.92 3.70

4.82 4.50 4.20 3.94 3.71

4.82 4.51 4.23 3.96 3.74

4.82 4.53 4.26 3.99 3.77

4.82 4.55 4.30 4.03 3.81

4.82 4.57 4.34 4.08 3.86

4.82 4.59 4.37 4.13 3.91

4.82 4.61 4.40 4.18 3.96

4.82 4.62 4.43 4.22 4.01

4.82 4.63 4.46 4.26 4.06

4.82 4.66 4.50 4.33 4.14

4.82 4.67 4.54 4.38 4.21

4.82 4.68 4.57 4.43 4.27

4.82 4.69 4.60 4.47 4.33

4.82 4.69 4.61 4.50 4.37

0.30 0.40 0.50 0.60 0.70

3.49 3.10 2.75 2.46 2.21

3.49 3.10 2.76 2.47 2.22

3.51 3.12 2.79 2.50 2.26

3.54 3.16 2.83 2.55 2.31

3.57 3.21 2.89 2.62 2.39

3.62 3.27 2.96 2.70 2.47

3.67 3.33 3.03 2.77 2.55

3.72 3.39 3.10 2.85 2.63

3.77 3.45 3.17 2.93 2.71

3.81 3.50 3.24 3.00 2.79

3.86 3.55 3.29 3.06 2.85

3.96 3.64 3.39 3.17 2.98

4.04 3.73 3.48 3.27 3.08

4.12 3.82 3.56 3.36 3.17

4.18 3.90 3.64 3.43 3.25

4.23 3.96 3.72 3.50 3.33

0.80 0.90 1.0 1.2 1.4

2.01 1.83 1.68 1.44 1.25

2.01 1.84 1.69 1.45 1.26

2.05 1.88 1.73 1.49 1.30

2.11 1.94 1.79 1.55 1.36

2.19 2.01 1.87 1.62 1.43

2.27 2.10 1.95 1.70 1.51

2.35 2.18 2.04 1.79 1.59

2.44 2.27 2.12 1.87 1.67

2.52 2.35 2.20 1.95 1.75

2.60 2.43 2.28 2.03 1.83

2.67 2.51 2.36 2.11 1.90

2.80 2.64 2.49 2.24 2.03

2.91 2.75 2.61 2.36 2.15

3.01 2.85 2.72 2.47 2.26

3.09 2.95 2.81 2.57 2.36

3.17 3.03 2.89 2.66 2.45

1.6 1.8 2.0 2.2 2.4

1.11 0.996 0.902 0.824 0.758

1.12 1.01 0.911 0.833 0.767

1.16 1.04 0.944 0.864 0.796

1.21 1.09 0.993 0.910 0.839

1.28 1.15 1.05 0.965 0.891

1.35 1.22 1.12 1.03 0.949

1.43 1.30 1.19 1.09 1.01

1.51 1.37 1.26 1.16 1.07

1.58 1.44 1.32 1.22 1.14

1.66 1.51 1.39 1.29 1.20

1.73 1.58 1.46 1.35 1.26

1.86 1.71 1.58 1.47 1.37

1.98 1.82 1.69 1.58 1.48

2.09 1.93 1.80 1.68 1.58

2.19 2.03 1.90 1.78 1.67

2.28 2.12 1.99 1.87 1.76

2.6 2.8 3.0

0.702 0.711 0.738 0.778 0.827 0.882 0.940 1.00 1.06 1.12 1.17 1.28 1.39 1.49 1.58 1.66 0.653 0.662 0.688 0.726 0.772 0.823 0.879 0.936 0.992 1.05 1.10 1.21 1.31 1.40 1.49 1.58 0.611 0.619 0.644 0.680 0.723 0.772 0.825 0.879 0.932 0.986 1.04 1.14 1.24 1.33 1.42 1.50

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:28 AM

Page 70

8–70

DESIGN CONSIDERATIONS FOR WELDS

Table 8-4 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 60° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

5.21 4.86 4.61 4.36 4.13

5.21 4.87 4.62 4.37 4.14

5.21 4.90 4.65 4.41 4.17

5.21 4.94 4.70 4.46 4.23

5.21 4.99 4.77 4.54 4.31

5.21 5.03 4.84 4.62 4.40

5.21 5.07 4.91 4.71 4.51

5.21 5.10 4.96 4.79 4.61

5.21 5.12 5.01 4.86 4.70

5.21 5.13 5.04 4.92 4.78

5.21 5.14 5.07 4.97 4.84

5.21 5.15 5.10 5.03 4.94

5.21 5.15 5.12 5.07 5.00

5.21 5.15 5.13 5.09 5.04

5.21 5.15 5.14 5.11 5.06

5.21 5.15 5.14 5.12 5.08

0.30 0.40 0.50 0.60 0.70

3.93 3.58 3.26 2.98 2.74

3.94 3.59 3.27 2.99 2.75

3.97 3.62 3.31 3.03 2.79

4.03 3.68 3.37 3.10 2.86

4.10 3.75 3.45 3.19 2.95

4.19 3.84 3.54 3.28 3.05

4.30 3.93 3.64 3.39 3.16

4.41 4.04 3.74 3.49 3.26

4.52 4.15 3.84 3.59 3.37

4.62 4.27 3.95 3.69 3.47

4.70 4.39 4.07 3.78 3.56

4.83 4.57 4.29 4.01 3.76

4.91 4.71 4.47 4.22 3.97

4.97 4.81 4.61 4.39 4.16

5.01 4.88 4.71 4.52 4.32

5.04 4.93 4.79 4.63 4.45

0.80 0.90 1.0 1.2 1.4

2.52 2.34 2.17 1.89 1.67

2.53 2.35 2.18 1.90 1.69

2.58 2.39 2.23 1.95 1.73

2.65 2.47 2.31 2.03 1.81

2.75 2.56 2.40 2.12 1.90

2.85 2.67 2.50 2.23 2.00

2.96 2.78 2.61 2.33 2.10

3.06 2.88 2.72 2.44 2.20

3.17 2.99 2.83 2.54 2.31

3.27 3.09 2.93 2.65 2.41

3.37 3.19 3.03 2.74 2.50

3.55 3.37 3.21 2.93 2.68

3.74 3.54 3.37 3.09 2.85

3.94 3.72 3.54 3.24 2.99

4.11 3.90 3.71 3.39 3.13

4.26 4.07 3.88 3.54 3.27

1.6 1.8 2.0 2.2 2.4

1.50 1.35 1.23 1.13 1.04

1.51 1.36 1.24 1.14 1.06

1.56 1.41 1.29 1.18 1.10

1.63 1.48 1.35 1.24 1.15

1.71 1.56 1.43 1.32 1.22

1.81 1.65 1.51 1.40 1.30

1.91 1.74 1.60 1.48 1.38

2.01 1.84 1.70 1.57 1.46

2.11 1.94 1.79 1.66 1.55

2.20 2.03 1.88 1.75 1.63

2.30 2.12 1.97 1.83 1.71

2.47 2.29 2.13 1.99 1.87

2.63 2.45 2.29 2.14 2.02

2.78 2.60 2.43 2.28 2.15

2.92 2.73 2.56 2.41 2.28

3.05 2.85 2.69 2.54 2.40

2.6 2.8 3.0

0.970 0.981 1.02 1.07 1.14 1.21 1.29 1.37 1.45 1.53 1.61 1.76 1.90 2.03 2.16 2.28 0.905 0.916 0.951 1.00 1.06 1.13 1.21 1.29 1.36 1.44 1.51 1.66 1.80 1.93 2.05 2.16 0.848 0.859 0.892 0.941 1.00 1.07 1.14 1.21 1.28 1.36 1.43 1.57 1.70 1.83 1.95 2.06

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:28 AM

Page 71

DESIGN TABLES

8–71

Table 8-4 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 75° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

5.47 5.17 5.00 4.85 4.71

5.47 5.19 5.03 4.87 4.73

5.47 5.25 5.10 4.95 4.80

5.47 5.32 5.19 5.06 4.92

5.47 5.38 5.28 5.16 5.04

5.47 5.42 5.34 5.25 5.15

5.47 5.44 5.38 5.32 5.24

5.47 5.45 5.41 5.36 5.30

5.47 5.45 5.43 5.39 5.34

5.47 5.46 5.44 5.41 5.37

5.47 5.46 5.45 5.42 5.39

5.47 5.46 5.45 5.44 5.42

5.47 5.46 5.45 5.45 5.43

5.47 5.46 5.45 5.45 5.44

5.47 5.45 5.45 5.45 5.44

5.47 5.45 5.45 5.45 5.45

0.30 0.40 0.50 0.60 0.70

4.57 4.32 4.09 3.88 3.69

4.59 4.33 4.11 3.90 3.71

4.65 4.39 4.17 3.96 3.77

4.78 4.51 4.27 4.07 3.87

4.92 4.67 4.43 4.21 4.01

5.04 4.82 4.60 4.38 4.18

5.15 4.95 4.76 4.56 4.36

5.23 5.06 4.89 4.71 4.53

5.28 5.15 5.00 4.84 4.68

5.33 5.22 5.09 4.95 4.80

5.36 5.27 5.16 5.04 4.91

5.40 5.33 5.25 5.16 5.06

5.42 5.37 5.32 5.25 5.17

5.43 5.40 5.35 5.30 5.24

5.44 5.41 5.38 5.34 5.29

5.44 5.42 5.40 5.36 5.33

0.80 0.90 1.0 1.2 1.4

3.51 3.34 3.18 2.90 2.65

3.53 3.36 3.20 2.92 2.67

3.59 3.42 3.27 2.99 2.74

3.70 3.53 3.37 3.09 2.85

3.83 3.66 3.50 3.22 2.97

3.99 3.81 3.65 3.37 3.11

4.17 3.99 3.83 3.53 3.27

4.35 4.18 4.01 3.70 3.43

4.51 4.35 4.19 3.88 3.61

4.65 4.50 4.35 4.06 3.78

4.77 4.64 4.49 4.22 3.95

4.96 4.84 4.73 4.49 4.24

5.08 4.99 4.90 4.69 4.48

5.17 5.10 5.02 4.85 4.67

5.24 5.17 5.11 4.97 4.81

5.28 5.23 5.18 5.06 4.92

1.6 1.8 2.0 2.2 2.4

2.44 2.26 2.09 1.95 1.82

2.46 2.27 2.11 1.97 1.84

2.53 2.34 2.18 2.03 1.90

2.63 2.44 2.27 2.13 1.99

2.75 2.56 2.39 2.24 2.10

2.89 2.69 2.52 2.36 2.22

3.04 2.84 2.66 2.50 2.35

3.19 2.99 2.80 2.63 2.48

3.36 3.14 2.95 2.78 2.62

3.53 3.30 3.10 2.92 2.76

3.70 3.47 3.26 3.07 2.90

4.01 3.78 3.57 3.38 3.20

4.27 4.06 3.86 3.66 3.48

4.48 4.29 4.10 3.92 3.74

4.65 4.48 4.31 4.14 3.97

4.78 4.63 4.48 4.32 4.16

2.6 2.8 3.0

1.71 1.73 1.79 1.88 1.98 2.10 2.22 2.35 2.48 2.62 2.75 3.04 3.31 3.57 3.80 4.01 1.61 1.63 1.69 1.77 1.87 1.98 2.10 2.23 2.36 2.49 2.62 2.88 3.16 3.41 3.64 3.85 1.52 1.54 1.60 1.68 1.77 1.88 2.00 2.12 2.24 2.37 2.49 2.75 3.01 3.26 3.49 3.71

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:28 AM

Page 72

8–72

DESIGN CONSIDERATIONS FOR WELDS

Table 8-5

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 0° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

5.57 4.32 3.90 3.54 3.22

5.57 4.36 3.94 3.57 3.25

5.57 4.48 4.04 3.67 3.34

5.57 4.65 4.20 3.81 3.47

5.57 4.82 4.39 3.99 3.64

5.57 4.97 4.58 4.20 3.85

5.57 5.11 4.75 4.40 4.06

5.57 5.21 4.90 4.57 4.26

5.57 5.29 5.02 4.73 4.43

5.57 5.35 5.12 4.86 4.59

5.57 5.39 5.20 4.97 4.72

5.57 5.45 5.31 5.13 4.93

5.57 5.48 5.38 5.24 5.08

5.57 5.50 5.42 5.32 5.19

5.57 5.52 5.45 5.37 5.26

5.57 5.53 5.48 5.41 5.32

0.30 0.40 0.50 0.60 0.70

2.94 2.48 2.14 1.87 1.65

2.97 2.51 2.17 1.89 1.68

3.06 2.60 2.24 1.96 1.74

3.19 2.71 2.34 2.06 1.83

3.34 2.85 2.47 2.17 1.93

3.53 3.01 2.62 2.31 2.06

3.74 3.19 2.78 2.45 2.19

3.95 3.40 2.95 2.61 2.33

4.14 3.61 3.15 2.78 2.48

4.32 3.81 3.35 2.96 2.64

4.47 3.99 3.54 3.15 2.81

4.72 4.29 3.88 3.50 3.17

4.91 4.54 4.16 3.81 3.48

5.04 4.72 4.39 4.06 3.75

5.14 4.87 4.58 4.28 3.99

5.22 4.99 4.73 4.46 4.19

0.80 0.90 1.0 1.2 1.4

1.48 1.34 1.22 1.04 0.900

1.50 1.36 1.24 1.05 0.914

1.56 1.41 1.29 1.10 0.952

1.64 1.49 1.36 1.16 1.00

1.74 1.58 1.44 1.23 1.07

1.85 1.68 1.54 1.31 1.14

1.97 1.79 1.64 1.41 1.23

2.10 1.91 1.75 1.50 1.31

2.24 2.04 1.87 1.60 1.40

2.38 2.17 1.99 1.71 1.49

2.54 2.31 2.12 1.82 1.59

2.87 2.61 2.39 2.05 1.79

3.18 2.92 2.69 2.30 2.00

3.46 3.20 2.97 2.56 2.24

3.71 3.45 3.22 2.81 2.47

3.92 3.68 3.45 3.03 2.69

1.6 1.8 2.0 2.2 2.4

0.794 0.710 0.643 0.586 0.539

0.807 0.722 0.653 0.596 0.548

0.840 0.752 0.680 0.621 0.571

0.888 0.795 0.719 0.657 0.604

0.946 0.848 0.767 0.701 0.644

1.01 0.907 0.822 0.751 0.691

1.08 0.973 0.881 0.805 0.741

1.16 1.04 0.945 0.864 0.795

1.24 1.12 1.01 0.925 0.852

1.33 1.19 1.08 0.988 0.910

1.41 1.27 1.15 1.05 0.970

1.59 1.43 1.30 1.19 1.09

1.78 1.60 1.45 1.33 1.22

1.98 1.77 1.61 1.47 1.35

2.19 1.96 1.77 1.62 1.49

2.40 2.16 1.95 1.78 1.64

2.6 2.8 3.0

0.498 0.507 0.528 0.559 0.597 0.640 0.687 0.737 0.789 0.844 0.899 1.01 1.13 1.26 1.38 1.51 0.464 0.472 0.491 0.520 0.555 0.595 0.639 0.686 0.735 0.786 0.838 0.946 1.06 1.17 1.29 1.41 0.434 0.441 0.459 0.486 0.519 0.557 0.598 0.642 0.688 0.736 0.785 0.886 0.990 1.10 1.21 1.32

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:28 AM

Page 73

DESIGN TABLES

8–73

Table 8-5 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 15° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

5.47 4.38 3.97 3.60 3.29

5.47 4.40 3.98 3.62 3.30

5.47 4.46 4.04 3.69 3.37

5.47 4.58 4.15 3.79 3.48

5.47 4.73 4.29 3.92 3.61

5.47 4.88 4.47 4.09 3.76

5.47 5.01 4.64 4.27 3.94

5.47 5.11 4.78 4.45 4.12

5.47 5.19 4.91 4.60 4.29

5.47 5.25 5.01 4.74 4.45

5.47 5.29 5.09 4.85 4.59

5.47 5.35 5.20 5.01 4.81

5.47 5.39 5.28 5.13 4.96

5.47 5.41 5.32 5.21 5.07

5.47 5.42 5.36 5.27 5.15

5.47 5.43 5.38 5.31 5.21

0.30 0.40 0.50 0.60 0.70

3.01 2.55 2.20 1.92 1.71

3.03 2.57 2.22 1.94 1.72

3.09 2.64 2.29 2.01 1.78

3.20 2.74 2.38 2.10 1.87

3.33 2.87 2.50 2.21 1.97

3.48 3.01 2.63 2.33 2.09

3.64 3.16 2.77 2.47 2.21

3.82 3.32 2.92 2.60 2.34

4.00 3.49 3.07 2.74 2.47

4.17 3.66 3.23 2.89 2.61

4.33 3.83 3.40 3.04 2.74

4.58 4.13 3.71 3.35 3.03

4.78 4.38 3.99 3.63 3.30

4.92 4.58 4.23 3.88 3.56

5.03 4.74 4.42 4.10 3.79

5.11 4.86 4.58 4.29 4.00

0.80 0.90 1.0 1.2 1.4

1.53 1.38 1.26 1.07 0.931

1.55 1.40 1.28 1.09 0.944

1.60 1.45 1.33 1.13 0.982

1.68 1.53 1.40 1.19 1.04

1.78 1.62 1.48 1.26 1.10

1.89 1.72 1.58 1.35 1.18

2.00 1.83 1.68 1.44 1.26

2.12 1.94 1.79 1.53 1.34

2.25 2.06 1.90 1.63 1.43

2.37 2.18 2.01 1.73 1.52

2.50 2.29 2.12 1.83 1.61

2.76 2.53 2.34 2.03 1.79

3.02 2.77 2.56 2.23 1.97

3.27 3.02 2.79 2.42 2.14

3.50 3.24 3.01 2.63 2.32

3.72 3.46 3.22 2.82 2.50

1.6 1.8 2.0 2.2 2.4

0.822 0.735 0.665 0.607 0.558

0.834 0.746 0.675 0.616 0.566

0.868 0.777 0.703 0.642 0.590

0.916 0.821 0.743 0.678 0.624

0.975 0.874 0.792 0.723 0.666

1.04 0.935 0.848 0.775 0.713

1.12 1.00 0.909 0.831 0.765

1.19 1.07 0.973 0.890 0.820

1.27 1.14 1.04 0.951 0.877

1.35 1.22 1.11 1.01 0.935

1.43 1.29 1.18 1.08 0.994

1.60 1.44 1.31 1.21 1.11

1.76 1.59 1.45 1.33 1.23

1.92 1.74 1.59 1.46 1.35

2.08 1.88 1.72 1.58 1.47

2.24 2.03 1.85 1.71 1.58

2.6 2.8 3.0

0.516 0.524 0.546 0.578 0.617 0.661 0.709 0.760 0.813 0.867 0.922 1.03 1.15 1.26 1.37 1.47 0.480 0.488 0.508 0.538 0.574 0.615 0.660 0.708 0.758 0.808 0.860 0.965 1.07 1.17 1.28 1.38 0.449 0.456 0.475 0.503 0.537 0.576 0.618 0.663 0.709 0.757 0.806 0.905 1.00 1.10 1.20 1.30

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:28 AM

Page 74

8–74

DESIGN CONSIDERATIONS FOR WELDS

Table 8-5 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 30° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

k a

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

5.21 4.49 4.09 3.76 3.47

5.21 4.50 4.10 3.77 3.48

5.21 4.54 4.13 3.80 3.51

5.21 4.59 4.19 3.86 3.57

5.21 4.66 4.27 3.93 3.65

5.21 4.74 4.36 4.01 3.74

5.21 4.82 4.46 4.12 3.83

5.21 4.89 4.57 4.23 3.93

5.21 4.94 4.66 4.35 4.04

5.21 4.99 4.75 4.46 4.16

5.21 5.02 4.81 4.56 4.28

5.21 5.07 4.91 4.71 4.48

5.21 5.10 4.98 4.82 4.63

5.21 5.11 5.03 4.90 4.74

5.21 5.12 5.05 4.95 4.83

5.21 5.13 5.07 4.99 4.89

0.30 0.40 0.50 0.60 0.70

3.21 2.76 2.40 2.11 1.88

3.21 2.77 2.41 2.12 1.89

3.25 2.81 2.45 2.17 1.94

3.32 2.88 2.53 2.25 2.01

3.40 2.97 2.62 2.34 2.11

3.49 3.07 2.73 2.45 2.21

3.59 3.17 2.84 2.55 2.32

3.69 3.28 2.94 2.66 2.42

3.79 3.38 3.05 2.77 2.53

3.89 3.48 3.15 2.87 2.63

4.01 3.58 3.25 2.97 2.73

4.24 3.77 3.43 3.15 2.91

4.42 3.99 3.60 3.31 3.07

4.57 4.18 3.79 3.47 3.22

4.68 4.33 3.97 3.64 3.37

4.76 4.46 4.13 3.81 3.52

0.80 0.90 1.0 1.2 1.4

1.69 1.53 1.40 1.19 1.03

1.70 1.54 1.41 1.20 1.05

1.75 1.59 1.46 1.24 1.08

1.82 1.66 1.53 1.31 1.14

1.91 1.75 1.61 1.38 1.21

2.01 1.84 1.70 1.47 1.29

2.12 1.94 1.80 1.55 1.37

2.22 2.05 1.89 1.65 1.45

2.32 2.15 1.99 1.74 1.54

2.42 2.24 2.09 1.83 1.62

2.52 2.34 2.18 1.91 1.70

2.70 2.51 2.35 2.08 1.85

2.86 2.68 2.51 2.23 2.00

3.01 2.82 2.66 2.37 2.14

3.15 2.96 2.79 2.50 2.26

3.28 3.09 2.92 2.62 2.38

1.6 1.8 2.0 2.2 2.4

0.914 0.818 0.740 0.675 0.621

0.925 0.829 0.750 0.685 0.630

0.960 0.861 0.780 0.712 0.656

1.01 0.908 0.823 0.752 0.693

1.07 0.965 0.876 0.801 0.738

1.14 1.03 0.935 0.856 0.789

1.22 1.10 0.999 0.915 0.845

1.30 1.17 1.07 0.978 0.902

1.37 1.24 1.13 1.04 0.961

1.45 1.31 1.20 1.10 1.02

1.53 1.38 1.27 1.17 1.08

1.67 1.52 1.40 1.29 1.19

1.81 1.65 1.52 1.41 1.31

1.94 1.78 1.64 1.52 1.41

2.06 1.90 1.75 1.63 1.52

2.18 2.01 1.86 1.73 1.62

2.6 2.8 3.0

0.575 0.583 0.607 0.642 0.684 0.732 0.784 0.838 0.893 0.948 1.00 1.11 1.22 1.32 1.42 1.52 0.535 0.543 0.565 0.598 0.637 0.682 0.731 0.782 0.834 0.886 0.939 1.04 1.14 1.24 1.34 1.43 0.500 0.508 0.529 0.559 0.596 0.639 0.684 0.732 0.781 0.831 0.881 0.980 1.08 1.17 1.26 1.35

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:28 AM

Page 75

DESIGN TABLES

8–75

Table 8-5 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 45° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

4.82 4.49 4.18 3.92 3.70

4.82 4.49 4.18 3.92 3.70

4.82 4.50 4.20 3.94 3.71

4.82 4.51 4.23 3.96 3.74

4.82 4.53 4.26 3.99 3.77

4.82 4.55 4.30 4.03 3.81

4.82 4.57 4.34 4.08 3.86

4.82 4.59 4.37 4.13 3.91

4.82 4.61 4.40 4.18 3.96

4.82 4.62 4.43 4.22 4.01

4.82 4.63 4.46 4.26 4.06

4.82 4.66 4.50 4.33 4.14

4.82 4.67 4.54 4.38 4.21

4.82 4.68 4.57 4.43 4.27

4.82 4.69 4.60 4.47 4.33

4.82 4.69 4.61 4.50 4.37

0.30 0.40 0.50 0.60 0.70

3.49 3.10 2.75 2.46 2.21

3.49 3.10 2.76 2.47 2.22

3.51 3.12 2.79 2.50 2.26

3.54 3.16 2.83 2.55 2.31

3.57 3.21 2.89 2.62 2.39

3.62 3.27 2.96 2.70 2.47

3.67 3.33 3.03 2.77 2.55

3.72 3.39 3.10 2.85 2.63

3.77 3.45 3.17 2.93 2.71

3.81 3.50 3.24 3.00 2.79

3.86 3.55 3.29 3.06 2.85

3.96 3.64 3.39 3.17 2.98

4.04 3.73 3.48 3.27 3.08

4.12 3.82 3.56 3.36 3.17

4.18 3.90 3.64 3.43 3.25

4.23 3.96 3.72 3.50 3.33

0.80 0.90 1.0 1.2 1.4

2.01 1.83 1.68 1.44 1.25

2.01 1.84 1.69 1.45 1.26

2.05 1.88 1.73 1.49 1.30

2.11 1.94 1.79 1.55 1.36

2.19 2.01 1.87 1.62 1.43

2.27 2.10 1.95 1.70 1.51

2.35 2.18 2.04 1.79 1.59

2.44 2.27 2.12 1.87 1.67

2.52 2.35 2.20 1.95 1.75

2.60 2.43 2.28 2.03 1.83

2.67 2.51 2.36 2.11 1.90

2.80 2.64 2.49 2.24 2.03

2.91 2.75 2.61 2.36 2.15

3.01 2.85 2.72 2.47 2.26

3.09 2.95 2.81 2.57 2.36

3.17 3.03 2.89 2.66 2.45

1.6 1.8 2.0 2.2 2.4

1.11 0.996 0.902 0.824 0.758

1.12 1.01 0.911 0.833 0.767

1.16 1.04 0.944 0.864 0.796

1.21 1.09 0.993 0.910 0.839

1.28 1.15 1.05 0.965 0.891

1.35 1.22 1.12 1.03 0.949

1.43 1.30 1.19 1.09 1.01

1.51 1.37 1.26 1.16 1.07

1.58 1.44 1.32 1.22 1.14

1.66 1.51 1.39 1.29 1.20

1.73 1.58 1.46 1.35 1.26

1.86 1.71 1.58 1.47 1.37

1.98 1.82 1.69 1.58 1.48

2.09 1.93 1.80 1.68 1.58

2.19 2.03 1.90 1.78 1.67

2.28 2.12 1.99 1.87 1.76

2.6 2.8 3.0

0.702 0.711 0.738 0.778 0.827 0.882 0.940 1.00 1.06 1.12 1.17 1.28 1.39 1.49 1.58 1.66 0.653 0.662 0.688 0.726 0.772 0.823 0.879 0.936 0.992 1.05 1.10 1.21 1.31 1.40 1.49 1.58 0.611 0.619 0.644 0.680 0.723 0.772 0.825 0.879 0.932 0.986 1.04 1.14 1.24 1.33 1.42 1.50

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:28 AM

Page 76

8–76

DESIGN CONSIDERATIONS FOR WELDS

Table 8-5 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 60° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

4.37 4.26 4.12 3.97 3.86

4.37 4.26 4.12 3.97 3.86

4.37 4.26 4.13 3.97 3.86

4.37 4.25 4.13 3.97 3.86

4.37 4.25 4.13 3.98 3.86

4.37 4.25 4.13 3.98 3.86

4.37 4.25 4.13 3.99 3.87

4.37 4.24 4.14 4.00 3.87

4.37 4.24 4.14 4.01 3.88

4.37 4.23 4.14 4.01 3.89

4.37 4.23 4.13 4.02 3.90

4.37 4.22 4.13 4.03 3.92

4.37 4.21 4.13 4.03 3.93

4.37 4.20 4.12 4.03 3.94

4.37 4.19 4.11 4.03 3.94

4.37 4.17 4.10 4.02 3.94

0.30 0.40 0.50 0.60 0.70

3.74 3.51 3.26 3.02 2.80

3.74 3.51 3.26 3.02 2.80

3.74 3.51 3.27 3.04 2.81

3.75 3.52 3.29 3.06 2.85

3.75 3.54 3.31 3.09 2.89

3.76 3.55 3.34 3.13 2.93

3.76 3.56 3.36 3.17 2.98

3.77 3.57 3.38 3.20 3.02

3.78 3.59 3.40 3.23 3.06

3.78 3.60 3.42 3.26 3.09

3.79 3.61 3.44 3.28 3.13

3.81 3.63 3.48 3.33 3.18

3.83 3.65 3.50 3.36 3.23

3.84 3.67 3.53 3.40 3.27

3.85 3.69 3.55 3.42 3.30

3.86 3.70 3.57 3.45 3.33

0.80 0.90 1.0 1.2 1.4

2.59 2.40 2.23 1.94 1.72

2.59 2.40 2.23 1.95 1.72

2.61 2.43 2.26 1.98 1.75

2.65 2.47 2.31 2.03 1.81

2.70 2.52 2.36 2.09 1.87

2.75 2.58 2.43 2.16 1.95

2.80 2.64 2.49 2.23 2.02

2.85 2.70 2.56 2.30 2.09

2.90 2.75 2.61 2.37 2.16

2.94 2.80 2.67 2.43 2.23

2.98 2.84 2.71 2.48 2.28

3.05 2.92 2.80 2.58 2.39

3.10 2.98 2.87 2.66 2.48

3.15 3.04 2.93 2.73 2.56

3.19 3.09 2.98 2.79 2.62

3.23 3.13 3.03 2.85 2.68

1.6 1.8 2.0 2.2 2.4

1.53 1.38 1.25 1.15 1.06

1.54 1.39 1.26 1.16 1.07

1.57 1.42 1.30 1.19 1.10

1.63 1.48 1.35 1.24 1.15

1.69 1.54 1.42 1.31 1.21

1.77 1.62 1.49 1.38 1.28

1.84 1.69 1.56 1.45 1.35

1.91 1.76 1.63 1.52 1.42

1.98 1.83 1.70 1.59 1.48

2.05 1.90 1.77 1.65 1.55

2.11 1.96 1.83 1.71 1.61

2.22 2.07 1.94 1.82 1.72

2.31 2.17 2.04 1.92 1.82

2.40 2.25 2.13 2.01 1.91

2.47 2.33 2.21 2.09 1.99

2.53 2.40 2.28 2.17 2.06

2.6 2.8 3.0

0.983 0.991 1.02 1.07 1.13 1.20 1.26 1.33 1.39 1.46 1.51 1.62 1.72 1.81 1.90 1.97 0.917 0.925 0.956 1.00 1.06 1.12 1.19 1.25 1.31 1.37 1.43 1.54 1.64 1.73 1.81 1.88 0.858 0.866 0.897 0.942 0.996 1.06 1.12 1.18 1.24 1.30 1.36 1.46 1.56 1.65 1.73 1.81

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:28 AM

Page 77

DESIGN TABLES

8–77

Table 8-5 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 75° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

3.96 3.82 3.85 3.84 3.83

3.96 3.83 3.86 3.84 3.83

3.96 3.84 3.86 3.84 3.83

3.96 3.84 3.86 3.84 3.82

3.96 3.85 3.86 3.83 3.82

3.96 3.85 3.85 3.83 3.81

3.96 3.85 3.85 3.82 3.80

3.96 3.85 3.85 3.82 3.80

3.96 3.85 3.84 3.81 3.79

3.96 3.85 3.83 3.80 3.78

3.96 3.85 3.83 3.80 3.77

3.96 3.84 3.81 3.78 3.75

3.96 3.82 3.79 3.76 3.73

3.96 3.80 3.77 3.74 3.72

3.96 3.78 3.75 3.72 3.70

3.96 3.76 3.73 3.71 3.68

0.30 0.40 0.50 0.60 0.70

3.82 3.78 3.72 3.65 3.56

3.82 3.78 3.72 3.64 3.55

3.81 3.77 3.71 3.64 3.55

3.81 3.76 3.70 3.63 3.54

3.80 3.75 3.69 3.62 3.54

3.79 3.74 3.68 3.61 3.53

3.78 3.73 3.67 3.60 3.52

3.77 3.72 3.66 3.60 3.52

3.76 3.71 3.65 3.59 3.51

3.76 3.70 3.64 3.58 3.51

3.75 3.69 3.64 3.57 3.50

3.73 3.67 3.62 3.56 3.49

3.71 3.66 3.60 3.54 3.48

3.69 3.64 3.59 3.53 3.47

3.67 3.62 3.57 3.52 3.47

3.66 3.61 3.56 3.51 3.46

0.80 0.90 1.0 1.2 1.4

3.46 3.35 3.23 3.00 2.78

3.45 3.35 3.23 3.00 2.78

3.45 3.35 3.24 3.01 2.79

3.45 3.35 3.24 3.02 2.81

3.45 3.35 3.25 3.04 2.84

3.44 3.35 3.25 3.06 2.87

3.44 3.35 3.26 3.08 2.90

3.44 3.35 3.27 3.09 2.93

3.44 3.35 3.27 3.11 2.95

3.43 3.36 3.28 3.12 2.97

3.43 3.36 3.28 3.14 2.99

3.43 3.36 3.29 3.16 3.02

3.42 3.36 3.30 3.17 3.05

3.42 3.36 3.30 3.19 3.07

3.41 3.36 3.30 3.20 3.09

3.41 3.35 3.30 3.20 3.10

1.6 1.8 2.0 2.2 2.4

2.57 2.38 2.21 2.05 1.92

2.57 2.38 2.21 2.06 1.92

2.59 2.40 2.24 2.09 1.95

2.62 2.44 2.27 2.13 2.00

2.65 2.48 2.32 2.18 2.05

2.69 2.53 2.38 2.24 2.12

2.73 2.58 2.43 2.30 2.18

2.77 2.62 2.48 2.35 2.24

2.80 2.66 2.52 2.40 2.29

2.83 2.69 2.56 2.44 2.33

2.85 2.72 2.60 2.48 2.38

2.90 2.78 2.66 2.56 2.45

2.93 2.82 2.72 2.61 2.52

2.96 2.86 2.76 2.66 2.57

2.99 2.89 2.80 2.71 2.62

3.01 2.91 2.83 2.74 2.66

2.6 2.8 3.0

1.80 1.80 1.83 1.88 1.94 2.00 2.07 2.13 2.18 2.23 2.28 2.36 2.43 2.49 2.54 2.58 1.69 1.69 1.72 1.77 1.83 1.90 1.97 2.03 2.09 2.14 2.19 2.27 2.35 2.41 2.46 2.51 1.59 1.60 1.63 1.68 1.74 1.81 1.87 1.94 2.00 2.05 2.10 2.19 2.27 2.33 2.39 2.44

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:28 AM

Page 78

8–78

DESIGN CONSIDERATIONS FOR WELDS

Table 8-6

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 0° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

3.71 3.72 3.67 3.51 3.31

4.08 4.09 4.06 3.93 3.72

4.45 4.55 4.49 4.34 4.13

4.83 5.04 4.94 4.77 4.54

5.38 5.54 5.41 5.21 4.96

5.94 6.04 5.89 5.66 5.39

6.50 6.55 6.38 6.13 5.84

7.05 7.07 6.87 6.59 6.29

7.61 7.58 7.36 7.07 6.74

8.17 8.10 7.86 7.54 7.20

8.72 8.62 8.36 8.03 7.67

9.84 10.9 12.1 13.2 14.3 9.66 10.7 11.8 12.8 13.9 9.36 10.4 11.4 12.4 13.4 9.00 9.98 11.0 12.0 13.0 8.61 9.57 10.5 11.5 12.5

0.30 0.40 0.50 0.60 0.70

3.09 2.66 2.30 2.00 1.76

3.48 3.01 2.60 2.27 2.00

3.89 3.39 2.94 2.57 2.27

4.29 3.77 3.30 2.90 2.57

4.69 4.16 3.67 3.25 2.90

5.11 4.55 4.04 3.60 3.24

5.53 4.94 4.41 3.96 3.57

5.97 5.35 4.79 4.32 3.91

6.41 5.76 5.19 4.69 4.26

6.86 6.19 5.59 5.07 4.63

7.31 6.62 6.00 5.46 5.00

8.23 7.50 6.84 6.27 5.77

9.17 8.40 7.71 7.11 6.58

10.1 9.33 8.61 7.97 7.41

11.1 10.3 9.52 8.86 8.27

12.1 11.2 10.5 9.77 9.15

0.80 0.90 1.0 1.2 1.4

1.57 1.41 1.28 1.08 0.928

1.78 1.60 1.45 1.22 1.05

2.02 1.82 1.66 1.40 1.21

2.30 2.08 1.90 1.61 1.40

2.61 2.36 2.16 1.84 1.60

2.93 2.67 2.45 2.09 1.83

3.25 2.97 2.73 2.35 2.06

3.57 3.27 3.02 2.61 2.29

3.90 3.59 3.32 2.87 2.53

4.24 3.91 3.62 3.15 2.78

4.60 4.25 3.94 3.43 3.03

5.34 4.95 4.61 4.03 3.58

6.11 5.69 5.31 4.67 4.16

6.91 6.45 6.04 5.34 4.77

7.74 7.25 6.81 6.04 5.42

8.59 8.07 7.60 6.77 6.09

1.6 1.8 2.0 2.2 2.4

0.815 0.727 0.655 0.597 0.547

0.927 0.827 0.746 0.679 0.623

1.07 0.954 0.861 0.785 0.721

1.23 1.10 0.996 0.908 0.835

1.42 1.27 1.15 1.05 0.963

1.62 1.45 1.31 1.20 1.10

1.83 1.64 1.49 1.36 1.25

2.04 1.83 1.66 1.52 1.41

2.25 2.03 1.85 1.69 1.56

2.48 2.24 2.04 1.87 1.72

2.71 2.45 2.23 2.05 1.89

3.21 2.90 2.65 2.44 2.26

3.74 3.39 3.10 2.86 2.65

4.30 3.92 3.59 3.31 3.07

4.90 4.47 4.10 3.79 3.52

5.53 5.05 4.65 4.30 4.00

2.6 2.8 3.0

0.506 0.576 0.666 0.772 0.891 1.02 1.16 1.30 1.45 1.60 1.76 2.10 0.470 0.536 0.620 0.718 0.829 0.950 1.08 1.21 1.35 1.49 1.64 1.96 0.439 0.500 0.579 0.671 0.775 0.888 1.01 1.14 1.27 1.40 1.54 1.84

2.47 2.86 3.29 3.74 2.31 2.68 3.08 3.50 2.17 2.52 2.90 3.30

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 79

DESIGN TABLES

8–79

Table 8-6 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 15° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

3.96 3.79 3.68 3.51 3.31

4.39 4.22 4.14 3.95 3.72

4.94 4.70 4.59 4.40 4.16

5.48 5.19 5.05 4.85 4.61

6.03 5.70 5.53 5.31 5.04

6.57 6.21 6.01 5.76 5.49

7.12 6.73 6.49 6.23 5.93

7.66 7.25 6.98 6.69 6.38

8.21 7.77 7.48 7.17 6.84

8.75 8.29 7.97 7.64 7.30

9.30 10.4 11.5 12.6 13.7 14.7 8.82 9.87 10.9 12.0 13.0 14.1 8.47 9.47 10.5 11.5 12.5 13.6 8.12 9.09 10.1 11.1 12.1 13.1 7.76 8.71 9.66 10.6 11.6 12.6

0.30 0.40 0.50 0.60 0.70

3.09 2.68 2.32 2.03 1.79

3.48 3.02 2.62 2.29 2.03

3.90 3.39 2.95 2.59 2.30

4.33 3.79 3.31 2.92 2.60

4.76 4.20 3.70 3.28 2.93

5.19 4.62 4.10 3.65 3.28

5.62 5.02 4.49 4.03 3.64

6.06 5.44 4.88 4.41 4.00

6.50 5.86 5.29 4.79 4.36

6.95 6.29 5.69 5.17 4.73

7.40 6.72 6.10 5.57 5.11

8.32 7.60 6.95 6.39 5.89

9.26 8.51 7.83 7.23 6.70

10.2 9.43 8.73 8.10 7.55

11.2 10.4 9.65 8.99 8.41

12.2 11.3 10.6 9.91 9.30

0.80 0.90 1.0 1.2 1.4

1.60 1.44 1.31 1.10 0.954

1.81 1.63 1.48 1.25 1.08

2.05 1.86 1.69 1.43 1.24

2.33 2.11 1.93 1.64 1.43

2.64 2.40 2.20 1.88 1.64

2.97 2.71 2.49 2.14 1.87

3.31 3.03 2.80 2.41 2.11

3.65 3.36 3.10 2.68 2.36

4.00 3.68 3.40 2.95 2.60

4.35 4.01 3.72 3.24 2.86

4.71 4.35 4.05 3.53 3.12

5.45 5.07 4.72 4.14 3.68

6.23 5.81 5.43 4.79 4.27

7.04 6.59 6.18 5.47 4.90

7.88 7.39 6.95 6.19 5.56

8.73 8.22 7.75 6.93 6.25

1.6 1.8 2.0 2.2 2.4

0.839 0.748 0.675 0.615 0.565

0.953 0.850 0.768 0.700 0.642

1.10 0.980 0.885 0.808 0.742

1.26 1.13 1.02 0.934 0.859

1.45 1.30 1.18 1.08 0.990

1.66 1.49 1.35 1.23 1.13

1.87 1.68 1.53 1.40 1.29

2.10 1.89 1.72 1.57 1.45

2.32 2.09 1.90 1.75 1.61

2.55 2.31 2.10 1.93 1.78

2.79 2.53 2.30 2.12 1.96

3.30 3.00 2.74 2.52 2.33

3.85 3.50 3.20 2.95 2.74

4.43 4.03 3.70 3.41 3.17

5.04 4.60 4.23 3.91 3.63

5.68 5.19 4.78 4.43 4.12

2.6 2.8 3.0

0.522 0.594 0.687 0.795 0.916 1.05 1.19 1.34 1.50 1.65 1.82 0.485 0.552 0.639 0.739 0.853 0.977 1.11 1.25 1.40 1.54 1.70 0.453 0.516 0.597 0.691 0.798 0.914 1.04 1.17 1.31 1.45 1.59

2.17 2.55 2.96 3.39 3.85 2.03 2.38 2.77 3.18 3.61 1.90 2.24 2.60 2.99 3.40

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 80

8–80

DESIGN CONSIDERATIONS FOR WELDS

Table 8-6 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 30° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

4.37 4.05 3.83 3.64 3.43

4.89 4.60 4.33 4.09 3.85

5.40 5.13 4.85 4.57 4.30

5.91 5.65 5.36 5.06 4.77

6.43 6.16 5.86 5.55 5.24

6.94 6.67 6.36 6.04 5.72

7.46 7.17 6.86 6.52 6.20

7.97 7.68 7.35 7.00 6.66

8.48 8.18 7.85 7.48 7.12

9.00 8.69 8.35 7.97 7.59

9.51 10.5 11.6 12.6 13.6 14.7 9.20 10.2 11.2 12.3 13.3 14.4 8.85 9.85 10.9 11.9 12.9 14.0 8.46 9.45 10.4 11.5 12.5 13.5 8.06 9.03 10.0 11.0 12.1 13.1

0.30 0.40 0.50 0.60 0.70

3.22 2.81 2.46 2.17 1.93

3.61 3.15 2.77 2.44 2.17

4.03 3.53 3.10 2.75 2.45

4.47 3.93 3.47 3.08 2.76

4.93 4.36 3.86 3.45 3.11

5.40 4.80 4.28 3.84 3.47

5.87 5.25 4.71 4.25 3.86

6.33 5.71 5.15 4.67 4.26

6.78 6.15 5.58 5.09 4.67

7.24 6.59 6.01 5.50 5.06

7.70 7.03 6.44 5.91 5.46

8.64 7.94 7.31 6.76 6.27

9.61 8.86 8.21 7.64 7.12

10.6 9.81 9.14 8.54 7.99

11.6 10.8 10.1 9.45 8.88

12.6 11.8 11.0 10.4 9.79

0.80 0.90 1.0 1.2 1.4

1.73 1.57 1.43 1.21 1.05

1.95 1.77 1.61 1.37 1.19

2.21 2.00 1.83 1.56 1.36

2.50 2.28 2.09 1.79 1.56

2.82 2.58 2.37 2.04 1.79

3.16 2.90 2.68 2.31 2.03

3.53 3.25 3.00 2.61 2.29

3.91 3.61 3.35 2.91 2.57

4.30 3.97 3.69 3.22 2.85

4.67 4.33 4.03 3.53 3.13

5.05 4.70 4.38 3.85 3.42

5.84 5.44 5.09 4.50 4.02

6.65 6.23 5.84 5.19 4.66

7.49 7.04 6.63 5.92 5.33

8.35 7.87 7.44 6.67 6.03

9.24 8.74 8.27 7.46 6.76

1.6 1.8 2.0 2.2 2.4

0.926 0.827 0.747 0.681 0.626

1.05 0.938 0.848 0.774 0.711

1.20 1.08 0.977 0.892 0.821

1.38 1.24 1.13 1.03 0.948

1.59 1.43 1.29 1.18 1.09

1.81 1.63 1.48 1.35 1.25

2.05 1.84 1.68 1.54 1.42

2.29 2.07 1.89 1.73 1.60

2.55 2.30 2.10 1.93 1.78

2.80 2.54 2.32 2.13 1.97

3.07 2.78 2.54 2.34 2.16

3.62 3.29 3.02 2.78 2.58

4.21 3.84 3.52 3.26 3.02

4.84 4.42 4.07 3.76 3.50

5.49 5.03 4.64 4.30 4.00

6.18 5.67 5.24 4.86 4.53

2.6 2.8 3.0

0.579 0.658 0.760 0.878 1.01 1.16 1.31 1.48 1.65 1.83 2.01 0.538 0.612 0.707 0.818 0.942 1.08 1.23 1.38 1.54 1.71 1.88 0.503 0.572 0.661 0.765 0.882 1.01 1.15 1.29 1.45 1.60 1.77

2.40 2.82 3.27 3.74 4.24 2.25 2.64 3.06 3.51 3.99 2.11 2.48 2.88 3.31 3.76

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 81

DESIGN TABLES

8–81

Table 8-6 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 45° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

4.82 4.49 4.18 3.92 3.70

5.14 4.99 4.69 4.39 4.13

5.61 5.48 5.19 4.87 4.58

6.08 5.96 5.67 5.36 5.05

6.54 6.45 6.16 5.84 5.52

7.01 6.94 6.65 6.33 6.01

7.48 7.43 7.15 6.83 6.50

7.95 7.92 7.65 7.33 7.00

8.41 8.41 8.15 7.84 7.50

8.88 8.90 8.65 8.34 8.02

9.35 10.3 11.2 12.2 13.1 14.0 9.39 10.4 11.4 12.3 13.3 14.3 9.14 10.1 11.1 12.1 13.1 14.1 8.85 9.86 10.9 11.9 12.9 13.9 8.53 9.54 10.6 11.6 12.6 13.6

0.30 0.40 0.50 0.60 0.70

3.49 3.10 2.75 2.46 2.21

3.89 3.45 3.07 2.75 2.48

4.32 3.84 3.42 3.08 2.78

4.76 4.25 3.81 3.44 3.12

5.22 4.68 4.22 3.83 3.49

5.70 5.13 4.65 4.24 3.88

6.18 5.60 5.10 4.67 4.30

6.67 6.07 5.56 5.11 4.73

7.18 6.56 6.03 5.58 5.17

7.69 7.06 6.52 6.05 5.62

8.20 7.57 7.01 6.52 6.08

9.21 8.56 7.96 7.43 6.96

10.2 9.57 8.94 8.38 7.87

11.3 10.6 9.96 9.37 8.83

12.3 11.6 11.0 10.4 9.81

13.3 12.7 12.0 11.4 10.8

0.80 0.90 1.0 1.2 1.4

2.01 1.83 1.68 1.44 1.25

2.25 2.06 1.89 1.62 1.41

2.53 2.32 2.13 1.84 1.61

2.85 2.62 2.42 2.10 1.84

3.20 2.95 2.73 2.38 2.10

3.57 3.31 3.08 2.69 2.38

3.97 3.69 3.44 3.02 2.68

4.39 4.08 3.81 3.36 2.99

4.81 4.49 4.20 3.71 3.32

5.25 4.91 4.60 4.08 3.65

5.69 5.33 5.01 4.46 4.00

6.54 6.16 5.81 5.20 4.69

7.42 7.01 6.63 5.97 5.41

8.34 7.89 7.48 6.77 6.17

9.29 8.81 8.38 7.60 6.95

10.3 9.76 9.30 8.47 7.76

1.6 1.8 2.0 2.2 2.4

1.11 0.996 0.902 0.824 0.758

1.25 1.13 1.02 0.934 0.860

1.43 1.29 1.17 1.07 0.990

1.64 1.48 1.35 1.24 1.14

1.88 1.70 1.55 1.42 1.31

2.13 1.93 1.76 1.62 1.49

2.40 2.18 1.99 1.83 1.69

2.69 2.44 2.23 2.06 1.90

2.99 2.72 2.49 2.29 2.12

3.30 3.00 2.75 2.54 2.36

3.62 3.30 3.03 2.80 2.60

4.27 3.90 3.59 3.32 3.09

4.94 4.53 4.18 3.88 3.62

5.65 5.20 4.81 4.47 4.17

6.38 5.89 5.46 5.09 4.76

7.15 6.62 6.15 5.74 5.37

2.6 2.8 3.0

0.702 0.797 0.918 1.06 1.22 1.39 1.57 1.77 1.98 2.19 2.42 0.653 0.742 0.855 0.987 1.14 1.30 1.47 1.66 1.85 2.05 2.27 0.611 0.694 0.801 0.925 1.06 1.22 1.38 1.55 1.74 1.93 2.13

2.89 3.38 3.91 4.46 5.05 2.71 3.18 3.67 4.20 4.76 2.55 2.99 3.47 3.97 4.50

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 82

8–82

DESIGN CONSIDERATIONS FOR WELDS

Table 8-6 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 60° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

5.21 4.86 4.61 4.36 4.13

5.58 5.29 5.04 4.80 4.56

6.01 5.73 5.48 5.23 4.99

6.45 6.19 5.93 5.67 5.43

6.89 6.65 6.40 6.14 5.89

7.33 7.12 6.88 6.63 6.37

7.76 7.59 7.37 7.13 6.87

8.20 8.06 7.86 7.62 7.38

8.64 8.52 8.34 8.12 7.89

9.07 8.98 8.81 8.61 8.39

9.51 9.43 9.28 9.10 8.89

10.4 10.3 10.2 10.1 9.87

11.3 11.2 11.1 11.0 10.8

12.1 12.1 12.0 11.9 11.8

13.0 13.0 12.9 12.8 12.7

13.9 13.9 13.8 13.7 13.6

0.30 0.40 0.50 0.60 0.70

3.93 3.58 3.26 2.98 2.74

4.34 3.95 3.60 3.30 3.04

4.76 4.35 3.98 3.66 3.38

5.19 4.77 4.39 4.05 3.75

5.64 5.20 4.82 4.47 4.17

6.12 5.66 5.27 4.92 4.60

6.62 6.15 5.74 5.39 5.06

7.13 6.66 6.24 5.86 5.52

7.65 7.17 6.75 6.36 6.00

8.16 7.69 7.27 6.87 6.50

8.67 8.21 7.78 7.38 7.01

9.67 9.24 8.81 8.41 8.03

10.6 10.2 9.83 9.44 9.05

11.6 11.2 10.8 10.4 10.1

12.5 12.2 11.8 11.4 11.1

13.5 13.2 12.8 12.4 12.1

0.80 0.90 1.0 1.2 1.4

2.52 2.34 2.17 1.89 1.67

2.81 2.60 2.42 2.12 1.88

3.13 2.91 2.71 2.39 2.12

3.49 3.26 3.05 2.70 2.41

3.89 3.64 3.42 3.04 2.73

4.31 4.05 3.82 3.41 3.07

4.75 4.48 4.23 3.79 3.43

5.21 4.92 4.66 4.20 3.80

5.68 5.38 5.11 4.61 4.20

6.16 5.85 5.56 5.05 4.60

6.65 6.33 6.03 5.49 5.02

7.66 7.32 6.99 6.40 5.89

8.68 8.32 7.98 7.33 6.76

9.70 9.32 8.96 8.28 7.66

10.7 10.3 9.95 9.24 8.60

11.7 11.3 10.9 10.2 9.55

1.6 1.8 2.0 2.2 2.4

1.50 1.35 1.23 1.13 1.04

1.68 1.52 1.39 1.28 1.18

1.91 1.73 1.59 1.46 1.35

2.18 1.98 1.81 1.67 1.55

2.47 2.25 2.07 1.91 1.77

2.78 2.54 2.34 2.16 2.01

3.12 2.86 2.63 2.44 2.27

3.47 3.19 2.94 2.73 2.54

3.84 3.53 3.26 3.03 2.83

4.22 3.89 3.60 3.35 3.13

4.62 4.26 3.96 3.68 3.44

5.44 5.04 4.69 4.38 4.10

6.26 5.82 5.44 5.10 4.79

7.12 6.63 6.20 5.82 5.49

8.01 7.49 7.02 6.59 6.22

8.93 8.37 7.86 7.41 6.99

2.6 2.8 3.0

0.970 1.10 1.26 1.45 1.65 1.88 2.12 2.38 2.65 2.94 3.23 0.905 1.02 1.18 1.35 1.55 1.76 1.99 2.23 2.49 2.76 3.04 0.848 0.961 1.10 1.27 1.46 1.66 1.88 2.11 2.35 2.61 2.87

3.86 4.51 5.18 5.88 6.62 3.64 4.26 4.90 5.57 6.28 3.44 4.04 4.65 5.29 5.97

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 83

DESIGN TABLES

8–83

Table 8-6 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 75° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

0.00 0.10 0.15 0.20 0.25

5.47 5.17 5.00 4.85 4.71

5.83 5.55 5.38 5.22 5.07

6.22 5.97 5.80 5.64 5.48

6.60 6.41 6.25 6.09 5.94

6.99 6.84 6.70 6.56 6.41

7.37 7.26 7.14 7.01 6.87

7.76 7.67 7.57 7.46 7.33

8.14 8.07 7.99 7.89 7.78

8.53 8.47 8.40 8.31 8.21

8.91 8.86 8.80 8.72 8.63

9.30 10.1 10.8 11.6 12.4 13.1 9.25 10.0 10.8 11.6 12.3 13.1 9.20 9.98 10.8 11.5 12.3 13.1 9.13 9.93 10.7 11.5 12.3 13.1 9.05 9.87 10.7 11.5 12.2 13.0

0.30 0.40 0.50 0.60 0.70

4.57 4.32 4.09 3.88 3.69

4.94 4.68 4.45 4.23 4.03

5.34 5.07 4.84 4.62 4.41

5.79 5.52 5.27 5.05 4.84

6.26 5.99 5.74 5.51 5.29

6.73 6.48 6.23 5.99 5.77

7.20 6.95 6.72 6.49 6.26

7.66 7.42 7.20 6.98 6.76

8.10 7.88 7.67 7.46 7.25

8.54 8.32 8.13 7.94 7.74

8.96 8.76 8.58 8.40 8.21

9.79 9.62 9.44 9.28 9.12

0.80 0.90 1.0 1.2 1.4

3.51 3.34 3.18 2.90 2.65

3.84 3.66 3.49 3.19 2.93

4.22 4.03 3.86 3.55 3.27

4.64 4.45 4.27 3.95 3.65

5.09 4.90 4.72 4.38 4.07

5.56 5.36 5.17 4.82 4.51

6.05 5.84 5.64 5.28 4.95

6.55 6.34 6.14 5.76 5.41

7.04 6.84 6.64 6.25 5.89

7.54 7.34 7.14 6.75 6.38

8.02 7.83 7.63 7.25 6.88

8.96 8.78 8.60 8.24 7.88

1.6 1.8 2.0 2.2 2.4

2.44 2.26 2.09 1.95 1.82

2.71 2.51 2.33 2.18 2.04

3.03 2.82 2.63 2.46 2.31

3.40 3.17 2.96 2.78 2.61

3.79 3.55 3.33 3.13 2.95

4.22 3.96 3.72 3.50 3.31

4.65 4.38 4.13 3.90 3.69

5.10 4.82 4.55 4.31 4.09

5.56 5.26 4.99 4.74 4.50

6.04 5.73 5.44 5.17 4.93

6.53 6.21 5.90 5.62 5.36

7.52 7.19 6.86 6.56 6.28

2.6 2.8 3.0

1.71 1.92 2.18 2.47 2.79 3.13 3.50 3.89 4.29 4.70 5.12 1.61 1.81 2.06 2.34 2.64 2.97 3.33 3.70 4.09 4.49 4.90 1.52 1.71 1.95 2.21 2.51 2.83 3.17 3.53 3.90 4.29 4.69

10.6 10.5 10.3 10.1 10.0

1.6

1.8

2.0

11.4 11.3 11.1 11.0 10.8

12.2 12.1 11.9 11.8 11.7

13.0 12.9 12.7 12.6 12.5

9.85 9.70 9.54 9.21 8.86

10.7 10.6 10.4 10.1 9.82

11.5 11.4 11.3 11.0 10.8

12.4 12.3 12.2 11.9 11.7

8.51 8.17 7.84 7.53 7.22

9.49 9.16 8.83 8.50 8.19

10.4 10.1 9.80 9.47 9.16

11.4 11.1 10.8 10.4 10.1

6.01 6.93 7.88 8.85 9.81 5.76 6.66 7.60 8.55 9.51 5.53 6.41 7.32 8.26 9.21

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 84

8–84

DESIGN CONSIDERATIONS FOR WELDS

Table 8-7

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 0° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

5.57 4.32 3.90 3.54 3.22

5.88 4.68 4.24 3.86 3.53

6.20 5.08 4.65 4.26 3.91

6.51 5.54 5.08 4.69 4.34

6.83 6.02 5.55 5.14 4.77

7.15 6.49 6.04 5.61 5.23

7.46 6.95 6.52 6.10 5.71

7.78 7.40 7.00 6.60 6.20

8.09 7.82 7.47 7.08 6.69

8.41 8.23 7.92 7.56 7.19

8.72 8.62 8.36 8.03 7.67

9.35 9.98 10.6 11.2 11.9 9.37 10.1 10.8 11.5 12.1 9.18 9.96 10.7 11.4 12.1 8.92 9.76 10.6 11.3 12.1 8.61 9.50 10.3 11.2 12.0

0.30 0.40 0.50 0.60 0.70

2.94 2.48 2.14 1.87 1.65

3.24 2.76 2.38 2.09 1.86

3.60 3.09 2.69 2.37 2.11

4.01 3.46 3.03 2.68 2.40

4.44 3.87 3.40 3.02 2.71

4.88 4.30 3.80 3.39 3.05

5.35 4.73 4.21 3.78 3.41

5.83 5.18 4.64 4.18 3.79

6.32 5.65 5.07 4.59 4.18

6.82 6.13 5.53 5.02 4.58

7.31 6.62 6.00 5.46 5.00

8.27 7.60 6.96 6.38 5.87

9.20 8.57 7.93 7.34 6.79

10.1 9.52 8.90 8.30 7.73

11.0 10.4 9.85 9.26 8.69

11.8 11.3 10.8 10.2 9.64

0.80 0.90 1.0 1.2 1.4

1.48 1.34 1.22 1.04 0.900

1.67 1.51 1.38 1.17 1.02

1.90 1.73 1.58 1.35 1.17

2.16 1.97 1.81 1.55 1.35

2.45 2.24 2.06 1.76 1.54

2.77 2.53 2.33 2.00 1.75

3.10 2.84 2.62 2.26 1.98

3.46 3.17 2.92 2.53 2.22

3.82 3.52 3.25 2.82 2.48

4.20 3.88 3.59 3.12 2.75

4.60 4.25 3.94 3.43 3.03

5.42 5.03 4.68 4.10 3.64

6.30 5.86 5.47 4.81 4.29

7.21 6.73 6.31 5.57 4.98

8.14 7.64 7.18 6.37 5.71

9.09 8.56 8.07 7.21 6.48

1.6 1.8 2.0 2.2 2.4

0.794 0.710 0.643 0.586 0.539

0.902 0.807 0.731 0.667 0.613

1.04 0.930 0.842 0.770 0.708

1.19 1.07 0.972 0.888 0.818

1.37 1.23 1.12 1.02 0.941

1.56 1.40 1.27 1.17 1.07

1.76 1.59 1.44 1.32 1.22

1.98 1.78 1.62 1.49 1.37

2.21 1.99 1.81 1.66 1.54

2.45 2.22 2.02 1.85 1.71

2.71 2.45 2.23 2.05 1.89

3.26 2.95 2.69 2.48 2.29

3.85 3.49 3.19 2.94 2.72

4.48 4.08 3.73 3.44 3.18

5.16 4.69 4.30 3.97 3.68

5.85 5.33 4.89 4.51 4.19

2.6 2.8 3.0

0.498 0.568 0.656 0.758 0.872 0.996 1.13 1.27 1.43 1.59 1.76 2.13 0.464 0.528 0.611 0.706 0.812 0.929 1.05 1.19 1.33 1.48 1.64 1.99 0.434 0.494 0.571 0.661 0.760 0.870 0.988 1.11 1.25 1.39 1.54 1.87

2.53 2.97 3.42 3.90 2.37 2.77 3.20 3.65 2.22 2.60 3.01 3.43

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 85

DESIGN TABLES

8–85

Table 8-7 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 15° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

5.47 4.38 3.97 3.60 3.29

5.83 4.75 4.32 3.94 3.60

6.22 5.14 4.71 4.32 3.98

6.60 5.59 5.13 4.75 4.39

6.99 6.06 5.60 5.19 4.84

7.37 6.54 6.09 5.67 5.29

7.76 7.02 6.58 6.16 5.77

8.14 7.48 7.07 6.66 6.27

8.53 7.93 7.55 7.16 6.77

8.91 8.38 8.01 7.64 7.27

9.30 10.1 10.8 11.6 12.4 13.1 8.82 9.67 10.5 11.3 12.1 12.9 8.47 9.35 10.2 11.0 11.8 12.7 8.12 9.05 9.93 10.8 11.6 12.4 7.76 8.72 9.65 10.5 11.4 12.2

0.30 0.40 0.50 0.60 0.70

3.01 2.55 2.20 1.92 1.71

3.31 2.82 2.45 2.15 1.91

3.67 3.16 2.75 2.43 2.17

4.07 3.53 3.10 2.75 2.46

4.51 3.94 3.47 3.09 2.78

4.95 4.37 3.87 3.46 3.12

5.42 4.81 4.30 3.86 3.49

5.91 5.26 4.73 4.27 3.88

6.40 5.74 5.17 4.69 4.28

6.90 6.22 5.63 5.12 4.69

7.40 6.72 6.10 5.57 5.11

8.39 7.71 7.08 6.50 5.99

9.34 8.70 8.06 7.46 6.92

10.3 9.67 9.05 8.44 7.87

11.2 10.6 10.0 9.41 8.83

12.0 11.5 11.0 10.4 9.79

0.80 0.90 1.0 1.2 1.4

1.53 1.38 1.26 1.07 0.931

1.72 1.56 1.42 1.21 1.05

1.95 1.78 1.63 1.39 1.21

2.22 2.03 1.86 1.59 1.39

2.52 2.30 2.12 1.82 1.59

2.84 2.60 2.39 2.06 1.81

3.18 2.92 2.69 2.32 2.04

3.54 3.25 3.01 2.60 2.29

3.92 3.61 3.34 2.90 2.55

4.31 3.98 3.69 3.21 2.83

4.71 4.35 4.05 3.53 3.12

5.54 5.15 4.80 4.21 3.74

6.42 5.99 5.59 4.93 4.40

7.34 6.86 6.44 5.70 5.09

8.28 7.77 7.31 6.48 5.80

9.23 8.70 8.20 7.30 6.56

1.6 1.8 2.0 2.2 2.4

0.822 0.735 0.665 0.607 0.558

0.932 0.834 0.755 0.690 0.634

1.07 0.961 0.870 0.795 0.732

1.23 1.11 1.00 0.918 0.845

1.41 1.27 1.15 1.05 0.972

1.61 1.45 1.31 1.20 1.11

1.82 1.64 1.49 1.37 1.26

2.04 1.84 1.68 1.54 1.42

2.28 2.06 1.87 1.72 1.59

2.53 2.29 2.08 1.91 1.77

2.79 2.53 2.30 2.12 1.96

3.36 3.04 2.78 2.55 2.36

3.96 3.59 3.29 3.03 2.80

4.60 4.18 3.83 3.53 3.27

5.25 4.78 4.39 4.05 3.76

5.93 5.42 4.98 4.60 4.27

2.6 2.8 3.0

0.516 0.587 0.678 0.783 0.901 1.03 1.17 1.32 1.47 1.64 1.82 0.480 0.546 0.631 0.730 0.840 0.960 1.09 1.23 1.38 1.53 1.70 0.449 0.511 0.591 0.683 0.786 0.899 1.02 1.15 1.29 1.44 1.59

2.20 2.61 3.05 3.50 3.99 2.05 2.44 2.85 3.28 3.73 1.93 2.29 2.67 3.08 3.51

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 86

8–86

DESIGN CONSIDERATIONS FOR WELDS

Table 8-7 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 30° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

5.21 4.49 4.09 3.76 3.47

5.58 4.93 4.51 4.15 3.83

6.01 5.36 4.94 4.56 4.22

6.45 5.81 5.38 4.99 4.64

6.89 6.28 5.84 5.43 5.07

7.33 6.77 6.32 5.90 5.52

7.76 7.26 6.82 6.40 6.01

8.20 7.75 7.33 6.91 6.51

8.64 8.24 7.84 7.42 7.03

9.07 8.72 8.35 7.94 7.55

9.51 10.4 11.3 12.1 13.0 13.9 9.20 10.1 11.1 12.0 12.9 13.8 8.85 9.83 10.8 11.7 12.7 13.6 8.46 9.47 10.5 11.4 12.4 13.3 8.06 9.09 10.1 11.1 12.1 13.0

0.30 0.40 0.50 0.60 0.70

3.21 2.76 2.40 2.11 1.88

3.54 3.06 2.67 2.35 2.10

3.92 3.40 2.98 2.64 2.37

4.32 3.77 3.33 2.98 2.68

4.75 4.19 3.72 3.34 3.02

5.20 4.62 4.14 3.73 3.38

5.67 5.08 4.57 4.14 3.77

6.16 5.55 5.02 4.56 4.17

6.67 6.03 5.48 5.00 4.59

7.19 6.53 5.95 5.45 5.02

7.70 7.03 6.44 5.91 5.46

8.73 8.06 7.43 6.87 6.37

9.75 9.08 8.44 7.85 7.29

10.8 10.1 9.45 8.82 8.24

11.7 11.1 10.4 9.81 9.20

0.80 0.90 1.0 1.2 1.4

1.69 1.53 1.40 1.19 1.03

1.89 1.72 1.57 1.34 1.17

2.14 1.95 1.79 1.53 1.34

2.43 2.22 2.04 1.76 1.54

2.75 2.52 2.32 2.00 1.76

3.09 2.84 2.62 2.27 2.00

3.45 3.18 2.94 2.55 2.25

3.83 3.53 3.28 2.85 2.52

4.22 3.91 3.63 3.17 2.81

4.63 4.30 4.00 3.50 3.11

5.05 4.70 4.38 3.85 3.42

5.92 5.52 5.17 4.56 4.07

6.80 6.36 5.96 5.30 4.75

7.71 7.23 6.79 6.05 5.45

8.64 8.13 7.66 6.84 6.17

9.59 9.05 8.56 7.68 6.94

1.6 1.8 2.0 2.2 2.4

0.914 0.818 0.740 0.675 0.621

1.03 0.927 0.840 0.767 0.706

1.19 1.07 0.966 0.884 0.814

1.37 1.23 1.11 1.02 0.939

1.56 1.41 1.28 1.17 1.08

1.78 1.60 1.46 1.34 1.23

2.01 1.81 1.65 1.51 1.40

2.25 2.04 1.86 1.70 1.57

2.51 2.27 2.07 1.90 1.76

2.79 2.52 2.30 2.12 1.96

3.07 2.78 2.54 2.34 2.16

3.67 3.33 3.05 2.81 2.61

4.30 3.92 3.59 3.31 3.07

4.94 4.51 4.15 3.83 3.56

5.61 5.14 4.74 4.39 4.08

6.32 5.80 5.35 4.97 4.63

2.6 2.8 3.0

0.575 0.653 0.754 0.871 1.00 1.14 1.30 1.46 1.64 1.82 2.01 0.535 0.608 0.702 0.812 0.934 1.07 1.21 1.37 1.53 1.70 1.88 0.500 0.569 0.657 0.760 0.874 1.00 1.14 1.28 1.43 1.59 1.77

12.7 12.1 11.4 10.8 10.2

2.43 2.87 3.32 3.81 4.33 2.27 2.68 3.11 3.57 4.06 2.13 2.52 2.93 3.36 3.83

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 87

DESIGN TABLES

8–87

Table 8-7 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 45° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

4.82 4.49 4.18 3.92 3.70

5.14 4.99 4.69 4.39 4.13

5.61 5.48 5.19 4.87 4.58

6.08 5.96 5.67 5.36 5.05

6.54 6.45 6.16 5.84 5.52

7.01 6.94 6.65 6.33 6.01

7.48 7.43 7.15 6.83 6.50

7.95 7.92 7.65 7.33 7.00

8.41 8.41 8.15 7.84 7.50

8.88 8.90 8.65 8.34 8.02

9.35 10.3 11.2 12.2 13.1 14.0 9.39 10.4 11.4 12.3 13.3 14.3 9.14 10.1 11.1 12.1 13.1 14.1 8.85 9.86 10.9 11.9 12.9 13.9 8.53 9.54 10.6 11.6 12.6 13.6

0.30 0.40 0.50 0.60 0.70

3.49 3.10 2.75 2.46 2.21

3.89 3.45 3.07 2.75 2.48

4.32 3.84 3.42 3.08 2.78

4.76 4.25 3.81 3.44 3.12

5.22 4.68 4.22 3.83 3.49

5.70 5.13 4.65 4.24 3.88

6.18 5.60 5.10 4.67 4.30

6.67 6.07 5.56 5.11 4.73

7.18 6.56 6.03 5.58 5.17

7.69 7.06 6.52 6.05 5.62

8.20 7.57 7.01 6.52 6.08

9.21 8.56 7.96 7.43 6.96

10.2 9.57 8.94 8.38 7.87

11.3 10.6 9.96 9.37 8.83

12.3 11.6 11.0 10.4 9.81

13.3 12.7 12.0 11.4 10.8

0.80 0.90 1.0 1.2 1.4

2.01 1.83 1.68 1.44 1.25

2.25 2.06 1.89 1.62 1.41

2.53 2.32 2.13 1.84 1.61

2.85 2.62 2.42 2.10 1.84

3.20 2.95 2.73 2.38 2.10

3.57 3.31 3.08 2.69 2.38

3.97 3.69 3.44 3.02 2.68

4.39 4.08 3.81 3.36 2.99

4.81 4.49 4.20 3.71 3.32

5.25 4.91 4.60 4.08 3.65

5.69 5.33 5.01 4.46 4.00

6.54 6.16 5.81 5.20 4.69

7.42 7.01 6.63 5.97 5.41

8.34 7.89 7.48 6.77 6.17

9.29 8.81 8.38 7.60 6.95

10.3 9.76 9.30 8.47 7.76

1.6 1.8 2.0 2.2 2.4

1.11 0.996 0.902 0.824 0.758

1.25 1.13 1.02 0.934 0.860

1.43 1.29 1.17 1.07 0.990

1.64 1.48 1.35 1.24 1.14

1.88 1.70 1.55 1.42 1.31

2.13 1.93 1.76 1.62 1.49

2.40 2.18 1.99 1.83 1.69

2.69 2.44 2.23 2.06 1.90

2.99 2.72 2.49 2.29 2.12

3.30 3.00 2.75 2.54 2.36

3.62 3.30 3.03 2.80 2.60

4.27 3.90 3.59 3.32 3.09

4.94 4.53 4.18 3.88 3.62

5.65 5.20 4.81 4.47 4.17

6.38 5.89 5.46 5.09 4.76

7.15 6.62 6.15 5.74 5.37

2.6 2.8 3.0

0.702 0.797 0.918 1.06 1.22 1.39 1.57 1.77 1.98 2.19 2.42 0.653 0.742 0.855 0.987 1.14 1.30 1.47 1.66 1.85 2.05 2.27 0.611 0.694 0.801 0.925 1.06 1.22 1.38 1.55 1.74 1.93 2.13

2.89 3.38 3.91 4.46 5.05 2.71 3.18 3.67 4.20 4.76 2.55 2.99 3.47 3.97 4.50

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 88

8–88

DESIGN CONSIDERATIONS FOR WELDS

Table 8-7 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 60° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

4.37 4.26 4.12 3.97 3.86

4.89 4.79 4.67 4.51 4.36

5.40 5.31 5.19 5.05 4.88

5.91 5.82 5.71 5.57 5.39

6.43 6.34 6.22 6.07 5.90

6.94 6.85 6.73 6.58 6.40

7.46 7.37 7.24 7.08 6.90

7.97 7.88 7.75 7.58 7.39

8.48 8.40 8.26 8.09 7.89

9.00 8.91 8.77 8.59 8.39

9.51 9.43 9.28 9.10 8.89

10.5 10.5 10.3 10.1 9.90

11.6 11.5 11.3 11.1 10.9

12.6 12.5 12.4 12.2 11.9

13.6 13.6 13.4 13.2 13.0

14.7 14.6 14.5 14.2 14.0

0.30 0.40 0.50 0.60 0.70

3.74 3.51 3.26 3.02 2.80

4.22 3.94 3.66 3.39 3.14

4.72 4.40 4.09 3.79 3.51

5.22 4.88 4.54 4.21 3.91

5.72 5.36 5.00 4.66 4.33

6.21 5.84 5.47 5.11 4.77

6.70 6.32 5.94 5.57 5.23

7.19 6.79 6.40 6.03 5.68

7.68 7.25 6.86 6.48 6.12

8.17 7.73 7.32 6.93 6.56

8.67 8.21 7.78 7.38 7.01

9.67 9.19 8.73 8.30 7.91

10.7 10.2 9.70 9.25 8.84

11.7 11.2 10.7 10.2 9.78

12.7 12.2 11.7 11.2 10.8

13.8 13.3 12.7 12.2 11.8

0.80 0.90 1.0 1.2 1.4

2.59 2.40 2.23 1.94 1.72

2.91 2.70 2.51 2.19 1.94

3.26 3.03 2.82 2.47 2.19

3.64 3.39 3.17 2.79 2.48

4.04 3.78 3.54 3.13 2.80

4.47 4.19 3.93 3.50 3.14

4.90 4.61 4.34 3.88 3.50

5.35 5.05 4.77 4.28 3.88

5.79 5.48 5.20 4.69 4.27

6.22 5.90 5.61 5.09 4.64

6.65 6.33 6.03 5.49 5.02

7.54 7.20 6.88 6.31 5.80

8.45 8.09 7.76 7.15 6.61

9.38 9.01 8.67 8.02 7.45

10.3 9.95 9.59 8.92 8.31

11.3 10.9 10.5 9.84 9.20

1.6 1.8 2.0 2.2 2.4

1.53 1.38 1.25 1.15 1.06

1.73 1.56 1.42 1.30 1.20

1.96 1.77 1.62 1.49 1.37

2.23 2.02 1.85 1.70 1.58

2.52 2.30 2.11 1.94 1.80

2.85 2.60 2.39 2.21 2.05

3.19 2.92 2.69 2.49 2.31

3.54 3.25 3.00 2.78 2.59

3.90 3.59 3.32 3.08 2.87

4.26 3.92 3.63 3.38 3.15

4.62 4.26 3.96 3.68 3.44

5.36 4.97 4.62 4.32 4.05

6.13 5.71 5.33 4.99 4.69

6.94 6.48 6.07 5.70 5.37

7.77 7.28 6.83 6.43 6.07

8.62 8.10 7.63 7.20 6.81

2.6 2.8 3.0

0.983 1.11 1.28 1.47 1.68 1.91 2.16 2.42 2.69 2.96 3.23 0.917 1.04 1.19 1.37 1.57 1.79 2.03 2.27 2.53 2.78 3.04 0.858 0.973 1.12 1.29 1.48 1.69 1.91 2.14 2.38 2.62 2.87

3.81 4.42 5.07 5.75 6.45 3.59 4.18 4.80 5.45 6.13 3.40 3.96 4.55 5.18 5.84

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 89

DESIGN TABLES

8–89

Table 8-7 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 75° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes)

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

3.96 3.82 3.85 3.84 3.83

4.39 4.36 4.32 4.26 4.23

4.94 4.90 4.86 4.81 4.75

5.48 5.44 5.41 5.36 5.30

6.03 5.99 5.95 5.90 5.84

6.57 6.53 6.49 6.44 6.38

7.12 7.07 7.03 6.98 6.91

7.66 7.62 7.57 7.52 7.45

8.21 8.16 8.11 8.05 7.98

8.75 8.70 8.65 8.59 8.52

9.30 9.25 9.20 9.13 9.05

10.4 10.3 10.3 10.2 10.1

11.5 11.4 11.4 11.3 11.2

12.6 12.5 12.4 12.4 12.3

13.7 13.6 13.5 13.4 13.3

14.7 14.7 14.6 14.5 14.4

0.30 0.40 0.50 0.60 0.70

3.82 3.78 3.72 3.65 3.56

4.22 4.21 4.17 4.10 4.00

4.72 4.68 4.63 4.56 4.46

5.24 5.18 5.11 5.02 4.91

5.77 5.68 5.59 5.49 5.37

6.30 6.18 6.08 5.96 5.83

6.84 6.69 6.57 6.44 6.30

7.37 7.21 7.07 6.92 6.77

7.90 7.72 7.57 7.41 7.25

8.43 8.24 8.07 7.90 7.73

8.96 10.0 11.1 12.1 13.2 14.3 8.76 9.81 10.9 11.9 13.0 14.0 8.58 9.59 10.6 11.7 12.7 13.7 8.40 9.39 10.4 11.4 12.4 13.5 8.21 9.19 10.2 11.2 12.2 13.2

0.80 0.90 1.0 1.2 1.4

3.46 3.35 3.23 3.00 2.78

3.89 3.76 3.64 3.38 3.13

4.34 4.20 4.06 3.79 3.51

4.78 4.65 4.51 4.21 3.92

5.23 5.09 4.94 4.64 4.34

5.69 5.54 5.38 5.06 4.75

6.14 5.98 5.82 5.49 5.17

6.61 6.44 6.27 5.92 5.59

7.07 6.90 6.72 6.36 6.01

7.54 7.36 7.17 6.80 6.44

8.02 7.83 7.63 7.25 6.88

8.98 8.77 8.57 8.16 7.77

9.96 9.74 9.52 9.10 8.69

10.9 10.7 10.5 10.0 9.62

11.9 11.7 11.5 11.0 10.6

12.9 12.7 12.5 12.0 11.5

1.6 1.8 2.0 2.2 2.4

2.57 2.38 2.21 2.05 1.92

2.90 2.69 2.50 2.32 2.17

3.26 3.02 2.81 2.63 2.46

3.64 3.39 3.16 2.96 2.77

4.05 3.78 3.54 3.32 3.12

4.46 4.19 3.93 3.70 3.48

4.86 4.58 4.32 4.08 3.86

5.27 4.98 4.70 4.45 4.22

5.69 5.38 5.10 4.84 4.59

6.11 5.79 5.50 5.23 4.97

6.53 6.21 5.90 5.62 5.36

7.41 7.06 6.74 6.44 6.16

8.30 7.94 7.61 7.29 7.00

9.22 8.85 8.49 8.16 7.85

10.2 9.77 9.40 9.06 8.74

11.1 10.7 10.3 9.97 9.64

2.6 2.8 3.0

1.80 2.03 2.30 2.61 2.94 3.29 3.66 4.01 4.37 4.74 5.12 1.69 1.91 2.17 2.46 2.78 3.12 3.47 3.82 4.17 4.53 4.90 1.59 1.80 2.05 2.32 2.63 2.96 3.30 3.64 3.98 4.33 4.69

5.91 6.72 7.56 8.43 9.32 5.66 6.46 7.29 8.14 9.01 5.44 6.22 7.02 7.86 8.71

Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 90

8–90

DESIGN CONSIDERATIONS FOR WELDS

Table 8-8

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 0° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

k 0.8

0.9

1.0

1.2

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

1.86 1.86 1.83 1.76 1.66

2.23 2.28 2.25 2.18 2.07

2.69 2.78 2.73 2.63 2.51

3.25 3.30 3.23 3.11 2.96

3.80 3.83 3.75 3.60 3.42

4.36 4.37 4.27 4.11 3.90

4.92 4.92 4.80 4.61 4.38

5.47 5.46 5.33 5.13 4.87

6.03 6.01 5.87 5.64 5.37

6.59 6.56 6.41 6.16 5.86

7.15 7.11 6.94 6.68 6.36

8.26 8.22 8.02 7.72 7.37

9.37 10.5 9.32 10.4 9.11 10.2 8.77 9.83 8.39 9.42

11.6 11.5 11.3 10.9 10.5

12.7 12.7 12.4 12.0 11.5

0.30 0.40 0.50 0.60 0.70

1.55 1.33 1.15 0.999 0.879

1.95 1.69 1.46 1.27 1.12

2.36 2.07 1.79 1.57 1.38

2.79 2.45 2.14 1.88 1.66

3.23 2.84 2.49 2.19 1.95

3.68 3.24 2.85 2.52 2.24

4.14 3.65 3.22 2.85 2.55

4.60 4.07 3.60 3.20 2.87

5.08 4.50 4.00 3.57 3.20

5.55 4.94 4.40 3.94 3.55

6.03 5.39 4.82 4.33 3.91

7.01 6.30 5.67 5.13 4.66

8.00 7.24 6.56 5.97 5.46

9.00 10.0 11.0 8.19 9.16 10.1 7.47 8.40 9.35 6.84 7.74 8.65 6.29 7.15 8.04

0.80 0.90 1.0 1.2 1.4

0.783 0.704 0.639 0.538 0.464

0.996 0.896 0.813 0.684 0.589

1.23 1.11 1.00 0.845 0.729

1.48 1.34 1.21 1.02 0.883

1.75 1.58 1.44 1.21 1.05

2.02 1.83 1.67 1.42 1.23

2.30 2.09 1.91 1.63 1.42

2.59 2.36 2.16 1.85 1.61

2.90 2.65 2.43 2.08 1.82

3.22 2.95 2.71 2.33 2.04

3.56 3.26 3.01 2.59 2.27

4.27 3.93 3.64 3.15 2.77

5.02 4.65 4.31 3.75 3.31

5.82 5.40 5.03 4.39 3.89

6.64 6.19 5.78 5.07 4.50

7.50 7.01 6.56 5.79 5.15

1.6 1.8 2.0 2.2 2.4

0.408 0.363 0.328 0.298 0.274

0.517 0.461 0.415 0.378 0.347

0.640 0.570 0.514 0.468 0.429

0.775 0.691 0.623 0.567 0.521

0.924 0.825 0.744 0.678 0.623

1.09 0.970 0.877 0.800 0.735

1.25 1.12 1.01 0.926 0.852

1.43 1.28 1.16 1.06 0.973

1.61 1.45 1.31 1.20 1.10

1.81 1.62 1.47 1.35 1.24

2.02 1.81 1.64 1.50 1.38

2.46 2.22 2.01 1.84 1.70

2.95 2.66 2.42 2.22 2.04

3.48 3.14 2.86 2.62 2.42

4.04 3.66 3.34 3.07 2.84

4.64 4.21 3.85 3.54 3.28

2.6 2.8 3.0

0.253 0.320 0.396 0.481 0.576 0.680 0.788 0.901 1.02 1.15 1.28 1.57 1.90 0.235 0.297 0.368 0.447 0.535 0.632 0.734 0.839 0.950 1.07 1.19 1.47 1.77 0.219 0.278 0.343 0.417 0.500 0.591 0.686 0.784 0.889 1.00 1.12 1.37 1.66

2.25 2.10 1.97

2.64 2.46 2.31

3.05 2.85 2.68

a

x

1.4

0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 91

DESIGN TABLES

8–91

Table 8-8 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 15° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

k 0.8

0.9

1.0

1.2

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

1.98 1.90 1.84 1.76 1.65

2.47 2.35 2.30 2.21 2.08

3.01 2.87 2.79 2.68 2.54

3.56 3.41 3.30 3.16 3.00

4.10 3.95 3.81 3.65 3.47

4.65 4.50 4.33 4.15 3.94

5.19 5.05 4.86 4.65 4.42

5.74 5.60 5.39 5.16 4.91

6.28 6.15 5.92 5.67 5.39

6.83 6.70 6.45 6.18 5.89

7.37 7.24 6.98 6.69 6.38

8.46 8.34 8.06 7.72 7.38

9.55 10.6 9.43 10.5 9.13 10.2 8.76 9.80 8.39 9.40

11.7 11.6 11.3 10.9 10.4

12.8 12.7 12.4 11.9 11.5

0.30 0.40 0.50 0.60 0.70

1.55 1.34 1.16 1.01 0.895

1.95 1.69 1.47 1.28 1.13

2.39 2.07 1.80 1.58 1.40

2.82 2.47 2.16 1.89 1.68

3.27 2.88 2.53 2.23 1.98

3.72 3.28 2.89 2.56 2.29

4.18 3.70 3.27 2.91 2.60

4.64 4.12 3.66 3.26 2.93

5.11 4.55 4.05 3.63 3.27

5.58 4.99 4.46 4.00 3.62

6.06 5.43 4.87 4.39 3.98

7.03 6.34 5.73 5.20 4.74

8.01 7.27 6.62 6.04 5.54

9.00 10.0 11.0 8.23 9.19 10.2 7.53 8.46 9.41 6.91 7.81 8.73 6.38 7.24 8.13

0.80 0.90 1.0 1.2 1.4

0.799 0.720 0.654 0.552 0.477

1.01 0.912 0.829 0.700 0.604

1.25 1.12 1.02 0.863 0.746

1.50 1.35 1.23 1.04 0.902

1.77 1.60 1.46 1.24 1.07

2.06 1.87 1.70 1.45 1.26

2.35 2.14 1.96 1.67 1.46

2.65 2.42 2.22 1.90 1.66

2.96 2.71 2.49 2.14 1.87

3.29 3.01 2.78 2.40 2.10

3.63 3.33 3.08 2.66 2.34

4.35 4.01 3.72 3.23 2.84

5.11 4.74 4.40 3.84 3.39

5.91 5.50 5.12 4.49 3.98

6.74 6.29 5.88 5.18 4.61

7.60 7.11 6.67 5.90 5.27

1.6 1.8 2.0 2.2 2.4

0.420 0.374 0.338 0.308 0.282

0.531 0.474 0.427 0.389 0.357

0.656 0.585 0.528 0.481 0.441

0.794 0.709 0.640 0.583 0.535

0.946 0.845 0.764 0.696 0.640

1.11 0.995 0.900 0.822 0.756

1.29 1.16 1.05 0.956 0.880

1.47 1.32 1.19 1.09 1.00

1.66 1.49 1.35 1.24 1.14

1.86 1.68 1.52 1.39 1.28

2.08 1.87 1.70 1.55 1.43

2.53 2.28 2.08 1.90 1.75

3.03 2.74 2.49 2.28 2.11

3.57 3.23 2.94 2.70 2.50

4.14 3.75 3.43 3.16 2.92

4.75 4.32 3.95 3.64 3.37

2.6 2.8 3.0

0.261 0.330 0.408 0.495 0.592 0.699 0.814 0.931 1.05 1.19 1.32 1.63 1.96 0.242 0.307 0.379 0.460 0.551 0.651 0.758 0.866 0.982 1.10 1.23 1.51 1.83 0.226 0.286 0.354 0.430 0.515 0.609 0.709 0.810 0.918 1.03 1.15 1.42 1.71

2.32 2.17 2.03

2.72 2.54 2.38

3.14 2.94 2.76

a

x

1.4

0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 92

8–92

DESIGN CONSIDERATIONS FOR WELDS

Table 8-8 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 30° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

k 0.8

0.9

1.0

1.2

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.18 2.02 1.92 1.82 1.71

2.70 2.57 2.43 2.29 2.15

3.21 3.10 2.95 2.79 2.62

3.73 3.62 3.47 3.29 3.10

4.24 4.14 3.98 3.78 3.58

4.76 4.67 4.49 4.28 4.06

5.27 5.19 5.00 4.77 4.53

5.78 5.71 5.52 5.27 5.01

6.30 6.23 6.03 5.77 5.49

6.81 6.75 6.54 6.27 5.97

7.33 7.28 7.05 6.77 6.46

8.35 8.32 8.09 7.78 7.45

9.38 10.4 9.37 10.4 9.12 10.2 8.80 9.83 8.45 9.47

11.4 11.5 11.2 10.9 10.5

12.5 12.5 12.2 11.9 11.5

0.30 0.40 0.50 0.60 0.70

1.61 1.41 1.23 1.08 0.964

2.01 1.76 1.54 1.36 1.21

2.45 2.15 1.88 1.66 1.48

2.91 2.55 2.24 1.99 1.77

3.37 2.97 2.62 2.33 2.08

3.83 3.40 3.01 2.68 2.41

4.29 3.83 3.41 3.06 2.75

4.75 4.26 3.81 3.43 3.11

5.21 4.69 4.22 3.81 3.46

5.68 5.13 4.63 4.20 3.83

6.15 5.57 5.05 4.60 4.20

7.11 6.49 5.92 5.42 4.99

8.09 7.42 6.82 6.28 5.81

9.10 10.1 11.1 8.38 9.36 10.4 7.74 8.68 9.65 7.17 8.09 9.03 6.67 7.56 8.47

0.80 0.90 1.0 1.2 1.4

0.865 0.783 0.714 0.606 0.525

1.09 0.986 0.900 0.764 0.663

1.33 1.21 1.10 0.939 0.815

1.60 1.45 1.33 1.13 0.983

1.88 1.71 1.57 1.34 1.17

2.18 1.99 1.83 1.57 1.37

2.50 2.29 2.10 1.81 1.58

2.83 2.60 2.39 2.07 1.81

3.16 2.91 2.69 2.33 2.05

3.51 3.23 3.00 2.60 2.29

3.86 3.57 3.31 2.89 2.55

4.61 4.28 3.98 3.49 3.09

5.40 5.03 4.70 4.13 3.67

6.22 5.81 5.45 4.81 4.30

7.07 6.63 6.23 5.53 4.96

7.95 7.47 7.04 6.29 5.66

1.6 1.8 2.0 2.2 2.4

0.463 0.414 0.374 0.341 0.313

0.584 0.522 0.472 0.430 0.395

0.719 0.643 0.581 0.530 0.487

0.868 0.777 0.703 0.642 0.590

1.03 0.925 0.838 0.766 0.705

1.21 1.09 0.988 0.903 0.832

1.41 1.27 1.15 1.05 0.970

1.61 1.45 1.32 1.21 1.11

1.82 1.64 1.49 1.37 1.26

2.04 1.84 1.67 1.53 1.41

2.27 2.05 1.87 1.71 1.58

2.77 2.50 2.28 2.09 1.93

3.30 2.99 2.73 2.51 2.32

3.87 3.52 3.22 2.97 2.75

4.49 4.09 3.75 3.46 3.21

5.13 4.69 4.31 3.98 3.70

2.6 2.8 3.0

0.289 0.365 0.451 0.546 0.653 0.771 0.899 1.03 1.17 1.31 1.47 1.80 2.16 0.269 0.340 0.419 0.508 0.608 0.718 0.838 0.960 1.09 1.22 1.37 1.68 2.02 0.251 0.317 0.392 0.475 0.569 0.672 0.784 0.899 1.02 1.15 1.28 1.57 1.89

2.56 2.39 2.25

2.99 2.80 2.63

3.45 3.24 3.04

a

x

1.4

0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 93

DESIGN TABLES

8–93

Table 8-8 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 45° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

k 0.8

0.9

1.0

1.2

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.41 2.24 2.09 1.96 1.85

2.80 2.74 2.60 2.44 2.29

3.27 3.24 3.09 2.92 2.75

3.74 3.73 3.58 3.40 3.21

4.21 4.23 4.07 3.88 3.68

4.67 4.73 4.57 4.37 4.16

5.14 5.22 5.06 4.86 4.64

5.61 5.72 5.56 5.36 5.13

6.08 6.21 6.06 5.85 5.62

6.54 6.71 6.55 6.35 6.11

7.01 7.20 7.05 6.84 6.60

7.95 8.19 8.04 7.83 7.58

8.88 9.82 9.17 10.1 9.03 10.0 8.83 9.82 8.58 9.58

10.8 11.1 11.0 10.8 10.6

11.7 12.1 12.0 11.8 11.6

0.30 0.40 0.50 0.60 0.70

1.74 1.55 1.38 1.23 1.11

2.16 1.91 1.70 1.52 1.38

2.59 2.30 2.05 1.84 1.66

3.03 2.70 2.42 2.18 1.97

3.48 3.12 2.80 2.53 2.30

3.94 3.55 3.20 2.90 2.65

4.42 3.99 3.62 3.29 3.01

4.89 4.44 4.04 3.70 3.40

5.38 4.91 4.48 4.11 3.79

5.86 5.37 4.93 4.54 4.20

6.34 5.83 5.37 4.96 4.61

7.32 6.77 6.27 5.83 5.44

8.31 7.75 7.22 6.73 6.30

9.32 10.3 11.3 8.76 9.77 10.8 8.20 9.20 10.2 7.68 8.65 9.65 7.21 8.15 9.12

0.80 0.90 1.0 1.2 1.4

1.00 0.915 0.839 0.719 0.627

1.25 1.14 1.05 0.900 0.786

1.51 1.39 1.28 1.10 0.961

1.80 1.65 1.52 1.31 1.15

2.11 1.94 1.79 1.55 1.36

2.43 2.24 2.08 1.80 1.59

2.77 2.56 2.38 2.08 1.84

3.13 2.91 2.71 2.37 2.11

3.51 3.27 3.05 2.68 2.39

3.91 3.64 3.40 3.00 2.67

4.29 4.01 3.75 3.31 2.96

5.08 4.76 4.47 3.98 3.57

5.91 5.56 5.24 4.68 4.22

6.78 6.39 6.04 5.43 4.91

7.69 7.27 6.89 6.22 5.65

8.64 8.19 7.77 7.04 6.42

1.6 1.8 2.0 2.2 2.4

0.555 0.498 0.451 0.412 0.379

0.697 0.625 0.567 0.518 0.477

0.854 0.767 0.696 0.636 0.586

1.03 0.923 0.839 0.768 0.708

1.22 1.10 0.997 0.914 0.844

1.42 1.29 1.17 1.08 0.995

1.65 1.49 1.36 1.25 1.16

1.89 1.72 1.57 1.44 1.33

2.15 1.95 1.78 1.63 1.51

2.40 2.18 1.99 1.83 1.70

2.67 2.42 2.22 2.04 1.89

3.23 2.94 2.70 2.49 2.31

3.83 3.50 3.22 2.97 2.76

4.48 4.10 3.78 3.50 3.26

5.16 4.74 4.38 4.07 3.79

5.88 5.42 5.02 4.67 4.36

2.6 2.8 3.0

0.351 0.442 0.543 0.657 0.784 0.924 1.08 1.24 1.40 1.58 1.76 2.15 2.58 0.327 0.411 0.506 0.612 0.731 0.863 1.01 1.16 1.31 1.47 1.64 2.01 2.42 0.306 0.385 0.474 0.573 0.685 0.809 0.943 1.09 1.23 1.38 1.54 1.89 2.27

3.05 2.86 2.69

3.55 3.33 3.14

4.09 3.84 3.63

a

x

1.4

0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 94

8–94

DESIGN CONSIDERATIONS FOR WELDS

Table 8-8 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 60° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

k 0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.60 2.43 2.31 2.18 2.07

3.01 2.86 2.74 2.61 2.49

3.44 3.30 3.17 3.04 2.91

3.88 3.75 3.62 3.47 3.33

4.32 4.21 4.07 3.93 3.77

4.76 4.68 4.54 4.39 4.23

5.19 5.14 5.01 4.86 4.70

5.63 5.61 5.49 5.34 5.18

6.07 6.07 5.96 5.83 5.67

6.50 6.53 6.44 6.31 6.16

6.94 6.99 6.90 6.79 6.64

7.82 7.89 7.83 7.73 7.61

8.69 8.79 8.74 8.66 8.55

9.56 9.67 9.64 9.57 9.48

10.4 10.5 10.5 10.5 10.4

11.3 11.4 11.4 11.4 11.3

0.30 0.40 0.50 0.60 0.70

1.97 1.79 1.63 1.49 1.37

2.37 2.16 1.98 1.81 1.67

2.78 2.55 2.34 2.15 1.99

3.20 2.94 2.71 2.50 2.32

3.63 3.35 3.10 2.87 2.67

4.07 3.77 3.50 3.26 3.05

4.54 4.22 3.93 3.67 3.44

5.02 4.69 4.38 4.10 3.86

5.51 5.17 4.85 4.55 4.29

6.00 5.66 5.33 5.02 4.74

6.49 6.15 5.82 5.50 5.21

7.46 7.14 6.80 6.48 6.16

8.42 8.12 7.79 7.46 7.11

9.36 10.3 9.09 10.0 8.77 9.73 8.42 9.38 8.07 9.04

0.80 0.90 1.0 1.2 1.4

1.26 1.17 1.08 0.946 0.837

1.54 1.43 1.33 1.17 1.04

1.84 1.71 1.60 1.41 1.25

2.16 2.02 1.89 1.67 1.49

2.50 2.34 2.19 1.95 1.75

2.85 2.68 2.52 2.25 2.03

3.23 3.04 2.87 2.58 2.33

3.63 3.43 3.24 2.92 2.65

4.05 3.83 3.63 3.28 2.98

4.48 4.25 4.03 3.65 3.33

4.94 4.68 4.45 4.04 3.69

5.85 5.57 5.30 4.82 4.42

6.78 6.47 6.18 5.65 5.19

7.73 7.40 7.09 6.52 6.01

8.69 8.35 8.03 7.42 6.87

9.65 9.31 8.98 8.35 7.77

1.6 1.8 2.0 2.2 2.4

0.748 0.676 0.616 0.565 0.522

0.930 0.842 0.768 0.706 0.653

1.13 1.02 0.936 0.861 0.797

1.34 1.22 1.12 1.03 0.958

1.58 1.44 1.32 1.22 1.14

1.84 1.68 1.55 1.43 1.33

2.12 1.94 1.79 1.66 1.55

2.42 2.22 2.05 1.90 1.77

2.73 2.51 2.32 2.15 2.01

3.05 2.81 2.60 2.42 2.26

3.38 3.12 2.90 2.69 2.52

4.07 3.76 3.50 3.26 3.05

4.79 4.45 4.14 3.87 3.63

5.56 5.17 4.83 4.53 4.25

6.38 5.95 5.56 5.22 4.91

7.24 6.77 6.34 5.96 5.62

2.6 2.8 3.0

0.485 0.607 0.742 0.893 1.06 1.25 1.44 1.66 1.88 2.12 2.36 2.87 3.42 0.453 0.567 0.694 0.835 0.994 1.17 1.36 1.56 1.77 1.99 2.22 2.70 3.22 0.424 0.531 0.651 0.785 0.934 1.10 1.28 1.47 1.67 1.88 2.09 2.55 3.05

4.01 3.79 3.59

4.64 4.39 4.17

5.31 5.03 4.78

a

x

11.2 11.0 10.7 10.3 10.0

0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 95

DESIGN TABLES

8–95

Table 8-8 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 75° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

k 0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.74 2.59 2.50 2.43 2.35

3.11 2.95 2.87 2.79 2.72

3.49 3.34 3.26 3.18 3.10

3.88 3.75 3.67 3.59 3.51

4.26 4.16 4.09 4.01 3.93

4.65 4.58 4.51 4.44 4.36

5.03 4.99 4.94 4.87 4.80

5.42 5.40 5.35 5.29 5.23

5.80 5.80 5.76 5.71 5.66

6.19 6.20 6.17 6.13 6.08

6.57 6.59 6.57 6.53 6.49

7.34 7.37 7.36 7.33 7.30

8.11 8.15 8.14 8.12 8.09

8.88 8.92 8.91 8.90 8.88

9.65 9.69 9.69 9.67 9.66

10.4 10.5 10.5 10.4 10.4

0.30 0.40 0.50 0.60 0.70

2.28 2.16 2.05 1.94 1.85

2.65 2.52 2.40 2.28 2.18

3.03 2.88 2.75 2.63 2.52

3.43 3.27 3.13 3.00 2.88

3.85 3.69 3.54 3.40 3.26

4.28 4.12 3.97 3.82 3.68

4.72 4.57 4.41 4.26 4.11

5.16 5.01 4.86 4.71 4.56

5.59 5.45 5.30 5.16 5.02

6.02 5.88 5.75 5.61 5.47

6.44 6.31 6.18 6.06 5.92

7.26 7.15 7.04 6.93 6.81

8.06 7.97 7.86 7.77 7.67

8.85 8.78 8.68 8.59 8.51

9.63 9.57 9.48 9.39 9.32

10.4 10.4 10.3 10.2 10.1

0.80 0.90 1.0 1.2 1.4

1.75 1.67 1.59 1.45 1.33

2.08 1.98 1.90 1.74 1.60

2.41 2.31 2.21 2.04 1.89

2.76 2.65 2.55 2.36 2.20

3.14 3.02 2.91 2.71 2.53

3.54 3.42 3.30 3.08 2.88

3.97 3.84 3.71 3.47 3.26

4.42 4.28 4.14 3.89 3.66

4.87 4.73 4.59 4.32 4.07

5.33 5.19 5.04 4.77 4.51

5.79 5.64 5.50 5.22 4.95

6.69 6.56 6.42 6.15 5.87

7.57 7.45 7.33 7.07 6.79

8.42 8.32 8.21 7.97 7.71

9.25 10.1 9.16 9.98 9.07 9.91 8.86 9.72 8.62 9.51

1.6 1.8 2.0 2.2 2.4

1.22 1.13 1.05 0.975 0.912

1.48 1.37 1.28 1.19 1.12

1.75 1.63 1.52 1.43 1.34

2.05 1.91 1.79 1.69 1.59

2.37 2.22 2.09 1.97 1.86

2.71 2.54 2.40 2.27 2.15

3.06 2.89 2.73 2.58 2.45

3.44 3.25 3.08 2.92 2.77

3.85 3.64 3.45 3.27 3.11

4.27 4.04 3.84 3.65 3.47

4.70 4.46 4.24 4.04 3.85

5.60 5.34 5.10 4.87 4.65

6.52 6.25 5.99 5.74 5.50

7.44 7.17 6.90 6.62 6.36

8.36 8.10 7.81 7.53 7.25

9.27 9.01 8.73 8.44 8.15

2.6 2.8 3.0

0.856 1.05 1.27 1.50 1.76 2.04 2.33 2.64 2.97 3.31 3.68 4.45 5.26 0.806 0.993 1.20 1.42 1.67 1.94 2.22 2.52 2.83 3.17 3.52 4.27 5.05 0.762 0.940 1.14 1.35 1.59 1.84 2.12 2.40 2.71 3.03 3.37 4.09 4.84

6.10 5.86 5.64

6.98 6.72 6.47

7.87 7.60 7.34

a

x

0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 96

8–96

DESIGN CONSIDERATIONS FOR WELDS

Table 8-9

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 0° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

k 0.8

0.9

1.0

1.2

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

1.86 1.86 1.83 1.76 1.66

2.23 2.30 2.26 2.18 2.06

2.69 2.80 2.73 2.62 2.48

3.25 3.30 3.21 3.07 2.91

3.80 3.82 3.69 3.53 3.35

4.36 4.32 4.18 3.99 3.79

4.92 4.83 4.66 4.45 4.23

5.47 5.34 5.14 4.91 4.67

6.03 5.84 5.62 5.37 5.11

6.59 6.34 6.10 5.83 5.55

7.15 6.84 6.58 6.30 6.00

8.26 7.84 7.54 7.22 6.90

9.37 10.5 8.84 9.83 8.51 9.48 8.16 9.11 7.81 8.73

11.6 10.8 10.4 10.1 9.67

12.7 11.8 11.4 11.0 10.6

0.30 0.40 0.50 0.60 0.70

1.55 1.33 1.15 0.999 0.879

1.93 1.67 1.45 1.26 1.11

2.33 2.03 1.75 1.52 1.34

2.74 2.39 2.07 1.81 1.60

3.15 2.77 2.41 2.11 1.88

3.57 3.15 2.76 2.43 2.18

3.99 3.53 3.12 2.77 2.48

4.41 3.92 3.47 3.10 2.80

4.84 4.32 3.84 3.44 3.12

5.27 4.72 4.21 3.79 3.44

5.70 5.12 4.59 4.14 3.78

6.57 5.95 5.37 4.88 4.47

7.46 6.79 6.17 5.65 5.20

8.37 7.66 7.00 6.45 5.96

9.29 10.2 8.54 9.44 7.86 8.73 7.27 8.11 6.75 7.56

0.80 0.90 1.0 1.2 1.4

0.783 0.704 0.639 0.538 0.464

0.982 0.882 0.800 0.674 0.582

1.20 1.08 0.980 0.829 0.717

1.43 1.30 1.18 1.00 0.869

1.69 1.53 1.40 1.19 1.04

1.96 1.78 1.64 1.40 1.22

2.25 2.05 1.88 1.61 1.41

2.55 2.33 2.14 1.84 1.61

2.84 2.61 2.41 2.08 1.83

3.15 2.90 2.69 2.33 2.05

3.47 3.20 2.97 2.58 2.28

4.12 3.82 3.55 3.11 2.76

4.81 4.47 4.17 3.67 3.27

5.54 5.16 4.83 4.27 3.82

6.29 5.89 5.52 4.90 4.40

7.07 6.64 6.24 5.57 5.01

1.6 1.8 2.0 2.2 2.4

0.408 0.363 0.328 0.298 0.274

0.511 0.456 0.411 0.375 0.344

0.631 0.563 0.508 0.463 0.425

0.766 0.684 0.618 0.563 0.518

0.915 0.818 0.740 0.675 0.620

1.08 0.964 0.872 0.796 0.732

1.25 1.12 1.01 0.926 0.852

1.43 1.29 1.17 1.06 0.980

1.63 1.46 1.33 1.21 1.11

1.83 1.65 1.49 1.37 1.26

2.04 1.84 1.67 1.53 1.41

2.48 2.24 2.05 1.88 1.73

2.95 2.67 2.45 2.25 2.09

3.45 3.14 2.88 2.65 2.46

3.98 3.63 3.34 3.08 2.86

4.55 4.16 3.82 3.54 3.29

2.6 2.8 3.0

0.253 0.318 0.393 0.479 0.574 0.678 0.789 0.908 1.03 1.16 1.30 1.61 1.94 0.235 0.295 0.365 0.445 0.534 0.630 0.735 0.845 0.960 1.08 1.21 1.50 1.81 0.219 0.276 0.341 0.416 0.499 0.589 0.687 0.791 0.897 1.01 1.13 1.40 1.70

2.29 2.15 2.02

2.67 2.50 2.35

3.07 2.88 2.71

a

x

1.4

0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 97

DESIGN TABLES

8–97

Table 8-9 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 15° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

k 0.8

0.9

1.0

1.2

1.8

2.0

0.00 0.10 0.15 0.20 0.25

1.98 1.90 1.84 1.76 1.65

2.47 2.36 2.30 2.20 2.07

3.01 2.87 2.78 2.65 2.49

3.56 3.38 3.26 3.11 2.93

4.10 3.88 3.74 3.56 3.37

4.65 4.38 4.21 4.02 3.80

5.19 4.88 4.69 4.47 4.23

5.74 5.38 5.16 4.92 4.66

6.28 5.87 5.63 5.37 5.09

6.83 6.37 6.10 5.82 5.53

7.37 6.86 6.57 6.27 5.96

8.46 7.85 7.52 7.18 6.84

9.55 10.6 11.7 8.84 9.84 10.8 8.47 9.43 10.4 8.10 9.04 9.98 7.74 8.65 9.58

12.8 11.9 11.4 10.9 10.5

0.30 0.40 0.50 0.60 0.70

1.55 1.34 1.16 1.01 0.895

1.93 1.67 1.45 1.27 1.12

2.33 2.02 1.75 1.53 1.35

2.74 2.38 2.06 1.80 1.60

3.16 2.75 2.39 2.10 1.88

3.58 3.13 2.74 2.42 2.17

3.99 3.52 3.10 2.75 2.48

4.41 3.92 3.47 3.10 2.80

4.82 4.31 3.85 3.46 3.14

5.24 4.70 4.22 3.82 3.48

5.66 5.10 4.60 4.19 3.83

6.52 5.90 5.38 4.92 4.53

7.39 6.74 6.18 5.69 5.26

8.28 7.59 7.00 6.48 6.02

9.19 10.1 8.47 9.37 7.85 8.73 7.30 8.15 6.81 7.62

0.80 0.90 1.0 1.2 1.4

0.799 0.720 0.654 0.552 0.477

0.997 0.898 0.816 0.689 0.596

1.21 1.09 0.996 0.845 0.733

1.44 1.31 1.20 1.02 0.886

1.69 1.54 1.41 1.21 1.05

1.96 1.79 1.64 1.41 1.23

2.25 2.05 1.89 1.63 1.43

2.55 2.33 2.15 1.86 1.63

2.86 2.63 2.43 2.10 1.85

3.19 2.94 2.72 2.36 2.08

3.52 3.25 3.02 2.63 2.32

4.19 3.89 3.63 3.18 2.83

4.89 4.56 4.26 3.76 3.36

5.61 5.25 4.92 4.37 3.91

6.37 5.97 5.62 5.01 4.50

7.15 6.73 6.34 5.68 5.12

1.6 1.8 2.0 2.2 2.4

0.420 0.374 0.338 0.308 0.282

0.525 0.468 0.423 0.385 0.354

0.646 0.577 0.522 0.476 0.437

0.782 0.700 0.633 0.578 0.532

0.933 0.836 0.757 0.692 0.636

1.10 0.983 0.891 0.815 0.750

1.27 1.14 1.04 0.948 0.873

1.45 1.31 1.19 1.09 1.00

1.65 1.49 1.35 1.24 1.14

1.86 1.68 1.53 1.40 1.29

2.08 1.88 1.71 1.57 1.45

2.54 2.30 2.10 1.93 1.79

3.03 2.75 2.52 2.32 2.15

3.54 3.23 2.96 2.73 2.54

4.08 3.73 3.43 3.17 2.95

4.66 4.27 3.93 3.64 3.39

2.6 2.8 3.0

0.261 0.327 0.404 0.492 0.589 0.695 0.809 0.931 1.06 1.20 1.34 1.66 2.00 0.242 0.304 0.376 0.458 0.548 0.647 0.754 0.868 0.989 1.12 1.25 1.54 1.87 0.226 0.284 0.352 0.428 0.513 0.606 0.706 0.812 0.926 1.04 1.17 1.45 1.75

2.36 2.21 2.08

2.75 2.58 2.43

3.17 2.97 2.80

a

x

1.4

1.6

0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 98

8–98

DESIGN CONSIDERATIONS FOR WELDS

Table 8-9 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 30° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

k 0.8

0.9

1.0

1.2

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.18 2.02 1.92 1.82 1.71

2.70 2.56 2.41 2.27 2.13

3.21 3.06 2.90 2.72 2.55

3.73 3.54 3.37 3.16 2.97

4.24 4.02 3.83 3.60 3.37

4.76 4.50 4.28 4.03 3.78

5.27 4.98 4.73 4.46 4.19

5.78 5.46 5.19 4.89 4.60

6.30 5.94 5.65 5.34 5.02

6.81 6.43 6.12 5.78 5.46

7.33 6.92 6.58 6.23 5.90

8.35 7.90 7.54 7.16 6.79

9.38 10.4 8.89 9.89 8.51 9.50 8.11 9.08 7.72 8.68

11.4 10.9 10.5 10.1 9.66

12.5 11.9 11.5 11.1 10.7

0.30 0.40 0.50 0.60 0.70

1.61 1.41 1.23 1.08 0.964

1.99 1.74 1.52 1.34 1.20

2.38 2.08 1.82 1.60 1.43

2.77 2.43 2.13 1.88 1.69

3.16 2.78 2.45 2.18 1.96

3.55 3.14 2.79 2.50 2.26

3.94 3.50 3.14 2.83 2.57

4.34 3.89 3.51 3.18 2.90

4.75 4.29 3.89 3.54 3.25

5.18 4.70 4.28 3.92 3.60

5.61 5.12 4.69 4.30 3.97

6.48 5.95 5.50 5.09 4.73

7.38 6.81 6.31 5.88 5.48

8.31 7.69 7.16 6.69 6.26

9.27 10.2 8.61 9.54 8.04 8.94 7.53 8.40 7.07 7.91

0.80 0.90 1.0 1.2 1.4

0.865 0.783 0.714 0.606 0.525

1.07 0.970 0.885 0.753 0.653

1.29 1.17 1.07 0.918 0.800

1.53 1.40 1.28 1.10 0.963

1.79 1.64 1.51 1.30 1.14

2.06 1.89 1.75 1.51 1.33

2.35 2.16 2.00 1.74 1.53

2.66 2.45 2.28 1.98 1.75

2.99 2.76 2.56 2.24 1.98

3.32 3.08 2.87 2.51 2.23

3.67 3.41 3.18 2.80 2.49

4.40 4.11 3.85 3.40 3.04

5.13 4.81 4.53 4.03 3.63

5.88 5.53 5.22 4.67 4.22

6.66 6.29 5.94 5.34 4.84

7.47 7.07 6.70 6.05 5.50

1.6 1.8 2.0 2.2 2.4

0.463 0.414 0.374 0.341 0.313

0.577 0.516 0.467 0.426 0.392

0.708 0.634 0.574 0.525 0.483

0.854 0.767 0.695 0.636 0.586

1.01 0.913 0.829 0.759 0.699

1.19 1.07 0.974 0.893 0.823

1.37 1.24 1.13 1.04 0.956

1.57 1.42 1.29 1.19 1.10

1.78 1.61 1.47 1.35 1.25

2.00 1.81 1.66 1.52 1.41

2.24 2.03 1.85 1.71 1.58

2.74 2.49 2.28 2.11 1.95

3.29 3.00 2.75 2.54 2.36

3.84 3.51 3.23 2.99 2.78

4.42 4.05 3.74 3.47 3.23

5.03 4.63 4.28 3.97 3.71

2.6 2.8 3.0

0.289 0.362 0.447 0.542 0.649 0.764 0.888 1.02 1.16 1.31 1.47 1.82 2.20 0.269 0.337 0.416 0.505 0.604 0.713 0.829 0.953 1.09 1.23 1.38 1.70 2.06 0.251 0.315 0.389 0.473 0.566 0.667 0.777 0.894 1.02 1.15 1.29 1.60 1.93

2.60 2.44 2.29

3.02 2.84 2.68

3.47 3.27 3.08

a

x

1.4

0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 99

DESIGN TABLES

8–99

Table 8-9 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 45° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

k 0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.41 2.24 2.09 1.96 1.85

2.80 2.72 2.57 2.41 2.27

3.27 3.17 3.00 2.83 2.66

3.74 3.61 3.41 3.21 3.02

4.21 4.05 3.82 3.59 3.38

4.67 4.49 4.24 3.99 3.76

5.14 4.94 4.67 4.41 4.16

5.61 5.41 5.13 4.85 4.59

6.08 5.88 5.59 5.30 5.03

6.54 6.35 6.06 5.77 5.49

7.01 6.82 6.54 6.24 5.95

7.95 7.78 7.51 7.21 6.91

8.88 8.74 8.48 8.19 7.88

9.82 9.71 9.46 9.17 8.87

10.8 10.7 10.4 10.2 9.87

11.7 11.7 11.4 11.2 10.9

0.30 0.40 0.50 0.60 0.70

1.74 1.55 1.38 1.23 1.11

2.13 1.89 1.68 1.50 1.36

2.50 2.22 1.98 1.77 1.60

2.86 2.55 2.29 2.06 1.88

3.20 2.89 2.61 2.37 2.17

3.57 3.24 2.96 2.71 2.48

3.96 3.62 3.32 3.05 2.81

4.38 4.01 3.69 3.41 3.16

4.81 4.42 4.08 3.78 3.52

5.25 4.84 4.49 4.17 3.89

5.70 5.28 4.91 4.58 4.28

6.64 6.18 5.78 5.42 5.09

7.59 7.11 6.69 6.30 5.94

8.56 8.05 7.60 7.18 6.79

9.55 10.6 8.99 9.95 8.52 9.45 8.08 8.99 7.67 8.57

0.80 0.90 1.0 1.2 1.4

1.00 0.915 0.839 0.719 0.627

1.23 1.12 1.03 0.886 0.775

1.46 1.34 1.24 1.07 0.943

1.72 1.59 1.47 1.28 1.13

2.00 1.84 1.71 1.50 1.33

2.29 2.12 1.98 1.73 1.54

2.61 2.42 2.26 1.99 1.77

2.93 2.73 2.56 2.26 2.02

3.28 3.06 2.87 2.54 2.28

3.63 3.41 3.20 2.84 2.55

4.01 3.76 3.54 3.16 2.84

4.79 4.51 4.26 3.83 3.46

5.61 5.31 5.03 4.54 4.12

6.43 6.10 5.80 5.26 4.81

7.29 6.93 6.60 6.01 5.50

8.16 7.78 7.43 6.79 6.23

1.6 1.8 2.0 2.2 2.4

0.555 0.498 0.451 0.412 0.379

0.688 0.618 0.561 0.513 0.473

0.840 0.756 0.687 0.630 0.581

1.01 0.910 0.829 0.760 0.702

1.19 1.08 0.984 0.904 0.836

1.39 1.26 1.15 1.06 0.981

1.60 1.45 1.33 1.22 1.14

1.82 1.66 1.52 1.40 1.30

2.06 1.87 1.72 1.59 1.48

2.31 2.11 1.94 1.79 1.66

2.58 2.36 2.17 2.01 1.86

3.15 2.89 2.66 2.47 2.30

3.77 3.47 3.20 2.97 2.77

4.41 4.07 3.78 3.52 3.29

5.07 4.69 4.36 4.07 3.81

5.75 5.34 4.97 4.65 4.36

2.6 2.8 3.0

0.351 0.438 0.539 0.652 0.777 0.913 1.06 1.21 1.38 1.55 1.74 2.15 2.60 0.327 0.408 0.502 0.608 0.726 0.853 0.990 1.14 1.29 1.46 1.63 2.02 2.44 0.306 0.382 0.470 0.570 0.680 0.801 0.930 1.07 1.21 1.37 1.54 1.90 2.30

3.08 2.90 2.74

3.58 3.37 3.19

4.10 3.87 3.66

a

x

0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 100

8–100

DESIGN CONSIDERATIONS FOR WELDS

Table 8-9 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 60° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

k 0.8

0.9

1.0

1.2

1.4

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.60 2.43 2.31 2.18 2.07

3.01 2.84 2.70 2.58 2.46

3.44 3.23 3.07 2.92 2.79

3.88 3.62 3.44 3.27 3.12

4.32 4.04 3.84 3.65 3.49

4.76 4.47 4.26 4.06 3.89

5.19 4.91 4.69 4.48 4.30

5.63 5.36 5.14 4.92 4.73

6.07 5.81 5.59 5.37 5.17

6.50 6.26 6.05 5.83 5.62

6.94 6.71 6.51 6.30 6.08

7.82 7.61 7.43 7.23 7.01

8.69 8.51 8.34 8.16 7.95

9.56 10.4 9.40 10.3 9.25 10.2 9.08 9.99 8.89 9.81

11.3 11.2 11.1 10.9 10.7

0.30 0.40 0.50 0.60 0.70

1.97 1.79 1.63 1.49 1.37

2.34 2.13 1.95 1.79 1.64

2.67 2.45 2.25 2.08 1.92

3.00 2.78 2.57 2.39 2.22

3.36 3.12 2.91 2.72 2.54

3.75 3.49 3.27 3.06 2.88

4.15 3.89 3.65 3.43 3.23

4.58 4.30 4.05 3.82 3.60

5.01 4.72 4.46 4.22 4.00

5.45 5.16 4.89 4.64 4.40

5.90 5.60 5.33 5.07 4.83

6.81 6.49 6.21 5.95 5.70

7.73 7.39 7.11 6.85 6.59

8.68 8.30 8.01 7.75 7.49

9.62 10.6 9.22 10.1 8.92 9.82 8.65 9.56 8.40 9.30

0.80 0.90 1.0 1.2 1.4

1.26 1.17 1.08 0.946 0.837

1.52 1.41 1.31 1.15 1.02

1.78 1.66 1.56 1.38 1.23

2.07 1.94 1.82 1.62 1.46

2.38 2.24 2.11 1.88 1.70

2.71 2.55 2.41 2.16 1.96

3.05 2.88 2.73 2.46 2.23

3.41 3.23 3.07 2.78 2.53

3.79 3.60 3.42 3.11 2.84

4.19 3.98 3.79 3.46 3.17

4.60 4.38 4.18 3.82 3.51

5.45 5.22 5.00 4.59 4.24

6.33 6.09 5.85 5.41 5.02

7.23 6.98 6.74 6.27 5.84

8.14 7.89 7.64 7.15 6.69

9.05 8.80 8.54 8.04 7.56

1.6 1.8 2.0 2.2 2.4

0.748 0.676 0.616 0.565 0.522

0.919 0.832 0.760 0.699 0.647

1.11 1.01 0.924 0.852 0.790

1.32 1.20 1.11 1.02 0.948

1.54 1.41 1.30 1.21 1.12

1.78 1.64 1.51 1.40 1.31

2.04 1.88 1.73 1.61 1.51

2.32 2.13 1.97 1.84 1.72

2.61 2.41 2.23 2.08 1.94

2.91 2.69 2.50 2.33 2.19

3.24 3.00 2.79 2.60 2.44

3.92 3.65 3.40 3.19 2.99

4.66 4.35 4.07 3.82 3.59

5.45 5.09 4.78 4.49 4.24

6.27 5.88 5.52 5.20 4.91

7.10 6.67 6.28 5.93 5.61

2.6 2.8 3.0

0.485 0.602 0.735 0.885 1.05 1.22 1.41 1.61 1.82 2.05 2.30 2.82 3.39 0.453 0.562 0.688 0.829 0.983 1.15 1.33 1.52 1.72 1.94 2.17 2.66 3.21 0.424 0.528 0.646 0.779 0.926 1.08 1.25 1.43 1.62 1.83 2.05 2.52 3.04

4.00 3.79 3.60

4.65 4.42 4.20

5.32 5.05 4.81

a

x

1.6

0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 101

DESIGN TABLES

8–101

Table 8-9 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 75° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

k 0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.74 2.59 2.50 2.43 2.35

3.11 2.94 2.84 2.76 2.68

3.49 3.30 3.19 3.09 3.01

3.88 3.68 3.56 3.46 3.37

4.26 4.07 3.94 3.84 3.76

4.65 4.47 4.34 4.24 4.15

5.03 4.88 4.75 4.63 4.55

5.42 5.28 5.16 5.04 4.95

5.80 5.69 5.57 5.45 5.35

6.19 6.08 5.98 5.86 5.75

6.57 6.48 6.39 6.28 6.16

7.34 7.27 7.19 7.10 6.99

8.11 8.05 7.98 7.90 7.81

8.88 8.83 8.77 8.70 8.62

9.65 9.61 9.55 9.49 9.42

10.4 10.4 10.3 10.3 10.2

0.30 0.40 0.50 0.60 0.70

2.28 2.16 2.05 1.94 1.85

2.61 2.48 2.37 2.25 2.15

2.93 2.80 2.68 2.57 2.46

3.29 3.15 3.02 2.90 2.79

3.68 3.53 3.40 3.27 3.15

4.07 3.93 3.79 3.66 3.53

4.47 4.33 4.20 4.06 3.93

4.88 4.74 4.61 4.48 4.35

5.28 5.15 5.02 4.89 4.77

5.68 5.55 5.43 5.31 5.19

6.07 5.95 5.84 5.73 5.61

6.88 6.75 6.64 6.55 6.44

7.71 7.54 7.44 7.35 7.26

8.53 8.33 8.22 8.14 8.06

9.34 10.1 9.14 9.97 9.01 9.80 8.92 9.70 8.85 9.63

0.80 0.90 1.0 1.2 1.4

1.75 1.67 1.59 1.45 1.33

2.05 1.96 1.87 1.72 1.58

2.36 2.26 2.17 2.00 1.86

2.69 2.59 2.49 2.31 2.15

3.03 2.93 2.83 2.64 2.47

3.41 3.29 3.18 2.98 2.80

3.81 3.69 3.57 3.35 3.15

4.22 4.09 3.97 3.74 3.53

4.64 4.51 4.38 4.14 3.92

5.06 4.93 4.81 4.56 4.33

5.49 5.36 5.24 4.99 4.75

6.33 6.22 6.10 5.85 5.61

7.16 7.06 6.95 6.72 6.48

7.98 7.89 7.79 7.59 7.36

8.78 8.70 8.62 8.43 8.23

9.57 9.50 9.43 9.27 9.08

1.6 1.8 2.0 2.2 2.4

1.22 1.13 1.05 0.975 0.912

1.46 1.36 1.27 1.18 1.11

1.73 1.61 1.51 1.41 1.33

2.01 1.88 1.77 1.66 1.57

2.31 2.17 2.04 1.93 1.82

2.63 2.48 2.34 2.21 2.10

2.97 2.81 2.66 2.52 2.39

3.33 3.15 2.99 2.84 2.70

3.71 3.52 3.34 3.18 3.03

4.11 3.90 3.71 3.54 3.38

4.52 4.30 4.10 3.91 3.74

5.37 5.14 4.92 4.71 4.51

6.24 6.00 5.77 5.54 5.33

7.12 6.88 6.65 6.41 6.18

8.00 7.77 7.53 7.30 7.06

8.87 8.65 8.42 8.19 7.95

2.6 2.8 3.0

0.856 1.04 1.26 1.48 1.73 1.99 2.27 2.57 2.89 3.23 3.58 4.32 5.12 0.806 0.986 1.19 1.41 1.65 1.90 2.17 2.46 2.76 3.09 3.43 4.15 4.93 0.762 0.933 1.13 1.34 1.57 1.81 2.07 2.35 2.64 2.96 3.29 3.99 4.75

5.96 5.75 5.55

6.83 6.61 6.39

7.71 7.48 7.26

a

x

0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 102

8–102

DESIGN CONSIDERATIONS FOR WELDS

Table 8-10

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 0° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

1.86 1.86 1.83 1.76 1.66

2.04 2.04 2.03 1.97 1.86

2.23 2.28 2.25 2.18 2.07

2.41 2.53 2.49 2.40 2.29

2.69 2.78 2.74 2.64 2.50

2.97 3.04 2.99 2.87 2.73

3.25 3.31 3.24 3.11 2.95

3.53 3.57 3.50 3.36 3.19

3.80 3.84 3.75 3.60 3.42

4.08 4.11 4.01 3.85 3.66

4.36 4.38 4.28 4.11 3.90

4.92 4.93 4.81 4.62 4.40

5.47 5.48 5.34 5.14 4.90

6.03 6.00 5.89 5.66 5.42

6.59 6.55 6.44 6.20 5.94

7.15 7.10 7.00 6.73 6.47

0.30 0.40 0.50 0.60 0.70

1.55 1.33 1.15 0.999 0.879

1.74 1.49 1.29 1.12 0.987

1.94 1.67 1.44 1.25 1.10

2.15 1.85 1.60 1.39 1.22

2.36 2.05 1.77 1.54 1.35

2.57 2.24 1.95 1.70 1.50

2.78 2.44 2.13 1.87 1.66

3.00 2.63 2.31 2.04 1.82

3.22 2.84 2.50 2.21 1.98

3.45 3.05 2.70 2.40 2.15

3.69 3.27 2.90 2.59 2.32

4.17 3.73 3.33 2.99 2.71

4.66 4.20 3.78 3.42 3.11

5.17 4.69 4.25 3.87 3.55

5.68 5.19 4.74 4.34 4.00

6.20 5.70 5.23 4.82 4.47

0.80 0.90 1.0 1.2 1.4

0.783 0.704 0.639 0.538 0.464

0.878 0.790 0.717 0.603 0.520

0.978 0.879 0.797 0.671 0.579

1.09 0.976 0.885 0.745 0.643

1.20 1.08 0.983 0.828 0.715

1.34 1.20 1.09 0.922 0.796

1.48 1.33 1.21 1.03 0.888

1.63 1.48 1.35 1.14 0.991

1.78 1.62 1.48 1.26 1.10

1.94 1.77 1.62 1.38 1.21

2.11 1.92 1.76 1.51 1.32

2.46 2.26 2.08 1.79 1.57

2.85 2.63 2.43 2.10 1.85

3.27 3.02 2.80 2.44 2.15

3.70 3.43 3.20 2.80 2.48

4.15 3.86 3.61 3.18 2.83

1.6 1.8 2.0 2.2 2.4

0.408 0.363 0.328 0.298 0.274

0.457 0.407 0.367 0.334 0.306

0.508 0.453 0.408 0.372 0.341

0.564 0.503 0.454 0.413 0.379

0.628 0.560 0.505 0.460 0.422

0.700 0.625 0.564 0.514 0.472

0.783 0.699 0.632 0.576 0.529

0.874 0.782 0.706 0.644 0.592

0.972 0.871 0.788 0.719 0.661

1.07 0.957 0.867 0.792 0.728

1.17 1.05 0.952 0.870 0.801

1.40 1.26 1.14 1.04 0.960

1.65 1.49 1.35 1.24 1.14

1.93 1.74 1.58 1.45 1.34

2.22 2.01 1.84 1.69 1.56

2.54 2.31 2.11 1.94 1.79

2.6 2.8 3.0

0.253 0.283 0.315 0.350 0.390 0.437 0.489 0.547 0.611 0.674 0.741 0.890 1.06 1.24 1.45 1.67 0.235 0.263 0.293 0.325 0.363 0.406 0.455 0.509 0.568 0.628 0.690 0.829 0.986 1.16 1.35 1.56 0.219 0.246 0.273 0.304 0.339 0.379 0.425 0.475 0.531 0.587 0.645 0.776 0.924 1.09 1.27 1.46

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 103

DESIGN TABLES

8–103

Table 8-10 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 15° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

1.98 1.90 1.84 1.76 1.65

2.20 2.13 2.10 1.99 1.87

2.47 2.41 2.35 2.26 2.11

2.74 2.68 2.62 2.52 2.37

3.01 2.97 2.88 2.77 2.63

3.29 3.25 3.15 3.02 2.87

3.56 3.53 3.42 3.28 3.11

3.83 3.81 3.69 3.53 3.36

4.10 4.09 3.96 3.79 3.60

4.38 4.36 4.23 4.05 3.85

4.65 4.64 4.50 4.31 4.10

5.19 5.18 5.04 4.84 4.61

5.74 5.73 5.58 5.37 5.13

6.28 6.28 6.12 5.90 5.66

6.83 6.83 6.66 6.44 6.19

7.37 7.37 7.20 6.98 6.72

0.30 0.40 0.50 0.60 0.70

1.55 1.34 1.16 1.01 0.895

1.75 1.51 1.31 1.14 1.01

1.97 1.69 1.46 1.27 1.12

2.20 1.89 1.63 1.42 1.25

2.45 2.10 1.81 1.58 1.39

2.69 2.33 2.01 1.75 1.54

2.93 2.56 2.21 1.93 1.71

3.16 2.77 2.42 2.13 1.89

3.40 2.99 2.63 2.32 2.07

3.64 3.21 2.83 2.51 2.25

3.88 3.44 3.05 2.71 2.44

4.38 3.91 3.50 3.14 2.84

4.89 4.41 3.97 3.59 3.26

5.41 4.91 4.45 4.06 3.71

5.93 5.42 4.95 4.54 4.18

6.46 5.94 5.46 5.04 4.66

0.80 0.90 1.0 1.2 1.4

0.799 0.720 0.654 0.552 0.477

0.898 0.809 0.735 0.620 0.535

1.00 0.901 0.818 0.690 0.596

1.11 1.00 0.910 0.767 0.662

1.24 1.11 1.01 0.854 0.737

1.38 1.24 1.13 0.951 0.822

1.53 1.38 1.25 1.06 0.918

1.69 1.53 1.39 1.18 1.03

1.86 1.69 1.54 1.31 1.14

2.03 1.85 1.69 1.45 1.26

2.21 2.01 1.85 1.58 1.38

2.58 2.36 2.18 1.87 1.64

2.99 2.75 2.54 2.20 1.93

3.41 3.15 2.92 2.54 2.25

3.86 3.58 3.33 2.92 2.58

4.32 4.03 3.76 3.31 2.94

1.6 1.8 2.0 2.2 2.4

0.420 0.374 0.338 0.308 0.282

0.471 0.420 0.378 0.345 0.316

0.524 0.467 0.421 0.383 0.352

0.582 0.519 0.468 0.426 0.391

0.648 0.578 0.522 0.475 0.436

0.724 0.646 0.583 0.532 0.488

0.809 0.723 0.653 0.596 0.547

0.905 0.809 0.731 0.666 0.612

1.01 0.902 0.816 0.744 0.684

1.11 0.997 0.902 0.824 0.757

1.22 1.09 0.991 0.905 0.833

1.46 1.31 1.19 1.08 0.999

1.72 1.55 1.41 1.29 1.19

2.01 1.81 1.65 1.51 1.39

2.32 2.09 1.91 1.75 1.62

2.65 2.40 2.19 2.01 1.86

2.6 2.8 3.0

0.261 0.292 0.325 0.362 0.403 0.451 0.506 0.566 0.632 0.701 0.771 0.925 1.10 1.29 1.50 1.73 0.242 0.272 0.302 0.336 0.375 0.420 0.470 0.526 0.588 0.652 0.717 0.862 1.03 1.21 1.40 1.62 0.226 0.254 0.282 0.314 0.350 0.392 0.439 0.492 0.549 0.610 0.671 0.806 0.960 1.13 1.32 1.52

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 104

8–104

DESIGN CONSIDERATIONS FOR WELDS

Table 8-10 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 30° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.18 2.02 1.92 1.82 1.71

2.44 2.35 2.22 2.09 1.96

2.70 2.66 2.53 2.38 2.22

2.96 2.96 2.84 2.67 2.50

3.21 3.24 3.13 2.97 2.78

3.47 3.52 3.41 3.26 3.06

3.73 3.79 3.69 3.53 3.34

3.98 4.06 3.96 3.80 3.60

4.24 4.33 4.23 4.07 3.87

4.50 4.59 4.49 4.33 4.13

4.76 4.86 4.76 4.60 4.39

5.27 5.38 5.29 5.13 4.92

5.78 5.90 5.81 5.65 5.45

6.30 6.43 6.34 6.18 5.98

6.81 6.95 6.86 6.71 6.51

7.33 7.47 7.38 7.23 7.05

0.30 0.40 0.50 0.60 0.70

1.61 1.41 1.23 1.08 0.964

1.83 1.59 1.39 1.22 1.09

2.07 1.79 1.56 1.37 1.21

2.32 2.01 1.74 1.53 1.35

2.59 2.23 1.94 1.70 1.51

2.86 2.47 2.15 1.89 1.67

3.13 2.72 2.37 2.09 1.86

3.40 2.98 2.61 2.30 2.05

3.65 3.24 2.85 2.53 2.26

3.91 3.48 3.09 2.75 2.48

4.17 3.72 3.32 2.97 2.68

4.70 4.23 3.80 3.43 3.12

5.23 4.75 4.30 3.91 3.58

5.76 5.28 4.83 4.41 4.06

6.30 5.82 5.36 4.94 4.56

6.83 6.37 5.90 5.47 5.07

0.80 0.90 1.0 1.2 1.4

0.865 0.783 0.714 0.606 0.525

0.974 0.881 0.803 0.681 0.590

1.09 0.983 0.896 0.759 0.657

1.21 1.09 0.997 0.844 0.731

1.35 1.22 1.11 0.940 0.814

1.50 1.36 1.24 1.05 0.908

1.66 1.51 1.38 1.17 1.02

1.84 1.67 1.53 1.30 1.13

2.04 1.85 1.70 1.45 1.26

2.24 2.04 1.88 1.61 1.40

2.44 2.23 2.05 1.76 1.53

2.84 2.61 2.41 2.08 1.82

3.28 3.03 2.80 2.43 2.14

3.74 3.47 3.22 2.81 2.49

4.22 3.93 3.66 3.22 2.86

4.72 4.40 4.12 3.64 3.25

1.6 1.8 2.0 2.2 2.4

0.463 0.414 0.374 0.341 0.313

0.520 0.464 0.419 0.382 0.351

0.579 0.517 0.467 0.425 0.391

0.644 0.575 0.519 0.473 0.434

0.717 0.641 0.579 0.528 0.485

0.801 0.716 0.647 0.590 0.543

0.897 0.802 0.725 0.661 0.608

1.00 0.897 0.811 0.740 0.680

1.12 1.00 0.905 0.826 0.760

1.24 1.11 1.01 0.919 0.845

1.36 1.22 1.11 1.01 0.930

1.62 1.46 1.32 1.21 1.12

1.91 1.72 1.57 1.44 1.32

2.23 2.01 1.83 1.68 1.55

2.57 2.32 2.12 1.95 1.80

2.92 2.66 2.43 2.24 2.07

2.6 2.8 3.0

0.289 0.324 0.361 0.402 0.448 0.502 0.562 0.629 0.703 0.782 0.861 1.03 1.23 1.44 1.67 1.92 0.269 0.302 0.336 0.373 0.417 0.467 0.523 0.585 0.654 0.727 0.801 0.963 1.15 1.35 1.56 1.80 0.251 0.282 0.314 0.349 0.389 0.436 0.489 0.547 0.611 0.680 0.749 0.901 1.07 1.26 1.47 1.69

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 105

DESIGN TABLES

8–105

Table 8-10 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 45° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.41 2.24 2.09 1.96 1.85

2.57 2.54 2.41 2.26 2.12

2.80 2.83 2.71 2.56 2.40

3.04 3.12 3.00 2.84 2.68

3.27 3.40 3.28 3.13 2.96

3.51 3.67 3.57 3.42 3.25

3.74 3.94 3.85 3.71 3.54

3.97 4.20 4.13 4.00 3.83

4.21 4.45 4.40 4.28 4.12

4.44 4.71 4.67 4.56 4.41

4.67 4.95 4.93 4.84 4.69

5.14 5.44 5.43 5.35 5.22

5.61 5.93 5.92 5.85 5.74

6.08 6.41 6.41 6.35 6.25

6.54 6.89 6.90 6.85 6.75

7.01 7.36 7.38 7.34 7.25

0.30 0.40 0.50 0.60 0.70

1.74 1.55 1.38 1.23 1.11

1.99 1.76 1.56 1.39 1.25

2.25 1.98 1.75 1.56 1.40

2.51 2.21 1.95 1.74 1.56

2.79 2.46 2.17 1.93 1.73

3.07 2.71 2.40 2.14 1.92

3.35 2.98 2.64 2.36 2.13

3.64 3.26 2.90 2.60 2.35

3.93 3.54 3.17 2.85 2.59

4.23 3.83 3.45 3.12 2.84

4.52 4.13 3.74 3.39 3.10

5.06 4.68 4.29 3.92 3.59

5.59 5.23 4.84 4.46 4.12

6.11 5.77 5.40 5.02 4.66

6.63 6.31 5.95 5.58 5.21

7.14 6.84 6.49 6.13 5.77

0.80 0.90 1.0 1.2 1.4

1.00 0.915 0.839 0.719 0.627

1.13 1.03 0.945 0.809 0.705

1.26 1.15 1.06 0.902 0.786

1.41 1.28 1.18 1.00 0.875

1.57 1.43 1.31 1.12 0.975

1.74 1.59 1.46 1.25 1.09

1.93 1.76 1.62 1.39 1.22

2.14 1.96 1.80 1.55 1.36

2.36 2.16 2.00 1.72 1.51

2.59 2.38 2.20 1.90 1.67

2.84 2.61 2.42 2.10 1.84

3.30 3.06 2.84 2.48 2.19

3.80 3.53 3.29 2.88 2.56

4.33 4.04 3.77 3.32 2.96

4.87 4.56 4.28 3.79 3.39

5.42 5.10 4.80 4.28 3.85

1.6 1.8 2.0 2.2 2.4

0.555 0.498 0.451 0.412 0.379

0.624 0.559 0.506 0.462 0.425

0.695 0.623 0.564 0.515 0.474

0.774 0.693 0.628 0.573 0.527

0.863 0.773 0.700 0.639 0.588

0.964 0.865 0.783 0.716 0.659

1.08 0.968 0.877 0.801 0.738

1.20 1.08 0.980 0.896 0.825

1.34 1.20 1.09 0.999 0.920

1.49 1.34 1.21 1.11 1.02

1.64 1.48 1.34 1.23 1.13

1.96 1.76 1.61 1.47 1.36

2.30 2.08 1.89 1.74 1.61

2.66 2.42 2.21 2.03 1.88

3.06 2.78 2.55 2.35 2.17

3.48 3.17 2.91 2.69 2.49

2.6 2.8 3.0

0.351 0.394 0.438 0.488 0.545 0.610 0.683 0.764 0.853 0.948 1.05 1.26 1.49 1.75 2.03 2.32 0.327 0.366 0.408 0.454 0.507 0.568 0.636 0.712 0.794 0.883 0.979 1.18 1.39 1.63 1.89 2.18 0.306 0.343 0.381 0.424 0.474 0.531 0.595 0.666 0.743 0.826 0.916 1.10 1.31 1.53 1.78 2.04

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 106

8–106

DESIGN CONSIDERATIONS FOR WELDS

Table 8-10 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 60° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.60 2.43 2.31 2.18 2.07

2.79 2.70 2.59 2.47 2.35

3.01 2.97 2.86 2.74 2.62

3.23 3.23 3.13 3.01 2.89

3.44 3.48 3.40 3.29 3.16

3.66 3.72 3.66 3.56 3.44

3.88 3.96 3.91 3.83 3.72

4.10 4.19 4.16 4.09 3.99

4.32 4.42 4.40 4.35 4.26

4.54 4.64 4.64 4.59 4.52

4.76 4.87 4.87 4.84 4.77

5.19 5.31 5.32 5.30 5.26

5.63 5.75 5.77 5.76 5.73

6.07 6.18 6.21 6.21 6.19

6.50 6.62 6.64 6.65 6.64

6.94 7.05 7.08 7.09 7.08

0.30 0.40 0.50 0.60 0.70

1.97 1.79 1.63 1.49 1.37

2.24 2.03 1.84 1.68 1.54

2.50 2.27 2.06 1.88 1.73

2.76 2.52 2.29 2.09 1.92

3.03 2.77 2.53 2.31 2.12

3.31 3.04 2.78 2.55 2.35

3.59 3.32 3.05 2.81 2.59

3.88 3.61 3.34 3.08 2.85

4.16 3.90 3.63 3.37 3.12

4.43 4.19 3.93 3.66 3.41

4.69 4.48 4.22 3.96 3.71

5.20 5.02 4.79 4.55 4.30

5.68 5.54 5.34 5.11 4.87

6.15 6.04 5.87 5.66 5.43

6.61 6.52 6.37 6.19 5.97

7.06 6.98 6.86 6.69 6.50

0.80 0.90 1.0 1.2 1.4

1.26 1.17 1.08 0.946 0.837

1.42 1.32 1.22 1.07 0.942

1.59 1.47 1.36 1.19 1.05

1.77 1.63 1.52 1.32 1.17

1.96 1.81 1.69 1.47 1.30

2.17 2.01 1.87 1.64 1.45

2.40 2.23 2.08 1.82 1.62

2.64 2.46 2.30 2.02 1.80

2.90 2.71 2.53 2.23 1.99

3.18 2.97 2.78 2.46 2.20

3.47 3.25 3.05 2.70 2.42

4.05 3.82 3.60 3.21 2.88

4.64 4.39 4.15 3.72 3.36

5.20 4.95 4.71 4.26 3.86

5.74 5.50 5.26 4.80 4.38

6.28 6.04 5.80 5.34 4.92

1.6 1.8 2.0 2.2 2.4

0.748 0.676 0.616 0.565 0.522

0.842 0.760 0.692 0.635 0.586

0.939 0.847 0.772 0.708 0.653

1.04 0.943 0.859 0.788 0.728

1.16 1.05 0.958 0.879 0.812

1.30 1.17 1.07 0.983 0.908

1.45 1.31 1.20 1.10 1.02

1.61 1.46 1.33 1.23 1.13

1.79 1.62 1.48 1.36 1.26

1.98 1.80 1.64 1.51 1.40

2.18 1.98 1.82 1.67 1.55

2.60 2.37 2.18 2.01 1.86

3.04 2.78 2.55 2.36 2.19

3.52 3.23 2.97 2.75 2.56

4.02 3.70 3.42 3.17 2.95

4.53 4.19 3.88 3.61 3.37

2.6 2.8 3.0

0.485 0.544 0.607 0.675 0.754 0.844 0.944 1.05 1.17 1.30 1.44 1.74 2.05 2.39 2.76 3.16 0.453 0.508 0.566 0.630 0.704 0.787 0.881 0.984 1.10 1.22 1.35 1.63 1.92 2.24 2.59 2.97 0.424 0.476 0.530 0.590 0.659 0.738 0.826 0.923 1.03 1.14 1.26 1.53 1.80 2.11 2.44 2.80

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 107

DESIGN TABLES

8–107

Table 8-10 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 75° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.74 2.59 2.50 2.43 2.35

2.92 2.86 2.78 2.69 2.62

3.11 3.11 3.04 2.96 2.88

3.30 3.31 3.28 3.22 3.14

3.49 3.50 3.50 3.46 3.40

3.69 3.69 3.70 3.68 3.63

3.88 3.88 3.90 3.89 3.86

4.07 4.07 4.09 4.09 4.07

4.26 4.27 4.28 4.29 4.28

4.46 4.46 4.47 4.48 4.48

4.65 4.65 4.67 4.68 4.68

5.03 5.04 5.05 5.06 5.07

5.42 5.42 5.44 5.45 5.46

5.80 5.81 5.83 5.84 5.84

6.19 6.20 6.21 6.22 6.23

6.57 6.58 6.60 6.61 6.61

0.30 0.40 0.50 0.60 0.70

2.28 2.16 2.05 1.94 1.85

2.55 2.41 2.29 2.18 2.07

2.80 2.66 2.53 2.41 2.29

3.07 2.92 2.78 2.64 2.52

3.33 3.19 3.05 2.90 2.77

3.58 3.45 3.32 3.18 3.04

3.82 3.71 3.58 3.45 3.31

4.04 3.95 3.84 3.72 3.58

4.26 4.18 4.09 3.97 3.85

4.46 4.41 4.32 4.22 4.11

4.67 4.62 4.55 4.46 4.36

5.06 5.04 4.99 4.92 4.83

5.46 5.44 5.40 5.35 5.28

5.84 5.83 5.81 5.77 5.71

6.23 6.23 6.21 6.17 6.12

6.62 6.61 6.60 6.57 6.53

0.80 0.90 1.0 1.2 1.4

1.75 1.67 1.59 1.45 1.33

1.97 1.87 1.79 1.63 1.49

2.18 2.08 1.98 1.81 1.66

2.40 2.29 2.19 2.00 1.84

2.64 2.52 2.41 2.21 2.03

2.90 2.77 2.65 2.44 2.24

3.18 3.04 2.92 2.68 2.47

3.45 3.32 3.19 2.95 2.72

3.73 3.60 3.47 3.22 2.99

3.99 3.87 3.75 3.50 3.27

4.25 4.14 4.02 3.78 3.55

4.74 4.65 4.55 4.33 4.11

5.20 5.12 5.04 4.85 4.65

5.64 5.57 5.50 5.34 5.16

6.06 6.00 5.94 5.81 5.65

6.48 6.42 6.37 6.25 6.12

1.6 1.8 2.0 2.2 2.4

1.22 1.13 1.05 0.975 0.912

1.37 1.27 1.18 1.10 1.03

1.53 1.41 1.31 1.22 1.14

1.69 1.57 1.46 1.36 1.27

1.88 1.74 1.62 1.51 1.41

2.07 1.93 1.79 1.68 1.57

2.29 2.13 1.99 1.86 1.74

2.53 2.35 2.20 2.06 1.93

2.78 2.59 2.42 2.27 2.14

3.05 2.85 2.67 2.50 2.36

3.32 3.11 2.92 2.75 2.59

3.88 3.66 3.46 3.27 3.09

4.43 4.22 4.01 3.81 3.62

4.97 4.76 4.56 4.36 4.16

5.48 5.29 5.09 4.90 4.70

5.96 5.79 5.61 5.42 5.23

2.6 2.8 3.0

0.856 0.963 1.07 1.19 1.33 1.48 1.64 1.82 2.02 2.22 2.45 2.93 3.44 3.97 4.50 5.03 0.806 0.906 1.01 1.12 1.25 1.39 1.55 1.72 1.90 2.10 2.32 2.78 3.28 3.79 4.30 4.83 0.762 0.856 0.954 1.06 1.18 1.32 1.47 1.63 1.80 2.00 2.20 2.64 3.12 3.61 4.12 4.64

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:29 AM

Page 108

8–108

DESIGN CONSIDERATIONS FOR WELDS

Table 8-10a

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 15° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

1.98 1.90 1.84 1.76 1.65

2.20 2.08 2.04 1.97 1.86

2.47 2.30 2.25 2.17 2.07

2.74 2.54 2.47 2.38 2.26

3.01 2.97 2.70 2.59 2.46

3.29 3.04 2.94 2.82 2.67

3.56 3.30 3.18 3.04 2.89

3.83 3.57 3.43 3.28 3.11

4.10 3.84 3.68 3.52 3.33

4.38 4.12 3.94 3.76 3.57

4.65 4.41 4.19 4.00 3.80

5.19 4.99 4.72 4.51 4.29

5.74 5.57 5.26 5.02 4.79

6.28 6.15 5.82 5.55 5.30

6.83 6.72 6.38 6.08 5.82

7.37 7.29 6.95 6.63 6.35

0.30 0.40 0.50 0.60 0.70

1.55 1.34 1.16 1.01 0.895

1.74 1.51 1.31 1.15 1.01

1.95 1.70 1.47 1.29 1.13

2.13 1.87 1.63 1.42 1.25

2.32 2.04 1.79 1.57 1.39

2.52 2.22 1.95 1.72 1.53

2.72 2.40 2.12 1.88 1.68

2.93 2.59 2.29 2.04 1.82

3.15 2.79 2.47 2.21 1.98

3.37 3.00 2.67 2.38 2.15

3.60 3.21 2.87 2.57 2.32

4.07 3.66 3.29 2.97 2.70

4.56 4.12 3.74 3.40 3.11

5.06 4.61 4.20 3.85 3.54

5.57 5.10 4.69 4.32 3.99

6.09 5.61 5.18 4.80 4.46

0.80 0.90 1.0 1.2 1.4

0.799 0.720 0.654 0.552 0.477

0.906 0.816 0.742 0.626 0.540

1.01 0.909 0.825 0.695 0.600

1.12 1.01 0.915 0.771 0.665

1.24 1.12 1.01 0.856 0.739

1.37 1.24 1.12 0.950 0.822

1.51 1.37 1.25 1.06 0.916

1.65 1.50 1.37 1.17 1.02

1.79 1.63 1.50 1.29 1.12

1.95 1.78 1.64 1.41 1.23

2.11 1.94 1.78 1.54 1.35

2.47 2.27 2.10 1.82 1.60

2.86 2.64 2.45 2.13 1.88

3.27 3.04 2.83 2.47 2.19

3.71 3.45 3.22 2.84 2.52

4.16 3.89 3.64 3.22 2.87

1.6 1.8 2.0 2.2 2.4

0.420 0.374 0.338 0.308 0.282

0.474 0.422 0.381 0.346 0.318

0.527 0.469 0.423 0.385 0.353

0.585 0.521 0.470 0.428 0.393

0.650 0.580 0.523 0.476 0.437

0.724 0.646 0.584 0.532 0.489

0.808 0.722 0.653 0.595 0.547

0.901 0.806 0.729 0.665 0.612

0.995 0.892 0.809 0.739 0.680

1.09 0.981 0.889 0.813 0.749

1.20 1.08 0.976 0.893 0.822

1.43 1.28 1.17 1.07 0.986

1.68 1.52 1.38 1.27 1.17

1.96 1.78 1.62 1.49 1.37

2.27 2.05 1.88 1.73 1.60

2.59 2.35 2.16 1.99 1.84

2.6 2.8 3.0

0.261 0.294 0.326 0.363 0.404 0.452 0.506 0.566 0.630 0.694 0.762 0.914 1.09 1.28 1.49 1.71 0.242 0.273 0.303 0.337 0.376 0.420 0.470 0.526 0.586 0.646 0.710 0.852 1.01 1.19 1.39 1.60 0.226 0.255 0.283 0.315 0.351 0.392 0.439 0.492 0.549 0.604 0.664 0.798 0.949 1.12 1.30 1.50

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 109

DESIGN TABLES

8–109

Table 8-10a (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 30° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.18 2.02 1.92 1.82 1.71

2.44 2.24 2.13 2.02 1.91

2.70 2.47 2.34 2.23 2.11

2.96 2.70 2.55 2.43 2.31

3.21 2.94 2.77 2.64 2.50

3.47 3.18 3.00 2.85 2.70

3.73 3.43 3.23 3.07 2.91

3.98 3.69 3.47 3.29 3.12

4.24 3.95 3.71 3.52 3.34

4.50 4.21 3.96 3.76 3.57

4.76 4.48 4.21 4.00 3.80

5.27 5.01 4.73 4.50 4.28

5.78 5.56 5.27 5.01 4.78

6.30 6.11 5.82 5.55 5.30

6.81 6.65 6.37 6.09 5.83

7.33 7.20 6.93 6.64 6.37

0.30 0.40 0.50 0.60 0.70

1.61 1.41 1.23 1.08 0.964

1.79 1.57 1.38 1.22 1.08

1.98 1.74 1.53 1.36 1.21

2.18 1.92 1.70 1.51 1.35

2.37 2.10 1.87 1.66 1.49

2.56 2.28 2.03 1.81 1.63

2.75 2.45 2.19 1.96 1.77

2.96 2.64 2.36 2.13 1.92

3.17 2.84 2.55 2.30 2.08

3.39 3.04 2.74 2.48 2.26

3.61 3.26 2.94 2.67 2.44

4.08 3.71 3.37 3.08 2.83

4.57 4.18 3.83 3.52 3.25

5.08 4.67 4.30 3.98 3.69

5.60 5.18 4.80 4.46 4.15

6.13 5.69 5.30 4.95 4.64

0.80 0.90 1.0 1.2 1.4

0.865 0.783 0.714 0.606 0.525

0.974 0.882 0.805 0.684 0.593

1.09 0.989 0.904 0.769 0.665

1.22 1.10 1.01 0.852 0.737

1.34 1.22 1.11 0.944 0.818

1.48 1.34 1.23 1.05 0.908

1.61 1.47 1.35 1.16 1.01

1.75 1.60 1.48 1.27 1.11

1.90 1.74 1.61 1.39 1.22

2.06 1.90 1.75 1.52 1.34

2.23 2.06 1.91 1.66 1.46

2.60 2.41 2.24 1.96 1.73

3.01 2.80 2.61 2.29 2.04

3.44 3.21 3.00 2.65 2.37

3.89 3.64 3.42 3.04 2.72

4.35 4.09 3.86 3.44 3.09

1.6 1.8 2.0 2.2 2.4

0.463 0.414 0.374 0.341 0.313

0.523 0.468 0.423 0.386 0.354

0.585 0.522 0.471 0.429 0.394

0.649 0.579 0.523 0.476 0.437

0.720 0.644 0.581 0.530 0.487

0.801 0.717 0.648 0.591 0.543

0.892 0.799 0.724 0.661 0.608

0.990 0.890 0.807 0.738 0.679

1.09 0.978 0.889 0.814 0.750

1.19 1.07 0.977 0.895 0.825

1.30 1.18 1.07 0.982 0.906

1.55 1.40 1.28 1.17 1.08

1.83 1.66 1.51 1.39 1.29

2.13 1.93 1.77 1.63 1.51

2.46 2.23 2.05 1.89 1.75

2.80 2.56 2.35 2.17 2.02

2.6 2.8 3.0

0.289 0.327 0.364 0.404 0.450 0.503 0.562 0.628 0.696 0.766 0.841 1.01 1.20 1.40 1.63 1.88 0.269 0.304 0.338 0.376 0.418 0.467 0.523 0.585 0.648 0.714 0.784 0.940 1.12 1.31 1.53 1.76 0.251 0.284 0.316 0.351 0.391 0.437 0.489 0.547 0.607 0.668 0.734 0.881 1.05 1.23 1.44 1.66

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 110

8–110

DESIGN CONSIDERATIONS FOR WELDS

Table 8-10a (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 45° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.41 2.24 2.09 1.96 1.85

2.57 2.44 2.28 2.14 2.02

2.80 2.65 2.48 2.33 2.21

3.04 2.86 2.68 2.54 2.40

3.27 3.07 2.89 2.74 2.61

3.51 3.29 3.11 2.95 2.81

3.74 3.52 3.33 3.16 3.01

3.97 3.76 3.56 3.38 3.22

4.21 4.00 3.79 3.61 3.44

4.44 4.24 4.03 3.84 3.67

4.67 4.49 4.28 4.08 3.90

5.14 5.01 4.79 4.58 4.39

5.61 5.53 5.32 5.10 4.90

6.08 6.06 5.85 5.64 5.43

6.54 6.59 6.40 6.19 5.98

7.01 7.12 6.94 6.74 6.53

0.30 0.40 0.50 0.60 0.70

1.74 1.55 1.38 1.23 1.11

1.91 1.70 1.52 1.36 1.23

2.09 1.87 1.67 1.50 1.36

2.28 2.04 1.84 1.66 1.50

2.47 2.23 2.01 1.82 1.66

2.67 2.42 2.19 1.99 1.82

2.87 2.60 2.36 2.16 1.97

3.07 2.80 2.55 2.33 2.13

3.29 3.00 2.74 2.51 2.31

3.51 3.21 2.94 2.70 2.49

3.73 3.43 3.15 2.90 2.68

4.21 3.89 3.60 3.33 3.10

4.72 4.38 4.07 3.80 3.55

5.24 4.89 4.57 4.28 4.02

5.78 5.41 5.09 4.79 4.52

6.33 5.95 5.62 5.31 5.03

0.80 0.90 1.0 1.2 1.4

1.00 0.915 0.839 0.719 0.627

1.12 1.02 0.938 0.805 0.704

1.24 1.13 1.04 0.900 0.788

1.37 1.26 1.16 1.00 0.880

1.52 1.39 1.29 1.12 0.979

1.67 1.54 1.42 1.24 1.08

1.81 1.67 1.55 1.35 1.19

1.97 1.82 1.69 1.48 1.31

2.13 1.98 1.84 1.61 1.43

2.31 2.14 2.00 1.76 1.56

2.49 2.32 2.17 1.91 1.70

2.89 2.71 2.54 2.25 2.01

3.33 3.12 2.94 2.62 2.36

3.79 3.57 3.37 3.02 2.73

4.27 4.04 3.83 3.45 3.13

4.77 4.53 4.30 3.90 3.54

1.6 1.8 2.0 2.2 2.4

0.555 0.498 0.451 0.412 0.379

0.624 0.560 0.508 0.464 0.428

0.700 0.629 0.571 0.522 0.480

0.783 0.701 0.635 0.579 0.532

0.868 0.778 0.704 0.643 0.592

0.962 0.864 0.784 0.716 0.660

1.07 0.961 0.873 0.799 0.736

1.17 1.06 0.964 0.885 0.818

1.28 1.16 1.06 0.974 0.900

1.40 1.27 1.16 1.07 0.989

1.53 1.39 1.27 1.17 1.08

1.82 1.66 1.52 1.40 1.30

2.14 1.95 1.79 1.65 1.53

2.48 2.27 2.09 1.93 1.79

2.85 2.61 2.41 2.23 2.08

3.24 2.98 2.75 2.55 2.38

2.6 2.8 3.0

0.351 0.396 0.444 0.493 0.548 0.611 0.683 0.760 0.837 0.920 1.01 1.21 1.43 1.67 1.94 2.23 0.327 0.369 0.413 0.458 0.510 0.569 0.636 0.709 0.781 0.859 0.943 1.13 1.34 1.57 1.82 2.10 0.306 0.345 0.386 0.428 0.477 0.532 0.595 0.665 0.733 0.806 0.885 1.06 1.26 1.48 1.72 1.98

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 111

DESIGN TABLES

8–111

Table 8-10a (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 60° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.60 2.43 2.31 2.18 2.07

2.79 2.59 2.45 2.32 2.21

3.01 2.76 2.62 2.49 2.38

3.23 2.94 2.80 2.67 2.56

3.44 3.14 3.00 2.87 2.75

3.66 3.35 3.21 3.08 2.96

3.88 3.57 3.43 3.30 3.17

4.10 3.80 3.66 3.52 3.40

4.32 4.03 3.89 3.75 3.62

4.54 4.28 4.13 3.99 3.86

4.76 4.52 4.38 4.23 4.10

5.19 5.04 4.89 4.75 4.60

5.63 5.56 5.43 5.28 5.14

6.07 6.07 5.96 5.83 5.69

6.50 6.56 6.48 6.37 6.24

6.94 7.03 6.97 6.88 6.78

0.30 0.40 0.50 0.60 0.70

1.97 1.79 1.63 1.49 1.37

2.11 1.93 1.76 1.62 1.49

2.27 2.08 1.91 1.76 1.63

2.45 2.25 2.08 1.92 1.78

2.64 2.44 2.26 2.09 1.95

2.84 2.64 2.45 2.28 2.12

3.06 2.84 2.65 2.47 2.31

3.28 3.06 2.86 2.67 2.50

3.50 3.27 3.06 2.87 2.70

3.73 3.50 3.28 3.08 2.90

3.97 3.73 3.51 3.30 3.12

4.47 4.22 3.99 3.77 3.58

5.00 4.74 4.50 4.28 4.07

5.55 5.28 5.03 4.80 4.59

6.11 5.84 5.58 5.35 5.13

6.66 6.41 6.15 5.91 5.68

0.80 0.90 1.0 1.2 1.4

1.26 1.17 1.08 0.946 0.837

1.38 1.28 1.19 1.05 0.928

1.51 1.41 1.31 1.16 1.03

1.66 1.55 1.45 1.28 1.14

1.82 1.70 1.59 1.41 1.27

1.99 1.86 1.75 1.56 1.40

2.17 2.04 1.92 1.71 1.54

2.35 2.21 2.08 1.87 1.68

2.54 2.39 2.26 2.03 1.83

2.74 2.58 2.45 2.20 2.00

2.95 2.79 2.64 2.39 2.17

3.39 3.23 3.07 2.79 2.54

3.88 3.70 3.53 3.22 2.96

4.39 4.20 4.02 3.69 3.40

4.92 4.72 4.53 4.17 3.86

5.46 5.25 5.05 4.68 4.34

1.6 1.8 2.0 2.2 2.4

0.748 0.676 0.616 0.565 0.522

0.832 0.754 0.688 0.632 0.585

0.926 0.840 0.768 0.707 0.655

1.03 0.936 0.857 0.790 0.733

1.14 1.04 0.957 0.883 0.818

1.27 1.16 1.07 0.981 0.909

1.40 1.28 1.17 1.08 1.01

1.53 1.40 1.29 1.19 1.11

1.67 1.53 1.41 1.30 1.21

1.82 1.67 1.54 1.43 1.33

1.98 1.82 1.68 1.56 1.46

2.33 2.15 1.99 1.85 1.73

2.72 2.52 2.34 2.18 2.04

3.14 2.91 2.71 2.53 2.37

3.58 3.33 3.11 2.91 2.73

4.04 3.77 3.53 3.31 3.11

2.6 2.8 3.0

0.485 0.544 0.609 0.682 0.760 0.845 0.940 1.03 1.13 1.24 1.36 1.62 1.91 2.23 2.57 2.93 0.453 0.508 0.570 0.638 0.709 0.789 0.879 0.969 1.06 1.17 1.28 1.53 1.80 2.10 2.43 2.78 0.424 0.476 0.535 0.598 0.665 0.740 0.825 0.911 1.00 1.10 1.21 1.44 1.70 1.99 2.30 2.63

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 112

8–112

DESIGN CONSIDERATIONS FOR WELDS

Table 8-10a (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 75° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.74 2.59 2.50 2.43 2.35

2.92 2.68 2.60 2.53 2.46

3.11 2.81 2.74 2.66 2.60

3.30 2.97 2.90 2.83 2.76

3.49 3.16 3.08 3.01 2.94

3.69 3.36 3.29 3.22 3.15

3.88 3.58 3.51 3.44 3.37

4.07 3.82 3.75 3.68 3.61

4.26 4.07 4.00 3.93 3.86

4.46 4.33 4.26 4.19 4.12

4.65 4.58 4.52 4.46 4.39

5.03 5.06 5.02 4.98 4.92

5.42 5.50 5.48 5.45 5.42

5.80 5.91 5.90 5.88 5.86

6.19 6.31 6.30 6.29 6.28

6.57 6.69 6.69 6.69 6.68

0.30 0.40 0.50 0.60 0.70

2.28 2.16 2.05 1.94 1.85

2.39 2.27 2.16 2.05 1.96

2.53 2.41 2.30 2.19 2.10

2.69 2.57 2.46 2.35 2.25

2.88 2.76 2.64 2.54 2.43

3.09 2.96 2.85 2.73 2.63

3.31 3.18 3.06 2.95 2.84

3.54 3.42 3.30 3.18 3.07

3.79 3.66 3.54 3.42 3.31

4.05 3.92 3.80 3.68 3.56

4.32 4.19 4.06 3.93 3.81

4.86 4.72 4.59 4.46 4.33

5.37 5.27 5.13 5.00 4.87

5.84 5.77 5.66 5.54 5.42

6.26 6.22 6.15 6.06 5.95

6.67 6.64 6.59 6.54 6.45

0.80 0.90 1.0 1.2 1.4

1.75 1.67 1.59 1.45 1.33

1.87 1.78 1.70 1.56 1.43

2.00 1.92 1.84 1.69 1.56

2.16 2.07 1.99 1.84 1.70

2.34 2.25 2.16 2.00 1.86

2.53 2.44 2.35 2.18 2.04

2.74 2.65 2.55 2.38 2.23

2.97 2.87 2.77 2.60 2.44

3.20 3.10 3.00 2.82 2.65

3.45 3.34 3.24 3.04 2.86

3.69 3.58 3.47 3.27 3.08

4.21 4.09 3.97 3.76 3.55

4.75 4.62 4.50 4.27 4.06

5.30 5.17 5.05 4.81 4.59

5.84 5.72 5.60 5.37 5.13

6.35 6.24 6.13 5.91 5.68

1.6 1.8 2.0 2.2 2.4

1.22 1.13 1.05 0.975 0.912

1.32 1.23 1.14 1.07 1.00

1.45 1.35 1.26 1.18 1.11

1.58 1.48 1.38 1.30 1.22

1.74 1.63 1.52 1.44 1.35

1.91 1.79 1.68 1.59 1.50

2.09 1.97 1.85 1.75 1.66

2.29 2.16 2.03 1.92 1.82

2.49 2.34 2.21 2.09 1.98

2.69 2.54 2.40 2.27 2.16

2.91 2.75 2.60 2.47 2.34

3.37 3.19 3.03 2.88 2.74

3.86 3.67 3.50 3.33 3.18

4.37 4.17 3.99 3.81 3.64

4.91 4.70 4.50 4.31 4.13

5.46 5.24 5.03 4.83 4.64

2.6 2.8 3.0

0.856 0.943 1.04 1.15 1.28 1.42 1.57 1.72 1.88 2.05 2.23 2.62 3.04 3.49 3.96 4.46 0.806 0.890 0.986 1.09 1.21 1.35 1.49 1.64 1.79 1.95 2.12 2.50 2.91 3.35 3.81 4.29 0.762 0.842 0.934 1.04 1.15 1.28 1.42 1.56 1.70 1.86 2.03 2.39 2.78 3.21 3.66 4.13

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 113

DESIGN TABLES

8–113

Table 8-11

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 0° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

1.86 1.86 1.83 1.76 1.66

2.04 2.06 2.04 1.96 1.85

2.23 2.32 2.27 2.17 2.03

2.41 2.57 2.51 2.38 2.22

2.69 2.83 2.74 2.59 2.40

2.97 3.08 2.97 2.78 2.58

3.25 3.32 3.18 2.98 2.76

3.53 3.55 3.39 3.17 2.95

3.80 3.77 3.58 3.36 3.14

4.08 3.98 3.78 3.56 3.34

4.36 4.19 3.97 3.76 3.55

4.92 4.60 4.37 4.16 3.95

5.47 5.02 4.79 4.57 4.36

6.03 5.45 5.22 5.00 4.78

6.59 5.89 5.66 5.44 5.22

7.15 6.35 6.11 5.89 5.67

0.30 0.40 0.50 0.60 0.70

1.55 1.33 1.15 0.999 0.879

1.72 1.48 1.28 1.11 0.979

1.89 1.63 1.40 1.22 1.08

2.06 1.76 1.52 1.33 1.18

2.22 1.90 1.65 1.45 1.29

2.39 2.05 1.79 1.58 1.41

2.56 2.22 1.94 1.72 1.54

2.74 2.40 2.11 1.88 1.69

2.94 2.59 2.29 2.05 1.85

3.14 2.78 2.48 2.23 2.01

3.35 2.99 2.68 2.41 2.19

3.76 3.40 3.08 2.81 2.56

4.16 3.80 3.48 3.20 2.95

4.58 4.21 3.88 3.59 3.33

5.02 4.64 4.30 3.99 3.72

5.46 5.08 4.73 4.41 4.12

0.80 0.90 1.0 1.2 1.4

0.783 0.704 0.639 0.538 0.464

0.871 0.783 0.711 0.599 0.517

0.960 0.865 0.786 0.664 0.574

1.06 0.954 0.869 0.735 0.636

1.16 1.05 0.959 0.814 0.706

1.27 1.15 1.06 0.900 0.782

1.39 1.27 1.16 0.993 0.865

1.53 1.39 1.28 1.09 0.956

1.67 1.53 1.41 1.21 1.06

1.83 1.68 1.55 1.33 1.17

2.00 1.84 1.69 1.46 1.28

2.35 2.17 2.01 1.75 1.54

2.73 2.53 2.36 2.07 1.83

3.10 2.89 2.71 2.40 2.14

3.48 3.26 3.06 2.72 2.44

3.87 3.63 3.42 3.06 2.76

1.6 1.8 2.0 2.2 2.4

0.408 0.363 0.328 0.298 0.274

0.454 0.405 0.365 0.333 0.305

0.505 0.450 0.406 0.370 0.340

0.560 0.500 0.451 0.411 0.378

0.622 0.556 0.502 0.458 0.421

0.691 0.618 0.559 0.510 0.469

0.766 0.686 0.621 0.567 0.522

0.847 0.760 0.689 0.630 0.580

0.937 0.841 0.763 0.698 0.643

1.04 0.931 0.845 0.773 0.713

1.14 1.03 0.935 0.856 0.789

1.38 1.24 1.13 1.04 0.959

1.64 1.48 1.35 1.24 1.15

1.92 1.75 1.60 1.47 1.36

2.21 2.02 1.85 1.71 1.58

2.51 2.29 2.11 1.95 1.82

2.6 2.8 3.0

0.253 0.282 0.314 0.349 0.389 0.434 0.483 0.537 0.596 0.661 0.731 0.890 1.07 1.26 1.47 1.69 0.235 0.262 0.292 0.324 0.362 0.403 0.450 0.500 0.555 0.615 0.682 0.830 0.997 1.18 1.37 1.58 0.219 0.245 0.272 0.303 0.338 0.377 0.420 0.468 0.519 0.576 0.638 0.777 0.934 1.10 1.28 1.48

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 114

8–114

DESIGN CONSIDERATIONS FOR WELDS

Table 8-11 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 15° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

1.98 1.90 1.84 1.76 1.65

2.20 2.09 2.05 1.96 1.85

2.47 2.32 2.26 2.17 2.05

2.74 2.55 2.48 2.38 2.25

3.01 2.79 2.70 2.58 2.44

3.29 3.02 2.92 2.78 2.63

3.56 3.26 3.13 2.99 2.82

3.83 3.49 3.35 3.19 3.01

4.10 3.71 3.56 3.38 3.20

4.38 3.94 3.77 3.58 3.39

4.65 4.16 3.98 3.78 3.58

5.19 4.60 4.40 4.19 3.99

5.74 5.04 4.83 4.61 4.41

6.28 5.49 5.27 5.05 4.84

6.83 5.95 5.72 5.49 5.28

7.37 6.42 6.18 5.95 5.74

0.30 0.40 0.50 0.60 0.70

1.55 1.34 1.16 1.01 0.895

1.74 1.51 1.31 1.14 1.01

1.92 1.67 1.44 1.26 1.12

2.10 1.82 1.58 1.38 1.23

2.28 1.97 1.71 1.51 1.34

2.46 2.12 1.86 1.65 1.47

2.64 2.29 2.02 1.79 1.61

2.82 2.48 2.19 1.95 1.75

3.01 2.67 2.37 2.12 1.91

3.21 2.87 2.56 2.31 2.09

3.40 3.08 2.77 2.50 2.27

3.81 3.47 3.17 2.91 2.66

4.22 3.88 3.57 3.29 3.04

4.65 4.29 3.97 3.69 3.43

5.09 4.73 4.39 4.09 3.82

5.54 5.17 4.83 4.51 4.23

0.80 0.90 1.0 1.2 1.4

0.799 0.720 0.654 0.552 0.477

0.897 0.809 0.735 0.621 0.536

0.995 0.897 0.816 0.689 0.595

1.10 0.991 0.902 0.763 0.660

1.21 1.09 0.996 0.845 0.733

1.32 1.20 1.10 0.936 0.813

1.45 1.32 1.21 1.03 0.900

1.59 1.45 1.33 1.14 0.994

1.74 1.59 1.46 1.25 1.10

1.90 1.74 1.60 1.38 1.21

2.07 1.90 1.76 1.52 1.33

2.44 2.26 2.09 1.82 1.60

2.83 2.63 2.45 2.15 1.90

3.19 2.99 2.80 2.48 2.22

3.58 3.36 3.16 2.81 2.53

3.97 3.74 3.53 3.16 2.85

1.6 1.8 2.0 2.2 2.4

0.420 0.374 0.338 0.308 0.282

0.471 0.420 0.379 0.345 0.317

0.523 0.467 0.421 0.384 0.352

0.581 0.519 0.468 0.426 0.391

0.646 0.577 0.521 0.475 0.436

0.718 0.642 0.580 0.529 0.486

0.796 0.713 0.645 0.589 0.542

0.881 0.790 0.716 0.654 0.602

0.974 0.874 0.793 0.725 0.668

1.08 0.967 0.877 0.803 0.739

1.19 1.07 0.969 0.888 0.818

1.43 1.29 1.18 1.08 0.994

1.70 1.54 1.41 1.29 1.19

2.00 1.81 1.66 1.52 1.41

2.29 2.09 1.92 1.77 1.64

2.59 2.37 2.19 2.02 1.88

2.6 2.8 3.0

0.261 0.292 0.325 0.362 0.403 0.450 0.501 0.557 0.619 0.685 0.758 0.923 1.11 1.31 1.52 1.75 0.242 0.272 0.302 0.336 0.375 0.418 0.466 0.519 0.576 0.638 0.707 0.860 1.03 1.22 1.42 1.64 0.226 0.254 0.282 0.314 0.350 0.391 0.436 0.485 0.539 0.598 0.662 0.806 0.967 1.14 1.33 1.53

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 115

DESIGN TABLES

8–115

Table 8-11 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 30° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.18 2.02 1.92 1.82 1.71

2.44 2.24 2.12 2.01 1.90

2.70 2.47 2.33 2.21 2.08

2.96 2.70 2.54 2.41 2.28

3.21 2.93 2.76 2.62 2.47

3.47 3.17 2.98 2.83 2.67

3.73 3.40 3.20 3.03 2.88

3.98 3.63 3.42 3.24 3.08

4.24 3.87 3.64 3.46 3.28

4.50 4.10 3.86 3.67 3.49

4.76 4.34 4.09 3.89 3.70

5.27 4.82 4.55 4.33 4.13

5.78 5.31 5.02 4.79 4.57

6.30 5.80 5.51 5.26 5.03

6.81 6.30 6.01 5.74 5.50

7.33 6.81 6.53 6.24 5.99

0.30 0.40 0.50 0.60 0.70

1.61 1.41 1.23 1.08 0.964

1.78 1.56 1.37 1.21 1.07

1.96 1.72 1.50 1.33 1.19

2.14 1.87 1.66 1.48 1.33

2.32 2.05 1.82 1.63 1.47

2.52 2.24 2.00 1.80 1.62

2.72 2.43 2.19 1.96 1.77

2.91 2.63 2.37 2.13 1.93

3.11 2.82 2.56 2.31 2.10

3.31 3.01 2.75 2.51 2.28

3.51 3.21 2.95 2.71 2.48

3.93 3.62 3.34 3.10 2.87

4.37 4.04 3.75 3.50 3.26

4.82 4.48 4.18 3.91 3.66

5.29 4.93 4.62 4.33 4.08

5.76 5.39 5.06 4.77 4.50

0.80 0.90 1.0 1.2 1.4

0.865 0.783 0.714 0.606 0.525

0.965 0.874 0.798 0.678 0.589

1.07 0.976 0.893 0.761 0.661

1.20 1.09 0.997 0.847 0.734

1.33 1.21 1.10 0.938 0.815

1.46 1.33 1.22 1.04 0.904

1.60 1.46 1.34 1.15 1.00

1.75 1.60 1.48 1.27 1.11

1.92 1.76 1.62 1.39 1.22

2.09 1.92 1.77 1.53 1.35

2.27 2.10 1.94 1.68 1.48

2.67 2.47 2.30 2.01 1.78

3.05 2.85 2.68 2.37 2.10

3.44 3.23 3.04 2.71 2.44

3.84 3.62 3.42 3.07 2.77

4.25 4.03 3.81 3.44 3.12

1.6 1.8 2.0 2.2 2.4

0.463 0.414 0.374 0.341 0.313

0.520 0.465 0.421 0.384 0.353

0.582 0.520 0.469 0.427 0.392

0.647 0.577 0.521 0.475 0.436

0.719 0.642 0.580 0.529 0.486

0.799 0.715 0.647 0.590 0.542

0.887 0.795 0.720 0.657 0.604

0.982 0.882 0.799 0.730 0.672

1.09 0.975 0.885 0.809 0.745

1.20 1.08 0.978 0.895 0.825

1.32 1.19 1.08 0.989 0.912

1.59 1.43 1.31 1.20 1.11

1.89 1.71 1.56 1.44 1.32

2.21 2.01 1.84 1.69 1.56

2.52 2.31 2.12 1.96 1.81

2.85 2.61 2.41 2.24 2.08

2.6 2.8 3.0

0.289 0.326 0.363 0.403 0.450 0.502 0.559 0.622 0.690 0.765 0.845 1.03 1.23 1.45 1.68 1.94 0.269 0.303 0.337 0.375 0.418 0.467 0.520 0.579 0.643 0.712 0.788 0.958 1.15 1.35 1.57 1.81 0.251 0.283 0.315 0.350 0.391 0.436 0.487 0.542 0.602 0.667 0.738 0.898 1.07 1.26 1.47 1.70

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 116

8–116

DESIGN CONSIDERATIONS FOR WELDS

Table 8-11 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 45° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.41 2.24 2.09 1.96 1.85

2.57 2.44 2.28 2.14 2.02

2.80 2.65 2.48 2.32 2.19

3.04 2.87 2.69 2.51 2.37

3.27 3.09 2.91 2.72 2.56

3.51 3.32 3.14 2.94 2.76

3.74 3.56 3.38 3.17 2.98

3.97 3.79 3.62 3.42 3.21

4.21 4.03 3.85 3.66 3.45

4.44 4.26 4.09 3.90 3.70

4.67 4.50 4.33 4.15 3.95

5.14 4.99 4.83 4.65 4.45

5.61 5.47 5.32 5.15 4.95

6.08 5.96 5.82 5.65 5.46

6.54 6.45 6.31 6.15 5.97

7.01 6.94 6.81 6.65 6.47

0.30 0.40 0.50 0.60 0.70

1.74 1.55 1.38 1.23 1.11

1.90 1.69 1.51 1.35 1.22

2.06 1.84 1.64 1.48 1.34

2.23 1.99 1.80 1.63 1.48

2.41 2.17 1.97 1.79 1.64

2.61 2.36 2.15 1.97 1.81

2.82 2.56 2.35 2.16 1.99

3.04 2.77 2.56 2.36 2.19

3.26 2.99 2.77 2.57 2.38

3.50 3.22 2.98 2.78 2.59

3.74 3.44 3.20 2.99 2.80

4.24 3.89 3.63 3.41 3.20

4.75 4.36 4.07 3.84 3.62

5.26 4.86 4.54 4.28 4.05

5.77 5.37 5.02 4.74 4.50

6.28 5.88 5.52 5.21 4.95

0.80 0.90 1.0 1.2 1.4

1.00 0.915 0.839 0.719 0.627

1.11 1.01 0.929 0.799 0.699

1.22 1.12 1.03 0.891 0.782

1.36 1.25 1.15 0.997 0.877

1.51 1.39 1.29 1.12 0.981

1.67 1.54 1.43 1.25 1.09

1.84 1.71 1.59 1.38 1.21

2.03 1.88 1.75 1.52 1.34

2.22 2.07 1.92 1.67 1.47

2.42 2.25 2.10 1.83 1.62

2.62 2.44 2.28 2.00 1.78

3.01 2.84 2.68 2.37 2.11

3.42 3.24 3.07 2.76 2.49

3.84 3.65 3.47 3.14 2.86

4.28 4.07 3.88 3.53 3.23

4.72 4.51 4.31 3.94 3.62

1.6 1.8 2.0 2.2 2.4

0.555 0.498 0.451 0.412 0.379

0.620 0.557 0.505 0.462 0.426

0.695 0.625 0.568 0.520 0.479

0.781 0.701 0.634 0.579 0.532

0.870 0.780 0.706 0.644 0.593

0.967 0.868 0.786 0.718 0.661

1.07 0.965 0.875 0.800 0.737

1.19 1.07 0.972 0.889 0.819

1.31 1.18 1.08 0.986 0.909

1.45 1.31 1.19 1.09 1.01

1.59 1.44 1.31 1.20 1.11

1.90 1.72 1.57 1.44 1.33

2.24 2.04 1.86 1.72 1.59

2.61 2.38 2.18 2.01 1.87

2.97 2.73 2.53 2.33 2.17

3.34 3.09 2.86 2.67 2.49

2.6 2.8 3.0

0.351 0.394 0.443 0.492 0.549 0.612 0.682 0.760 0.843 0.933 1.03 1.24 1.48 1.74 2.02 2.32 0.327 0.367 0.412 0.458 0.510 0.570 0.635 0.707 0.786 0.870 0.961 1.16 1.38 1.63 1.89 2.18 0.306 0.344 0.385 0.428 0.477 0.533 0.594 0.662 0.735 0.814 0.900 1.09 1.29 1.53 1.78 2.05

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 117

DESIGN TABLES

8–117

Table 8-11 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 60° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.60 2.43 2.31 2.18 2.07

2.79 2.59 2.45 2.32 2.21

3.01 2.76 2.61 2.48 2.35

3.23 2.94 2.79 2.64 2.51

3.44 3.14 2.98 2.83 2.70

3.66 3.36 3.20 3.04 2.91

3.88 3.59 3.42 3.27 3.14

4.10 3.83 3.67 3.51 3.38

4.32 4.07 3.91 3.75 3.62

4.54 4.30 4.16 4.00 3.87

4.76 4.54 4.41 4.25 4.11

5.19 5.00 4.89 4.76 4.61

5.63 5.46 5.36 5.24 5.11

6.07 5.92 5.82 5.72 5.60

6.50 6.37 6.28 6.19 6.08

6.94 6.82 6.74 6.65 6.55

0.30 0.40 0.50 0.60 0.70

1.97 1.79 1.63 1.49 1.37

2.10 1.92 1.75 1.61 1.48

2.24 2.05 1.88 1.74 1.61

2.40 2.21 2.04 1.89 1.76

2.59 2.39 2.22 2.07 1.93

2.79 2.59 2.42 2.26 2.12

3.01 2.81 2.63 2.47 2.32

3.25 3.03 2.85 2.68 2.53

3.50 3.27 3.07 2.90 2.75

3.75 3.52 3.31 3.13 2.97

3.99 3.77 3.55 3.36 3.20

4.48 4.26 4.06 3.85 3.67

4.97 4.75 4.55 4.36 4.16

5.47 5.23 5.04 4.85 4.67

5.96 5.71 5.52 5.34 5.16

6.44 6.20 5.99 5.81 5.64

0.80 0.90 1.0 1.2 1.4

1.26 1.17 1.08 0.946 0.837

1.37 1.27 1.18 1.04 0.921

1.49 1.39 1.30 1.15 1.02

1.64 1.53 1.44 1.27 1.14

1.81 1.69 1.59 1.41 1.27

1.99 1.87 1.76 1.57 1.41

2.18 2.06 1.94 1.74 1.57

2.39 2.26 2.14 1.92 1.74

2.60 2.46 2.34 2.11 1.90

2.82 2.68 2.55 2.30 2.07

3.04 2.90 2.76 2.49 2.26

3.51 3.35 3.21 2.92 2.66

3.98 3.82 3.67 3.37 3.09

4.48 4.30 4.13 3.83 3.55

4.98 4.79 4.61 4.29 4.00

5.47 5.29 5.11 4.75 4.45

1.6 1.8 2.0 2.2 2.4

0.748 0.676 0.616 0.565 0.522

0.827 0.749 0.684 0.629 0.582

0.920 0.836 0.765 0.704 0.652

1.03 0.935 0.856 0.790 0.732

1.15 1.05 0.961 0.887 0.822

1.28 1.17 1.08 0.991 0.916

1.43 1.31 1.20 1.10 1.02

1.58 1.44 1.32 1.22 1.13

1.73 1.58 1.45 1.34 1.24

1.89 1.72 1.59 1.47 1.36

2.06 1.88 1.73 1.61 1.49

2.43 2.23 2.06 1.91 1.78

2.84 2.62 2.43 2.26 2.11

3.28 3.04 2.83 2.64 2.47

3.74 3.49 3.25 3.04 2.85

4.17 3.92 3.69 3.46 3.26

2.6 2.8 3.0

0.485 0.541 0.607 0.682 0.763 0.851 0.948 1.05 1.16 1.27 1.39 1.67 1.98 2.32 2.68 3.07 0.453 0.506 0.568 0.638 0.712 0.794 0.885 0.984 1.08 1.19 1.31 1.57 1.86 2.18 2.53 2.90 0.424 0.475 0.533 0.599 0.667 0.744 0.830 0.923 1.02 1.12 1.23 1.47 1.75 2.06 2.39 2.74

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 118

8–118

DESIGN CONSIDERATIONS FOR WELDS

Table 8-11 (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 75° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.74 2.59 2.50 2.43 2.35

2.92 2.67 2.59 2.52 2.44

3.11 2.78 2.70 2.63 2.56

3.30 2.93 2.86 2.79 2.73

3.49 3.12 3.05 2.98 2.92

3.69 3.32 3.26 3.19 3.13

3.88 3.53 3.48 3.42 3.36

4.07 3.75 3.70 3.64 3.59

4.26 3.96 3.92 3.87 3.82

4.46 4.17 4.13 4.09 4.04

4.65 4.38 4.34 4.30 4.26

5.03 4.78 4.74 4.71 4.68

5.42 5.22 5.15 5.11 5.08

5.80 5.64 5.58 5.52 5.48

6.19 6.06 6.01 5.95 5.89

6.57 6.46 6.42 6.37 6.31

0.30 0.40 0.50 0.60 0.70

2.28 2.16 2.05 1.94 1.85

2.38 2.25 2.14 2.04 1.94

2.50 2.38 2.27 2.17 2.08

2.66 2.55 2.44 2.34 2.24

2.85 2.74 2.63 2.52 2.42

3.07 2.95 2.83 2.73 2.63

3.30 3.17 3.06 2.95 2.85

3.53 3.41 3.30 3.19 3.08

3.77 3.66 3.55 3.43 3.32

4.00 3.90 3.79 3.69 3.58

4.22 4.13 4.04 3.94 3.83

4.65 4.58 4.50 4.42 4.33

5.06 5.00 4.94 4.87 4.80

5.45 5.41 5.35 5.30 5.24

5.85 5.80 5.76 5.71 5.66

6.26 6.19 6.15 6.11 6.07

0.80 0.90 1.0 1.2 1.4

1.75 1.67 1.59 1.45 1.33

1.85 1.77 1.69 1.55 1.43

1.99 1.90 1.82 1.68 1.55

2.15 2.06 1.98 1.83 1.70

2.33 2.24 2.16 2.00 1.86

2.53 2.44 2.36 2.20 2.05

2.75 2.66 2.57 2.40 2.25

2.98 2.89 2.80 2.62 2.47

3.22 3.12 3.03 2.85 2.69

3.47 3.37 3.27 3.09 2.92

3.73 3.62 3.52 3.33 3.15

4.23 4.14 4.04 3.83 3.64

4.72 4.63 4.54 4.35 4.15

5.17 5.10 5.02 4.85 4.67

5.60 5.54 5.47 5.33 5.16

6.02 5.97 5.91 5.78 5.64

1.6 1.8 2.0 2.2 2.4

1.22 1.13 1.05 0.975 0.912

1.32 1.22 1.14 1.06 0.998

1.44 1.34 1.25 1.17 1.10

1.58 1.47 1.38 1.30 1.22

1.74 1.63 1.53 1.44 1.36

1.92 1.80 1.69 1.60 1.51

2.11 1.99 1.87 1.77 1.68

2.32 2.19 2.07 1.95 1.85

2.54 2.40 2.27 2.14 2.03

2.76 2.61 2.46 2.33 2.21

2.98 2.82 2.67 2.53 2.40

3.45 3.27 3.11 2.95 2.81

3.96 3.76 3.58 3.41 3.25

4.48 4.28 4.09 3.90 3.73

4.99 4.81 4.61 4.42 4.23

5.48 5.31 5.14 4.95 4.75

2.6 2.8 3.0

0.856 0.940 1.04 1.15 1.29 1.43 1.59 1.76 1.92 2.09 2.28 2.67 3.11 3.57 4.06 4.57 0.806 0.887 0.983 1.09 1.22 1.36 1.51 1.67 1.83 1.99 2.17 2.55 2.97 3.42 3.90 4.40 0.762 0.839 0.932 1.04 1.16 1.29 1.44 1.59 1.74 1.90 2.07 2.44 2.84 3.28 3.75 4.24

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 119

DESIGN TABLES

8–119

Table 8-11a

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 15° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

1.98 1.90 1.84 1.76 1.65

2.20 2.15 2.09 1.98 1.85

2.47 2.44 2.34 2.20 2.05

2.74 2.71 2.58 2.41 2.24

3.01 2.97 2.80 2.61 2.42

3.29 3.20 3.00 2.79 2.59

3.56 3.42 3.19 2.97 2.76

3.83 3.62 3.38 3.15 2.94

4.10 3.82 3.57 3.35 3.14

4.38 4.02 3.77 3.55 3.34

4.65 4.22 3.98 3.76 3.55

5.19 4.64 4.40 4.18 3.97

5.74 5.07 4.83 4.61 4.40

6.28 5.52 5.28 5.05 4.84

6.83 5.99 5.75 5.51 5.30

7.37 6.47 6.22 5.99 5.77

0.30 0.40 0.50 0.60 0.70

1.55 1.34 1.16 1.01 0.895

1.73 1.49 1.29 1.13 0.998

1.90 1.64 1.41 1.24 1.10

2.07 1.77 1.54 1.35 1.20

2.24 1.92 1.67 1.47 1.31

2.40 2.07 1.81 1.60 1.43

2.57 2.24 1.97 1.75 1.57

2.75 2.42 2.14 1.91 1.72

2.94 2.60 2.32 2.08 1.88

3.14 2.80 2.50 2.26 2.05

3.35 3.00 2.70 2.44 2.22

3.78 3.42 3.11 2.83 2.60

4.20 3.84 3.52 3.25 3.00

4.64 4.27 3.94 3.65 3.39

5.09 4.71 4.37 4.06 3.79

5.56 5.17 4.81 4.50 4.21

0.80 0.90 1.0 1.2 1.4

0.799 0.720 0.654 0.552 0.477

0.889 0.801 0.728 0.615 0.532

0.980 0.885 0.806 0.682 0.590

1.08 0.975 0.889 0.755 0.654

1.18 1.07 0.980 0.835 0.725

1.29 1.18 1.08 0.921 0.803

1.42 1.29 1.19 1.02 0.887

1.56 1.42 1.31 1.12 0.980

1.71 1.56 1.44 1.24 1.08

1.87 1.71 1.58 1.36 1.20

2.03 1.87 1.73 1.50 1.32

2.39 2.21 2.05 1.79 1.58

2.77 2.58 2.40 2.11 1.87

3.16 2.95 2.77 2.45 2.19

3.55 3.33 3.13 2.79 2.51

3.95 3.71 3.50 3.14 2.83

1.6 1.8 2.0 2.2 2.4

0.420 0.374 0.338 0.308 0.282

0.468 0.417 0.377 0.343 0.315

0.520 0.464 0.419 0.382 0.350

0.577 0.515 0.465 0.424 0.390

0.640 0.573 0.518 0.472 0.434

0.710 0.636 0.576 0.526 0.483

0.786 0.706 0.639 0.584 0.538

0.870 0.781 0.709 0.648 0.597

0.963 0.866 0.786 0.719 0.662

1.07 0.958 0.870 0.797 0.735

1.17 1.06 0.962 0.882 0.813

1.42 1.28 1.16 1.07 0.987

1.68 1.52 1.39 1.28 1.18

1.97 1.79 1.64 1.51 1.40

2.27 2.07 1.91 1.76 1.63

2.58 2.36 2.17 2.01 1.87

2.6 2.8 3.0

0.261 0.291 0.324 0.360 0.401 0.447 0.498 0.553 0.614 0.681 0.754 0.917 1.10 1.30 1.51 1.74 0.242 0.271 0.301 0.335 0.373 0.416 0.464 0.516 0.572 0.635 0.703 0.856 1.03 1.21 1.41 1.63 0.226 0.253 0.281 0.313 0.349 0.389 0.434 0.483 0.536 0.594 0.659 0.802 0.963 1.14 1.32 1.53

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 120

8–120

DESIGN CONSIDERATIONS FOR WELDS

Table 8-11a (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 30° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.18 2.02 1.92 1.82 1.71

2.44 2.34 2.20 2.07 1.93

2.70 2.61 2.46 2.30 2.14

2.96 2.86 2.68 2.50 2.33

3.21 3.08 2.88 2.68 2.50

3.47 3.27 3.05 2.85 2.66

3.73 3.46 3.23 3.02 2.83

3.98 3.66 3.42 3.21 3.02

4.24 3.86 3.63 3.41 3.22

4.50 4.08 3.85 3.63 3.43

4.76 4.31 4.07 3.86 3.65

5.27 4.78 4.54 4.33 4.12

5.78 5.27 5.03 4.81 4.61

6.30 5.76 5.52 5.30 5.09

6.81 6.26 6.02 5.79 5.58

7.33 6.77 6.52 6.29 6.07

0.30 0.40 0.50 0.60 0.70

1.61 1.41 1.23 1.08 0.964

1.81 1.57 1.37 1.21 1.08

1.99 1.72 1.50 1.33 1.18

2.16 1.87 1.63 1.45 1.29

2.32 2.02 1.78 1.57 1.41

2.49 2.18 1.93 1.72 1.54

2.66 2.35 2.09 1.88 1.69

2.84 2.53 2.26 2.04 1.85

3.04 2.72 2.45 2.21 2.01

3.25 2.92 2.64 2.40 2.19

3.47 3.13 2.84 2.59 2.37

3.93 3.58 3.27 3.00 2.77

4.41 4.05 3.73 3.45 3.19

4.89 4.53 4.20 3.91 3.64

5.38 5.01 4.67 4.36 4.08

5.87 5.49 5.14 4.82 4.53

0.80 0.90 1.0 1.2 1.4

0.865 0.783 0.714 0.606 0.525

0.965 0.873 0.796 0.676 0.586

1.06 0.964 0.881 0.749 0.650

1.17 1.06 0.971 0.828 0.720

1.28 1.16 1.07 0.914 0.797

1.40 1.28 1.17 1.01 0.881

1.54 1.40 1.29 1.11 0.974

1.68 1.54 1.42 1.23 1.08

1.84 1.69 1.56 1.35 1.19

2.01 1.85 1.71 1.49 1.31

2.18 2.02 1.87 1.63 1.44

2.56 2.38 2.22 1.95 1.73

2.97 2.77 2.59 2.29 2.04

3.40 3.19 2.99 2.66 2.38

3.83 3.60 3.39 3.04 2.74

4.27 4.03 3.81 3.42 3.10

1.6 1.8 2.0 2.2 2.4

0.463 0.414 0.374 0.341 0.313

0.516 0.462 0.417 0.380 0.349

0.574 0.513 0.464 0.423 0.389

0.636 0.570 0.515 0.470 0.432

0.706 0.633 0.573 0.523 0.481

0.782 0.702 0.637 0.582 0.536

0.865 0.778 0.706 0.646 0.595

0.958 0.862 0.783 0.717 0.661

1.06 0.955 0.868 0.795 0.733

1.17 1.06 0.961 0.881 0.813

1.29 1.17 1.06 0.974 0.900

1.55 1.41 1.28 1.18 1.09

1.84 1.67 1.53 1.41 1.30

2.15 1.96 1.80 1.66 1.54

2.49 2.27 2.09 1.93 1.79

2.82 2.59 2.39 2.21 2.06

2.6 2.8 3.0

0.289 0.323 0.360 0.400 0.445 0.496 0.552 0.613 0.680 0.755 0.836 1.01 1.21 1.44 1.67 1.92 0.269 0.300 0.334 0.372 0.415 0.462 0.514 0.571 0.634 0.704 0.780 0.947 1.14 1.34 1.56 1.80 0.251 0.281 0.313 0.348 0.388 0.432 0.481 0.535 0.594 0.659 0.731 0.889 1.07 1.26 1.47 1.69

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 121

DESIGN TABLES

8–121

Table 8-11a (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 45° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.41 2.24 2.09 1.96 1.85

2.57 2.52 2.38 2.23 2.10

2.80 2.76 2.61 2.45 2.30

3.04 2.97 2.80 2.63 2.47

3.27 3.17 2.98 2.80 2.63

3.51 3.37 3.17 2.98 2.81

3.74 3.58 3.37 3.18 3.00

3.97 3.80 3.58 3.39 3.21

4.21 4.02 3.81 3.61 3.44

4.44 4.25 4.04 3.84 3.67

4.67 4.49 4.28 4.08 3.90

5.14 4.98 4.77 4.57 4.39

5.61 5.47 5.27 5.06 4.88

6.08 5.96 5.77 5.57 5.38

6.54 6.45 6.27 6.08 5.88

7.01 6.94 6.77 6.59 6.39

0.30 0.40 0.50 0.60 0.70

1.74 1.55 1.38 1.23 1.11

1.97 1.73 1.54 1.38 1.24

2.16 1.90 1.68 1.51 1.36

2.33 2.06 1.83 1.64 1.48

2.49 2.22 1.99 1.79 1.62

2.65 2.38 2.15 1.95 1.77

2.84 2.56 2.32 2.11 1.93

3.05 2.76 2.51 2.29 2.10

3.27 2.97 2.71 2.48 2.28

3.50 3.19 2.92 2.69 2.48

3.73 3.43 3.15 2.90 2.68

4.22 3.91 3.62 3.36 3.13

4.71 4.40 4.12 3.85 3.60

5.21 4.90 4.62 4.34 4.09

5.71 5.41 5.12 4.84 4.59

6.22 5.91 5.62 5.35 5.09

0.80 0.90 1.0 1.2 1.4

1.00 0.915 0.839 0.719 0.627

1.12 1.02 0.937 0.802 0.700

1.23 1.13 1.04 0.889 0.777

1.35 1.24 1.14 0.982 0.860

1.48 1.36 1.25 1.08 0.950

1.62 1.49 1.38 1.19 1.05

1.77 1.64 1.51 1.31 1.16

1.94 1.79 1.66 1.45 1.28

2.11 1.96 1.82 1.59 1.41

2.29 2.13 1.99 1.75 1.55

2.49 2.32 2.17 1.91 1.70

2.92 2.73 2.56 2.27 2.03

3.38 3.17 2.99 2.66 2.40

3.85 3.64 3.44 3.09 2.79

4.34 4.12 3.90 3.53 3.20

4.84 4.60 4.38 3.98 3.64

1.6 1.8 2.0 2.2 2.4

0.555 0.498 0.451 0.412 0.379

0.620 0.556 0.504 0.460 0.423

0.689 0.618 0.560 0.512 0.471

0.764 0.686 0.622 0.569 0.524

0.846 0.761 0.691 0.632 0.583

0.935 0.843 0.766 0.702 0.648

1.03 0.933 0.849 0.779 0.719

1.14 1.03 0.942 0.864 0.798

1.27 1.14 1.04 0.959 0.886

1.40 1.26 1.15 1.06 0.982

1.53 1.39 1.27 1.17 1.08

1.84 1.67 1.53 1.41 1.31

2.17 1.98 1.82 1.69 1.57

2.54 2.32 2.14 1.98 1.84

2.93 2.69 2.48 2.30 2.15

3.34 3.08 2.85 2.65 2.47

2.6 2.8 3.0

0.351 0.392 0.436 0.485 0.540 0.601 0.668 0.741 0.823 0.913 1.01 1.22 1.46 1.72 2.01 2.31 0.327 0.365 0.406 0.452 0.503 0.560 0.623 0.692 0.768 0.852 0.943 1.14 1.37 1.62 1.88 2.17 0.306 0.341 0.380 0.423 0.471 0.525 0.584 0.649 0.720 0.799 0.885 1.07 1.29 1.52 1.77 2.04

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 122

8–122

DESIGN CONSIDERATIONS FOR WELDS

Table 8-11a (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 60° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.60 2.43 2.31 2.18 2.07

2.79 2.68 2.56 2.44 2.32

3.01 2.91 2.77 2.63 2.50

3.23 3.12 2.97 2.82 2.68

3.44 3.34 3.18 3.02 2.88

3.66 3.56 3.40 3.24 3.09

3.88 3.79 3.62 3.46 3.31

4.10 4.01 3.85 3.69 3.54

4.32 4.24 4.08 3.92 3.77

4.54 4.46 4.32 4.15 4.01

4.76 4.69 4.55 4.39 4.24

5.19 5.14 5.01 4.87 4.71

5.63 5.58 5.47 5.34 5.19

6.07 6.02 5.93 5.81 5.67

6.50 6.47 6.38 6.27 6.15

6.94 6.91 6.83 6.73 6.61

0.30 0.40 0.50 0.60 0.70

1.97 1.79 1.63 1.49 1.37

2.21 2.00 1.82 1.67 1.53

2.39 2.19 1.99 1.82 1.68

2.56 2.35 2.16 1.99 1.83

2.75 2.53 2.33 2.15 2.00

2.96 2.72 2.51 2.33 2.17

3.18 2.94 2.72 2.52 2.35

3.41 3.16 2.94 2.74 2.55

3.64 3.40 3.17 2.97 2.77

3.88 3.64 3.41 3.20 3.01

4.11 3.88 3.65 3.44 3.24

4.58 4.35 4.14 3.94 3.74

5.05 4.83 4.62 4.43 4.23

5.53 5.29 5.10 4.91 4.73

6.01 5.76 5.57 5.39 5.21

6.49 6.23 6.03 5.86 5.69

0.80 0.90 1.0 1.2 1.4

1.26 1.17 1.08 0.946 0.837

1.41 1.30 1.21 1.06 0.935

1.55 1.44 1.34 1.17 1.04

1.70 1.57 1.47 1.29 1.15

1.85 1.73 1.61 1.42 1.26

2.02 1.89 1.77 1.56 1.39

2.20 2.06 1.93 1.71 1.53

2.39 2.24 2.11 1.88 1.69

2.60 2.44 2.30 2.06 1.85

2.83 2.66 2.51 2.25 2.03

3.06 2.89 2.73 2.45 2.22

3.55 3.37 3.20 2.89 2.63

4.04 3.86 3.69 3.36 3.08

4.54 4.36 4.18 3.85 3.55

5.03 4.86 4.68 4.35 4.04

5.52 5.35 5.18 4.84 4.53

1.6 1.8 2.0 2.2 2.4

0.748 0.676 0.616 0.565 0.522

0.837 0.756 0.689 0.632 0.584

0.929 0.840 0.766 0.703 0.650

1.03 0.931 0.850 0.781 0.722

1.13 1.03 0.941 0.866 0.802

1.25 1.14 1.04 0.960 0.889

1.38 1.26 1.15 1.06 0.986

1.53 1.39 1.28 1.18 1.09

1.68 1.54 1.41 1.30 1.21

1.85 1.69 1.56 1.44 1.34

2.02 1.85 1.71 1.58 1.47

2.41 2.21 2.05 1.90 1.77

2.83 2.61 2.42 2.26 2.11

3.28 3.04 2.83 2.64 2.48

3.75 3.49 3.26 3.05 2.87

4.23 3.96 3.71 3.49 3.28

2.6 2.8 3.0

0.485 0.542 0.604 0.671 0.746 0.828 0.918 1.02 1.13 1.25 1.38 1.66 1.98 2.33 2.70 3.10 0.453 0.506 0.563 0.626 0.697 0.774 0.859 0.954 1.06 1.17 1.29 1.56 1.86 2.19 2.55 2.93 0.424 0.474 0.528 0.587 0.653 0.727 0.807 0.896 0.995 1.10 1.22 1.47 1.76 2.07 2.41 2.77

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 123

DESIGN TABLES

8–123

Table 8-11a (continued)

Coefficients, C, for Eccentrically Loaded Weld Groups Angle = 75° Available strength of a weld group, φRn or Rn /Ω, is determined with Rn = CC1Dl (φ = 0.75, Ω = 2.00) LRFD Cmin =

Pu φC1Dl

Dmin =

ASD

Pu φCC1l

lmin =

Pu ΩPa Cmin = φCC1D C1Dl

Dmin =

ΩPa CC1l

lmin =

ΩPa CC1D

where P = required force, Pu or Pa , kips D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = ex /l ex = horizontal component of eccentricity of P with respect to centroid of weld group, in. C = coefficient tabulated below C1 = electrode strength coefficient from Table 8-3 (1.0 for E70XX electrodes) Note: Shaded values indicate the value is based on the greatest available strength permitted by AISC Specification Sections J2.4, J2.4(a), J2.4(b) and J2.4(c).

a

k 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.10 0.15 0.20 0.25

2.74 2.59 2.50 2.43 2.35

2.92 2.86 2.76 2.67 2.59

3.11 3.11 3.02 2.92 2.83

3.30 3.30 3.26 3.17 3.07

3.49 3.49 3.48 3.40 3.30

3.69 3.69 3.68 3.63 3.53

3.88 3.88 3.88 3.84 3.76

4.07 4.07 4.07 4.05 3.97

4.26 4.26 4.26 4.25 4.19

4.46 4.46 4.45 4.45 4.39

4.65 4.65 4.65 4.64 4.59

5.03 5.03 5.03 5.03 4.99

5.42 5.42 5.42 5.41 5.39

5.80 5.80 5.80 5.80 5.78

6.19 6.19 6.19 6.18 6.17

6.57 6.57 6.57 6.57 6.56

0.30 0.40 0.50 0.60 0.70

2.28 2.16 2.05 1.94 1.85

2.52 2.39 2.27 2.16 2.05

2.74 2.59 2.46 2.35 2.24

2.97 2.81 2.67 2.54 2.43

3.21 3.04 2.89 2.76 2.64

3.44 3.27 3.13 2.99 2.86

3.67 3.50 3.36 3.23 3.10

3.89 3.73 3.60 3.47 3.34

4.10 3.95 3.82 3.70 3.58

4.32 4.16 4.04 3.93 3.82

4.53 4.37 4.25 4.15 4.05

4.93 4.79 4.67 4.58 4.49

5.34 5.21 5.07 4.99 4.91

5.73 5.62 5.48 5.38 5.32

6.13 6.02 5.90 5.78 5.71

6.52 6.42 6.31 6.18 6.11

0.80 0.90 1.0 1.2 1.4

1.75 1.67 1.59 1.45 1.33

1.95 1.86 1.77 1.62 1.48

2.14 2.04 1.95 1.78 1.64

2.32 2.22 2.13 1.95 1.80

2.52 2.41 2.31 2.13 1.97

2.74 2.63 2.52 2.32 2.15

2.98 2.86 2.75 2.54 2.35

3.22 3.10 2.98 2.77 2.57

3.46 3.35 3.23 3.01 2.81

3.71 3.59 3.48 3.26 3.05

3.95 3.84 3.73 3.51 3.30

4.40 4.31 4.21 4.01 3.81

4.84 4.76 4.67 4.49 4.31

5.25 5.19 5.11 4.96 4.79

5.66 5.60 5.54 5.40 5.25

6.05 6.00 5.95 5.83 5.70

1.6 1.8 2.0 2.2 2.4

1.22 1.13 1.05 0.975 0.912

1.36 1.26 1.17 1.09 1.02

1.51 1.40 1.30 1.21 1.13

1.66 1.54 1.43 1.34 1.26

1.82 1.69 1.58 1.48 1.39

2.00 1.86 1.74 1.63 1.53

2.19 2.04 1.91 1.80 1.69

2.40 2.24 2.10 1.97 1.86

2.62 2.45 2.30 2.17 2.05

2.86 2.68 2.52 2.38 2.25

3.11 2.92 2.75 2.60 2.46

3.61 3.42 3.24 3.07 2.92

4.12 3.93 3.75 3.57 3.41

4.61 4.43 4.25 4.07 3.91

5.09 4.92 4.75 4.58 4.41

5.55 5.40 5.23 5.07 4.90

2.6 2.8 3.0

0.856 0.959 1.07 1.18 1.31 1.44 1.59 1.76 1.94 2.13 2.33 2.78 3.25 3.74 4.24 4.74 0.806 0.903 1.00 1.11 1.23 1.36 1.51 1.67 1.84 2.02 2.21 2.64 3.11 3.59 4.08 4.58 0.762 0.853 0.949 1.05 1.17 1.29 1.43 1.58 1.74 1.92 2.11 2.52 2.97 3.44 3.93 4.42

x y

0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 8B:14th Ed.

2/24/11

8:30 AM

Page 124

8–124

DESIGN CONSIDERATIONS FOR WELDS

Table 8-12

Approximate Number of Passes for Welds Single-Bevel Groove Welds (Back-Up Weld Not Included)

Single-V Groove Welds (Back-Up Weld Not Included)

Weld Size* in.

Fillet Welds

30º Bevel

45º Bevel

30º Groove Angle

3/16

1 1 1 3 4 4 6 8 — — — — — — —

— 1 1 2 2 2 3 4 5 5 7 8 9 9 11

— 1 1 2 2 2 3 5 8 11 11 11 15 18 21

— 2 2 3 3 4 4 4 5 5 9 12 13 13 13

1/4 5/16 3/8 7/16 1/2 5/8 3/4 7/8

1 11/8 11/4 13/8 11/2 13/4

*Plate thickness for groove welds.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

60º 90º Groove Angle Groove Angle — 3 3 4 4 5 6 7 10 13 15 16 21 25 25

— 3 3 6 6 7 8 9 10 22 27 32 36 40 40

AISC_PART 9:14th Ed.

4/1/11

8:58 AM

Page 1

9–1

PART 9 DESIGN OF CONNECTING ELEMENTS

SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–3 GROSS AREA, EFFECTIVE NET AREA, AND WHITMORE SECTION . . . . . . . . . 9–3 Gross Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–3 Effective Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–3 Whitmore Section (Effective Width) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–3 CONNECTING ELEMENTS SUBJECT TO COMBINED LOADING . . . . . . . . . . . . 9–3 CONNECTING ELEMENTS SUBJECT TO TENSION . . . . . . . . . . . . . . . . . . . . . . . . 9–4 CONNECTING ELEMENTS SUBJECT TO SHEAR . . . . . . . . . . . . . . . . . . . . . . . . . . 9–4 CONNECTING ELEMENTS SUBJECT TO BLOCK SHEAR RUPTURE . . . . . . . . . 9–5 CONNECTING ELEMENT RUPTURE STRENGTH AT WELDS . . . . . . . . . . . . . . . 9–5 CONNECTING ELEMENTS SUBJECT TO COMPRESSION YIELDING AND BUCKLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–5 AFFECTED AND CONNECTING ELEMENTS SUBJECT TO FLEXURE . . . . . . . . 9–6 Yielding, Lateral-Torsional Buckling, and Local Buckling . . . . . . . . . . . . . . . . . . . . 9–6 Rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–6 Coped Beam Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–6 BEARING LIMIT STATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–10 Bearing Strength at Bolt Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–10 Steel-on-Steel Bearing Strength (Other Than at Bolt Holes) . . . . . . . . . . . . . . . . . . 9–10 Bearing Strength on Concrete or Masonry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–10 OTHER SPECIFICATION REQUIREMENTS AND DESIGN CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–10 Prying Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–10 Rotational Ductility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–14 Concentrated Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–15 Shims and Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–15 Copes, Blocks and Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–16 Web Reinforcement of Coped Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–17

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

9–2

2/24/11

8:19 AM

Page 2

DESIGN OF CONNECTING ELEMENTS

DESIGN TABLE DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–19 PART 9 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–22 DESIGN TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–23 Table 9-1. Reduction in Area for Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–23 Table 9-2. Elastic Section Modulus for Coped W-Shapes . . . . . . . . . . . . . . . . . . . . 9–24 Table 9-3. Block Shear Rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–33 Table 9-4. Beam Bearing Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–40

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:19 AM

Page 3

CONNECTING ELEMENTS SUBJECT TO COMBINED LOADING

9–3

SCOPE The specification requirements and other design considerations summarized in this Part apply to the design of connecting elements (angles, plates, tees, gussets, etc.) used to transfer load from one structural member to another, as well as the affected elements of the connected members (beam webs, beam flanges, column webs, column flanges, etc.). For design considerations for bolts and welds, see Parts 7 and 8, respectively. For design provisions specific to particular connection configurations, see Parts 10 through 15.

GROSS AREA, EFFECTIVE NET AREA, AND WHITMORE SECTION In the determination of the available strength of connecting elements, the gross area, Ag, is used for the yielding limit states, and the net area, An, is used for the rupture limit states. In either case, the Whitmore section may limit the effective width to less than the overall dimension of a connecting element.

Gross Area The gross area, Ag, is determined as specified in AISC Specification Section B4.3, subject to the limitations given below for the Whitmore section.

Effective Net Area The effective net area, Ae, is determined as specified in AISC Specification Section J4.1, subject to the limitations given below for the Whitmore section. The reduction in area for bolt holes can be determined using Table 9-1.

Whitmore Section (Effective Width) When connecting elements are large in comparison to the bolted or welded joints within them, the Whitmore section may limit the gross and net areas of the connecting element to less than the full area (Whitmore, 1952). As illustrated in Figure 9-1, the width of the Whitmore section, lw, is determined at the end of the joint by spreading the force from the start of the joint 30° to each side in the connecting element along the line of force. The Whitmore section may spread across the joint between connecting elements, but cannot spread beyond an unconnected edge.

CONNECTING ELEMENTS SUBJECT TO COMBINED LOADING Connection design has traditionally been based on simple stresses, such as shear, tension, compression or flexure, not taken in combination. This simplification is adequate because connection elements are usually small or short enough that an interaction-type distribution cannot form. Even a theoretical combination analysis using the von Mises criterion for plane stress is not any more refined. To illustrate this point, von Mises criterion is expressed as fe =

f x2 − f x f y + f y2 + 3 f xy2 ≤ Fy

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where fx and fy = normal stresses, ksi = shear stress, ksi fxy = specified minimum yield stress, ksi Fy This formulation requires three stresses at any one point. Assuming fxy and fx are known for any one cut section, fy on the perpendicular cut section is still undefined and must be assumed, thereby bringing inaccuracy into the formulation. Compounding this dilemma, fy could be assumed as equal to zero, equal to and having the same sign as fx, or equal to and having the opposite sign of fx. Thus, what might appear to be a more sophisticated approach to the analysis and design of a connection does not necessarily add any reliability to the resulting design. Though shear and normal stress interaction is generally not included in AISC design procedures, it is explicitly considered in the design of the extended configuration of the single plate shear connection in Part 10 (Muir and Hewitt, 2009). The intent is to prevent other limit states from controlling.

CONNECTING ELEMENTS SUBJECT TO TENSION The available strength due to tension yielding and tension rupture, φRn or Rn /Ω, which must equal or exceed the required tensile strength, Ru or Ra, respectively, is determined in accordance with AISC Specification Section J4.1.

CONNECTING ELEMENTS SUBJECT TO SHEAR

The available strength due to shear yielding and shear rupture, φRn or Rn /Ω, which must equal or exceed the required shear strength, Ru or Ra, respectively, are determined in accordance with AISC Specification Section J4.2.

Fig. 9-1. Illustration of the width of the Whitmore section.

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CONNECTING ELEMENTS SUBJECT TO BLOCK SHEAR RUPTURE The available strength due to block shear rupture, φRn or Rn /Ω, which must equal or exceed the required strength, Ru or Ra, respectively, is determined in accordance with AISC Specification Section J4.3. The values tabulated in Table 9-3 are used to calculate the available block shear rupture strength.

CONNECTING ELEMENT RUPTURE STRENGTH AT WELDS In many cases, the load path from a weld to the connecting element is such that the strength of the connecting element can be evaluated directly. However, in some cases, the available strength of the connecting element is not directly calculable. For example, while the strength of the beam-web welds for a double-angle connection can be directly calculated, the strength of the beam web at this weld cannot. In cases such as these, it is often convenient to calculate the minimum base metal thickness that will match the available shear rupture strength of the base metal to the available shear rupture strength of the weld(s). For fillet welds with FEXX = 70 ksi on one side of the connection, the minimum base metal thickness required to match the shear rupture strength of the connecting element to the shear rupture strength of the base metal is

tmin

⎛ 2⎞⎛ D⎞ 0.60 FEXX ⎜ ⎜ ⎟ ⎝ 2 ⎟⎠ ⎝ 16 ⎠ = 0.6 Fu 3.09 D = Fu

(9-2)

For fillet welds with FEXX = 70 ksi on both sides of the connecting element, the minimum base metal thickness required to match the shear rupture strength of the connecting element to the shear rupture strength of the base metal is 2 times Equation 9-2: tmin =

6.19 D Fu

(9-3)

where D = number of sixteenths of an inch in the weld size on each side of the connecting element Fu = specified minimum tensile strength of the connecting element, ksi

CONNECTING ELEMENTS SUBJECT TO COMPRESSION YIELDING AND BUCKLING When connecting elements are subject to compression, the available strength, φPn or Pn /Ω, which must equal or exceed the required compressive strength, Pu or Pa, respectively, is determined in accordance with AISC Specification Section J4.4.

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AFFECTED AND CONNECTING ELEMENTS SUBJECT TO FLEXURE Affected and connecting elements are normally short enough and thick enough that flexural effects, if present at all, do not impact the design. When such elements are long enough and thin enough that flexural effects must be considered, the following provisions are used for determining the available strength.

Yielding, Lateral-Torsional Buckling, and Local Buckling Generally, the available flexural strength, φMn or Mn /Ω, which must equal or exceed the required flexural strength of affected and connecting elements, Mu or Ma, respectively, is determined in accordance with AISC Specification Section J4.5 and Chapter F. Section F1.1 provides guidance based upon cross-section shape for the applicable Chapter F section. Treatment of coped beams is provided in the following.

Rupture For beams and rolled girders with bolt holes in the tension flange, see AISC Specification Section F13.1. For affected and connecting elements, the available flexural rupture strength, φb Mn or Mn /Ωb, is Mn = Fu Znet φb = 0.75

(9-4)

Ωb = 2.00

where Znet = net plastic section modulus of the affected or connecting element, in.3

Coped Beam Strength For beam ends with short copes no greater than the length of the connection angle(s), plate, or tee, flexural local web buckling will generally not occur. Otherwise, the end reaction for a coped beam may be limited by the flexural limit states of yielding, rupture, flexural local buckling, or lateral-torsional buckling. The strength of coped beams with bolted shear connections as shown in Part 10 will rarely be governed by flexural rupture. Other limit states, such as block shear rupture, bolt shear rupture, and bolt bearing will generally limit the strength of the connection. For a coped beam, the required flexural strength is LRFD Mu = Rue

ASD (9-5a)

Ma = Ra e

(9-5b)

where Ru or Ra = beam end reaction (LRFD or ASD), kips e = distance from the face of the cope to the point of inflection of the beam, in. It is usually assumed that the point of inflection is located at the face of the supporting member and e is as shown in Figure 9-2. However, depending upon the connection type and stiffness and support condition, the point of inflection may move away from the face of the supporting member; when this is the AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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case, a lesser value of e may be justified, and the use of e shown in Figure 9-2 is conservative. The available flexural local buckling strength of a beam coped at the top flange or both the top and bottom flanges must equal or exceed the required strength. The available strength, φb Mn or Mn /Ωb, is Mn = Fcr Snet φb = 0.90

(9-6)

Ωb = 1.67

where Fcr = flexural local buckling stress, determined according to the following, ksi Snet = net section modulus, in.3 Values of Snet for beams coped at the top flange only are tabulated in Table 9-2.

1. When a beam is coped at the top flange only, the flexural local buckling stress is based upon the classical plate buckling formula with buckling coefficient, k, corresponding to the condition with three edges simply supported and one free edge. An additional plate buckling model adjustment factor, f, is applied to account for stress concentrations at the cope and to correlate the solution with experimental results (Cheng and Yura, 1986). The flexural local buckling stress for a beam coped at the top flange only when c ≤ 2d and dc ≤ d/2 (see Figure 9-2) is Fcr =

π2E

2

⎛ tw ⎞ ⎜ ⎟ fk ≤ Fy 12 1 − ν2 ⎝ ho ⎠

(

)

2

⎛t ⎞ = 26, 210 ⎜ w ⎟ fk ≤ Fy ( ksi) ⎝ ho ⎠

(9-7)

where E = 29,000 ksi = modulus of elasticity of steel Fy = specified minimum yield stress of beam web material, ksi ν = 0.3 = Poisson’s ratio f = plate buckling model adjustment factor determined as follows When

c ≤ 1.0 d f =

When

2c d

c > 1.0 d f = 1+

c d

tw = thickness of web, in. k = plate buckling coefficient determined as follows

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c ≤ 1.0 ho

When

⎛h ⎞ k = 2.2 ⎜ o ⎟ ⎝ c⎠ When

c > 1.0 ho k=

1.65

2.2 ho c

(9-10)

(9-11)

ho = d–dc, reduced beam depth, in. Note that, for convenience, the dimension ho, as illustrated in Figure 9-2, is used in these calculations instead of the more precise dimension h1 to eliminate the detailed calculation required to locate the neutral axis of the coped beam. Alternatively, the dimension h1 may be substituted for ho in the local buckling calculations. c = cope length as illustrated in Figure 9-2, in. d = beam depth, in. dc = cope depth as illustrated in Figure 9-2, in. 2. For a beam with the same cope length at both flanges, the flexural local buckling stress when c ≤ 2d and dc ≤ 0.2d (see Figure 9-3) is (Cheng and Yura, 1986) Fcr = 0.62πE

tw2 fd ≤ Fy cho

(9-12)

where ⎛d fd = 3.5 − 7.5 ⎜ ct ⎞⎟ ⎝ d ⎠ dct = cope depth at the compression flange as illustrated in Figure 9-3, in. ho = reduced beam depth as illustrated in Figure 9-3, in.

Fig. 9-2. Flexural local buckling of beam web coped at top flange only.

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3. For all other conditions, a conservative procedure also based upon the classical plate buckling equation can be used. Including both elastic and inelastic buckling, the available buckling stress, φFcr or Fcr /Ω, is Fcr = QFy

(9-14)

Q=1

(9-15)

Q = (1.34 − 0.486λ)

(9-16)

When λ ≤ 0.7 When 0.7 < λ ≤ 1.41 When λ > 1.41 Q=

1.30 λ2

(9-17)

where ho Fy

λ = 10 t w

⎛h ⎞ 475 + 280 ⎜ o ⎟ ⎝ c⎠

(9-18)

2

ho = reduced beam depth as illustrated in Figure 9-3, in. 4. When the tension flange cope is longer than the compression flange cope, flexural yielding should be checked at the end of the tension flange cope. The available strength, φb Mn or Mn /Ωb, is Mn = Fy Snet φb = 0.90

Ωb = 1.67

where Snet = net elastic section modulus at the end of the tension flange cope, in.3

Fig. 9-3. Flexural local buckling of beam web coped at both flanges.

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BEARING LIMIT STATES Bearing Strength at Bolt Holes For available bearing strength at bolt holes, see Part 7.

Steel-on-Steel Bearing Strength (Other Than at Bolt Holes) Bearing strength for applications other than at bolt holes is determined as given in AISC Specification Section J7. The fabrication and erection requirements in AISC Specification Sections M2.6, M2.8 and M4.4 are applicable to connecting elements that transfer load by contact bearing on steel.

Bearing Strength on Concrete or Masonry The bearing strength of concrete is determined as given in AISC Specification Section J8. For bearing on masonry, see Building Code Requirements for Masonry Structures, ACI 530/ ASCE 5/TMS 402 (ACI/ASCE/TMS, 2005a) and Specification for Masonry Structures, ACI 530.1/ASCE 6/TMS 602 (ACI/ASCE/TMS, 2005b). The fabrication and erection requirements in AISC Specification Sections M2.8 and M4.1 are applicable to connecting elements that transfer load by contact bearing on concrete or masonry.

OTHER SPECIFICATION REQUIREMENTS AND DESIGN CONSIDERATIONS The following other specification requirements and design considerations apply to the design of connecting elements:

Prying Action Prying action is a phenomenon whereby the deformation of a connecting element under a tensile force increases the tensile force in the bolt above that due to the applied tensile force alone. Design for prying action includes the selection of bolt diameter and fitting thickness such that there is sufficient strength in the connecting element and the bolt. The following discussion of prying action is similar to what has been considered prior to the 13th Edition Steel Construction Manual, except that the design is based on Fu, which provides better correlation with available test data than previous design methods. For the development of the prying action equations presented here, see Thornton (1992) and Swanson (2002). Consider the tee or angle used in a hanger connection as shown in Figure 9-4. The deformation of the connected tee flange or angle leg is assumed to be in double curvature, as shown in Figure 9-4. The dimension p identifies the tributary length for each bolt shown. Note that p may be limited by the edge of the plate for the bolt closest to the edge. The thickness required to eliminate prying action, tmin, is determined as LRFD tmin =

ASD

4 Tb ′ φpFu

φ = 0.90

(9-20a)

tmin =

Ω4 Tb ′ pFu

Ω = 1.67

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where Fu = specified minimum tensile strength of connecting element, ksi T = required strength, rut or rat, per bolt, kips d ⎛ b′ = ⎜ b − b ⎞⎟ (9-21) ⎝ 2⎠ b = for a tee-type connecting element, the distance from bolt centerline to the face of the tee stem, in.; for an angle-type connecting element, the distance from bolt centerline to centerline of angle leg, in. db = bolt diameter, in. p = tributary length; maximum = 2b, but ≤ s, unless tests indicate larger lengths can be used. See Dowswell (2011) and Wheeler et al. (1998). s = bolt spacing, in. When the fitting thickness, t, is greater than or equal to tmin, no further check of prying action is necessary. In this solution, the additional force in the bolt due to prying action, q, is essentially zero. Alternatively, it is usually possible to determine a lesser required thickness by designing the connecting element and bolted joint for the actual effects of prying action with q greater

(a) Prying forces in tee

(b) Prying forces in angle

Fig. 9-4. Illustration of variables in prying action calculations.

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than zero. To do so, a preliminary fitting thickness, t, can be selected based upon flexural yielding such that LRFD T≤

ASD

φFu t 2 p 2b

T≤

(9-22a)

φ = 0.90

Fu t 2 p Ω 2b

(9-22b)

Ω = 1.67

Table 15-2 can be used to select the preliminary fitting thickness. Subsequently, the thickness required to ensure an acceptable combination of fitting strength and stiffness and bolt strength, tmin, can be determined as LRFD tmin =

ASD

4 Tb ′ φpFu (1 + δα ′ )

Ω4 Tb ′ pFu (1 + δα ′ )

tmin =

(9-23a)

φ = 0.90

(9-23b)

Ω = 1.67

where δ = 1−

d′ p

(9-24)

= ratio of the net length at bolt line to gross length at the face of the stem or leg of angle α′ = 1.0 if β ≥ 1

d′ β ρ a′ a B

= the lesser of 1 and 1 ⎛ β ⎞ if β < 1 δ ⎜⎝ 1 − β ⎟⎠ = width of the hole along the length of the fitting, in. 1⎛ B ⎞ = ⎜ − 1⎟ ρ⎝T ⎠ b′ = a′ d ⎞ ⎛ d ⎞ ⎛ = ⎜ a + b ⎟ ≤ ⎜ 1.25 b + b ⎟ ⎝ 2⎠ ⎝ 2⎠ = distance from the bolt centerline to the edge of the fitting, in. = available tension per bolt, φrn or rn /Ω, kips

(9-25) (9-26) (9-27)

If tmin ≤ t, the preliminary fitting thickness is satisfactory. Otherwise, a fitting with a thicker flange, or a change in geometry (i.e., b and p) is required. Although it is not necessary to do so, if desired, the prying force per bolt, q, can be determined as 2 ⎡ ⎛ t⎞ ⎤ q = B ⎢δαρ ⎜ ⎟ ⎥ ⎝ tc ⎠ ⎥ ⎢

⎣

⎦

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⎤ 1 ⎡ T ⎛ tc ⎞ ⎢ ⎜ ⎟ − 1⎥ where 0 ≤ α ≤ 1.0 (9-29) δ ⎢B⎝ t ⎠ ⎥⎦ ⎣ The parameter α is the ratio of the moment at the face of the tee stem or at the center of the unconnected angle leg thickness, to the moment at the bolt line. When α = 0, the connection is strong enough to prevent prying action. When α > 1 the connection is not adequate. 2

α=

LRFD

tc =

ASD

4 Bb ′ φpFu

tc =

(9-30a)

Ω4 Bb′ pFu

(9-30b)

tc = flange or angle thickness required to develop the available strength of the bolt, B, with no prying action, in. The total force per bolt including the effects of prying action is then T + q. Alternatively, when the fitting geometry is known, the available tensile strength per bolt, B, determined per AISC Specification Sections J3.6 or J3.7, can be multiplied by Q to determine the available tensile strength including the effects of prying action, Tavail, as follows: Tavail = BQ

(9-31)

When α′ < 0, which means that the fitting has sufficient strength and stiffness to develop the full bolt available tensile strength, Q=1 (9-32) When 0 ≤ α′ ≤ 1, which means that the fitting has sufficient strength to develop the full bolt available tensile strength, but insufficient stiffness to prevent prying action, 2

⎛t⎞ Q = ⎜ ⎟ (1 + δα ′ ) ⎝ tc ⎠

(9-33)

When α′ > 1, which means that the fitting has insufficient strength to develop the full bolt available tensile strength, 2

⎛t⎞ Q = ⎜ ⎟ (1 + δ ) ⎝ tc ⎠

(9-34)

where α′ =

2 ⎤ 1 ⎡ ⎛ tc ⎞ ⎢⎜ ⎟ − 1⎥ δ (1 + ρ) ⎢⎣⎝ t ⎠ ⎥⎦

(9-35)

= value of α that either maximizes the bolt available tensile strength for a given thickness or minimizes the thickness required for a given bolt available tensile strength

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Rotational Ductility Simple shear connections provide for the rotational ductility required by AISC Specification Section J1.2 as follows: 1. For double-angle, shear end-plate, single-angle, and tee shear connections, the geometry and thickness of the connecting elements attached to the support (angle legs, plate, or tee flange) are configured so that flexing of those connecting elements accommodates the simple-beam end rotation. 2. For unstiffened and stiffened seated connections, the geometry and thickness of the top or side stability angle is configured so that flexing of that connecting element accommodates the simple-beam end rotation. 3. For single-plate connections, the geometry and thickness of the plate are configured so that the plate will yield, bolt group will rotate, and/or the bolt holes will elongate at failure prior to the failure of the welds or bolts. For each of the simple-shear connections in Part 10, except tee shear connections, prescriptive guidance is provided to ensure adequate rotational ductility. Rotational ductility can be ensured for tee shear connections as follows. Note that this approach can also be used to demonstrate adequate rotational ductility in other simple shear connections that flex to accommodate the simple beam end rotation, but with configurations that differ from those prescribed in Part 10. When the flanges of the tee stub are welded to the support and bolted to the supported beam, weld size, w, with FEXX = 70 ksi, must be such that the minimum weld size, wmin, is wmin = 0.0155

⎞ Fy t 2f ⎛ b 2 + 2⎟ ⎜ 2 b ⎝L ⎠

(9-36)

but need not exceed 共5⁄ 8 兲ts (Thornton, 1996), where b = flexible width in connecting element as illustrated in Figure 9-5, in. tf = thickness of the tee flange, in. ts = thickness of the tee stem, in. L = depth of connecting element as illustrated in Figure 9-5, in. For a tee bolted to the support and bolted or welded to the supported beam, the minimum diameter for bolts through the tee flange for ductility is d min = 0.163t f

⎞ Fy ⎛ b 2 + 2⎟ b ⎜⎝ L2 ⎠

(9-37)

but need not exceed 0.69 ts . Additionally, to provide for rotational ductility when the tee stem is bolted to the supported beam, the maximum tee stem thickness is ts max =

d 1 + /16 in. 2

where d = bolt diameter, in.

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When the tee stem is welded to the supported beam, there is no perceived ductility problem for this weld.

Concentrated Forces If the connecting element delivers a concentrated force to a member or other connecting element, see AISC Specification Section J10 or Section K1, as appropriate. See also AISC Design Guide 13, Stiffening of Wide-Flange Columns at Moment Connections: Wind and Seismic Applications (Carter, 1999).

Shims and Fillers Shims are furnished to the erector for use in filling the spaces allowed for field clearance which might be present at connections such as simple shear connections, PR and FR moment connections, column base plates, and column splices. These shims, illustrated in Figure 9-6, may be either strip shims, with round punched holes, or finger shims, with slots cut through the edge. Whereas strip shims are less expensive to fabricate, finger shims may be laterally inserted and eliminate the need to remove erection bolts or pins already in place. Finger shims, when inserted fully against the bolt shank, are acceptable for slip-critical connections and are not to be considered as an internal ply with the slotted hole determining

(a) Welded flange

(b) Bolted flange

Fig. 9-5. Illustration of variables in shear connection ductility checks.

Fig. 9-6. Shims. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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the available strength of the connection. This is because less than 25% of the contact surface is lost, which is not enough to affect the performance of the joint. A filler is furnished to occupy spaces which will be present because of dimensional separations between elements of a connection across which load transfer occurs. Examples where fillers might be used are beams framing off center on a column and raised beams. For the effect of fillers and shims on available joint strength, see AISC Specification Sections J3.8 and J5.2.

Copes, Blocks and Cuts When structural members frame together, a minimum clearance of 1⁄ 2 in. should be provided, when possible. In cases where material removal is necessary to provide such a clearance, material may be removed by coping, blocking or cutting as illustrated in Figure 9-7. Material removal is costly and should be avoided when possible. In some cases, it may be possible to do so by setting the elevations of the tops of infill beams a sufficient distance below the tops of girders to clear the girder fillet radius. Alternatively, a connection such as that illustrated in Figure 9-8 could be used. When material removal is necessary, coping is usually the most economical method to remove material. The recommended practices for coping are illustrated in Figure 9-9. The potential notch left by the first cut will occur in waste material and subsequently be removed by the second cut. All re-entrant corners must be shaped notch-free per AWS D1.1/D1.1M (AWS, 2010) to a radius. An approximate minimum radius to which this corner must be shaped is 1⁄ 2 in. Copes, blocks and cuts can significantly reduce the available strengths of members and may require web reinforcement; it may be more economical to use a heavier member than to provide such reinforcement.

(a) Cope

(b) Blocks Fig. 9-7. Copes, blocks and cuts.

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Web Reinforcement of Coped Beams When the strength of a coped beam is inadequate, either a different beam with a thicker web can be selected to eliminate the need for reinforcement, or reinforcement can be provided to increase the strength. In spite of the increase in material cost, the former solution may be the most economical option due to the appreciable labor cost associated with adding stiffeners and/or doubler plates. When the latter solution is required, some typical reinforcing details are illustrated in Figure 9-10. The doubler plate illustrated in Figure 9-10(a) and the longitudinal stiffener illustrated in Figure 9-10b are used with rolled sections where h/tw ≤ 60. When a doubler plate is used, the required doubler-plate thickness, td req, is determined by substituting the quantity (tw + td req ) for tw in the available strength calculations for flexural yielding and local web buckling. To prevent local crippling of the beam web, the doubler plate must be extended at least a distance dc (depth of cope) beyond the cope as illustrated in Figure 9-10(a). When longitudinal stiffening is used, the stiffening elements must be proportioned to meet the width-to-thickness ratios specified in AISC Specification Table B4.1b. The stiffened cross section must then be checked for flexural yielding, but web local buckling need not be

(a) Coping Required

(b) Coping Eliminated

Fig. 9-8. Eliminating coping requirements.

Fig. 9-9. Recommended coping practices.

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checked. To prevent local crippling of the beam web, the longitudinal stiffening must be extended a distance dc beyond the cope as illustrated in Figure 9-10(b). The combination of longitudinal and transverse stiffeners shown in Figure 9-10(c) may be required for thin-web plate girders, where h/tw > 60. When longitudinal and transverse stiffening is used, the stiffening elements must be proportioned to meet the width-to-thickness ratios specified in AISC Specification Table B4.1b. The stiffened cross section must then be checked for flexural yielding, but web local buckling need not be checked. To prevent local crippling of the beam web, longitudinal stiffeners must be extended a distance c/3 beyond the cope, as illustrated in Figure 9-10(c).

(a) Doubler plate

(b) Longitudinal stiffener

(c) Combination longitudinal and transverse stiffeners Fig. 9-10. Web reinforcement of coped beams.

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DESIGN TABLE DISCUSSION

DESIGN TABLE DISCUSSION Table 9-1. Reduction in Area for Hole Area reduction for standard, oversized, short-slotted and long-slotted holes in material thicknesses from 3/ 16 in. to 1 in. are given in Table 9-1. For material thicknesses not listed, the tabular value for 1-in. thickness can be multiplied by the actual thickness. The table is based on a net area using a width that is 1/16 in. greater than the actual hole width.

Table 9-2. Elastic Section Modulus for Coped W-Shapes Values are given for the gross and net elastic section modulus for coped W-shapes, as illustrated in the table header.

Tables 9-3. Block Shear Rupture The terms in AISC Specification Equation J4-5 are tabulated in Tables 9-3a, 9-3b and 9-3c. The indicated values are given per inch of material thickness. Note that when the stress distribution is nonuniform, the tension component from Table 9-3a must be reduced by a factor of 0.5 to account for Ubs.

Table 9-4. Beam Bearing Constants At beam ends and at any location on beams or columns where concentrated loads occur, the available strength for web local yielding and web local crippling, φRn or Rn /Ω, at concentrated loads is determined per AISC Specification Sections J10.2 and J10.3. Values of Rn are given for a bearing length, lb = 31/4 in. The web local yielding (Equations J10-2 and J10-3) and web local crippling (Equations J10-4, J10-5a and J10-5b) equations can be simplified using the bearing length, lb, and the constants R1 through R6 as follows. R1 = 2.5kFyw t w

(9-39)

R2 = Fyw t w

(9-40)

R3 = 0 . 40 t w2

EFyw t f tw

⎛ 3⎞ ⎛ t ⎞ R4 = 0 . 40 t w2 ⎜ ⎟ ⎜ w ⎟ ⎝ d⎠ ⎝ tf ⎠

1.5

EFyw t f tw

1.5 ⎛ ⎛ t ⎞ ⎞ EFyw t f R5 = 0 . 40 t w2 ⎜ 1 − 0 . 2 ⎜ w ⎟ ⎟ tw ⎜⎝ ⎝ t f ⎠ ⎟⎠

⎛ 4⎞ ⎛ t ⎞ R6 = 0 . 40 t w2 ⎜ ⎟ ⎜ w ⎟ ⎝ d⎠ ⎝ tf ⎠

1.5

EFyw t f tw

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(9-41)

(9-42)

(9-43)

(9-44)

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Web Local Yielding The available strength for web local yielding, φRn or Rn /Ω, is determined per AISC Specification Section J10.2 using Equations J10-2 or J10-3, which can be simplified using the constants R1 and R2 from Table 9-4 as follows, where φ = 1.00 and Ω = 1.50. When the compressive force to be resisted is applied at a distance, x, from the member end that is less than or equal to the depth of the member (x ≤ d), LRFD

ASD

φRn = φR1 + lb(φR2)

(9-45a)

Rn /Ω = R1/Ω + lb(R2 /Ω)

(9-45b)

When the compressive force to be resisted is applied at a distance, x, from the member end that is greater than the depth of the member (x > d), LRFD

ASD

φRn = 2(φR1) + lb(φR2)

(9-46a)

Rn /Ω = 2(R1 /Ω) + lb(R2 /Ω)

(9-46b)

Note that the minimum length of bearing, lb, is k, per AISC Specification Section J10.2 for end beam reactions, where k = kdes for W-shapes.

Web Local Crippling The available strength for web local crippling, φRn or Rn /Ω, is determined per AISC Specification Section J10.3 using Equations J10-4, J10-5a or J10-5b, which can be simplified using constants R3, R4, R5 and R6 from Table 9-4 as follows, where φ = 0.75 and Ω = 2.00. When the compressive force to be resisted is applied at a distance, x, from the member end that is less than one-half of the depth of the member (x < d/2), For lb /d ≤ 0.2: LRFD

ASD

φRn = φR3 + lb(φR4)

(9-47a)

Rn /Ω = R3 /Ω + lb(R4 /Ω)

(9-47b)

For lb /d > 0.2: LRFD

ASD

φRn = φR5 + lb(φR6)

(9-48a)

Rn /Ω = R5 /Ω + lb(R6 /Ω)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(9-48b)

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DESIGN TABLE DISCUSSION

When the compressive force to be resisted is applied at a distance, x, from the member end that is greater than or equal to one-half of the depth of the member (x ≥ d/2), LRFD

ASD

φRn = 2[(φR3) + lb(φR4)]

(9-49a)

Rn /Ω = 2[(R3 /Ω) + lb(R4 /Ω)]

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(9-49b)

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DESIGN OF CONNECTING ELEMENTS

PART 9 REFERENCES ACI/ASCE/TMS (2005a), Building Code Requirements for Masonry Structures, ACI 530/ASCE 5/TMS 402, Farmington Hills, MI. ACI/ASCE/TMS (2005b), Specification for Masonry Structures, ACI 530.1/ASCE 6/ TMS 602, Farmington Hills, MI. AWS (2010), Structural Welding Code—Steel, AWS D1.1/D1.1M, American Welding Society, Miami, FL. Carter, C.J. (1999), Stiffening of Wide-Flange Columns at Moment Connections: Wind and Seismic Applications, Design Guide 13, AISC, Chicago, IL. Cheng J.J. and Yura, J.A. (1986), “Local Web Buckling of Coped Beams,” Journal of Structural Engineering, ASCE Vol. 112, No. 10, pp. 2,314–2,331. Dowswell, R.S. (2011), “A Yield Line Component Method for Bolted Flange Connections,” Engineering Journal, AISC, Vol. 48, No. 2, 2nd Quarter, Chicago, IL. Muir, L.S. and Hewitt, C.M. (2009), “Design of Unstiffened Extended Single-Plate Shear Connections,” Engineering Journal, AISC, Vol. 46, No. 2, 2nd Quarter, pp. 67–79, Chicago, IL. Swanson, J.A. (2002), “Ultimate Strength Prying Models for Bolted T-Stub Connections,” Engineering Journal, Vol. 39, No. 3, 3rd Quarter, pp. 136–147, AISC, Chicago, IL. Thornton, W.A. (1992), “Strength and Serviceability of Hanger Connections,” Engineering Journal, AISC, Vol. 29, No. 4, 4th Quarter, pp. 145–149, Chicago, IL. See also ERRATA, Engineering Journal, Vol. 33, No. 1, 1st Quarter, 1996, pp. 39, 40. Thornton, W.A. (1996), “Rational Design of Tee Shear Connections,” Engineering Journal, AISC, Vol. 33, No.1, 1st Quarter, pp. 34–37, Chicago, IL. Wheeler, A.T., Clarke, M.J., Hancock, G.J. and Murray, T.M. (1998), “Design Model for Bolted Moment End-Plate Connections Joining Rectangular Hollow Sections,” Journal of Structural Engineering, ASCE, Vol. 124, No. 2. Whitmore, R.E. (1952), “Experimental Investigation of Stresses in Gusset Plates,” Bulletin No. 16, Civil Engineering, The University of Tennessee Engineering Experiment Station, Knoxville, TN.

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DESIGN TABLES

Table 9-1

Reduction in Area for Holes, in.2

Thickness t, in. 3⁄16 1⁄4 5⁄16 3⁄8 7⁄16 1⁄2 9⁄16 5⁄8 11⁄16 3⁄4 13⁄16 7⁄8 15⁄16

1 Thickness t, in. 3⁄16 1⁄4 5⁄16 3⁄8 7⁄16 1⁄2 9⁄16 5⁄8 11⁄16 3⁄4 13⁄16 7⁄8 15⁄16

1

3

/4

7

/8

A×t Bolt Diameter, d , in. 11/8 11/4 1

13/8

11/2

3

/4

7

/8

B×t Bolt Diameter, d , in. 11/8 11/4 1

13/8

11/2

0.164 0.188 0.211 0.234 0.258 0.281 0.305 0.188 0.211 0.246 0.281 0.305 0.328 0.352 0.219 0.250 0.281 0.313 0.344 0.375 0.406 0.250 0.281 0.328 0.375 0.406 0.438 0.469 0.273 0.328 0.383 0.438

0.313 0.375 0.438 0.500

0.352 0.422 0.492 0.563

0.391 0.469 0.547 0.625

0.430 0.516 0.602 0.688

0.469 0.563 0.656 0.750

0.508 0.609 0.711 0.813

0.313 0.375 0.438 0.500

0.352 0.422 0.492 0.563

0.410 0.492 0.574 0.656

0.469 0.563 0.656 0.750

0.508 0.609 0.711 0.813

0.547 0.656 0.766 0.875

0.586 0.703 0.820 0.938

0.492 0.547 0.602 0.656

0.563 0.625 0.688 0.750

0.633 0.703 0.773 0.844

0.703 0.781 0.859 0.938

0.773 0.859 0.945 1.03

0.844 0.938 1.03 1.13

0.914 1.02 1.12 1.22

0.563 0.625 0.688 0.750

0.633 0.703 0.773 0.844

0.738 0.820 0.902 0.984

0.844 0.938 1.03 1.13

0.914 1.02 1.12 1.22

0.984 1.09 1.20 1.31

1.05 1.17 1.29 1.41

0.711 0.766 0.820 0.875

0.813 0.875 0.938 1.00

0.914 0.984 1.05 1.13

1.02 1.09 1.17 1.25

1.12 1.20 1.29 1.38

1.22 1.31 1.41 1.50

1.32 1.42 1.52 1.63

0.813 0.875 0.938 1.00

0.914 0.984 1.05 1.13

1.07 1.15 1.23 1.31

1.22 1.31 1.41 1.50

1.32 1.42 1.52 1.63

1.42 1.53 1.64 1.75

1.52 1.64 1.76 1.88

13/8

11/2

3

/4

7

/8

C×t Bolt Diameter, d , in. 11/8 11/4 1

13/8

11/2

3

/4

7

/8

D×t Bolt Diameter, d , in. 11/8 11/4 1

0.199 0.223 0.258 0.293 0.316 0.340 0.363 0.363 0.422 0.480 0.539 0.598 0.656 0.715 0.266 0.297 0.344 0.391 0.422 0.453 0.484 0.484 0.563 0.641 0.719 0.797 0.875 0.953 0.332 0.371 0.430 0.488 0.527 0.566 0.605 0.605 0.703 0.801 0.898 0.996 1.09 0.398 0.445 0.516 0.586 0.633 0.680 0.727 0.727 0.844 0.961 1.08 1.20 1.31 0.465 0.520 0.602 0.684 0.738 0.793 0.848 0.848 0.984 1.12 1.26 1.39 1.53

1.19 1.43 1.67

0.531 0.598 0.664 0.730 0.797

0.594 0.668 0.742 0.816 0.891

0.688 0.773 0.859 0.945 1.03

0.781 0.879 0.977 1.07 1.17

0.844 0.949 1.05 1.16 1.27

0.906 1.02 1.13 1.25 1.36

0.969 1.09 1.21 1.33 1.45

0.969 1.09 1.21 1.33 1.45

1.13 1.27 1.41 1.55 1.69

1.28 1.44 1.60 1.76 1.92

1.44 1.62 1.80 1.98 2.16

1.59 1.79 1.99 2.19 2.39

1.75 1.97 2.19 2.41 2.63

1.91 2.14 2.38 2.62 2.86

0.863 0.930 0.996 1.06

0.965 1.04 1.11 1.19

1.12 1.20 1.29 1.38

1.27 1.37 1.46 1.56

1.37 1.48 1.58 1.69

1.47 1.59 1.70 1.81

1.57 1.70 1.82 1.94

1.57 1.70 1.82 1.94

1.83 1.97 2.11 2.25

2.08 2.24 2.40 2.56

2.34 2.52 2.70 2.88

2.59 2.79 2.99 3.19

2.84 3.06 3.28 3.50

3.10 3.34 3.57 3.81

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Table 9-2

Elastic Section Modulus for Coped W-Shapes

Snet , in.3 dc , in.

Shape

d, in.

tf , in.

Sx , in.3

So , in.3

2

3

4

5

6

7

8

9

10

W44×335 ×290 ×262 ×230

44.0 43.6 43.3 42.9

1.77 1.58 1.42 1.22

1410 1240 1110 971

494 415 372 330

453 380 340 301

433 363 325 288

413 346 310 274

394 330 295 261

375 314 281 249

357 298 267 236

339 283 253 224

321 268 240 212

304 254 227 200

W40×593 ×503 ×431 ×397 ×372 ×362 ×324 ×297 ×277 ×249 ×215 ×199

43.0 42.1 41.3 41.0 40.6 40.6 40.2 39.8 39.7 39.4 39.0 38.7

3.23 2.75 2.36 2.20 2.05 2.01 1.81 1.65 1.58 1.42 1.22 1.07

2340 1980 1690 1560 1460 1420 1280 1170 1100 993 859 770

810 671 567 512 480 463 408 374 335 299 256 247

— — — — — — 371 339 304 271 231 224

— 582 491 444 415 400 352 323 289 258 220 213

671 554 467 422 394 380 335 306 274 245 208 202

639 527 444 400 374 361 317 290 260 232 197 191

607 500 421 379 354 342 300 275 246 219 186 180

575 473 398 359 335 323 284 259 232 207 176 170

545 448 376 339 316 305 268 245 219 195 166 160

515 423 355 319 298 287 252 230 206 183 156 150

486 398 334 300 280 270 237 216 193 172 146 141

W40×392 ×331 ×327 ×294 ×278 ×264 ×235 ×211 ×183 ×167 ×149

41.6 40.8 40.8 40.4 40.2 40.0 39.7 39.4 39.0 38.6 38.2

2.52 2.13 2.13 1.93 1.81 1.73 1.58 1.42 1.20 1.03 0.830

1440 1210 1200 1080 1020 971 875 786 675 600 513

579 483 470 417 397 371 320 286 243 234 217

— — — 379 361 337 291 259 221 212 196

503 419 407 360 344 321 276 246 210 201 186

478 398 387 342 326 305 262 234 199 191 177

454 378 367 325 310 289 249 221 188 181 167

431 358 348 308 293 274 235 209 178 171 158

408 339 329 291 277 259 222 198 168 161 149

386 320 311 275 262 244 210 186 158 152 140

364 302 293 259 246 230 197 175 149 143 132

343 284 276 243 232 216 185 165 140 134 123

—Indicates that cope depth is less than flange thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN TABLES

Table 9-2 (continued)

Elastic Section Modulus for Coped W-Shapes

Snet , in.3 dc , in.

Shape

d, in.

tf , in.

Sx , in.3

So , in.3

2

3

4

5

6

7

8

9

10

W36×652 ×529 ×487 ×441 ×395 ×361 ×330 ×302 ×282 ×262 ×247 ×231

41.1 39.8 39.3 38.9 38.4 38.0 37.7 37.3 37.1 36.9 36.7 36.5

3.54 2.91 2.68 2.44 2.20 2.01 1.85 1.68 1.57 1.44 1.35 1.26

2460 1990 1830 1650 1490 1350 1240 1130 1050 972 913 854

816 636 581 518 457 412 371 338 314 294 277 260

— — — — — — 335 305 283 264 249 234

— 547 499 444 391 352 317 289 268 250 236 222

669 519 473 420 370 333 300 273 253 236 223 209

635 491 448 398 350 315 283 258 239 223 210 197

601 464 423 375 330 297 267 243 225 210 198 186

568 438 399 354 311 279 251 228 211 197 185 174

536 413 375 332 292 262 235 214 198 185 174 163

505 388 352 312 274 246 220 200 185 172 162 152

475 364 330 292 256 230 206 187 173 161 151 142

W36×256 ×232 ×210 ×194 ×182 ×170 ×160 ×150 ×135

37.4 37.1 36.7 36.5 36.3 36.2 36.0 35.9 35.6

1.73 1.57 1.36 1.26 1.18 1.10 1.02 0.940 0.790

895 809 719 664 623 581 542 504 439

329 295 272 249 234 218 206 195 181

297 266 245 224 211 196 185 176 163

281 251 232 212 199 185 175 166 154

266 238 219 201 188 175 165 157 145

251 224 207 189 178 165 156 148 137

237 211 195 178 167 155 147 139 129

223 199 183 167 157 146 138 130 121

209 186 172 157 147 137 129 122 113

196 174 161 146 137 128 120 114 105

183 163 150 137 128 119 112 106 98.1

W33×387 ×354 ×318 ×291 ×263 ×241 ×221 ×201

36.0 35.6 35.2 34.8 34.5 34.2 33.9 33.7

2.28 2.09 1.89 1.73 1.57 1.40 1.28 1.15

1350 1240 1110 1020 919 831 759 686

413 373 330 300 268 250 230 209

— — 295 268 239 223 205 186

349 315 278 253 226 210 193 175

329 297 262 238 212 197 181 165

310 279 246 223 199 185 170 154

291 262 230 209 186 173 159 144

272 245 216 195 174 162 148 135

254 229 201 182 162 150 138 125

237 213 187 169 151 140 128 116

220 198 173 157 139 129 118 107

—Indicates that cope depth is less than flange thickness.

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Table 9-2 (continued)

Elastic Section Modulus for Coped W-Shapes

So , in.3

Snet , in.3 dc , in.

Shape

d, in.

tf , in.

Sx , in.3

2

3

4

5

W33×169 ×152 ×141 ×130 ×118

33.8 33.5 33.3 33.1 32.9

1.22 1.06 0.960 0.855 0.740

549 487 448 406 359

191 176 165 155 143

170 157 147 138 128

161 148 139 130 120

151 139 130 122 113

141 130 122 114 106

132 124 115 107 122 114 106 97.9 114 106 98.8 91.6 107 99.6 92.5 85.7 98.6 91.9 85.4 79.1

W30×391 ×357 ×326 ×292 ×261 ×235 ×211 ×191 ×173

33.2 32.8 32.4 32.0 31.6 31.3 30.9 30.7 30.4

2.44 2.24 2.05 1.85 1.65 1.50 1.32 1.19 1.07

1250 1140 1040 930 829 748 665 600 541

378 339 305 269 240 211 192 174 158

— — — 238 212 186 170 153 139

315 282 254 223 198 174 159 143 130

295 264 237 208 185 163 148 133 121

276 246 221 194 172 152 138 124 112

257 230 206 180 160 141 128 115 104

W30×148 ×132 ×124 ×116 ×108 ×99 ×90

30.7 30.3 30.2 30.0 29.8 29.7 29.5

1.18 1.00 0.930 0.850 0.760 0.670 0.610

436 380 355 329 299 269 245

152 139 131 124 118 110 98.7

134 123 115 109 103 96.4 86.7

125 117 109 101 115 107 99.3 92.1 108 100 93.4 86.5 102 95.3 88.6 82.1 96.5 89.9 83.6 77.4 90.0 83.9 77.9 72.1 80.9 75.4 70.0 64.8

W27×539 ×368 ×336 ×307 ×281 ×258 ×235 ×217 ×194 ×178 ×161 ×146

32.5 30.4 30.0 29.6 29.3 29.0 28.7 28.4 28.1 27.8 27.6 27.4

3.54 1570 509 2.48 1060 321 2.28 972 287 2.09 887 259 1.93 814 233 1.77 745 212 1.61 677 193 1.50 627 174 1.34 559 155 1.19 505 145 1.08 458 131 0.975 414 118

— — — — 203 185 168 152 134 126 113 102

— 262 234 211 189 172 156 141 125 117 105 95.0

394 244 218 196 176 159 145 130 115 108 97.2 87.7

367 226 202 181 162 147 134 120 106 99.7 89.5 80.7

6

341 209 186 167 150 136 123 111 97.6 91.5 82.0 74.0

—Indicates that cope depth is less than flange thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7

8

9

10 98.6 90.5 84.6 79.2 73.0

239 213 191 167 148 130 118 106 96.1

222 197 177 155 137 120 109 97.7 88.4

205 182 163 142 126 110 99.8 89.6 81.0

188 167 150 130 115 101 91.2 81.8 73.9

93.3 85.1 79.9 75.8 71.4 66.5 59.7

86.0 78.3 73.6 69.7 65.7 61.1 54.9

78.9 71.8 67.4 63.9 60.1 56.0 50.2

72.1 65.5 61.5 58.2 54.8 51.0 45.7

316 193 172 154 137 124 113 101 89.3 83.6 74.9 67.5

292 177 157 141 126 114 103 92.3 81.3 76.1 68.1 61.3

269 162 143 128 114 103 93.2 83.7 73.6 68.8 61.5 55.3

247 147 130 116 104 93.3 84.2 75.5 66.3 61.9 55.3 49.7

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DESIGN TABLES

Table 9-2 (continued)

Elastic Section Modulus for Coped W-Shapes

Shape

tf , in.

Sx , in.3

W27×129 ×114 ×102 ×94 ×84

27.6 27.3 27.1 26.9 26.7

1.10 0.930 0.830 0.745 0.640

345 299 267 243 213

117 101 106 91.6 94.2 81.6 88.0 76.2 80.5 69.7

W24×370 ×335 ×306 ×279 ×250 ×229 ×207 ×192 ×176 ×162 ×146 ×131 ×117 ×104

28.0 27.5 27.1 26.7 26.3 26.0 25.7 25.5 25.2 25.0 24.7 24.5 24.3 24.1

2.72 2.48 2.28 2.09 1.89 1.73 1.57 1.46 1.34 1.22 1.09 0.960 0.850 0.750

957 864 789 718 644 588 531 491 450 414 371 329 291 258

295 261 234 210 184 167 149 136 124 115 104 94.4 84.4 75.4

W24×103 ×94 ×84 ×76 ×68

24.5 24.3 24.1 23.9 23.7

0.980 0.875 0.770 0.680 0.585

245 222 196 176 154

W24×62 ×55

23.7 0.590 23.6 0.505

131 114

W21×201 ×182 ×166 ×147 ×132 ×122 ×111 ×101

23.0 22.7 22.5 22.1 21.8 21.7 21.5 21.4

461 417 380 329 295 273 249 227

1.63 1.48 1.36 1.15 1.04 0.960 0.875 0.800

So , in.3

Snet , in.3 dc , in.

d, in.

2

3

4

5

6

7

8

9

10

94.0 84.9 75.6 70.6 64.5

86.9 78.4 69.8 65.1 59.5

80.1 72.2 64.2 59.9 54.7

73.5 66.2 58.9 54.9 50.1

67.2 60.5 53.7 50.1 45.7

61.1 54.9 48.8 45.4 41.4

55.3 49.6 44.0 41.0 37.4

49.7 44.6 39.5 36.8 33.5

— — — — 158 143 127 117 106 98.0 88.5 80.3 71.7 64.1

237 209 186 167 146 132 117 107 97.6 90.0 81.2 73.7 65.7 58.7

219 193 172 154 134 121 107 98.2 89.4 82.3 74.2 67.3 60.0 53.5

201 177 157 141 123 111 98.0 89.5 81.4 74.9 67.5 61.1 54.5 48.6

184 162 144 128 112 101 89.0 81.2 73.8 67.9 61.1 55.3 49.2 43.8

168 147 131 116 101 91.0 80.4 73.3 66.5 61.1 54.9 49.7 44.2 39.3

82.9 76.2 68.3 62.6 57.5

70.7 64.9 58.0 53.2 48.8

64.9 59.5 53.2 48.7 44.7

59.3 54.3 48.6 44.5 40.8

53.9 49.4 44.1 40.4 37.0

48.8 44.6 39.8 36.4 33.4

43.9 40.1 35.8 32.7 29.9

39.2 35.8 31.9 29.1 26.6

34.8 31.7 28.2 25.8 23.5

30.6 27.9 24.8 22.6 20.6

56.9 51.1

48.3 43.4

44.3 39.7

40.4 36.2

36.7 32.9

33.1 29.7

29.7 26.6

26.5 23.7

23.4 20.9

20.5 18.3

125 105 111 93.3 99.3 83.0 91.2 76.1 81.0 67.5 74.1 61.6 67.1 55.7 60.4 50.1

95.2 84.8 75.3 68.9 61.1 55.7 50.4 45.3

86.2 76.6 68.0 62.1 55.0 50.2 45.3 40.7

77.6 68.8 61.0 55.7 49.2 44.8 40.4 36.3

69.4 61.4 54.4 49.5 43.7 39.8 35.9 32.1

61.6 54.4 48.1 43.7 38.5 35.0 31.5 28.2

54.2 47.8 42.2 38.2 33.6 30.5 27.4 24.5

47.3 41.6 36.6 33.1 29.0 26.3 23.6 21.1

40.8 35.8 31.4 28.2 24.7 22.4 20.1 17.9

—Indicates that cope depth is less than flange thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

153 138 124 133 120 108 118 106 94.9 105 94.3 84.0 91.2 81.7 72.6 81.8 73.1 64.9 72.2 64.4 57.0 65.8 58.6 51.8 59.6 53.0 46.8 54.7 48.6 42.8 49.1 43.6 38.3 44.3 39.3 34.5 39.4 34.8 30.5 35.0 30.9 27.1

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9–28

DESIGN OF CONNECTING ELEMENTS

Table 9-2 (continued)

Elastic Section Modulus for Coped W-Shapes

Snet , in.3 dc , in.

Shape

d, in.

tf , in.

Sx , in.3

So , in.3

2

3

4

5

6

7

8

9

10

W21×93 ×83 ×73 ×68 ×62 ×55 ×48

21.6 21.4 21.2 21.1 21.0 20.8 20.6

0.930 0.835 0.740 0.685 0.615 0.522 0.430

192 171 151 140 127 110 93.0

67.2 59.0 51.5 48.1 44.1 40.1 36.2

56.0 49.1 42.7 39.9 36.5 33.2 30.0

50.7 44.4 38.7 36.1 33.0 30.0 27.0

45.7 40.0 34.8 32.4 29.7 26.9 24.2

40.9 35.7 31.0 29.0 26.5 24.0 21.6

36.3 31.7 27.5 25.6 23.4 21.2 19.1

32.0 27.9 24.2 22.5 20.5 18.6 16.7

27.9 24.3 21.0 19.6 17.8 16.1 14.5

24.1 20.9 18.1 16.8 15.3 13.8 12.4

20.5 17.8 15.3 14.2 12.9 11.7 10.4

W21×57 ×50 ×44

21.1 0.650 111 20.8 0.535 94.5 20.7 0.450 81.6

43.4 39.2 35.2

36.1 32.5 29.1

32.6 29.4 26.3

29.3 26.4 23.6

26.2 23.6 21.0

23.2 20.4 20.8 18.3 18.6 16.3

17.7 15.9 14.1

15.2 13.6 12.1

12.9 11.5 10.2

W18×311 ×283 ×258 ×234 ×211 ×192 ×175 ×158 ×143 ×130 ×119 ×106 ×97 ×86 ×76

22.3 21.9 21.5 21.1 20.7 20.4 20.0 19.7 19.5 19.3 19.0 18.7 18.6 18.4 18.2

2.74 2.50 2.30 2.11 1.91 1.75 1.59 1.44 1.32 1.20 1.06 0.940 0.870 0.770 0.680

66.5 57.6 50.0 43.0 37.1 32.1 28.4 24.6 21.5 19.0 17.6 15.2 13.5 11.7 10.1

56.8 48.9 42.3 36.1 31.0 26.7 23.5

W18×71 ×65 ×60 ×55 ×50

18.5 18.4 18.2 18.1 18.0

0.810 127 0.750 117 0.695 108 0.630 98.3 0.570 88.9

W18×46 ×40 ×35

18.1 0.605 17.9 0.525 17.7 0.425

624 565 514 466 419 380 344 310 282 256 231 204 188 166 146

78.8 68.4 57.6

186 166 148 130 115 102 92.1 81.7 72.5 65.2 61.7 54.4 48.9 43.1 37.6

— 140 126 113 100 — 124 111 99.3 87.8 — 110 98.3 87.4 77.2 — 96.1 85.9 76.2 67.1 94.5 84.8 75.6 66.9 58.7 83.4 74.7 66.5 58.7 51.4 75.1 67.2 59.7 52.6 45.9 66.4 59.3 52.6 46.2 40.2 58.8 52.4 46.4 40.7 35.4 52.8 47.0 41.5 36.4 31.5 49.8 44.3 39.1 34.2 29.5 43.8 38.9 34.3 29.9 25.8 39.3 34.9 30.7 26.8 23.1 34.6 30.6 26.9 23.4 20.2 30.1 26.7 23.4 20.3 17.5

88.2 77.1 67.5 58.5 51.0 44.5 39.6 34.6 30.4 27.0 25.2 22.0 19.6 17.1 14.8

77.0 67.0 58.5 50.4 43.8 38.1 33.8 29.4 25.7 22.8 21.2 18.5 16.4 14.3 12.3

42.4 38.3 35.0 32.4 29.1

34.1 30.8 28.1 26.0 23.4

30.3 27.3 24.9 23.0 20.7

26.7 24.0 21.9 20.2 18.2

23.3 20.9 19.1 17.6 15.8

20.1 18.0 16.4 15.1 13.5

17.1 15.3 13.9 12.8 11.5

14.3 11.8 12.8 10.5 11.6 9.53 10.7 8.72 9.54

28.9 24.9 22.7

23.2 20.0 18.2

20.6 17.7 16.1

18.1 15.5 14.1

15.7 13.5 12.3

13.5 11.5 11.6 9.80 10.5 8.88

—Indicates that cope depth is less than flange thickness. Note: Values are omitted when cope depth exceeds d /2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.56 8.16 7.37

7.81

AISC_PART 9:14th Ed.

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Page 29

9–29

DESIGN TABLES

Table 9-2 (continued)

Elastic Section Modulus for Coped W-Shapes

Shape

d, in.

tf , in.

W16×100 ×89 ×77 ×67

17.0 16.8 16.5 16.3

0.985 0.875 0.760 0.665

W16×57 ×50 ×45 ×40 ×36

16.4 16.3 16.1 16.0 15.9

0.715 0.630 0.565 0.505 0.430

W16×31 ×26

15.9 0.440 15.7 0.345

W14×730 ×665 ×605 ×550 ×500 ×455 ×426 ×398 ×370 ×342 ×311 ×283 ×257 ×233 ×211 ×193 ×176 ×159 ×145

22.4 21.6 20.9 20.2 19.6 19.0 18.7 18.3 17.9 17.5 17.1 16.7 16.4 16.0 15.7 15.5 15.2 15.0 14.8

Sx , in.3

So , in.3

Snet , in.3 dc , in. 2

3

4

5

6

44.4 39.0 33.1 28.3

34.9 30.6 25.9 22.1

30.5 26.7 22.6 19.2

26.4 23.1 19.4 16.5

22.6 19.7 16.5 14.0

19.0 16.5 13.8 11.7

92.2 81.0 72.7 64.7 56.5

29.4 25.6 22.9 20.1 18.8

23.0 20.0 17.9 15.6 14.6

20.1 17.4 15.5 13.6 12.7

17.3 15.0 13.4 11.7 10.9

14.8 12.4 10.2 12.7 10.7 8.74 11.3 9.47 7.75 9.89 8.24 6.73 9.21 7.67 6.25

47.2 38.4

17.1 14.9

13.3 11.6

11.6 10.1

175 155 134 117

4.91 1280 4.52 1150 4.16 1040 3.82 931 3.50 838 3.21 756 3.04 706 2.85 656 2.66 607 2.47 558 2.26 506 2.07 459 1.89 415 1.72 375 1.56 338 1.44 310 1.31 281 1.19 254 1.09 232

365 317 275 238 208 182 164 150 135 122 107 94.4 83.1 73.2 64.9 57.6 52.2 45.7 40.9

— — — — — — — — — — — — — — — 104 — 93.7 — 83.4 — 72.7 — 63.6 64.1 55.5 56.1 48.4 49.5 42.6 43.8 37.5 39.5 33.8 34.5 29.4 30.7 26.1

9.96 8.64 — — — 153 131 113 101 91.1 81.4 72.3 62.7 54.6 47.4 41.3 36.1 31.7 28.5 24.7 21.9

8.44 7.31 220 187 158 134 115 98.2 87.6 78.7 70.1 61.9 53.5 46.3 40.0 34.6 30.2 26.4 23.6 20.4 18.0

7.03 6.08 195 165 139 117 99.4 84.6 75.2 67.2 59.6 52.3 44.9 38.7 33.3 28.6 24.8 21.6 19.2 16.5 14.5

—Indicates that cope depth is less than flange thickness. Note: Values are omitted when cope depth exceeds d /2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7

8

9

10

15.7 12.8 13.6 11.0 11.4 9.13 9.58 7.66 8.17 6.99 6.19 5.35

5.73 4.95 172 151 132 114 144 126 109 93.3 121 105 89.6 76.2 101 86.9 73.8 62.1 85.3 72.5 60.9 72.1 60.7 50.6 63.8 53.4 44.2 56.7 47.2 38.7 50.0 41.3 43.6 35.8 37.2 30.2 31.8 25.6 27.1 21.6 23.2 18.3 19.9 17.3 15.2 13.0 11.4

AISC_PART 9:14th Ed.

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Page 30

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DESIGN OF CONNECTING ELEMENTS

Table 9-2 (continued)

Elastic Section Modulus for Coped W-Shapes

Shape

tf , in.

W14×132 ×120 ×109 ×99 ×90

14.7 14.5 14.3 14.2 14.0

1.03 0.940 0.860 0.780 0.710

W14×82 ×74 ×68 ×61

14.3 14.2 14.0 13.9

0.855 123 0.785 112 0.720 103 0.645 92.1

W14×53 ×48 ×43

13.9 0.660 13.8 0.595 13.7 0.530

77.8 70.2 62.6

19.1 14.2 17.3 12.8 15.3 11.3

12.0 10.8 9.49

W14×38 ×34 ×30

14.1 0.515 14.0 0.455 13.8 0.385

54.6 48.6 42.0

W14×26 ×22

13.9 0.420 13.7 0.335

35.3 29.0

W12×336 ×305 ×279 ×252 ×230 ×210 ×190 ×170 ×152 ×136 ×120 ×106 ×96 ×87 ×79 ×72 ×65

16.8 16.3 15.9 15.4 15.1 14.7 14.4 14.0 13.7 13.4 13.1 12.9 12.7 12.5 12.4 12.3 12.1

2.96 2.71 2.47 2.25 2.07 1.90 1.74 1.56 1.40 1.25 1.11 0.990 0.900 0.810 0.735 0.670 0.605

Sx , in.3 209 190 173 157 143

So , in.3

Snet , in.3 dc , in.

d, in.

2

3

4

5

38.1 34.2 30.0 27.2 24.3

28.6 25.5 22.3 20.2 18.0

24.3 21.7 18.9 17.0 15.2

20.3 18.1 15.7 14.2 12.6

16.7 14.8 12.8 11.5 10.2

28.0 24.4 22.2 19.7

20.9 18.2 16.5 14.6

17.7 15.4 13.9 12.3

14.8 12.8 11.6 10.2

12.1 10.4 9.41 8.28

9.64 8.31 7.46 6.54

9.93 8.93 7.84

8.07 7.23 6.34

6.39 5.71 4.99

16.0 12.0 10.2 14.4 10.8 9.14 13.2 9.88 8.37

8.48 7.62 6.96

6.94 6.22 5.68

5.54 4.95 4.51

12.3 10.7

7.80 6.75

6.50 5.62

5.31 4.58

4.23 3.64

83.1 71.4 63.1 54.2 47.5 41.6 35.7 30.7 26.5 22.9 19.7 16.3 14.3 13.0 11.5 10.3 9.16

71.4 61.0 53.5 45.7 39.9 34.7 29.7 25.3 21.7 18.7 16.0 13.2 11.5 10.4 9.23 8.24 7.28

60.6 51.4 44.8 38.0 32.9 28.5 24.2 20.5 17.5 14.9 12.6 10.4 9.03 8.11 7.16 6.37 5.61

50.8 42.7 36.9 31.0 26.7 22.9 19.3 16.2 13.7 11.6 9.70 7.91 6.83 6.09 5.35 4.73 4.14

483 123 435 108 393 96.1 353 83.7 321 74.2 292 65.6 263 57.0 235 49.6 209 43.3 186 37.9 163 32.8 145 27.6 131 24.3 118 22.2 107 19.9 97.4 17.9 87.9 16.0

9.20 7.97 — — — — — 49.0 42.3 36.5 31.6 27.5 23.7 19.8 17.4 15.8 14.1 12.6 11.2

6

7

8

13.4 10.5 11.8 9.20 10.2 7.91 9.15 7.04 8.07 6.18

—Indicates that cope depth is less than flange thickness. Note: Values are omitted when cope depth exceeds d /2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7.46 6.40 5.72

4.28

41.9 34.9 29.8 24.8 21.1 17.9 14.9 12.4

34.1 28.0

9

10

AISC_PART 9:14th Ed.

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8:19 AM

Page 31

9–31

DESIGN TABLES

Table 9-2 (continued)

Elastic Section Modulus for Coped W-Shapes

Shape

d, in.

tf , in.

Sx , in.3

Snet , in.3 dc , in.

So , in.3

2

3

W12×58 ×53

12.2 0.640 12.1 0.575

78.0 14.8 70.6 13.9

10.4 9.75

8.52 7.94

6.79 5.24 6.31 4.85

3.88 3.58

W12×50 ×45 ×40

12.2 0.640 12.1 0.575 11.9 0.515

64.2 14.8 57.7 13.1 51.5 11.4

10.4 9.27 8.03

8.54 7.56 6.54

6.82 5.27 6.02 4.63 5.19 3.98

3.91 3.42

W12×35 ×30 ×26

12.5 0.520 12.3 0.440 12.2 0.380

45.6 12.3 38.6 10.5 33.4 9.08

8.85 7.47 6.47

7.30 6.15 5.32

5.89 4.61 4.94 3.86 4.27 3.32

3.48 2.90 2.48

W12×22 ×19 ×16 ×14

12.3 12.2 12.0 11.9

0.425 0.350 0.265 0.225

25.4 21.3 17.1 14.9

9.60 8.39 7.43 6.61

6.89 6.01 5.30 4.71

5.69 4.95 4.36 3.86

4.59 3.98 3.50 3.10

3.59 3.11 2.72 2.41

2.71 2.33

W10×112 ×100 ×88 ×77 ×68 ×60 ×54 ×49

11.4 11.1 10.8 10.6 10.4 10.2 10.1 10.0

1.25 126 1.12 112 0.990 98.5 0.870 85.9 0.770 75.7 0.680 66.7 0.615 60.0 0.560 54.6

25.7 22.3 19.1 16.2 13.9 12.1 10.5 9.49

17.5 13.9 10.8 15.0 11.9 9.12 12.8 10.0 7.62 10.7 8.35 6.29 9.13 7.10 5.30 7.88 6.09 4.52 6.78 5.22 3.85 6.13 4.71 3.46

8.02 6.72 5.54 4.52 3.77 3.18 2.69 2.40

W10×45 ×39 ×33

10.1 0.620 9.92 0.530 9.73 0.435

49.1 42.1 35.0

9.75 8.49 7.49

6.33 5.48 4.80

4.88 4.20 3.67

3.61 2.52 3.08 2.67

W10×30 ×26 ×22

10.5 0.510 10.3 0.440 10.2 0.360

32.4 27.9 23.2

8.64 7.33 6.51

5.75 4.86 4.29

4.51 3.80 3.34

3.41 2.45 2.85 2.04 2.50 1.77

W10×19 ×17 ×15 ×12

10.2 10.1 9.99 9.87

18.8 16.2 13.8 10.9

6.52 6.01 5.53 4.43

4.33 3.98 3.65 2.91

3.39 3.10 2.84 2.26

2.55 1.82 2.33 1.65 2.12 1.50 1.68

0.395 0.330 0.270 0.210

4

5

6

Note: Values are omitted when cope depth exceeds d /2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7

8

9

10

AISC_PART 9:14th Ed.

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Page 32

9–32

DESIGN OF CONNECTING ELEMENTS

Table 9-2 (continued)

Elastic Section Modulus for Coped W-Shapes

Shape

d, in.

tf , in.

Sx , in.3

So , in.3

W8×67 ×58 ×48 ×40 ×35 ×31

9.00 8.75 8.50 8.25 8.12 8.00

0.935 0.810 0.685 0.560 0.495 0.435

60.4 52.0 43.2 35.5 31.2 27.5

12.2 10.4 7.89 6.71 5.66 5.06

W8×28 ×24

Snet , in.3 dc , in. 2

3

4

7.42 6.24 4.63 3.89 3.24 2.88

5.44 4.52 3.32 2.74 2.28 2.01

3.77 3.08 2.21 1.80 1.47 1.28

8.06 0.465 24.3 7.93 0.400 20.9

5.04 2.89 4.23 2.40

2.02 1.67

1.30

W8×21 ×18

8.28 0.400 18.2 8.14 0.330 15.2

4.55 2.67 4.02 2.35

1.91 1.66

1.26 1.09

W8×15 ×13 ×10

8.11 0.315 11.8 7.99 0.255 9.91 7.89 0.205 7.81

4.03 2.36 3.61 2.10 2.65 1.54

1.68 1.49 1.08

1.10

5

6

Note: Values are omitted when cope depth exceeds d /2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7

8

9

10

AISC_PART 9:14th Ed.

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8:19 AM

Page 33

9–33

DESIGN TABLES

Table 9-3a

Block Shear Tension Rupture Component

Ubs = 1.0

per inch of thickness, kips/in. Fu

58 ksi Bolt diameter, d , in. 3

7

/4

/8

Leh , in.

F u A nt ᎏ tΩ

φ Fu A nt ᎏ t

ASD 1 11⁄8 11⁄4 13⁄8 11⁄2 15⁄8 13⁄4 17⁄8 2 21⁄4 21⁄2 23⁄4 3

16.3 19.9 23.6 27.2 30.8 34.4 38.1 41.7 45.3 52.6 59.8 67.1 74.3

φ Fu A nt ᎏ t

LRFD

ASD

LRFD

21.8 27.2 32.6 38.1 43.5 48.9 54.4 59.8 65.3 76.1 87.0 97.9 109

12.7 16.3 19.9 23.6 27.2 30.8 34.4 38.1 41.7 48.9 56.2 63.4 70.7

19.0 24.5 29.9 35.3 40.8 46.2 51.7 57.1 62.5 73.4 84.3 95.2 106

φ Fu A nt ᎏ t

LRFD

ASD

24.5 29.9 35.3 40.8 46.2 51.7 57.1 62.5 68.0 78.8 89.7 101 111

14.5 18.1 21.8 25.4 29.0 32.6 36.3 39.9 43.5 50.7 58.0 65.3 72.5

Fu

65 ksi Bolt diameter, d , in. 3

7

/4

/8

Leh , in.

F u A nt ᎏ tΩ

φ Fu A nt ᎏ t

ASD 1 11⁄ 8 11⁄4 13⁄ 8 11⁄2 15⁄ 8 13⁄4 17⁄ 8 2 21⁄4 21⁄2 23⁄4 3

18.3 22.3 26.4 30.5 34.5 38.6 42.7 46.7 50.8 58.9 67.0 75.2 83.3

ASD

1 F u A nt ᎏ tΩ

F u A nt ᎏ tΩ

1

F u A nt ᎏ tΩ

φ Fu A nt ᎏ t

F u A nt ᎏ tΩ

φ Fu A nt ᎏ t

LRFD

ASD

27.4 33.5 39.6 45.7 51.8 57.9 64.0 70.1 76.2 88.4 101 113 125

16.3 20.3 24.4 28.4 32.5 36.6 40.6 44.7 48.8 56.9 65.0 73.1 81.3

LRFD

ASD

LRFD

24.4 30.5 36.6 42.7 48.8 54.8 60.9 67.0 73.1 85.3 97.5 110 122

14.2 18.3 22.3 26.4 30.5 34.5 38.6 42.7 46.7 54.8 63.0 71.1 79.2

21.3 27.4 33.5 39.6 45.7 51.8 57.9 64.0 70.1 82.3 94.5 107 119

LRFD

Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:19 AM

Page 34

9–34

DESIGN OF CONNECTING ELEMENTS

Table 9-3b

Block Shear Shear Yielding Component per inch of thickness, kips/in. Fy , ksi

Fy , ksi

36

Lev , in.

n

50

36

0.6 Fy A gv φ 0.6 Fy A gv 0.6 Fy A gv φ 0.6 Fy A gv ᎏ ᎏᎏ ᎏ ᎏᎏ tΩ t tΩ t

n

50

0.6 Fy A gv φ 0.6 Fy A gv 0.6 Fy A gv φ 0.6 Fy A gv ᎏ ᎏᎏ ᎏ ᎏᎏ tΩ t tΩ t

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

13⁄8 11⁄2

370 371 373

555 557 559

514 516 518

771 773 776

273 274 275

409 411 413

379 381 383

568 571 574

15⁄8 13⁄4 17⁄8 2

374 375 377 378

561 563 565 567

519 521 523 525

779 782 785 788

277 278 279 281

415 417 419 421

384 386 388 390

577 579 582 585

21⁄4 21⁄2 23⁄4 3

381 383 386 389

571 575 579 583

529 533 536 540

793 799 804 810

284 286 289 292

425 429 433 437

394 398 401 405

591 596 602 608

11⁄4 13⁄8 11⁄2

337 339 340

506 508 510

469 471 473

703 706 709

240 242 243

360 362 364

334 336 338

501 503 506

15⁄8 13⁄4 17⁄8 2

342 343 344 346

512 514 516 518

474 476 478 480

712 714 717 720

244 246 247 248

367 369 371 373

339 341 343 345

509 512 515 518

21⁄4 21⁄2 23⁄4 3

348 351 354 356

522 526 531 535

484 488 491 495

726 731 737 743

251 254 257 259

377 381 385 389

349 353 356 360

523 529 534 540

11⁄4 13⁄8 11⁄2

305 306 308

458 460 462

424 426 428

636 638 641

208 209 211

312 314 316

289 291 293

433 436 439

15⁄8 13⁄4 17⁄8 2

309 310 312 313

464 466 468 470

429 431 433 435

644 647 650 653

212 213 215 216

318 320 322 324

294 296 298 300

442 444 447 450

316 319 321 324

474 478 482 486

439 443 446 450

658 664 669 675

219 221 224 227

328 332 336 340

304 308 311 315

456 461 467 473

11⁄4

21⁄4 21⁄2 23/4 3 ASD

12

11

10

9

8

7

LRFD

Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:20 AM

Page 35

9–35

DESIGN TABLES

Table 9-3b (continued)

Block Shear Shear Yielding Component per inch of thickness, kips/in. Fy , ksi

Fy , ksi

36

Lev , in.

n

50

36

0.6 Fy A gv φ 0.6 Fy A gv 0.6 Fy A gv φ 0.6 Fy A gv ᎏ ᎏᎏ ᎏ ᎏᎏ tΩ t tΩ t

n

50

0.6 Fy A gv φ 0.6 Fy A gv 0.6 Fy A gv φ 0.6 Fy A gv ᎏ ᎏᎏ ᎏ ᎏᎏ tΩ t tΩ t

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

13⁄8 11⁄2

175 177 178

263 265 267

244 246 248

366 368 371

78.3 79.6 81.0

117 119 121

109 111 113

163 166 169

15⁄8 13⁄4 17⁄8 2

180 181 182 184

269 271 273 275

249 251 253 255

374 377 380 383

82.3 83.7 85.0 86.4

124 126 128 130

114 116 118 120

172 174 177 180

21⁄4 21⁄2 23⁄4 3

186 189 192 194

279 283 288 292

259 263 266 270

388 394 399 405

89.1 91.8 94.5 97.2

134 138 142 146

124 128 131 135

186 191 197 203

11⁄4 13⁄8 11⁄2

143 144 146

215 217 219

199 201 203

298 301 304

45.9 47.2 48.6

68.8 70.9 72.9

63.8 65.6 67.5

95.6 98.4 101

15⁄8 13⁄4 17⁄8 2

147 148 150 151

221 223 225 227

204 206 208 210

307 309 312 315

49.9 51.3 52.7 54.0

74.9 76.9 79.0 81.0

69.4 71.3 73.1 75.0

104 107 110 113

21⁄4 21⁄2 23⁄4 3

154 157 159 162

231 235 239 243

214 218 221 225

321 326 332 338

56.7 59.4 62.1 64.8

85.0 89.1 93.1 97.2

78.8 82.5 86.3 90.0

118 124 129 135

11⁄4 13⁄8 11⁄2

111 112 113

166 168 170

154 156 158

231 233 236

15⁄8 13⁄4 17⁄8 2

115 116 117 119

172 174 176 178

159 161 163 165

239 242 245 248

121 124 127 130

182 186 190 194

169 173 176 180

253 259 264 270

11⁄4

21⁄4 21⁄2 23⁄4 3 ASD

6

5

4

3

2

LRFD

Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:20 AM

Page 36

9–36

DESIGN OF CONNECTING ELEMENTS

Table 9-3c

Block Shear Shear Rupture Component per inch of thickness, kips/in. Fu , ksi 3

12

11

10

ASD

Lev , in.

Bolt diameter, d , in. 3 /4 1

7

/4

n

65

58 /8

7

/8

1

0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ tΩ t tΩ t tΩ t tΩ t tΩ t tΩ t

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

11/4 13/8 11/2

421 423 425

631 635 638

396 398 400

594 597 600

371 373 375

556 560 563

472 474 477

707 711 715

444 446 449

665 669 673

416 418 420

623 627 631

15/8 13/4 17/8 2

427 430 432 434

641 644 648 651

402 405 407 409

604 607 610 613

377 380 382 384

566 569 573 576

479 481 484 486

718 722 726 729

451 453 456 458

676 680 684 687

423 425 428 430

634 638 642 645

21/4 21/2 23/4 3

438 443 447 451

657 664 670 677

413 418 422 426

620 626 633 639

388 393 397 401

582 589 595 602

491 496 501 506

737 744 751 759

463 468 473 478

695 702 709 717

435 440 445 450

653 660 667 675

11⁄4 13⁄8 11⁄2

384 386 388

576 579 582

361 363 365

542 545 548

338 340 343

507 511 514

430 433 435

645 649 653

405 407 410

607 611 614

379 381 384

569 572 576

15⁄8 13⁄4 17⁄8 2

390 393 395 397

586 589 592 595

368 370 372 374

551 555 558 561

345 347 349 351

517 520 524 527

438 440 442 445

656 660 664 667

412 414 417 419

618 622 625 629

386 389 391 394

580 583 587 590

21⁄4 21⁄2 23⁄4 3

401 406 410 414

602 608 615 622

378 383 387 391

568 574 581 587

356 360 364 369

533 540 546 553

450 455 459 464

675 682 689 697

424 429 434 439

636 644 651 658

399 403 408 413

598 605 612 620

11⁄4 13⁄8 11⁄2

347 349 351

520 524 527

326 328 331

489 493 496

306 308 310

458 462 465

389 391 394

583 587 590

366 368 371

548 552 556

342 345 347

514 517 521

15⁄8 13⁄4 17⁄8 2

353 356 358 360

530 533 537 540

333 335 337 339

499 502 506 509

312 314 316 319

468 471 475 478

396 399 401 403

594 598 601 605

373 375 378 380

559 563 567 570

350 352 355 357

525 528 532 536

21⁄4 21⁄2 23⁄4 3

364 369 373 377

546 553 560 566

344 348 352 357

515 522 529 535

323 327 332 336

484 491 498 504

408 413 418 423

612 620 627 634

385 390 395 400

578 585 592 600

362 367 372 377

543 550 558 565

LRFD

Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:20 AM

Page 37

9–37

DESIGN TABLES

Table 9-3c (continued)

Block Shear Shear Rupture Component per inch of thickness, kips/in. Fu , ksi 3

9

8

7

ASD

Lev , in.

Bolt diameter, d , in. 3 /4 1

7

/4

n

65

58 /8

7

/8

1

0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ tΩ t tΩ t tΩ t tΩ t tΩ t tΩ t

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

11⁄4 13⁄8 11⁄2

310 312 314

465 468 471

291 294 296

437 440 444

273 275 277

409 413 416

347 350 352

521 525 528

327 329 332

490 494 497

306 308 311

459 463 466

15⁄8 13⁄4 17⁄8 2

316 319 321 323

475 478 481 484

298 300 302 305

447 450 453 457

279 282 284 286

419 422 426 429

355 357 360 362

532 536 539 543

334 336 339 341

501 505 508 512

313 316 318 321

470 473 477 481

21⁄4 21⁄2 23⁄4 3

327 332 336 340

491 498 504 511

309 313 318 322

463 470 476 483

290 295 299 303

436 442 449 455

367 372 377 381

550 558 565 572

346 351 356 361

519 527 534 541

325 330 335 340

488 495 503 510

11⁄4 13⁄8 11⁄2

273 275 277

409 413 416

257 259 261

385 388 392

240 243 245

361 364 367

306 308 311

459 463 466

288 290 293

431 435 439

269 272 274

404 408 411

15⁄8 13⁄4 17⁄8 2

279 282 284 286

419 422 426 429

263 265 268 270

395 398 401 405

247 249 251 253

370 374 377 380

313 316 318 321

470 473 477 481

295 297 300 302

442 446 450 453

277 279 282 284

415 419 422 426

21⁄4 21⁄2 23⁄4 3

290 295 299 303

436 442 449 455

274 278 283 287

411 418 424 431

258 262 266 271

387 393 400 406

325 330 335 340

488 495 503 510

307 312 317 322

461 468 475 483

289 294 299 303

433 441 448 455

11⁄4 13⁄8 11⁄2

236 238 240

354 357 361

222 224 226

333 336 339

208 210 212

312 315 318

264 267 269

397 400 404

249 251 254

373 377 380

233 235 238

349 353 356

15⁄8 13⁄4 17⁄8 2

243 245 247 249

364 367 370 374

228 231 233 235

343 346 349 352

214 216 219 221

321 325 328 331

272 274 277 279

408 411 415 419

256 258 261 263

384 388 391 395

240 243 245 247

360 364 367 371

21/4 21/2 23/4 3

253 258 262 266

380 387 393 400

239 244 248 252

359 365 372 378

225 229 234 238

338 344 351 357

284 289 294 299

426 433 441 448

268 273 278 283

402 410 417 424

252 257 262 267

378 386 393 400

LRFD

Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:20 AM

Page 38

9–38

DESIGN OF CONNECTING ELEMENTS

Table 9-3c (continued)

Block Shear Shear Rupture Component per inch of thickness, kips/in. Fu , ksi

58 3

7

/4

n

6

5

4

ASD

Lev , in.

65 Bolt diameter, d , in. 3 /4 1

/8

7

/8

1

0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ tΩ t tΩ t tΩ t tΩ t tΩ t tΩ t

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

11⁄4 13⁄8 11⁄2

199 201 203

299 302 305

187 189 191

281 284 287

175 177 179

263 266 269

223 225 228

335 338 342

210 212 215

314 318 322

196 199 201

294 298 302

15⁄8 13⁄4 17⁄8 2

206 208 210 212

308 312 315 318

194 196 198 200

290 294 297 300

182 184 186 188

272 276 279 282

230 233 235 238

346 349 353 356

217 219 222 224

325 329 333 336

204 206 208 211

305 309 313 316

21⁄4 21⁄2 23⁄4 3

216 221 225 229

325 331 338 344

204 209 213 217

307 313 320 326

192 197 201 206

289 295 302 308

243 247 252 257

364 371 378 386

229 234 239 244

344 351 358 366

216 221 225 230

324 331 338 346

11⁄4 13⁄8 11⁄2

162 164 166

243 246 250

152 154 157

228 232 235

142 145 147

214 217 220

182 184 186

272 276 280

171 173 176

256 260 263

160 162 165

239 243 247

15⁄8 13⁄4 17⁄8 2

169 171 173 175

253 256 259 263

159 161 163 165

238 241 245 248

149 151 153 156

223 227 230 233

189 191 194 196

283 287 291 294

178 180 183 185

267 271 274 278

167 169 172 174

250 254 258 261

21⁄4 21⁄2 23⁄4 3

179 184 188 192

269 276 282 289

170 174 178 183

254 261 268 274

160 164 169 173

240 246 253 259

201 206 211 216

302 309 316 324

190 195 200 205

285 293 300 307

179 184 189 194

269 276 283 291

11⁄4 13⁄8 11⁄2

125 127 129

188 191 194

117 120 122

176 179 183

110 112 114

165 168 171

140 143 145

210 214 218

132 134 137

197 201 205

123 126 128

185 188 192

15⁄8 13⁄4 17⁄8 2

132 134 136 138

197 201 204 207

124 126 128 131

186 189 192 196

116 119 121 123

175 178 181 184

147 150 152 155

221 225 229 232

139 141 144 146

208 212 216 219

130 133 135 138

196 199 203 207

21⁄4 21⁄2 23⁄4 3

142 147 151 156

214 220 227 233

135 139 144 148

202 209 215 222

127 132 136 140

191 197 204 210

160 165 169 174

239 247 254 261

151 156 161 166

227 234 241 249

143 147 152 157

214 221 229 236

LRFD

Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:20 AM

Page 39

9–39

DESIGN TABLES

Table 9-3c (continued)

Block Shear Shear Rupture Component per inch of thickness, kips/in. Fu , ksi

58 3

7

/4

n

Lev , in.

3

2

ASD

/8

7

/8

1

0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv 0.6Fu Anv φ0.6Fu Anv ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ ᎏᎏ tΩ t tΩ t tΩ t tΩ t tΩ t tΩ t

ASD 11⁄4 13⁄8 11⁄2

65 Bolt diameter, d , in. 3 /4 1

LRFD

88.1 132 90.3 135 92.4 139

15⁄8 13⁄4 17⁄8 2

94.6 96.8 99.0 101

142 145 148 152

21⁄4 21⁄2 23⁄4 3

105 110 114 119

158 165 171 178

ASD

LRFD

ASD

LRFD

ASD

ASD

LRFD

LRFD

98.7 148 101 152 104 155

89.2 91.4 93.5 95.7

134 137 140 144

83.7 85.9 88.1 90.3

126 129 132 135

106 108 111 113

159 163 166 170

99.9 102 105 107

150 154 157 161

93.8 96.3 98.7 101

141 144 148 152

150 157 163 170

94.6 99.0 103 108

142 148 155 161

118 123 128 133

177 185 192 199

112 117 122 127

168 176 183 190

106 111 116 121

159 166 174 181

100 104 109 113

51.1 53.3 55.5

76.7 79.9 83.2

47.8 50.0 52.2

71.8 75.0 78.3

44.6 46.8 48.9

66.9 70.1 73.4

57.3 59.7 62.2

15/8 13/4 17/8 2

57.6 59.8 62.0 64.2

86.5 89.7 93.0 96.2

54.4 56.6 58.7 60.9

81.6 84.8 88.1 91.4

51.1 53.3 55.5 57.6

76.7 79.9 83.2 86.5

21⁄4 21⁄2 23⁄4 3

68.5 72.9 77.2 81.6

65.3 97.9 69.6 104 73.9 111 78.3 117

62.0 93.0 66.3 99.5 70.7 106 75.0 113

85.9 89.6 93.2

92.6 139 95.1 143 97.5 146

ASD

77.2 116 79.4 119 81.6 122

11⁄4 13⁄8 11⁄2

103 109 116 122

LRFD

82.6 124 84.8 127 87.0 131

80.4 84.1 87.8

50.0 52.4 54.8

75.0 78.6 82.3

64.6 96.9 67.0 101 69.5 104 71.9 108

60.9 91.4 63.4 95.1 65.8 98.7 68.3 102

57.3 59.7 62.2 64.6

85.9 89.6 93.2 96.9

76.8 81.7 86.5 91.4

73.1 78.0 82.9 87.8

69.5 74.3 79.2 84.1

115 122 130 137

LRFD

Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

53.6 56.1 58.5

86.5 130 89.0 133 91.4 137

110 117 124 132

104 112 119 126

AISC_PART 9:14th Ed.

2/24/11

8:21 AM

Page 40

9–40

DESIGN OF CONNECTING ELEMENTS

Table 9-4

Beam Bearing Constants

Fy = 50 ksi

Shape

R 1/Ω kips

φR 1 kips

R 2 /Ω kips/in.

φR 2 kips/in.

R 3 /Ω kips

φR 3 kips

R 4 /Ω kips/in.

φR 4 kips/in.

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

W44×335 ×290 ×262 ×230

220 170 144 119

330 255 216 178

34.3 28.8 26.2 23.7

51.5 43.3 39.3 35.5

335 244 200 159

502 365 299 239

10.1 6.79 5.68 4.94

15.2 10.2 8.53 7.41

W40×593 ×503 ×431 ×397 ×372 ×362 ×324 ×297 ×277 ×249 ×215 ×199

658 506 395 344 312 298 249 219 191 163 130 122

987 758 593 515 468 447 374 329 286 244 195 183

59.7 51.3 44.7 40.7 38.7 37.3 33.3 31.0 27.7 25.0 21.7 21.7

89.5 77.0 67.0 61.0 58.0 56.0 50.0 46.5 41.5 37.5 32.5 32.5

1040 765 574 481 431 405 324 277 229 186 139 131

1550 1150 861 722 646 607 486 416 343 280 209 196

29.8 22.7 17.8 14.5 13.5 12.4 9.93 8.85 6.59 5.45 4.17 4.79

44.8 34.1 26.8 21.8 20.3 18.7 14.9 13.3 9.88 8.17 6.26 7.19

W40×392 ×331 ×327 ×294 ×278 ×264 ×235 ×211 ×183 ×167 ×149

438 337 325 275 257 233 191 163 129 120 106

657 505 488 412 385 349 286 244 193 180 158

47.3 40.7 39.3 35.3 34.3 32.0 27.7 25.0 21.7 21.7 21.0

71.0 61.0 59.0 53.0 51.5 48.0 41.5 37.5 32.5 32.5 31.5

647 474 451 365 339 298 229 186 138 128 110

970 710 676 548 508 447 343 280 207 192 165

19.7 15.1 13.7 11.0 10.9 9.24 6.59 5.45 4.24 4.99 5.70

29.6 22.6 20.5 16.6 16.3 13.9 9.88 8.17 6.36 7.49 8.55

W36×652 ×529 ×487 ×441 ×395 ×361 ×330 ×302 ×282 ×262 ×247 ×231

737 518 454 384 320 276 238 207 186 167 153 140

1110 777 681 576 480 414 357 311 279 251 230 210

65.7 53.7 50.0 45.3 40.7 37.3 34.0 31.5 29.5 28.0 26.7 25.3

98.5 80.5 75.0 68.0 61.0 56.0 51.0 47.3 44.3 42.0 40.0 38.0

1250 839 724 597 481 405 337 287 251 222 200 179

1880 1260 1090 895 722 607 506 430 377 334 300 269

38.0 26.0 23.2 19.1 15.5 13.3 11.0 9.73 8.60 8.06 7.47 6.90

56.9 39.1 34.7 28.7 23.3 19.9 16.5 14.6 12.9 12.1 11.2 10.3

For R1 and R2 ASD

LRFD

For R3, R4, R5, R6 ASD

LRFD

Ω = 1.50 φ = 1.00 Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:21 AM

Page 41

9–41

DESIGN TABLES

Table 9-4 (continued)

Beam Bearing Constants

Fy = 50 ksi

(lb = 31/4 in.) Nominal Wt.

R 5 /Ω kips

kips

lb/ft

ASD

335 290 262 230

φR 5

R 6 /Ω

φR 6

LRFD

ASD

LRFD

ASD

305 224 183 145

458 336 275 218

13.5 9.05 7.58 6.59

20.3 13.6 11.4 9.88

593 503 431 397 372 362 324 297 277 249 215 199

951 701 525 442 394 371 297 254 211 172 129 118

1430 1050 787 662 591 557 446 381 317 258 193 177

39.8 30.3 23.8 19.4 18.1 16.6 13.2 11.8 8.78 7.26 5.56 6.39

392 331 327 294 278 264 235 211 183 167 149

592 433 413 335 310 273 211 172 127 115 95.2

888 649 620 503 464 410 317 258 191 173 143

652 529 487 441 395 361 330 302 282 262 247 231

1150 770 664 547 442 371 310 263 230 203 182 162

1720 1160 995 820 662 557 465 394 345 304 273 243

x < d /2 R n /Ω φR n kips/in. kips/in. kips kips

Vnx / Ωv φvVnx

d /2 ≤ x ≤ d R n /Ω φR n kips kips

x>d R n /Ω φR n kips kips

kips

kips

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

331 264 218 175

497 396 327 263

331 264 229 196

497 396 344 293

551 434 373 315

827 651 560 471

906 754 680 547

1360 1130 1020 822

59.7 45.4 35.7 29.1 27.1 24.9 19.9 17.7 13.2 10.9 8.34 9.58

— — — — 438 419 356 306 250 204 153 147

— — — — 657 629 534 459 375 307 229 219

— — — — 438 419 357 320 281 244 201 193

— — — — 657 629 537 480 421 366 301 289

1510 1180 935 820 750 717 606 539 472 407 305 293

2260 1770 1400 1230 1120 1080 911 809 707 610 459 439

1540 1300 1110 1000 942 909 804 740 659 591 507 503

2310 1950 1660 1500 1410 1360 1210 1110 989 887 761 755

26.3 20.1 18.2 14.7 14.5 12.3 8.78 7.26 5.65 6.65 7.60

39.5 30.2 27.3 22.1 21.7 18.5 13.2 10.9 8.48 9.98 11.4

— — — 390 368 328 250 204 152 144 129

— — — 584 552 492 375 307 228 216 193

— — — 390 368 337 281 244 200 191 174

— — — 584 552 505 421 366 299 286 260

1030 806 778 665 625 570 472 407 304 288 257

1540 1210 1170 996 937 854 707 610 455 433 386

1180 996 963 856 828 768 659 591 507 502 432

1770 1490 1440 1280 1240 1150 989 887 761 753 650

50.6 34.7 30.9 25.5 20.7 17.7 14.7 13.0 11.5 10.7 9.96 9.19

75.9 52.1 46.3 38.3 31.1 26.6 22.0 19.5 17.2 16.1 14.9 13.8

— — — — 452 397 349 309 279 248 224 201

— — — — 678 596 523 465 419 373 336 302

— — — — 452 397 349 309 282 258 240 222

— — — — 678 596 523 465 423 388 360 334

1690 1210 1070 915 772 673 587 516 468 425 393 362

2540 1820 1610 1370 1160 1010 880 776 702 639 590 544

1620 1280 1180 1060 937 851 769 705 657 620 587 555

2430 1920 1770 1590 1410 1280 1150 1060 985 930 881 832

—Indicates that 31/4-in. bearing length is insufficient for end beam reactions since lb < k. lb = length of bearing, in. x = location of concentrated force with respect to the member end, in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:21 AM

Page 42

9–42

DESIGN OF CONNECTING ELEMENTS

Table 9-4 (continued)

Beam Bearing Constants

Fy = 50 ksi

φR 1 kips

R 2 /Ω kips/in.

φR 2 kips/in.

ASD

LRFD

ASD

LRFD

198 168 146 128 117 105 95.9 88.0 77.0

298 252 219 192 175 157 144 132 116

32.0 29.0 27.7 25.5 24.2 22.7 21.7 20.8 20.0

48.0 43.5 41.5 38.3 36.3 34.0 32.5 31.3 30.0

322 278 232 202 171 151 133 116

484 418 348 302 257 227 200 173

42.0 38.7 34.7 32.0 29.0 27.7 25.8 23.8

63.0 58.0 52.0 48.0 43.5 41.5 38.8 35.8

W33×169 ×152 ×141 ×130 ×118

107 93.1 83.7 75.4 66.0

161 140 126 113 99.0

22.3 21.2 20.2 19.3 18.3

W30×391 ×357 ×326 ×292 ×261 ×235 ×211 ×191 ×173

366 313 270 224 189 158 136 117 101

549 470 405 337 284 238 203 175 151 149 127 116 106 96.1 85.8 74.0

Shape

R 1/Ω kips

W36×256 ×232 ×210 ×194 ×182 ×170 ×160 ×150 ×135 W33×387 ×354 ×318 ×291 ×263 ×241 ×221 ×201

W30×148 ×132 ×124 ×116 ×108 ×99 ×90 For R1 and R2 ASD

LRFD

99.1 84.6 77.0 70.6 64.0 57.2 49.4

φR 3 kips

R 4 /Ω kips/in.

φR 4 kips/in.

ASD

LRFD

ASD

LRFD

298 245 212 181 161 142 127 115 99.5

447 367 319 271 242 212 191 173 149

9.88 8.17 8.28 7.03 6.43 5.71 5.40 5.23 5.55

14.8 12.3 12.4 10.5 9.64 8.56 8.11 7.84 8.32

514 435 351 298 245 215 186 156

771 652 527 447 367 323 279 234

17.6 15.2 12.2 10.6 8.78 8.63 7.75 6.81

26.4 22.7 18.3 15.9 13.2 12.9 11.6 10.2

33.5 31.8 30.3 29.0 27.5

146 125 111 98.4 84.5

219 188 167 148 127

5.27 5.21 5.00 4.98 4.94

7.90 7.81 7.51 7.47 7.41

45.3 41.3 38.0 34.0 31.0 27.7 25.8 23.7 21.8

68.0 62.0 57.0 51.0 46.5 41.5 38.8 35.5 32.8

597 498 420 337 277 223 189 157 132

895 747 630 506 416 335 283 236 198

22.4 18.7 16.1 13.0 11.1 8.80 8.25 7.08 6.24

33.7 28.1 24.2 19.4 16.7 13.2 12.4 10.6 9.36

21.7 20.5 19.5 18.8 18.2 17.3 15.7

32.5 30.8 29.3 28.3 27.3 26.0 23.5

137 116 104 94.3 84.5 73.9 60.6

206 174 156 141 127 111 90.9

5.48 5.55 5.15 5.11 5.16 5.11 4.17

8.22 8.32 7.73 7.67 7.75 7.66 6.25

R 3 /Ω kips

For R3, R4, R5, R6 ASD

LRFD

Ω = 1.50 φ = 1.00 Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:21 AM

Page 43

9–43

DESIGN TABLES

Table 9-4 (continued)

Beam Bearing Constants

Fy = 50 ksi

(lb = 31/4 in.) Nominal Wt.

R 5 /Ω kips

kips

lb/ft

ASD

256 232 210 194 182 170 160 150 135

φR 5

R 6 /Ω

φR 6

LRFD

ASD

LRFD

ASD

273 225 192 164 146 128 114 103 86.3

410 337 288 246 219 192 172 154 129

13.2 10.9 11.0 9.38 8.57 7.61 7.20 6.97 7.40

19.8 16.3 16.6 14.1 12.9 11.4 10.8 10.5 11.1

387 354 318 291 263 241 221 201

472 399 322 273 225 196 168 141

708 599 484 410 337 294 253 211

23.5 20.2 16.3 14.2 11.7 11.5 10.3 9.09

169 152 141 130 118

134 114 99.9 87.4 73.7

201 171 150 131 111

391 357 326 292 261 235 211 191 173

547 457 385 310 254 205 172 143 119

820 685 577 465 381 307 258 214 179

148 132 124 116 108 99 90

126 105 93.5 84.1 74.2 63.8 52.4

189 157 140 126 111 95.7 78.6

x < d /2 R n /Ω φR n kips/in. kips/in. kips kips

Vnx / Ωv φvVnx

d /2 ≤ x ≤ d R n /Ω φR n kips kips

x>d R n /Ω φR n kips kips

kips

kips

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

302 262 236 204 182 161 145 132 118

454 393 354 305 273 240 217 198 176

302 262 236 211 196 179 166 156 142

454 393 354 316 293 268 250 234 214

500 430 382 339 313 284 262 244 219

752 645 573 508 468 425 394 366 330

718 646 609 558 526 492 468 449 384

1080 968 914 838 790 738 702 673 577

35.2 30.3 24.4 21.2 17.6 17.3 15.5 13.6

459 404 345 306 265 241 211 178

689 607 517 458 398 362 317 267

459 404 345 306 265 241 217 193

689 607 517 458 398 362 326 289

781 682 577 508 436 392 350 309

1170 1020 865 760 655 589 526 462

907 826 732 668 600 568 525 482

1360 1240 1100 1000 900 852 788 723

7.03 6.95 6.67 6.64 6.58

10.5 10.4 10.0 9.96 9.87

163 142 127 115 101

245 213 191 172 151

179 162 149 138 125

270 243 224 207 188

286 255 233 214 191

431 383 350 320 287

453 425 403 384 325

679 638 604 576 489

29.9 25.0 21.5 17.3 14.9 11.7 11.0 9.44 8.32

44.9 37.5 32.2 25.9 22.3 17.6 16.5 14.2 12.5

513 447 394 335 290 248 216 180 152

770 672 590 503 435 373 323 270 228

513 447 394 335 290 248 220 194 172

770 672 590 503 435 373 329 290 258

879 760 664 559 479 406 356 311 273

1320 1140 995 840 719 611 532 465 409

903 813 739 653 588 520 479 436 398

1350 1220 1110 979 882 779 718 654 597

7.30 7.40 6.87 6.81 6.89 6.81 5.56

11.0 11.1 10.3 10.2 10.3 10.2 8.34

155 134 121 111 101 90.5 74.2

233 201 181 166 152 136 111

170 151 140 132 123 113 100

255 227 211 198 185 170 150

269 236 217 202 187 171 148

404 354 327 304 281 256 222

399 373 353 339 325 309 249

599 559 530 509 487 463 374

—Indicates that 31/4-in. bearing length is insufficient for end beam reactions since lb < k. lb = length of bearing, in. x = location of concentrated force with respect to the member end, in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:21 AM

Page 44

9–44

DESIGN OF CONNECTING ELEMENTS

Table 9-4 (continued)

Beam Bearing Constants

Fy = 50 ksi

φR 1 kips

R 2 /Ω kips/in.

φR 2 kips/in.

ASD

LRFD

ASD

LRFD

ASD

711 376 322 278 240 209 182 158 133 120 103 88.7

1070 564 484 418 360 314 273 238 200 179 154 133

65.7 46.0 42.0 38.7 35.3 32.7 30.3 27.7 25.0 24.2 22.0 20.2

98.5 69.0 63.0 58.0 53.0 49.0 45.5 41.5 37.5 36.3 33.0 30.3

1250 615 514 435 365 311 265 223 181 162 134 112

130 109 92.1 82.1 71.3

20.3 19.0 17.2 16.3 15.3

30.5 28.5 25.8 24.5 23.0

120 99.9 81.1 71.3 60.1

408 343 292 250 207 178 150 132 115 101 86.1 73.6 61.9 52.1

612 514 438 376 311 268 225 198 173 152 129 110 92.8 78.1

50.7 46.0 42.0 38.7 34.7 32.0 29.0 27.0 25.0 23.5 21.7 20.2 18.3 16.7

76.0 69.0 63.0 58.0 52.0 48.0 43.5 40.5 37.5 35.3 32.5 30.3 27.5 25.0

744 615 514 435 351 298 245 212 181 157 132 111 90.6 73.7

67.8 59.2 49.7 43.3 37.7 39.1 33.2

102 88.8 74.6 64.9 56.5 58.6 49.9

18.3 17.2 15.7 14.7 13.8 14.3 13.2

27.5 25.8 23.5 22.0 20.8 21.5 19.8

97.2 83.3 68.1 58.0 49.2 52.2 42.5

Shape

R 1/Ω kips

W27×539 ×368 ×336 ×307 ×281 ×258 ×235 ×217 ×194 ×178 ×161 ×146 W27×129 ×114 ×102 ×94 ×84

86.4 72.7 61.4 54.7 47.5

W24×370 ×335 ×306 ×279 ×250 ×229 ×207 ×192 ×176 ×162 ×146 ×131 ×117 ×104 W24×103 ×94 ×84 ×76 ×68 ×62 ×55 For R1 and R2 ASD

LRFD

R 3 /Ω kips

For R3, R4, R5, R6 ASD

LRFD

Ω = 1.50 φ = 1.00 Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

φR 3 kips LRFD 1880 922 771 652 548 466 398 335 272 243 201 168 181 150 122 107 90.2 1120 922 771 652 527 447 367 318 272 236 198 167 136 111 146 125 102 86.9 73.9 78.2 63.7

R 4 /Ω kips/in.

φR 4 kips/in.

ASD

LRFD

48.0 25.2 21.1 18.2 15.2 13.2 11.8 9.70 8.09 8.32 6.97 5.99

72.0 37.8 31.7 27.3 22.8 19.9 17.7 14.5 12.1 12.5 10.5 8.98

5.40 5.27 4.39 4.24 4.12

8.10 7.91 6.58 6.36 6.17

33.3 27.8 23.4 20.2 16.3 14.2 11.8 10.3 9.03 8.30 7.37 6.80 5.82 5.00

50.0 41.8 35.1 30.3 24.5 21.3 17.7 15.5 13.5 12.5 11.1 10.2 8.73 7.49

5.01 4.64 4.04 3.79 3.72 4.11 3.74

7.51 6.96 6.06 5.68 5.59 6.16 5.60

AISC_PART 9:14th Ed.

2/24/11

8:21 AM

Page 45

9–45

DESIGN TABLES

Table 9-4 (continued)

Beam Bearing Constants

Fy = 50 ksi

(lb = 31/4 in.) Nominal Wt.

R 5 /Ω kips

kips

lb/ft

ASD

539 368 336 307 281 258 235 217 194 178 161 146

1150 564 472 399 335 285 243 205 166 147 121 101

φR 5

R 6 /Ω

φR 6

LRFD

ASD

LRFD

ASD

1720 846 708 599 503 428 364 307 249 220 182 151

64.0 33.6 28.2 24.3 20.3 17.7 15.7 12.9 10.8 11.1 9.29 7.99

96.0 50.4 42.3 36.5 30.4 26.5 23.6 19.4 16.2 16.6 13.9 12.0

x < d /2 R n /Ω φR n kips/in. kips/in. kips kips

Vnx / Ωv φvVnx

d /2 ≤ x ≤ d R n /Ω φR n kips kips

x>d R n /Ω φR n kips kips

kips

kips

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

— — 459 404 355 315 280 248 207 189 157 131

— — 689 607 532 473 421 373 311 284 235 197

— — 459 404 355 315 280 248 214 199 175 154

— — 689 607 532 473 421 373 322 297 261 231

1640 902 781 682 595 524 462 406 347 319 278 243

2460 1350 1170 1020 892 787 694 611 522 476 415 364

1280 839 756 687 621 568 522 471 422 403 364 332

1920 1260 1130 1030 932 853 784 707 632 605 546 497

129 114 102 94 84

110 90.4 73.2 63.7 52.8

166 136 110 95.5 79.2

7.20 7.03 5.85 5.66 5.49

10.8 10.5 8.77 8.48 8.23

138 117 95.4 85.1 73.5

207 176 143 128 110

152 134 117 108 97.2

229 202 176 162 146

239 207 179 162 145

359 311 268 244 217

337 311 279 264 246

505 467 419 395 368

370 335 306 279 250 229 207 192 176 162 146 131 117 104

682 1020 564 846 472 708 399 599 322 484 273 410 225 337 195 292 166 249 144 215 120 179 99.9 150 81.1 122 65.7 98.6

44.4 37.1 31.2 26.9 21.8 18.9 15.7 13.8 12.0 11.1 9.83 9.07 7.76 6.66

66.6 55.7 46.8 40.4 32.7 28.4 23.6 20.6 18.1 16.6 14.7 13.6 11.6 9.99

573 493 429 376 320 282 244 220 196 177 156 133 110 90.0

859 738 643 565 480 424 366 330 295 267 234 200 164 135

573 493 429 376 320 282 244 220 196 177 157 139 121 106

859 738 643 565 480 424 366 330 295 267 235 208 182 159

981 836 721 626 527 460 394 352 311 278 243 213 183 158

1470 1250 1080 941 791 692 591 528 468 419 364 318 275 237

851 759 683 619 547 499 447 413 378 353 321 296 267 241

1280 1140 1020 929 821 749 671 620 567 529 482 445 401 362

6.68 6.19 5.39 5.05 4.97 5.48 4.98

10.0 9.28 8.08 7.57 7.45 8.22 7.47

113 98.4 81.2 70.3 61.3 65.6 54.7

170 148 122 105 92.1 98.2 81.9

127 115 101 91.1 82.6 85.6 76.1

191 173 151 136 124 128 114

195 174 150 134 120 125 109

293 261 226 201 181 187 164

270 250 227 210 197 204 167

404 375 340 315 295 306 252

103 94 84 76 68 62 55

89.1 75.7 61.6 51.9 43.4 45.7 36.6

134 114 92.4 77.9 65.0 68.5 54.9

—Indicates that 31/4-in. bearing length is insufficient for end beam reactions since lb < k. lb = length of bearing, in. x = location of concentrated force with respect to the member end, in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:21 AM

Page 46

9–46

DESIGN OF CONNECTING ELEMENTS

Table 9-4 (continued)

Beam Bearing Constants

Fy = 50 ksi

Shape

R 1/Ω kips

φR 1 kips

R 2 /Ω kips/in.

φR 2 kips/in.

ASD

LRFD

ASD

W21×201 ×182 ×166 ×147 ×132 ×122 ×111 ×101

162 137 116 99.0 83.4 73.0 63.3 54.2

242 205 174 149 125 110 94.9 81.3

30.3 27.7 25.0 24.0 21.7 20.0 18.3 16.7

W21×93 ×83 ×73 ×68 ×62 ×55 ×48

69.1 57.5 47.0 42.6 37.3 31.9 27.1

104 86.3 70.5 64.0 56.0 47.8 40.7

W21×57 ×50 ×44

38.8 32.9 27.7

W18×311 ×283 ×258 ×234 ×211 ×192 ×175 ×158 ×143 ×130 ×119 ×106 ×97 ×86 ×76 W18×71 ×65 ×60 ×55 ×50 For R1 and R2 ASD

LRFD

R 4 /Ω kips/in.

φR 4 kips/in.

LRFD

ASD

LRFD

400 332 274 237 193 165 138 114

14.5 12.3 9.96 10.6 8.75 7.49 6.39 5.28

21.8 18.4 14.9 15.9 13.1 11.2 9.58 7.91

154 122 95.4 84.3 71.7 59.9 49.1

7.02 5.52 4.34 3.97 3.58 3.51 3.50

10.5 8.28 6.51 5.96 5.37 5.26 5.25

50.0 41.3 33.5

75.1 61.9 50.2

3.50 3.56 3.33

5.25 5.34 4.99

76.0 70.0 64.0 58.0 53.0 48.0 44.5 40.5 36.5 33.5 32.8 29.5 26.8 24.0 21.3

747 631 529 437 363 300 255 211 173 145 131 106 87.9 70.3 55.0

1120 946 793 656 545 450 382 316 259 217 197 159 132 105 82.5

41.5 36.2 30.6 25.3 21.8 17.9 16.0 13.5 10.9 9.38 10.1 8.44 6.84 5.64 4.48

62.3 54.3 46.0 38.0 32.6 26.9 24.0 20.3 16.4 14.1 15.1 12.7 10.3 8.46 6.72

24.8 22.5 20.8 19.5 17.8

75.5 63.0 53.7 46.6 38.5

113 94.4 80.5 69.8 57.7

5.85 4.77 4.08 3.76 3.15

8.77 7.16 6.12 5.64 4.73

R 3 /Ω kips

φR 3 kips

LRFD

ASD

45.5 41.5 37.5 36.0 32.5 30.0 27.5 25.0

267 222 182 158 129 110 91.9 76.2

19.3 17.2 15.2 14.3 13.3 12.5 11.7

29.0 25.8 22.8 21.5 20.0 18.8 17.5

103 81.3 63.6 56.2 47.8 40.0 32.7

58.2 49.4 41.6

13.5 12.7 11.7

20.3 19.0 17.5

410 350 288 243 204 172 148 124 105 89.3 79.7 65.9 56.6 46.8 38.3

616 525 432 364 306 258 221 186 157 134 120 98.8 84.9 70.2 57.4

50.7 46.7 42.7 38.7 35.3 32.0 29.7 27.0 24.3 22.3 21.8 19.7 17.8 16.0 14.2

49.9 43.1 38.0 33.5 28.8

74.9 64.7 57.1 50.2 43.1

16.5 15.0 13.8 13.0 11.8

For R3, R4, R5, R6 ASD

LRFD

Ω = 1.50 φ = 1.00 Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:21 AM

Page 47

9–47

DESIGN TABLES

Table 9-4 (continued)

Beam Bearing Constants

Fy = 50 ksi

(lb = 31/4 in.) Nominal Wt.

R 5 /Ω kips

kips

lb/ft

ASD

201 182 166 147 132 122 111 101

245 203 167 142 116 98.8 82.7 68.6

93 83 73 68 62 55 48

92.5 73.5 57.5 50.6 42.8 35.1 27.9

57 50 44

45.1 36.3 28.9

311 283 258 234 211 192 175 158 143 130 119 106 97 86 76 71 65 60 55 50

φR 5

R 6 /Ω

φR 6

LRFD

ASD

LRFD

ASD

367 304 251 213 174 148 124 103

19.4 16.4 13.3 14.1 11.7 9.99 8.52 7.03

29.0 24.6 19.9 21.2 17.5 15.0 12.8 10.6

139 110 86.2 75.9 64.2 52.6 41.8

9.36 7.36 5.78 5.30 4.77 4.68 4.66

67.7 54.5 43.3

685 1030 578 867 485 728 401 602 333 500 275 413 234 350 193 289 158 238 133 199 119 178 95.3 143 79.4 119 63.4 95.0 49.6 74.4 68.3 57.1 48.7 42.0 34.7

102 85.7 73.1 63.0 52.0

x < d /2 R n /Ω φR n kips/in. kips/in. kips kips

d /2 ≤ x ≤ d R n /Ω φR n kips kips

x>d R n /Ω φR n kips kips

LRFD

ASD

LRFD

ASD

260 227 197 177 154 134 113 93.4

390 340 296 266 231 201 169 140

260 227 197 177 154 138 123 108

390 340 296 266 231 208 184 163

14.0 11.0 8.68 7.95 7.16 7.02 6.99

126 99.2 77.7 69.1 59.4 51.4 44.1

188 149 117 104 89.2 77.0 66.2

132 113 96.4 89.1 80.5 72.5 65.1

4.67 4.75 4.43

7.00 7.13 6.65

61.4 52.9 44.3

92.2 79.3 66.4

82.7 74.2 65.7

55.4 48.3 40.9 33.8 29.0 23.9 21.4 18.0 14.6 12.5 13.4 11.3 9.12 7.52 5.98

83.1 72.4 61.3 50.7 43.5 35.8 32.0 27.1 21.8 18.8 20.2 16.9 13.7 11.3 8.96

575 502 427 369 319 276 245 212 184 162 151 130 110 88.6 69.6

7.80 6.36 5.44 5.01 4.20

11.7 9.54 8.16 7.52 6.30

94.5 78.5 67.0 58.8 48.7

Vnx / Ωv φvVnx kips

kips

LRFD

ASD

LRFD

422 364 313 276 237 211 186 163

632 545 470 415 356 318 279 244

419 377 338 318 283 260 237 214

628 565 506 477 425 391 355 321

198 170 145 134 121 109 97.6

201 171 143 132 118 103 88.2

302 256 215 198 177 154 132

251 220 193 181 168 156 144

376 331 289 272 252 234 216

124 111 98.5

121 106 88.6

182 159 133

171 158 145

256 237 217

1480 1280 1070 917 784 672 587 504 433 377 347 293 257 218 184

678 613 550 490 439 392 356 319 285 259 249 221 199 177 155

1020 920 826 734 658 588 534 479 427 388 373 331 299 265 232

230 203 182 164 144

183 166 151 141 128

275 248 227 212 192

863 753 640 553 478 414 366 318 276 243 227 195 165 132 104

575 502 427 369 319 276 245 212 184 162 151 130 114 98.8 84.5

863 753 640 553 478 414 366 318 276 243 227 195 172 148 127

985 852 715 612 523 448 393 336 289 251 230 196 171 146 123

142 118 100 88.1 73.1

104 91.9 82.9 75.8 67.2

156 138 125 114 101

153 135 121 109 96.0

lb = length of bearing, in. x = location of concentrated force with respect to the member end, in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:21 AM

Page 48

9–48

DESIGN OF CONNECTING ELEMENTS

Table 9-4 (continued)

Beam Bearing Constants

Fy = 50 ksi

Shape

R 1/Ω kips

φR 1 kips

ASD

LRFD

R 2 /Ω kips/in.

φR 2 kips/in.

R 3 /Ω kips

φR 3 kips

R 4 /Ω kips/in.

φR 4 kips/in.

ASD

LRFD

ASD

LRFD

ASD

LRFD

W18×46 ×40 ×35

30.3 24.3 20.7

45.5 36.5 31.0

12.0 10.5 10.0

18.0 15.8 15.0

40.5 30.9 25.8

60.7 46.3 38.7

3.08 2.40 2.59

4.62 3.60 3.89

W16×100 ×89 ×77 ×67

67.8 56.0 44.0 35.2

102 84.0 66.0 52.8

19.5 17.5 15.2 13.2

29.3 26.3 22.8 19.8

107 85.7 64.4 48.8

160 129 96.7 73.1

8.64 7.11 5.43 4.11

13.0 10.7 8.14 6.16

W16×57 ×50 ×45 ×40 ×36

40.1 32.6 27.8 23.1 20.5

60.2 48.9 41.7 34.6 30.7

14.3 12.7 11.5 10.2 9.83

21.5 19.0 17.3 15.3 14.8

57.4 44.8 36.7 28.8 25.3

86.1 67.2 55.0 43.2 38.0

4.90 3.86 3.26 2.54 2.71

7.35 5.79 4.89 3.81 4.07

W16×31 ×26

19.3 15.6

28.9 23.3

9.17 8.33

13.8 12.5

23.0 17.7

34.6 26.5

2.15 2.08

3.22 3.13

W14×730 ×665 ×605 ×550 ×500 ×455 ×426 ×398 ×370 ×342 ×311 ×283 ×257 ×233 ×211 ×193 ×176 ×159 ×145

1410 1210 1030 877 748 641 569 507 451 394 336 287 245 207 176 151 132 111 95.8

W14×132 ×120 ×109 ×99 ×90

87.6 75.7 63.9 55.8 48.0

For R1 and R2 ASD

LRFD

2110 1810 1550 1310 1120 962 853 761 676 591 504 431 367 310 265 227 198 167 144 131 114 95.8 83.7 72.1

102 94.3 86.7 79.3 73.0 67.3 62.7 59.0 55.3 51.3 47.0 43.0 39.3 35.7 32.7 29.7 27.7 24.8 22.7

154 142 130 119 110 101 94.0 88.5 83.0 77.0 70.5 64.5 59.0 53.5 49.0 44.5 41.5 37.3 34.0

21.5 19.7 17.5 16.2 14.7

32.3 29.5 26.3 24.3 22.0

2870 2440 2060 1730 1460 1240 1080 957 840 723 606 508 424 350 292 243 208 169 141 127 106 85.0 71.8 59.2

For R3, R4, R5, R6 ASD

LRFD

Ω = 1.50 φ = 1.00 Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4310 3660 3090 2590 2190 1860 1620 1440 1260 1090 909 762 637 524 438 364 313 253 211 190 159 127 108 88.8

190 168 146 126 111 97.6 84.4 76.8 69.4 61.0 52.4 44.9 38.3 32.2 27.8 22.8 20.7 16.7 14.1 12.8 10.9 8.50 7.44 6.19

285 252 219 189 166 146 127 115 104 91.6 78.6 67.3 57.4 48.2 41.6 34.2 31.1 25.1 21.1 19.2 16.3 12.8 11.2 9.29

AISC_PART 9:14th Ed.

2/24/11

8:22 AM

Page 49

9–49

DESIGN TABLES

Table 9-4 (continued)

Beam Bearing Constants

Fy = 50 ksi

(lb = 31/4 in.) Nominal Wt.

R 5 /Ω kips

kips

lb/ft

ASD

LRFD

φR 5

R 6 /Ω

φR 6

ASD

LRFD

x < d /2 R n /Ω φR n kips/in. kips/in. kips kips

d /2 ≤ x ≤ d R n /Ω φR n kips kips

x>d R n /Ω φR n kips kips ASD

ASD

LRFD

ASD

LRFD 104 87.9 79.8

46 40 35

36.7 28.0 22.7

55.1 42.0 34.1

4.10 3.20 3.46

6.16 4.81 5.19

50.5 38.7 34.2

75.7 58.0 51.3

69.3 58.4 53.2

100 89 77 67

97.2 77.7 58.5 44.3

146 117 87.7 66.4

11.5 9.48 7.24 5.48

17.3 14.2 10.9 8.22

131 109 82.0 62.2

197 164 123 93.1

131 113 93.4 78.1

57 50 45 40 36

52.1 40.6 33.2 26.1 22.4

78.1 60.9 49.8 39.2 33.6

6.53 5.15 4.35 3.38 3.62

9.80 7.72 6.52 5.07 5.43

73.3 57.3 47.3 37.1 34.2

110 86.0 71.0 55.7 51.2

31 26

20.8 15.5

31.1 23.3

2.86 2.78

4.30 4.17

30.1 24.5

45.1 36.9

730 665 605 550 500 455 426 398 370 342 311 283 257 233 211 193 176 159 145 132 120 109 99 90

2590 2200 1860 1560 1320 1120 977 864 757 652 546 458 383 315 263 219 187 152 127 114 95.3 76.9 64.8 53.4

3880 3290 2780 2340 1970 1670 1470 1300 1140 978 820 687 574 473 394 329 281 228 191 171 143 115 97.2 80.2

253 224 195 168 147 130 113 102 92.5 81.4 69.9 59.8 51.1 42.9 37.0 30.4 27.7 22.3 18.8

380 335 292 252 221 195 169 154 139 122 105 89.7 76.6 64.3 55.5 45.6 41.5 33.5 28.2

17.1 14.5 11.3 9.92 8.26

25.6 21.8 17.0 14.9 12.4

99.6 77.4 68.4

Vnx / Ωv φvVnx kips

kips

LRFD

ASD

LRFD

150 116 103

130 113 106

195 169 159

197 169 140 117

199 169 137 113

299 253 206 170

199 176 150 129

298 265 225 193

86.6 73.9 65.2 56.3 52.4

130 111 97.9 84.3 78.8

127 106 93.0 74.1 68.2

190 160 140 111 102

141 124 111 97.6 93.8

212 186 167 146 141

49.1 42.7

73.8 63.9

60.0 48.9

87.5 70.5

131 106

90.1 73.3

— — — — — — — — — 561 489 427 373 323 282 248 222 192 170

— — — — — — — — — 841 733 641 559 484 424 372 333 288 255

— — — — — — — — — 561 489 427 373 323 282 248 222 192 170

— — — — — — — — — 841 733 641 559 484 424 372 333 288 255

3150 2730 2340 2010 1730 1500 1340 1210 1080 955 825 714 618 530 458 399 354 303 265

4720 4080 3520 3010 2600 2250 2010 1810 1620 1430 1240 1070 926 794 689 599 531 455 399

1380 1220 1090 962 858 768 703 648 594 539 482 431 387 342 308 276 252 224 201

2060 1830 1630 1440 1290 1150 1050 972 891 809 723 646 581 514 462 414 378 335 302

157 140 114 97.0 80.2

236 210 170 146 121

157 140 121 108 95.8

236 210 181 163 144

245 215 185 164 144

367 324 277 246 216

190 171 150 138 123

284 257 225 207 185

—Indicates that 31/4-in. bearing length is insufficient for end beam reactions since lb < k. lb = length of bearing, in. x = location of concentrated force with respect to the member end, in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:22 AM

Page 50

9–50

DESIGN OF CONNECTING ELEMENTS

Table 9-4 (continued)

Beam Bearing Constants

Fy = 50 ksi

Shape

R 1/Ω kips

φR 1 kips

ASD

R 2 /Ω kips/in.

φR 2 kips/in.

R 3 /Ω kips

φR 3 kips

R 4 /Ω kips/in.

φR 4 kips/in.

ASD

LRFD

ASD

LRFD

LRFD

ASD

LRFD

W14×82 ×74 ×68 ×61

61.6 51.8 45.3 38.8

92.4 77.6 68.0 58.1

17.0 15.0 13.8 12.5

25.5 22.5 20.8 18.8

81.1 64.4 54.6 44.4

122 96.6 81.9 66.6

7.84 5.91 5.12 4.25

11.8 8.86 7.68 6.37

W14×53 ×48 ×43

38.5 33.7 28.5

57.8 50.6 42.7

12.3 11.3 10.2

18.5 17.0 15.3

44.0 36.8 29.5

66.1 55.2 44.3

3.99 3.46 2.82

5.98 5.19 4.23

W14×38 ×34 ×30

23.6 20.3 17.7

35.5 30.5 26.5

10.3 9.50 9.00

15.5 14.3 13.5

29.8 24.7 21.0

44.7 37.1 31.4

2.96 2.63 2.68

4.45 3.94 4.01

W14×26 ×22

17.4 14.1

26.1 21.1

8.50 7.67

12.8 11.5

20.1 15.4

30.1 23.1

2.05 1.92

3.08 2.87

W12×336 ×305 ×279 ×252 ×230 ×210 ×190 ×170 ×152 ×136 ×120 ×106 ×96 ×87 ×79 ×72 ×65

527 448 391 333 287 246 206 173 145 122 101 80.8 68.8 60.5 52.1 45.5 39.0

790 672 587 499 431 369 309 259 218 183 151 121 103 90.8 78.1 68.3 58.5

59.3 54.3 51.0 46.7 43.0 39.3 35.3 32.0 29.0 26.3 23.7 20.3 18.3 17.2 15.7 14.3 13.0

89.0 81.5 76.5 70.0 64.5 59.0 53.0 48.0 43.5 39.5 35.5 30.5 27.5 25.8 23.5 21.5 19.5

984 825 716 598 508 426 347 283 231 189 152 114 93.2 80.1 66.5 55.6 45.6

1480 1240 1070 898 762 638 520 424 347 284 228 171 140 120 99.8 83.4 68.4

81.9 70.8 65.9 57.2 49.6 42.5 34.3 29.3 24.8 21.3 17.8 12.8 10.5 9.75 8.23 6.97 5.85

123 106 98.8 85.8 74.4 63.8 51.5 43.9 37.2 31.9 26.7 19.3 15.8 14.6 12.3 10.5 8.78

W12×58 ×53

37.2 33.9

55.8 50.9

12.0 11.5

18.0 17.3

41.6 37.0

62.4 55.5

4.32 4.26

6.48 6.40

W12×50 ×45 ×40

35.2 30.2 25.1

52.7 45.2 37.6

12.3 11.2 9.83

18.5 16.8 14.8

43.4 35.4 27.7

65.0 53.1 41.5

4.69 3.90 3.03

7.03 5.86 4.54

W12×35 ×30 ×26

20.5 16.0 13.0

30.8 24.1 19.6

10.0 8.67 7.67

15.0 13.0 11.5

28.5 21.2 16.4

42.8 31.8 24.6

3.00 2.35 1.90

4.50 3.52 2.84

For R1 and R2 ASD

LRFD

For R3, R4, R5, R6 ASD

LRFD

Ω = 1.50 φ = 1.00 Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:22 AM

Page 51

9–51

DESIGN TABLES

Table 9-4 (continued)

Beam Bearing Constants

Fy = 50 ksi

(lb = 31/4 in.) Nominal Wt.

R 5 /Ω kips

kips

lb/ft

ASD

82 74 68 61

φR 5

R 6 /Ω

φR 6

LRFD

ASD

LRFD

ASD

73.6 58.8 49.9 40.5

110 88.2 74.8 60.7

10.5 7.88 6.83 5.67

15.7 11.8 10.2 8.50

53 48 43

40.3 33.6 27.0

60.5 50.5 40.4

5.32 4.61 3.76

38 34 30

27.0 22.3 18.5

40.6 33.4 27.8

26 22

18.2 13.6

27.3 20.4

336 305 279 252 230 210 190 170 152 136 120 106 96 87 79 72 65

x < d /2 R n /Ω φR n kips/in. kips/in. kips kips

Vnx / Ωv φvVnx

d /2 ≤ x ≤ d R n /Ω φR n kips kips

x>d R n /Ω φR n kips kips

kips

kips

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

108 84.4 72.1 58.9

161 127 108 88.3

117 101 90.2 79.4

175 151 136 119

178 152 135 116

268 228 204 175

146 128 116 104

219 192 174 156

7.98 6.92 5.65

57.6 48.6 39.2

86.4 73.0 58.8

78.5 70.4 61.7

118 106 92.4

114 96.1 77.3

171 144 116

103 93.8 83.6

154 141 125

3.95 3.50 3.57

5.93 5.25 5.35

39.8 33.7 30.1

59.9 50.5 45.2

57.1 51.2 47.0

85.9 77.0 70.4

78.8 66.5 59.4

118 99.8 88.9

87.4 79.8 74.5

131 120 112

2.74 2.55

4.10 3.83

27.1 21.9

40.6 32.8

45.0 39.0

67.7 58.5

53.5 43.3

80.2 64.9

70.9 63.0

106 94.5

— — 557 485 427 374 321 277 239 207 178 147 128 114 95.5 80.1 66.3

— — 836 727 641 561 481 415 359 311 266 220 192 171 143 120 99.4

— — 557 485 427 374 321 277 239 207 178 147 128 116 103 92.0 81.3

— — 836 727 641 561 481 415 359 311 266 220 192 175 154 138 122

1250 1070 948 818 714 620 527 450 384 329 279 228 197 177 155 137 120

1870 1610 1420 1230 1070 930 790 674 577 494 417 341 295 265 233 206 180

598 531 487 431 390 347 305 269 238 212 186 157 140 129 117 106 94.4

897 797 730 647 584 520 458 403 358 318 279 236 210 193 175 159 142

892 1340 109 748 1120 94.4 646 970 87.9 540 809 76.3 458 687 66.2 384 576 56.7 314 471 45.8 256 383 39.0 209 313 33.1 170 255 28.4 136 204 23.7 103 155 17.1 84.3 126 14.0 72.0 108 13.0 59.7 89.6 11.0 49.9 74.8 9.29 40.9 61.4 7.81

164 142 132 114 99.2 85.0 68.7 58.5 49.6 42.5 35.6 25.7 21.0 19.5 16.5 13.9 11.7

58 53

38.1 33.6

57.2 50.3

5.76 5.69

8.63 8.53

56.8 52.1

85.2 78.0

76.2 71.3

114 107

111 102

167 153

87.8 83.5

132 125

50 45 40

39.5 32.3 25.3

59.3 48.4 37.9

6.25 5.21 4.04

9.37 7.81 6.05

59.8 49.2 38.4

89.8 73.8 57.6

75.2 66.6 57.0

113 99.8 85.7

110 96.2 75.1

166 144 113

90.3 81.1 70.2

135 122 105

35 30 26

26.0 19.3 14.8

39.1 28.9 22.3

4.00 3.13 2.53

6.00 4.69 3.79

39.0 29.5 23.0

58.6 44.1 34.6

53.0 44.2 37.9

79.6 66.4 57.0

73.5 57.7 45.2

110 86.5 67.7

75.0 64.0 56.1

113 95.9 84.2

—Indicates that 31/4-in. bearing length is insufficient for end beam reactions since lb < k. lb = length of bearing, in. x = location of concentrated force with respect to the member end, in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:22 AM

Page 52

9–52

DESIGN OF CONNECTING ELEMENTS

Table 9-4 (continued)

Beam Bearing Constants

Fy = 50 ksi

Shape

R 1/Ω kips

φR 1 kips

R 2 /Ω kips/in.

φR 2 kips/in.

R 3 /Ω kips

φR 3 kips

R 4 /Ω kips/in.

φR 4 kips/in.

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

W12×22 ×19 ×16 ×14

15.7 12.7 10.4 8.75

8.67 7.83 7.33 6.67

13.0 11.8 11.0 10.0

20.8 16.2 12.8 10.2

31.2 24.3 19.2 15.3

2.43 2.20 2.42 2.16

3.64 3.29 3.63 3.24

23.6 19.1 15.5 13.1

W10×112 ×100 ×88 ×77 ×68 ×60 ×54 ×49

110 91.8 75.1 60.5 49.7 41.3 34.5 30.0

165 138 113 90.8 74.6 62.0 51.8 45.1

25.2 22.7 20.2 17.7 15.7 14.0 12.3 11.3

37.8 34.0 30.3 26.5 23.5 21.0 18.5 17.0

177 143 113 86.7 68.1 54.1 42.5 35.7

265 214 169 130 102 81.1 63.8 53.6

21.8 18.3 15.0 11.7 9.37 7.72 5.89 5.07

32.7 27.4 22.4 17.5 14.1 11.6 8.84 7.61

W10×45 ×39 ×33

32.7 27.0 22.6

49.0 40.6 33.9

11.7 10.5 9.67

17.5 15.8 14.5

39.3 31.0 24.8

58.9 46.5 37.2

4.95 4.30 4.16

7.42 6.44 6.24

W10×30 ×26 ×22

20.3 16.0 13.2

30.4 24.1 19.8

10.0 8.67 8.00

15.0 13.0 12.0

28.3 21.2 17.0

42.4 31.8 25.5

3.64 2.80 2.72

5.46 4.20 4.08

W10×19 ×17 ×15 ×12

14.5 12.6 10.9 8.08

21.7 18.9 16.4 12.1

8.33 8.00 7.67 6.33

12.5 12.0 11.5 9.50

18.9 16.3 13.8 9.14

28.4 24.4 20.7 13.7

2.80 3.00 3.26 2.39

4.20 4.49 4.89 3.59

W8×67 ×58 ×48 ×40 ×35 ×31

63.2 51.0 36.0 28.6 23.0 19.7

94.8 76.5 54.0 42.9 34.4 29.5

19.0 17.0 13.3 12.0 10.3 9.50

28.5 25.5 20.0 18.0 15.5 14.3

100 78.9 50.4 38.9 29.2 24.2

150 118 75.6 58.4 43.9 36.3

15.9 13.5 7.94 7.30 5.35 4.81

23.9 20.3 11.9 10.9 8.03 7.21

W8×28 ×24

20.4 16.2

30.6 24.3

9.50 8.17

14.3 12.3

25.0 18.5

37.5 27.7

4.46 3.35

6.69 5.02

W8×21 ×18

14.6 12.1

21.9 18.1

8.33 7.67

12.5 11.5

19.0 15.3

28.6 22.9

3.41 3.27

5.11 4.91

W8×15 ×13 ×10

12.6 10.6 7.15

18.8 16.0 10.7

8.17 7.67 5.67

12.3 11.5 8.50

16.4 13.4 7.64

24.6 20.1 11.5

4.16 4.31 2.19

6.24 6.47 3.29

For R1 and R2 ASD

LRFD

For R3, R4, R5, R6 ASD

LRFD

Ω = 1.50 φ = 1.00 Ω = 2.00 φ = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 9:14th Ed.

2/24/11

8:22 AM

Page 53

9–53

DESIGN TABLES

Table 9-4 (continued)

Beam Bearing Constants

Fy = 50 ksi

(lb = 31/4 in.) Nominal Wt.

R 5 /Ω kips

kips

lb/ft

ASD

22 19 16 14

18.8 14.4 10.9 8.51

φR 5

R 6 /Ω

φR 6

LRFD

ASD

LRFD

ASD

28.2 21.7 16.3 12.8

3.24 2.93 3.23 2.88

4.86 4.39 4.84 4.32

x < d /2 R n /Ω φR n kips/in. kips/in. kips kips

43.6 36.5 29.9 23.3 18.7 15.4 11.8 10.1

Vnx / Ωv φvVnx

d /2 ≤ x ≤ d R n /Ω φR n kips kips

x>d R n /Ω φR n kips kips

kips

kips

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

29.3 23.9 21.4 17.9

44.0 36.0 32.0 26.8

43.9 38.1 34.2 30.4

65.9 57.5 51.3 45.6

57.4 46.7 41.3 34.4

86.1 70.0 62.0 51.7

64.0 57.3 52.8 42.8

95.9 86.0 79.2 64.3

192 166 141 118 101 82.3 64.0 54.3

288 249 211 177 151 123 96.2 81.3

192 166 141 118 101 86.8 74.5 66.7

112 100 88 77 68 60 54 49

160 129 102 78.4 61.6 48.8 38.5 32.3

240 194 153 118 92.4 73.2 57.8 48.5

29.1 24.4 20.0 15.6 12.5 10.3 7.86 6.76

288 249 211 177 151 130 112 100

302 257 216 179 150 128 109 96.7

453 387 324 268 226 192 164 145

172 151 131 112 97.8 85.7 74.7 68.0

45 39 33

35.9 28.2 22.1

53.9 42.2 33.2

6.60 5.73 5.55

9.89 8.59 8.33

57.4 46.8 40.1

86.0 70.1 60.3

30 26 22

25.7 19.3 15.1

38.6 28.9 22.7

4.86 3.74 3.63

7.29 5.60 5.44

41.5 31.5 26.9

19 17 15 12

17.0 14.2 11.6 7.57

25.5 21.4 17.4 11.4

3.74 4.00 4.35 3.19

5.60 5.99 6.52 4.78

67 58 48 40 35 31

90.7 71.1 45.9 34.9 26.3 21.6

136 107 68.9 52.4 39.5 32.4

21.2 18.0 10.6 9.73 7.14 6.41

70.7 61.1 54.0

106 92.0 81.0

103 88.1 76.6

155 133 115

70.7 62.5 56.4

106 93.7 84.7

62.3 47.1 40.4

52.8 44.2 39.2

79.2 66.4 58.8

73.1 60.2 51.7

110 90.5 77.5

63.0 53.6 49.0

94.5 80.3 73.4

29.2 27.2 25.7 17.9

43.7 40.9 38.6 26.9

41.6 38.6 35.8 28.7

62.3 57.9 53.8 43.0

56.0 51.2 46.7 33.8

84.0 76.8 70.2 50.7

51.0 48.5 46.0 37.5

76.5 72.7 68.9 56.3

31.8 27.0 15.9 14.6 10.7 9.61

125 106 79.2 66.5 49.5 42.4

187 159 119 99.9 74.3 63.6

125 106 79.2 67.6 56.5 50.6

187 159 119 101 84.8 76.0

188 157 115 96.2 79.5 70.3

103 89.3 68.0 59.4 50.3 45.6

154 134 102 89.1 75.5 68.4

28 24

22.6 16.7

33.9 25.1

5.95 4.47

8.93 6.70

41.9 31.2

62.9 46.9

51.3 42.8

77.1 64.3

71.7 58.8

108 88.0

45.9 38.9

68.9 58.3

21 18

17.2 13.5

25.7 20.2

4.54 4.36

6.82 6.55

32.0 27.7

47.9 41.5

41.7 37.0

62.5 55.5

56.3 49.1

84.4 73.6

41.4 37.4

62.1 56.2

15 13 10

14.1 11.1 6.49

21.2 16.7 9.73

5.55 5.75 2.93

8.32 8.63 4.39

32.1 29.8 16.0

48.2 44.7 24.0

39.2 35.5 25.6

58.8 53.4 38.3

51.8 46.1 29.5

77.6 69.4 44.4

39.7 36.8 26.8

59.6 55.1 40.2

lb = length of bearing, in. x = location of concentrated force with respect to the member end, in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

282 236 173 144 119 105

258 226 196 169 147 129 112 102

AISC_PART 9:14th Ed.

9–54

2/24/11

8:22 AM

Page 54

DESIGN OF CONNECTING ELEMENTS

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

4/1/11

9:00 AM

Page 1

10–1

PART 10 DESIGN OF SIMPLE SHEAR CONNECTIONS

SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–4 FORCE TRANSFER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–4 COMPARING CONNECTION ALTERNATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–5 Two-Sided Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–5 Seated Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–5 One-Sided Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–5 CONSTRUCTABILITY CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–5 Double Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–6 Accessibility in Column Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–7 Field-Welded Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–7 Riding the Fillet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–7 DOUBLE-ANGLE CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–7 Available Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–9 Recommended Angle Length and Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–9 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–9 DESIGN TABLE DISCUSSION (TABLES 10-1, 10-2 AND 10-3) . . . . . . . . . . . . . . 10–9 Table 10-1. All-Bolted Double-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . . 10–13 Table 10-2. Available Weld Strength of Bolted/Welded Double-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–46 Table 10-3. Available Weld Strength of All-Welded Double-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–47 SHEAR END-PLATE CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–49 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–49 Recommended End-Plate Dimensions and Thickness . . . . . . . . . . . . . . . . . . . . . . 10–49 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–49 DESIGN TABLE DISCUSSION (TABLE 10-4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–50 Table 10-4. Bolted/Welded Shear End-Plate Connections . . . . . . . . . . . . . . . . . . . 10–51 UNSTIFFENED SEATED CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–84 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–85 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–85 Bolted/Welded Unstiffened Seated Connections . . . . . . . . . . . . . . . . . . . . . . . . . . 10–85 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

10–2

2/24/11

9:13 AM

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DESIGN OF SIMPLE SHEAR CONNECTIONS

DESIGN TABLE DISCUSSION (TABLES 10-5 AND 10-6) . . . . . . . . . . . . . . . . . . 10–85 Table 10-5. All-Bolted Unstiffened Seated Connections . . . . . . . . . . . . . . . . . . . . 10–89 Table 10-6. All-Welded Unstiffened Seated Connections . . . . . . . . . . . . . . . . . . . 10–91 STIFFENED SEATED CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–93 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–94 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–95 DESIGN TABLE DISCUSSION (TABLES 10-7 AND 10-8) . . . . . . . . . . . . . . . . . . 10–95 Table 10-7. All-Bolted Stiffened Seated Connections . . . . . . . . . . . . . . . . . . . . . . 10–97 Table 10-8. Bolted/Welded Stiffened Seated Connections . . . . . . . . . . . . . . . . . . . 10–98 SINGLE-PLATE CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–102 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–102 Conventional Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–102 Dimensional Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–102 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–103 Table 10-9. Design Values for Conventional Single-Plate Shear Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–103 Extended Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–103 Dimensional Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–104 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–104 Requirement for Stabilizer Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–105 Recommended Plate Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–106 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–106 DESIGN TABLE DISCUSSION (TABLE 10-10) . . . . . . . . . . . . . . . . . . . . . . . . . . 10–107 Table 10-10. Single-Plate Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–108 SINGLE-ANGLE CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–132 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–133 Recommended Angle Length and Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–133 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–133 DESIGN TABLE DISCUSSION (TABLES 10-11 AND 10-12) . . . . . . . . . . . . . . . 10–134 Table 10-11. All-Bolted Single-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . 10–135 Table 10-12. Bolted/Welded Single-Angle Connections . . . . . . . . . . . . . . . . . . . 10–136 TEE CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–138 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–138 Recommended Tee Length and Flange and Web Thicknesses . . . . . . . . . . . . . . . 10–139 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–139 SHEAR SPLICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–139 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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SPECIAL CONSIDERATIONS FOR SIMPLE SHEAR CONNECTIONS . . . . . . . 10–141 Simple Shear Connections Subject to Axial Forces . . . . . . . . . . . . . . . . . . . . . . . 10–141 Simple Shear Connections at Stiffened Column-Web Locations . . . . . . . . . . . . . 10–141 Eccentric Effect of Extended Gages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–143 Column-Web Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–143 Girder-Web Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–146 Alternative Treatment of Eccentric Moment . . . . . . . . . . . . . . . . . . . . . . . . . . 10–147 Double Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–147 Supported Beams of Different Nominal Depths . . . . . . . . . . . . . . . . . . . . . . . 10–147 Supported Beams Offset Laterally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–147 Beams Offset from Column Centerline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–147 Framing to the Column Flange from the Strong Axis . . . . . . . . . . . . . . . . . . . 10–147 Framing to the Column Flange from the Weak Axis . . . . . . . . . . . . . . . . . . . . 10–150 Framing to the Column Web . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–153 Connections for Raised Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–153 Non-Rectangular Simple Shear Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–157 Skewed Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–159 Sloped Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–162 Canted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–164 Inclines in Two or More Directions (Hip and Valley Framing) . . . . . . . . . . . 10–166 DESIGN CONSIDERATIONS FOR SIMPLE SHEAR CONNECTIONS TO HSS COLUMNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–167 Double-Angle Connections to HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–167 Single-Plate Connections to HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–167 Unstiffened Seated Connections to HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–167 Stiffened Seated Connections to HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–168 Through-Plate Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–168 Single-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–169 DESIGN TABLE DISCUSSION (TABLES 10-13, 10-14A, 10-14B, 10-14C AND 10-15) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–169 Table 10-13. Minimum Inside Radius for Cold-Blending . . . . . . . . . . . . . . . . . . 10–172 Table 10-14A. Clearances for All-Bolted Skewed Connections . . . . . . . . . . . . . 10–173 Table 10-14B. Clearances for Bolted/Welded Skewed Connections . . . . . . . . . . 10–174 Table 10-14C. Welding Details for Skewed Single-Plate Connections . . . . . . . . 10–176 Table 10-15. Required Length and Thickness for Stiffened Seated Connections to HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–178 PART 10 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–181 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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SCOPE The specification requirements and other design considerations summarized in this Part apply to the design of simple shear connections. For the design of partially restrained moment connections, see Part 11. For the design of fully restrained (FR) moment connections, see Part 12.

FORCE TRANSFER The required strength (end reaction), Ru or Ra, is determined by analysis as indicated in AISC Specification Section B3.6a. Per AISC Specification Section J1.2, the ends of members with simple shear connections are normally assumed to be free to rotate under load. While simple shear connections do actually possess some rotational restraint (see curve A in Figure 10-1), this small amount can be neglected and the connection idealized as completely flexible. The simple shear connections shown in this Manual are suitable to accommodate the end rotations required per AISC Specification Section J1.2. Support rotation is acceptably limited for most framing details involving simple shear connections without explicit consideration. The case of a bare spandrel girder supporting infill beams, however, may require consideration to verify that an acceptable level of support rotational stiffness is present. Sumner (2003) showed that a nominal interconnection between

Fig. 10-1. Illustration of typical moment rotation curve for simple shear connection. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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the top flange of the girder and the top flange of the framing beam is sufficient to limit support rotation.

COMPARING CONNECTION ALTERNATIVES Two-Sided Connections Two-sided connections, such as double-angle and shear end-plate connections, offer the following advantages: 1. suitability for use when the end reaction is large; 2. compact connections (usually, the entire connection is contained within the flanges of the supported beam); and, 3. eccentricity perpendicular to the beam axis need not be considered for workable gages (see Table 1-7A). Note that two-sided connections may require additional consideration for erectability, as discussed in “Constructability Considerations” below.

Seated Connections Unstiffened and stiffened seated connections offer the following advantages: 1. 2. 3. 4.

seats can be shop attached to the support, simplifying erection; ample erection clearance is provided; excellent safety during erection since double connections often can be eliminated; and, the bay length of the structure is easily maintained (seated connections may be preferable when maintaining bay length is a concern for repetitive bays of framing).

One-Sided Connections One-sided connections such as single-plate, single-angle and tee connections offer the following advantages: 1. shop attachment of connection elements to the support, simplifying shop fabrication and erection; 2. reduced material and shop labor requirements; 3. ample erection clearance is provided; and, 4. excellent safety during erection since double connections often can be eliminated.

CONSTRUCTABILITY CONSIDERATIONS Double Connections A double connection occurs in field-bolted construction when beams or girders frame opposite each other. Double connections are a safety concern when they occur in the web of a column (see Figure 10-2) or the web of a beam that frames continuously over the top of a column1 and all field bolts take the same open holes. A positive connection must be made 1

This requirement applies only at the location of the column, not at locations away from the column.

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and maintained for the first member to be erected while the second member to be erected is brought into its final position. Conditions requiring the connector to hang one beam temporarily on a partially inserted bolt or drift pin are not allowed by OSHA. Framing details can be configured using staggered angles or other similar details to provide a means to make a positive connection for the first member while the second member is brought into its final position. Alternatively, a temporary erection seat, as shown in Figure 10-2, can be provided. The erection seat, usually an angle, is sized and attached to the column web to support the dead weight of the member, unless additional loading is indicated in the contract documents. It is located to clear the bottom flange of the supported member by approximately 3/8 in. to accommodate mill, fabrication and erection tolerances. The sequence of erection is most important in determining the need for erection seats. If the erection sequence is known, the erection seat is provided on the side needing the support. If the erection sequence is not known, a seat can be provided on both sides of the column web. Temporary erection seats may be reused at other locations after the connection(s) are made, but need not be removed unless they create an interference or removal is required in the contract documents. See also the discussion under “Special Considerations for Simple Shear Connections.”

Accessibility in Column Webs Because of bolting and welding clearances, double-angle, shear end-plate, single-plate, single-angle, and tee shear connections may not be suitable for connections to the webs of W-shape and similar columns, particularly for W8 columns, unless gages are reduced. Such connections may be impossible for W6, W5 and W4 columns. There is also an accessibility concern for entering and tightening the field bolts when the connection material is shop-attached to the supporting column web and contained within the column flanges.

Fig. 10-2. Erection seat. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Field-Welded Connections In field-welded connections, temporary erection bolts are usually provided to support the member until final welding is performed. A minimum of two bolts (one bolt in bracing members) must be placed for erection safety per OSHA requirements. Additional erection bolts may be required for loads during erection, to assist in pulling the connection angles up tightly against the web of the supporting beam prior to welding or for other reasons. Temporary erection bolts may be reused at other locations after final welding, but need not be removed unless they create an interference or removal is required in the contract documents.

Riding the Fillet The detailed dimensions of connection elements must be compatible with the T-dimension of an uncoped beam and the remaining web depth of a coped beam. Note that the element may encroach upon the fillet(s), as given in Figure 10-3.

DOUBLE-ANGLE CONNECTIONS A double-angle connection is made with two angles, one on each side of the web of the beam to be supported, as illustrated in Figure 10-4. These angles may be bolted or welded to the supported beam as well as to the supporting member. When the angles are welded to the support, adequate flexibility must be provided in the connection. As illustrated in Figure 10-4(c), line welds are placed along the toes of the angles with a return at the top per AISC Specification Section J2.2b. Note that welding across the entire top of the angles must be avoided as it inhibits the flexibility and, therefore, the necessary end rotation of the connection. The performance of the resulting connection would not be as intended for simple shear connections.

Available Strength The available strength of a double-angle connection is determined from the applicable limit states for bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). In all cases, the available strength, φRn or Rn /Ω, must equal or exceed the required strength, Ru or Ra.

Fig. 10-3. Fillet encroachment (riding the fillet). AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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For standard or short-slotted holes, eccentricity on the supported side of double angle connections may be neglected for gages [distance from the face of the outstanding angle legs to the centerline of the vertical bolt row, shown as dimension a in Figure 10-4(a)] not exceeding 3 in., except in the case of a double vertical row of bolts through the web of the supported beam. Eccentricity should always be considered in the design of welds for double-angle connections.

(a) All-bolted

(b) Bolted/welded, angles welded to support beam

(c) Bolted/welded, angles welded to support Fig. 10-4. Double-angle connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Recommended Angle Length and Thickness To provide for stability during erection, it is recommended that the minimum angle length be one-half the T-dimension of the beam to be supported. The maximum length of the connection angles must be compatible with the T-dimension of an uncoped beam and the remaining web depth of a coped beam. Note that the element may encroach upon the fillet(s), as given in Figure 10-3. To provide for flexibility, the maximum angle thickness for use with workable gages should be limited to 5/8 in. Alternatively, the shear-connection ductility checks illustrated in Part 9 can be used to justify other combinations of gage and angle thickness.

Shop and Field Practices When framing to a girder web, both angles are usually shop-attached to the web of the supported beam. When framing to a column web, both angles should be shop-attached to the supported beam, when possible, and the associated constructability considerations should be addressed (see the preceding discussion under “Constructability Considerations”). When framing to a column flange, both angles can be shop-attached to the column flange or the supported beam. In the former case, this is a knifed connection, as illustrated in Figure 10-4(c), which requires an erection clearance, as illustrated in Figure 10-5(a), and that the bottom flange be coped. Also, provision must be made for possible mill variation in the depth of the columns, particularly in fairly long runs (i.e., six or more bays of framing). If both angles are shop-attached to the beam web, the beam length can be shortened to provide for mill overrun with shims furnished at the appropriate intervals to fill the resulting gaps or to provide for mill underrun. If both angles are shop-attached to the column flange, the erected beam is knifed into place and play in the open holes is normally sufficient to provide for the necessary adjustment. Alternatively, short-slotted holes can also be used. When special requirements preclude the use of any of the foregoing practices, one angle could be shop-attached to the support and the other shipped loose. In this case, the spread between the outstanding legs should equal the decimal beam web thickness plus a clearance that will produce an opening to the next higher 1/16-in. increment, as illustrated in Figure 10-5(b). Alternatively, short-slotted holes in the support leg of the angle eliminate the need to provide for variations in web thickness. Note that the practice of shipping one angle loose is not desirable because it requires additional material handling as well as added erection costs and complexity.

DESIGN TABLE DISCUSSION (TABLES 10-1, 10-2 AND 10-3) Table 10-1. All-Bolted Double-Angle Connections Table 10-1 is a design aid for all-bolted double-angle connections. Available strengths are tabulated for supported and supporting member material with Fy = 50 ksi and Fu = 65 ksi and angle material with Fy = 36 ksi and Fu = 58 ksi. Eccentricity effects on the supported (beam) side of the connections are neglected, as discussed previously for gages not exceeding 3 in. All values, including slip-critical bolt available strengths, are for comparison with the governing LRFD or ASD load combination. Tabulated bolt and angle available strengths consider the limit states of bolt shear, bolt bearing on the angles, shear yielding of the angles, shear rupture of the angles, and block AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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shear rupture of the angles. Values are tabulated for 2 through 12 rows of 3/4-in.-, 7/8-in.- and 1-in.-diameter Group A and Group B bolts (as defined in AISC Specification Section J3.1) at 3-in. spacing. For calculation purposes, angle edge distances, Lev and Leh, are assumed to be 11/4 in. Tabulated beam web available strengths, per in. of web thickness, consider the limit state of bolt bearing on the beam web. For beams coped at the top flange only, the limit state of block shear rupture is also considered. Additionally, for beams coped at both the top and bottom flanges, the tabulated values consider the limit states of shear yielding and shear rupture of the beam web. Values are tabulated for beam web edge distances, Lev , from 11/4 in. to 3 in. and for beam end distances, Leh, of 11/2 in. and 13/4 in. For calculation purposes, these end distances have been reduced to 11/4 in. and 11/2 in., respectively, to account for possible underrun in beam length. For coped members, the limit states of flexural yielding and local buckling must be checked independently per Part 9. When required, web reinforcement of coped members is treated as in Part 9.

(a) Both angles shop attached to the column flange (beam knifed into place)

(b) One shop attached to the column flange, other shipped loose Fig. 10-5. Erection clearances for double-angle connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Tabulated supporting member available strengths, per in. of flange or web thickness, consider the limit state of bolt bearing on the support. Note that resistance and safety factors are not noted in these tables, as they vary by limit state.

Table 10-2. Available Weld Strength of Bolted/Welded Double-Angle Connections Table 10-2 is a design aid arranged to permit substitution of welds for bolts in connections designed with Table 10-1. Electrode strength is assumed to be 70 ksi. Holes for erection bolts may be placed as required in angle legs that are to be field-welded. Welds A may be used in place of bolts through the supported-beam web legs of the double angles or welds B may be used in place of bolts through the support legs of the double angles. Although it is permissible to use welds A and B from Table 10-2 in combination to obtain all-welded connections, it is recommended that such connections be selected from Table 10-3. This table will allow increased flexibility in the selection of angle lengths and connection strengths because Table 10-2 conforms to the bolt spacing and edge distance requirements for the all-bolted double-angle connections of Table 10-1. Weld available strengths are tabulated for the limit state of weld shear. Available strengths for welds A are determined by the instantaneous center of rotation method using Table 8-8 with θ = 0°. Available strengths for welds B are determined by the elastic method. With the neutral axis assumed at one-sixth the depth of the angles measured downward and the tops of the angles in compression against each other through the beam web, the available strength, φRn or Rn /Ω, of these welds is determined by ASD

LRFD ⎛ ⎜ 1.392 DL φRn = 2 ⎜ ⎜ 12.96e 2 ⎜ 1+ ⎝ L2

⎞ ⎟ ⎟ ⎟ ⎟ ⎠

⎛ ⎜ Rn 0.928 DL = 2⎜ ⎜ Ω 12.96e 2 ⎜ 1+ ⎝ L2

(10-1a)

⎞ ⎟ ⎟ ⎟ ⎟ ⎠

(10-1b)

where D = number of sixteenths-of-an-inch in the weld size L = length of the connection angles, in. e = width of the leg of the connection angle attached to the support, in. Note that φ = 0.75 is included in the right hand side of Equation 10-1a and Ω = 2.00 is included in the right hand side of Equation 10-1b. The tabulated minimum thicknesses of the supported beam web for welds A and the support for welds B match the shear rupture strength of these elements with the strength of the weld metal. As derived in Part 9, the minimum supported beam web thickness for welds A (two lines of weld) is tmin =

6.19 D Fu

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and the minimum supporting flange or web thickness for welds B (one line of weld) is tmin =

3.09 D Fu

(9-2)

When welds B line up on opposite sides of the support, the minimum thickness is the sum of the thicknesses required for each weld. In either case, when less than the minimum material thickness is present, the tabulated weld available strength must be reduced by the ratio of the thickness provided to the minimum thickness. When Table 10-2 is used, the minimum angle thickness is the weld size plus 1/16 in., but not less than the angle thickness determined from Table 10-1. The angle length, L, must be as tabulated in Table 10-2. In general, 2L4×31/2 will accommodate workable gages, with the 4-in. leg attached to the supporting member. The width of web legs in Case I (web legs welded and outstanding legs bolted) may be optionally reduced from 31/2 in. to 3 in. The width of outstanding legs in Case II (web legs bolted and outstanding legs welded) may be optionally reduced from 4 in. to 3 in. for values of L from 51/2 through 171/2 in.

Table 10-3. Available Weld Strength of All-Welded Double-Angle Connections Table 10-3 is a design aid for all-welded double-angle connections. Electrode strength is assumed to be 70 ksi. Holes for erection bolts may be placed as required in angle legs that are to be field-welded. Weld available strengths are tabulated for the limit state of weld shear. Available strengths for welds A are determined by the instantaneous center of rotation method using Table 8-8 with θ = 0°. Available strengths for welds B are determined by the elastic method as discussed previously for bolted/welded double-angle connections. The tabulated minimum thicknesses of the supported beam web for welds A and the support for welds B match the shear rupture strength of these elements with the strength of the weld metal and are determined as discussed previously for Table 10-2. When welds B line up on opposite sides of the support, the minimum thickness is the sum of the thicknesses required for each weld. When less than the minimum material thickness is present, the tabulated weld available strength must be reduced by the ratio of the thickness provided to the minimum thickness. When Table 10-3 is used, the minimum angle thickness must be equal to the weld size plus 1/16 in. The angle length, L, must be as tabulated in Table 10-3. 2L4×31/2 should be used for angle lengths equal to or greater than 18 in. For angle length less than 18 in., the 4-in. leg can be reduced to 3 in.

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Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 12 Rows W44

Table 10-1

All-Bolted Double-Angle Connections

3

/Bolts 4-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/ 2 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD ASD LRFD N STD 197 295 246 369 286 430 286 430 X STD 197 295 246 369 295 443 361 541 STD 152 228 152 228 152 228 152 228 SC OVS 129 194 129 194 129 194 129 194 Group Class A SSLT 152 228 152 228 152 228 152 228 A STD 197 295 246 369 253 380 253 380 SC OVS 196 294 216 323 216 323 216 323 Class B SSLT 195 293 244 366 253 380 253 380 N STD 197 295 246 369 295 443 361 541 X STD 197 295 246 369 295 443 393 590 STD 190 285 190 285 190 285 190 285 SC Group OVS 162 242 162 242 162 242 162 242 Class A B SSLT 190 285 190 285 190 285 190 285 STD 197 295 246 369 295 443 316 475 SC OVS 196 294 245 367 270 403 270 403 Class B SSLT 195 293 244 366 293 440 316 475 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

1400

2110

11/2 ASD LRFD 498 747 501 751 503 754 505 758 513 769 532 798 488 731 492 739 497 746 502 753 513 769 532 798 702 1050

13/4 ASD LRFD 506 759 509 763 511 767 514 770 521 781 540 810 488 731 492 739 497 746 502 753 517 775 540 810 702 1050

OVS Leh *, in. 11/2 ASD LRFD 468 702 470 706 473 709 475 713 483 724 502 753 458 687 463 695 468 702 473 709 483 724 502 753 702 1050

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 476 714 479 718 481 722 483 725 491 736 510 765 458 687 463 695 468 702 473 709 488 731 510 765 702 1050

SSLT 11/2 ASD LRFD 495 743 497 746 500 750 502 753 510 764 529 794 488 731 492 739 497 746 502 753 510 764 529 794 702 1050

13/4 ASD LRFD 503 755 506 758 508 762 510 766 518 777 537 806 488 731 492 739 497 746 502 753 517 775 537 806 702 1050

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:14 AM

Page 14

Angle Beam

10–14

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 11 Rows W44, 40

Table 10-1 (continued)

All-Bolted Double-Angle Connections

3

/Bolts 4-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 181 271 226 338 263 394 X STD 181 271 226 338 271 406 STD 139 209 139 209 139 209 SC OVS 119 178 119 178 119 178 Group Class A SSLT 139 209 139 209 139 209 A STD 181 271 226 338 232 348 SC OVS 180 269 198 296 198 296 Class B SSLT 179 269 224 336 232 348 N STD 181 271 226 338 271 406 X STD 181 271 226 338 271 406 STD 174 261 174 261 174 261 SC Group OVS 148 222 148 222 148 222 Class A B SSLT 174 261 174 261 174 261 STD 181 271 226 338 271 406 SC OVS 180 269 225 337 247 370 Class B SSLT 179 269 224 336 269 403 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

1290

1930

11/2 ASD LRFD 457 685 459 689 462 692 464 696 471 707 491 736 446 669 451 676 456 684 461 691 471 707 491 736 644 965

13/4 ASD LRFD 465 697 467 701 470 704 472 708 479 719 499 748 446 669 451 676 456 684 461 691 475 713 499 748 644 965

OVS Leh *, in. 11/2 ASD LRFD 429 644 431 647 434 651 436 654 444 665 463 695 419 629 424 636 429 644 434 651 444 665 463 695 644 965

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 437 656 440 659 442 663 444 667 452 678 471 707 419 629 424 636 429 644 434 651 449 673 471 707 644 965

1/ 2 ASD LRFD 263 394 331 496 139 209 119 178 139 209 232 348 198 296 232 348 331 496 361 542 174 261 148 222 174 261 290 435 247 370 290 435

SSLT 11/2 ASD LRFD 454 680 456 684 458 688 461 691 468 702 488 732 446 669 451 676 456 684 461 691 468 702 488 732 644 965

13/4 ASD LRFD 462 693 464 696 467 700 469 704 476 714 496 744 446 669 451 676 456 684 461 691 475 713 496 744 644 965

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:14 AM

Page 15

10–15

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 10 Rows W44, 40, 36

Table 10-1 (continued)

All-Bolted Double-Angle Connections

3

/Bolts 4-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 164 246 205 308 239 358 X STD 164 246 205 308 246 370 STD 127 190 127 190 127 190 SC OVS 108 161 108 161 108 161 Group Class A SSLT 127 190 127 190 127 190 A STD 164 246 205 308 211 316 SC OVS 163 245 180 269 180 269 Class B SSLT 163 244 204 306 211 316 N STD 164 246 205 308 246 370 X STD 164 246 205 308 246 370 STD 158 237 158 237 158 237 SC Group OVS 135 202 135 202 135 202 Class A B SSLT 158 237 158 237 158 237 STD 164 246 205 308 246 370 SC OVS 163 245 204 306 225 336 Class B SSLT 163 244 204 306 244 367 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

1170

1760

11/2 ASD LRFD 415 623 418 626 420 630 423 634 430 645 449 674 405 607 410 614 414 622 419 629 430 645 449 674 585 878

13/4 ASD LRFD 423 635 426 639 428 642 431 646 438 657 457 686 405 607 410 614 414 622 419 629 434 651 457 686 585 878

OVS Leh *, in. 11/2 ASD LRFD 390 585 392 589 395 592 397 596 405 607 424 636 380 570 385 578 390 585 395 592 405 607 424 636 585 878

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 398 597 401 601 403 605 405 608 413 619 432 648 380 570 385 578 390 585 395 592 410 614 432 648 585 878

1/ 2 ASD LRFD 239 358 301 451 127 190 108 161 127 190 211 316 180 269 211 316 301 451 329 493 158 237 135 202 158 237 264 396 225 336 264 396

SSLT 11/2 ASD LRFD 412 618 415 622 417 626 419 629 427 640 446 669 405 607 410 614 414 622 419 629 427 640 446 669 585 878

13/4 ASD LRFD 420 630 423 634 425 638 428 641 435 652 454 682 405 607 410 614 414 622 419 629 434 651 454 682 585 878

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:14 AM

Page 16

Angle Beam

10–16

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 9 Rows

W44, 40, 36, 33

Table 10-1 (continued)

All-Bolted Double-Angle Connections

3

/Bolts 4-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 148 222 185 278 215 322 X STD 148 222 185 278 222 333 STD 114 171 114 171 114 171 SC OVS 97.1 145 97.1 145 97.1 145 Group Class A SSLT 114 171 114 171 114 171 A STD 148 222 185 278 190 285 SC OVS 147 221 162 242 162 242 Class B SSLT 147 220 183 275 190 285 N STD 148 222 185 278 222 333 X STD 148 222 185 278 222 333 STD 142 214 142 214 142 214 SC Group OVS 121 182 121 182 121 182 Class A B SSLT 142 214 142 214 142 214 STD 148 222 185 278 222 333 SC OVS 147 221 184 276 202 303 Class B SSLT 147 220 183 275 220 330 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

1050

1580

11/2 ASD LRFD 374 561 376 564 379 568 381 572 388 583 408 612 363 545 368 552 373 559 378 567 388 583 408 612 527 790

13/4 ASD LRFD 382 573 384 576 387 580 389 584 397 595 416 624 363 545 368 552 373 559 378 567 392 589 416 624 527 790

OVS Leh *, in. 11/2 ASD LRFD 351 527 353 530 356 534 358 537 366 548 385 578 341 512 346 519 351 527 356 534 366 548 385 578 527 790

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 359 539 362 542 364 546 366 550 374 561 393 590 341 512 346 519 351 527 356 534 371 556 393 590 527 790

1/ 2

ASD 215 271 114 97.1 114 190 162 190 271 296 142 121 142 237 202 237

LRFD 322 406 171 145 171 285 242 285 406 444 214 182 214 356 303 356

SSLT 11/2 ASD LRFD 371 556 373 560 376 563 378 567 385 578 405 607 363 545 368 552 373 559 378 567 385 578 405 607 527 790

13/4 ASD LRFD 379 568 381 572 384 576 386 579 393 590 413 619 363 545 368 552 373 559 378 567 392 589 413 619 527 790

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/17/12

10:35 AM

Page 17

Angle Beam

DESIGN TABLES

10–17

Fy = 50 ksi Fu = 65 ksi

Table 10-1 (continued)

All-Bolted Double-Angle Connections

Fy = 36 ksi Fu = 58 ksi

3

/Bolts 4-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. 8 Rows Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type W44, 40, 36, 33, 30 ASD LRFD ASD LRFD ASD LRFD N STD 132 198 165 247 191 286 X STD 132 198 165 247 198 297 STD 101 152 101 152 101 152 SC OVS 86.3 129 86.3 129 86.3 129 Group Class A SSLT 101 152 101 152 101 152 A STD 132 198 165 247 169 253 SC OVS 131 197 144 215 144 215 Class B SSLT 131 196 163 245 169 253 N STD 132 198 165 247 198 297 X STD 132 198 165 247 198 297 STD 127 190 127 190 127 190 SC Group OVS 108 161 108 161 108 161 Class A B SSLT 127 190 127 190 127 190 STD 132 198 165 247 198 297 SC OVS 131 197 164 246 180 269 Class B SSLT 131 196 163 245 196 294 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

936

1400

11/2 ASD LRFD 332 498 335 502 337 506 340 509 347 520 366 550 322 483 327 490 332 497 336 505 347 520 366 550 468 702

13/4 ASD LRFD 340 511 343 514 345 518 348 522 355 533 375 562 322 483 327 490 332 497 336 505 351 527 375 562 468 702

OVS Leh *, in. 11/2 ASD LRFD 312 468 314 472 317 475 319 479 327 490 346 519 302 453 307 461 312 468 317 475 327 490 346 519 468 702

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 320 480 323 484 325 488 327 491 335 502 354 531 302 453 307 461 312 468 317 475 332 497 354 531 468 702

1/ 2

ASD 191 240 101 86.3 101 169 144 169 240 264 127 108 127 211 180 211

LRFD 286 361 152 129 152 253 215 253 361 396 190 161 190 316 269 316

SSLT 11/2 ASD LRFD 329 494 332 498 334 501 337 505 344 516 363 545 322 483 327 490 332 497 336 505 344 516 363 545 468 702

13/4 ASD LRFD 337 506 340 510 342 513 345 517 352 528 372 557 322 483 327 490 332 497 336 505 351 527 372 557 468 702

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:14 AM

Page 18

Angle Beam

10–18

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi

Table 10-1 (continued)

All-Bolted Double-Angle Connections

Fy = 36 ksi Fu = 58 ksi

3

/Bolts 4-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 W44, 40, 36, 33, 30, Group Cond. Type 27, 24 ASD LRFD ASD LRFD ASD LRFD N STD 116 174 145 217 167 251 X STD 116 174 145 217 174 260 STD 88.6 133 88.6 133 88.6 133 SC OVS 75.5 113 75.5 113 75.5 113 Group Class A SSLT 88.6 133 88.6 133 88.6 133 A STD 116 174 145 217 148 221 SC OVS 115 172 126 188 126 188 Class B SSLT 114 172 143 214 148 221 N STD 116 174 145 217 174 260 X STD 116 174 145 217 174 260 STD 111 166 111 166 111 166 SC Group OVS 94.4 141 94.4 141 94.4 141 Class A B SSLT 111 166 111 166 111 166 STD 116 174 145 217 174 260 SC OVS 115 172 144 215 157 235 Class B SSLT 114 172 143 214 172 257 Beam Web Available Strength per Inch Thickness, kips/in. 7 Rows

STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

819

1230

11/2 ASD LRFD 291 436 293 440 296 444 298 447 306 458 325 488 280 420 285 428 290 435 295 442 306 458 325 488 410 614

13/4 ASD LRFD 299 449 301 452 304 456 306 459 314 470 333 500 280 420 285 428 290 435 295 442 310 464 333 500 410 614

OVS Leh *, in. 11/2 ASD LRFD 273 410 275 413 278 417 280 420 288 431 307 461 263 395 268 402 273 410 278 417 288 431 307 461 410 614

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 281 422 284 425 286 429 288 433 296 444 315 473 263 395 268 402 273 410 278 417 293 439 315 473 410 614

1/ 2

ASD 167 210 88.6 75.5 88.6 148 126 148 210 231 111 94.4 111 185 157 185

LRFD 251 316 133 113 133 221 188 221 316 347 166 141 166 277 235 277

SSLT 11/2 ASD LRFD 288 432 290 435 293 439 295 443 302 454 322 483 280 420 285 428 290 435 295 442 302 454 322 483 410 614

13/4 ASD LRFD 296 444 298 448 301 451 303 455 311 466 330 495 280 420 285 428 290 435 295 442 310 464 330 495 410 614

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:14 AM

Page 19

10–19

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi

Table 10-1 (continued)

All-Bolted Double-Angle Connections

Fy = 36 ksi Fu = 58 ksi

3

/Bolts 4-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 W40, 36, 33, 30, 27, Group Cond. Type 24, 21 ASD LRFD ASD LRFD ASD LRFD N STD 99.5 149 124 187 143 215 X STD 99.5 149 124 187 149 224 STD 75.9 114 75.9 114 75.9 114 SC OVS 64.7 96.8 64.7 96.8 64.7 96.8 Group Class A SSLT 75.9 114 75.9 114 75.9 114 A STD 99.5 149 124 187 127 190 SC OVS 98.6 148 108 161 108 161 Class B SSLT 98.2 147 123 184 127 190 N STD 99.5 149 124 187 149 224 X STD 99.5 149 124 187 149 224 STD 94.9 142 94.9 142 94.9 142 SC Group OVS 80.9 121 80.9 121 80.9 121 Class A B SSLT 94.9 142 94.9 142 94.9 142 STD 99.5 149 124 187 149 224 SC OVS 98.6 148 123 185 135 202 Class B SSLT 98.2 147 123 184 147 221 Beam Web Available Strength per Inch Thickness, kips/in. 6 Rows

STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

702

1050

11/2 ASD LRFD 249 374 252 378 254 381 257 385 264 396 284 425 239 358 244 366 249 373 254 380 264 396 284 425 351 527

13/4 ASD LRFD 258 386 260 390 262 394 265 397 272 408 292 438 239 358 244 366 249 373 254 380 268 402 292 438 351 527

OVS Leh *, in. 11/2 ASD LRFD 234 351 236 355 239 358 241 362 249 373 268 402 224 336 229 344 234 351 239 358 249 373 268 402 351 527

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 242 363 245 367 247 371 249 374 257 385 276 414 224 336 229 344 234 351 239 358 254 380 276 414 351 527

1/ 2

ASD 143 180 75.9 64.7 75.9 127 108 127 180 199 94.9 80.9 94.9 158 135 158

LRFD 215 271 114 96.8 114 190 161 190 271 299 142 121 142 237 202 237

SSLT 11/2 ASD LRFD 246 370 249 373 251 377 254 381 261 392 281 421 239 358 244 366 249 373 254 380 261 392 281 421 351 527

13/4 ASD LRFD 255 382 257 385 259 389 262 393 269 404 289 433 239 358 244 366 249 373 254 380 268 402 289 433 351 527

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:14 AM

Page 20

Angle Beam

10–20

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi

Table 10-1 (continued)

All-Bolted Double-Angle Connections

Fy = 36 ksi Fu = 58 ksi

3

/Bolts 4-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. 5 Rows Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type W30, 27, 24, 21, 18 ASD LRFD ASD LRFD ASD LRFD N STD 83.3 125 104 156 119 179 X STD 83.3 125 104 156 125 187 STD 63.3 94.9 63.3 94.9 63.3 94.9 SC OVS 53.9 80.7 53.9 80.7 53.9 80.7 Group Class A SSLT 63.3 94.9 63.3 94.9 63.3 94.9 A STD 83.3 125 104 156 105 158 SC OVS 82.4 124 89.9 134 89.9 134 Class B SSLT 82.0 123 102 154 105 158 N STD 83.3 125 104 156 125 187 X STD 83.3 125 104 156 125 187 STD 79.1 119 79.1 119 79.1 119 SC Group OVS 67.4 101 67.4 101 67.4 101 Class A B SSLT 79.1 119 79.1 119 79.1 119 STD 83.3 125 104 156 125 187 SC OVS 82.4 124 103 155 112 168 Class B SSLT 82.0 123 102 154 123 184 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

585

878

11/2 ASD LRFD 208 312 210 316 213 319 215 323 223 334 242 363 197 296 202 303 207 311 212 318 223 334 242 363 293 439

13/4 ASD LRFD 216 324 219 328 221 332 223 335 231 346 250 375 197 296 202 303 207 311 212 318 227 340 250 375 293 439

OVS Leh *, in. 11/2 ASD LRFD 195 293 197 296 200 300 202 303 210 314 229 344 185 278 190 285 195 293 200 300 210 314 229 344 293 439

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 203 305 206 308 208 312 210 316 218 327 237 356 185 278 190 285 195 293 200 300 215 322 237 356 293 439

1/ 2

ASD 119 150 63.3 53.9 63.3 105 89.9 105 150 167 79.1 67.4 79.1 132 112 132

LRFD 179 225 94.9 80.7 94.9 158 134 158 225 250 119 101 119 198 168 198

SSLT 11/2 ASD LRFD 205 307 207 311 210 315 212 318 220 329 239 359 197 296 202 303 207 311 212 318 220 329 239 359 293 439

13/4 ASD LRFD 213 320 216 323 218 327 220 331 228 342 247 371 197 296 202 303 207 311 212 318 227 340 247 371 293 439

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:15 AM

Page 21

10–21

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 4 Rows

W24, 21, 18, 16

Table 10-1 (continued)

All-Bolted Double-Angle Connections

3

/Bolts 4-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 67.1 101 83.9 126 95.5 143 X STD 67.1 101 83.9 126 101 151 STD 50.6 75.9 50.6 75.9 50.6 75.9 SC OVS 43.1 64.5 43.1 64.5 43.1 64.5 Group Class A SSLT 50.6 75.9 50.6 75.9 50.6 75.9 A STD 67.1 101 83.9 126 84.4 127 SC OVS 65.3 97.9 71.9 108 71.9 108 Class B SSLT 65.8 98.7 82.2 123 84.4 127 N STD 67.1 101 83.9 126 101 151 X STD 67.1 101 83.9 126 101 151 STD 63.3 94.9 63.3 94.9 63.3 94.9 SC Group OVS 53.9 80.7 53.9 80.7 53.9 80.7 Class A B SSLT 63.3 94.9 63.3 94.9 63.3 94.9 STD 67.1 101 83.9 126 101 151 SC OVS 65.3 97.9 81.6 122 89.9 134 Class B SSLT 65.8 98.7 82.2 123 98.7 148 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

468

702

11/2 ASD LRFD 167 250 169 254 171 257 174 261 181 272 201 301 156 234 161 241 166 249 171 256 181 272 201 301 234 351

13/4 ASD LRFD 175 262 177 266 180 269 182 273 189 284 209 313 156 234 161 241 166 249 171 256 185 278 209 313 234 351

OVS Leh *, in. 11/2 ASD LRFD 156 234 158 238 161 241 163 245 171 256 190 285 146 219 151 227 156 234 161 241 171 256 190 285 234 351

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 164 246 167 250 169 254 171 257 179 268 198 297 146 219 151 227 156 234 161 241 176 263 198 297 234 351

1/ 2

ASD 95.5 120 50.6 43.1 50.6 84.4 71.9 84.4 120 134 63.3 53.9 63.3 105 89.9 105

LRFD 143 180 75.9 64.5 75.9 127 108 127 180 201 94.9 80.7 94.9 158 134 158

SSLT 11/2 ASD LRFD 164 245 166 249 168 253 171 256 178 267 198 296 156 234 161 241 166 249 171 256 178 267 198 296 234 351

13/4 ASD LRFD 172 257 174 261 177 265 179 268 186 279 206 309 156 234 161 241 166 249 171 256 185 278 206 309 234 351

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:15 AM

Page 22

Angle Beam

10–22

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi

Table 10-1 (continued)

All-Bolted Double-Angle Connections

3

/Bolts 4-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Thread Hole 5/16 3/ 8 1/ 2 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD ASD LRFD N STD 50.9 76.4 63.7 95.5 71.6 107 71.6 107 X STD 50.9 76.4 63.7 95.5 76.4 115 90.2 135 STD 38.0 57.0 38.0 57.0 38.0 57.0 38.0 57.0 SC OVS 32.4 48.4 32.4 48.4 32.4 48.4 32.4 48.4 Group Class A SSLT 38.0 57.0 38.0 57.0 38.0 57.0 38.0 57.0 A STD 50.9 76.4 63.3 94.9 63.3 94.9 63.3 94.9 SC OVS 47.9 71.8 53.9 80.7 53.9 80.7 53.9 80.7 Class B SSLT 49.6 74.4 62.0 92.9 63.3 94.9 63.3 94.9 N STD 50.9 76.4 63.7 95.5 76.4 115 90.2 135 X STD 50.9 76.4 63.7 95.5 76.4 115 102 153 STD 47.5 71.2 47.5 71.2 47.5 71.2 47.5 71.2 SC Group OVS 40.4 60.5 40.4 60.5 40.4 60.5 40.4 60.5 Class A B SSLT 47.5 71.2 47.5 71.2 47.5 71.2 47.5 71.2 STD 50.9 76.4 63.7 95.5 76.4 115 79.1 119 SC OVS 47.9 71.8 59.8 89.7 67.4 101 67.4 101 Class B SSLT 49.6 74.4 62.0 92.9 74.4 112 79.1 119 Beam Web Available Strength per Inch Thickness, kips/in.

3 Rows W18, 16, 14, 12, 10+ Bolt +

Ltd. to W10x12, 15, 17, 19, 22, 26, 30

STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

351

526

11/2 ASD LRFD 125 188 128 191 130 195 132 199 140 210 159 239 115 172 119 179 124 186 129 194 140 210 159 239 176 263

13/4 ASD LRFD 133 200 136 204 138 207 141 211 148 222 167 251 115 172 119 179 124 186 129 194 144 216 167 251 176 263

OVS Leh *, in. 11/2 ASD LRFD 117 176 119 179 122 183 124 186 132 197 151 227 107 161 112 168 117 176 122 183 132 197 151 227 176 263

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 125 188 128 191 130 195 132 199 140 210 159 239 107 161 112 168 117 176 122 183 137 205 159 239 176 263

SSLT 11/2 ASD LRFD 122 183 125 187 127 190 129 194 137 205 156 234 115 172 119 179 124 186 129 194 137 205 156 234 176 263

13/4 ASD LRFD 130 195 133 199 135 203 138 206 145 217 164 246 115 172 119 179 124 186 129 194 144 216 164 246 176 263

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:15 AM

Page 23

10–23

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 2 Rows W12, 10, 8

Table 10-1 (continued)

All-Bolted Double-Angle Connections

3

/Bolts 4-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 32.6 48.9 40.8 61.2 47.7 71.6 X STD 32.6 48.9 40.8 61.2 48.9 73.4 STD 25.3 38.0 25.3 38.0 25.3 38.0 SC OVS 21.6 32.3 21.6 32.3 21.6 32.3 Group Class A SSLT 25.3 38.0 25.3 38.0 25.3 38.0 A STD 32.6 48.9 40.8 61.2 42.2 63.3 SC OVS 30.5 45.7 36.0 53.8 36.0 53.8 Class B SSLT 32.6 48.9 40.8 61.2 42.2 63.3 N STD 32.6 48.9 40.8 61.2 48.9 73.4 X STD 32.6 48.9 40.8 61.2 48.9 73.4 STD 31.6 47.5 31.6 47.5 31.6 47.5 SC Group OVS 27.0 40.3 27.0 40.3 27.0 40.3 Class A B SSLT 31.6 47.5 31.6 47.5 31.6 47.5 STD 32.6 48.9 40.8 61.2 48.9 73.4 SC OVS 30.5 45.7 38.1 57.1 44.9 67.2 Class B SSLT 32.6 48.9 40.8 61.2 48.9 73.4 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

234

351

11/2 ASD LRFD 83.7 126 86.1 129 88.6 133 91.0 137 98.3 147 116 175 73.1 110 78.0 117 82.9 124 87.8 132 98.3 147 116 175 117 176

13/4 ASD LRFD 91.4 137 94.3 141 96.7 145 99.1 149 106 160 117 176 73.1 110 78.0 117 82.9 124 87.8 132 102 154 117 176 117 176

OVS Leh *, in. 11/2 ASD LRFD 78.0 117 80.4 121 82.9 124 85.3 128 92.6 139 112 168 68.3 102 73.1 110 78.0 117 82.9 124 92.6 139 112 168 117 176

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 86.1 129 88.6 133 91.0 137 93.4 140 101 151 117 176 68.3 102 73.1 110 78.0 117 82.9 124 97.5 146 117 176 117 176

1/ 2 ASD LRFD 47.7 71.6 60.1 90.2 25.3 38.0 21.6 32.3 25.3 38.0 42.2 63.3 36.0 53.8 42.2 63.3 60.1 90.2 65.3 97.9 31.6 47.5 27.0 40.3 31.6 47.5 52.7 79.1 44.9 67.2 52.7 79.1

SSLT 11/2 ASD LRFD 80.6 121 83.1 125 85.5 128 88.0 132 95.3 143 113 170 73.1 110 78.0 117 82.9 124 87.8 132 95.3 143 113 170 117 176

13/4 ASD LRFD 88.8 133 91.2 137 93.6 140 96.1 144 103 155 117 176 73.1 110 78.0 117 82.9 124 87.8 132 102 154 117 176 117 176

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:15 AM

Page 24

Angle Beam

10–24

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 12 Rows W44

Table 10-1 (continued)

All-Bolted Double-Angle Connections

7

/Bolts 8-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 196 294 245 367 294 441 X STD 196 294 245 367 294 441 STD 196 294 212 317 212 317 SC OVS 180 270 180 270 180 270 Group Class A SSLT 194 292 212 317 212 317 A STD 196 294 245 367 294 441 SC OVS 191 287 239 359 287 431 Class B SSLT 194 292 243 365 292 438 N STD 196 294 245 367 294 441 X STD 196 294 245 367 294 441 STD 196 294 245 367 266 399 SC Group OVS 191 287 227 339 227 339 Class A B SSLT 194 292 243 365 266 399 STD 196 294 245 367 294 441 SC OVS 191 287 239 359 287 431 Class B SSLT 194 292 243 365 292 438 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

1640

2460

11/2 ASD LRFD 468 702 470 706 473 709 475 713 483 724 502 753 458 687 463 695 468 702 473 709 483 724 502 753 819 1230

13/4 ASD LRFD 476 714 479 718 481 722 483 725 491 736 510 765 458 687 463 695 468 702 473 709 488 731 510 765 819 1230

OVS Leh *, in. 11/2 ASD LRFD 438 657 440 661 443 664 445 668 453 679 472 708 429 644 434 651 439 658 444 665 453 679 472 708 819 1230

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 446 669 449 673 451 676 453 680 461 691 480 720 429 644 434 651 439 658 444 665 458 687 480 720 819 1230

1/ 2 ASD LRFD 389 584 392 587 212 317 180 270 212 317 353 529 300 450 353 529 392 587 392 587 266 399 227 339 266 399 392 587 378 565 389 583

SSLT 11/2 ASD LRFD 465 697 467 701 470 705 472 708 480 719 499 749 458 687 463 695 468 702 472 708 480 719 499 749 819 1230

13/4 ASD LRFD 473 710 476 713 478 717 480 721 488 732 507 761 458 687 463 695 468 702 473 709 488 731 507 761 819 1230

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:15 AM

Page 25

10–25

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 11 Rows W44, 40

Table 10-1 (continued)

All-Bolted Double-Angle Connections

7

/Bolts 8-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 180 269 225 337 269 404 X STD 180 269 225 337 269 404 STD 180 269 194 291 194 291 SC OVS 165 247 165 247 165 247 Group Class A SSLT 178 267 194 291 194 291 A STD 180 269 225 337 269 404 SC OVS 175 263 219 328 263 394 Class B SSLT 178 267 223 334 267 401 N STD 180 269 225 337 269 404 X STD 180 269 225 337 269 404 STD 180 269 225 337 244 365 SC Group OVS 175 263 208 311 208 311 Class A B SSLT 178 267 223 334 244 365 STD 180 269 225 337 269 404 SC OVS 175 263 219 328 263 394 Class B SSLT 178 267 223 334 267 401 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

1500

2250

11/2 ASD LRFD 429 644 431 647 434 651 436 654 444 665 463 695 419 629 424 636 429 644 434 651 444 665 463 695 751 1130

13/4 ASD LRFD 437 656 440 659 442 663 444 667 452 678 471 707 419 629 424 636 429 644 434 651 449 673 471 707 751 1130

OVS Leh *, in. 11/2 ASD LRFD 401 602 404 606 406 609 409 613 416 624 436 653 392 589 397 596 402 603 407 611 416 624 436 653 751 1130

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 410 614 412 618 414 622 417 625 424 636 444 665 392 589 397 596 402 603 407 611 422 633 444 665 751 1130

1/ 2 ASD LRFD 357 535 359 539 194 291 165 247 194 291 323 485 275 412 323 485 359 539 359 539 244 365 208 311 244 365 359 539 346 518 357 535

SSLT 11/2 ASD LRFD 426 639 428 643 431 646 433 650 441 661 460 690 419 629 424 636 429 644 433 650 441 661 460 690 751 1130

13/4 ASD LRFD 434 651 437 655 439 658 441 662 449 673 468 702 419 629 424 636 429 644 434 651 449 673 468 702 751 1130

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:15 AM

Page 26

Angle Beam

10–26

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 10 Rows W44, 40, 36

Table 10-1 (continued)

All-Bolted Double-Angle Connections

7

/Bolts 8-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 163 245 204 306 245 368 X STD 163 245 204 306 245 368 STD 163 245 176 264 176 264 SC OVS 150 225 150 225 150 225 Group Class A SSLT 162 243 176 264 176 264 A STD 163 245 204 306 245 368 SC OVS 159 238 198 298 238 357 Class B SSLT 162 243 203 304 243 365 N STD 163 245 204 306 245 368 X STD 163 245 204 306 245 368 STD 163 245 204 306 221 332 SC Group OVS 159 238 189 282 189 282 Class A B SSLT 162 243 203 304 221 332 STD 163 245 204 306 245 368 SC OVS 159 238 198 298 238 357 Class B SSLT 162 243 203 304 243 365 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

1370

2050

11/2 ASD LRFD 390 585 392 589 395 592 397 596 405 607 424 636 380 570 385 578 390 585 395 592 405 607 424 636 683 1020

13/4 ASD LRFD 398 597 401 601 403 605 405 608 413 619 432 648 380 570 385 578 390 585 395 592 410 614 432 648 683 1020

OVS Leh *, in. 11/2 ASD LRFD 365 547 367 551 370 555 372 558 379 569 399 598 356 534 361 541 366 548 371 556 379 569 399 598 683 1020

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 373 559 375 563 378 567 380 570 388 581 407 611 356 534 361 541 366 548 371 556 385 578 407 611 683 1020

1/ 2 ASD LRFD 325 487 327 490 176 264 150 225 176 264 294 441 250 375 294 441 327 490 327 490 221 332 189 282 221 332 327 490 315 471 324 486

SSLT 11/2 ASD LRFD 387 580 389 584 392 588 394 591 402 602 421 632 380 570 385 578 390 585 394 591 402 602 421 632 683 1020

13/4 ASD LRFD 395 593 398 596 400 600 402 604 410 615 429 644 380 570 385 578 390 585 395 592 410 614 429 644 683 1020

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:15 AM

Page 27

10–27

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 9 Rows

W44, 40, 36, 33

Table 10-1 (continued)

All-Bolted Double-Angle Connections

7

/Bolts 8-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 147 221 184 276 221 331 X STD 147 221 184 276 221 331 STD 147 221 159 238 159 238 SC OVS 135 202 135 202 135 202 Group Class A SSLT 146 219 159 238 159 238 A STD 147 221 184 276 221 331 SC OVS 142 214 178 267 214 321 Class B SSLT 146 219 182 273 219 328 N STD 147 221 184 276 221 331 X STD 147 221 184 276 221 331 STD 147 221 184 276 199 299 SC Group OVS 142 214 170 254 170 254 Class A B SSLT 146 219 182 273 199 299 STD 147 221 184 276 221 331 SC OVS 142 214 178 267 214 321 Class B SSLT 146 219 182 273 219 328 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

1230

1840

11/2 13/4 ASD LRFD ASD LRFD 351 527 359 539 353 530 362 542 356 534 364 546 358 537 366 550 366 548 374 561 385 578 393 590 341 512 341 512 346 519 346 519 351 527 351 527 356 534 356 534 366 548 371 556 385 578 393 590 614 921 614 921

OVS Leh *, in. 11/2 ASD LRFD 328 492 331 496 333 500 336 503 343 514 362 544 319 479 324 486 329 494 334 501 343 514 362 544 614 921

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 336 505 339 508 341 512 344 516 351 527 371 556 319 479 324 486 329 494 334 501 349 523 371 556 614 921

1/ 2 ASD LRFD 292 438 294 442 159 238 135 202 159 238 264 397 225 337 264 397 294 442 294 442 199 299 170 254 199 299 294 442 283 424 292 438

SSLT 11/2 ASD LRFD 348 522 350 526 353 529 355 533 363 544 382 573 341 512 346 519 351 527 355 533 363 544 382 573 614 921

13/4 ASD LRFD 356 534 359 538 361 541 363 545 371 556 390 585 341 512 346 519 351 527 356 534 371 556 390 585 614 921

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:16 AM

Page 28

Angle Beam

10–28

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi

Table 10-1 (continued)

All-Bolted Double-Angle Connections

Fy = 36 ksi Fu = 58 ksi

7

/Bolts 8-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. 8 Rows Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type W44, 40, 36, 33, 30 ASD LRFD ASD LRFD ASD LRFD N STD 131 197 164 246 197 295 X STD 131 197 164 246 197 295 STD 131 197 141 212 141 212 SC OVS 120 180 120 180 120 180 Group Class A SSLT 130 194 141 212 141 212 A STD 131 197 164 246 197 295 SC OVS 126 189 158 237 189 284 Class B SSLT 130 194 162 243 194 292 N STD 131 197 164 246 197 295 X STD 131 197 164 246 197 295 STD 131 197 164 246 177 266 SC Group OVS 126 189 151 226 151 226 Class A B SSLT 130 194 162 243 177 266 STD 131 197 164 246 197 295 SC OVS 126 189 158 237 189 284 Class B SSLT 130 194 162 243 194 292 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

1090

1640

11/2 ASD LRFD 312 468 314 472 317 475 319 479 327 490 346 519 302 453 307 461 312 468 317 475 327 490 346 519 546 819

13/4 ASD LRFD 320 480 323 484 325 488 327 491 335 502 354 531 302 453 307 461 312 468 317 475 332 497 354 531 546 819

OVS Leh *, in. 11/2 ASD LRFD 292 438 294 441 297 445 299 449 306 459 326 489 283 424 288 431 293 439 297 446 306 459 326 489 546 819

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 300 450 302 453 305 457 307 461 314 472 334 501 283 424 288 431 293 439 297 446 312 468 334 501 546 819

1/ 2 ASD LRFD 260 389 262 393 141 212 120 180 141 212 235 353 200 300 235 353 262 393 262 393 177 266 151 226 177 266 262 393 252 377 259 389

SSLT 11/2 ASD LRFD 309 463 311 467 314 471 316 474 324 485 343 515 302 453 307 461 312 468 316 474 324 485 343 515 546 819

13/4 ASD LRFD 317 476 320 479 322 483 324 487 332 498 351 527 302 453 307 461 312 468 317 475 332 497 351 527 546 819

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:16 AM

Page 29

10–29

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi

Table 10-1 (continued)

All-Bolted Double-Angle Connections

Fy = 36 ksi Fu = 58 ksi

7

/Bolts 8-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 W44, 40, 36, 33, 30, Group Cond. Type 27, 24 ASD LRFD ASD LRFD ASD LRFD N STD 115 172 144 215 172 258 X STD 115 172 144 215 172 258 STD 115 172 123 185 123 185 SC OVS 105 157 105 157 105 157 Group Class A SSLT 113 170 123 185 123 185 A STD 115 172 144 215 172 258 SC OVS 110 165 137 206 165 247 Class B SSLT 113 170 142 213 170 255 N STD 115 172 144 215 172 258 X STD 115 172 144 215 172 258 STD 115 172 144 215 155 233 SC Group OVS 110 165 132 198 132 198 Class A B SSLT 113 170 142 213 155 233 STD 115 172 144 215 172 258 SC OVS 110 165 137 206 165 247 Class B SSLT 113 170 142 213 170 255 Beam Web Available Strength per Inch Thickness, kips/in. 7 Rows

STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

956

1430

11/2 ASD LRFD 273 410 275 413 278 417 280 420 288 431 307 461 263 395 268 402 273 410 278 417 288 431 307 461 478 717

13/4 ASD LRFD 281 422 284 425 286 429 288 433 296 444 315 473 263 395 268 402 273 410 278 417 293 439 315 473 478 717

OVS Leh *, in. 11/2 ASD LRFD 255 383 258 386 260 390 262 394 270 405 289 434 246 369 251 377 256 384 261 391 270 405 289 434 478 717

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 263 395 266 399 268 402 271 406 278 417 297 446 246 369 251 377 256 384 261 391 275 413 297 446 478 717

1/ 2 ASD LRFD 227 341 230 344 123 185 105 157 123 185 206 308 175 262 206 308 230 344 230 344 155 233 132 198 155 233 230 344 220 329 227 340

SSLT 11/2 ASD LRFD 270 405 272 409 275 412 277 416 285 427 304 456 263 395 268 402 273 410 277 416 285 427 304 456 478 717

13/4 ASD LRFD 278 417 281 421 283 424 285 428 293 439 312 468 263 395 268 402 273 410 278 417 293 439 312 468 478 717

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:16 AM

Page 30

Angle Beam

10–30

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi

Table 10-1 (continued)

All-Bolted Double-Angle Connections

Fy = 36 ksi Fu = 58 ksi

7

/Bolts 8-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 W40, 36, 33, 30, 27, Group Cond. Type 24, 21 ASD LRFD ASD LRFD ASD LRFD N STD 98.6 148 123 185 148 222 X STD 98.6 148 123 185 148 222 STD 98.6 148 106 159 106 159 SC OVS 90.1 135 90.1 135 90.1 135 Group Class A SSLT 97.3 146 106 159 106 159 A STD 98.6 148 123 185 148 222 SC OVS 93.5 140 117 175 140 210 Class B SSLT 97.3 146 122 182 146 219 N STD 98.6 148 123 185 148 222 X STD 98.6 148 123 185 148 222 STD 98.6 148 123 185 133 199 SC Group OVS 93.5 140 113 169 113 169 Class A B SSLT 97.3 146 122 182 133 199 STD 98.6 148 123 185 148 222 SC OVS 93.5 140 117 175 140 210 Class B SSLT 97.3 146 122 182 146 219 Beam Web Available Strength per Inch Thickness, kips/in. 6 Rows

STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

819

1230

11/2 ASD LRFD 234 351 236 355 239 358 241 362 249 373 268 402 224 336 229 344 234 351 239 358 249 373 268 402 410 614

13/4 ASD LRFD 242 363 245 367 247 371 249 374 257 385 276 414 224 336 229 344 234 351 239 358 254 380 276 414 410 614

OVS Leh *, in. 11/2 ASD LRFD 219 328 221 332 223 335 226 339 233 350 253 379 210 314 215 322 219 329 224 336 233 350 253 379 410 614

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 227 340 229 344 232 347 234 351 241 362 261 391 210 314 215 322 219 329 224 336 239 358 261 391 410 614

1/ 2

ASD 195 197 106 90.1 106 176 150 176 197 197 133 113 133 197 187 195

LRFD 292 296 159 135 159 264 225 264 296 296 199 169 199 296 281 292

SSLT 11/2 ASD LRFD 231 346 233 350 236 354 238 357 246 368 265 398 224 336 229 344 234 351 238 357 246 368 265 398 410 614

13/4 ASD LRFD 239 359 242 362 244 366 246 370 254 381 273 410 224 336 229 344 234 351 239 358 254 380 273 410 410 614

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:16 AM

Page 31

10–31

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi

Table 10-1 (continued)

All-Bolted Double-Angle Connections

Fy = 36 ksi Fu = 58 ksi

7

/Bolts 8-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. 5 Rows Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type W30, 27, 24, 21, 18 ASD LRFD ASD LRFD ASD LRFD N STD 82.4 124 103 155 124 185 X STD 82.4 124 103 155 124 185 STD 82.4 124 88.1 132 88.1 132 SC OVS 75.1 112 75.1 112 75.1 112 Group Class A SSLT 81.1 122 88.1 132 88.1 132 A STD 82.4 124 103 155 124 185 SC OVS 77.2 116 96.5 145 116 174 Class B SSLT 81.1 122 101 152 122 182 N STD 82.4 124 103 155 124 185 X STD 82.4 124 103 155 124 185 STD 82.4 124 103 155 111 166 SC Group OVS 77.2 116 94.4 141 94.4 141 Class A B SSLT 81.1 122 101 152 111 166 STD 82.4 124 103 155 124 185 SC OVS 77.2 116 96.5 145 116 174 Class B SSLT 81.1 122 101 152 122 182 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

683

1020

11/2 ASD LRFD 195 293 197 296 200 300 202 303 210 314 229 344 185 278 190 285 195 293 200 300 210 314 229 344 341 512

13/4 ASD LRFD 203 305 206 308 208 312 210 316 218 327 237 356 185 278 190 285 195 293 200 300 215 322 237 356 341 512

OVS Leh *, in. 11/2 ASD LRFD 182 273 184 277 187 280 189 284 197 295 216 324 173 260 178 267 183 274 188 282 197 295 216 324 341 512

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 190 285 193 289 195 293 197 296 205 307 224 336 173 260 178 267 183 274 188 282 202 303 224 336 341 512

1/ 2

ASD 162 165 88.1 75.1 88.1 147 125 147 165 165 111 94.4 111 165 154 162

LRFD 243 247 132 112 132 220 187 220 247 247 166 141 166 247 232 243

SSLT 11/2 ASD LRFD 192 288 194 292 197 295 199 299 207 310 226 339 185 278 190 285 195 293 199 299 207 310 226 339 341 512

13/4 ASD LRFD 200 300 203 304 205 307 207 311 215 322 234 351 185 278 190 285 195 293 200 300 215 322 234 351 341 512

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:16 AM

Page 32

Angle Beam

10–32

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 4 Rows

W24, 21, 18, 16

Table 10-1 (continued)

All-Bolted Double-Angle Connections

7

/Bolts 8-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 65.3 97.9 81.6 122 97.9 147 X STD 65.3 97.9 81.6 122 97.9 147 STD 65.3 97.9 70.5 106 70.5 106 SC OVS 60.1 89.9 60.1 89.9 60.1 89.9 Group Class A SSLT 64.9 97.3 70.5 106 70.5 106 A STD 65.3 97.9 81.6 122 97.9 147 SC OVS 60.9 91.4 76.1 114 91.4 137 Class B SSLT 64.9 97.3 81.1 122 97.3 146 N STD 65.3 97.9 81.6 122 97.9 147 X STD 65.3 97.9 81.6 122 97.9 147 STD 65.3 97.9 81.6 122 88.6 133 SC Group OVS 60.9 91.4 75.5 113 75.5 113 Class A B SSLT 64.9 97.3 81.1 122 88.6 133 STD 65.3 97.9 81.6 122 97.9 147 SC OVS 60.9 91.4 76.1 114 91.4 137 Class B SSLT 64.9 97.3 81.1 122 97.3 146 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

546

819

11/2 ASD LRFD 156 234 158 238 161 241 163 245 171 256 190 285 146 219 151 227 156 234 161 241 171 256 190 285 273 410

13/4 ASD LRFD 164 246 167 250 169 254 171 257 179 268 198 297 146 219 151 227 156 234 161 241 176 263 198 297 273 410

OVS Leh *, in. 11/2 ASD LRFD 145 218 148 222 150 225 153 229 160 240 180 269 137 205 141 212 146 219 151 227 160 240 180 269 273 410

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 154 230 156 234 158 238 161 241 168 252 188 282 137 205 141 212 146 219 151 227 166 249 188 282 273 410

1/ 2

ASD 130 131 70.5 60.1 70.5 118 100 118 131 131 88.6 75.5 88.6 131 122 130

LRFD 195 196 106 89.9 106 176 150 176 196 196 133 113 133 196 183 195

SSLT 11/2 ASD LRFD 153 229 155 233 158 237 160 240 168 251 187 281 146 219 151 227 156 234 160 240 168 251 187 281 273 410

13/4 ASD LRFD 161 242 164 245 166 249 168 253 176 264 195 293 146 219 151 227 156 234 161 241 176 263 195 293 273 410

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:16 AM

Page 33

10–33

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi

Table 10-1 (continued)

All-Bolted Double-Angle Connections

7

/Bolts 8-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 47.9 71.8 59.8 89.7 71.8 108 X STD 47.9 71.8 59.8 89.7 71.8 108 STD 47.9 71.8 52.9 79.3 52.9 79.3 SC OVS 44.6 66.9 45.1 67.4 45.1 67.4 Group Class A SSLT 47.9 71.8 52.9 79.3 52.9 79.3 A STD 47.9 71.8 59.8 89.7 71.8 108 SC OVS 44.6 66.9 55.7 83.6 66.9 100 Class B SSLT 47.9 71.8 59.8 89.7 71.8 108 N STD 47.9 71.8 59.8 89.7 71.8 108 X STD 47.9 71.8 59.8 89.7 71.8 108 STD 47.9 71.8 59.8 89.7 66.4 99.7 SC Group OVS 44.6 66.9 55.7 83.6 56.6 84.7 Class A B SSLT 47.9 71.8 59.8 89.7 66.4 99.7 STD 47.9 71.8 59.8 89.7 71.8 108 SC OVS 44.6 66.9 55.7 83.6 66.9 100 Class B SSLT 47.9 71.8 59.8 89.7 71.8 108 Beam Web Available Strength per Inch Thickness, kips/in.

3 Rows W18, 16, 14, 12, 10+ Bolt +

Ltd. to W10x12, 15, 17, 19, 22, 26, 30

STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

409

614

11/2 ASD LRFD 117 176 119 179 122 183 124 186 132 197 151 227 107 161 112 168 117 176 122 183 132 197 151 227 205 307

13/4 ASD LRFD 125 188 128 191 130 195 132 199 140 210 159 239 107 161 112 168 117 176 122 183 137 205 159 239 205 307

OVS Leh *, in. 11/2 ASD LRFD 109 163 111 167 114 171 116 174 124 185 143 215 99.9 150 105 157 110 165 115 172 124 185 143 215 205 307

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 117 176 119 179 122 183 124 186 132 197 151 227 99.9 150 105 157 110 165 115 172 129 194 151 227 205 307

1/ 2

ASD 95.7 95.7 52.9 45.1 52.9 88.1 75.1 88.1 95.7 95.7 66.4 56.6 66.4 95.7 89.2 95.7

LRFD 144 144 79.3 67.4 79.3 132 112 132 144 144 99.7 84.7 99.7 144 134 144

SSLT 11/2 ASD LRFD 114 171 116 175 119 178 121 182 129 193 148 222 107 161 112 168 117 176 121 182 129 193 148 222 205 307

13/4 ASD LRFD 122 183 125 187 127 190 129 194 137 205 156 234 107 161 112 168 117 176 122 183 137 205 156 234 205 307

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:17 AM

Page 34

Angle Beam

10–34

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 2 Rows W12, 10, 8

Table 10-1 (continued)

All-Bolted Double-Angle Connections

7

/Bolts 8-in.

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 30.5 45.7 38.1 57.1 45.7 68.5 X STD 30.5 45.7 38.1 57.1 45.7 68.5 STD 30.5 45.7 35.3 52.9 35.3 52.9 SC OVS 28.3 42.4 30.0 45.0 30.0 45.0 Group Class A SSLT 30.5 45.7 35.3 52.9 35.3 52.9 A STD 30.5 45.7 38.1 57.1 45.7 68.5 SC OVS 28.3 42.4 35.3 53.0 42.4 63.6 Class B SSLT 30.5 45.7 38.1 57.1 45.7 68.5 N STD 30.5 45.7 38.1 57.1 45.7 68.5 X STD 30.5 45.7 38.1 57.1 45.7 68.5 STD 30.5 45.7 38.1 57.1 44.3 66.4 SC Group OVS 28.3 42.4 35.3 53.0 37.8 56.5 Class A B SSLT 30.5 45.7 38.1 57.1 44.3 66.4 STD 30.5 45.7 38.1 57.1 45.7 68.5 SC OVS 28.3 42.4 35.3 53.0 42.4 63.6 Class B SSLT 30.5 45.7 38.1 57.1 45.7 68.5 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ OVS/ SSLT

273

410

11/2 ASD LRFD 78.0 117 80.4 121 82.9 124 85.3 128 92.6 139 112 168 68.3 102 73.1 110 78.0 117 82.9 124 92.6 139 112 168 137 205

13/4 ASD LRFD 86.1 129 88.6 133 91.0 137 93.4 140 101 151 120 180 68.3 102 73.1 110 78.0 117 82.9 124 97.5 146 120 180 137 205

OVS Leh *, in. 11/2 ASD LRFD 72.3 108 74.8 112 77.2 116 79.6 119 86.9 130 106 160 63.4 95.1 68.3 102 73.1 110 78.0 117 86.9 130 106 160 137 205

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 80.4 121 82.9 124 85.3 128 87.8 132 95.1 143 115 172 63.4 95.1 68.3 102 73.1 110 78.0 117 92.6 139 115 172 137 205

1/ 2 ASD LRFD 60.9 91.4 60.9 91.4 35.3 52.9 30.0 45.0 35.3 52.9 58.8 88.1 50.1 74.9 58.8 88.1 60.9 91.4 60.9 91.4 44.3 66.4 37.8 56.5 44.3 66.4 60.9 91.4 56.6 84.8 60.9 91.4

SSLT 11/2 ASD LRFD 75.0 112 77.4 116 79.8 120 82.3 123 89.6 134 109 164 68.3 102 73.1 110 78.0 117 82.3 123 89.6 134 109 164 137 205

13/4 ASD LRFD 83.1 125 85.5 128 88.0 132 90.4 136 97.7 147 117 176 68.3 102 73.1 110 78.0 117 82.9 124 97.5 146 117 176 137 205

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:17 AM

Page 35

10–35

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 12 Rows W44

Table 10-1 (continued)

-in. 1 Bolts

All-Bolted Double-Angle Connections Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 191 287 239 359 287 431 X STD 191 287 239 359 287 431 STD 191 287 239 359 277 415 SC OVS 172 258 215 322 236 353 Group Class A SSLT 191 287 239 359 277 415 A STD 191 287 239 359 287 431 SC OVS 172 258 215 322 258 387 Class B SSLT 191 287 239 359 287 431 N STD 191 287 239 359 287 431 X STD 191 287 239 359 287 431 STD 191 287 239 359 287 431 SC Group OVS 172 258 215 322 258 387 Class A B SSLT 191 287 239 359 287 431 STD 191 287 239 359 287 431 SC OVS 172 258 215 322 258 387 Class B SSLT 191 287 239 359 287 431 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ SSLT

1820

2730

OVS

1660

2490

11/2 ASD LRFD 438 657 440 661 443 664 445 668 453 679 472 708 429 644 434 651 439 658 444 665 453 679 472 708 909 1360

13/4 ASD LRFD 446 669 449 673 451 676 453 680 461 691 480 720 429 644 434 651 439 658 444 665 458 687 480 720 909 1360

OVS Leh *, in. 11/2 ASD LRFD 393 589 395 593 398 597 400 600 407 611 427 640 385 578 390 585 395 592 400 600 407 611 427 640 829 1240

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 401 601 403 605 406 609 408 612 416 623 435 653 385 578 390 585 395 592 400 600 414 622 435 653 829 1240

1/ 2 ASD LRFD 383 574 383 574 277 415 236 353 277 415 383 574 344 515 383 574 383 574 383 574 347 521 296 443 347 521 383 574 344 515 383 574

SSLT 11/2 ASD LRFD 434 651 436 654 439 658 441 662 449 673 468 702 429 644 434 651 439 658 441 662 449 673 468 702 909 1360

13/4 ASD LRFD 442 663 444 667 447 670 449 674 457 685 476 714 429 644 434 651 439 658 444 665 457 685 476 714 909 1360

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:17 AM

Page 36

Angle Beam

10–36

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 11 Rows W44, 40

Table 10-1 (continued)

-in. 1 Bolts

All-Bolted Double-Angle Connections Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 175 263 219 328 263 394 X STD 175 263 219 328 263 394 STD 175 263 219 328 254 380 SC OVS 157 236 196 295 216 323 Group Class A SSLT 175 263 219 328 254 380 A STD 175 263 219 328 263 394 SC OVS 157 236 196 295 236 354 Class B SSLT 175 263 219 328 263 394 N STD 175 263 219 328 263 394 X STD 175 263 219 328 263 394 STD 175 263 219 328 263 394 SC OVS 157 236 196 295 236 354 Group Class A SSLT 175 263 219 328 263 394 B STD 175 263 219 328 263 394 SC OVS 157 236 196 295 236 354 Class B SSLT 175 263 219 328 263 394 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ SSLT

1670

2500

OVS

1520

2280

11/2 ASD LRFD 401 602 404 606 406 609 409 613 416 624 436 653 392 589 397 596 402 603 407 611 416 624 436 653 834 1250

13/4 ASD LRFD 410 614 412 618 414 622 417 625 424 636 444 665 392 589 397 596 402 603 407 611 422 633 444 665 834 1250

OVS Leh *, in. 11/2 ASD LRFD 360 540 362 544 365 547 367 551 375 562 394 591 352 528 357 536 362 543 367 550 375 562 394 591 761 1140

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 368 552 371 556 373 559 375 563 383 574 402 603 352 528 357 536 362 543 367 550 381 572 402 603 761 1140

1/ 2 ASD LRFD 350 525 350 525 254 380 216 323 254 380 350 525 314 471 350 525 350 525 350 525 318 477 271 406 318 477 350 525 314 471 350 525

SSLT 11/2 ASD LRFD 397 596 400 600 402 603 405 607 412 618 431 647 392 589 397 596 402 603 405 607 412 618 431 647 834 1250

13/4 ASD LRFD 405 608 408 612 410 615 413 619 420 630 440 659 392 589 397 596 402 603 407 611 420 630 440 659 834 1250

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:17 AM

Page 37

10–37

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 10 Rows W44, 40, 36

Table 10-1 (continued)

-in. 1 Bolts

All-Bolted Double-Angle Connections Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 159 238 198 298 238 357 X STD 159 238 198 298 238 357 STD 159 238 198 298 231 346 SC OVS 142 214 178 267 196 294 Group Class A SSLT 159 238 198 298 231 346 A STD 159 238 198 298 238 357 SC OVS 142 214 178 267 214 321 Class B SSLT 159 238 198 298 238 357 N STD 159 238 198 298 238 357 X STD 159 238 198 298 238 357 STD 159 238 198 298 238 357 SC Group OVS 142 214 178 267 214 321 Class A B SSLT 159 238 198 298 238 357 STD 159 238 198 298 238 357 SC OVS 142 214 178 267 214 321 Class B SSLT 159 238 198 298 238 357 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ SSLT

1520

2270

OVS

1380

2080

11/2 13/4 ASD LRFD ASD LRFD 365 547 373 559 367 551 375 563 370 555 378 567 372 558 380 570 379 569 388 581 399 598 407 611 356 534 356 534 361 541 361 541 366 548 366 548 371 556 371 556 379 569 385 578 399 598 407 611 758 1140 758 1140

OVS Leh *, in. 11/2 ASD LRFD 327 491 329 494 332 498 334 502 342 512 361 542 319 479 324 486 329 494 334 501 342 512 361 542 692 1040

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 335 503 338 506 340 510 342 514 350 525 369 554 319 479 324 486 329 494 334 501 349 523 369 554 692 1040

1/ 2 ASD LRFD 318 476 318 476 231 346 196 294 231 346 318 476 285 427 318 476 318 476 318 476 289 434 247 369 289 434 318 476 285 427 318 476

SSLT 11/2 ASD LRFD 361 541 363 545 366 548 368 552 375 563 395 592 356 534 361 541 366 548 368 552 375 563 395 592 758 1140

13/4 ASD LRFD 369 553 371 557 374 561 376 564 384 575 403 605 356 534 361 541 366 548 371 556 384 575 403 605 758 1140

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:17 AM

Page 38

Angle Beam

10–38

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 9 Rows

W44, 40, 36, 33

Table 10-1 (continued)

-in. 1 Bolts

All-Bolted Double-Angle Connections Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 142 214 178 267 214 321 X STD 142 214 178 267 214 321 STD 142 214 178 267 207 311 SC OVS 128 192 160 240 177 265 Group Class A SSLT 142 214 178 267 207 311 A STD 142 214 178 267 214 321 SC OVS 128 192 160 240 192 288 Class B SSLT 142 214 178 267 214 321 N STD 142 214 178 267 214 321 X STD 142 214 178 267 214 321 STD 142 214 178 267 214 321 SC Group OVS 128 192 160 240 192 288 Class A B SSLT 142 214 178 267 214 321 STD 142 214 178 267 214 321 SC OVS 128 192 160 240 192 288 Class B SSLT 142 214 178 267 214 321 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ SSLT

1370

2050

OVS

1250

1870

11/2 ASD LRFD 328 492 331 496 333 500 336 503 343 514 362 544 319 479 324 486 329 494 334 501 343 514 362 544 683 1020

13/4 ASD LRFD 336 505 339 508 341 512 344 516 351 527 371 556 319 479 324 486 329 494 334 501 349 523 371 556 683 1020

OVS Leh *, in. 11/2 ASD LRFD 294 441 297 445 299 449 301 452 309 463 328 492 286 430 291 437 296 444 301 452 309 463 328 492 624 936

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 302 453 305 457 307 461 310 464 317 475 336 505 286 430 291 437 296 444 301 452 316 473 336 505 624 936

1/ 2 ASD LRFD 285 427 285 427 207 311 177 265 207 311 285 427 256 383 285 427 285 427 285 427 260 391 222 332 260 391 285 427 256 383 285 427

SSLT 11/2 ASD LRFD 324 486 327 490 329 494 332 497 339 508 358 537 319 479 324 486 329 494 332 497 339 508 358 537 683 1020

13/4 ASD LRFD 332 498 335 502 337 506 340 509 347 520 366 550 319 479 324 486 329 494 334 501 347 520 366 550 683 1020

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:17 AM

Page 39

10–39

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi

Table 10-1 (continued)

-in. 1 Bolts

All-Bolted Double-Angle Connections

Fy = 36 ksi Fu = 58 ksi

Bolt and Angle Available Strength, kips Angle Thickness, in. 8 Rows Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type W44, 40, 36, 33, 30 ASD LRFD ASD LRFD ASD LRFD N STD 126 189 158 237 189 284 X STD 126 189 158 237 189 284 STD 126 189 158 237 184 277 SC OVS 113 170 141 212 157 235 Group Class A SSLT 126 189 158 237 184 277 A STD 126 189 158 237 189 284 SC OVS 113 170 141 212 170 254 Class B SSLT 126 189 158 237 189 284 N STD 126 189 158 237 189 284 X STD 126 189 158 237 189 284 STD 126 189 158 237 189 284 SC Group OVS 113 170 141 212 170 254 Class A B SSLT 126 189 158 237 189 284 STD 126 189 158 237 189 284 SC OVS 113 170 141 212 170 254 Class B SSLT 126 189 158 237 189 284 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ SSLT

1210

1820

OVS

1110

1670

11/2 ASD LRFD 292 438 294 441 297 445 299 449 306 459 326 489 283 424 288 431 293 439 297 446 306 459 326 489 607 910

13/4 ASD LRFD 300 450 302 453 305 457 307 461 314 472 334 501 283 424 288 431 293 439 297 446 312 468 334 501 607 910

OVS Leh *, in. 11/2 ASD LRFD 261 392 264 395 266 399 269 403 276 414 295 443 254 380 258 388 263 395 268 402 276 414 295 443 556 834

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 269 404 272 408 274 411 277 415 284 426 303 455 254 380 258 388 263 395 268 402 283 424 303 455 556 834

1/ 2 ASD LRFD 252 378 252 378 184 277 157 235 184 277 252 378 226 339 252 378 252 378 252 378 231 347 197 295 231 347 252 378 226 339 252 378

SSLT 11/2 ASD LRFD 288 431 290 435 293 439 295 442 302 453 322 483 283 424 288 431 293 439 295 442 302 453 322 483 607 910

13/4 ASD LRFD 296 444 298 447 301 451 303 455 310 466 330 495 283 424 288 431 293 439 297 446 310 466 330 495 607 910

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:17 AM

Page 40

Angle Beam

10–40

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi

Table 10-1 (continued)

-in. 1 Bolts

All-Bolted Double-Angle Connections

Fy = 36 ksi Fu = 58 ksi

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 W44, 40, 36, 33, 30, Group Cond. Type 27, 24 ASD LRFD ASD LRFD ASD LRFD N STD 110 165 137 206 165 247 X STD 110 165 137 206 165 247 STD 110 165 137 206 161 242 SC OVS 98.4 148 123 185 138 206 Group Class A SSLT 110 165 137 206 161 242 A STD 110 165 137 206 165 247 SC OVS 98.4 148 123 185 148 221 Class B SSLT 110 165 137 206 165 247 N STD 110 165 137 206 165 247 X STD 110 165 137 206 165 247 STD 110 165 137 206 165 247 SC Group OVS 98.4 148 123 185 148 221 Class A B SSLT 110 165 137 206 165 247 STD 110 165 137 206 165 247 SC OVS 98.4 148 123 185 148 221 Class B SSLT 110 165 137 206 165 247 Beam Web Available Strength per Inch Thickness, kips/in. 7 Rows

STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ SSLT

1060

1590

OVS

975

1460

11/2 13/4 ASD LRFD ASD LRFD 255 383 263 395 258 386 266 399 260 390 268 402 262 394 271 406 270 405 278 417 289 434 297 446 246 369 246 369 251 377 251 377 256 384 256 384 261 391 261 391 270 405 275 413 289 434 297 446 531 797 531 797

OVS Leh *, in. 11/2 ASD LRFD 228 342 231 346 233 350 236 353 243 364 262 394 221 331 225 338 230 346 235 353 243 364 262 394 488 731

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 236 355 239 358 241 362 244 366 251 377 271 406 221 331 225 338 230 346 235 353 250 375 271 406 488 731

1/ 2 ASD LRFD 220 330 220 330 161 242 138 206 161 242 220 330 197 295 220 330 220 330 220 330 202 304 173 258 202 304 220 330 197 295 220 330

SSLT 11/2 ASD LRFD 251 377 254 380 256 384 258 388 266 399 285 428 246 369 251 377 256 384 258 388 266 399 285 428 531 797

13/4 ASD LRFD 259 389 262 392 264 396 267 400 274 411 293 440 246 369 251 377 256 384 261 391 274 411 293 440 531 797

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:18 AM

Page 41

10–41

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi

Table 10-1 (continued)

-in. 1 Bolts

All-Bolted Double-Angle Connections

Fy = 36 ksi Fu = 58 ksi

Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 W40, 36, 33, 30, 27, Group Cond. Type 24, 21 ASD LRFD ASD LRFD ASD LRFD N STD 93.5 140 117 175 140 210 X STD 93.5 140 117 175 140 210 STD 93.5 140 117 175 138 207 SC OVS 83.7 126 105 157 118 176 Group Class A SSLT 93.5 140 117 175 138 207 A STD 93.5 140 117 175 140 210 SC OVS 83.7 126 105 157 126 188 Class B SSLT 93.5 140 117 175 140 210 N STD 93.5 140 117 175 140 210 X STD 93.5 140 117 175 140 210 STD 93.5 140 117 175 140 210 SC Group OVS 83.7 126 105 157 126 188 Class A B SSLT 93.5 140 117 175 140 210 STD 93.5 140 117 175 140 210 SC OVS 83.7 126 105 157 126 188 Class B SSLT 93.5 140 117 175 140 210 Beam Web Available Strength per Inch Thickness, kips/in. 6 Rows

STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ SSLT

912

1370

OVS

839

1260

11/2 13/4 ASD LRFD ASD LRFD 219 328 227 340 221 332 229 344 223 335 232 347 226 339 234 351 233 350 241 362 253 379 261 391 210 314 210 314 215 322 215 322 219 329 219 329 224 336 224 336 233 350 239 358 253 379 261 391 456 684 456 684

OVS Leh *, in. 11/2 ASD LRFD 195 293 198 297 200 300 203 304 210 315 230 344 188 282 193 289 197 296 202 303 210 315 230 344 419 629

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 204 305 206 309 208 313 211 316 218 327 238 356 188 282 193 289 197 296 202 303 217 325 238 356 419 629

1/ 2 ASD LRFD 187 281 187 281 138 207 118 176 138 207 187 281 167 251 187 281 187 281 187 281 174 260 148 221 174 260 187 281 167 251 187 281

SSLT 11/2 ASD LRFD 215 322 217 325 219 329 222 333 229 344 249 373 210 314 215 322 219 329 222 333 229 344 249 373 456 684

13/4 ASD LRFD 223 334 225 338 228 341 230 345 237 356 257 385 210 314 215 322 219 329 224 336 237 356 257 385 456 684

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:18 AM

Page 42

Angle Beam

10–42

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi

Table 10-1 (continued)

-in. 1 Bolts

All-Bolted Double-Angle Connections

Fy = 36 ksi Fu = 58 ksi

Bolt and Angle Available Strength, kips Angle Thickness, in. 5 Rows Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type W30, 27, 24, 21, 18 ASD LRFD ASD LRFD ASD LRFD N STD 77.2 116 96.5 145 116 174 X STD 77.2 116 96.5 145 116 174 STD 77.2 116 96.5 145 115 173 SC OVS 69.1 104 86.3 129 98.2 147 Group Class A SSLT 77.2 116 96.5 145 115 173 A STD 77.2 116 96.5 145 116 174 SC OVS 69.1 104 86.3 129 104 155 Class B SSLT 77.2 116 96.5 145 116 174 N STD 77.2 116 96.5 145 116 174 X STD 77.2 116 96.5 145 116 174 STD 77.2 116 96.5 145 116 174 SC Group OVS 69.1 104 86.3 129 104 155 Class A B SSLT 77.2 116 96.5 145 116 174 STD 77.2 116 96.5 145 116 174 SC OVS 69.1 104 86.3 129 104 155 Class B SSLT 77.2 116 96.5 145 116 174 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ SSLT

761

1140

OVS

702

1050

11/2 ASD LRFD 182 273 184 277 187 280 189 284 197 295 216 324 173 260 178 267 183 274 188 282 197 295 216 324 380 570

13/4 ASD LRFD 190 285 193 289 195 293 197 296 205 307 224 336 173 260 178 267 183 274 188 282 202 303 224 336 380 570

OVS Leh *, in. 11/2 ASD LRFD 163 244 165 247 167 251 170 255 177 266 197 295 155 232 160 239 165 247 169 254 177 266 197 295 351 527

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 171 256 173 260 176 263 178 267 185 278 205 307 155 232 160 239 165 247 169 254 184 276 205 307 351 527

1/ 2

ASD 154 154 115 98.2 115 154 138 154 154 154 145 123 145 154 138 154

LRFD 232 232 173 147 173 232 207 232 232 232 217 184 217 232 207 232

SSLT 11/2 ASD LRFD 178 267 180 271 183 274 185 278 193 289 212 318 173 260 178 267 183 274 185 278 193 289 212 318 380 570

13/4 ASD LRFD 186 279 189 283 191 286 193 290 201 301 220 330 173 260 178 267 183 274 188 282 201 301 220 330 380 570

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:18 AM

Page 43

10–43

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 4 Rows

W24, 21, 18, 16

Table 10-1 (continued)

-in. 1 Bolts

All-Bolted Double-Angle Connections Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 60.9 91.4 76.1 114 91.4 137 X STD 60.9 91.4 76.1 114 91.4 137 STD 60.9 91.4 76.1 114 91.4 137 SC OVS 54.4 81.6 68.0 102 78.6 118 Group Class A SSLT 60.9 91.4 76.1 114 91.4 137 A STD 60.9 91.4 76.1 114 91.4 137 SC OVS 54.4 81.6 68.0 102 81.6 122 Class B SSLT 60.9 91.4 76.1 114 91.4 137 N STD 60.9 91.4 76.1 114 91.4 137 X STD 60.9 91.4 76.1 114 91.4 137 STD 60.9 91.4 76.1 114 91.4 137 SC Group OVS 54.4 81.6 68.0 102 81.6 122 Class A B SSLT 60.9 91.4 76.1 114 91.4 137 STD 60.9 91.4 76.1 114 91.4 137 SC OVS 54.4 81.6 68.0 102 81.6 122 Class B SSLT 60.9 91.4 76.1 114 91.4 137 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ SSLT

609

914

OVS

566

848

11/2 ASD LRFD 145 218 148 222 150 225 153 229 160 240 180 269 137 205 141 212 146 219 151 227 160 240 180 269 305 457

13/4 ASD LRFD 154 230 156 234 158 238 161 241 168 252 188 282 137 205 141 212 146 219 151 227 166 249 188 282 305 457

OVS Leh *, in. 11/2 ASD LRFD 130 194 132 198 134 202 137 205 144 216 164 246 122 183 127 190 132 197 137 205 144 216 164 246 283 424

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 138 207 140 210 143 214 145 218 152 229 172 258 122 183 127 190 132 197 137 205 151 227 172 258 283 424

1/ 2

ASD 122 122 92.2 78.6 92.2 122 109 122 122 122 116 98.6 116 122 109 122

LRFD 183 183 138 118 138 183 163 183 183 183 174 148 174 183 163 183

SSLT 11/2 ASD LRFD 141 212 144 216 146 219 149 223 156 234 176 263 137 205 141 212 146 219 149 223 156 234 176 263 305 457

13/4 ASD LRFD 150 224 152 228 154 232 157 235 164 246 184 275 137 205 141 212 146 219 151 227 164 246 184 275 305 457

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:18 AM

Page 44

Angle Beam

10–44

DESIGN OF SIMPLE SHEAR CONNECTIONS

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi

Table 10-1 (continued)

-in. 1 Bolts

All-Bolted Double-Angle Connections Bolt and Angle Available Strength, kips Angle Thickness, in. Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 44.6 66.9 55.7 83.6 66.9 100 X STD 44.6 66.9 55.7 83.6 66.9 100 STD 44.6 66.9 55.7 83.6 66.9 100 SC OVS 39.7 59.5 49.6 74.4 58.9 88.2 Group Class A SSLT 44.6 66.9 55.7 83.6 66.9 100 A STD 44.6 66.9 55.7 83.6 66.9 100 SC OVS 39.7 59.5 49.6 74.4 59.5 89.3 Class B SSLT 44.6 66.9 55.7 83.6 66.9 100 N STD 44.6 66.9 55.7 83.6 66.9 100 X STD 44.6 66.9 55.7 83.6 66.9 100 STD 44.6 66.9 55.7 83.6 66.9 100 SC Group OVS 39.7 59.5 49.6 74.4 59.5 89.3 Class A B SSLT 44.6 66.9 55.7 83.6 66.9 100 STD 44.6 66.9 55.7 83.6 66.9 100 SC OVS 39.7 59.5 49.6 74.4 59.5 89.3 Class B SSLT 44.6 66.9 55.7 83.6 66.9 100 Beam Web Available Strength per Inch Thickness, kips/in.

3 Rows W18, 16, 14, 12, 10+ Bolt +

Ltd. to W10x12, 15, 17, 19, 22, 26, 30

STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ SSLT

458

687

OVS

429

644

11/2 ASD LRFD 109 163 111 167 114 171 116 174 124 185 143 215 99.9 150 105 157 110 165 115 172 124 185 143 215 229 344

13/4 ASD LRFD 117 176 119 179 122 183 124 186 132 197 151 227 99.9 150 105 157 110 165 115 172 129 194 151 227 229 344

OVS Leh *, in. 11/2 ASD LRFD 96.7 145 99.1 149 102 152 104 156 111 167 131 196 89.0 133 93.8 141 98.7 148 104 155 111 167 131 196 215 322

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 105 157 107 161 110 165 112 168 119 179 139 208 89.0 133 93.8 141 98.7 148 104 155 118 177 139 208 215 322

1/ 2

ASD 89.2 89.2 69.2 58.9 69.2 89.2 79.4 89.2 89.2 89.2 86.8 74.0 86.8 89.2 79.4 89.2

LRFD 134 134 104 88.2 104 134 119 134 134 134 130 111 130 134 119 134

SSLT 11/2 ASD LRFD 105 157 107 161 110 165 112 168 119 179 139 208 99.9 150 105 157 110 165 112 168 119 179 139 208 229 344

13/4 ASD LRFD 113 169 115 173 118 177 120 180 128 191 147 221 99.9 150 105 157 110 165 115 172 128 191 147 221 229 344

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:18 AM

Page 45

10–45

Angle Beam

DESIGN TABLES

Fy = 50 ksi Fu = 65 ksi Fy = 36 ksi Fu = 58 ksi 2 Rows W12, 10, 8

Table 10-1 (continued)

-in. 1 Bolts

All-Bolted Double-Angle Connections Bolt and Angle Available Strength, kips Angle Thickness, in. Bolt Thread Hole 5/16 3/ 8 1/4 Group Cond. Type ASD LRFD ASD LRFD ASD LRFD N STD 28.3 42.4 35.3 53.0 42.4 63.6 X STD 28.3 42.4 35.3 53.0 42.4 63.6 STD 28.3 42.4 35.3 53.0 42.4 63.6 SC OVS 25.0 37.5 31.3 46.9 37.5 56.3 Group Class A SSLT 28.3 42.4 35.3 53.0 42.4 63.6 A STD 28.3 42.4 35.3 53.0 42.4 63.6 SC OVS 25.0 37.5 31.3 46.9 37.5 56.3 Class B SSLT 28.3 42.4 35.3 53.0 42.4 63.6 N STD 28.3 42.4 35.3 53.0 42.4 63.6 X STD 28.3 42.4 35.3 53.0 42.4 63.6 STD 28.3 42.4 35.3 53.0 42.4 63.6 SC Group OVS 25.0 37.5 31.3 46.9 37.5 56.3 Class A B SSLT 28.3 42.4 35.3 53.0 42.4 63.6 STD 28.3 42.4 35.3 53.0 42.4 63.6 SC OVS 25.0 37.5 31.3 46.9 37.5 56.3 Class B SSLT 28.3 42.4 35.3 53.0 42.4 63.6 Beam Web Available Strength per Inch Thickness, kips/in. STD

Hole Type

Lev , in. 11/4 13/8 11/2 15/8 2 3 11/4 13/8 11/2 15/8 2 3

Coped at Top Flange Only

Coped at Both Flanges

Uncoped Support Available Strength per Inch Thickness, kips/in. Hole Type

ASD

LRFD

STD/ SSLT

307

461

OVS

293

439

11/2 ASD LRFD 72.3 108 74.8 112 77.2 116 79.6 119 86.9 130 106 160 63.4 95.1 68.3 102 73.1 110 78.0 117 86.9 130 106 160 154 230

OVS Leh *, in.

13/4 11/2 ASD LRFD ASD LRFD 80.4 121 63.8 95.7 82.9 124 66.2 99.3 85.3 128 68.7 103 87.8 132 71.1 107 95.1 143 78.4 118 115 172 97.9 147 63.4 95.1 56.1 84.1 68.3 102 60.9 91.4 73.1 110 65.8 98.7 78.0 117 70.7 106 92.6 139 78.4 118 115 172 97.9 147 154 230 146 219

Notes: STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

13/4 ASD LRFD 71.9 108 74.3 112 76.8 115 79.2 119 86.5 130 106 159 56.1 84.1 60.9 91.4 65.8 98.7 70.7 106 85.3 128 106 159 146 219

1/ 2 ASD LRFD 56.6 84.8 56.6 84.8 46.1 69.2 39.3 58.8 46.1 69.2 56.6 84.8 50.0 75.0 56.6 84.8 56.6 84.8 56.6 84.8 56.6 84.8 49.3 73.8 56.6 84.8 56.6 84.8 50.0 75.0 56.6 84.8

SSLT 11/2 ASD LRFD 68.3 102 70.7 106 73.1 110 75.6 113 82.9 124 102 154 63.4 95.1 68.3 102 73.1 110 75.6 113 82.9 124 102 154 154 230

13/4 ASD LRFD 76.4 115 78.8 118 81.3 122 83.7 126 91.0 137 111 166 63.4 95.1 68.3 102 73.1 110 78.0 117 91.0 137 111 166 154 230

N = Threads included X = Threads excluded SC = Slip critical

* Tabulated values include 1/4-in. reduction in end distance, Leh , to account for possible underrun in beam length. Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:18 AM

Page 46

10–46

DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-2

Available Weld Strength of Bolted/Welded Double-Angle Connections

n

L , in.

Weld Size, in.

12

351/2

5/16 1/4 3/16

11

321/2

5/16 1/4 3/16

10

291/2

5/16 1/4 3/16

9

261/2

5/16 1/4 3/16

8

231/2

5/16 1/4 3/16

7

201/2

5/16 1/4 3/16

6

171/2

5/16 1/4 3/16

5

141/2

5/16 1/4 3/16

4

111/2

5/16 1/4 3/16

3

81/2

5/16 1/4 3/16

2

51/2

5/16 1/4 3/16

Welds A (70 ksi) Rn /Ω φRn kips kips ASD

LRFD

393 314 236 365 292 219 337 269 202 309 247 185 281 225 169 253 202 152 222 178 133 191 153 115 158 127 95.0 122 98.0 73.5 83.7 66.9 50.2

589 471 353 548 438 329 505 404 303 463 371 278 422 337 253 379 303 227 334 267 200 287 229 172 237 190 142 184 147 110 125 100 75.3

Minimum Weld Web Thickness, Size, in. in. 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286

3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4

Welds B (70 ksi) Rn /Ω φRn kips kips ASD

LRFD

Minimum Support Thickness, in.

366 305 244 331 276 221 295 246 197 259 216 173 223 186 149 187 156 125 150 125 100 115 95.5 76.4 79.9 66.6 53.3 48.1 40.1 32.1 21.9 18.2 14.6

550 458 366 496 414 331 443 369 295 389 324 259 335 279 223 280 234 187 226 188 150 172 143 115 120 99.9 79.9 72.2 60.2 48.1 32.8 27.3 21.9

0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190

ASD

LRFD

Beam

Ω = 2.00

φ = 0.75

Fy = 50 ksi Fu = 65 ksi

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10A:14th Ed.

2/24/11

9:18 AM

Page 47

10–47

DESIGN TABLES

Table 10-3

Available Weld Strength of All-Welded Double-Angle Connections

L , in.

Weld Size, in.

36

5/16 1/4 3/16

34

5/16 1/4 3/16

32

5/16 1/4 3/16

30

5/16 1/4 3/16

28

5/16 1/4 3/16

26

5/16 1/4 3/16

24

5/16 1/4 3/16

22

5/16 1/4 3/16

20

5/16 1/4 3/16

18

5/16 1/4 3/16

16

5/16 1/4 3/16

ASD

LRFD

Ω = 2.00

φ = 0.75

Welds A (70 ksi) Rn /Ω φRn kips kips ASD

LRFD

397 318 238 379 303 227 360 288 216 341 273 205 323 258 194 304 243 183 286 229 171 267 214 160 248 198 149 227 182 136 207 166 124

596 477 357 568 455 341 541 432 324 512 410 307 484 387 291 457 365 274 429 343 257 401 321 240 372 297 223 341 273 205 310 248 186

Minimum Web Thickness, in. 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286

Weld Size, in. 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4

Welds B (70 ksi) Rn /Ω φRn kips kips ASD

LRFD

372 310 248 349 291 232 325 271 217 301 251 201 277 231 185 253 211 169 229 191 153 205 171 137 181 151 121 157 130 104 148 123 98.5

558 465 372 523 436 349 487 406 325 452 377 301 416 347 277 380 317 253 344 286 229 308 256 205 271 226 181 235 196 157 222 185 148

Minimum Web Thickness, in. 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190

Beam Fy = 50 ksi

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Fu = 65 ksi

AISC_PART 10A:14th Ed.

2/24/11

9:19 AM

Page 48

10–48

DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-3 (continued)

Available Weld Strength of All-Welded Double-Angle Connections

L , in.

Weld Size, in.

14

5/16 1/4 3/16

12

5/16 1/4 3/16

10

5/16 1/4 3/16

9

5/16 1/4 3/16

8

5/16 1/4 3/16

7

5/16 1/4 3/16

6

5/16 1/4 3/16

5

5/16 1/4 3/16

4

5/16 1/4 3/16

ASD

LRFD

Ω = 2.00

φ = 0.75

Welds A (70 ksi) Rn /Ω φRn kips kips ASD

LRFD

186 149 111 164 131 98.5 141 112 84.3 129 103 77.2 116 92.9 69.7 103 82.6 62.0 90.4 72.3 54.2 77.1 61.7 46.3 64.2 51.4 38.5

279 223 167 246 197 148 211 169 127 193 154 116 174 139 105 155 124 92.9 136 108 81.3 116 92.6 69.4 96.3 77.0 57.8

Minimum Web Thickness, in. 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286 0.476 0.381 0.286

Weld Size, in. 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4 3/8 5/16 1/4

Welds B (70 ksi) Rn /Ω φRn kips kips ASD

LRFD

123 103 82.3 99.3 82.8 66.2 75.7 63.1 50.4 64.2 53.5 42.8 53.0 44.2 35.4 42.4 35.3 28.3 32.5 27.0 21.6 23.4 19.5 15.6 15.5 12.9 10.3

185 154 123 149 124 99.3 113 94.6 75.7 96.3 80.2 64.2 79.5 66.3 53.0 63.6 53.0 42.4 48.7 40.6 32.5 35.1 29.2 23.4 23.2 19.3 15.5

Minimum Web Thickness, in. 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190 0.286 0.238 0.190

Beam Fy = 50 ksi

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Fu = 65 ksi

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SHEAR END-PLATE CONNECTIONS

10–49

SHEAR END-PLATE CONNECTIONS A shear end-plate connection is made with a plate length less than the supported beam depth, as illustrated in Figure 10-6. The end plate is always shop-welded to the beam web with fillet welds on each side and usually field-bolted to the supporting member. Welds connecting the end plate to the beam web should not be returned across the thickness of the beam web at the top or bottom of the end plate because of the danger of creating a notch in the beam web. If the end plate is field-welded to the support, adequate flexibility must be provided in the connection. Line welds are placed along the vertical edges of the plate with a return at the top per AISC Specification Section J2.2b. Note that welding across the entire top of the plate must be avoided as it would inhibit the flexibility and, therefore, the necessary end rotation of the connection. The performance of the resulting connection would not be as intended for simple shear connections.

Design Checks The available strength of a shear end-plate connection is determined from the applicable limit states for bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). Note that the limit state of shear rupture of the beam web must be checked along the length of weld connecting the end plate to the beam web. In all cases, the available strength, φRn or Rn/Ω, must equal or exceed the required strength, Ru or Ra.

Recommended End-Plate Dimensions and Thickness To provide for stability during erection, it is recommended that the minimum end-plate length be one-half the T-dimension of the beam to be supported. The maximum length of the end plate must be compatible with the clear distance between the flanges of an uncoped beam and the remaining clear distance of a coped beam. To provide for flexibility, the combination of plate thickness and gage should be consistent with the recommendations given previously for a double-angle connection of similar thickness and gage.

Shop and Field Practices When framing to a column web, the associated constructability considerations should be addressed (see the preceding discussion under “Constructability Considerations”).

Fig. 10-6. Shear end-plate connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF SIMPLE SHEAR CONNECTIONS

When framing to a column flange, provision must be made for possible mill variation in the depth of the columns, particularly in fairly long runs (i.e., six or more bays of framing). The beam length can be shortened to provide for mill overrun with shims furnished at the appropriate intervals to fill the resulting gaps or to provide for mill underrun. Shear end-plate connections require close control in cutting the beam to the proper length and in squaring the beam ends such that both end plates are parallel, particularly when beams are cambered.

DESIGN TABLE DISCUSSION (TABLE 10-4) Table 10-4. Bolted/Welded Shear End-Plate Connections Table 10-4 is a design aid for shear end-plate connections bolted to the supporting member and welded to the supported beam. Available strengths are tabulated for supported and supporting member material with Fy = 50 ksi and Fu = 65 ksi, and end-plate material with Fy = 36 ksi and Fu = 58 ksi. Electrode strength is assumed to be 70 ksi. All values, including slip-critical bolt available strengths, are for comparison with the governing LRFD or ASD load combination. Tabulated bolt and end-plate available strengths consider the limit states of bolt shear, bolt bearing on the end plate, shear yielding of the end plate, shear rupture of the end plate, and block shear rupture of the end plate. Values are included for 2 through 12 rows of 3 /4-in., 7/8-in. and 1-in.-diameter Group A and Group B bolts at 3-in. spacing. End-plate edge distances, Lev and Leh, are assumed to be 11/4 in. Tabulated weld available strengths consider the limit state of weld shear assuming an effective weld length equal to the end-plate length minus twice the weld size. The tabulated minimum beam web thickness matches the shear rupture strength of the web material to the strength of the weld metal. As derived in Part 9, the minimum supported beam web thickness for two lines of weld is tmin =

6.19 D Fu

(9-3)

where D is the number of sixteenths-of-an-inch in the weld size. When less than the minimum material thickness is present, the tabulated weld available strength must be reduced by the ratio of the thickness provided to the minimum thickness. Tabulated supporting member available strengths, per in. of flange or web thickness, consider the limit state of bolt bearing.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN TABLES

10–51

Table 10-4

3

/4-in. Bolts

Bolted/Welded Shear End-Plate Connections

W44

12 Rows L = 35 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

3/8

ASD 246 246 152 129 152 246 216 244 246 246

LRFD 369 369 228 194 228 369 323 366 369 369

ASD 286 295 152 129 152 253 216 253 295 295

LRFD 430 443 228 194 228 380 323 380 443 443

190 285 162 242 SSLT 190 285 STD 197 295 OVS SC Class B 196 294 SSLT 195 293 Weld and Beam Web Available Strength, kips

190 162 190 246 245 244

285 242 285 369 367 366

190 162 190 295 270 293

285 242 285 443 403 440

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 197 197 152 129 152 197 196 195 197 197

SSLT STD OVS SSLT STD STD STD OVS

N X

70-ksi Weld Size, in.

5/16

1/4

LRFD 295 295 228 194 228 295 294 293 295 295

SC Class B

Group B

End-Plate Thickness, in.

Hole Type

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

196 260 324 387

293 390 486 581

1400

2110

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

3

/4-in. Bolts

Bolted/Welded Shear End-Plate Connections

11 Rows L = 32 1/2 in.

W44, 40

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 226 226 139 119 139 226 198 224 226 226

LRFD 338 338 209 178 209 338 296 336 338 338

ASD 263 271 139 119 139 232 198 232 271 271

LRFD 394 406 209 178 209 348 296 348 406 406

174 261 148 222 SSLT 174 261 STD 181 271 OVS SC Class B 180 269 SSLT 179 269 Weld and Beam Web Available Strength, kips

174 148 174 226 225 224

261 222 261 338 337 336

174 148 174 271 247 269

261 222 261 406 370 403

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 181 181 139 119 139 181 180 179 181 181

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 271 271 209 178 209 271 269 269 271 271

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

179 238 296 354

268 356 444 530

1290

1930

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

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DESIGN TABLES

10–53

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

W44, 40, 36

3

/4-in. Bolts

10 Rows L = 29 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 205 205 127 108 127 205 180 204 205 205

LRFD 308 308 190 161 190 308 269 306 308 308

ASD 239 246 127 108 127 211 180 211 246 246

LRFD 358 370 190 161 190 316 269 316 370 370

158 237 135 202 SSLT 158 237 STD 164 246 OVS SC Class B 163 245 SSLT 163 244 Weld and Beam Web Available Strength, kips

158 135 158 205 204 204

237 202 237 308 306 306

158 135 158 246 225 244

237 202 237 370 336 367

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 164 164 127 108 127 164 163 163 164 164

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 246 246 190 161 190 246 245 244 246 246

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

162 215 268 320

243 323 402 480

1170

1760

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

3

/4-in. Bolts

Bolted/Welded Shear End-Plate Connections

9 Rows L = 26 1/2 in.

W44, 40, 36, 33

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

N X

STD STD

SC Class A

STD OVS

N X

Group B

70-ksi Weld Size, in.

ASD 148 148 114 97.1 114 148 147 147 148 148

SSLT STD OVS SSLT STD STD

SC Class B

End-Plate Thickness, in. 5/16

1/4

LRFD 222 222 171 145 171 222 221 220 222 222

STD OVS

142 214 121 182 SSLT 142 214 STD 148 222 OVS SC Class B 147 221 SSLT 147 220 Weld and Beam Web Available Strength, kips SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Rn / Ω

3/8

ASD 185 185 114 97.1 114 185 162 183 185 185

LRFD 278 278 171 145 171 278 242 275 278 278

ASD 215 222 114 97.1 114 190 162 190 222 222

142 121 142 185 184 183

214 182 214 278 276 275

142 121 142 222 202 220

φ Rn

LRFD 322 333 171 145 171 285 242 285 333 333 214 182 214 333 303 330

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

145 193 240 287

218 290 360 430

1050

1580

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

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DESIGN TABLES

10–55

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

W44, 40, 36, 33, 30

3

/4-in. Bolts

8 Rows L = 23 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Thread Cond.

Hole Type

Group A

STD STD OVS

SC Class A

SSLT STD OVS SSLT STD STD

SC Class B N X

Group B

70-ksi Weld Size, in.

ASD 132 132 101 86.3 101 132 131 131 132 132

STD

N X

End-Plate Thickness, in. 5/16

1/4

LRFD 198 198 152 129 152 198 197 196 198 198

STD OVS

127 190 108 161 SSLT 127 190 STD 132 198 OVS SC Class B 131 197 SSLT 131 196 Weld and Beam Web Available Strength, kips SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Rn / Ω

3/8

ASD 165 165 101 86.3 101 165 144 163 165 165

LRFD 247 247 152 129 152 247 215 245 247 247

ASD 191 198 101 86.3 101 169 144 169 198 198

127 108 127 165 164 163

190 161 190 247 246 245

127 108 127 198 180 196

φ Rn

LRFD 286 297 152 129 152 253 215 253 297 297 190 161 190 297 269 294

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

129 171 212 253

193 256 318 380

936

1400

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

3

/4-in. Bolts

W44, 40, 36, 33, 30, 27, 24

Bolted/Welded Shear End-Plate Connections

7 Rows L = 20 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 145 145 88.6 75.5 88.6 145 126 143 145 145

LRFD 217 217 133 113 133 217 188 214 217 217

ASD 167 174 88.6 75.5 88.6 148 126 148 174 174

LRFD 251 260 133 113 133 221 188 221 260 260

111 166 94.4 141 SSLT 111 166 STD 116 174 OVS SC Class B 115 172 SSLT 114 172 Weld and Beam Web Available Strength, kips

111 94.4 111 145 144 143

166 141 166 217 215 214

111 94.4 111 174 157 172

166 141 166 260 235 257

N X

STD STD

SC Class A

STD OVS

ASD 116 116 88.6 75.5 88.6 116 115 114 116 116

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 174 174 133 113 133 174 172 172 174 174

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Rn / Ω

φ Rn

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

112 148 184 220

168 223 277 330

819

1230

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

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DESIGN TABLES

10–57

Table 10-4 (continued)

W44, 40, 36, 33, 30, 27, 24, 21

3

/4-in. Bolts

Bolted/Welded Shear End-Plate Connections

6 Rows L = 17 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

N X

STD STD

SC Class A

STD OVS

N X

Group B

70-ksi Weld Size, in.

ASD 99.5 99.5 75.9 64.7 75.9 99.5 98.6 98.2 99.5 99.5

SSLT STD OVS SSLT STD STD

SC Class B

End-Plate Thickness, in. 5/16

1/4

LRFD 149 149 114 96.8 114 149 148 147 149 149

STD OVS

94.9 142 80.9 121 SSLT 94.9 142 STD 99.5 149 OVS SC Class B 98.6 148 SSLT 98.2 147 Weld and Beam Web Available Strength, kips SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Rn / Ω

3/8

ASD 124 124 75.9 64.7 75.9 124 108 123 124 124

LRFD 187 187 114 96.8 114 187 161 184 187 187

ASD 143 149 75.9 64.7 75.9 127 108 127 149 149

LRFD 215 224 114 96.8 114 190 161 190 224 224

94.9 80.9 94.9 124 123 123

142 121 142 187 185 184

94.9 80.9 94.9 149 135 147

142 121 142 224 202 221

φ Rn

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

95.4

143 189 235 280

702

1050

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

126 157 187 N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

3

/4-in. Bolts

Bolted/Welded Shear End-Plate Connections

5 Rows L = 14 1/2 in.

W30, 27, 24, 21, 18

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

N X

STD STD

SC Class A

STD OVS

N X

Group B

70-ksi Weld Size, in.

ASD 83.3 83.3 63.3 53.9 63.3 83.3 82.4 82.0 83.3 83.3

SSLT STD OVS SSLT STD STD

SC Class B

End-Plate Thickness, in. 5/16

1/4

LRFD 125 125 94.9 80.7 94.9 125 124 123 125 125

STD OVS

79.1 119 67.4 101 SSLT 79.1 119 STD 83.3 125 OVS SC Class B 82.4 124 SSLT 82.0 123 Weld and Beam Web Available Strength, kips SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Rn / Ω

3/8

ASD 104 104 63.3 53.9 63.3 104 89.9 102 104 104

LRFD 156 156 94.9 80.7 94.9 156 134 154 156 156

ASD 119 125 63.3 53.9 63.3 105 89.9 105 125 125

LRFD 179 187 94.9 80.7 94.9 158 134 158 187 187

79.1 67.4 79.1 104 103 102

119 101 119 156 155 154

79.1 67.4 79.1 125 112 123

119 101 119 187 168 184

φ Rn

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

78.7

118 156 193 230

585

878

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

104 129 153 N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

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DESIGN TABLES

10–59

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

W24, 21, 18, 16

3

/4-in. Bolts

4 Rows L = 111/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Thread Cond.

Hole Type

ASD 83.9 83.9 50.6 43.1 50.6 83.9 71.9 82.2 83.9 83.9

LRFD 126 126 75.9 64.5 75.9 126 108 123 126 126

ASD 95.5 101 50.6 43.1 50.6 84.4 71.9 84.4 101 101

LRFD 143 151 75.9 64.5 75.9 127 108 127 151 151

63.3 94.9 53.9 80.7 SSLT 63.3 94.9 STD 67.1 101 OVS SC Class B 65.3 97.9 SSLT 65.8 98.7 Weld and Beam Web Available Strength, kips

63.3 53.9 63.3 83.9 81.6 82.2

94.9 80.7 94.9 126 122 123

63.3 53.9 63.3 101 89.9 98.7

94.9 80.7 94.9 151 134 148

Rn / Ω

φ Rn

STD STD OVS

SC Class A

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

ASD 67.1 67.1 50.6 43.1 50.6 67.1 65.3 65.8 67.1 67.1

STD

SC Class B

Group B

3/8

LRFD 101 101 75.9 64.5 75.9 101 97.9 98.7 101 101

N X

Group A

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

kips

kips

ASD

LRFD

61.9 81.7 101 120

123 151 180

Support Available Strength per Inch Thickness, kip/in. ASD

LRFD

468

702

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

92.9

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

3

/4-in. Bolts

Bolted/Welded Shear End-Plate Connections

3 Rows L = 8 1/2 in.

W18, 16, 14, 12, 10*

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 63.7 63.7 38.0 32.4 38.0 63.3 53.9 62.0 63.7 63.7

LRFD 95.5 95.5 57.0 48.4 57.0 94.9 80.7 92.9 95.5 95.5

ASD 71.6 76.4 38.0 32.4 38.0 63.3 53.9 63.3 76.4 76.4

LRFD 107 115 57.0 48.4 57.0 94.9 80.7 94.9 115 115

47.5 71.2 40.4 60.5 SSLT 47.5 71.2 STD 50.9 76.4 OVS SC Class B 47.9 71.8 SSLT 49.6 74.4 Weld and Beam Web Available Strength, kips

47.5 40.4 47.5 63.7 59.8 62.0

71.2 60.5 71.2 95.5 89.7 92.9

47.5 40.4 47.5 76.4 67.4 74.4

71.2 60.5 71.2 115 101 112

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 50.9 50.9 38.0 32.4 38.0 50.9 47.9 49.6 50.9 50.9

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 76.4 76.4 57.0 48.4 57.0 76.4 71.8 74.4 76.4 76.4

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

45.2 59.4 73.1 88.3

67.9 89.1 110 129

351

526

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

*Limited to W10×12, 15,17, 19, 22, 26, 30 Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

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DESIGN TABLES

10–61

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

W12, 10, 8

3

/4-in. Bolts 2 Rows L = 5 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 40.8 40.8 25.3 21.6 25.3 40.8 36.0 40.8 40.8 40.8

LRFD 61.2 61.2 38.0 32.3 38.0 61.2 53.8 61.2 61.2 61.2

ASD 47.7 48.9 25.3 21.6 25.3 42.2 36.0 42.2 48.9 48.9

LRFD 71.6 73.4 38.0 32.3 38.0 63.3 53.8 63.3 73.4 73.4

31.6 47.5 27.0 40.3 SSLT 31.6 47.5 STD 32.6 48.9 OVS SC Class B 30.5 45.7 SSLT 32.6 48.9 Weld and Beam Web Available Strength, kips

31.6 27.0 31.6 40.8 38.1 40.8

47.5 40.3 47.5 61.2 57.1 61.2

31.6 27.0 31.6 48.9 44.9 48.9

47.5 40.3 47.5 73.4 67.2 73.4

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 32.6 32.6 25.3 21.6 25.3 32.6 30.5 32.6 32.6 32.6

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 48.9 48.9 38.0 32.3 38.0 48.9 45.7 48.9 48.9 48.9

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

28.5 37.1 45.2 52.9

42.8 55.7 67.9 79.4

234

351

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 62

10–62

DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

7

/8-in. Bolts

Bolted/Welded Shear End-Plate Connections

12 Rows L = 35 1/2 in.

W44

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 245 245 212 180 212 245 239 243 245 245

LRFD 367 367 317 270 317 367 359 365 367 367

ASD 294 294 212 180 212 294 287 292 294 294

LRFD 441 441 317 270 317 441 431 438 441 441

196 294 191 287 SSLT 194 292 STD 196 294 OVS SC Class B 191 287 SSLT 194 292 Weld and Beam Web Available Strength, kips

245 227 243 245 239 243

367 339 365 367 359 365

266 227 266 294 287 292

399 339 399 441 431 438

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 196 196 196 180 194 196 191 194 196 196

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 294 294 294 270 292 294 287 292 294 294

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

196 260 324 387

293 390 486 581

1640

2460

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 10B:14th Ed.

2/24/11

9:21 AM

Page 63

DESIGN TABLES

10–63

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

W44, 40

7

/8-in. Bolts 11 Rows L = 32 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 225 225 194 165 194 225 219 223 225 225

LRFD 337 337 291 247 291 337 328 334 337 337

ASD 269 269 194 165 194 269 263 267 269 269

LRFD 404 404 291 247 291 404 394 401 404 404

180 269 175 263 SSLT 178 267 STD 180 269 OVS SC Class B 175 263 SSLT 178 267 Weld and Beam Web Available Strength, kips

225 208 223 225 219 223

337 311 334 337 328 334

244 208 244 269 263 267

365 311 365 404 394 401

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 180 180 180 165 178 180 175 178 180 180

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 269 269 269 247 267 269 263 267 269 269

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

179 238 296 354

268 356 444 530

1500

2250

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 10B:14th Ed.

2/24/11

9:21 AM

Page 64

10–64

DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

7

/8-in. Bolts

Bolted/Welded Shear End-Plate Connections

10 Rows L = 29 1/2 in.

W44, 40, 36

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 204 204 176 150 176 204 198 203 204 204

LRFD 306 306 264 225 264 306 298 304 306 306

ASD 245 245 176 150 176 245 238 243 245 245

LRFD 368 368 264 225 264 368 357 365 368 368

163 245 159 238 SSLT 162 243 STD 163 245 OVS SC Class B 159 238 SSLT 162 243 Weld and Beam Web Available Strength, kips

204 189 203 204 198 203

306 282 304 306 298 304

221 189 221 245 238 243

332 282 332 368 357 365

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 163 163 163 150 162 163 159 162 163 163

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 245 245 245 225 243 245 238 243 245 245

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

162 215 268 320

243 323 402 480

1370

2050

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 10B:14th Ed.

2/24/11

9:21 AM

Page 65

DESIGN TABLES

10–65

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

W44, 40, 36, 33

7

/8-in. Bolts 9 Rows L = 26 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 184 184 159 135 159 184 178 182 184 184

LRFD 276 276 238 202 238 276 267 273 276 276

ASD 221 221 159 135 159 221 214 219 221 221

LRFD 331 331 238 202 238 331 321 328 331 331

147 221 142 214 SSLT 146 219 STD 147 221 OVS SC Class B 142 214 SSLT 146 219 Weld and Beam Web Available Strength, kips

184 170 182 184 178 182

276 254 273 276 267 273

199 170 199 221 214 219

299 254 299 331 321 328

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 147 147 147 135 146 147 142 146 147 147

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 221 221 221 202 219 221 214 219 221 221

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

145 193 240 287

218 290 360 430

1230

1840

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 10B:14th Ed.

2/24/11

9:21 AM

Page 66

10–66

DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

7

/8-in. Bolts

Bolted/Welded Shear End-Plate Connections

8 Rows L = 23 1/2 in.

W44, 40, 36, 33, 30

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 164 164 141 120 141 164 158 162 164 164

LRFD 246 246 212 180 212 246 237 243 246 246

ASD 197 197 141 120 141 197 189 194 197 197

LRFD 295 295 212 180 212 295 284 292 295 295

131 197 126 189 SSLT 130 194 STD 131 197 OVS SC Class B 126 189 SSLT 130 194 Weld and Beam Web Available Strength, kips

164 151 162 164 158 162

246 226 243 246 237 243

177 151 177 197 189 194

266 226 266 295 284 292

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 131 131 131 120 130 131 126 130 131 131

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 197 197 197 180 194 197 189 194 197 197

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

129 171 212 253

193 256 318 380

1090

1640

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 10B:14th Ed.

2/24/11

9:21 AM

Page 67

DESIGN TABLES

10–67

Table 10-4 (continued)

W44, 40, 36, 33, 30, 27, 24

Bolted/Welded Shear End-Plate Connections

7

/8-in. Bolts 7 Rows L = 20 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 144 144 123 105 123 144 137 142 144 144

LRFD 215 215 185 157 185 215 206 213 215 215

ASD 172 172 123 105 123 172 165 170 172 172

LRFD 258 258 185 157 185 258 247 255 258 258

115 172 110 165 SSLT 113 170 STD 115 172 OVS SC Class B 110 165 SSLT 113 170 Weld and Beam Web Available Strength, kips

144 132 142 144 137 142

215 198 213 215 206 213

155 132 155 172 165 170

233 198 233 258 247 255

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 115 115 115 105 113 115 110 113 115 115

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 172 172 172 157 170 172 165 170 172 172

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

112 148 184 220

168 223 277 330

956

1430

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 10B:14th Ed.

2/24/11

9:22 AM

Page 68

10–68

DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

7

/8-in. Bolts

W40, 36, 33, 30, 27, 24, 21

Bolted/Welded Shear End-Plate Connections

6 Rows L = 17 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

N X

STD STD

SC Class A

STD OVS

N X

Group B

70-ksi Weld Size, in.

ASD 98.6 98.6 98.6 90.1 97.3 98.6 93.5 97.3 98.6 98.6

SSLT STD OVS SSLT STD STD

SC Class B

End-Plate Thickness, in. 5/16

1/4

LRFD 148 148 148 135 146 148 140 146 148 148

STD OVS

98.6 148 93.5 140 SSLT 97.3 146 STD 98.6 148 OVS SC Class B 93.5 140 SSLT 97.3 146 Weld and Beam Web Available Strength, kips SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Rn / Ω

3/8

ASD 123 123 106 90.1 106 123 117 122 123 123

LRFD 185 185 159 135 159 185 175 182 185 185

ASD 148 148 106 90.1 106 148 140 146 148 148

123 113 122 123 117 122

185 169 182 185 175 182

133 113 133 148 140 146

φ Rn

LRFD 222 222 159 135 159 222 210 219 222 222 199 169 199 222 210 219

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

95.4

143 189 235 280

819

1230

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

126 157 187 N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 10B:14th Ed.

2/24/11

9:22 AM

Page 69

DESIGN TABLES

10–69

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

W30, 27, 24, 21, 18

7

/8-in. Bolts 5 Rows L = 14 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 103 103 88.1 75.1 88.1 103 96.5 101 103 103

LRFD 155 155 132 112 132 155 145 152 155 155

ASD 124 124 88.1 75.1 88.1 124 116 122 124 124

LRFD 185 185 132 112 132 185 174 182 185 185

82.4 124 77.2 116 SSLT 81.1 122 STD 82.4 124 OVS SC Class B 77.2 116 SSLT 81.1 122 Weld and Beam Web Available Strength, kips

103 94.4 101 103 96.5 101

155 141 152 155 145 152

111 94.4 111 124 116 122

166 141 166 185 174 182

N X

STD STD

SC Class A

STD OVS

ASD 82.4 82.4 82.4 75.1 81.1 82.4 77.2 81.1 82.4 82.4

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 124 124 124 112 122 124 116 122 124 124

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Rn / Ω

φ Rn

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

78.7

118 156 193 230

683

1020

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

104 193 153 N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 10B:14th Ed.

2/24/11

9:22 AM

Page 70

10–70

DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

7

/8-in. Bolts

Bolted/Welded Shear End-Plate Connections

4 Rows L = 111/2 in.

W24, 21, 18, 16

Bolt and End-Plate Available Strength, kips Bolt Group

Thread Cond.

Hole Type

ASD 81.6 81.6 70.5 60.1 70.5 81.6 76.1 81.1 81.6 81.6

LRFD 122 122 106 89.9 106 122 114 122 122 122

ASD 97.9 97.9 70.5 60.1 70.5 97.9 91.4 97.3 97.9 97.9

LRFD 147 147 106 89.9 106 147 137 146 147 147

65.3 97.9 60.9 91.4 SSLT 64.9 97.3 STD 65.3 97.9 OVS SC Class B 60.9 91.4 SSLT 64.9 97.3 Weld and Beam Web Available Strength, kips

81.6 75.5 81.1 81.6 76.1 81.1

122 113 122 122 114 122

88.6 75.5 88.6 97.9 91.4 97.3

133 113 133 147 137 146

Rn / Ω

φ Rn

STD STD OVS

SC Class A

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

ASD 65.3 65.3 65.3 60.1 64.9 65.3 60.9 64.9 65.3 65.3

STD

SC Class B

Group B

3/8

LRFD 97.9 97.9 97.9 89.9 97.3 97.9 91.4 97.3 97.9 97.9

N X

Group A

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

kips

kips

ASD

LRFD

61.9 81.7 101 120

123 151 180

Support Available Strength per Inch Thickness, kip/in. ASD

LRFD

546

819

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

92.9

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 10B:14th Ed.

2/24/11

9:22 AM

Page 71

DESIGN TABLES

10–71

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

W18, 16, 14, 12, 10*

7

/8-in. Bolts 3 Rows L = 8 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 59.8 59.8 52.9 45.1 52.9 59.8 55.7 59.8 59.8 59.8

LRFD 89.7 89.7 79.3 67.4 79.3 89.7 83.6 89.7 89.7 89.7

ASD 71.8 71.8 52.9 45.1 52.9 71.8 66.9 71.8 71.8 71.8

LRFD 108 108 79.3 67.4 79.3 108 100 108 108 108

47.9 71.8 44.6 66.9 SSLT 47.9 71.8 STD 47.9 71.8 OVS SC Class B 44.6 66.9 SSLT 47.9 71.8 Weld and Beam Web Available Strength, kips

59.8 55.7 59.8 59.8 55.7 59.8

89.7 83.6 89.7 89.7 83.6 89.7

66.4 56.6 66.4 71.8 66.9 71.8

99.7 84.7 99.7 108 100 108

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 47.9 47.9 47.9 44.6 47.9 47.9 44.6 47.9 47.9 47.9

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 71.8 71.8 71.8 66.9 71.8 71.8 66.9 71.8 71.8 71.8

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

45.2 59.4 73.1 86.3

67.9 89.1 110 129

409

614

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

*Limited to W10×12, 15, 17, 19, 22, 26, 30 Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_Part 10B:14th Ed.

2/24/11

9:22 AM

Page 72

10–72

DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

7

/8-in. Bolts

Bolted/Welded Shear End-Plate Connections

2 Rows L = 5 1/2 in.

W12, 10, 8

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 38.1 38.1 35.3 30.0 35.3 38.1 35.3 38.1 38.1 38.1

LRFD 57.1 57.1 52.9 45.0 52.9 57.1 53.0 57.1 57.1 57.1

ASD 45.7 45.7 35.3 30.0 35.3 45.7 42.4 45.7 45.7 45.7

LRFD 68.5 68.5 52.9 45.0 52.9 68.5 63.6 68.5 68.5 68.5

30.5 45.7 28.3 42.4 SSLT 30.5 45.7 STD 30.5 45.7 OVS SC Class B 28.3 42.4 SSLT 30.5 45.7 Weld and Beam Web Available Strength, kips

38.1 35.3 38.1 38.1 35.3 38.1

57.1 53.0 57.1 57.1 53.0 57.1

44.3 37.8 44.3 45.7 42.4 45.7

66.4 56.5 66.4 68.5 63.6 68.5

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 30.5 30.5 30.5 28.3 30.5 30.5 28.3 30.5 30.5 30.5

SSLT STD OVS SSLT STD

N X

70-ksi Weld Size, in.

3/8

LRFD 45.7 45.7 45.7 42.4 45.7 45.7 42.4 45.7 45.7 45.7

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

Support Available Strength per Inch Thickness, kip/in.

kips

kips

ASD

LRFD

ASD

LRFD

28.5 37.1 45.2 52.9

42.8 55.7 67.9 79.4

273

409

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

N = Threads included X = Threads excluded SC = Slip critical

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 73

DESIGN TABLES

10–73

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

W44

1-in. Bolts 12 Rows L = 35 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 239 239 239 215 239 239 215 239 239 239

LRFD 359 359 359 322 359 359 322 359 359 359

ASD 287 287 277 236 277 287 258 287 287 287

LRFD 431 431 415 353 415 431 387 431 431 431

191 287 172 258 SSLT 191 287 STD 191 287 OVS SC Class B 172 258 SSLT 191 287 Weld and Beam Web Available Strength, kips

239 215 239 239 215 239

359 322 359 359 322 359

287 258 287 287 258 287

431 387 431 431 387 431

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 191 191 191 172 191 191 172 191 191 191

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 287 287 287 258 287 287 258 287 287 287

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

kips

kips

ASD

LRFD

196 260 324 387

293 390 486 581

N = Threads included X = Threads excluded SC = Slip critical

Support Available Strength per Inch Thickness, kip/in. ASD 1820

STD/ SSLT

LRFD 2730

STD/ SSLT

1660 OVS

2490 OVS

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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10–74

DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

1-in. Bolts 11 Rows L = 32 1/2 in.

W44, 40

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 219 219 219 196 219 219 196 219 219 219

LRFD 328 328 328 295 328 328 295 328 328 328

ASD 263 263 254 216 254 263 236 263 263 263

LRFD 394 394 380 323 380 394 354 394 394 394

175 263 157 236 SSLT 175 263 STD 175 263 OVS SC Class B 157 236 SSLT 175 263 Weld and Beam Web Available Strength, kips

219 196 219 219 196 219

328 295 328 328 295 328

263 236 263 263 236 263

394 354 394 394 354 394

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 175 175 175 157 175 175 157 175 175 175

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 263 263 263 236 263 263 236 263 263 263

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

kips

kips

ASD

LRFD

179 238 296 354

268 356 444 530

N = Threads included X = Threads excluded SC = Slip critical

Support Available Strength per Inch Thickness, kip/in. ASD 1670

STD/ SSLT

LRFD 2500

STD/ SSLT

1520 OVS

2280 OVS

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 75

DESIGN TABLES

10–75

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

W44, 40, 36

1-in. Bolts 10 Rows L = 29 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 198 198 198 178 198 198 178 198 198 198

LRFD 298 298 298 267 298 298 267 298 298 298

ASD 238 238 231 196 231 238 214 238 238 238

LRFD 357 357 346 294 346 357 321 357 357 357

159 238 142 214 SSLT 159 238 STD 159 238 OVS SC Class B 142 214 SSLT 159 238 Weld and Beam Web Available Strength, kips

198 178 198 198 178 198

298 267 298 298 267 298

238 214 238 238 214 238

357 321 357 357 321 357

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 159 159 159 142 159 159 142 159 159 159

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 238 238 238 214 238 238 214 238 238 238

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

kips

kips

ASD

LRFD

162 215 268 320

243 323 402 480

N = Threads included X = Threads excluded SC = Slip critical

Support Available Strength per Inch Thickness, kip/in. ASD 1520

STD/ SSLT

LRFD 2270

STD/ SSLT

1380 OVS

2080 OVS

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 76

10–76

DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

1-in. Bolts 9 Rows L = 26 1/2 in.

W44, 40, 36, 33

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 178 178 178 160 178 178 160 178 178 178

LRFD 267 267 267 240 267 267 240 267 267 267

ASD 214 214 207 177 207 214 192 214 214 214

LRFD 321 321 311 265 311 321 288 321 321 321

142 214 128 192 SSLT 142 214 STD 142 214 OVS SC Class B 128 192 SSLT 142 214 Weld and Beam Web Available Strength, kips

178 160 178 178 160 178

267 240 267 267 240 267

214 192 214 214 192 214

321 288 321 321 288 321

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 142 142 142 128 142 142 128 142 142 142

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 214 214 214 192 214 214 192 214 214 214

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

kips

kips

ASD

LRFD

145 193 240 287

218 290 360 430

N = Threads included X = Threads excluded SC = Slip critical

Support Available Strength per Inch Thickness, kip/in. ASD 1370

STD/ SSLT

LRFD 2050

STD/ SSLT

1250 OVS

1870 OVS

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

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Page 77

DESIGN TABLES

10–77

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

W44, 40, 36, 33, 30

1-in. Bolts 8 Rows L = 23 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 158 158 158 141 158 158 141 158 158 158

LRFD 237 237 237 212 237 237 212 237 237 237

ASD 189 189 184 157 184 189 170 189 189 189

LRFD 284 284 277 235 277 284 254 284 284 284

126 189 113 170 SSLT 126 189 STD 126 189 OVS SC Class B 113 170 SSLT 126 189 Weld and Beam Web Available Strength, kips

158 141 158 158 141 158

237 212 237 237 212 237

189 170 189 189 170 189

284 254 284 284 254 284

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 126 126 126 113 126 126 113 126 126 126

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 189 189 189 170 189 189 170 189 189 189

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

kips

kips

ASD

LRFD

129 171 212 253

193 256 318 380

N = Threads included X = Threads excluded SC = Slip critical

Support Available Strength per Inch Thickness, kip/in. ASD 1210

STD/ SSLT

LRFD 1820

STD/ SSLT

1110 OVS

1670 OVS

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 78

10–78

DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

W44, 40, 36, 33, 30, 27, 24

Bolted/Welded Shear End-Plate Connections

1-in. Bolts 7 Rows L = 20 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Thread Cond.

Hole Type

ASD 137 137 137 123 137 137 123 137 137 137

LRFD 206 206 206 185 206 206 185 206 206 206

ASD 165 165 161 138 161 165 148 165 165 165

LRFD 247 247 242 206 242 247 221 247 247 247

110 165 98.4 148 SSLT 110 165 STD 110 165 OVS SC Class B 98.4 148 SSLT 110 165 Weld and Beam Web Available Strength, kips

137 123 137 137 123 137

206 185 206 206 185 206

165 148 165 165 148 165

247 221 247 247 221 247

Rn / Ω

φ Rn

STD STD OVS

SC Class A

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

ASD 110 110 110 98.4 110 110 98.4 110 110 110

STD

SC Class B

Group B

3/8

LRFD 165 165 165 148 165 165 148 165 165 165

N X

Group A

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

kips

kips

ASD

LRFD

112 148 184 220

168 223 277 330

N = Threads included X = Threads excluded SC = Slip critical

Support Available Strength per Inch Thickness, kip/in. ASD

LRFD

1060

STD/ SSLT

1590

STD/ SSLT

975

OVS

1460 OVS

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 79

DESIGN TABLES

10–79

Table 10-4 (continued)

W40, 36, 33, 30, 27, 24, 21

Bolted/Welded Shear End-Plate Connections

1-in. Bolts 6 Rows L = 17 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 117 117 117 105 117 117 105 117 117 117

LRFD 175 175 175 157 175 175 157 175 175 175

ASD 140 140 138 118 138 140 126 140 140 140

LRFD 210 210 207 176 207 210 188 210 210 210

93.5 140 83.7 126 SSLT 93.5 140 STD 93.5 140 OVS SC Class B 83.7 126 SSLT 93.5 140 Weld and Beam Web Available Strength, kips

117 105 117 117 105 117

175 157 175 175 157 175

140 126 140 140 126 140

210 188 210 210 188 210

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 93.5 93.5 93.5 83.7 93.5 93.5 83.7 93.5 93.5 93.5

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 140 140 140 126 140 140 126 140 140 140

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

kips

kips

ASD

LRFD

95.4

143 189 235 280

126 157 187 N = Threads included X = Threads excluded SC = Slip critical

Support Available Strength per Inch Thickness, kip/in. ASD

LRFD

912

STD/ SSLT

1370

STD/ SSLT

839

OVS

1260 OVS

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

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Page 80

10–80

DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

1-in. Bolts 5 Rows L = 14 1/2 in.

W30, 27, 24, 21, 18

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 96.5 96.5 96.5 86.3 96.5 96.5 86.3 96.5 96.5 96.5

LRFD 145 145 145 129 145 145 129 145 145 145

ASD 116 116 115 98.2 115 116 104 116 116 116

77.2 116 69.1 104 SSLT 77.2 116 STD 77.2 116 OVS SC Class B 69.1 104 SSLT 77.2 116 Weld and Beam Web Available Strength, kips

96.5 86.3 96.5 96.5 86.3 96.5

145 129 145 145 129 145

116 104 116 116 104 116

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 77.2 77.2 77.2 69.1 77.2 77.2 69.1 77.2 77.2 77.2

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 116 116 116 104 116 116 104 116 116 116

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

kips

kips

ASD

LRFD

78.7

118 156 193 230

104 129 153 N = Threads included X = Threads excluded SC = Slip critical

LRFD 174 174 173 147 173 174 155 174 174 174 174 155 174 174 155 174

Support Available Strength per Inch Thickness, kip/in. ASD

LRFD

761

STD/ SSLT

1140

STD/ SSLT

702

OVS

1050 OVS

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 81

DESIGN TABLES

10–81

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

W24, 21, 18, 16

1-in. Bolts 4 Rows L = 111/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 76.1 76.1 76.1 68.0 76.1 76.1 68.0 76.1 76.1 76.1

LRFD 114 114 114 102 114 114 102 114 114 114

ASD 91.4 91.4 91.4 78.6 91.4 91.4 81.6 91.4 91.4 91.4

LRFD 137 137 137 118 137 137 122 137 137 137

60.9 91.4 54.4 81.6 SSLT 60.9 91.4 STD 60.9 91.4 OVS SC Class B 54.4 81.6 SSLT 60.9 91.4 Weld and Beam Web Available Strength, kips

76.1 68.0 76.1 76.1 68.0 76.1

114 102 114 114 102 114

91.4 81.6 91.4 91.4 81.6 91.4

137 122 137 137 122 137

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 60.9 60.9 60.9 54.4 60.9 60.9 54.4 60.9 60.9 60.9

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 91.4 91.4 91.4 81.6 91.4 91.4 81.6 91.4 91.4 91.4

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

kips

kips

ASD

LRFD

61.9 81.7 101 120

123 151 180

92.9

N = Threads included X = Threads excluded SC = Slip critical

Support Available Strength per Inch Thickness, kip/in. ASD

LRFD

609

STD/ SSLT

914

STD/ SSLT

566

OVS

848 OVS

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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10–82

DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

1-in. Bolts 3 Rows L = 8 1/2 in.

W18, 16, 14, 12, 10*

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 55.7 55.7 55.7 49.6 55.7 55.7 49.6 55.7 55.7 55.7

LRFD 83.6 83.6 83.6 74.4 83.6 83.6 74.4 83.6 83.6 83.6

ASD 66.9 66.9 66.9 58.9 66.9 66.9 59.5 66.9 66.9 66.9

LRFD 100 100 100 88.2 100 100 89.3 100 100 100

44.6 66.9 39.7 59.5 SSLT 44.6 66.9 STD 44.6 66.9 OVS SC Class B 39.7 59.5 SSLT 44.6 66.9 Weld and Beam Web Available Strength, kips

55.7 49.6 55.7 55.7 49.6 55.7

83.6 74.4 83.6 83.6 74.4 83.6

66.9 59.5 66.9 66.9 59.5 66.9

100 89.3 100 100 89.3 100

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 44.6 44.6 44.6 39.7 44.6 44.6 39.7 44.6 44.6 44.6

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 66.9 66.9 66.9 59.5 66.9 66.9 59.5 66.9 66.9 66.9

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

kips

kips

ASD

LRFD

45.2 59.4 73.1 86.3

67.9 89.1 110 129

N = Threads included X = Threads excluded SC = Slip critical

Support Available Strength per Inch Thickness, kip/in. ASD

LRFD

458

STD/ SSLT

687

STD/ SSLT

429

OVS

644 OVS

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

*Limited to W10×12, 15, 17, 19, 22, 26, 30 Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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2/24/11

9:22 AM

Page 83

DESIGN TABLES

10–83

Table 10-4 (continued)

Bolted/Welded Shear End-Plate Connections

W12, 10, 8

1-in. Bolts 2 Rows L = 5 1/2 in.

Bolt and End-Plate Available Strength, kips Bolt Group

Group A

Thread Cond.

Hole Type

ASD 35.3 35.3 35.3 31.3 35.3 35.3 31.3 35.3 35.3 35.3

LRFD 53.0 53.0 53.0 46.9 53.0 53.0 46.9 53.0 53.0 53.0

ASD 42.4 42.4 42.4 37.5 42.4 42.4 37.5 42.4 42.4 42.4

LRFD 63.6 63.6 63.6 56.3 63.6 63.6 56.3 63.6 63.6 63.6

28.3 42.4 25.0 37.5 SSLT 28.3 42.4 STD 28.3 42.4 OVS SC Class B 25.0 37.5 SSLT 28.3 42.4 Weld and Beam Web Available Strength, kips

35.3 31.3 35.3 35.3 31.3 35.3

53.0 46.9 53.0 53.0 46.9 53.0

42.4 37.5 42.4 42.4 37.5 42.4

63.6 56.3 63.6 63.6 56.3 63.6

Rn / Ω

φ Rn

N X

STD STD

SC Class A

STD OVS

ASD 28.3 28.3 28.3 25.0 28.3 28.3 25.0 28.3 28.3 28.3

SSLT STD OVS SSLT STD STD

N X

70-ksi Weld Size, in.

3/8

LRFD 42.4 42.4 42.4 37.5 42.4 42.4 37.5 42.4 42.4 42.4

SC Class B

Group B

End-Plate Thickness, in. 5/16

1/4

STD OVS

SC Class A

Minimum Beam Web Thickness, in.

3/16

0.286 0.381 0.476 0.571

1/4 5/16 3/8

STD = Standard holes OVS = Oversized holes SSLT = Short-slotted holes transverse to direction of load

kips

kips

ASD

LRFD

28.5 37.1 45.2 52.9

42.8 55.7 67.9 79.4

N = Threads included X = Threads excluded SC = Slip critical

Support Available Strength per Inch Thickness, kip/in. ASD

LRFD

307

STD/ SSLT

461

STD/ SSLT

293

OVS

439 OVS

End-Plate

Beam

Fy = 36 ksi Fu = 58 ksi

Fy = 50 ksi Fu = 65 ksi

Note: Slip-critical bolt values assume no more than one filler has been provided or bolts have been added to distribute loads in the fillers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 10C:14th Ed.

10–84

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DESIGN OF SIMPLE SHEAR CONNECTIONS

UNSTIFFENED SEATED CONNECTIONS An unstiffened seated connection is made with a seat angle and a top angle, as illustrated in Figure 10-7. These angles may be bolted or welded to the supported beam as well as to the supporting member. While the seat angle is assumed to carry the entire end reaction of the supported beam, the top angle must be placed as shown or in the optional side location for satisfactory performance and stability (Roeder and Dailey, 1989). The top angle and its connections are not usually sized for any calculated strength requirement. A 1/4-in.-thick angle with a 4-in. vertical leg dimension will generally be adequate. It may be bolted with two bolts through each leg or welded with minimum size welds to either the supported or the supporting members. When the top angle is welded to the support and/or the supported beam, adequate flexibility must be provided in the connection. As illustrated in Figure 10-7(b), line welds are placed along the toe of each angle leg. Note that welding along the sides of the vertical angle leg must be avoided as it would inhibit the flexibility and, therefore, the necessary end rotation of the connection. The performance of such a connection would not be as intended for unstiffened seated connections.

(a) All-bolted

(b) All-welded Fig. 10-7. Unstiffened seated connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Page 85

DESIGN TABLE DISCUSSION (TABLES 10-5 AND 10-6)

10–85

Design Checks The available strength of an unstiffened seated connection is determined from the applicable limit states for bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). Additionally, the strength of the supported beam web must be checked for the limit states of web local yielding and web local crippling. In all cases, the available strength, φRn or Rn /Ω, must equal or exceed the required strength, Ru or Ra. The available strength for web local yielding and web local crippling, φRn or Rn /Ω, is determined per AISC Specification Sections J10.2 and J10.3, respectively, which is simplified using the constants in Table 9-4. For further information, see Carter et al. (1997).

Shop and Field Practices Unstiffened seated connections may be made to the webs and flanges of supporting columns. If adequate clearance exists, unstiffened seated connections may also be made to the webs of supporting girders. To provide for overrun in beam length, the nominal setback for the beam end is 1/2 in. To provide for underrun in beam length, this setback is assumed to be 3/4 in. for calculation purposes. The seat angle is preferably shop-attached to the support. Since the bottom flange typically establishes the plane of reference for seated connections, mill variation in beam depth may result in variation in the elevation of the top flange. Such variation is usually of no consequence with concrete slab and metal deck floors, but may be a concern when a grating or steel-plate floor is used. Unless special care is required, the usual mill tolerances for member depth of 1/8 in. to 1/4 in. are ignored. However, when the top angle is shopattached to the supported beam and field bolted to the support, mill variation in beam depth must be considered. Slotted holes, as illustrated in Figure 10-8(a), will accommodate both overrun and underrun in the beam depth and are the preferred method for economy and convenience to both the fabricator and erector. Alternatively, the angle could be shipped loose with clearance provided, as shown in Figure 10-8(b). When the top angle is to be fieldwelded to the support, no provision for mill variation in the beam depth is necessary. When the top angle is shop-attached to the support, an appropriate erection clearance is provided, as illustrated in Figure 10-8(c).

Bolted/Welded Unstiffened Seated Connections Tables 10-5 and 10-6 may be used in combination to design unstiffened seated connections that are welded to the supporting member and bolted to the supported beam, or bolted to the supporting member and welded to the supported beam.

DESIGN TABLE DISCUSSION (TABLES 10-5 AND 10-6) Table 10-5. All-Bolted Unstiffened Seated Connections Table 10-5 is a design aid for all-bolted unstiffened seats. Seat available strengths are tabulated, assuming a 4-in. outstanding leg, for angle material with Fy = 36 ksi and Fu = 58 ksi and beam material with Fy = 50 ksi and Fu = 65 ksi. All values are for comparison with the governing LRFD or ASD load combination. Tabulated seat available strengths consider the limit states of shear yielding and flexural yielding of the outstanding angle leg. The required bearing length, lb, req, is determined by AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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the designer as the larger value of lb required for the limit states of local yielding and crippling of the beam web. As noted in AISC Specification Section J10.2, lb, req must not be less than kdes. A nominal beam setback of 1/2 in. is assumed in these tables. However, this setback is increased to 3/4 in. for calculation purposes in determining the tabulated values to account for the possibility of underrun in beam length. Bolt available strengths are tabulated for the seat types illustrated in Figure 10-7(a) with 3 /4-in.-, 7/8-in.- and 1-in.-diameter Group A and Group B bolts. Vertical spacing of bolts and gages in seat angles may be arranged to suit conditions, provided the edge distance and spacing requirements in AISC Specification Section J3 are met. Where thick angles are used, larger entering and tightening clearances may be required in the outstanding angle leg. The suitability of angle sizes and thicknesses for the seat types illustrated in Figure 10-7(a) is also listed in Table 10-5.

(a) Vertical slots

(b) Loose angle with clearance as shown

(c) Shop-attached to column flange with clearance as shown

Fig. 10-8. Providing for variation in beam depth with seated connections.

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DESIGN TABLE DISCUSSION (TABLES 10-5 AND 10-6)

Table 10-6. All-Welded Unstiffened Seated Connections Table 10-6 is a design aid for all-welded unstiffened seats (exception: the beam is bolted to the seat). Seat available strengths are tabulated, assuming either a 31/2-in. or 4-in. outstanding leg (as indicated in the table), for angle material with Fy = 36 ksi and Fu = 58 ksi and beam material with Fy = 50 ksi and Fu = 65 ksi. Electrode strength is assumed to be 70 ksi. Tabulated seat available strengths consider the limit states of shear yielding and flexural yielding of the outstanding angle leg. The required bearing length, lb, req, is to be determined by the designer as the larger value of lb required for the limit states of local yielding and crippling of the beam web. As noted in AISC Specification Section J10.2, lb, req must not be less than kdes. A nominal beam setback of 1/2 in. is assumed in these tables. However, this setback is increased to 3/4 in. for calculation purposes in determining the tabulated values to account for the possibility of underrun in beam length. Tabulated weld available strengths are determined using the elastic method. The minimum and maximum angle thickness for each case is also tabulated. While these tabular values are based upon 70-ksi electrodes, they may be used for other electrodes, provided the tabular values are adjusted for the electrodes used (e.g., for 60-ksi electrodes, the tabular values are to be multiplied by 60/70 = 0.866, etc.) and the welds and base metal meet the required strength level provisions of AISC Specification Table J2.5. Should combinations of material thickness and weld size selected from Table 10-6 exceed the limits in AISC Specification Section J2.2, the weld size or material thickness should be increased as required. Table 8-4 is not applicable to the design of these welds in this type of connection. As can be seen from the following, reduction of the tabulated weld strength is not normally required when unstiffened seats line up on opposite sides of the supporting web. From Salmon et al. (2009), the available strength, φRn or Rn /Ω, of the welds to the support is LRFD

ASD

⎛ ⎜ 1.392 DL φRn = 2 ⎜ ⎜ 20.25e 2 ⎜ 1+ ⎝ L2

⎞ ⎟ ⎟ ⎟ ⎟ ⎠

(10-2a)

⎛ ⎜ φRn 0.928 DL = 2⎜ ⎜ Ω 20.25e 2 ⎜ 1+ ⎝ L2

⎞ ⎟ ⎟ ⎟ ⎟ ⎠

(10-2b)

where D = number of sixteenths-of-an-inch in the weld size L = vertical leg dimension of the seat angle, in. e = eccentricity of the beam end reaction with respect to the weld lines, in. The term in the denominator that accounts for the eccentricity, e, increases the weld size far beyond what is required for shear alone, but with seats on both sides of the supporting member web, the forces due to eccentricity react against each other and have no effect on the web. Furthermore, as illustrated in Figure 10-9, there are actually two shear planes per weld; one at each weld toe and heel for a total of four shear planes. Thus, for an 8-in.-long L7×4×1 seat angle supporting a LRFD required strength of 70 kips or an equivalent ASD required strength of 46.7 kips, the minimum support thickness is determined as follows:

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DESIGN OF SIMPLE SHEAR CONNECTIONS

LRFD

ASD

70 kips = 0.0855 in. 0.75 ( 0.6 ) ( 65 ksi) ( 7 in.) ( 4 planes )

2.0 ( 46.7 kips ) = 0.0855 in. 0.6 ( 65 ksi) ( 7 in.) ( 4 planes )

For the identical connection on both sides of the support, the minimum support thickness is less than 3/16 in. Thus, the supporting web thickness is generally not a concern.

(a) Plan view

(b) Elevation Fig. 10-9. Shear planes in column web for unstiffened seated connections.

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DESIGN TABLES

Table 10-5

Angle Fy = 36 ksi

3/8

1/2 9/16 5/8 11/16 3/4 13/16 7/8 15/16

1 11/16 11/8 13/16 11/4 15/16 13/8 17/16 11/2 15/8 13/4 17/8 2 21/8 21/4 23/8 21/2 25/8 23/4 27/8 3 31/8 31/4

3/ 4

7/ 8

1

L6

Outstanding Angle Leg Length Strength, kips Angle Length, in. 6 Angle Thickness, in.

Required Bearing Length lb , req , in.

Bolt Dia., in.

All-Bolted Unstiffened Seated Connections

5/8

1/2

Min. Angle Leg

3/4

1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

18.2 16.2 14.6 13.2 12.1 11.2 10.4 9.70 9.09 8.56 8.08 7.66 7.28 6.93 6.61 6.33 6.06 5.60 5.20 4.85 4.55 4.28 4.04 3.83 3.64 3.46 3.31 3.16 3.03 2.91 2.80

27.3 24.3 21.9 19.9 18.2 16.8 15.6 14.6 13.7 12.9 12.2 11.5 10.9 10.4 9.94 9.51 9.11 8.41 7.81 7.29 6.83 6.43 6.08 5.76 5.47 5.21 4.97 4.75 4.56 4.37 4.21

43.2 43.1 37.0 32.3 28.7 25.9 23.5 21.6 19.9 18.5 17.2 16.2 15.2 14.4 13.6 12.9 11.8 10.8 10.0 9.24 8.62 8.08 7.61 7.19 6.81 6.47 6.16 5.88 5.62 5.39

64.8 64.8 55.5 48.6 43.2 38.9 35.3 32.4 29.9 27.8 25.9 24.3 22.9 21.6 20.5 19.4 17.7 16.2 15.0 13.9 13.0 12.2 11.4 10.8 10.2 9.72 9.26 8.84 8.45 8.10

54.0 50.5 44.9 40.4 36.7 33.7 31.1 28.9 26.9 25.3 22.5 20.2 18.4 16.8 15.5 14.4 13.5 12.6 11.9 11.2 10.6 10.1 9.62 9.19

81.0 75.9 67.5 60.8 55.2 50.6 46.7 43.4 40.5 38.0 33.8 30.4 27.6 25.3 23.4 21.7 20.3 19.0 17.9 16.9 16.0 15.2 14.5 13.8

64.8 64.7 58.2 52.9 48.5 41.6 36.4 32.3 29.1 26.5 24.3 22.4 20.8 19.4 18.2 17.1 16.2 15.3 14.6

97.2 97.2 87.5 79.5 72.9 62.5 54.7 48.6 43.7 39.8 36.5 33.6 31.2 29.2 27.3 25.7 24.3 23.0 21.9

Bolt Available Strength, kips Connection Type from Figure 10-7(a) Bolt Thread B C A Group Cond. ASD LRFD ASD LRFD ASD LRFD Group A Group B Group A Group B Group A Group B

N X N X N X N X N X N X

ASD

LRFD

Ω = 2.00

φ = 0.75

ASD

LRFD

31/2

86.4 86.2 73.9 64.7 57.5 51.7 47.0 43.1 39.8 37.0 34.5 32.3

130 130 111 97.2 86.4 77.8 70.7 64.8 59.8 55.5 51.8 48.6

4

Available Angles Connection Type

Angle Size

4×3 23.9 35.8 47.7 71.6 71.6 107 4×31/2 A, D 30.1 45.1 60.1 90.2 90.2 135 4×4 30.1 45.1 60.1 90.2 90.2 135 6×4 37.1 55.7 74.3 111 111 167 B, E 7×4 32.5 48.7 64.9 97.4 97.4 146 8×4 40.9 61.3 81.7 123 123 184 8×4 40.9 61.3 81.7 123 123 184 Cb , F b 50.5 75.7 101 151 151 227 42.4 63.6 84.8 127 — — b Not suitable for use with 53.4 80.1 107 160 — — 1-in.-diameter bolts. 53.4 80.1 107 160 — — 65.9 98.9 132 198 — — For tabulated values above the heavy line, shear yielding of the angle leg controls the available strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

t, in. 3/8 3/8

– 1/2 – 1/2 3/8 – 3/4 3/8 – 3/4 3/8 – 3/4 1/2 – 1 1/2 – 1

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Table 10-5 (continued)

All-Bolted Unstiffened Seated Connections

L8

Outstanding Angle Leg Length Strength, kips Angle Length, in. 8 Angle Thickness, in.

Required Bearing Length lb , req , in.

3/8

1/2 9/16 5/8 11/16 3/4 13/16 7/8 15/16

1 11/16 11/8 13/16 11/4 15/16 13/8 17/16 11/2 15/8 13/4 17/8 2 21/8 21/4 23/8 21/2 25/8 23/4 27/8 3 31/8 31/4

Bolt Dia., in. 3/ 4

7/ 8

1

Angle Fy = 36 ksi

5/8

1/2

Min. Angle Leg

3/4

1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

24.3 21.6 19.4 17.6 16.2 14.9 13.9 12.9 12.1 11.4 10.8 10.2 9.70 9.24 8.82 8.44 8.08 7.46 6.93 6.47 6.06 5.71 5.39 5.11 4.85 4.62 4.41 4.22 4.04 3.88 3.73

36.5 32.4 29.2 26.5 24.3 22.4 20.8 19.4 18.2 17.2 16.2 15.3 14.6 13.9 13.3 12.7 12.2 11.2 10.4 9.72 9.11 8.58 8.10 7.67 7.29 6.94 6.63 6.34 6.08 5.83 5.61

57.6 57.5 49.3 43.1 38.3 34.5 31.4 28.7 26.5 24.6 23.0 21.6 20.3 19.2 18.2 17.2 15.7 14.4 13.3 12.3 11.5 10.8 10.1 9.58 9.08 8.62 8.21 7.84 7.50 7.19

86.4 86.4 74.1 64.8 57.6 51.8 47.1 43.2 39.9 37.0 34.6 32.4 30.5 28.8 27.3 25.9 23.6 21.6 19.9 18.5 17.3 16.2 15.2 14.4 13.6 13.0 12.3 11.8 11.3 10.8

72.0 67.4 59.9 53.9 49.0 44.9 41.5 38.5 35.9 33.7 29.9 26.9 24.5 22.5 20.7 19.2 18.0 16.8 15.9 15.0 14.2 13.5 12.8 12.2

108 101 90 81.0 73.6 67.5 62.3 57.9 54.0 50.6 45.0 40.5 36.8 33.8 31.2 28.9 27.0 25.3 23.8 22.5 21.3 20.3 19.3 18.4

86.4 86.2 77.6 70.5 64.7 55.4 48.5 43.1 38.8 35.3 32.3 29.8 27.7 25.9 24.3 22.8 21.6 20.4 19.4

130 130 117 106 97.2 83.3 72.9 64.8 58.3 53.0 48.6 44.9 41.7 38.9 36.5 34.3 32.4 30.7 29.2

Bolt Available Strength, kips Connection Type from Figure 10-7(a) Bolt Thread E F D Group Cond. ASD LRFD ASD LRFD ASD LRFD Group A Group B Group A Group B Group A Group B

N X N X N X N X N X N X

ASD

LRFD

Ω = 2.00

φ = 0.75

ASD

LRFD

31/2

115 98.5 86.2 76.6 69.0 62.7 57.5 53.1 49.3 46.0 43.1

173 148 130 115 104 94.3 86.4 79.8 74.1 69.1 64.8

4

Available Angles Connection Type

Angle Size

4×3 35.8 53.7 71.6 107 107 161 A, D 4×31/2 45.1 67.6 90.2 135 135 203 4×4 45.1 67.6 90.2 135 135 203 6×4 55.7 83.5 111 167 167 251 B, E 7×4 48.7 73.0 97.4 146 146 219 8×4 61.3 92.0 123 184 184 276 8×4 61.3 92.0 123 184 184 276 Cb , F b 75.7 114 151 227 227 341 63.6 95.4 127 191 — — b Not suitable for use with 80.1 120 160 240 — — 1-in.-diameter bolts. 80.1 120 160 240 — — 98.9 148 198 297 — — For tabulated values above the heavy line, shear yielding of the angle leg controls the available strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

t, in. 3/8 3/8

– 1/2 – 1/2 3/8 – 3/4 3/8 – 3/4 3/8 – 3/4 1/2 – 1 1/2 – 1

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DESIGN TABLES

Table 10-6

Angle Fy = 36 ksi

All-Welded Unstiffened Seated Connections

L6

Outstanding Angle Leg Length Strength, kips Angle Length, in. 6 Angle Thickness, in.

Required Bearing Length lb , req , in.

3/8

1/2 9/16 5/8 11/16 3/4 13/16 7/8 15/16

1 11/16 11/8 13/16 11/4 15/16 13/8 17/16 11/2 15/8 13/4 17/8 2 21/8 21/4 23/8 21/2 25/8 23/4 27/8 3 31/8 31/4

5/8

1/2

Min. Angle Leg

3/4

1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

18.2 16.2 14.6 13.2 12.1 11.2 10.4 9.70 9.09 8.56 8.08 7.66 7.28 6.93 6.61 6.33 6.06 5.60 5.20 4.85 4.55 4.28 4.04 3.83 3.64 3.46 3.31 3.16 3.03 2.91 2.80

27.3 24.3 21.9 19.9 18.2 16.8 15.6 14.6 13.7 12.9 12.2 11.5 10.9 10.4 9.94 9.51 9.11 8.41 7.81 7.29 6.83 6.43 6.08 5.76 5.47 5.21 4.97 4.75 4.56 4.37 4.21

43.1 37.0 32.3 28.7 25.9 23.5 21.6 19.9 18.5 17.2 16.2 15.2 14.4 13.6 12.9 11.8 10.8 9.95 9.24 8.62 8.08 7.61 7.19 6.81 6.47 6.16 5.88 5.62 5.39

64.8 55.5 48.6 43.2 38.9 35.3 32.4 29.9 27.8 25.9 24.3 22.9 21.6 20.5 19.4 17.7 16.2 15.0 13.9 13.0 12.2 11.4 10.8 10.2 9.72 9.26 8.84 8.45 8.10

54.0 50.5 44.9 40.4 36.7 33.7 31.1 28.9 26.9 25.3 22.5 20.2 18.4 16.8 15.5 14.4 13.5 12.6 11.9 11.2 10.6 10.1 9.62 9.19

81.0 75.9 67.5 60.8 55.2 50.6 46.7 43.4 40.5 38.0 33.8 30.4 27.6 25.3 23.4 21.7 20.3 19.0 17.9 16.9 16.0 15.2 14.5 13.8

64.7 58.2 52.9 48.5 41.6 36.4 32.3 29.1 26.5 24.3 22.4 20.8 19.4 18.2 17.1 16.2 15.3 14.6

97.2 87.5 79.5 72.9 62.5 54.7 48.6 43.7 39.8 36.5 33.6 31.2 29.2 27.3 25.7 24.3 23.0 21.9

ASD

LRFD

31/2

86.2 73.9 64.7 57.5 51.7 47.0 43.1 39.8 37.0 34.5 32.3

130 111 97.2 86.4 77.8 70.7 64.8 59.8 55.5 51.8 48.6

Weld (70 ksi) Available Strength, kips Seat Angle Size (long leg vertical)

70-ksi Weld Size, in.

5 × 31/2

4 × 31/2

Design

ASD

LRFD

ASD

LRFD

1/4 5/16 3/8 7/16 1/2 9/16 5/8 11/16

11.5 14.3 17.2 20.1 — — — —

17.2 21.5 25.8 30.1 — — — —

17.2 21.5 25.8 30.1 34.4 38.7 43.0 47.3

25.8 32.2 38.7 45.2 51.6 58.1 64.5 71.0

Available Angle Thickness, in. Minimum Maximum ASD LRFD Ω = 2.00

φ = 0.75

3/8

3/8

1/2

3/4

For tabulated values above the heavy line, shear yielding of the angle leg controls the available strength. — Indicates weld size exceeds that permitted for maximum angle thickness of 1/2 in.

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4

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-6 (continued)

All-Welded Unstiffened Seated Connections

L8

Angle Fy = 36 ksi

Outstanding Angle Leg Length Strength, kips Angle Length, in. 8 Angle Thickness, in.

Required Bearing Length lb , req , in.

3/8

1/2

9/16 5/8 11/16 3/4 13/16 7/8 15/16

1 11/16 11/8 13/16 11/4 15/16 13/8 17/16 11/2 15/8 13/4 17/8 2 21/8 21/4 23/8 21/2 25/8 23/4 27/8 3 31/8 31/4

5/8

1/2

Min. Angle Leg

3/4

1

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

24.3 21.6 19.4 17.6 16.2 14.9 13.9 12.9 12.1 11.4 10.8 10.2 9.70 9.24 8.82 8.44 8.08 7.46 6.93 6.47 6.06 5.71 5.39 5.11 4.85 4.62 4.41 4.22 4.04 3.88 3.73

36.5 32.4 29.2 26.5 24.3 22.4 20.8 19.4 18.2 17.2 16.2 15.3 14.6 13.9 13.3 12.7 12.2 11.2 10.4 9.72 9.11 8.58 8.10 7.67 7.29 6.94 6.63 6.34 6.08 5.83 5.61

57.5 49.3 43.1 38.3 34.5 31.4 28.7 26.5 24.6 23.0 21.6 20.3 19.2 18.2 17.2 15.7 14.4 13.3 12.3 11.5 10.8 10.1 9.58 9.08 8.62 8.21 7.84 7.50 7.19

86.4 74.1 64.8 57.6 51.8 47.1 43.2 39.9 37.0 34.6 32.4 30.5 28.8 27.3 25.9 23.6 21.6 19.9 18.5 17.3 16.2 15.2 14.4 13.6 13.0 12.3 11.8 11.3 10.8

72.0 67.4 59.9 53.9 49.0 44.9 41.5 38.5 35.9 33.7 29.9 26.9 24.5 22.5 20.7 19.2 18.0 16.8 15.9 15.0 14.2 13.5 12.8 12.2

108 101 90.0 81.0 73.6 67.5 62.3 57.9 54.0 50.6 45.0 40.5 36.8 33.8 31.2 28.9 27.0 25.3 23.8 22.5 21.3 20.3 19.3 18.4

86.2 77.6 70.5 64.7 55.4 48.5 43.1 38.8 35.3 32.3 29.8 27.7 25.9 24.3 22.8 21.6 20.4 19.4

130 117 106 97.2 83.3 72.9 64.8 58.3 53.0 48.6 44.9 41.7 38.9 36.5 34.3 32.4 30.7 29.2

ASD

LRFD

in.

31/2

115 98.5 86.2 76.6 69.0 62.7 57.5 53.1 49.3 46.0 43.1

173 148 130 115 104 94.3 86.4 79.8 74.1 69.1 64.8

4

Weld (70 ksi) Available Strength, kips 70-ksi Weld Size, in.

Seat Angle Size (long leg vertical) 7×4

6×4

8×4

Design

ASD

LRFD

ASD

LRFD

ASD

LRFD

1/4 5/16 3/8 7/16 1/2 9/16 5/8 11/16

21.8 27.3 32.7 38.2 43.6 49.1 54.5 60.0

32.7 40.9 49.1 57.2 65.4 73.6 81.8 90.0

28.5 35.6 42.7 49.8 57.0 64.1 71.2 78.3

42.7 53.4 64.1 74.7 85.4 96.1 107 117

35.6 44.5 53.4 62.3 71.2 80.1 89.0 97.9

53.4 66.7 80.1 93.4 107 120 133 147

Available Angle Thickness, in. Minimum Maximum ASD LRFD Ω = 2.00

φ = 0.75

3/8

3/8

1/2

3/4

3/4

1

For tabulated values above the heavy line, shear yielding of the angle leg controls the available strength.

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STIFFENED SEATED CONNECTIONS

STIFFENED SEATED CONNECTIONS A stiffened seated connection is made with a seat plate and stiffening element (e.g., a plate, structural tee, or pair of angles) and a top angle, as illustrated in Figure 10-10. The top angle may be bolted or welded to the supported beam as well as to the supporting member and the stiffening element may be bolted or welded to the support. The supported beam is bolted to the seat plate.

(a) All-bolted

(b) Bolted/welded Fig. 10-10. Stiffened seated connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF SIMPLE SHEAR CONNECTIONS

The stiffening element is assumed to carry the entire end reaction of the supported beam applied at a distance equal to 0.8W, where W is the dimension of the stiffening element parallel to the beam web. The top angle must be placed as shown or in the optional side location for satisfactory performance and stability (Roeder and Dailey, 1989). The top angle and its connections are not usually sized for any calculated strength requirement. A 1/4-in.thick angle with a 4-in. vertical leg dimension will generally be adequate. It may be fastened with two bolts through each leg or welded with minimum size welds to either the supported or the supporting members. When the top angle is welded to the support and/or the supported beam, adequate flexibility must be provided in the connection. As illustrated in Figure 10-10(b), line welds are placed along the toe of each angle leg. Note that welding along the sides of the vertical angle leg must be avoided as it would inhibit the flexibility and, therefore, the necessary end rotation of the connection. The performance of such a connection would not be as intended for simple shear connections.

Design Checks The available strength of a stiffened seated connection is determined from the applicable limit states for the bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). Additionally, the strength of the supported beam web must be checked for the limit states of web local yielding and web local crippling. In all cases, the available strength, φRn or Rn /Ω, must equal or exceed the required strength, Ru or Ra. The available strength for web local yielding and web local crippling, φRn or Rn /Ω, is determined per AISC Specification Sections J10.2 and J10.3, respectively, which is simplified using the constants in Table 9-4. When stiffened seated connections, such as the one shown in Figure 10-10(b), are made to one side of a supporting column web, the column web may also need to be investigated for resistance to punching shear. In lieu of a more detailed analysis, Sputo and Ellifritt (1991) showed that punching shear will not be critical if the design parameters following and those summarized graphically in Figure 10-10(b) are met. 1. This simplified approach is applicable to the following column sections: W14×43 to 730 W12×40 to 336 W10×33 to 112 W8×24 to 67 W6×20 and 25 W5×16 and 19 2. The supported beam must be bolted to the seat plate with high-strength bolts to account for the prying action caused by rotation of the connection. Welding the beam to the seat plate is not recommended because welds may lack the required strength and ductility. The centerline of the bolts should be located no more than the greater of W/2 or 25/ 8 in. from the column web face. 3. For seated connections where W = 8 in. or 9 in. and 31/2 in. < B ≤ W/2, or where W = 7 in. and 3 in. < B ≤ W/2 for a W14×43 column, refer to Sputo and Ellifritt (1991). 4. The top angle may be bolted or welded, but must have a minimum 1/4-in. thickness. 5. The seat plate should not be welded to the beam flange. See also Ellifritt and Sputo (1999).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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10–95

Shop and Field Practices The comments for unstiffened seated connections are equally applicable to stiffened seated connections.

DESIGN TABLE DISCUSSION (TABLES 10-7 AND 10-8) Table 10-7. All-Bolted Stiffened Seated Connections Table 10-7 is a design aid for all-bolted stiffened seats. Stiffener available strengths are tabulated for stiffener material with Fy = 36 ksi and Fu = 58 ksi and with Fy = 50 ksi and Fu = 65 ksi. Tabulated values consider the limit state of bearing on the stiffening material. The designer must independently check the available strength of the beam web based upon the limit states of web local yielding and web local crippling. A nominal beam setback of 1/2 in. is assumed in these tables. However, this setback is increased to 3/4 in. for calculation purposes in determining the tabulated values to account for the possibility of underrun in beam length. Bolt available strengths are tabulated for two vertical rows of from three to seven 3/4-in.-, 7 /8-in.- and 1-in.-diameter Group A and Group B high-strength bolts based upon the limit state of bolt shear. Vertical spacing of bolts and gages in seat angles may be arranged to suit conditions, provided the edge distance and spacing requirements in AISC Specification Section J3 are met.

Table 10-8. Bolted/Welded Stiffened Seated Connections Table 10-8 is a design aid for stiffened seated connections welded to the support and bolted to the supported beam. Electrode strength is assumed to be 70 ksi. Weld available strengths are tabulated using the elastic method. While these tabular values are based upon 70-ksi electrodes, they may be used for other electrodes, provided the tabular values are adjusted for the electrodes used (e.g., for 60-ksi electrodes, the tabular values are multiplied by 60/70 = 0.866, etc.) and the weld and base metal meet the required strength provisions of AISC Specification Table J2.5. The thickness of the horizontal seat plate or tee flange should not be less than 3/8 in. If the seat and stiffener are built up from separate plates, the stiffener should be finished to bear under the seat. The welds connecting the two plates should have a strength equal to or greater than the horizontal welds to the support under the seat plate. The designer must independently check the beam web for web local yielding and web local crippling. The nominal beam setback of 1/2 in. should be assumed to be 3/4 in. for calculation purposes to account for possible underrun in beam length. The stiffener thickness is conservatively determined as follows. The minimum stiffener plate thickness, t, for supported beams with unstiffened webs is the supported beam web thickness, tw, multiplied by the ratio of Fy of the beam material to Fy of the stiffener material (e.g., Fy,beam = 50 ksi, Fy, stiffener = 36 ksi, t = tw × 50/36 minimum). Additionally, the minimum stiffener plate thickness, t, should be at least 2w for stiffener material with

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Fy = 36 ksi or 1.5w for stiffener material with Fy = 50 ksi, where w is the weld size for 70-ksi electrodes. For 70-ksi electrodes, the minimum column web thickness is tmin =

3 . 09 D Fu

(9-2)

where D = weld size in sixteenths of an inch Fu = specified minimum tensile strength of the connecting element, ksi When welds line up on opposite sides of the support, the minimum thickness is the sum of the thicknesses required for each weld. In either case, when less than the minimum material thickness is present, the weld available strength must be reduced by the ratio of the thickness provided to the minimum thickness. As with unstiffened seated connections, the contribution of eccentricity to the required shear yielding strength is negligible. Should combinations of material thickness and weld size selected from Table 10-8 exceed the limits of AISC Specification Section J2.2, the weld size or material thickness must be increased.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN TABLES

Table 10-7

All-Bolted Stiffened Seated Connections Outstanding Angle Leg Available Strength, kipsa

Stiffener Material Stiffener Outstanding Leg, W , in.b

LRFD

ASD

LRFD

ASD

LRFD

5/8

55.7 83.5 65.8 98.7 86.1 66.8 100 79.0 118 103 89.1 134 105 158 138 111 167 132 197 172

129 155 207 258

77.3 92.8 124 155

116 139 186 232

91.4 110 146 183

137 165 219 274

120 143 191 239

179 215 287 359

3/4

134

310

186

278

219

329

287

430

1/2

LRFD

200

ASD

LRFD

158

237

ASD

5

ASD

3/8

ASD

Fy = 50 ksi 4

31/2

5 LRFD

5/16

Thickness of Stiffener Outstanding Legs, in.

Fy = 36 ksi 4

31/2

207

Use minimum 3/8-in.-thick seat plate wide enough to extend beyond outstanding legs of stiffener. a See AISC Specification Section J7. b Beam bearing length assumed 3/4 in. less for calculation purposes.

Bolt Diameter, in.

3/4

Bolt Thread Group Cond. Group A Group B

7/8

Group A Group B

1

Bolt Available Strength, kips Number of Bolts in One Vertical Row

Group A Group B

N X N X N X N X N X N X

3 ASD LRFD 71.6 107 90.2 135 90.2 135 111 167 97.4 146 123 184 123 184 151 227 127 191 160 240 160 240 198 297

ASD

LRFD

Ω = 2.00

φ = 0.75

R n 1.8Fy Apb = Ω 2.00

φRn = 0.75 (1.8Fy Apb )

4 ASD 95.5 120 120 149 130 163 163 202 170 214 214 264

5 LRFD 143 180 180 223 195 245 245 303 254 320 320 396

ASD 119 150 150 186 162 204 204 252 212 267 267 330

6 LRFD 179 225 225 278 243 307 307 379 318 400 400 495

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ASD 143 180 180 223 195 245 245 303 254 320 320 396

7 LRFD 215 271 271 334 292 368 368 454 382 480 480 593

ASD 167 210 210 260 227 286 286 353 297 374 374 462

LRFD 251 316 316 390 341 429 429 530 445 560 560 692

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Table 10-8

Bolted/Welded Stiffened Seated Connections Weld Available Strength, kips Width of Seat, W, in.

L , in. 1/4

4

5

70-ksi Weld Size, in.

70-ksi Weld Size, in.

5/16

3/8

7/16

5/16

3/8

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

6 7 8 9 10

22.7 29.9 37.8 46.1 54.9

34.0 44.9 56.7 69.2 82.3

28.4 37.4 47.2 57.7 68.6

42.5 56.1 70.8 86.5 103

34.0 44.9 56.7 69.2 82.3

51.1 67.3 85.0 104 123

39.7 52.4 66.1 80.7 96.0

59.6 78.6 99.2 121 144

23.5 31.2 39.8 49.1 59.0

35.2 46.9 59.8 73.7 88.5

28.2 37.5 47.8 59.0 70.8

42.2 56.2 71.7 88.5 106

11 12 13 14 15

63.9 73.1 82.5 92.1 102

95.8 110 124 138 152

79.8 91.4 103 115 127

120 137 155 173 191

95.8 110 124 138 152

144 165 186 207 229

112 128 144 161 178

168 192 217 242 267

69.4 80.2 91.3 103 114

104 120 137 154 171

83.3 96.2 110 123 137

125 144 164 185 206

16 17 18 19 20

111 121 131 140 150

167 181 196 211 225

139 151 163 175 188

209 227 245 263 281

167 181 196 211 225

250 272 294 316 338

195 212 229 246 263

292 318 343 369 394

126 138 150 162 174

189 207 225 243 261

151 165 180 194 209

227 248 270 291 313

21 22 23 24 25

160 169 179 189 198

240 254 269 283 297

200 212 224 236 248

300 318 336 354 372

240 254 269 283 297

359 381 403 425 446

280 296 313 330 347

419 445 470 495 520

186 198 210 222 235

279 297 315 334 352

223 238 252 267 281

335 357 378 400 422

26 27

208 217

312 326

260 272

390 408

312 326

468 489

364 380

546 571

247 259

370 388

296 310

444 466

Limitations for Connections to Column Webs B = 2 5/8 in. max W12×40, W14×43 for L ≥ 9 in. limit weld ≤ 1/4 in.

B = 2 5/8 in. max None

Notes: 1. Values shown assume 70-ksi electrodes. For 60-ksi electrodes, multiply tabular values by 0.857, or enter table with 1.17 times the required strength, Ru or Ra. For 80-ksi electrodes, multiply tabular values by 1.14, or enter table with 0.875 times the required strength. 2. Tabulated values are valid for stiffeners with minimum thickness of ⎛ Fy , beam ⎞ t min = ⎜ ⎟ tw ⎝ Fy , stiffener ⎠ but not less than 2w for stiffeners with Fy = 36 ksi nor 1.5w for stiffeners with Fy = 50 ksi. In the above, tw is the thickness of the unstiffened supported beam web and w is the nominal weld size. 3. Tabulated values may be limited by shear yielding of, or bearing on, the stiffener; refer to AISC Specification Sections J4.2 and J7, respectively.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ASD Ω = 2.00

LRFD φ = 0.75

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DESIGN TABLES

Table 10-8 (continued)

Bolted/Welded Stiffened Seated Connections Weld Available Strength, kips Width of Seat, W, in.

L , in.

5

6

70-ksi Weld Size, in. 7/16 1/2

70-ksi Weld Size, in. 3/8 7/16

5/16

1/2

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

6 7 8 9 10

32.8 43.7 55.8 68.8 82.6

49.3 65.6 83.7 103 124

37.5 50.0 63.8 78.6 94.4

56.3 75.0 95.6 118 142

19.9 26.7 34.3 42.5 51.4

29.9 40.1 51.4 63.8 77.2

23.9 32.0 41.1 51.1 61.7

35.9 48.1 61.7 76.6 92.6

27.9 37.4 48.0 59.6 72.0

41.9 56.1 72.0 89.3 108

31.9 42.7 54.8 68.1 82.3

47.8 64.1 82.2 102 123

11 12 13 14 15

97.2 112 128 144 160

146 168 192 216 240

111 128 146 164 183

167 192 219 246 274

60.9 70.8 81.2 91.9 103

91.3 106 122 138 154

73.1 85.0 97.4 110 123

110 127 146 165 185

85.3 99.2 114 129 144

128 149 170 193 216

97.4 113 130 147 165

146 170 195 220 247

16 17 18 19 20

176 193 210 227 244

265 290 315 340 365

202 221 240 259 278

302 331 360 388 417

114 126 137 149 161

171 188 206 223 241

137 151 165 179 193

205 226 247 268 289

160 176 192 208 225

240 264 288 313 337

183 201 219 238 257

274 301 329 357 386

21 22 23 24 25

260 277 294 311 328

391 416 442 467 492

298 317 336 356 375

446 476 505 534 563

173 185 197 209 221

259 277 295 313 331

207 222 236 250 265

311 332 354 376 397

242 258 275 292 309

362 388 413 438 464

276 295 315 334 353

414 443 472 501 530

26 27

345 362

518 543

395 414

592 621

233 245

349 368

280 294

419 441

326 343

489 515

373 392

559 588

B = 2 5/8 in. max None

Limitations for Connections to Column Webs B = 3 in. max None

Notes: 1. Values shown assume 70-ksi electrodes. For 60-ksi electrodes, multiply tabular values by 0.857, or enter table with 1.17 times the required strength, Ru or Ra. For 80-ksi electrodes, multiply tabular values by 1.14, or enter table with 0.875 times the required strength. 2. Tabulated values are valid for stiffeners with minimum thickness of ⎛ Fy , beam ⎞ t min = ⎜ ⎟ tw ⎝ Fy , stiffener ⎠ but not less than 2w for stiffeners with Fy = 36 ksi nor 1.5w for stiffeners with Fy = 50 ksi. In the above, tw is the thickness of the unstiffened supported beam web and w is the nominal weld size. 3. Tabulated values may be limited by shear yielding of, or bearing on, the stiffener; refer to AISC Specification Sections J4.2 and J7, respectively.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ASD Ω = 2.00

LRFD φ = 0.75

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Table 10-8 (continued)

Bolted/Welded Stiffened Seated Connections Weld Available Strength, kips Width of Seat, W, in.

L , in.

7

8

70-ksi Weld Size, in.

70-ksi Weld Size, in.

5/16

11 12 13 14 15

3/8

7/16

1/2

5/16

3/8

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

54.0 63.1 72.7 82.6 93.0

81.0 94.7 109 124 139

64.8 75.7 87.2 99.2 112

97.2 114 131 149 167

75.6 88.4 102 116 130

113 133 153 174 195

86.4 101 116 132 149

130 151 174 198 223

48.4 56.7 65.6 74.8 84.5

72.5 85.1 98.3 112 127

58.0 68.1 78.7 89.8 101

87.1 102 118 135 152

16 17 18 19 20

104 114 126 137 148

155 172 188 205 223

124 137 151 164 178

186 206 226 246 267

145 160 176 192 208

217 240 264 287 312

166 183 201 219 237

249 275 301 329 356

94.4 105 115 126 137

142 157 173 189 206

113 126 138 151 165

170 189 208 227 247

21 22 23 24 25

160 172 184 195 207

240 258 275 293 311

192 206 220 234 249

288 309 330 352 373

224 240 257 274 290

336 361 385 410 435

256 275 294 313 332

384 412 440 469 498

148 160 171 183 195

222 240 257 274 292

178 192 205 219 233

267 287 308 329 350

26 27 28 29 30

219 231 244 256 268

329 347 365 383 402

263 278 292 307 321

395 417 438 460 482

307 324 341 358 375

461 486 511 537 562

351 370 390 409 428

526 555 584 613 643

206 218 230 242 254

309 327 345 363 381

248 262 276 291 305

371 393 414 436 457

31 32

280 292

420 438

336 350

504 526

392 409

588 613

448 467

672 701

266 278

399 417

319 334

479 501

Limitations for Connections to Column Webs B = 31/2 in. max W14×43, limit B ≤ 3 in. See item 3 in preceding discussion “Design Checks”

B = 31/2 in. max See item 3 in preceding discussion “Design Checks”

Notes: 1. Values shown assume 70-ksi electrodes. For 60-ksi electrodes, multiply tabular values by 0.857, or enter table with 1.17 times the required strength, Ru or Ra. For 80-ksi electrodes, multiply tabular values by 1.14, or enter table with 0.875 times the required strength. 2. Tabulated values are valid for stiffeners with minimum thickness of ⎛ Fy , beam ⎞ t min = ⎜ ⎟ tw ⎝ Fy , stiffener ⎠ but not less than 2w for stiffeners with Fy = 36 ksi nor 1.5w for stiffeners with Fy = 50 ksi. In the above, tw is the thickness of the unstiffened supported beam web and w is the nominal weld size. 3. Tabulated values may be limited by shear yielding of, or bearing on, the stiffener; refer to AISC Specification Sections J4.2 and J7, respectively.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ASD Ω = 2.00

LRFD φ = 0.75

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DESIGN TABLES

Table 10-8 (continued)

Bolted/Welded Stiffened Seated Connections Weld Available Strength, kips Width of Seat, W, in.

L , in.

8

9

70-ksi Weld Size, in.

70-ksi Weld Size, in.

1/2

5/8

11 12 13 14 15

ASD 77.4 90.8 105 120 135

LRFD 116 136 157 180 203

16 17 18 19 20

151 168 184 202 219

227 251 277 303 329

21 22 23 24 25

237 256 274 292 311

26 27 28 29 30 31 32

ASD 96.7 113 131 150 169

5/16

LRFD 145 170 197 224 253

ASD 43.7 51.4 59.6 68.2 77.2

189 209 231 252 274

283 314 346 378 411

86.5 96.2 106 117 127

130 144 159 175 191

356 383 411 439 467

297 319 342 366 389

445 479 514 548 584

138 149 160 171 183

330 349 368 387 407

495 524 552 581 610

413 436 460 484 508

619 655 690 726 762

426 445

639 668

532 557

799 835

B = 31/2 in. max

LRFD 65.6 77.1 89.3 102 116

3/8

ASD 52.5 61.7 71.5 81.8 92.6

1/2

5/8

LRFD 78.7 92.5 107 123 139

ASD 69.9 82.2 95.3 109 123

LRFD 105 123 143 164 185

ASD 87.4 103 119 136 154

LRFD 131 154 179 204 232

104 115 127 140 152

156 173 191 210 229

138 154 170 186 203

208 231 255 280 305

173 192 212 233 254

260 289 319 350 381

207 223 240 257 274

165 178 192 205 219

248 268 288 308 329

220 238 256 274 292

331 357 384 411 438

276 297 320 342 365

413 446 480 513 548

194 206 217 229 241

291 308 326 344 362

233 247 261 275 289

349 370 391 412 434

310 329 348 367 386

466 494 522 550 578

388 411 435 458 482

582 617 652 687 723

253 265

379 397

304 318

455 477

405 424

607 636

506 530

759 795

Limitations for Connections to Column Webs B = 31/2 in. max

See item 3 in preceding discussion “Design Checks”

See item 3 in preceeding discussion “Design Checks”

Notes: 1. Values shown assume 70-ksi electrodes. For 60-ksi electrodes, multiply tabular values by 0.857, or enter table with 1.17 times the required strength, Ru or Ra. For 80-ksi electrodes, multiply tabular values by 1.14, or enter table with 0.875 times the required strength. 2. Tabulated values are valid for stiffeners with minimum thickness of ⎛ Fy , beam ⎞ t min = ⎜ ⎟ tw ⎝ Fy , stiffener ⎠ but not less than 2w for stiffeners with Fy = 36 ksi nor 1.5w for stiffeners with Fy = 50 ksi. In the above, tw is the thickness of the unstiffened supported beam web and w is the nominal weld size. 3. Tabulated values may be limited by shear yielding of, or bearing on, the stiffener; refer to AISC Specification Sections J4.2 and J7, respectively.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ASD Ω = 2.00

LRFD φ = 0.75

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SINGLE-PLATE CONNECTIONS A single-plate connection is made with a plate, as illustrated in Figure 10-11. The plate must be welded to the support on both sides of the plate and bolted to the supported member.

Design Checks The available strength of a single-plate connection is determined from the applicable limit states for the bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). In all cases, the available strength, φRn or Rn/Ω, must equal or exceed the required strength, Ru or Ra, respectively. Single-plate shear connections that satisfy the corresponding dimensional limitations can be designed using the simplified design procedure for the “conventional” configuration. Other single-plate shear connections can be designed using the procedure for the “extended” configuration, which is applicable to any configuration of single-plate shear connections, regardless of connection geometry. Both the conventional and extended configurations permit the use of Group A or Group B bolts. The procedure is valid for bolts that are snug-tightened, pretensioned or slip-critical. In both the conventional and extended configuration, the design recommendations are equally applicable to plate and beam web material with Fy = 36 ksi or 50 ksi. In both cases, the weld between the single plate and the support should be sized as (5/ 8)tp, which will develop the strength of either a 36-ksi or 50-ksi plate.

Conventional Configuration The following method may be used when the dimensional and other limitations upon which it is based are satisfied. See Muir and Thornton (2011).

Dimensional Limitations 1. Only a single vertical row of bolts is permitted. The number of bolts in the connection, n, must be between 2 and 12. 2. The distance from the bolt line to the weld line, a, must be equal to or less than 31/2 in.

Fig. 10-11. Single-plate connection. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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SINGLE-PLATE CONNECTIONS

Table 10-9

Design Values for Conventional Single-Plate Shear Connections n

Hole Type

e, in.

Maximum tp or tw, in.

SSLT

a /2

None

STD

a /2

d /2 + 1/16

SSLT

a /2

d /2 + 1/16

STD

a

d /2 − 1/16

2 to 5

6 to 12

3. Standard holes (STD) or short-slotted holes transverse to the direction of the supported member reaction (SSLT) are permitted to be used as noted in Table 10-9. 4. The vertical edge distance, Lev, must satisfy AISC Specification Table J3.4 requirements. The horizontal edge distance, Leh, should be greater than or equal to 2d, where d is the bolt diameter. 5. Either the plate thickness, tp, or the beam web thickness, tw, must satisfy the maximum thickness requirement given in Table 10-9.

Design Checks 1. The bolts and plate must be checked for required shear with an eccentricity equal to e, as given in Table 10-9. 2. Plate buckling will not control for the conventional configuration.

Extended Configuration The following method can be used when the dimensional and other limitations of the conventional method are not satisfied. This procedure can be used to determine the strength of single-plate shear connections with multiple vertical rows or in the extended configuration, as shown in Figure 10-12.

Stabilizer plates, if required

Fig. 10-12. Single-plate connection—Extended Configuration. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Dimensional Limitations 1. 2. 3. 4.

The number of bolts, n, is not limited. The distance from the weld line to the bolt line closest to the support, a, is not limited. The use of holes must satisfy AISC Specification Section J3.2 requirements. The horizontal and vertical edge distances, Leh and Lev, must satisfy AISC Specification Table J3.4 requirements.

Design Checks 1. Determine the bolt group required for bolt shear and bolt bearing with eccentricity e, where e is defined as the distance from the support to the centroid of the bolt group. Exception: Alternative considerations of the design eccentricity are acceptable when justified by rational analysis. For example, see Sherman and Ghorbanpoor (2002). 2. Determine the maximum plate thickness permitted such that the plate moment strength does not exceed the moment strength of the bolt group in shear, as follows: tmax =

6 M max Fy d 2

(10-3)

where Mmax =

Fnv ( Ab C ′ ) 0 . 90

(10−4)

Fnv = shear strength of an individual bolt from AISC Specification Table J3.2, ksi, 0 . 90 divided by a factor of 0.90 to remove the 10% reduction for uneven force distribution in end-loaded bolt groups (Kulak, 2002). The joint in question is not end-loaded. Ab = area of an individual bolt, in.2 C′ = coefficient from Part 7 for the moment-only case (instantaneous center of rotation at the centroid of the bolt group) Fy = specified minimum yield stress of plate, ksi d = depth of plate, in. The foregoing check is made at the nominal strength level, since the check is to ensure ductility, not strength. Exceptions: a. For a single vertical row of bolts only, the foregoing criterion need not be satisfied if either the beam web or the plate satisfies t ≤ db /2 + 1/16 and both satisfy Leh ≥ 2db. b. For a double vertical row of bolts only, the foregoing criterion need not be satisfied if both the beam web and the plate satisfy t ≤ db /2 + 1/16 and Leh ≥ 2db. 3. Check the plate for the limit states of shear yielding, shear rupture, and block shear rupture. 4. Check the plate for the limit states of shear yielding, shear buckling, and yielding due to flexure as follows: 2

2

⎛ Mr ⎞ ⎛ Vr ⎞ ⎜⎝ V ⎟⎠ + ⎜⎝ M ⎟⎠ ≤ 1.0 c c AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(10-5)

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SINGLE-PLATE CONNECTIONS

where Ag = gross cross-sectional area of the shear plate, in.2 Mc = φbMn (LRFD) or Mn/Ωb (ASD), kip-in. Mn = FyZpl, kip-in. Mr = Mu (LRFD) or Ma (ASD) = Vre, kip-in. Vc = φvVn (LRFD) or Vn/Ωv, (ASD), kips Vn = 0.6FyAg, kips Vr = Vu (LRFD) or Va (ASD), kips Zpl = plastic section modulus of the shear plate, in.3 e = distance from support to centroid of bolt group, in. φb = 0.90 φv = 1.00 Ωb = 1.67 Ωv = 1.50 5. Check the plate for the limit state of buckling using the double-coped beam procedure given in Part 9. 6. Ensure that the supported beam is braced at points of support. The design procedure for extended single-plate shear connections permits the column to be designed for an axial force without eccentricity. In some cases, economy may be gained by considering alternative design procedures that allow the transfer of some moment into the column. A percentage of the column’s weak-axis flexural strength, such as 5%, may be used as a mechanism to reduce the required eccentricity on the bolt group, provided that this moment is also considered in the design of the column. Larger percentages of the column’s weak-axis flexural strength may be justified at the roof level. Short-slotted holes can be used with the extended configuration with the bolts designed as bearing. Any slip of the bolts is a serviceability issue and does not affect the connection strength (Muir and Hewitt, 2009).

Requirement for Stabilizer Plates Lateral displacement of beams with extended single-plate connections is resisted by the torsional strength of the plate and beam in the connection region. Thornton and Fortney (2011) show that stabilizing plates are not required when the required shear strength, Ru or Ra, respectively, is equal to or less than the available strength to resist lateral displacement, φRn or Rn /Ω, where Rn = 1, 500 π φ = 0.90

Lt 3p a2

(10-6)

Ω = 1.67

where a = distance from the support to the first line of bolts, in. L = depth of plate, in. tp = thickness of plate, in. When the required shear strength exceeds the available strength to resist lateral displacement, stabilizer plates are required. These plates can be of nominal size and are connected AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF SIMPLE SHEAR CONNECTIONS

to the single plate and column flanges with minimum size fillet welds as shown in Figure 10-12. They need not be connected to the column web. The torsional strength of single-plate shear connections is the sum of two components: the lateral shear strength of the single plate and the lateral bending strength of the beam in the connection region. The first component always is present. The second component occurs as bending of the beam flange in contact with the slab, and should only be considered when a slab is present. Thornton and Fortney (2011) provide the sum of these components as follows: LRFD

ASD

⎡ R ⎤ Lt 2p M tu ≤ ⎢ φ v ( 0 . 6 Fyp ) − u ⎥ Lt p ⎦ 2 ⎣ +

(10-7a)

2 Ru2 ( t w + t p ) b f

(

⎛ 0 . 6 Fyp Ra ⎞ Lt 2p M ta ≤ ⎜ − Lt p ⎟⎠ 2 ⎝ Ωv +

)

φ b Fyb Ls t w2

(10-7b)

Ω b 2 Ra2 ( t w + t p ) b f Fyb Ls t w2

where Fyp = specified minimum yield stress of the plate, ksi t +t Mtu = Ru ⎛⎜ w p ⎞⎟ (LRFD) ⎝ 2 ⎠

(10-8a)

⎛ tw + t p ⎞ Mta = Ra ⎜ (ASD) ⎝ 2 ⎟⎠

(10-8b)

Ls Ra Ru bf tw φb φv Ωb Ωv

= span length of beam, in. = required strength (ASD), kips = required strength (LRFD), kips = width of beam flange, in. = thickness of beam web, in. = 0.90 = 1.00 = 1.67 = 1.50

Recommended Plate Length To provide for stability during erection, it is recommended that the minimum plate length be one-half the T-dimension of the beam to be supported. The maximum length of the plate must be compatible with the T-dimension of an uncoped beam and the remaining web depth, exclusive of fillets, of a coped beam. Note that the plate may encroach upon the fillet(s) as given in Figure 10-3.

Shop and Field Practices Conventional and extended single-plate connections may be made to the webs of supporting girders and to the flanges of supporting columns. Extended single-plate connections are suitable for connections to the webs of supporting columns when the bolt line is located a sufficient distance beyond the column flanges. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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10–107

With the plate shop-attached to the support, side erection of the beam is permitted. Play in the open holes usually compensates for mill variation in column flange supports and other field adjustments.

DESIGN TABLE DISCUSSION (TABLE 10-10) Table 10-10. Single-Plate Connections Table 10-10 is a design aid for single-plate connections welded to the support and bolted to the supported beam. Available strengths are tabulated in Table 10-10a for plate material with Fy = 36 ksi and Table 10-10b for plate material with Fy = 50 ksi. Tabulated bolt and plate available strengths consider the limit states of bolt shear, bolt bearing on the plate, shear yielding of the plate, shear rupture of the plate, block shear rupture of the plate, and weld shear. Values are tabulated for two through twelve rows of 3 /4-in.-, 7/8-in.-, 1-in.- and 11/8-in.-diameter Group A and Group B bolts at 3-in. spacing. For calculation purposes, plate edge distance, Lev, is in accordance with AISC Specification Section J3.10 and Table J3.4. End distance, Leh, is provided as 2 times the diameter of the bolt, to match tested connections. Weld sizes are tabulated equal to (5/8)tp. While the tabular values are based on a = 3 in., they may conservatively be used when the distance from the support to the bolt line, a, is between 21/2 in. and 3 in. The tabulated values are valid for laterally supported beams in steel and composite construction, all types of loading, snug-tightened or pretensioned bolts, and for supported and supporting members of all grades of steel.

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-10a

3

/ 4-in.diameter

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips

bolts n

Bolt Group

Thread Cond.

Hole Type

N

STD SSLT

Plate Fy = 36 ksi

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 12 (L = 351/2) Group B

Group A 11 (L = 321/2) Group B

Group A 10 (L = 291/2) Group B

Group A 9 (L = 261/2) Group B

X N X N X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

100 150 125 188

—

—

—

—

—

—

—

—

99.5 100 99.5 100 99.5 100 99.5 92.1 91.4 92.1 91.4 92.1 91.4 92.1 91.4 84.0 83.3 84.0 83.3 84.0 83.3 84.0 83.3 75.9 75.2 75.9 75.2 75.9 75.2 75.9 75.2

138 — 149 — 149 — 149 — 126 — 137 — 137 — 137 — 115 — 125 — 125 — 125 — 103 — 113 — 113 — 113

208 — 224 — 224 — 224 — 190 — 206 — 206 — 206 — 173 — 187 — 187 — 187 — 155 — 169 — 169 — 169

138 — 174 — 174 — 174 — 126 — 159 — 159 — 160 — 115 — 145 — 145 — 146 — 103 — 130 — 130 — 132

208 — 261 — 261 — 261 — 190 — 239 — 239 — 240 — 173 — 217 — 217 — 219 — 155 — 194 — 194 — 197

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

149 150 149 150 149 150 149 138 137 138 137 138 137 138 137 126 125 126 125 126 125 126 125 114 113 114 113 114 113 114 113

124 125 124 125 124 125 124 115 114 115 114 115 114 115 114 105 104 105 104 105 104 105 104 94.8 94.0 94.8 94.0 94.8 94.0 94.8 94.0

187 188 187 188 187 188 187 173 171 173 171 173 171 173 171 157 156 157 156 157 156 157 156 142 141 142 141 142 141 142 141

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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3/8

N = Threads included X = Threads excluded

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DESIGN TABLES

Table 10-10a (continued) Plate Fy = 36 ksi

n

Bolt Group

3

/ 4-in.diameter

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips Thread Cond.

Hole Type

N

STD SSLT

bolts

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 8 (L = 231/2) Group B

Group A 7 (L = 201/2) Group B

Group A 6 (L = 171/2) Group B

Group A 5 (L = 141/2) Group B

X N X N X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

67.8 102 84.7 127 67.1 67.8 67.1 67.8 67.1 67.8 67.1 59.7 59.0 59.7 59.0 59.7 59.0 59.7 59.0 51.6 50.9 51.6 50.9 51.6 50.9 51.6 50.9 43.5 42.8 43.5 42.8 43.5 42.8 43.5 42.8

101 102 101 102 101 102 101 89.5 88.5 89.5 88.5 89.5 88.5 89.5 88.5 77.4 76.3 77.4 76.3 77.4 76.3 77.4 76.3 65.2 64.2 65.2 64.2 65.2 64.2 65.2 64.2

83.9 84.7 83.9 84.7 83.9 84.7 83.9 72.1 73.7 74.6 73.7 74.6 73.7 74.6 73.7 59.3 63.6 64.5 63.6 64.5 63.6 64.5 63.6 54.1 53.5 54.3 53.5 54.3 53.5 54.3 53.5

126 127 126 127 126 127 126 108 111 112 111 112 111 112 111 89.1 95.4 96.7 95.4 96.7 95.4 96.7 95.4 81.3 80.2 81.5 80.2 81.5 80.2 81.5 80.2

—

—

—

—

—

—

—

—

90.8 — 101 — 101 — 101 — 78.7 — 88.5 — 88.5 — 88.5 — 66.5 — 76.3 — 76.3 — 76.3 54.1 54.1 65.2 64.2 65.2 64.2 65.2 64.2

137 — 151 — 151 — 151 — 118 — 133 — 133 — 133 — 100 — 115 — 115 — 115 81.3 81.3 97.8 96.3 97.8 96.3 97.8 96.3

90.8 — 114 — 114 — 117 — 78.7 — 99.2 — 99.2 — 103 — 66.5 — 83.8 — 83.8 — 89.1 54.1 54.1 68.1 68.1 68.1 68.1 76.1 74.9

137 — 172 — 172 — 176 — 118 — 149 — 149 — 155 — 100 — 126 — 126 — 134 81.3 81.3 102 102 102 102 114 112

— — — — — — — — — — — — — — — — — — — — — — — — 54.1 — 68.1 — 68.1 — 84.5

— — — — — — — — — — — — — — — — — — — — — — — — 81.3 — 102 — 102 — 126

— — — — — — — — — — — — — — — — — — — — — — — — 54.1 — 68.1 — 68.1 — 84.5

— — — — — — — — — — — — — — — — — — — — — — — — 81.3 — 102 — 102 — 126

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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3/8

N = Threads included X = Threads excluded

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-10a (continued)

3

/ 4-in.diameter

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips

bolts n

Bolt Group

Thread Cond.

Hole Type

N

STD SSLT

Plate Fy = 36 ksi

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 4 (L = 111/2) Group B

Group A 3 (L = 81/2) Group B

Group A 2 (L = 51/2) Group B

X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

34.8 52.2 41.5 62.5 41.5 62.5 41.5 62.5 — 34.7 34.8 34.7 34.8 34.7 34.8 34.7 25.6 25.6 25.6 25.6 25.6 25.6 25.6 25.6 16.3 16.3 16.3 16.3 16.3 16.3 16.3 16.3

52.0 52.2 52.0 52.2 52.0 52.2 52.0 38.3 38.3 38.3 38.3 38.3 38.3 38.3 38.3 24.5 24.5 24.5 24.5 24.5 24.5 24.5 24.5

41.5 43.5 43.4 43.5 43.4 43.5 43.4 28.8 28.8 31.9 31.9 31.9 31.9 31.9 31.9 16.5 16.5 20.4 20.4 20.4 20.4 20.4 20.4

62.5 65.3 65.1 65.3 65.1 65.3 65.1 43.4 43.4 47.9 47.9 47.9 47.9 47.9 47.9 24.8 24.8 30.6 30.6 30.6 30.6 30.6 30.6

41.5 52.2 52.0 52.2 52.0 52.2 52.0 28.8 28.8 36.3 36.3 36.3 36.3 38.3 38.3 16.5 16.5 20.8 20.8 20.8 20.8 24.5 24.5

62.5 78.3 78.1 78.3 78.1 78.3 78.1 43.4 43.4 54.5 54.5 54.5 54.5 57.5 57.5 24.8 24.8 31.2 31.2 31.2 31.2 36.7 36.7

41.5 52.4 52.4 52.4 52.4 60.9 60.7 28.8 28.8 36.3 36.3 36.3 36.3 44.7 44.7 16.5 16.5 20.8 20.8 20.8 20.8 25.8 25.8

62.5 78.5 78.5 78.5 78.5 91.4 91.1 43.4 43.4 54.5 54.5 54.5 54.5 67.1 67.1 24.8 24.8 31.2 31.2 31.2 31.2 38.5 38.5

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

41.5 — 52.4 — 52.4 — 64.9 — 28.8 — 36.3 — 36.3 — 45.1 — 16.5 — 20.8 — 20.8 — 25.8

—

—

—

62.5 — 78.5 — 78.5 — 97.0 — 43.4 — 54.5 — 54.5 — 67.3 — 24.8 — 31.2 — 31.2 — 38.5

41.5 — 52.4 — 52.4 — 64.9 — 28.8 — 36.3 — 36.3 — 45.1 — 16.5 — 20.8 — 20.8 — 25.8

62.5 — 78.5 — 78.5 — 97.0 — 43.4 — 54.5 — 54.5 — 67.3 — 24.8 — 31.2 — 31.2 — 38.5

5/16

3/8

N = Threads included X = Threads excluded

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DESIGN TABLES

Table 10-10a (continued) Plate Fy = 36 ksi

n

Bolt Group

7

/ 8-in.diameter

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips Thread Cond.

Hole Type

N

STD SSLT

bolts

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 12 (L = 36) Group B

X N X

Group A 11 (L = 33) Group B

Group A 10 (L = 30) Group B

Group A 9 (L = 27) Group B

N X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

102 153 128 192 153 230

—

—

—

—

—

—

102 102 102 102 102 102 102 94.1 93.4 94.1 93.4 94.1 93.4 94.1 93.4 86.0 85.3 86.0 85.3 86.0 85.3 86.0 85.3 77.9 77.2 77.9 77.2 77.9 77.2 77.9 77.2

178 — 178 — 178 — 178 — 164 — 164 — 164 — 164 — 149 — 149 — 149 — 149 — 135 — 135 — 135 — 135

267 — 267 — 267 — 267 — 245 — 245 — 245 — 245 — 224 — 224 — 224 — 224 — 203 — 203 — 203 — 203

188 — 203 — 203 — 203 — 172 — 187 — 187 — 187 — 156 — 171 — 171 — 171 — 140 — 154 — 154 — 154

282 — 305 — 305 — 305 — 258 — 280 — 280 — 280 — 234 — 256 — 256 — 256 — 210 — 232 — 232 — 232

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

152 153 152 153 152 153 152 141 140 141 140 141 140 141 140 129 128 129 128 129 128 129 128 117 116 117 116 117 116 117 116

127 128 127 128 127 128 127 118 117 118 117 118 117 118 117 108 107 108 107 108 107 108 107 97.4 96.5 97.4 96.5 97.4 96.5 97.4 96.5

190 192 190 192 190 192 190 176 175 176 175 176 175 176 175 161 160 161 160 161 160 161 160 146 145 146 145 146 145 146 145

152 153 152 153 152 153 152 141 140 141 140 141 140 141 140 129 128 129 128 129 128 129 128 117 116 117 116 117 116 117 116

228 230 228 230 228 230 228 212 210 212 210 212 210 212 210 194 192 194 192 194 192 194 192 175 174 175 174 175 174 175 174

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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3/8

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-10a (continued)

7

/ 8-in.diameter

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips

bolts n

Bolt Group

Thread Cond.

Hole Type

N

STD SSLT

Plate Fy = 36 ksi

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 8 (L = 24) Group B

Group A 7 (L = 21) Group B

Group A 6 (L = 18) Group B

Group A 5 (L = 15) Group B

X N X N X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

69.6 104 87.0 131 104 157 69.1 69.6 69.1 69.6 69.1 69.6 69.1 60.9 60.9 60.9 60.9 60.9 60.9 60.9 60.9 52.2 52.2 52.2 52.2 52.2 52.2 52.2 52.2 43.5 43.5 43.5 43.5 43.5 43.5 43.5 43.5

104 104 104 104 104 104 104 91.4 91.4 91.4 91.4 91.4 91.4 91.4 91.4 78.3 78.3 78.3 78.3 78.3 78.3 78.3 78.3 65.3 65.3 65.3 65.3 65.3 65.3 65.3 65.3

86.4 87.0 86.4 87.0 86.4 87.0 86.4 76.1 76.1 76.1 76.1 76.1 76.1 76.1 76.1 65.3 65.3 65.3 65.3 65.3 65.3 65.3 65.3 54.4 54.4 54.4 54.4 54.4 54.4 54.4 54.4

130 131 130 131 130 131 130 114 114 114 114 114 114 114 114 97.9 97.9 97.9 97.9 97.9 97.9 97.9 97.9 81.6 81.6 81.6 81.6 81.6 81.6 81.6 81.6

104 104 104 104 104 104 104 91.4 91.4 91.4 91.4 91.4 91.4 91.4 91.4 78.3 78.3 78.3 78.3 78.3 78.3 78.3 78.3 65.3 65.3 65.3 65.3 65.3 65.3 65.3 65.3

156 157 156 157 156 157 156 137 137 137 137 137 137 137 137 117 117 117 117 117 117 117 117 97.9 97.9 97.9 97.9 97.9 97.9 97.9 97.9

—

—

—

—

—

—

121 — 121 — 121 — 121 — 107 — 107 — 107 — 107 — 90.5 — 91.4 — 91.4 — 91.4 73.6 73.6 76.1 76.1 76.1 76.1 76.1 76.1

181 — 181 — 181 — 181 — 160 — 160 — 160 — 160 — 136 — 137 — 137 — 137 110 110 114 114 114 114 114 114

124 — 138 — 138 — 138 — 107 — 122 — 122 — 122 — 90.5 — 104 — 104 — 104 73.6 73.6 87.0 87.0 87.0 87.0 87.0 87.0

185 — 207 — 207 — 207 — 161 — 183 — 183 — 183 — 136 — 157 — 157 — 157 110 110 131 131 131 131 131 131

— — — — — — — — — — — — — — — — — — — — — — — — 73.6 — 92.7 — 92.7 — 97.9

— — — — — — — — — — — — — — — — — — — — — — — — 110 — 139 — 139 — 147

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5/16

3/8

N = Threads included X = hreads excluded

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DESIGN TABLES

Table 10-10a (continued) Plate Fy = 36 ksi

n

Bolt Group

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips Thread Cond.

Hole Type

N

STD SSLT

7

/ 8-in.diameter bolts

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 4 (L = 12) Group B

Group A 3 (L = 9) Group B

Group A 2 (L = 6) Group B

X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

34.8 52.2 43.5 65.3 52.2 78.3 56.5 84.8 56.5 84.8 — 34.8 34.8 34.8 34.8 34.8 34.8 34.8 26.1 26.1 26.1 26.1 26.1 26.1 26.1 26.1 17.4 17.4 17.4 17.4 17.4 17.4 17.4 17.4

52.2 52.2 52.2 52.2 52.2 52.2 52.2 39.2 39.2 39.2 39.2 39.2 39.2 39.2 39.2 26.1 26.1 26.1 26.1 26.1 26.1 26.1 26.1

43.5 43.5 43.5 43.5 43.5 43.5 43.5 32.6 32.6 32.6 32.6 32.6 32.6 32.6 32.6 21.8 21.8 21.8 21.8 21.8 21.8 21.8 21.8

65.3 65.3 65.3 65.3 65.3 65.3 65.3 48.9 48.9 48.9 48.9 48.9 48.9 48.9 48.9 32.6 32.6 32.6 32.6 32.6 32.6 32.6 32.6

52.2 52.2 52.2 52.2 52.2 52.2 52.2 39.2 39.2 39.2 39.2 39.2 39.2 39.2 39.2 22.4 22.4 26.1 26.1 26.1 26.1 26.1 26.1

78.3 78.3 78.3 78.3 78.3 78.3 78.3 58.7 58.7 58.7 58.7 58.7 58.7 58.7 58.7 33.7 33.7 39.2 39.2 39.2 39.2 39.2 39.2

56.5 60.9 60.9 60.9 60.9 60.9 60.9 39.2 39.2 45.7 45.7 45.7 45.7 45.7 45.7 22.4 22.4 28.3 28.3 28.3 28.3 30.5 30.5

84.8 91.4 91.4 91.4 91.4 91.4 91.4 58.9 58.9 68.5 68.5 68.5 68.5 68.5 68.5 33.7 33.7 42.5 42.5 42.5 42.5 45.7 45.7

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

56.5 69.6 69.6 69.6 69.6 69.6 69.6 39.2 39.2 49.4 49.4 49.4 49.4 52.2 52.2 22.4 22.4 28.3 28.3 28.3 28.3 34.8 34.8

84.8 104 104 104 104 104 104 58.9 58.9 74.4 74.4 74.4 74.4 78.3 78.3 33.7 33.7 42.5 42.5 42.5 42.5 52.2 52.2

5/16

—

56.5 — 71.2 — 71.2 — 78.3 — 39.2 — 49.4 — 49.4 — 58.7 — 22.4 — 28.3 — 28.3 — 34.9

84.8 — 107 — 107 — 117 — 58.9 — 74.4 — 74.4 — 88.1 — 33.7 — 42.5 — 42.5 — 52.5

3/8

N = Threads included X = Threads excluded

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-10a

1

-in.-

Single-Plate Connections

diameter bolts

n

Bolt Group

Bolt, Weld and Single-Plate Available Strengths, kips Thread Cond.

Hole Type

N

STD SSLT

Plate Fy = 36 ksi

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 12 (L = 361/2) Group B

Group A 11 (L = 331/2) Group B

Group A 10 (L = 301/2) Group B

Group A 9 (L = 271/2) Group B

X N X N X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

100 150 125 188 150 225 175 263

—

—

—

—

100 100 100 100 100 100 100 91.9 91.9 91.9 91.9 91.9 91.9 91.9 91.9 83.7 83.7 83.7 83.7 83.7 83.7 83.7 83.7 75.6 75.6 75.6 75.6 75.6 75.6 75.6 75.6

200 — 200 — 200 — 200 — 184 — 184 — 184 — 184 — 167 — 167 — 167 — 167 — 151 — 151 — 151 — 151

300 — 300 — 300 — 300 — 276 — 276 — 276 — 276 — 251 — 251 — 251 — 251 — 227 — 227 — 227 — 227

225 — 225 — 225 — 225 — 207 — 207 — 207 — 207 — 188 — 188 — 188 — 188 — 170 — 170 — 170 — 170

338 — 338 — 338 — 338 — 310 — 310 — 310 — 310 — 283 — 283 — 283 — 283 — 255 — 255 — 255 — 255

150 150 150 150 150 150 150 138 138 138 138 138 138 138 138 126 126 126 126 126 126 126 126 113 113 113 113 113 113 113 113

125 125 125 125 125 125 125 115 115 115 115 115 115 115 115 105 105 105 105 105 105 105 105 94.5 94.5 94.5 94.5 94.5 94.5 94.5 94.5

188 188 188 188 188 188 188 172 172 172 172 172 172 172 172 157 157 157 157 157 157 157 157 142 142 142 142 142 142 142 142

150 150 150 150 150 150 150 138 138 138 138 138 138 138 138 126 126 126 126 126 126 126 126 113 113 113 113 113 113 113 113

225 225 225 225 225 225 225 207 207 207 207 207 207 207 207 188 188 188 188 188 188 188 188 170 170 170 170 170 170 170 170

175 175 175 175 175 175 175 161 161 161 161 161 161 161 161 147 147 147 147 147 147 147 147 132 132 132 132 132 132 132 132

263 263 263 263 263 263 263 241 241 241 241 241 241 241 241 220 220 220 220 220 220 220 220 198 198 198 198 198 198 198 198

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5/16

3/8

N = Threads included X = Threads excluded

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DESIGN TABLES

Table 10-10a (continued) Plate Fy = 36 ksi

n

Bolt Group

-in.1 diameter

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips Thread Cond.

Hole Type

bolts

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 8 (L = 241/2) Group B

Group A 7 (L = 211/2) Group B

Group A 6 (L = 181/2) Group B

5 (L = 151/2)

4 (L = 121/2)

N X N X N X N X N X N X

Group B

N X N X

Group A

N X

Group B

N X

Group A

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD/ SSLT

STD/ SSLT

67.4 101 84.3 126 101 152 118 177 67.4 67.4 67.4 67.4 67.4 67.4 67.4 59.3 59.3 59.3 59.3 59.3 59.3 59.3 59.3 51.1 51.1 51.1 51.1 51.1 51.1 51.1 51.1 43.0 43.0 43.0 43.0 34.8 34.8 34.8 34.8

101 101 101 101 101 101 101 88.9 88.9 88.9 88.9 88.9 88.9 88.9 88.9 76.7 76.7 76.7 76.7 76.7 76.7 76.7 76.7 64.4 64.4 64.4 64.4 52.2 52.2 52.2 52.2

84.3 84.3 84.3 84.3 84.3 84.3 84.3 74.1 74.1 74.1 74.1 74.1 74.1 74.1 74.1 63.9 63.9 63.9 63.9 63.9 63.9 63.9 63.9 53.7 53.7 53.7 53.7 43.5 43.5 43.5 43.5

126 126 126 126 126 126 126 111 111 111 111 111 111 111 111 95.8 95.8 95.8 95.8 95.8 95.8 95.8 95.8 80.5 80.5 80.5 80.5 65.3 65.3 65.3 65.3

101 101 101 101 101 101 101 88.9 88.9 88.9 88.9 88.9 88.9 88.9 88.9 76.7 76.7 76.7 76.7 76.7 76.7 76.7 76.7 64.4 64.4 64.4 64.4 52.2 52.2 52.2 52.2

152 152 152 152 152 152 152 133 133 133 133 133 133 133 133 115 115 115 115 115 115 115 115 96.7 96.7 96.7 96.7 78.3 78.3 78.3 78.3

118 118 118 118 118 118 118 104 104 104 104 104 104 104 104 89.4 89.4 89.4 89.4 89.4 89.4 89.4 89.4 75.2 75.2 75.2 75.2 60.9 60.9 60.9 60.9

177 177 177 177 177 177 177 156 156 156 156 156 156 156 156 134 134 134 134 134 134 134 134 113 113 113 113 91.4 91.4 91.4 91.4

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load STD/SSLT = Standard holes or short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9. Tabulated values are grouped when available strength is independent of hole type.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

—

—

—

—

135 — 135 — 135 — 135 — 119 — 119 — 119 — 119 — 102 — 102 — 102 — 102 85.9 85.9 85.9 85.9 69.6 69.6 69.6 69.6

202 — 202 — 202 — 202 — 178 — 178 — 178 — 178 — 153 — 153 — 153 — 153 129 129 129 129 104 104 104 104

152 — 152 — 152 — 152 — 133 — 133 — 133 — 133 — 115 — 115 — 115 — 115 96.3 96.7 96.7 96.7 74.0 78.3 78.3 78.3

228 — 228 — 228 — 228 — 200 — 200 — 200 — 200 — 173 — 173 — 173 — 173 144 145 145 145 111 117 117 117

5/16

3/8

N = Threads included X = Threads excluded

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-10a (continued)

1

-in.-

Single-Plate Connections

diameter bolts

n

Bolt, Weld and Single-Plate Available Strengths, kips

Bolt Group

Thread Cond.

Group A

N X N X N X N X

Hole Type

Plate Fy = 36 ksi

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

3 (L = 91/2)

2 (L = 61/2)

Group B Group A Group B

26.6 40.0 33.3 50.0 40.0 59.9 46.6 69.9 51.4 77.0 51.4 77.0 STD/ SSLT

STD/ SSLT

26.6 26.6 26.6 18.5 18.5 18.5 18.5

40.0 40.0 40.0 27.7 27.7 27.7 27.7

33.3 33.3 33.3 23.1 23.1 23.1 23.1

50.0 50.0 50.0 34.7 34.7 34.7 34.7

40.0 40.0 40.0 27.7 27.7 27.7 27.7

59.9 59.9 59.9 41.6 41.6 41.6 41.6

46.6 46.6 46.6 29.4 32.4 32.4 32.4

69.9 69.9 69.9 44.0 48.5 48.5 48.5

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load STD/SSLT = Standard holes or short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9. Tabulated values are grouped when available strength is independent of hole type.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

53.3 53.3 53.3 29.4 37.0 37.0 37.0

79.9 79.9 79.9 44.0 55.4 55.4 55.5

5/16

59.9 59.9 59.9 29.4 37.0 37.0 41.6

89.9 89.9 89.9 44.0 55.4 55.4 62.4

3/8

N = Threads included X = Threads excluded

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DESIGN TABLES

Table 10-10a (continued) Plate Fy = 36 ksi

n

Bolt Group

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips Thread Cond.

Hole Type

N

STD SSLT

1 -in.1diameter /8 bolts

Plate Thickness, in. 5/16

3/8

7/16

1/2

9/16

5/8

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 12 (L = 37) Group B

X N X

Group A 11 (L = 34) Group B

Group A 10 (L = 31) Group B

Group A 9 (L = 28) Group B

N X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

120 179 144 215 167 251 191 287

—

—

—

—

120 120 120 120 120 120 120 110 110 110 110 110 110 110 110 101 101 101 101 101 101 101 101 91.1 91.1 91.1 91.1 91.1 91.1 91.1 91.1

215 — 215 — 215 — 215 — 198 — 198 — 198 — 198 — 181 — 181 — 181 — 181 — 164 — 164 — 164 — 164

323 — 323 — 323 — 323 — 297 — 297 — 297 — 297 — 272 — 272 — 272 — 272 — 246 — 246 — 246 — 246

239 — 239 — 239 — 239 — 220 — 220 — 220 — 220 — 201 — 201 — 201 — 201 — 182 — 182 — 182 — 182

359 — 359 — 359 — 359 — 330 — 330 — 330 — 330 — 302 — 302 — 302 — 302 — 273 — 273 — 273 — 273

179 179 179 179 179 179 179 165 165 165 165 165 165 165 165 151 151 151 151 151 151 151 151 137 137 137 137 137 137 137 137

144 144 144 144 144 144 144 132 132 132 132 132 132 132 132 121 121 121 121 121 121 121 121 109 109 109 109 109 109 109 109

215 215 215 215 215 215 215 198 198 198 198 198 198 198 198 181 181 181 181 181 181 181 181 164 164 164 164 164 164 164 164

167 167 167 167 167 167 167 154 154 154 154 154 154 154 154 141 141 141 141 141 141 141 141 128 128 128 128 128 128 128 128

251 251 251 251 251 251 251 231 231 231 231 231 231 231 231 211 211 211 211 211 211 211 211 191 191 191 191 191 191 191 191

191 191 191 191 191 191 191 176 176 176 176 176 176 176 176 161 161 161 161 161 161 161 161 146 146 146 146 146 146 146 146

287 287 287 287 287 287 287 264 264 264 264 264 264 264 264 241 241 241 241 241 241 241 241 219 219 219 219 219 219 219 219

1/4 1/4 5/16 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3/8

7/16

N = Threads included X = Threads excluded

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-10a (continued)

1

1diameter /8-in.-

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips

bolts n

Bolt Group

Thread Cond.

Hole Type

N

STD SSLT

Plate Fy = 36 ksi

Plate Thickness, in. 5/16

3/8

7/16

1/2

9/16

5/8

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 8 (L = 25) Group B

Group A 7 (L = 22) Group B

Group A 6 (L = 19) Group B

5 (L = 16)

4 (L = 13)

X N X N X N X N X N X

Group A

N X

Group B

N X N X N X

Group A Group B

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD/ SSLT

STD/ SSLT

81.6 122 97.9 147 114 171 131 196 81.6 81.6 81.6 81.6 81.6 81.6 81.6 72.0 72.0 72.0 72.0 72.0 72.0 72.0 72.0 62.5 62.5 62.5 62.5 62.5 62.5 62.5 62.5 53.0 53.0 53.0 53.0 43.5 43.5 43.5 43.5

122 122 122 122 122 122 122 108 108 108 108 108 108 108 108 93.8 93.8 93.8 93.8 93.8 93.8 93.8 93.8 79.5 79.5 79.5 79.5 65.3 65.3 65.3 65.3

97.9 97.9 97.9 97.9 97.9 97.9 97.9 86.5 86.5 86.5 86.5 86.5 86.5 86.5 86.5 75.0 75.0 75.0 75.0 75.0 75.0 75.0 75.0 63.6 63.6 63.6 63.6 52.2 52.2 52.2 52.2

147 147 147 147 147 147 147 130 130 130 130 130 130 130 130 113 113 113 113 113 113 113 113 95.4 95.4 95.4 95.4 78.3 78.3 78.3 78.3

114 114 114 114 114 114 114 101 101 101 101 101 101 101 101 87.5 87.5 87.5 87.5 87.5 87.5 87.5 87.5 74.2 74.2 74.2 74.2 60.9 60.9 60.9 60.9

171 171 171 171 171 171 171 151 151 151 151 151 151 151 151 131 131 131 131 131 131 131 131 111 111 111 111 91.4 91.4 91.4 91.4

131 131 131 131 131 131 131 115 115 115 115 115 115 115 115 100 100 100 100 100 100 100 100 84.8 84.8 84.8 84.8 69.6 69.6 69.6 69.6

196 196 196 196 196 196 196 173 173 173 173 173 173 173 173 150 150 150 150 150 150 150 150 127 127 127 127 104 104 104 104

1/4 1/4 5/16 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load STD/SSLT = Standard holes or short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9. Tabulated values are grouped when available strength is independent of hole type.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

—

—

—

—

147 — 147 — 147 — 147 — 130 — 130 — 130 — 130 — 113 — 113 — 113 — 113 95.4 95.4 95.4 95.4 78.3 78.3 78.3 78.3

220 — 220 — 220 — 220 — 195 — 195 — 195 — 195 — 169 — 169 — 169 — 169 143 143 143 143 117 117 117 117

163 — 163 — 163 — 163 — 144 — 144 — 144 — 144 — 125 — 125 — 125 — 125 106 106 106 106 87.0 87.0 87.0 87.0

245 — 245 — 245 — 245 — 216 — 216 — 216 — 216 — 188 — 188 — 188 — 188 159 159 159 159 131 131 131 131

3/8

7/16

N = Threads included X = Threads excluded

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DESIGN TABLES

Table 10-10a (continued) Plate Fy = 36 ksi

n

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips

Bolt Group

Thread Cond.

Group A

N X

Group B

N X N X N X

Hole Type

1 -in.1diameter /8 bolts

Plate Thickness, in. 5/16

3/8

7/16

1/2

9/16

5/8

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

3 (L = 10)

2 (L = 7)

Group A Group B

34.0 51.0 40.8 61.2 47.6 71.4 54.4 81.6 61.2 91.8 64.9 97.6 STD/ SSLT

STD/ SSLT

34.0 34.0 34.0 24.5 24.5 24.5 24.5

51.0 51.0 51.0 36.7 36.7 36.7 36.7

40.8 40.8 40.8 29.4 29.4 29.4 29.4

61.2 61.2 61.2 44.0 44.0 44.0 44.0

47.6 47.6 47.6 34.3 34.3 34.3 34.3

71.4 71.4 71.4 51.4 51.4 51.4 51.4

54.4 54.4 54.4 37.1 39.2 39.2 39.2

81.6 81.6 81.6 55.8 58.7 58.7 58.7

1/4 1/4 5/16 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load STD/SSLT = Standard holes or short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9. Tabulated values are grouped when available strength is independent of hole type.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

61.2 61.2 61.2 37.1 44.0 44.0 44.0

91.8 91.8 91.8 55.8 66.1 66.1 66.1

3/8

68.0 68.0 68.0 37.1 46.8 46.8 48.9

102 102 102 55.8 70.2 70.2 73.4

7/16

N = Threads included X = Threads excluded

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-10b

3

/ 4-in.diameter

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips

bolts n

Bolt Group

Thread Cond.

Hole Type

N

STD SSLT

Plate Fy = 50 ksi

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 12 (L = 351/2) Group B

Group A 11 (L = 321/2) Group B

Group A 10 (L = 291/2) Group B

Group A 9 (L = 261/2) Group B

X N X N X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

122 183 134 202

—

—

—

—

—

—

—

—

122 122 122 122 122 122 122 112 112 112 112 112 112 112 112 101 101 101 101 101 101 101 101 90.8 90.8 90.8 90.8 90.8 90.8 90.8 90.8

138 — 174 — 174 — 183 — 126 — 159 — 159 — 167 — 115 — 145 — 145 — 152 — 103 — 130 — 130 — 136

208 — 262 — 262 — 274 — 190 — 239 — 239 — 251 — 173 — 217 — 217 — 228 — 155 — 194 — 194 — 204

138 — 174 — 174 — 213 — 126 — 159 — 159 — 195 — 115 — 145 — 145 — 177 — 103 — 130 — 130 — 159

208 — 262 — 262 — 320 — 190 — 239 — 239 — 293 — 173 — 217 — 217 — 266 — 155 — 194 — 194 — 238

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

183 183 183 183 183 183 183 167 167 167 167 167 167 167 167 152 152 152 152 152 152 152 152 136 136 136 136 136 136 136 136

138 152 152 152 152 152 152 121 126 139 139 139 139 139 139 110 115 126 126 126 126 126 126 97.2 103 113 113 113 113 113 113

208 229 229 229 229 229 229 183 190 209 209 209 209 209 209 165 173 190 190 190 190 190 190 146 155 170 170 170 170 170 170

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5/16

3/8

N = Threads included X = Threads excluded

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Page 121

10–121

DESIGN TABLES

Table 10-10b (continued) Plate Fy = 50 ksi

n

Bolt Group

3

/ 4-in.diameter

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips Thread Cond.

Hole Type

N

STD SSLT

bolts

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 8 (L = 231/2) Group B

Group A 7 (L = 201/2) Group B

Group A 6 (L = 171/2) Group B

Group A 5 (L = 141/2) Group B

X N X N X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

80.4 121 84.7 127 80.4 80.4 80.4 80.4 80.4 80.4 80.4 70.1 70.1 70.1 70.1 70.1 70.1 70.1 70.1 59.3 59.7 59.7 59.7 59.7 59.7 59.7 59.7 49.4 49.4 49.4 49.4 49.4 49.4 49.4 49.4

121 121 121 121 121 121 121 105 105 105 105 105 105 105 105 89.1 89.6 89.6 89.6 89.6 89.6 89.6 89.6 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0

90.8 101 101 101 101 101 101 72.1 78.7 87.6 87.6 87.6 87.6 87.6 87.6 59.3 66.5 74.6 74.6 74.6 74.6 74.6 74.6 54.1 54.1 61.7 61.7 61.7 61.7 61.7 61.7

137 151 151 151 151 151 151 108 118 131 131 131 131 131 131 89.1 100 112 112 112 112 112 112 81.3 81.3 92.5 92.5 92.5 92.5 92.5 92.5

—

—

—

—

—

—

—

—

90.8 — 114 — 114 — 121 — 78.7 — 99.2 — 99.2 — 105 — 66.5 — 83.8 — 83.8 — 89.6 54.1 54.1 68.1 68.1 68.1 68.1 74.0 74.0

137 — 172 — 172 — 181 — 118 — 149 — 149 — 158 — 100 — 126 — 126 — 134 81.3 81.3 102 102 102 102 111 111

90.8 — 114 — 114 — 141 — 78.7 — 99.2 — 99.2 — 123 — 66.5 — 83.8 — 83.8 — 104 54.1 54.1 68.1 68.1 68.1 68.1 84.5 84.5

137 — 172 — 172 — 211 — 118 — 149 — 149 — 184 — 100 — 126 — 126 — 155 81.3 81.3 102 102 102 102 126 126

— — — — — — — — — — — — — — — — — — — — — — — — 54.1 — 68.1 — 68.1 — 84.5

— — — — — — — — — — — — — — — — — — — — — — — — 81.3 — 102 — 102 — 126

— — — — — — — — — — — — — — — — — — — — — — — — 54.1 — 68.1 — 68.1 — 84.5

— — — — — — — — — — — — — — — — — — — — — — — — 81.3 — 102 — 102 — 126

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5/16

3/8

N = Threads included X = Threads excluded

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-10b (continued)

3

/ 4-in.diameter

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips

bolts n

Bolt Group

Thread Cond.

Hole Type

N

STD SSLT

Plate Fy = 50 ksi

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 4 (L = 111/2) Group B

Group A 3 (L = 81/2) Group B

Group A 2 (L = 51/2) Group B

X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

39.0 58.5 41.5 62.5 41.5 62.5 41.5 62.5 — 39.0 39.0 39.0 39.0 39.0 39.0 39.0 28.6 28.6 28.6 28.6 28.6 28.6 28.6 28.6 16.5 16.5 18.3 18.3 18.3 18.3 18.3 18.3

58.5 58.5 58.5 58.5 58.5 58.5 58.5 43.0 43.0 43.0 43.0 43.0 43.0 43.0 43.0 24.8 24.8 27.4 27.4 27.4 27.4 27.4 27.4

41.5 48.8 48.8 48.8 48.8 48.8 48.8 28.8 28.8 35.8 35.8 35.8 35.8 35.8 35.8 16.5 16.5 20.8 20.8 20.8 20.8 22.9 22.9

62.5 73.1 73.1 73.1 73.1 73.1 73.1 43.4 43.4 53.7 53.7 53.7 53.7 53.7 53.7 24.8 24.8 31.2 31.2 31.2 31.2 34.3 34.3

41.5 52.4 52.4 52.4 52.4 58.5 58.5 28.8 28.8 36.3 36.3 36.3 36.3 43.0 43.0 16.5 16.5 20.8 20.8 20.8 20.8 25.8 25.8

62.5 78.5 78.5 78.5 78.5 87.8 87.8 43.4 43.4 54.5 54.5 54.5 54.5 64.4 64.4 24.8 24.8 31.2 31.2 31.2 31.2 38.5 38.5

41.5 52.4 52.4 52.4 52.4 64.9 64.9 28.8 28.8 36.3 36.3 36.3 36.3 45.1 45.1 16.5 16.5 20.8 20.8 20.8 20.8 25.8 25.8

62.5 78.5 78.5 78.5 78.5 97.0 97.0 43.4 43.4 54.5 54.5 54.5 54.5 67.3 67.3 24.8 24.8 31.2 31.2 31.2 31.2 38.5 38.5

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

41.5 — 52.4 — 52.4 — 64.9 — 28.8 — 36.3 — 36.3 — 45.1 — 16.5 — 20.8 — 20.8 — 25.8

—

—

—

62.5 — 78.5 — 78.5 — 97.0 — 43.4 — 54.5 — 54.5 — 67.3 — 24.8 — 31.2 — 31.2 — 38.5

41.5 — 52.4 — 52.4 — 64.9 — 28.8 — 36.3 — 36.3 — 45.1 — 16.5 — 20.8 — 20.8 — 25.8

62.5 — 78.5 — 78.5 — 97.0 — 43.4 — 54.5 — 54.5 — 67.3 — 24.8 — 31.2 — 31.2 — 38.5

5/16

3/8

N = Threads included X = Threads excluded

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DESIGN TABLES

Table 10-10b (continued) Plate Fy = 50 ksi

n

Bolt Group

7

/ 8-in.diameter

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips Thread Cond.

Hole Type

N

STD SSLT

bolts

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 12 (L = 36) Group B

X N X

Group A 11 (L = 33) Group B

Group A 10 (L = 30) Group B

Group A 9 (L = 27) Group B

N X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

117 176 146 219 176 263

—

—

—

—

—

—

117 117 117 117 117 117 117 107 107 107 107 107 107 107 107 97.5 97.5 97.5 97.5 97.5 97.5 97.5 97.5 87.8 87.8 87.8 87.8 87.8 87.8 87.8 87.8

188 — 205 — 205 — 205 — 172 — 188 — 188 — 188 — 156 — 171 — 171 — 171 — 140 — 154 — 154 — 154

282 — 307 — 307 — 307 — 258 — 282 — 282 — 282 — 234 — 256 — 256 — 256 — 210 — 230 — 230 — 230

188 — 234 — 234 — 234 — 172 — 215 — 215 — 215 — 156 — 195 — 195 — 195 — 140 — 176 — 176 — 176

282 — 351 — 351 — 351 — 258 — 322 — 322 — 322 — 234 — 293 — 293 — 293 — 210 — 263 — 263 — 263

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

176 176 176 176 176 176 176 161 161 161 161 161 161 161 161 146 146 146 146 146 146 146 146 132 132 132 132 132 132 132 132

146 146 146 146 146 146 146 134 134 134 134 134 134 134 134 122 122 122 122 122 122 122 122 110 110 110 110 110 110 110 110

219 219 219 219 219 219 219 201 201 201 201 201 201 201 201 183 183 183 183 183 183 183 183 165 165 165 165 165 165 165 165

176 176 176 176 176 176 176 161 161 161 161 161 161 161 161 146 146 146 146 146 146 146 146 132 132 132 132 132 132 132 132

263 263 263 263 263 263 263 241 241 241 241 241 241 241 241 219 219 219 219 219 219 219 219 197 197 197 197 197 197 197 197

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5/16

3/8

N = Threads included X = Threads excluded

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-10b (continued)

7

/ 8-in.diameter

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips

bolts n

Bolt Group

Thread Cond.

Hole Type

N

STD SSLT

Plate Fy = 50 ksi

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 8 (L = 24) Group B

Group A 7 (L = 21) Group B

Group A 6 (L = 18) Group B

Group A 5 (L = 15) Group B

X N X N X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

78.0 117 97.5 146 115 173 78.0 78.0 78.0 78.0 78.0 78.0 78.0 68.3 68.3 68.3 68.3 68.3 68.3 68.3 68.3 58.5 58.5 58.5 58.5 58.5 58.5 58.5 58.5 48.8 48.8 48.8 48.8 48.8 48.8 48.8 48.8

117 117 117 117 117 117 117 102 102 102 102 102 102 102 102 87.8 87.8 87.8 87.8 87.8 87.8 87.8 87.8 73.1 73.1 73.1 73.1 73.1 73.1 73.1 73.1

97.5 97.5 97.5 97.5 97.5 97.5 97.5 85.3 85.3 85.3 85.3 85.3 85.3 85.3 85.3 73.1 73.1 73.1 73.1 73.1 73.1 73.1 73.1 60.9 60.9 60.9 60.9 60.9 60.9 60.9 60.9

146 146 146 146 146 146 146 128 128 128 128 128 128 128 128 110 110 110 110 110 110 110 110 91.4 91.4 91.4 91.4 91.4 91.4 91.4 91.4

117 117 117 117 117 117 117 98.2 102 102 102 102 102 102 102 80.7 87.8 87.8 87.8 87.8 87.8 87.8 87.8 73.1 73.1 73.1 73.1 73.1 73.1 73.1 73.1

176 176 176 176 176 176 176 147 154 154 154 154 154 154 154 121 132 132 132 132 132 132 132 110 110 110 110 110 110 110 110

—

—

—

—

—

—

124 — 137 — 137 — 137 — 107 — 119 — 119 — 119 — 90.5 — 102 — 102 — 102 73.6 73.6 85.3 85.3 85.3 85.3 85.3 85.3

185 — 205 — 205 — 205 — 161 — 179 — 179 — 179 — 136 — 154 — 154 — 154 110 110 128 128 128 128 128 128

124 — 156 — 156 — 156 — 107 — 135 — 135 — 137 — 90.5 — 114 — 114 — 117 73.6 73.6 92.7 92.7 92.7 92.7 97.5 97.5

185 — 234 — 234 — 234 — 161 — 203 — 203 — 205 — 136 — 172 — 172 — 176 110 110 139 139 139 139 146 146

— — — — — — — — — — — — — — — — — — — — — — — — 73.6 — 92.7 — 92.7 — 110

— — — — — — — — — — — — — — — — — — — — — — — — 110 — 139 — 139 — 165

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5/16

3/8

N = Threads included X = Threads excluded

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DESIGN TABLES

Table 10-10b (continued) Plate Fy = 50 ksi

n

Bolt Group

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips Thread Cond.

Hole Type

N

STD SSLT

7

/ 8-in.diameter bolts

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 4 (L = 12) Group B

Group A 3 (L = 9) Group B

Group A 2 (L = 6) Group B

X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

39.0 58.5 48.8 73.1 56.5 84.8 56.5 84.8 56.5 84.8 — 39.0 39.0 39.0 39.0 39.0 39.0 39.0 29.3 29.3 29.3 29.3 29.3 29.3 29.3 29.3 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5

58.5 58.5 58.5 58.5 58.5 58.5 58.5 43.9 43.9 43.9 43.9 43.9 43.9 43.9 43.9 29.3 29.3 29.3 29.3 29.3 29.3 29.3 29.3

48.8 48.8 48.8 48.8 48.8 48.8 48.8 36.6 36.6 36.6 36.6 36.6 36.6 36.6 36.6 22.4 22.4 24.4 24.4 24.4 24.4 24.4 24.4

73.1 73.1 73.1 73.1 73.1 73.1 73.1 54.8 54.8 54.8 54.8 54.8 54.8 54.8 54.8 33.7 33.7 36.6 36.6 36.6 36.6 36.6 36.6

56.5 58.5 58.5 58.5 58.5 58.5 58.5 39.2 39.2 43.9 43.9 43.9 43.9 43.9 43.9 22.4 22.4 28.3 28.3 28.3 28.3 29.3 29.3

84.8 87.8 87.8 87.8 87.8 87.8 87.8 58.9 58.9 65.8 65.8 65.8 65.8 65.8 65.8 33.7 33.7 42.5 42.5 42.5 42.5 43.9 43.9

56.5 68.3 68.3 68.3 68.3 68.3 68.3 39.2 39.2 49.4 49.4 49.4 49.4 51.2 51.2 22.4 22.4 28.3 28.3 28.3 28.3 34.1 34.1

84.8 102 102 102 102 102 102 58.9 58.9 74.4 74.4 74.4 74.4 76.8 76.8 33.7 33.7 42.5 42.5 42.5 42.5 51.2 51.2

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

56.5 71.2 71.2 71.2 71.2 78.0 78.0 39.2 39.2 49.4 49.4 49.4 49.4 58.5 58.5 22.4 22.4 28.3 28.3 28.3 28.3 34.9 34.9

84.8 107 107 107 107 117 117 58.9 58.9 74.4 74.4 74.4 74.4 87.8 87.8 33.7 33.7 42.5 42.5 42.5 42.5 52.5 52.5

5/16

—

56.5 — 71.2 — 71.2 — 87.8 — 39.2 — 49.4 — 49.4 — 61.0 — 22.4 — 28.3 — 28.3 — 34.9

84.8 — 107 — 107 — 132 — 58.9 — 74.4 — 74.4 — 91.8 — 33.7 — 42.5 — 42.5 — 52.5

3/8

N = Threads included X = Threads excluded

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-10b (continued)

1

-in.-

Single-Plate Connections

diameter bolts

n

Bolt Group

Bolt, Weld and Single-Plate Available Strengths, kips Thread Cond.

Hole Type

N

STD SSLT

Plate Fy = 50 ksi

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 12 (L = 361/2) Group B

Group A 11 (L = 331/2) Group B

Group A 10 (L = 301/2) Group B

Group A 9 (L = 271/2) Group B

X N X N X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

112 168 140 210 168 252 196 294

—

—

—

—

112 112 112 112 112 112 112 103 103 103 103 103 103 103 103 93.8 93.8 93.8 93.8 93.8 93.8 93.8 93.8 84.7 84.7 84.7 84.7 84.7 84.7 84.7 84.7

224 — 224 — 224 — 224 — 206 — 206 — 206 — 206 — 188 — 188 — 188 — 188 — 169 — 169 — 169 — 169

336 — 336 — 336 — 336 — 309 — 309 — 309 — 309 — 282 — 282 — 282 — 282 — 254 — 254 — 254 — 254

246 — 252 — 252 — 252 — 225 — 232 — 232 — 232 — 205 — 211 — 211 — 211 — 183 — 191 — 191 — 191

370 — 378 — 378 — 378 — 338 — 348 — 348 — 348 — 307 — 317 — 317 — 317 — 275 — 286 — 286 — 286

168 168 168 168 168 168 168 154 154 154 154 154 154 154 154 141 141 141 141 141 141 141 141 127 127 127 127 127 127 127 127

140 140 140 140 140 140 140 129 129 129 129 129 129 129 129 117 117 117 117 117 117 117 117 106 106 106 106 106 106 106 106

210 210 210 210 210 210 210 193 193 193 193 193 193 193 193 176 176 176 176 176 176 176 176 159 159 159 159 159 159 159 159

168 168 168 168 168 168 168 154 154 154 154 154 154 154 154 141 141 141 141 141 141 141 141 127 127 127 127 127 127 127 127

252 252 252 252 252 252 252 232 232 232 232 232 232 232 232 211 211 211 211 211 211 211 211 191 191 191 191 191 191 191 191

196 196 196 196 196 196 196 180 180 180 180 180 180 180 180 164 164 164 164 164 164 164 164 148 148 148 148 148 148 148 148

294 294 294 294 294 294 294 270 270 270 270 270 270 270 270 246 246 246 246 246 246 246 246 222 222 222 222 222 222 222 222

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5/16

3/8

N = Threads included X = Threads excluded

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Page 127

10–127

DESIGN TABLES

Table 10-10b (continued) Plate Fy = 50 ksi

n

Bolt Group

-in.1 diameter

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips Thread Cond.

Hole Type

bolts

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 8 (L = 241/2) Group B

Group A 7 (L = 211/2) Group B

Group A 6 (L = 181/2) Group B

5 (L = 151/2)

4 (L = 121/2)

N X N X N X N X N X N X

Group B

N X N X

Group A

N X

Group B

N X

Group A

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD/ SSLT

STD/ SSLT

75.6 113 94.5 142 113 170 132 198 75.6 75.6 75.6 75.6 75.6 75.6 75.6 66.4 66.4 66.4 66.4 66.4 66.4 66.4 66.4 57.3 57.3 57.3 57.3 57.3 57.3 57.3 57.3 48.1 48.1 48.1 48.1 39.0 39.0 39.0 39.0

113 113 113 113 113 113 113 99.6 99.6 99.6 99.6 99.6 99.6 99.6 99.6 85.9 85.9 85.9 85.9 85.9 85.9 85.9 85.9 72.2 72.2 72.2 72.2 58.5 58.5 58.5 58.5

94.5 94.5 94.5 94.5 94.5 94.5 94.5 83.0 83.0 83.0 83.0 83.0 83.0 83.0 83.0 71.6 71.6 71.6 71.6 71.6 71.6 71.6 71.6 60.2 60.2 60.2 60.2 48.8 48.8 48.8 48.8

142 142 142 142 142 142 142 125 125 125 125 125 125 125 125 107 107 107 107 107 107 107 107 90.3 90.3 90.3 90.3 73.1 73.1 73.1 73.1

113 113 113 113 113 113 113 99.6 99.6 99.6 99.6 99.6 99.6 99.6 99.6 85.9 85.9 85.9 85.9 85.9 85.9 85.9 85.9 72.2 72.2 72.2 72.2 58.5 58.5 58.5 58.5

170 170 170 170 170 170 170 149 149 149 149 149 149 149 149 129 129 129 129 129 129 129 129 108 108 108 108 87.8 87.8 87.8 87.8

132 132 132 132 132 132 132 116 116 116 116 116 116 116 116 100 100 100 100 100 100 100 100 84.2 84.2 84.2 84.2 68.3 68.3 68.3 68.3

198 198 198 198 198 198 198 174 174 174 174 174 174 174 174 150 150 150 150 150 150 150 150 126 126 126 126 102 102 102 102

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load STD/SSLT = Standard holes or short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9. Tabulated values are grouped when available strength is independent of hole type.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

—

—

—

—

151 — 151 — 151 — 151 — 133 — 133 — 133 — 133 — 115 — 115 — 115 — 115 96.3 96.3 96.3 96.3 74.0 78.0 78.0 78.0

227 — 227 — 227 — 227 — 199 — 199 — 199 — 199 — 172 — 172 — 172 — 172 144 144 144 144 111 117 117 117

162 — 170 — 170 — 170 — 140 — 149 — 149 — 149 — 118 — 129 — 129 — 129 96.3 108 108 108 74.0 87.8 87.8 87.8

243 — 255 — 255 — 255 — 210 — 224 — 224 — 224 — 178 — 193 — 193 — 193 144 162 162 162 111 132 132 132

5/16

3/8

N = Threads included X = Threads excluded

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-10b (continued)

1

-in.-

Single-Plate Connections

diameter bolts

n

Bolt, Weld and Single-Plate Available Strengths, kips

Bolt Group

Thread Cond.

Group A

N X N X N X N X

Hole Type

Plate Fy = 50 ksi

Plate Thickness, in. 1/4

5/16

3/8

7/16

1/2

9/16

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

3 (L = 91/2)

2 (L = 61/2)

Group B Group A Group B

29.9 44.8 37.3 56.0 44.8 67.2 51.4 77.0 51.4 77.0 51.4 77.0 STD/ SSLT

STD/ SSLT

29.9 29.9 29.9 20.7 20.7 20.7 20.7

44.8 44.8 44.8 31.1 31.1 31.1 31.1

37.3 37.3 37.3 25.9 25.9 25.9 25.9

56.0 56.0 56.0 38.8 38.8 38.8 38.8

44.8 44.8 44.8 29.4 31.1 31.1 31.1

67.2 67.2 67.2 44.0 46.6 46.6 46.6

52.3 52.3 52.3 29.4 36.3 36.3 36.3

78.4 78.4 78.4 44.0 54.4 54.4 54.4

3/16 1/4 1/4 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load STD/SSLT = Standard holes or short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9. Tabulated values are grouped when available strength is independent of hole type.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

59.7 59.7 59.7 29.4 37.0 37.0 41.4

89.6 89.6 89.6 44.0 55.4 55.4 62.2

5/16

64.7 64.7 67.2 29.4 37.0 37.0 45.7

96.9 96.9 101 44.0 55.4 55.4 68.6

3/8

N = Threads included X = Threads excluded

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10–129

DESIGN TABLES

Table 10-10b (continued) Plate Fy = 50 ksi

n

Bolt Group

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips Thread Cond.

Hole Type

N

STD SSLT

1 -in.1diameter /8 bolts

Plate Thickness, in. 5/16

3/8

7/16

1/2

9/16

5/8

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 12 (L = 37) Group B

X N X

Group A 11 (L = 34) Group B

Group A 10 (L = 31) Group B

Group A 9 (L = 28) Group B

N X N X N X N X N X N X

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT

134 201 161 241 188 282 215 322

—

—

—

—

134 134 134 134 134 134 134 123 123 123 123 123 123 123 123 113 113 113 113 113 113 113 113 102 102 102 102 102 102 102 102

241 — 241 — 241 — 241 — 222 — 222 — 222 — 222 — 203 — 203 — 203 — 203 — 184 — 184 — 184 — 184

362 — 362 — 362 — 362 — 333 — 333 — 333 — 333 — 304 — 304 — 304 — 304 — 276 — 276 — 276 — 276

268 — 268 — 268 — 268 — 247 — 247 — 247 — 247 — 225 — 225 — 225 — 225 — 204 — 204 — 204 — 204

402 — 402 — 402 — 402 — 370 — 370 — 370 — 370 — 338 — 338 — 338 — 338 — 306 — 306 — 306 — 306

201 201 201 201 201 201 201 185 185 185 185 185 185 185 185 169 169 169 169 169 169 169 169 153 153 153 153 153 153 153 153

161 161 161 161 161 161 161 148 148 148 148 148 148 148 148 135 135 135 135 135 135 135 135 122 122 122 122 122 122 122 122

241 241 241 241 241 241 241 222 222 222 222 222 222 222 222 203 203 203 203 203 203 203 203 184 184 184 184 184 184 184 184

188 188 188 188 188 188 188 173 173 173 173 173 173 173 173 158 158 158 158 158 158 158 158 143 143 143 143 143 143 143 143

282 282 282 282 282 282 282 259 259 259 259 259 259 259 259 237 237 237 237 237 237 237 237 214 214 214 214 214 214 214 214

215 215 215 215 215 215 215 197 197 197 197 197 197 197 197 180 180 180 180 180 180 180 180 163 163 163 163 163 163 163 163

322 322 322 322 322 322 322 296 296 296 296 296 296 296 296 271 271 271 271 271 271 271 271 245 245 245 245 245 245 245 245

1/4 1/4 5/16 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9. Tabulated values are grouped when available strength is independent of hole type.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3/8

7/16

N = Threads included X = Threads excluded

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DESIGN OF SIMPLE SHEAR CONNECTIONS

Table 10-10b (continued)

1

1diameter /8-in.-

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips

bolts n

Bolt Group

Thread Cond.

Hole Type

N

STD SSLT

Plate Fy = 50 ksi

Plate Thickness, in. 5/16

3/8

7/16

1/2

9/16

5/8

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

Group A 8 (L = 25) Group B

Group A 7 (L = 22) Group B

Group A 6 (L = 19) Group B

5 (L = 16)

4 (L = 13)

X N X N X N X N X N X

Group A

N X

Group B

N X N X N X

Group A Group B

STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD SSLT STD/ SSLT

STD/ SSLT

91.4 137 110 165 128 192 146 219 91.4 91.4 91.4 91.4 91.4 91.4 91.4 80.7 80.7 80.7 80.7 80.7 80.7 80.7 80.7 70.1 70.1 70.1 70.1 70.1 70.1 70.1 70.1 59.4 59.4 59.4 59.4 48.8 48.8 48.8 48.8

137 137 137 137 137 137 137 121 121 121 121 121 121 121 121 105 105 105 105 105 105 105 105 89.1 89.1 89.1 89.1 73.1 73.1 73.1 73.1

110 110 110 110 110 110 110 96.9 96.9 96.9 96.9 96.9 96.9 96.9 96.9 84.1 84.1 84.1 84.1 84.1 84.1 84.1 84.1 71.3 71.3 71.3 71.3 58.5 58.5 58.5 58.5

165 165 165 165 165 165 165 145 145 145 145 145 145 145 145 126 126 126 126 126 126 126 126 107 107 107 107 87.8 87.8 87.8 87.8

128 128 128 128 128 128 128 113 113 113 113 113 113 113 113 98.1 98.1 98.1 98.1 98.1 98.1 98.1 98.1 83.2 83.2 83.2 83.2 68.3 68.3 68.3 68.3

192 192 192 192 192 192 192 170 170 170 170 170 170 170 170 147 147 147 147 147 147 147 147 125 125 125 125 102 102 102 102

146 146 146 146 146 146 146 129 129 129 129 129 129 129 129 112 112 112 112 112 112 112 112 95.1 95.1 95.1 95.1 78.0 78.0 78.0 78.0

219 219 219 219 219 219 219 194 194 194 194 194 194 194 194 168 168 168 168 168 168 168 168 143 143 143 143 117 117 117 117

1/4 1/4 5/16 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load STD/SSLT = Standard holes or short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9. Tabulated values are grouped when available strength is independent of hole type.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

—

—

—

—

165 — 165 — 165 — 165 — 145 — 145 — 145 — 145 — 126 — 126 — 126 — 126 107 107 107 107 87.8 87.8 87.8 87.8

247 — 247 — 247 — 247 — 218 — 218 — 218 — 218 — 189 — 189 — 189 — 189 160 160 160 160 132 132 132 132

183 — 183 — 183 — 183 — 161 — 161 — 161 — 161 — 140 — 140 — 140 — 140 119 119 119 119 93.5 97.5 97.5 97.5

274 — 274 — 274 — 274 — 242 — 242 — 242 — 242 — 210 — 210 — 210 — 210 178 178 178 178 141 146 146 146

3/8

7/16

N = Threads included X = Threads excluded

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DESIGN TABLES

Table 10-10b (continued) Plate Fy = 50 ksi

n

Single-Plate Connections Bolt, Weld and Single-Plate Available Strengths, kips

Bolt Group

Thread Cond.

Group A

N X N X N X N X

Hole Type

1 -in.1diameter /8 bolts

Plate Thickness, in. 5/16

3/8

7/16

1/2

9/16

5/8

ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD ASD LRFD

3 (L = 10)

2 (L = 7)

Group B Group A Group B

38.1 57.1 45.7 68.6 53.3 80.0 60.9 91.4 64.9 97.6 64.9 97.6 STD/ SSLT

STD/ SSLT

38.1 38.1 38.1 27.4 27.4 27.4 27.4

57.1 57.1 57.1 41.1 41.1 41.1 41.1

45.7 45.7 45.7 32.9 32.9 32.9 32.9

68.6 68.6 68.6 49.4 49.4 49.4 49.4

53.3 53.3 53.3 37.1 38.4 38.4 38.4

80.0 80.0 80.0 55.8 57.6 57.6 57.6

60.9 60.9 60.9 37.1 43.9 43.9 43.9

91.4 91.4 91.4 55.8 65.8 65.8 65.8

1/4 1/4 5/16 5/16 Weld Size STD = Standard holes SSLT = Short-slotted holes transverse to direction of load STD/SSLT = Standard holes or short-slotted holes transverse to direction of load — Indicates that the plate thickness is greater than the maximum given in Table 10-9. Tabulated values are grouped when available strength is independent of hole type.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

68.6 68.6 68.6 37.1 46.8 46.8 49.4

103 103 103 55.8 70.2 70.2 74.0

3/8

76.2 76.2 76.2 37.1 46.8 46.8 54.8

114 114 114 55.8 70.2 70.2 82.3

7/16

N = Threads included X = Threads excluded

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SINGLE-ANGLE CONNECTIONS A single-angle connection is made with an angle on one side of the web of the beam to be supported, as illustrated in Figure 10-13. This angle is preferably shop-bolted or welded to the supporting member and field-bolted to the supported beam. When the angle is welded to the support, adequate flexibility must be provided in the connection. As illustrated in Figure 10-13(c), the weld is placed along the toe and across the bottom of the angle with a return at the top per AISC Specification Section J2.2b. Note that welding across the entire top of the angle must be avoided as it would inhibit the flexibility and, therefore, the necessary end rotation of the connection. The performance of the resulting connection would not be as intended for simple shear connections.

(a) All-bolted

(b) Bolted/welded, angle welded to supported beam

(c) Bolted/welded, angle welded to support Fig. 10-13. Single-angle connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Design Checks The available strength of a single-angle connection is determined from the applicable limit states for bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). In all cases, the available strength, φRn or Rn /Ω, must equal or exceed the required strength, Ru or Ra. As illustrated in Figure 10-14, the effect of eccentricity must be considered in the angle leg attached to the supporting member. Additionally, eccentricity must be considered if the eccentricity exceeds 3 in. (to the face of the supporting member) or if a double vertical row of bolts through the web of the supported member is used. Eccentricity must be considered in the design of welds for single-angle connections. Holes in the angle leg to the supporting member must be standard holes. Holes in the angle leg to the supported member can be standard holes or horizontal short slots.

Recommended Angle Length and Thickness To provide for stability during erection, it is recommended that the minimum angle length be one-half the T-dimension of the supported beam. The maximum length of the connection angle must be compatible with the T-dimension of an uncoped beam and the remaining web depth of a coped beam. Note that the angle may encroach upon the fillet(s) as given in Figure 10-3. A minimum angle thickness of 3/8-in. for 3/4-in.- and 7/8-in.-diameter bolts, and 1/2-in. for 1-in.-diameter bolts should be used. A 4×3 angle is normally selected for a single angle welded to the support with the 3-in. leg being the welded leg.

Shop and Field Practices Single-angle connections may be readily made to the webs of supporting girders and to the flanges of supporting columns. When framing to a column flange, provision must be made for possible mill variation in the depth of the column. Since the angle is usually shopattached to the column flange, play in the open holes or horizontal slots in the outstanding angle leg may be used to provide the necessary adjustment to compensate for the mill variation. Attaching the angle to the column flange offers the advantage of side erection of the beam. The same is true for a girder web or truss support. Additionally, proper bay dimensions may be maintained without the need for shims. This advantage is lost when the angle is shop-attached to the supported beam web.

Fig. 10-14. Eccentricity in angles. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN TABLE DISCUSSION (TABLES 10-11 AND 10-12) Table 10-11. All-Bolted Single-Angle Connections Table 10-11 is a design aid for all-bolted single-angle connections. The tabulated eccentrically loaded bolt group coefficients, C, are used to determine the available strength, φRn or Rn/Ω, where Rn = Crn φ = 0.75

(10-9)

Ω = 2.0

where C = coefficient from Table 10-11 rn = the nominal strength of one bolt in shear or bearing, kips

Table 10-12. Bolted/Welded Single-Angle Connections Table 10-12 is a design aid for bolted/welded single-angle connections. Electrode strength is assumed to be 70 ksi and Group A bolts are used. In the rare case where a single-angle connection must be field-welded, erection bolts may be placed in the field-welded leg. Weld available strengths are determined by the instantaneous center of rotation method using Table 8-10 with θ = 0°. The tabulated values assume a half-web thickness of 1/4 in. and may be used conservatively for lesser half-web thicknesses. For half-web thicknesses greater than 1/4 in., the tabulated values should be reduced proportionally by an amount up to 8% at a half-web thickness of 1/2 in. The tabulated minimum supporting flange or web thickness is the thickness that matches the strength of the support material to the strength of the weld material. In a manner similar to that illustrated previously for Table 10-2, the minimum material thickness (for one line of weld) is: tmin =

3 . 09 D Fu

(9-2)

where D is the number of sixteenths in the weld size. When welds line up on opposite sides of the support, the minimum thickness is the sum of the thicknesses required for each weld. In either case, when less than the minimum material thickness is present, the tabulated weld available strength should be multiplied by the ratio of the thickness provided to the minimum thickness.

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DESIGN TABLES

Table 10-11

All-Bolted Single-Angle Connections

Eccentrically Loaded Bolt Group Coefficients, C Number of Bolts in One Vertical Row, n

Case I

Case II

12 11 10

11.4 10.4 9.37

21.5 19.4 17.3

9 8 7

8.34 7.31 6.27

15.2 13.0 10.9

6 5 4

5.22 4.15 3.07

8.70 6.63 4.70

3 2 1

1.99 1.03 —

2.94 1.61 0.518

φ R n = C (φrn ) or Rn /Ω = C (rn /Ω) where C = coefficient from Table above φrn = design strength of one bolt in shear or bearing, kips/bolt rn /Ω = allowable strength of one bolt in shear or bearing, kips/bolt Notes: For eccentricities less than or equal to those shown above, tabulated values may be used. For greater eccentricities, coefficient C should be recalculated from Part 7. Connection may be bearing-type or slip-critical. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Table 10-12

Bolted/Welded Single-Angle Connections

Weld (70 ksi) Number of Bolts in One Vertical Row

Bolt and Angle Strength, kips Group A Bolts 3

Angle Length, (Fy = 36 ksi) in.

7

/4 in.

ASD

Angle Size

/8 in.

LRFD

ASD

Size, w, in.

LRFD 5/16

12

143

215

144

351/2

216

1/4 3/16 5/16

11

131

197

132

321/2

198

1/4 3/16

10

9

119

107

179

161

120

108

180

162

L4 ×3×3/8

5/16

291/2

1/4 3/16 5/16

261/2

1

/4

3/16 5/16

8

95.5

143

95.6

143

231/2

1/4 3/16 5/16

7

83.5

125

83.4

125

201/2

1/4 3/16

Available Strength, kips ASD

LRFD

179 143 107 165 132 98.8 151 121 90.4 137 110 82.2 123 98.5 73.9 109 87.4 65.6

268 214 161 247 198 148 226 181 136 205 164 123 185 148 111 164 131 98.4

Minimum tw of Supporting Member with Angles Both Sides of Web, in.

0.475 0.380 0.285 0.475 0.380 0.285 0.475 0.380 0.285 0.475 0.380 0.285 0.475 0.380 0.285 0.475 0.380 0.285

Notes: Gage in angle leg attached to beam web as well as leg width may be decreased. 3-in. welded leg may not be increased or decreased. Tabulated weld available strengths are based on a 1/4-in. half web for the supported member. Smaller half webs will result in these values being conservative. For half webs over 1/4 in., weld values must be reduced proportionally by an amount up to 8% for a 1/2-in. half web or recalculated. When the beam web thickness of the supporting member is less than the minimum and single-angle connections are back to back, either stagger the angles, or multiply the weld design strength by the ratio of the actual web thickness to the tabulated minimum thickness to determine the reduced weld design strength.

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DESIGN TABLES

Table 10-12 (continued)

Bolted/Welded Single-Angle Connections

Weld (70 ksi) Number of Bolts in One Vertical Row

Bolt and Angle Strength, kips Group A Bolts 3

Angle Length, (Fy = 36 ksi) in.

7

/4 in.

ASD

Angle Size

Size, w, in.

/8 in.

LRFD

ASD

LRFD 5/16

6

71.6

107

71.3

171/2

107

1/4 3/16 5/16

5

59.7

89.5

59.1

141/2

88.7

1/4

47.6

71.4

47.0

70.4

L4 ×3×3/8

3/16

4

5/16

111/2

1/4 3/16 5/16

3

35.5

53.2

34.8

52.2

81/2

1/4 3/16 5/16

2

23.3

Available Strength, kips

35.0

22.7

34.0

51/2

1/4 3/16

ASD

LRFD

94.3 75.5 56.6 79.1 63.3 47.4 62.9 50.3 37.8 45.7 36.6 27.4 28.2 22.5 16.9

141 113 84.9 119 94.9 71.2 94.4 75.5 56.6 68.5 54.8 41.1 42.2 33.8 25.3

Minimum tw of Supporting Member with Angles Both Sides of Web, in.

0.475 0.380 0.285 0.475 0.380 0.285 0.475 0.380 0.285 0.475 0.380 0.285 0.475 0.380 0.285

Notes: Gage in angle leg attached to beam web as well as leg width may be decreased. 3-in. welded leg may not be increased or decreased. Tabulated weld available strengths are based on a 1/4-in. half web for the supported member. Smaller half webs will result in these values being conservative. For half webs over 1/4 in., weld values must be reduced proportionally by an amount up to 8% for a 1/2-in. half web or recalculated. When the beam web thickness of the supporting member is less than the minimum and single-angle connections are back to back, either stagger the angles, or multiply the weld design strength by the ratio of the actual web thickness to the tabulated minimum thickness to determine the reduced weld design strength.

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TEE CONNECTIONS A tee connection is made with a structural tee, as illustrated in Figure 10-15. The tee is preferably shop-bolted or welded to the supporting member and field-bolted to the supported beam. When the tee is welded to the support, adequate flexibility must be provided in the connection. As illustrated in Figure 10-15(b), line welds are placed along the toes of the tee flange with a return at the top per AISC Specification Section J2.2b. Note that welding across the entire top of the tee must be avoided as it would inhibit the flexibility and, therefore, the necessary end rotation of the connection. The performance of the resulting connection would not be as intended for simple shear connections.

Design Checks The available strength of a tee connection is determined from the applicable limit states for bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). In all cases, the available strength, φRn or Rn/Ω, must equal or exceed the required strength, Ru or Ra. Eccentricity must be considered when determining the available strength of tee connections. For a flexible support, the bolts or welds attaching the tee flange to the support must be designed for the shear, Ru or Ra. Also, the bolts through the tee stem must be designed for the shear and the eccentric moment, Ru a or Ra a, where a is the distance from the face of the support to the centroid of the bolt group through the tee stem. For a rigid support, the bolts or welds attaching the tee flange to the support must be designed for the shear and the eccentric moment; the bolts through the tee stem must be designed for the shear.

(a) All-bolted

(b) Bolted/welded Fig. 10-15. Tee connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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SHEAR SPLICES

Recommended Tee Length and Flange and Web Thicknesses To provide for stability during erection, it is recommended that the mimimum tee length be one-half the T-dimension of the beam to be supported. The maximum length of the tee must be compatible with the T-dimension of an uncoped beam and the remaining web depth, exclusive of fillets, of a coped beam. Note that the tee may encroach upon the fillet(s) as given in Figure 10-3. To provide for flexibility, the tee selected should meet the ductility checks illustrated in Part 9. The flange thickness of tees used in simple shear connections should be held to a minimum to permit the flexure necessary to accommodate the end rotation of the beam, unless the tee stem connection is proportioned to meet the geometric requirements for single-plate connections.

Shop and Field Practices When framing to a column flange, provision must be made for possible mill variation in the depth of the columns. If the tee is shop-attached to the column flange, play in the open holes usually furnishes the necessary adjustment to compensate for the mill variation. This approach offers the advantage of side erection of the beam. Alternatively, if the tee is shopattached to the supported beam web, the beam length could be shortened to provide for mill overrun and shims could be furnished at the appropriate intervals to fill the resulting gaps or to provide for mill underrun. When a single vertical row of bolts is used in a tee stem, a 4-in. or 5-in. stem is required to accommodate the end distance of the supported beam and possible overrun/underrun in beam length. A double vertical row of bolts will require a 7-in. or 8-in. tee stem. There is no maximum limit on Leh for the tee stem.

SHEAR SPLICES Shear splices are usually made with a single plate, as shown in Figure 10-16(a), or two plates, as shown in Figures 10-16(b) and 10-16(c). Although the rotational flexibility required at a shear splice is usually much less than that required at the end of a simple-span beam, when a highly flexible splice is desired, the splice utilizing four framing angles, shown in Figure 10-17, is especially useful. These shear splices may be bolted and/or welded. The available strength of a shear splice is determined from the applicable limit states for the bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). In all cases, the available strength, φRn or Rn/Ω, must equal or exceed the required strength, Ru or Ra. Eccentricity must be considered in the design of shear splices, with the exception of allbolted shear splices utilizing four framing angles, as illustrated in Figure 10-17. When the splice is symmetrical, as shown for the bolted splice in Figure 10-16(a), each side of the splice is equally restrained regardless of the relative flexibility of the spliced members. Accordingly, as illustrated in Figure 10-18, the eccentricity of the shear to the center of gravity of either bolt group is equal to half the distance between the centroids of the bolt groups. Therefore, each bolt group can be designed for the shear, Ru or Ra, and one-half the eccentric moment, Ru e or Ra e (Kulak and Green, 1990). This approach is also applicable to symmetrical welded splices. When the splice is not symmetrical, as shown in Figures 10-16(b) and 10-16(c), one side of the splice will possess a higher degree of rigidity. For the splice shown in Figure 10-16(b), AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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the right side is more rigid because the stiffness of the weld group exceeds the stiffness of the bolt group, even if the bolts are pretensioned or slip-critical. Also, for the splice shown in Figure 10-16(c), the right side is more rigid since there are two vertical rows of bolts while the left side has only one. In these cases, it is conservative to design the side with the higher rigidity for the shear, Ru or Ra, and the full eccentric moment, Ru e or Ra e. The side with the lower rigidity can then be designed for the shear only. This approach is applicable regardless of the relative flexibility of the spliced members.

(a)

(b)

(c) Fig. 10-16. Plate-type shear splices.

Fig. 10-17. Angle-type shear splice.

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10–141

Some splices, such as those that occur at expansion joints, require special attention and are beyond the scope of this Manual.

SPECIAL CONSIDERATIONS FOR SIMPLE SHEAR CONNECTIONS Simple Shear Connections Subject to Axial Forces When simple shear connections are subjected to axial load in addition to the shear, the important limit states are outstanding angle leg bending and prying action. These tend to require that the angle, plate or flange thickness increase or the gage decrease, or both, and these requirements may compromise the connection’s ability to remain flexible enough to accommodate the simple beam end rotation. The shear connection rotational ductility checks derived in Part 9 can be used to ensure that adequate ductility exists.

Simple Shear Connections at Stiffened Column-Web Locations Stiffeners are obstacles to direct connections to the column web. Figure 10-19(a) illustrates a seat angle welded to the toes of the column flanges; Figure 10-19(d) shows a vertical plate extended beyond the column flanges. Figures 10-19(b) and 10-19(c) offer two additional options for framing at locations of diagonal stiffeners; these should be examined carefully as they may create erection problems. Additionally, the deep cope of Figure 10-19(c) may significantly reduce the available strength of the beam at the end connection. Alternatively, the bottom transverse stiffener could be extended to serve as a seat plate with a bearing stiffener provided to distribute the beam reaction.

Fig. 10-18. Eccentricity in a symmetrical shear splice.

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(a)

(b)

(c)

(d)

Fig. 10-19. Simple shear connections at stiffened column-web locations. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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10–143

Eccentric Effect of Extended Gages Consider a simple shear connection to the web of a column that requires transverse stiffeners for two concurrent beam-to-column-flange moment connections. If it were not possible to eliminate the stiffeners by selection of a heavier column section, the field connection would have to be located clear of the column flanges, as shown in Figure 10-20, to provide for access and erectability. The extension of the connection beyond normal gage lines results in an eccentric moment. While this eccentric moment is usually neglected in a connection framing to a column flange, the resistance of the column to weak-axis bending is typically only 20% to 50% of that in the strong axis. Thus the eccentric moment should be considered in this column-web connection, especially if the eccentricity, e, is large. Similarly, eccentricities larger than normal gages may also be a concern in connections to girder webs.

Column-Web Supports There are two components contributing to the total eccentric moment: (1) the eccentricity of the beam end reaction, Re; and (2) Mpr, the partial restraint of the connection. To determine what eccentric moment must be considered in the design, first assume that the column is part of a braced frame for weak-axis bending, is pinned-ended with K = 1, and will be concentrically loaded, as illustrated in Figure 10-21. The beam is loaded before the column and will deflect under load as shown in Figure 10-22. Because of the partial restraint of the connection, a couple, Mpr, develops between the beam and column and adds to the eccentric couple, Re. Thus, Mcon = Re + Mpr . As the loading of the column begins, the assembly will deflect further in the same direction under load, as indicated in Figure 10-23, until the column load reaches some magnitude, Psbr , when the rotation of the column will equal the simply supported beam end rotation. At this load, the rotation of the column negates Mpr since it also relieves the partial restraint effect of the connection, and Mcon = Re. As the column load is increased above Psbr , the column rotation exceeds the simply supported beam end rotation and a moment M′pr results such that Mcon = Re – M′pr .

Fig. 10-20. Eccentric effect of extended gages. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Fig. 10-21. Column subject to dual eccentric moments.

Fig. 10-22. Illustration of beam, column and connection behavior under loading of beam only.

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10–145

Note that the partial restraint of the connection now actually stabilizes the column and reduces its effective length factor, K, below the originally assumed value of 1. Thus, since M′pr must be greater than zero, it must also be true that Re > Mcon . It is therefore conservative to design the connection for the shear, R, and the eccentric moment, Re. The welds connecting the plate to the supporting column web should be designed to resist the full shear, R, only; the top and bottom plate-to-stiffener welds have minimal strength normal to their length, are not assumed to carry any calculated force, and may be of minimum size in accordance with AISC Specification Section J2. If simple shear connections frame to both sides of the column web, as illustrated in Figure 10-21, each connection should be designed for its respective shear, R1 and R2, and the eccentric moment ⎪R2 e2 – R1e1⎪ may be apportioned between the two simple shear connections as the designer sees fit. The total eccentric moment may be assumed to act on the larger connection, the moment may be divided proportionally among the connections according to the polar moments of inertia of the bolt groups (relative stiffness), or the moment may be divided proportionally between the connections according to the section moduli of the bolt groups (relative moment strength). If provision is made for ductility and stability, it follows from the lower bound theorem of limit states analysis that the distribution which yields the greatest strength is closest to the true strength. Note that the possibility exists that one of the beams may be devoid of live load at the same time that the opposite beam is fully loaded. This condition must be considered by the designer when apportioning the moment.

Fig. 10-23. Illustration of beam, column and connection behavior under loading of beam and column.

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Girder-Web Supports The girder-web support of Figure 10-24 usually provides only minimal torsional stiffness or strength. When larger-than-normal gages are used, the end rotation of the supported beam will usually be accommodated through rotation of the girder support. It follows that the bolt group should be designed to resist both the shear, R, and the eccentric moment, Re. The beam end reaction will then be carried through to the center of the supporting girder web. The welds connecting the plate to the supporting girder web should be designed to resist the shear, R, only; the top and bottom plate-to-girder-flange welds have minimal strength normal to their length, are not assumed to carry any calculated force, and may be of minimum size in accordance with AISC Specification Section J2. Similarly, for the girder illustrated in Figure 10-25 supporting two eccentric reactions, each connection should be designed for its respective shear, R1 and R2, and the eccentric moment, ⎪R2 e2 – R1e1⎪, may be apportioned between the two simple shear connections as the designer sees fit.

Fig. 10-24. Eccentric moment on girder-web support.

Fig. 10-25. Girder-web support subject to dual eccentric moments. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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10–147

Alternative Treatment of Eccentric Moment In the foregoing treatment of eccentric moments with column- and girder-web supports, it is possible to design the support (instead of the connection) for the eccentric moment, Re. Additionally, when metal deck is used with puddle welds or self-tapping screws, the metal deck tends to reduce relative movement between the two members and thus will tend to carry all or some of the eccentric moment. In these cases, the connection may be designed for the shear, R, only or the shear and a reduced eccentric moment.

Double Connections When beams frame opposite each other and are welded to the web of the supporting girder or column, there are usually no dimensional constraints imposed on one connection by the presence of the other connection unless erection bolts are common to each connection. When the connections are bolted to the web of the supporting column or girder, however, the close proximity of the connections requires that some or all fasteners be common to both connections. This is known as a double connection. See also the discussion under “Constructability Considerations” in an earlier section in this Part.

Supported Beams of Different Nominal Depths When beams of different nominal depths frame into a double connection, care must be taken to avoid interference from the bottom flange of the shallower beam with the entering and tightening clearances for the bolts of the connection for the deeper beam. Access to the bolts that will support the deeper beam may be provided by coping or blocking the bottom flange of the shallower beam. Alternatively, stagger may be used to favorably position the bolts around the bottom flange of the shallower beam.

Supported Beams Offset Laterally Frequently, beams do not frame exactly opposite each other, but are offset slightly, as illustrated in Figure 10-26. Several connection configurations are possible, depending on the offset dimension. If the offset were equal to the gage on the support, the connection could be designed with all bolts on the same gage lines, as shown in Figure 10-26(b), and the angles arranged, as shown in Figure 10-26(d). If the offset were less than the gage on the support, staggering the bolts, as shown in Figure 10-26(c), would reduce the required gage and the angles could be arranged, as shown in Figure 10-26(c). In any case, each bolt transmits an equal share of its beam reaction(s) to the supporting member, with the bolts that are loaded in double shear ultimately carrying twice as much force as those loaded in single shear. Once the geometry of the connection has been determined, the distribution of the forces is patterned after that in the design of a typical connection. For normal gages, eccentricity may be ignored in this type of connection.

Beams Offset From Column Centerline Framing to the Column Flange from the Strong Axis As illustrated in Figure 10-27, beam-to-column-flange connections offset from the column centerline may be supported on a typical welded seat, stiffened or unstiffened, provided the welds for the seat can be spaced approximately equal on either side of the beam centerline. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Two such seats offset from the W12×65 column centerline by 21/4 in. and 31/2 in. are shown in Figures 10-27(a) and 10-27(b), respectively. While not shown, top angles should be used with this connection. Since the entire seat fits within the flange width of the column, the connection of Figure 10-27(a) is readily selected from the design aids presented previously. However, the larger

(a)

(b)

(c)

(d)

(e) Fig. 10-26. Offset beams connected to girder. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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(a)

(b)

(c)

Fig. 10-27. Offset beams connected to column flanges.

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beam offsets in Figures 10-27(b) and 10-27(c) require that one of the welds be made along the edge of the column flange against the back side of the seat angle. Note that the end return is omitted because weld returns should not be carried around such a corner. For the beam offset of 51/2 in. shown in Figure 10-27(c), the seat angle overhangs the edge of the beam and the horizontal distance between the vertical welds is reduced to 31/2 in.; the center of gravity of the weld group is located 11/4 in. to the left of the beam centerline. The force on each weld may be determined by statics. In this case, the larger force is in the righthand weld and may be determined by summing moments about the lefthand weld. Once the larger force has been determined, each weld should be designed to share the force in the more highly loaded weld.

Framing to the Column Flange from the Weak Axis Spandrel beams X and Y in the partial plan shown in Figure 10-28 are offset 41/8 in. from the centerline of column C1, permitting the beam web to be connected directly to the column flange. At column B2, spandrel beam X is offset 5 in. and requires a 7/8-in. filler between the beam web and the column flange. Beams X and Y are both plain-punched beams, with flange cuts on one side, as noted in Figure 10-28(a), Section F-F. In establishing gages, the requirements of other connections to the column at adjacent locations must be considered. While the workable flange gage is 31/2 in. for the W8×28 columns supporting the spandrel beams, for beams Z, the combination of a 4-in. column gage and 11/2-in. stagger of fasteners is used to provide entering and tightening clearance for the field bolts and sufficient edge distance on the column flange, as illustrated in Figure 10-28(b). The 4-in. column gage also permits a 11/2-in. edge distance at the ends of the spandrel beams, which will accommodate the normal length tolerance of ± 1/4 in. as specified in “Standard Mill Practice” in Part 1. The spandrel beams are shown with the notation “Cut and Grind Flush FS” in Sections E-E and F-F. This cut permits the beam web to lie flush against the column flange. The uncut flange on the near side of the spandrel beam contributes to the stiffness of the connection. The 21/2×7/8-in. filler is required between the spandrel beam web and the flange of column B2 because of the 7/8-in. offset. Accordingly, the filler provisions of AISC Specification Section J5 must be satisfied. In the part plan in Figure 10-29(a), the W16×40 beam is offset 61/4 in. from the centerline of column D1. This prevents the web of the W16×40 from being placed flush against the side of the column flange. A plate and filler are used to connect the beam to the column flange, as shown in Figure 10-29(b). Such a connection is eccentric and one group of fasteners must be designed for the eccentricity. Lack of space on the inner flange face of the column requires development of the moment induced by the eccentricity in the beam web fasteners. To minimize the number of field fasteners, the plate in this case is shop-bolted to the beam and field-bolted to the column. A careful check must be made to ensure that the beam can be erected without interference from fittings on the column web. Some fabricators would elect to shop-attach the plate to the column to eliminate possible interference and permit use of plain-punched beams. Additionally, if the column were a heavy section, the fabricator may elect to shop-weld the plate to the column to avoid drilling the thick flanges. The welding of this plate to the column creates a much stiffer connection and the design should be modified to recognize the increased rigidity. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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(a)

(b) Fig. 10-28. Offset beams connected to column.

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(a)

(b) Fig. 10-29. Offset beam connected to column.

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If the centerline of the W16 were offset 61/16 in. from line 1, it would be possible to cope or cut the flanges flush top and bottom and frame the web directly to the column flange with details similar to those shown in Figure 10-29. This type of framing also provides a connection with more rigidity than normally contemplated in simple construction. A coped connection of this type would create a bending moment at the root of the cope that might require reinforcement of the beam web. One method frequently adopted to avoid moment transfer to the column because of beam connection rigidity is to use slotted holes and a bearing connection to provide some flexibility. The slotted holes would be provided in the connection plate only and would be in the field connection only. These slotted connections also would accommodate fabrication and erection tolerances. The type of connection detailed in Figure 10-29 is similar to a coped beam and should be checked for buckling, as illustrated in Part 9. The following differences are apparent and should be recognized in the analysis: 1. The effective length of equivalent “cope” is longer by the amount of end distance to the first bolt gage line. 2. There is an inherent eccentricity due to the beam web and plate thickness. The ordinary web and plate thicknesses normally will not require an analysis for this condition, since the inelastic rotation allowed by the AISC Specification will relieve this secondary moment effect. Two plates may sometimes be required to counter this eccentricity when dimensions are significant. 3. The connection plate can be made of sufficient thickness as required for bending or buckling stresses with a minimum thickness of 3/8 in.

Framing to the Column Web If the offset of the beam from the centerline of the column web is small enough that the connection may still be centered on or under the supported beam, no special considerations need be made. However, when the offset of the beam is too large to permit the centering of the connection under the beam, as in Figure 10-30, it may be necessary to consider the effect of eccentricity in the fastener group. The offset of the beam in Figure 10-30 requires that the top and bottom flanges be blocked to provide erection clearance at the column flange. Since only half of each flange, then, remains in which to punch holes, a 6-in. outstanding leg is used for both the seat and top angles of these connections; this permits the use of two field bolts to each of the seat and top angles, which are required by OSHA.

Connections for Raised Beams When raised beams are connected to column flanges or webs, there is usually no special consideration required. However, when the support is a girder, the differing tops of steel may preclude the use of typical connections. Figure 10-31 shows several typical details commonly used for such cases in bolted construction. Figure 10-32 shows several typical details commonly used in welded construction. In Figure 10-31(a), since the top of the W12×35 is located somewhat less than 12 in. above the top of the W18 supporting beam, a double-angle connection is used. This

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connection would be designed for the beam reaction and the shop bolts would be governed by double shear or bearing, just as if they were located in a vertical position. However, the field bolts are not required to carry any calculated force under gravity loading. The maximum permissible distance, m, depends on the beam reaction, since the web remaining after the bottom cope must provide sufficient area to resist the vertical shear as well as the bending moment which would be critical at the end of the cope. The beam can be reinforced by extending the angles beyond the cope and adding additional shop bolts for development. The angle size and/or thickness can be increased to gain shear area or section modulus, if required. The effect of any eccentricity would be a matter of judgment, but could be neglected for small dimensions. When this connection is used for flexure or for dynamic or cyclical loading, the web is subjected to high stress concentrations at the end of the cope, and it is good practice to extend the angles, as shown in Figure 10-31(a), to add at least two additional web fasteners.

Fig. 10-30. Offset beam connected to column web.

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Figure 10-31(b) covers the case where the bottom flange of the W12×35 is located a few inches above the top of the W18. The beam bears directly upon fillers and is connected to the W18 by four field bolts which are not required to transmit a calculated gravity load. If the distance m exceeds the thickest plate which can be punched, two or more plates may be used. Even though the fillers in this case need only be 61/2-in. square, the amount of material required increases rapidly as m increases. If m exceeds 2 or 3 in., another type of detail may be more economical.

(a)

(b)

(c)

(d)

(e) Fig. 10-31. Bolted raised-beam connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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The detail shown in Figure 10-31(c) is used frequently when m is up to 6 or 7 in. The load on the shop bolts in this case is no greater than that in Figure 10-31(a). However, to provide more lateral stiffness, the fittings are cut from a 15-in. channel and are detailed to overlap the beam web sufficiently to permit four shop bolts on two gage lines. A stool or pedestal, cut from a rolled shape, can be used with or without fillers to provide for the necessary m distance, as in Figure 10-31(d). A pair of connection angles and a tee will also serve a similar purpose, as shown in Figure 10-31(e). To provide adequate strength to carry the beam end reaction and to provide lateral stiffness, the web thickness of the pedestal in each of these cases should be at least as thick as the member being supported. In Figure 10-32(a), welded framing angles are substituted for the bolted angles of Figure 10-31(a). In Figure 10-32(b), a single horizontal plate is shown replacing the pair of framing angles; this results in a savings in material and the amount of shop-welding. In this case, particular care must be taken in cutting the beam web and positioning the plate at right angles to the beam web. For this reason, if only a few connections of this type are to be made, some fabricators prefer to use the angles, as in Figure 10-32(a). If sufficient duplication were available to warrant making a simple jig to position the plate during welding, the solution of Figure 10-32(b) may be economical. Figure 10-32(c) shows a tee centered on the beam web and welded to the bottom flange of the beam. The tee stem thickness should not be less than the beam web thickness. The welded solutions shown in Figures 10-32(d) and 10-32(e) are capable of providing good lateral stiffness. The latter two types also permit end rotation as the beam deflects under load. However, if the m distance exceeds 3 or 4 in., it is advisable to shop-weld a triangular bracket plate at one end of the beam, as indicated by the dashed lines, to prevent the beam from deflecting along its longitudinal axis. Other equally satisfactory details may be devised to meet the needs of connections for raised beams. They will vary depending on the size of the supported beam and the distance m. When using this type of connection where the load is transmitted through bearing, the provisions of AISC Specification Sections J10.2 and J10.3 must be satisfied for both the supported and supporting members. For the detail of Figure 10-32(b), since the rolled fillet has been removed by the cut, the value of k would be taken as the thickness of the plate plus the fillet weld size. AISC Specification Appendix 6 requires stability and restraint against rotation about the beam’s longitudinal axis. This provision is most easily accomplished with a floor on top of the supported beam. In the absence of a floor, the top flange may be supported by a strut or bracket attached to the supporting member. When the beam is encased in a wall, this stability may also be provided with wall anchors. This discussion has considered that the field bolts which attach the beam to the pedestal or support beam are subject to no calculated load. It is important, however, to recognize that when the beam deflects about its neutral axis, a tensile force can be exerted on the outside bolts. The intensity of this tensile force is a function of the dimension d, indicated in Figure 10-31, the span length of the supported member, and the beam stiffness. If these forces are large, high-strength bolts should be used and the connection analyzed for the effects of prying action. Raised-beam connections such as these are used frequently as equipment or machinery supports where it is important to maintain a true and level surface or elevation. When this tolerance becomes important, the dimension d should be noted “keep” to advise the fabricator of this importance, as shown in Figure 10-31(b). Since the supporting beam is AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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subject to certain camber/deflection tolerances, it also may be appropriate to furnish shim packs between the connection and the supporting member.

Non-Rectangular Simple Shear Connections It is often necessary to design connections for beams that do not frame into a support orthogonally. Such a beam may be inclined with respect to the supporting member in

(a)

(b)

(c)

(d)

(e) Fig. 10-32. Welded raised-beam connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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various directions. Depending upon the relative angular position which a beam assumes, the connection may be classified among three categories: skewed, sloped or canted. These conditions are illustrated in Figure 10-33 for beam-to-girder web connections; the same descriptions apply to beam-to-column-flange and web connections. Additionally, beams may be oriented in a combination of any or all of these conditions. For any condition of skewed, sloped or canted framing, the single-plate connection is generally the simplest and most economical of those illustrated in this text.

(a) Skewed beam

(c) Canted beam

(b) Sloped beam

(d) Skewed and sloped beam Fig. 10-33. Non-rectangular connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Skewed Connections A beam is said to be skewed when its flanges lie in a plane perpendicular to the plane of the face of the supporting member, but its web inclined to the face of the supporting member. The angle of skew A appears in Figure 10-33(a) and represents the horizontal bevel to which the fittings must be bent or set, or the direction of gage lines on a seated connection. When the skew angle is less than 5° (1-in-12 slope), a pair of double angles can be bent inward or outward to make the connection, as shown in Figure 10-34. While bent angle sections are usually drawn as bending in a straight line from the heel, rolled angles will tend to bend about the root of the fillet (dimension k in Manual Part 1). This produces a significant jog in the leg alignment, which is magnified by the amount of bend. Above this angle of skew, it becomes impractical to bend rolled angles. For skews approximately greater than 5° (1-in-12 slope), a pair of bent plates, shown in Figure 10-35, may be a more practical solution. Bent plates are not subject to the deformation problem described for bent angles, but the radius and direction of the bend must be considered to avoid cracking during the cold-bending operation. Bent plates exhibit better ductility when bent perpendicular to the rolling direction and are, therefore, less likely to crack. Whenever possible, bent connection plates should be billed with the width dimension parallel to the bend line. The length of the plate is measured

(a) All-bolted

(b) Bolted/welded

Fig. 10-34. Skewed beam connections with bent double angles.

Fig. 10-35. Skewed beam connections with double bent plates. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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on its mid-thickness, without regard to the radius of the bend. While this will provide a plate that is slightly longer than necessary, this will be corrected when the bend is laid out to the proper radius prior to fabrication. Before bending, special attention should be given to the condition of plate edges transverse to the bend lines. Flame-cut edges of hardenable steels should be machined or softened by heat treatment. Nicks should be ground out and sharp corners should be rounded. The strength of bent angles and bent plate connections may be calculated in the same manner as for square framed beams, making due allowances for eccentricity. The load is assumed to be applied at the point where the skewed beam center line intersects the face of the supporting member. As the angle of skew increases, entering and tightening clearances on the acutely angled side of the connection will require a larger gage on the support. If the gage were to become objectionable, a single bent plate, illustrated in Figure 10-36, may provide a better solution. Note that the single-bent plate may be of the conventional type, or a more compact connection may be developed by “wrapping” the single bent plate, as illustrated in Figure 10-36(c). In all-bolted construction, both the shop and field bolts should be designed for shear and the eccentric moment. A C-shaped weld is preferable to avoid turning the beam during shop fabrication. Single bent plates should be checked for flexural strength. Skewed single-plate and skewed end-plate connections, shown in Figures 10-37 and 10-38, provide a simple, direct connection with a minimum of fittings and multiple punching requirements. When fillet-welded, these connections may be used for skews up to 30° (or a slope of 6 5/16-in-12) provided the root opening formed does not exceed 3/16 in. For skew angles greater than 30°, see AWS D1.1/D1.1M, Section 2.3.5.2 (AWS, 2010).

(a) All-bolted

(b) Bolted/welded

(c) Configurations Fig. 10-36. Skewed-beam connections with single-bent plates.

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The maximum beam-web thickness which may be supported is a function of the maximum root opening and the angle of skew. If the thickness of the beam web were such that a larger root opening were encountered, the skewed single plate or the web connecting to the skewed end plate may be beveled, as shown in Figures 10-37(b) and 10-38(b). Since no root opening occurs with the bevel, there is no limitation on the thickness of the beam web. However, beveling, especially of the beam web, requires careful finishing and is an expensive procedure which may outweigh its advantages. The design of skewed end-plate connections is similar to that discussed previously in “Shear End-Plate Connections” in this Part. However, when the gage of the bolts is not centered on the beam web, this eccentric loading should be considered. The design of skewed single-plate connections is similar to that discussed previously in “Single-Plate Connections” in this Part. When skewed, stiffened seated connections are used, the stiffening element should be located so as to cross the skewed beam centerline well out on the seat. This can be accomplished by shifting the stiffener to the left or right of center to support beams which skew to the left or to the right, respectively. Alternatively, it may be possible to skew the stiffening element.

(a) Square edge (preferred)

(b) Beveled edge (alternative)

Fig. 10-37. Skewed single-plate connections.

(a) Square edge (preferred)

(b) Beveled edge (alternative)

Fig. 10-38. Skewed shear end-plate connections.

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Sloped Connections A beam is said to be sloped if the plane of its web is perpendicular to the plane of the face of the supporting member, but its flanges are not perpendicular to this face. The angle of slope B is shown in Figure 10-33(b) and represents the vertical angle to which the fittings must be set to the web of the sloped beam, or the amount that seat and top angles must be bent. The design of sloped connections usually can be adapted directly from the rectangular connections covered earlier in this part, with consideration of the geometry of the connection to establish the location of fittings and fasteners. Note that sloped beams often require copes to clear supporting girders, as illustrated in Figure 10-39. Figure 10-40 shows a sloped beam with double-angle connections, welded to the beam and bolted to the support. The design of this connection is essentially similar to that for rectangular double-angle connections. Alternatively, shear end-plate, tee, single-angle, single-plate, or seated connections could be used. Selection of a particular connection type may be influenced by fabrication economy, erectability, and/or by the types of connections used elsewhere in the structure. Sloped seated beam connections may utilize either bent angles or plates, depending on the angle of slope. Dimensioning and entering and clearance requirements for sloped seated connections are generally similar to those for skewed connections. The bent seat and top plate shown in Figure 10-41 may be used for smaller bevels. When the angle of slope is small, it is economical to place transverse holes in the beam web on lines perpendicular to the beam flange; this requires only one stroke of a multiple

Fig. 10-39. Sloped all-bolted double-angle connection. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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punch per line. Since non-standard hole arrangements, then, usually occur in the connecting materials (which are single-punched), this requires that sufficient dimensions be provided for the connecting material to contain fasteners with adequate edges and gages, and at the same time fit the angle to the web without encroaching on the flange fillets of the beam. For the end connection of the beam, this was accomplished by using a 6-in. angle leg; a 4-in. or even a 5-in. leg would not have furnished sufficient edge distance at the extreme fastener. As the angle of slope increases, however, bolts for the end connections cannot conveniently be lined up to permit simultaneous punching of all holes in a transverse row. In this case, the fabricator may choose to disregard beam gage lines and arrange the hole-punching so that ordinary square-framed connection material can be used throughout, as shown in Figure 10-42.

Fig. 10-40. Sloped bolted/welded double-angle connection.

Fig. 10-41. Sloped seated connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Canted Connections A beam perpendicular to the face of a supporting member, but rotated so that its flanges are tilted with respect to those of the support, is said to be canted. The angle of cant C is shown in Figure 10-33(c). The design of canted connections usually can be adapted directly from the rectangular connections covered earlier in this part. In Figure 10-43, a double-angle connection is used. Alternatively, shear end-plate, seated, single-angle, single-plate, and tee connections may also be used. For channel B2 in Figure 10-44, which is supported by a sloping member B1 (not shown), to match the hole pattern in supporting member B1, the holes in the connecting materials

Fig. 10-42. Sloped beam with rectangular connections.

Fig. 10-43. Canted double-angle connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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must be canted. As shown in Figure 10-44, the top flange of the channel and the connection angles, d R and d L, are cut to clear the flanges of beam B1. In this detail, with a 3-in-12 angle of cant, 4-in. legs were wide enough to contain the pattern of hole-punching. Since the multiple punching or drilling of column flanges requires strict adherence to column gage lines, punching is generally skewed in the fittings. When, for some reason, this is not possible, as in Figure 10-45, skewed reference lines are shown on the column to aid in matching connections. When canted connecting materials are assembled on the beam, particular care must be used in determining the direction of skew for punching the connection angles. An error reversing this skew may permit matching of holes in both members, but the beam will be canted opposite to the intended direction.

Fig. 10-44. Canted connections to a sloping support.

Fig. 10-45. Canted connection to column flange. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Note the connection angles in Figure 10-45 are shown shop-welded to the beam. This was done to provide tightening clearance for 3/ 4-in. high-strength field bolts in the opposite leg. Had the shop fasteners been bolts, it would have been necessary to stagger the field and shop fasteners and provide longer angles for the increased spacing. Canted seated beams, shown in Figure 10-46, present few problems other than those in ordinary square-end seated beams. Sufficient width and length of angle leg must be provided to contain the gage line punching or drilling in the column face, as well as the offcenter location of the holes matching the punching in the beam flange. The elevation of the top flange centerline and the bevel of the beam flange may be given for reference on the beam detail, although the bevel shown will not affect the fabrication.

Inclines in Two or More Directions (Hip and Valley Framing) When a beam inclines in two or more directions with respect to the axis of its supporting member, it can be classified as a combination of those inclination directions. For example, the beam of Figure 10-33(d) is both skewed and sloped. Angle A shows the skew and angle B shows the slope. Note that, since the inclined beam is foreshortened in the elevation, the

Fig. 10-46. Canted seated connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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true angle B appears only in the auxiliary projection, Section X-X. The development of these details is quite complicated and graphical solutions to this compound angle work can be found in any textbook on descriptive geometry. Accurate dimensions may then be determined with basic trigonometry.

DESIGN CONSIDERATIONS FOR SIMPLE SHEAR CONNECTIONS TO HSS COLUMNS Many of the familiar simple shear connections that are used to connect to wide-flange columns can be used with HSS columns. These include double and single angles, unstiffened and stiffened seats, single plates, and tee connections. One additional connection that is unique for HSS columns is the through-plate; note that this alternative is seldom required structurally and presents a significant economic penalty when a single plate connection would otherwise suffice. Variations in attachments are more limited with HSS columns since the connecting element will typically be shop-welded to the HSS and bolted to the supported beam. Except for seated connections, the bolting will be to the web of a wide-flange or other open profile section. Coping is not required except for bottom-flange copes that facilitate knifed erection with double-angle connections.

Double-Angle Connections to HSS Table 10-1 is a design aid for double-angle connections. The table shows the compatible sizes of W-shapes for the various connection configurations. Based on maximum beam web thickness, maximum weld size, maximum HSS corner radius and 4-in. outstanding angle legs, double-angle connections may be used with any HSS having a width greater than or equal to 12 in. If 3-in. outstanding angle legs are used for connections with six bolts or less, HSS with widths of 10 in. are acceptable for obtaining welds on the flat of the side. For smaller web thicknesses, welds and corner radii, it may be possible to fit the connection on widths of 10 in. if the outstanding angle legs are 4 in. and on widths of 8 in. for outstanding angle legs of 3 in. However, these dimensions must be verified for a particular case. See the tabulated workable flat dimensions for HSS in Part 1.

Single-Plate Connections to HSS As long as the HSS wall is not classified as a slender element, the local distortion caused by the single-plate connection will be insignificant in reducing the column strength of the HSS (Sherman, 1996). Therefore, single-plate connections may be used with HSS when b/t ≤ 1.40(E/Fy )0.5 or 35.1 for Fy = 46 ksi. Single-plate connections may also be used with round HSS as long as they are nonslender under axial load (D/t ≤ 0.11E/Fy ).

Unstiffened Seated Connections to HSS In order to properly attach seat angles to the flat of the HSS, the workable flat must be large enough to accommodate both the width of the seat angle and the welds. Seat widths are usually 6 in. or 8 in., but other widths may also be used. See the tabulated workable flat dimensions for HSS in Part 1. Table 10-6 may be used for unstiffened seated connections to HSS. The minimum HSS thicknesses are established based on the weld strength. If the HSS thickness is less than the minimum value, the weld strength must be reduced proportionally. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Stiffened Seated Connections to HSS Tables 10-8 and 10-14 are design aids for stiffened seated connections. Table 10-8 is applicable to all member types, and Table 10-14 presents specific limits for HSS, based on the yield-line mechanism limit state for HSS. Some values for small connection lengths, L, and large HSS widths, B, have been reduced to meet the limit state for a line load with a width of 0.4L across the HSS, per AISC Specification Section K1. The design procedure for stiffened seated connections to W-shape column webs (Sputo and Ellifritt, 1991) includes a yield line limit state based on an analysis by Abolitz and Warner (1965). This has been applied to the HSS wall which is also supported on two edges. However, since the HSS side supports are the same thickness rather than much heavier as in the case of W-shape flanges, the equation (Abolitz and Warner, 1965) for rotationally free edge supports has been used instead of fixed edge supports. The strength of the connection is obtained by multiplying the tabulated value for a particular HSS width and stiffener length by the square of the HSS thickness and dividing by the width of the seat. For combinations of B and L that are not listed in Table 10-14, the HSS does not have sufficient flat width to accommodate a weld to the seat that is 0.2L on each side of the stiffener. Because the required width also depends on the stiffener thickness and the HSS corner radius, the HSS width must be checked even when the values are tabulated. See the tabulated workable flat dimensions for HSS in Part 1. The minimum HSS thicknesses associated with the weld strengths of Table 10-8 are given in Table 10-14. If the HSS thickness is less than the minimum tabulated value, the weld strength must be reduced proportionally.

Through-Plate Connections In the through-plate connection shown in Figure 10-47, the front and rear faces of the HSS are slotted so that the plate can be passed completely through the HSS and welded to both faces. Through-plate connections should be used when the HSS wall is classified as a slender element (b/t > 1.40(E/Fy)0.5 or 35.1 for Fy = 46 ksi for rectangular HSS; D/t > 0.11E/Fy for round HSS and Pipe) or does not satisfy the punching shear limit state. A single-plate connection is more economical and should be used if the HSS is neither slender nor inadequate for the punching shear rupture limit state. Through-plate connections have the same limit states as single-plate connections and Table 10-10 may be used to determine the size and number of bolts and the plate thickness. The welds, however, are subject to direct shear and may not have to be as large as those for single-plate connections. For equilibrium of the forces in Figure 10-47, the shear in the welds on the front face should not exceed the strength of the pair of welds. The HSS wall strength can be matched to the weld shear strength to determine the minimum thickness, as illustrated in Part 9. If the thickness of the HSS is less than the minimum, the weld strength must be reduced proportionally. Conservatively, the welds on the rear face may be the same size. When a connection is made on both sides of the HSS with an extended through-plate, the portion of the plate inside the HSS is subject to a uniform bending moment. For long connections, this portion of the plate may buckle in a lateral-torsional mode prior to yielding, unless H is very small. Using a thicker plate to prevent lateral-torsional buckling would restrict the rotational flexibility of the connection. Therefore, it must be recognized that the plate may buckle and that the moment will be shared with the HSS wall in a complex AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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manner. However, if the HSS would be satisfactory for a single-plate connection, the lateraltorsional buckling limit state is not a critical concern involving loss of strength.

Single-Angle Connections For fillet welding on the flat of the HSS side, while keeping the center of the beam web in line with the center of the HSS, single-angle connections must be compatible with one-half the workable flat dimension provided in Part 1. Generally, the following HSS widths and thicknesses will work: b = 8 in. and t ≤ 1/4 in. b = 9 in. and t ≤ 3/ 8 in. b ≥ 10 in. and any nominal thickness Alternatively, single angles can be welded to narrow HSS with a flare-bevel weld.

DESIGN TABLE DISCUSSION (TABLES 10-13, 10-14A, 10-14B, 10-14C AND 10-15) Table 10-13. Minimum Inside Radius for Cold-Bending Table 10-13 is a design aid providing generally accepted minimum inside-bending radius for a given plate thickness, t, for various grades of steel. Values are for bend lines transverse to the direction of final rolling (Brockenbrough, 2006). When bend lines are parallel

Fig. 10-47. Shear forces in a through-plate connection. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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to the direction of final rolling, the tabular values should be increased by 50%. When bend lines are longer than 36 in., all radii may have to be increased if problems in bending are encountered.

Table 10-14A. Clearances for All-Bolted Skewed Connections Table 10-14A is a design aid providing clearance dimensions for skewed bent double-angle connections and double and single-bent plate all-bolted connections, and specifies beam setbacks and gages. Since these dimensions are based on the maximum material thicknesses and fastener sizes indicated, it is suggested that in cases where many duplicate connections with less than maximum material or fasteners are required, savings can be realized if these dimensions are developed from specific bevels, beam sizes and fitting thicknesses.

Table 10-14B. Clearances for Bolted/Welded Skewed Connections Table 10-14B is a design aid providing clearance dimensions, beam setbacks and gages for skewed bent double-angle connections and double and single-bent plate bolted/welded connections. Table 10-13B also specifies the dimension A which is added to the fillet weld size, S, to compensate for the root opening for skewed end-plate connections. This table is based conservatively on a gap of 1/8 in. For beam webs beveled to the appropriate skew, values of H1 for the entire table are valid and A = 0.

Table 10-14C. Welding Details for Skewed Single Plate Shear Connections Table 10-14C is a design aid providing weld information for skewed single-plate shear connections. Additionally, this table provides clearances and dimensions for groove-welded single-plate connections without backing bars for skews greater than 30°; refer to AWS D1.1/D1.1M for prequalified welds for both types of joints.

Table 10-15. Required Length and Thickness for Stiffened Seated Connections to HSS Table 10-15 is a design aid for stiffened seated connections to HSS. Specific limits are based on the yield-line mechanism limit state of the HSS wall. Some values for small connection lengths, L, and large HSS widths, B, have been reduced to meet the limit state for a line load with a width of 0.4L across the HSS, per AISC Specification Section K1. The design procedure for stiffened seated connections to W-shape column webs (Sputo and Ellifritt, 1991) includes a yield limit state based on an analysis by Abolitz and Warner (1965). This has been applied to the HSS wall which is also supported on two edges. However, since the HSS side supports are the same thickness rather than much heavier, as in the case of W-shape column flanges compared to the column web, the equation for rotationally free edge supports has been used instead of fixed edge supports (Abolitz and Warner, 1965). The strength of the connection is obtained by multiplying the tabulated value for a particular HSS width and stiffener length by the square of the HSS thickness and dividing by the width of the seat. For combinations of B and L that are not listed in Table 10-15, the HSS AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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does not have sufficient flat width to accommodate a weld to the seat that is 0.2L on each side of the stiffener. Since the required width also depends on the stiffener thickness and the HSS corner radius, the HSS width must be checked even when the values are tabulated. See the tabulated workable flat dimensions for HSS in Part 1. Table 10-8 is applicable to all member types for stiffened seated connections. The minimum HSS thicknesses associated with the weld strengths of Table 10-8 are given in Table 10-15. If the HSS thickness is less than the minimum tabulated value, the weld strength must be reduced proportionally.

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Table 10-13

Minimum Inside Radius for Cold-Bending1 ASTM Designation2

Thickness, t, in. Up to 3/4

Over 3/4 to 1

Over 1 to 2

A36, A572-42

11/2 t

11/2 t

11/2 t

2t

A242, A529-50, A529-55, A572-50, A588, A992

11/2 t

11/2 t

2t

21/2 t

A572-55, A852

11/2 t

11/2 t

21/2 t

3t

A572-60, A572-65

11/2

11/2

3t

31/2 t

A514

13/4 t

41/2 t

51/2 t

t

t

21/4 t

1

Over 2

Values are for bend lines perpendicular to direction of final rolling. If bend lines are parallel to final rolling direction, multiply values by 1.5. 2 The grade designation follows the dash; where no grade is shown, all grades and/or classes are included.

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Table 10-14A

Clearances for All-Bolted Skewed Connections

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Table 10-14B

Clearances for Bolted/Welded Skewed Connections

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Table 10-14B (continued)

Clearances for Bolted/Welded Skewed Connections

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Table 10-14C

Weld Details for Skewed Single-Plate Connections 5/16 - and 3/8 -in. Plate Thickness* For θ ≤ 17° from Perpendicular For 17°< θ ≤ 30° from Perpendicular

For 30°< θ < 45° from Perpendicular

For θ = 45° from Perpendicular

*Satisfies single-plate weld requirements for these thicknesses.

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DESIGN TABLES

Table 10-14C (continued)

Weld Details for Skewed Single-Plate Connections 1/2 -in.

For θ ≤ 17° from Perpendicular

Plate Thickness* For 17°< θ ≤ 22° from Perpendicular

For 22°< θ ≤ 45° from Perpendicular

For θ = 45° from Perpendicular

*Satisfies single-plate weld requirements for these thicknesses.

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Table 10-15

Required Length and Thickness for Stiffened Seated Connections to HSS L, in. 6 7 8 9 10 11 12 13 14 15 16 17

HSS Wall Strength Factor, R u W /t 2 or R a W /t 2, kips/in. HSS Width, B, in. 5.5 6 7

5

8

9

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

558 687

839 1030

545 664 798

819 997 1200

536 646 771 911 1070

805 971 1160 1370 1600

526 625 735 856 990 1140 1300

791 940 1100 1290 1490 1710 1960

525 615 714 823 942 1070 1210 1370 1540 1720

789 925 1070 1240 1420 1610 1820 2060 2310 2580

528 612 704 804 912 1030 1160 1290 1440 1600 1700 1960

793 920 1060 1210 1370 1550 1740 1940 2170 2410 2660 2940

Required HSS Thickness Weld Size, in. 1/4 5/16 3/8 7/16 1/2 5/8

Min. HSS Thickness, in. 0.224 0.280 0.336 0.392 0.448 0.560

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Table 10-15 (continued)

Required Length and Thickness for Stiffened Seated Connections to HSS HSS Wall Strength Factor, R u W /t 2 or R a W /t 2, kips/in. HSS Width, B, in. 12 14 16 18

10

20

L, in.

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

534 614 700 793 893 1000 1120 1240 1370 1520 1670 1830 2010 2190 2390

802 922 1050 1190 1340 1500 1680 1870 2070 2280 2510 2760 3020 3300 3600

552 625 704 787 876 971 1070 1180 1290 1410 1540 1680 1820 1970 2130 2300 2480 2670 2870 3080

830 940 1060 1180 1320 1460 1610 1770 1940 2120 2320 2520 2740 2970 3210 3460 3730 4020 4310 4630

561 644 717 794 876 962 1050 1150 1250 1360 1470 1590 1710 1840 1980 2120 2280 2440 2600 2780 2960 3150 3350 3560 3770

843 968 1080 1190 1320 1450 1580 1730 1880 2040 2210 2390 2570 2770 2980 3190 3420 3660 3910 4170 4450 4730 5030 5340 5660

491 667 736 809 885 965 1050 1140 1230 1330 1430 1540 1650 1760 1880 2010 2140 2280 2430 2580 2740 2900 3070 3250 3440 3630 3830

737 1000 1110 1220 1330 1450 1580 1710 1850 1990 2150 2310 2470 2650 2830 3020 3220 3430 3650 3880 4110 4360 4620 4890 5160 5450 5750

437 594 759 828 901 976 1060 1140 1220 1310 1410 1510 1610 1710 1820 1940 2060 2180 2310 2450 2590 2730 2880 3040 3200 3370 3540

656 892 1140 1240 1350 1470 1590 1710 1840 1980 2120 2260 2420 2580 2740 2910 3090 3280 3480 3680 3890 4110 4330 4570 4810 5070 5330

393 535 699 851 920 993 1070 1150 1230 1310 1400 1490 1590 1680 1790 1890 2000 2120 2230 2360 2480 2610 2750 2890 3040 3190 3340

590 803 1050 1280 1380 1490 1600 1720 1840 1970 2100 2240 2380 2530 2680 2840 3010 3180 3360 3540 3730 3930 4130 4340 4560 4790 5020

Required HSS Thickness Weld Size, in. 1/4 5/16 3/8 7/16 1/2 5/8

Min. HSS Thickness, in. 0.224 0.280 0.336 0.392 0.448 0.560

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Table 10-15 (continued)

Required Length and Thickness for Stiffened Seated Connections to HSS HSS Wall Strength Factor, R u W /t 2 or R a W /t 2, kips/in. HSS Width, B, in. 24 26 28 30

22

32

L, in.

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

357 486 635 804 943 1010 1080 1160 1240 1320 1400 1490 1580 1670 1760 1860 1960 2070 2180 2290 2410 2530 2650 2780 2920 3050 3190

536 730 953 1210 1420 1520 1630 1740 1860 1980 2100 2230 2370 2510 2650 2800 2950 3110 3280 3450 3620 3800 3990 4180 4380 4590 4800

328 446 582 737 910 1030 1100 1180 1250 1330 1410 1490 1570 1660 1750 1850 1940 2040 2140 2250 2360 2470 2590 2700 2830 2950 3080

492 669 874 1110 1370 1560 1660 1770 1880 2000 2120 2240 2370 2500 2630 2770 2920 3070 3220 3380 3540 3710 3890 4060 4250 4440 4630

302 412 537 680 840 1020 1130 1200 1270 1340 1420 1500 1580 1660 1750 1840 1930 2020 2120 2220 2320 2430 2540 2650 2760 2880 3000

454 618 807 1020 1260 1530 1690 1800 1910 2020 2130 2250 2370 2500 2630 2760 2900 3040 3190 3340 3490 3650 3810 3980 4150 4330 4510

281 382 499 632 780 944 1120 1220 1290 1360 1430 1510 1590 1670 1750 1840 1920 2010 2110 2200 2300 2400 2500 2610 2710 2820 2940

421 574 749 948 1170 1420 1690 1830 1940 2040 2160 2270 2390 2510 2630 2760 2890 3030 3170 3310 3450 3600 3760 3920 4080 4250 4420

262 357 466 590 728 881 1050 1230 1310 1380 1450 1530 1600 1680 1760 1840 1920 2010 2100 2190 2280 2380 2480 2580 2680 2780 2890

393 535 699 885 1090 1320 1570 1850 1970 2070 2180 2290 2410 2520 2640 2770 2890 3020 3160 3290 3430 3570 3720 3870 4030 4180 4350

246 334 437 553 682 826 983 1150 1330 1400 1470 1540 1620 1690 1770 1850 1930 2010 2100 2190 2280 2370 2460 2560 2650 2760 2860

369 502 656 830 1020 1240 1470 1730 2010 2110 2210 2320 2430 2540 2660 2780 2900 3030 3150 3290 3420 3560 3700 3840 3990 4140 4300

Required HSS Thickness Weld Size, in. 1/4 5/16 3/8 7/16 1/2 5/8

Min. HSS Thickness, in. 0.224 0.280 0.336 0.392 0.448 0.560

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PART 10 REFERENCES Abolitz, A.L. and Warner, M.E. (1965), “Bending Under Seated Connections,” Engineering Journal, AISC, January, pp. 1–5. Astaneh, A., Call, S.M. and McMullin, K.M. (1989), “Design of Single-Plate Shear Connections,” Engineering Journal, AISC, Vol. 26, No. 1, 1st Quarter, pp. 21–32, Chicago, IL. AWS (2010), Structural Welding Code—Steel, AWS D1.1/D1.1M, American Welding Society, Miami, FL. Brockenbrough, R.L. (2006), Development of Fabrication Guidelines for Cold Bending of Plates, Engineering Journal, AISC, 1st Quarter, pp. 49–56. Carter, C.J., Thornton, W.A. and Murray, T.M. (1997), “Discussion—The Behavior and Load-Carrying Capacity of Unstiffened Seated Beam Connections,” Engineering Journal, AISC, Vol. 34, No. 4, 4th Quarter, pp. 151–156. Roeder, C.W. and Dailey, R.H. (1989), “The Results of Experiments on Seated Beam Connections,” Engineering Journal, AISC, Vol. 26, No. 3, 3rd Quarter, pp. 90–95. Ellifritt, D.S. and Sputo, T. (1999), “Design Criteria for Stiffened Seated Connections to Column Webs,” Engineering Journal, AISC, Vol. 36, No. 4, 4th Quarter, pp. 160–167. Kulak, G.L. (2002), High Strength Bolts—A Primer For Structural Engineers, Design Guide 17, AISC, Chicago, IL. Kulak, G.L. and Green, D.L. (1990), “Design of Connectors in Web-Flange Beam or Girder Splices,” Engineering Journal, AISC, Vol. 27, No. 2, 2nd Quarter, pp. 41–48. Muir, L.S. and Hewitt, C.M. (2009), “Design of Unstiffened Extended Single-Plate Shear Connections,” Engineering Journal, AISC, Vol. 46, No. 2, 2nd Quarter, pp. 67–79. Muir, L.S. and Thornton, W.A. (2011), “The Development of a New Design Procedure for Conventional Single-Plate Shear Connections,” Engineering Journal, AISC, Vol. 48, No. 2, 2nd Quarter, pp. 141–152. Salmon, C.G., Johnson, J.E. and Malhas, F.A. (2009), Steel Structures: Design and Behavior, 5th Ed., Prentice Hall, Upper Saddle River, NJ. Sputo, T. and Ellifritt, D.S. (1991), “Proposed Design Criteria for Stiffened Seated Connections to Column Webs,” Proceedings of the 1991 National Steel Construction Conference, AISC, pp. 8.1–8.26, Chicago, IL. Sherman, D.R. (1996), “Designing With Structural Tubing,” Engineering Journal, AISC, Vol. 33, No. 3, 3rd Quarter, pp. 101–109. Sherman, D.R. and Ghorbanpoor, A. (2002), “Design of Extended Shear Tabs,” Final Report to the American Institute of Steel Construction, AISC, Chicago, IL. Sumner, E.A. (2003), “North Carolina State Research Report on Single Plate Shear Connections,” Report to the American Institute of Steel Construction, AISC, Chicago, IL. Thornton, W.A. and Fortney, P. (2011), “On the Need for Stiffeners for and the Effect of Lap Eccentricity on Extended Shear Tabs,” Engineering Journal, AISC, Vol. 48, No. 2, 2nd Quarter.

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PART 11 DESIGN OF PARTIALLY RESTRAINED MOMENT CONNECTIONS

SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–2 LOAD DETERMINATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–2 Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–2 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–3 FLANGE-ANGLE PR MOMENT CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 11–3 FLANGE-PLATED PR MOMENT CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 11–5 PART 11 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–6

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SCOPE The specification requirements and other design considerations summarized in this Part apply to the design of partially restrained moment connections. For the design of simple shear connections, see Part 10. For the design of fully restrained moment connections, see Part 12.

LOAD DETERMINATION The behavior of partially restrained (PR) moment connections is intermediate in degree between the flexibility of simple shear connections and the full rigidity of fully restrained (FR) moment connections. AISC Specification Section B3.6b(b), Partially Restrained (PR) Moment Connections, defines PR connections as ones that transfer moment but for which the rotation between connected members is not negligible. When used, the analytical model of the PR connection must include the force-deformation characteristics of the specific connection. For further information on the use of PR moment connections, see Geschwindner (1991), Nethercot and Chen (1988), Gerstle and Ackroyd (1989), Deierlein et al. (1990), Goverdhan (1983), and Kishi and Chen (1986). As an alternative, flexible moment connections (FMC) may be used as a simplified approach to PR moment connection design (Geschwindner and Disque, 2005), particularly for preliminary design. Using FMC, any end restraint that the connection may provide to the girder is assumed zero for gravity load because of the uncertainty of that restraint after repeated loading. The beam and its web connections are thus designed as simple, considering only the gravity loads. For lateral loads, the connection is assumed to behave as an FR moment connection for analysis and the full lateral load is carried by the assigned lateral frames. The resulting flexible moment connections are then designed as “fully restrained” for the calculated required strength due to lateral loads only.

Strength With PR moment connections, the full strength of the connection is accompanied by some definite amount of rotation between the connected members. The AISC Specification requires that the structural engineer have a reliable moment-rotation, M-θ, curve before a

(a)

(b) Fig. 11-1. Partially restrained moment connection behavior.

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design can proceed. These M-θ curves are generally taken directly from the results of multiple connection tests as found in compilations such as those presented by Goverdhan (1983) and Kishi and Chen (1986) or from normalized curves developed from these tests. For information on PR composite connection see AISC Design Guide 8, Partially Restrained Composite Connections (Leon et al., 1996). Although the M-θ curves are generally quite nonlinear in nature, as the connections undergo alternating cycles of loading and unloading, the connection “shakes down” so that its behavior may be modeled essentially as a linear relationship. This “Shakedown” process is fully described in Rex and Goverdhan (2002) and Geschwindner and Disque (2005). Both the nonlinear behavior and the shakedown behavior of the connection must be included in the determination of the connection strength and stiffness for design. PR moment connections deliver concentrated forces to the flanges of columns that must be accounted for in the design of the column and column panel-zone per AISC Specification Section J10. Either the column size can be selected with adequate flange and web thicknesses to eliminate the need for column stiffening, or transverse stiffeners and/or web doubler plates can be provided. For further information, refer to AISC Design Guide 13, Stiffening of Wide-Flange Columns at Moment Connections: Wind and Seismic Applications (Carter, 1999).

Stability Stability and second-order effects for frames that include PR moment connections are evaluated by the same methods as provided in the AISC Specification for frames with simple pin connections and FR moment connections. These are the direct analysis method of Chapter C and the effective length and the first-order analysis methods of Appendix 7. Although the analysis and design of frames with PR moment connections may be more complex than frames with simple or FR moment connections, there may be situations where using the exact behavior of the connection will be advantageous to the designer. For additional information on designing PR moment frames for stability, see the work of Chen and Lui (1991) and Chen et al. (1996).

FLANGE-ANGLE PR MOMENT CONNECTIONS Flange-angle PR moment connections are made with top and bottom angles and a simple shear connection. The available strength of a flange-angle PR moment connection is determined from the applicable limit states for the bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). In all cases, the available strength, φRn or Rn /Ω, must equal or exceed the required strength, Ru or Ra. The tensile force is carried to the angle by the flange bolts, with the angle assumed to deform as illustrated in Figure 11-1. A point of inflection is assumed between the bolt gage line and the face of the connection angle, for use in calculating the local bending moment and the corresponding required angle thickness. The effect of prying action must also be considered. The strength of this type of connection is often limited by the available angle thickness and the maximum number of fasteners that can be placed on a single gage line of the vertical leg of the connection angle at the tension flange. Figure 11-2 illustrates the column

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flange deformation and shows that only the fasteners closest to the column web are fully effective in transferring forces.

(a)

(b)

Fig. 11-2. Illustration of deformations in partially restrained moment connections.

Fig. 11-3. Flange-plated partially restrained moment connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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FLANGE-PLATED PR MOMENT CONNECTIONS Originally proposed by Blodgett (1966), and illustrated in Figure 11-3, a flange-plated PR moment connection consists of a simple shear connection and top and bottom flange plates that connect the flanges of the supported beam to the supporting column. These flange plates are welded to the supporting column and may be bolted or welded to the flanges of the supported beam. An unwelded length of 11/2 times the flange-plate width, bA, is normally assumed to permit the elongation of the plate necessary for PR moment connection behavior. Other flange-plated details are illustrated in Figures 11-4a and 11-4b. The available strength of a flange plated PR moment connection is determined from the applicable limit states for the bolts (see Part 7), welds (see Part 8) and connecting elements (see Part 9). In all cases, the available strength φRn or Rn /Ω, must equal or exceed the required strength, Ru or Ra. The shop and field practices for flange-plated FR moment connections (see Part 12) are equally applicable to flange-plated PR moment connections.

(a)

(b)

Fig. 11-4. Typical flange-plated partially restrained moment connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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PART 11 REFERENCES Blodgett, O.W. (1966), Design of Welded Structures, James F. Lincoln Arc Welding Foundation, Cleveland, OH. Carter, C.J. (1999), Stiffening of Wide-Flange Columns at Moment Connections: Wind and Seismic Applications, Design Guide 13, AISC, Chicago, IL. Chen, W.F., Goto, Y. and Liew, J.Y.R. (1996), “Stability Design of Semi-Rigid Frames,” John Wiley and Sons Inc., New York, NY. Chen, W.F. and Lui, E.M. (1991), “Stability Design of Steel Frames,” CRC Press, Boca Raton, FL. Deierlein, G.G, Hsieh, S.H. and Shen, Y.J. (1990), “Computer-Aided Design of Steel Structures with Flexible Connections,” Proceedings of the 1990 National Steel Construction Conference, AISC, pp. 9.1–9.21, Chicago, IL. Gerstle, K.H. and Ackroyd, M.H. (1989), “Behavior and Design of Flexibly Connected Building Frames,” Proceedings of the 1989 National Steel Construction Conference, AISC, pp. 1.1–1.28, Chicago, IL. Geschwindner, L.F. (1991), “A Simplified Look at Partially Restrained Connections,” Engineering Journal, AISC, Vol. 28, No. 2, 2nd Quarter, pp. 73–78, Chicago, IL. Geshwindner, L.F. and Disque, R.O. (2005), “Flexible Moment Connections for Unbraced Frames—A Return to Simplicity,” Engineering Journal, AISC, Vol. 42, No. 2, 2nd Quarter, Chicago, IL. Goverdhan, A.V. (1983), “A Collection of Experimental Moment Rotation Curves and Evaluation of Prediction Equations for Semi-Rigid Connections,” Master of Science Thesis, Vanderbilt University, Nashville, TN. Kishi, N. and Chen, W.F. (1986), “Database of Steel Beam-to-Column Connections,” CESTR-86-26, Purdue University, School of Engineering, West Lafayette, IN. Leon, R.T., Hoffman, J.J. and Staeger, T. (1996), Partially Restrained Composite Connections, Design Guide 8, AISC, Chicago, IL. Nethercot, D.A. and Chen, W.F. (1988), “Effects of Connections on Columns,” Journal of Constructional Steel Research, Elsevier Applied Science Publishers, pp. 201–239, Essex, England. Rex, C.O. and Goverdhan, A.V. (2002), “Design and Behavior of a Real PR Building,” Connections in Steel Structures IV: Behavior Strength and Design, Proceedings of the Fourth Workshop on Connections in Steel Structures, AISC, October 22-24, 2000, pp. 94–105, Chicago, IL.

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PART 12 DESIGN OF FULLY RESTRAINED MOMENT CONNECTIONS SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–2 FR MOMENT CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–2 Load Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–2 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–3 Temporary Support During Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–3 Welding Considerations for Fully Restrained Moment Connections . . . . . . . . . . . . 12–4 FR CONNECTIONS WITH WIDE-FLANGE COLUMNS . . . . . . . . . . . . . . . . . . . . . 12–4 Flange-Plated FR Moment Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–4 Directly Welded FR Moment Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–7 Extended End-Plate FR Moment Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–8 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–9 Design Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–9 Design Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–10 FR MOMENT SPLICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–10 Location of Moment Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–10 Force Transfer in Moment Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–10 Flange-Plated FR Moment Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–11 Directly Welded Flange FR Moment Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–13 Extended End-Plate FR Moment Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–13 SPECIAL CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–14 FR Moment Connections to Column Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–14 Recommended Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–14 Ductility Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–14 FR Moment Connections Across Girder Supports . . . . . . . . . . . . . . . . . . . . . . . . . 12–20 Top Flange Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–20 Bottom Flange Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–21 Web Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–21 FR CONNECTIONS WITH HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–21 HSS Through-Plate Flange-Plated FR Moment Connections . . . . . . . . . . . . . . . . 12–21 HSS Cut-out Plate Flange-Plated FR Moment Connections . . . . . . . . . . . . . . . . . 12–22 Design Considerations for HSS Directly Welded FR Moment Connections . . . . . 12–23 HSS Columns Above and Below Continuous Beams . . . . . . . . . . . . . . . . . . . . . . 12–24 HSS Welded Tee Flange Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–25 HSS Diaphragm Plate Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–26 Suggested Details for HSS to Wide-Flange Moment Connections . . . . . . . . . . . . 12–27 PART 12 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–29 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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SCOPE The specification requirements and other design considerations summarized in this Part apply to the design of fully restrained (FR) moment connections. For the design of simple shear connections, see Part 10. For the design of partially restrained moment connections, see Part 11.

FR MOMENT CONNECTIONS Load Determination As defined in AISC Specification Section B3.6b, FR moment connections possess sufficient rigidity to maintain the angles between connected members at the strength limit states, as illustrated in Figure 12-1. While connections considered to be fully restrained seldom actually provide for zero rotation between members, the small amount of rotation present is usually neglected and the connection is idealized as one exhibiting zero end rotation. End connections in FR construction are designed to carry the required forces and moments, except that some inelastic but self-limiting deformation of a part of the connection

Fig. 12-1. FR moment connection behavior.

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is permitted. Huang et al. (1973) showed that the moment can be resolved into an effective tension-compression couple acting as axial forces at the beam flanges. The flange force, Puf or Paf, is determined as: LRFD

Puf =

ASD

Mu dm

(12-1a)

Paf =

Ma dm

(12-1b)

where Mu or Ma = required beam end moment, kip-in. = moment arm between the flange forces, in. (varies for all FR connections dm and for stiffener design) Shear is transferred through the beam-web shear connection. Since, by definition, the angle between the beam and column in an FR moment connection remains unchanged under loading, eccentricity can be neglected entirely in the shear connection. Additionally, it is permissible to use bolts in bearing in either standard or slotted holes perpendicular to the line of force. Axial forces, if present, are normally assumed to be distributed uniformly across the beam flange cross-sectional area. However, if the beam-web connection has sufficient stiffness, it can also be assumed to participate in the transfer of beam axial force. Moment connections deliver concentrated forces to the flanges of columns that must be accounted for in the design of the column and column panel-zone per AISC Specification Section J10. Either the column size can be selected with adequate flange and web thickness to eliminate the need for column stiffening, or transverse stiffeners and/or web doubler plates can be provided. For further information, refer to AISC Design Guide 13, Stiffening of Wide-Flange Columns at Moment Connections: Wind and Seismic Applications (Carter, 1999).

Design Checks The available strength of an FR moment connection is determined from the applicable limit states for the bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). The effect of eccentricity in the shear connection can be neglected. Additionally, the strength of the supporting column (and thus the need for stiffening) must be checked. In all cases, the available strength, φRn or Rn /Ω , must equal or exceed the required strength, Ru or Ra.

Temporary Support During Erection Bolted construction provides a ready means to erect and temporarily connect members by use of the bolt holes. In contrast, FR moment connections in welded construction must be given special attention so that all pieces affecting the alignment of the welded joint may be erected, fitted and supported until the necessary welds are made. Temporary support can be provided in welded construction by furnishing holes for erection bolts, temporary seats, special lugs or by other means.

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The effects of temporary erection aids on the finished structure should be considered, particularly on members subjected to tension loading or fatigue. They should be permitted to remain in place whenever possible since they seldom are reusable and the cost to remove them can be significant. If left in place, erection aids should be located so as not to cause a stress concentration. If, however, erection aids are to be removed, care should be taken so that the base metal is not damaged. Temporary supports should be sufficient to carry any loads imposed by the erection process, such as the dead weight of the member, additional construction equipment, or material storage. Additionally, they must be flexible enough to allow plumbing of the structure, particularly in tier buildings.

Welding Considerations for Fully Restrained Moment Connections Field welding should be arranged for welding in the flat or horizontal position and preference should be given to fillet welds over groove welds, whenever possible. Additionally, the joint detail and welding procedure should be constructed to minimize distortion and the possibility of lamellar tearing. The typical complete-joint-penetration groove weld in a directly welded flange connection for a rolled beam can be expected to shrink about 1/16 in. in the length dimension of the beam when it cools and contracts. Thicker welds, such as for welded plate-girder flanges, will shrink even more—up to 1/8 in. or 3/ 16 in. This amount of shrinkage can cause erection problems in locating and plumbing the columns along lines of continuous beams. A method of calculating weld shrinkage can be found in Lincoln Electric Company (1973). Unnecessarily thick stiffeners with complete-joint-penetration groove welds should be avoided since the accompanying weld shrinkage may contribute to lamellar tearing and distortion. Weld shrinkage can best be controlled by fabricating the beam longer than required by the amount of the anticipated weld shrinkage. Alternatively, the weld-joint root opening can be increased. For further information, refer to AWS D1.1.

FR CONNECTIONS WITH WIDE-FLANGE COLUMNS Flange-Plated FR Moment Connections As illustrated in Figure 12-2, a flange-plated FR moment connection consists of a shear connection and top and bottom flange plates that connect the flanges of the supported beam to the supporting column. These flange plates are welded to the supporting column and may be bolted or welded to the flanges of the supported beam. In a column-flange connection, the flange plates are usually located with respect to the column web centerline. Because of the column-flange mill tolerance on out-of-squareness with the web, it is desirable to shop-fit long flange plates from the theoretical column-web centerline to assure good field fit-up with the beam. Misalignment on short connections, as illustrated in Figure 12-3, can be accommodated by providing oversized holes in the plates. Since mill tolerances in both the beam and the column may cause significant shop and/or field assembly problems, it may be desirable to ship the flange plates loose for field attachment to the column.

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(a) Column flange support, bolted flange plates

(b) Column web support, bolted flange plates Fig. 12-2. Flange-plated FR moment connections.

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(c) Column flange support, welded flange plates Fig. 12-2. (continued) Flange-plated FR moment connections.

Fig. 12-3. Effect of mill tolerances on flange-plated connections.

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Directly Welded Flange FR Moment Connections As illustrated in Figure 12-4, a directly welded flange FR moment connection consists of a shear connection and complete-joint-penetration (CJP) groove welds, which directly connect the top and bottom flanges of the supported beam to the supporting column. Note, in Figure 12-4b, the stiffener extends beyond the toe of the column flange to eliminate the effects of triaxial stresses.

(a) Column flange support

(b) Column web support Fig. 12-4. Directly welded flange FR moment connections.

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Extended End-Plate FR Moment Connections As illustrated in Figure 12-5, an extended end-plate moment connection consists of a plate of length greater than the beam depth, perpendicular to the longitudinal axis of the supported beam. The end-plate is always welded to the web and flanges of the supported beam and bolted to the supporting member. The principal advantage of extended end-plate moment connections is that all welding is done in the shop. Thus, the erection process is relatively fast and economical. Figure 12-6 illustrates three commonly used extended end-plate connections. The connections are classified by the number of bolts at the tension flange and by the presence of end-plate to beam flange stiffeners. The four-bolt unstiffened and stiffened extended end-plate connections of Figure 12-6a and 12-6b are generally limited by bolt strength. The

Fig. 12-5. Extended end-plate FR moment connection.

(a)

(b)

(c)

Fig. 12–6. Configurations of extended end-plate FR moment connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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connection is compatible for use with nearly one-half of the available beam sections. Alternatively, the eight-bolt stiffened extended end-plate connection shown in Figure 12-6c is generally compatible with approximately 90% of the available beam sections. Complete discussion of the design procedures, along with design examples, are found in AISC Design Guide 4, Extended End-Plate Moment Connections—Seismic and Wind Applications (Murray and Sumner, 2003). Design procedures and example calculations for nine other end-plate connections, which are commonly used in the metal building industry, are found in AISC Design Guide 16, Flush and Extended Multiple-Row Moment End-Plate Connections (Murray and Shoemaker, 2002). Recommended shop and field erection practices, basic design assumptions, and a brief overview of the design procedures follow.

Shop and Field Practices End-plate moment connections require extra care in shop fabrication and field erection. The fit-up of extended end-plate connections is sensitive to the column flange conditions and may be affected by column flange-to-web squareness, beam camber, or squareness of the beam end. The beam is frequently fabricated short to accommodate the column overrun tolerances with shims furnished to fill any gaps which might result. As reported by Meng and Murray (1997), use of weld access holes can result in beam flange cracking. If CJP welds are used, the weld cannot be inspected over the web; however, because this location is a relative “soft” spot in the connection, it is of no concern.

Design Assumptions A summary of the assumptions made in the design guide procedures follows: 1. Group A or Group B high-strength bolts of diameter not greater than 11/2 in. must be used. 2. The specified minimum yield stress of the end-plate material must be 50 ksi or less. 3. When the procedures in AISC Design Guide 16 are used, only static loading is permitted (wind, snow, temperature and seismic loads as defined in the Scope located at the front of this Manual are considered static loads). 4. The recommended minimum distance from the face of the beam flange to the nearest bolt centerline (the vertical bolt pitch) is the bolt diameter, db, plus 1/2 in. if the bolt diameter is not greater than 1 in., and plus 3/ 4 in. for larger diameter bolts. However, many fabricators prefer to use a standard pitch dimension of 2 in. or 21/2 in. for all bolt diameters. 5. All of the shear force at a connection is assumed to be resisted by the compression side bolts. End-plate connections need not be designed as slip-critical connections and it is noted that shear is rarely a major concern in the design of moment end-plate connections. 6. The end-plate width effective in resisting the applied moment must be taken as not greater than the beam flange width, bf, plus 1 in. 7. The gage of the tension bolts (horizontal distance between vertical bolt lines) must not exceed the beam tension flange width. 8. When CJP welds are used, weld access holes should not be used, and the weld between beam flange-to-web fillets should be treated as a partial-joint-penetration (PJP) weld. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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9. For nonseismic connections, when the required moment is less than the available flexural strength of the beam, the end-plate connection can be designed for the required moment but it is recommended that the connection be designed for not less than 60% of the available flexural strength of the beam. 10. Beam web-to-end-plate welds in the vicinity of the tension bolts should be designed to develop the yield stress of the beam web unless the required moment is less than 60% of the available flexural strength of the beam. 11. Only the web-to-end-plate weld between the mid-depth of the beam and the inside face of the beam compression flange or the weld between the inner row of tension bolts plus 2db and the inside face of the beam compression flange, whichever is smaller, is considered effective in resisting the beam end shear.

Design Procedures The design procedure in AISC Design Guide 4 and AISC Design Guide 16 differ from those in previous AISC design methods. The new procedures are based on yield-line analysis for determining end-plate thickness and modified tee-hanger analysis to determine required bolt strength. The procedures in AISC Design Guide 4 are for pretensioned bolts and “thick plates,” and result in connections with the smallest possible bolt diameter. For these connections, prying forces are zero. The procedures in AISC Design Guide 16 allow for both “thick plate” and “thin plate” designs. A thin plate design results in the smallest possible end-plate thickness and the maximum bolt prying force. In addition, connections can be designed using either pretensioned or snug-tight bolts. Column side design procedures are included in AISC Design Guide 4. Both Design Guides have complete examples for the various end-plate configurations.

FR MOMENT SPLICES Beams and girders sometimes are spliced in locations where both shear and moment must be transferred across the splice. Per AISC Specification Section J6, the nominal strength of the smaller section being spliced must be developed in groove-welded butt splices. Other types of beam or girder splices must develop the strength required by the actual forces at the point of the splice.

Location of Moment Splices A careful analysis is particularly important in continuous structures where a splice may be located at or near the point of inflection. Since this inflection point can and does migrate under service loading, actual forces and moments may differ significantly from those assumed. Furthermore, since loading application and frequency can change in the lifetime of the structure, it is prudent for the designer to specify some minimum strength requirement at the splice. Hart and Milek (1965) propose that splices in fixed-ended beams be located at the one-sixth point of the span and be adequate to resist a moment equal to one-sixth of the flexural strength of the member, as a minimum.

Force Transfer in Moment Splices Force transfer in moment splices can be assumed to occur in a manner similar to that developed for FR moment connections. That is, the required shear, Ru or Ra, is primarily transferred through the beam-web connection and the moment can be resolved into an AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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effective tension-compression couple where the required force at each flange, Puf or Paf, is determined by: LRFD

Puf =

ASD

Mu dm

(12-2a)

Paf =

Ma dm

(12-2b)

where Mu or Ma = required moment in the beam at the splice, kip-in. = moment arm, in. (varies based upon actual connection geometry) dm Axial forces, if present, are normally assumed to be distributed uniformly across the beam flange cross-sectional area. However, if the beam-web connection has sufficient stiffness, it can also be assumed to participate in the transfer of beam axial force.

Flange-Plated FR Moment Splices Moment splices can be designed as shown in Figure 12-7, to utilize flange plates and a web connection. The flange plates and web connection may be bolted or welded. The splice and spliced beams should be checked in a manner similar to that described previously under “Flange-Plated FR Moment Connections,” except that the web connection should be designed as illustrated previously for shear splices in Part 10 without consideration of eccentricity. Figure 12-7 illustrates two types of splices, bolted and welded. Figure 12-7a illustrates the detail of a bolted flange-plated moment splice. For this case, the flange plates are normally made approximately the same width as the beam flange as shown in Figure 12-7a. Alternatively, Figure 12-7b illustrates the detail of a welded splice. As shown in Figure 12-7b, the top plate is narrower and the bottom plate is wider than the beam flange,

(a) Bolted

(b) Welded

Fig. 12-7. Flange-plated moment splice. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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permitting the deposition of weld metal in the downhand or horizontal position without inverting the beam. While this is a benefit in shop fabrication (the beam does not have to be turned over), it is of extreme importance in the field where the weld can be made in the horizontal instead of the overhead position, since the beam cannot be turned over. This detail also provides tolerance for field alignment, since the joint gap can be opened or closed. When splices are field-welded, some means for temporary support must be provided as discussed previously in “Temporary Support During Erection.” If the beam or girder flange is thick and the flange forces are large, it may be desirable to place additional plates on the insides of the flanges. In a bolted splice (Figure 12-7a), the bolts are then loaded in double shear and a more compact joint may result. Note that these additional plates must have sufficient area to develop their share of the double-shear bolt load. In a welded splice (Figure 12-7b), these additional plates must have sufficient area to match the strength of the welds that connect them. Additionally, these plates must be set away from the beam web a distance sufficient to permit deposition of weld metal as shown in Figure 12-8a. This distance is a function of the beam depth and flange width, as well as the welding equipment to be used. A distance of 2 to 21/2 in. or more may be required for this access. One alternative is to bevel the bottom edge of the plate to clear the beam fillet and place the plate tight to the beam web with a fillet weld as illustrated in Figure 12-8a. The effects of this bevel on the area of the plate must be considered in determining the required plate width and thickness. Another alternative would be to use unbeveled inclined plates as shown in Figure 12-8b.

(a)

(b) Fig. 12-8. Welding clearances for flange-plated moment splices. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Directly Welded Flange FR Moment Splices Moment splices can be designed, as shown in Figure 12-9, to utilize a complete-jointpenetration groove weld connecting the flanges of the members being spliced. The web connection may then be bolted or welded. The splice and spliced beams should be checked in a manner similar to that described previously under “Directly Welded Flange FR Moment Connections,” except that the web connection should be designed as illustrated previously for shear splices in Part 10. Although rare in occurrence, some spliced members must be level on top. Where the depths of these spliced members differ, consideration should be given to the use of a flange plate of uniform thickness for the full length of the shallower member. This avoids the fabrication problems created by an inverted transition. Frequently, the spliced shapes are different sizes, but of the same shape depth grouping. Because rolled shapes from the same shape depth grouping have the same dimension between the flanges, aligning the inside flange surfaces avoids a more difficult offset transition. Eccentricity resulting from differing flange thicknesses is usually ignored in the design. The web plates normally are aligned to their center lines. The groove- (butt-) welded splice preparation shown in Figure 12-9 may be used for either shop or field welding. Alternatively, for shop welding where the beam may be turned over, the joint preparation of the bottom flange could be inverted. Sloped transitions as shown in Figure 12-10 are only required for splices subject to seismic and dynamic loads. In splices subjected to dynamic or fatigue loading, the backing bar should be removed and the weld should be ground flush when it is normal to the applied stress (AISC, 1977). The access holes should be free of notches and should provide a smooth transition at the juncture of the web and flange.

Extended End-Plate FR Moment Splices Moment splices can be designed as shown in Figure 12-11 where the tension force is in the bottom flange, to utilize four-bolt unstiffened extended end-plates connecting the members being spliced. If the end-plate and the bolts are designed properly, it is possible to load this type of connection to reach the full plastic moment capacity of the beam, φb Mp or Mp /Ωb. The splice and spliced beams should be checked in a manner similar to that described previously under “Extended End-Plate FR Moment Connections.” The comments for “Extended End-Plate Connections” are equally applicable to extended end-plate moment splices.

Fig. 12-9. Directly welded flange moment splice. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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SPECIAL CONSIDERATIONS FR Moment Connections to Column Webs It is frequently required that FR moment connections be made to column webs. While the mechanics of analysis and design do not differ from FR moment connections to column flanges, the details of the connection design as well as the ductility considerations required are significantly different.

Recommended Details When an FR moment connection is made to a column web, it is normal practice to stop the beam short and locate all bolts outside of the column flanges as illustrated in Figure 12-2b. This simplifies the erection of the beam and permits the use of an impact wrench to tighten all bolts. It is also preferable to locate welds outside the column flanges to provide adequate clearance.

Ductility Considerations Driscoll and Beedle (1982) discuss the testing and failure of two FR moment connections to column webs: a directly welded flange connection and a bolted flange-plated connection, shown respectively in Figures 12-12a and 12-12b. Although the connections in these tests were proportioned to be “critical,” they were expected to provide inelastic rotations at full plastic load. Failure occurred unexpectedly, however, on the first cycle of loading; brittle fracture occurred in the tension connection plate at the load corresponding to the plastic moment before significant inelastic rotation had occurred.

Fig. 12-10. Transitions at tension flange for directly welded flange moment splices, for seismic and dynamic loaded splices. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Examination and testing after the unexpected failure revealed that the welds were of proper size and quality and that the plate had normal strength and ductility. The following is quoted, with minor editorial changes relative to figure numbers, directly from Driscoll and Beedle (1982). Calculations indicate that the failures occurred due to high strain concentrations. These concentrations are: (1) at the junction of the connection plate and the column flange tip and (2) at the edge of the butt weld joining the beam flange and the connection plate. Figure 4 (Figure 12-13 here) illustrates the distribution of longitudinal stress across the width of the connection plate and the concentration of stress in the plate at the column flange tips. It also illustrates the uniform longitudinal stress

Fig. 12-11. Extended end-plate moment splice.

(a) Directly welded flange FR connection

(b) Bolted flange-plated FR connection

Fig. 12-12. Test specimens used by Driscoll and Beedle (1982). AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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distribution in the connection plate at some distance away from the connection. The stress distribution shown represents schematically the values measured during the load tests and those obtained from finite element analysis. (σo is a nominal stress in the elastic range.) The results of the analyses are valid up to the loading that causes the combined stress to equal the yield point. Furthermore, the analyses indicate that localized yielding could begin when the applied uniform stress is less than one-third of the yield point. Another contribution of the nonuniformity is the fact that there is no back-up stiffener. This means that the welds to the web near its center are not fully effective. The longitudinal stresses in the moment connection plate introduce strains in the transverse and the through-thickness directions (the Poisson effect). Because of the attachment of the connection plate to the column flanges, restraint is introduced; this causes tensile stresses in the transverse and the through-thickness directions. Thus, referring to Figure 12-13, tri-axial tensile stresses are present along Section A-A and they are at their maximum values at the intersections of Sections A-A and C-C. In such a situation, and when the magnitudes of the stresses are sufficiently high, materials that are otherwise ductile may fail by premature brittle fracture. The results of nine simulated weak-axis FR moment connection tests performed by Driscoll et al. (1983) are summarized in Figure 12-14. In these tests, the beam flange was simulated by a plate measuring either 1 in. × 10 in. or 11/8 in. × 9 in. The fracture strength exceeds the yield strength in every case, and sufficient ductility is provided in all cases except for that of Specimen D. Also, if the rolling direction in the first five specimens (A,

(a) Longitudinal stress distribution on Section A-A

(b) Longitudinal stress distribution on Section B-B

(c) Shear stress distribution on Section C-C

Fig. 12-13. Stress distributions in test specimens used by Driscoll and Beedle (1982). AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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B, C, D and E) were parallel to the loading direction, which would more closely approximate an actual beam flange, the ductility ratios for these would be higher. The connections with extended connection plates (i.e., projection of 3 in.), with extensions either rectangular or tapered, appeared equally suitable for the static loads of the tests. Based on the tests, Driscoll et. al. (1983) report that those specimens with extended connection plates have better toughness and ductility and are preferred in design for seismic loads, even though the other connection types (except D) may be deemed adequate to meet the requirements of many design situations. In accordance with the preceding discussion, the following suggestions are made regarding the design of this type of connection: 1. For directly welded (butt) flange-to-plate connections, the connection plate should be thicker than the beam flange. This greater area accounts for shear lag and also provides for misalignment tolerances. AWS D1.1, Section 5.22.3 restricts the misalignment of abutting parts such as this to 10% of the thickness, with 1/8-in. maximum for a part restrained against bending due to eccentricity of alignment. Considering the various tolerances in mill rolling (± 1/8 in. for W-shapes), fabrication and erection, it is prudent design to call for the connection plate thickness to be increased to accommodate these tolerances and avoid the subsequent problems encountered at erection. An increase of 1/8 in. to 1/4 in. generally is used. Frequently, this connection plate also serves as the stiffener for a strong axis FR or PR moment connection. The welds that attach the plate/stiffener to the column flange may then be subjected to combined tensile and shearing, or compression and shearing forces. Vector analysis is commonly used to determine weld size and stress. It is good practice to use fillet welds whenever possible. Welds should not be made in the column k-area. 2. The connection plate should extend at least 3/ 4 in. beyond the column flange to avoid intersecting welds and to provide for strain elongation of the plate. The extension should also provide adequate room for runout bars when required. 3. Tapering an extended connection plate is only necessary when the connection plate is not welded to the column web (Specimen E, Figure 12-14). Tapering is not necessary if the flange force is always compressive (e.g., at the bottom flange of a cantilevered beam). 4. To provide for increased ductility under seismic loading, a tapered connection plate should extend 3 in. Alternatively, a backup stiffener and an untapered connection plate with 3-in. extension could be used. Normal and acceptable quality of workmanship for connections involving gravity and wind loading in building construction would tolerate the following: 1. Runoff bars and backing bars may be left for beams with flange thicknesses greater than 2 in. (subject to tensile stress only) where they are welded to columns or used as tension members in a truss. 2. Welds need not be ground, except as required for nondestructive testing. 3. Connection plates that are made thicker or wider for control of tolerances, tensile stress and shear lag need not be ground or cut to a transition thickness or width to match the beam flange to which they connect. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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4. Connection plate edges may be sheared, or plasma- or gas-cut. 5. Intersections and transitions may be made without fillets or radii. 6. Flame-cut edges may have reasonable roughness and notches within AWS tolerances. If a structure is subjected to loads other than gravity and wind loads, such as seismic, dynamic or fatigue loading, more stringent control of the quality of fabrication and erection with regard to stress risers, notches, transition geometry, welding and testing may be necessary; refer to the AISC Seismic Provisions.

Fig. 12-14. Results of weak-axis FR moment connection ductility tests performed by Driscoll et al. (1983). AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Fig. 12-14. (continued) AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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FR Moment Connections Across Girder Supports Frequently, beam-to-girder-web connections must be made continuous across a girder-web support, as with continuous beams and with cantilevered beams at wall, roof-canopy or building lines. While the same principles of force transfer discussed previously for FR moment connections may be applied, the designer must carefully investigate the relative stiffness of the assembled members being subjected to moment or torsion and provide the fabricator and erector with reliable camber ordinates. Additionally, the design should still provide some means for final field adjustment to accommodate the accumulated tolerances of mill production, fabrication and erection; it is very desirable that the details of field connections provide for some adjustment during erection. Figure 12-15 illustrates several details that have been used in this type of connection and the designer may select the desirable components of one or more of the sketches to suit a particular application. Therefore, these components are discussed here as a top flange, bottom flange and web connection.

Top Flange Connection As shown in Figure 12-15a, the top flange connection may be directly welded to the top flange of the supporting girder. Figures 12-15b and 12-15c illustrate an independent splice plate that ties the two beams together by use of a longitudinal fillet weld or bolts. This tie plate does not require attachment to the girder flange, although it is sometimes so connected to control noise if the connection is subjected to vibration.

(a)

(b)

(c) Fig. 12-15. FR moment connections across girder-web supports. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Bottom Flange Connection When the bottom flanges deliver a compressive force only, the flange forces are frequently developed by directly welding these flanges to the girder web as illustrated in Figure 12-15a. Figure 12-15b illustrates the use of an angle or channel below the beam flange to provide for a horizontal fillet weld. The angle or channel should be wider than the beam flange to allow for downhand welding. Figure 12-15c is similar, but uses bolts instead of welds to develop the flange force.

Web Connection While a single-plate connection is shown in Figure 12-15a and unstiffened seated connections are shown in Figures 12-15b and 12-15c, any of the shear connections in Part 10 may be used. Note that the effect of eccentricity in the shear connection may be neglected.

FR CONNECTIONS WITH HSS HSS Through-Plate Flange-Plated FR Moment Connections If the required moment transfer to the column is larger than can be provided by the bolted base plate or cap plate, or if the HSS width is larger than that of the wide flange beam, a through-plate moment connection can be used as illustrated in Figure 12-16. It should be noted that through-plate connections are more difficult to erect than the continuous beam connected framing. When moment connections are made using through-plates such as is shown in Figure 12-16, the fabricator must allow adequate clearance between the through-plates and the structural section W-shape so as to allow for the combined effects of mill, fabrication and erection tolerances. The permissible mill tolerances for W-shape variations in depth and squareness are shown in Table 1-22. Shimming in the field during erection with conventional shims or finger shims is the most commonly used method to fill the gap between the W-shape and the through-plate. Specific design considerations for through-plate moment connections are as follows: 1. In Figures 12-16a and 12-16b, the column moment transfer into the joint is limited by the fillet weld of the HSS to the through-plates. If necessary, a partial-joint-penetration (PJP) groove weld can be used to improve the connection strength or a complete-jointpenetration (CJP) groove weld with backing bars can be used. 2. In Figure 12-16 an end plate (base plate) is employed to create a splice in the column. Bolt tension with prying on the base plate will determine its thickness and thus limit the moment that can be transferred to the upper HSS. 3. The cap plate, which is also a flange splice plate, should be at least the same thickness as the base plate so that moment transfer between the HSS columns need not rely on load transfer through the beam flanges. The cap plate may need to be thicker than the HSS base plate due to the combined effect of plate bending from the bolted base plate and plate tension or compression from the wide flange moment transfer. 4. The welding of the HSS to the cap and through-plate must be examined for both the HSS normal forces and the shear produced from the moment transfer from the W-shape. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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HSS Cut-out Plate Flange-Plated FR Moment Connections An alternative to interrupting the HSS for the cover or through-plate is to use a wider plate with a cut-out to slip around the HSS as illustrated in Figure 12-17. A shear plate can be placed on the front and rear of the HSS faces to provide simple connections for perpendicular beams. The cut-out plate can easily be extended on the near and far sides so that a moment splice is created about both horizontal axes through the joint. The perpendicular framing should ideally be of the same depth for this detail to work well or, in the case of the simple connections, the perpendicular beams could be shallower than the space between the horizontal plates. The cut-out plates are shown as shop-welded; however, they could be field-welded. For cut-out plate connections, the erection of the beams is more difficult than for continuous beam connections. The beams must be slipped between the two plates and

(a) Between column splices

(b) At column splice Fig. 12-16. Through-plate moment connection. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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against the single plate connection with shimming being required, unless the upper plate is field-welded in place.

Design Considerations for HSS Directly Welded FR Moment Connections It may be possible to accomplish the moment transfer to the HSS without having to use a WT splice plate, end-plates, or diaphragm plates. Significant moment transfer can be achieved by attaching the W-shape directly to the face of the HSS either by welding or by bolting. These connections are capable of developing the available flexural strength of the HSS. The available flexural strength of the W-shape, however, is seldom achieved because of the flexibility of the HSS wall.

Fig. 12-17. Exterior plate moment connection. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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The flexural strength for the welded W-shape is based on the strength of the respective flanges in tension and compression acting against the face of the HSS. This flange force can be considered to be the same as that of a plate with the dimensions of the flange. Several limit states exist for the plate length (flange width) oriented perpendicular to the length of the HSS (Packer and Henderson, 1997; Packer et al., 2010).

HSS Columns Above and Below Continuous Beams Field connection to the flanges of the beam and of continuous beams can be used at joints where there is an HSS above and below a continuous beam. This situation is illustrated in Figures 12-18 and 12-19. If the column load is not high, stiffener plates may be used to transfer the axial load across the beam as shown in Figure 12-18a. If the axial load is higher, it may be necessary to use a split HSS instead of plate stiffeners, as shown in Figure 12-18b. The width of the W-shape must be at least as wide as the HSS and should preferably be

(a)

(b)

Fig. 12-18. HSS columns spliced to continuous beams.

(a)

(b)

Fig. 12-19. Roof beam continuous over HSS column. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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wider than the HSS for this detail to be used as shown. It may be necessary to use a rectangular HSS column in order to fit the HSS base plate on the beam flange. The moment transfer to the HSS is limited by the strength of the four bolts, the W-shape flange thickness, and the base and cap plate thicknesses.

HSS Welded Tee Flange Connections If the primary moment transfer is from a wide flange to an HSS, rather than through the HSS to another wide flange, a number of other connection concepts will work well. One of these is to use structural tee sections to transfer the force from the flanges of the wide flange to the walls of the HSS as is illustrated in Figure 12-20. The tees should be long enough so that a flare bevel-groove (or single J-groove) weld with weld reinforcement can be used to connect the tee to the HSS. An alternative to using the tees to transfer the

.

Fig. 12-20. Tee splice plates to HSS column. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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beam shear would be to use a single plate connection, if a deep enough plate can be fitted between the flanges of the tees.

HSS Diaphragm Plate Connections If the moment delivered by the W-shape to the HSS cannot be transmitted by other means, then use of diaphragm plates that transfer the flange loads to the sides of the HSS is appropriate. This is illustrated in Figure 12-21. For this moment connection the limit states are those indicated for the cut-out plate connection plus a check of the weld transferring shear from the flange plate to the HSS wall.

Fig. 12-21. Diaphragm plate splice to exterior HSS column.

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Suggested Details for HSS to Wide-Flange Moment Connections The details shown in Figures 12-22 and 12-23 are suggested details only and are not intended to prohibit the use of other connection details.

Through-Plate Diaphragm

Interior Plate Diaphragm

HSS Column Reinforcement Fig. 12-22. Suggested detail.

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. Fig. 12-23. Suggested detail.

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PART 12 REFERENCES AISC (1977), Bridge Fatigue Guide Design and Details, American Institute of Steel Construction, Chicago, IL. Carter, C.J. (1999), Stiffening of Wide-Flange Columns at Moment Connections: Wind and Seismic Applications, Design Guide 13, AISC, Chicago, IL. Driscoll, G.C., Pourbohloul, A. and Wang, X. (1983), “Fracture of Moment Connections— Tests on Simulated Beam-to-Column Web Moment Connection Details,” Fritz Engineering Laboratory Report No. 469.7, Lehigh University, Bethlehem, PA. Driscoll, G.C. and Beedle, L.S. (1982), “Suggestions for Avoiding Beam-to-Column Web Connection Failures,” Engineering Journal, AISC, Vol. 19, No. 1, 1st Quarter, pp. 16–19, Chicago, IL. Hart, W.H. and Milek, W.A. (1965), “Splices in Plastically Designed Continuous Structures,” Engineering Journal, AISC, Vol. 2, No. 2, April, pp. 33–37, Chicago, IL. Huang, J.S., Chen, W.F. and Beedle, L.S. (1973), “Behavior and Design of Steel Beam-toColumn Moment Connections,” Bulletin 188, October, Welding Research Council, New York, NY. Lincoln Electric Company (1973), The Procedure Handbook of Arc Welding, Lincoln Electric Company, Cleveland, OH. Murray, T.M. and Sumner, E.A. (2003), Extended End-Plate Moment Connections— Seismic and Wind Applications, 2nd Ed., Design Guide 4, AISC, Chicago, IL. Murray, T.M. and Shoemaker, W.L. (2002), Flush and Extended Multiple-Row Moment End-Plate Connections, Design Guide 16, AISC and MBMA, Chicago, IL. Meng, R.L. and Murray, T.M. (1997), “Seismic Performance of Bolted End-Plate Moment Connection,” Proceedings, AISC National Steel Construction Conference, Chicago, IL, May 7–9, pages 30-1 to 30-14. Packer, J.A. and Henderson, J.E. (1997), Hollow Structural Section Connections and Trusses—A Design Guide, 2nd Ed., Canadian Institute of Steel Construction, Alliston, Ontario, Canada. Packer, J., Sherman, D. and Leece, M. (2010), Hollow Structural Section Connections, Design Guide 24, AISC, Chicago, IL.

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PART 13 DESIGN OF BRACING CONNECTIONS AND TRUSS CONNECTIONS

SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–2 BRACING CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–2 Diagonal Bracing Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–2 Force Transfer in Diagonal Bracing Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–3 The Uniform Force Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–3 Required Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–3 Special Case 1, Modified Working Point Location . . . . . . . . . . . . . . . . . . . . . . . 13–5 Special Case 2, Minimizing Shear in the Beam-to-Column Connection . . . . . . 13–7 Special Case 3, No Gusset-to-Column Web Connection . . . . . . . . . . . . . . . . . . . 13–7 Analysis of Existing Diagonal Bracing Connections . . . . . . . . . . . . . . . . . . . . . . . 13–10 Available Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–11 TRUSS CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–11 Members in Trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–11 Minimum Connection Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–12 Panel-Point Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–13 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–14 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–14 Support Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–14 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–15 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–16 Truss Chord Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–17 Design Considerations for HSS-to-HSS Truss Connections . . . . . . . . . . . . . . . . . 13–17 PART 13 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–18

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SCOPE The specification requirements and other design considerations summarized in this Part apply to the design of concentric bracing connections and truss connections.

BRACING CONNECTIONS Diagonal Bracing Members Diagonal bracing members can be rods, single angles, channels, double angles, tees, W-shapes or HSS as required by the loads. Slender diagonal bracing members are relatively flexible and, thus, vibration and sag may be considerations. In slender tension-only bracing composed of light angles, these problems can be minimized with “draw” or pretension created by shortening the fabricated length of the diagonal brace from the theoretical length, L, between member working points. In general, the following deductions will be sufficient to accomplish the required draw: no deduction for L ≤ 10 ft; deduct 1/16 in. for 10 ft < L ≤ 20 ft; deduct 1/8 in. for 20 ft < L ≤ 35 ft; and, deduct 3/ 16 in. for L > 35 ft. This approach is not applicable to heavier diagonal bracing members, since it is difficult to stretch these members; vibration and sag are not usually design considerations in heavier diagonal bracing members. In any diagonal bracing member, however, it is permissible to deduct an additional 1/32 in. when necessary to avoid dimensioning to thirty-seconds of an inch. When double-angle diagonal bracing members are separated, as at “sandwiched” end connections to gussets, intermittent connections should be provided if the unsupported length of the diagonal brace exceeds the limits specified in the User Note in AISC Specification Section D4 for tension members. For compression members, the provisions of AISC Specification Section E6 must be satisfied. Either bolted or welded stitch-fillers may be provided as stipulated in AISC Specification E6. Many fabricators prefer ring or rectangular bolted stitch-fillers when the angles require other punching, as at the end connections. In welded construction, a stitch-filler with protruding ends, as shown in Figure 13-1(a), is preferred because it is easy to fit and weld. The short stitch-filler shown in Figure 13-1(b) is used if a smooth appearance is desired. When a full-length filler is provided, as in corrosive environments, the maximum spacing of stitch bolts should be as specified in AISC Specification Section J3.5. Alternatively, the edges of the filler may be seal welded.

a) Protruding

b) Short

Fig. 13-1. Welded stitch-fillers.

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Force Transfer in Diagonal Bracing Connections There has been some discussion as to which of several available analysis methods provides the best means for the safe and economical design and analysis of diagonal bracing connections. To better understand the technical issues, starting in 1981, AISC sponsored extensive computer studies of this connection by Richard (1986). Associated with Richard’s work, full-scale tests were performed by Bjorhovde and Chakrabarti (1985), Gross and Cheok (1988), and Gross (1990). Also, AISC and ASCE formed a task group to recommend a design method for this connection. In 1990, this task group recommended three methods for further study; refer to Appendix A of Thornton (1991). Using the results of the aforementioned full scale tests, Thornton (1991) showed that these three methods yield safe designs, and that of the three methods, the Uniform Force Method [see model 3 of Thornton (1991)] best predicts both the available strength and critical limit state of the connection. Furthermore, Thornton (1992) showed that the Uniform Force Method yields the most economical design through comparison of actual designs by the different methods and through consideration of the efficiency of force transmission. For the above reasons, and also because it is the most versatile method, the Uniform Force Method has been adopted for use in this manual.

The Uniform Force Method The essence of the Uniform Force Method is to select the geometry of the connection so that moments do not exist on the three connection interfaces; i.e., gusset-to-beam, gusset-to-column, and beam-to-column. In the absence of moment, these connections may then be designed for shear and/or tension only, hence the origin of the name Uniform Force Method.

Required Strength With the control points (c.p.) as illustrated in Figure 13-2 and the working point (w.p.) chosen at the intersection of the centerlines of the beam, column and diagonal brace as shown in Figure 13-2(a), four geometric parameters eb, ec, α and β can be identified, where eb = one-half the depth of the beam, in. ec = one-half the depth of the column, in. Note that, for a column web support, ec ≈ 0. α = distance from the face of the column flange or web to the centroid of the gusset-tobeam connection, in. β = distance from the face of the beam flange to the centroid of the gusset-to-column connection, in. For the force distribution shown in the free-body diagrams of Figures 13-2(b), 13-2(c) and 13-2(d) to remain free of moments on the connection interfaces, the following expression must be satisfied: α − β tanθ = eb tanθ − ec

(13-1)

Since the variables on the right of the equal sign (eb, ec and θ) are all defined by the members being connected and the geometry of the structure, the designer may select values of α and β for which the equation is true, thereby locating the centroids of the gusset-to-beam and gusset-to-column connections.

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(a) Diagonal bracing connection and external forces

(b) Gusset free-body diagram

(c) Column free-body diagram

(d) Beam free-body diagram

Rb = Rub or Rab, required end reaction of the beam Rc = Ruc or Rac, required column axial load above the connection Ab = Aub or Aab, required transverse force from adjacent bay H = horizontal component of the required axial force Hb = Hub or Hab, required shear force on the gusset-to-beam connection Hc = Huc or Hac, required axial force on the gusset-to-column connection Vb = Vub or Vab, required axial force on the gusset-to-beam connection Vc = Vuc or Vac, required shear force on the gusset-to-column connection P = Pu or Pa, required axial force V = vertical component of the required axial force Fig. 13-2. Force transfer by the Uniform Force Method, work point (w.p.) and control points (c.p.) as indicated. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Once α and β have been determined, the required axial and shear forces for which these connections must be designed can be determined from the following equations: β Vc = ᎏ rP

(13-2)

ec Hc = ᎏ r P

(13-3)

eb Vb = ᎏ r P

(13-4)

α Hb = ᎏ rP

(13-5)

where r = (α + ec )2 + (β + eb )2

(13-6)

The gusset-to-beam connection must be designed for the required shear force, Hb, and the required axial force, Vb, the gusset-to-column connection must be designed for the required shear force, Vc , and the required axial force, Hc, and the beam-to-column connection must be designed for the required shear Rb – Vb and the required axial force Ab ± (H − Hb) Note that while the axial force, Pu or Pa , is shown as a tensile force, it may also be a compressive force; were this the case, the signs of the resulting gusset forces would change.

Special Case 1, Modified Working Point Location As illustrated in Figure 13-3(a), the working point in Special Case 1 of the Uniform Force Method is chosen at the corner of the gusset; this may be done to simplify layout or for a column web connection. With this assumption, the terms in the gusset force equations involving eb and ec drop out and the interface forces, as shown in Figures 13-3(b), 13-3(c) and 13-3(d), are: Vc = P cosθ = V

(13-7)

Vb = 0

(13-8)

Hb = P sinθ = H

(13-9)

Hc = 0

(13-10)

The gusset-to-beam connection must be designed for the required shear force, Hb, and the gusset-to-column connection must be designed for the required shear force, Vc. Note, however, that the change in working point requires that the beam be designed for the required moment, Mb, where Mb = Hbeb

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(a) Diagonal bracing connection

(b) Gusset free-body diagram

(c) Column free-body diagram

(d) Beam free-body diagram

Rb = Rub or Rab, required end reaction of the beam Rc = Ruc or Rac, required column axial load above the connection Ab = Aub or Aab, required transverse force from adjacent bay H = horizontal component of the required axial force Hb = Hub or Hab, required shear force on the gusset-to-beam connection Vc = Vuc or Vac, required shear force on the gusset-to-column connection P = Pu or Pa, required axial force V = vertical component of the required axial force Fig. 13-3. Force transfer, Uniform Force Method special case 1. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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and the column must be designed for the required moment, Mc. For an intermediate floor, this is determined as: Mc =

Vcec 2

(13-12)

An example demonstrating this eccentric special case is presented in AISC (1984). This eccentric case was endorsed by the AISC/ASCE task group (Thornton, 1991) as a reduction of the three recommended methods when the work point is located at the gusset corner. While calculations are somewhat simplified, it should be noted that resolution of the required force, P, into the shears, Vc and Hb , may not result in the most economical connection.

Special Case 2, Minimizing Shear in the Beam-to-Column Connection If the brace force, as illustrated in Figure 13-4(a), were compressive instead of tensile and the required beam reaction, R b , were high, the addition of the extra shear force, Vb , into the beam might exceed the available strength of the beam and require doubler plates or a haunched connection. Alternatively, the vertical force in the gusset-to-beam connection, Vb , can be limited in a manner which is somewhat analogous to using the gusset itself as a haunch. As illustrated in Figure 13-4(b), assume that Vb is reduced by an arbitrary amount, ΔVb. By statics, the vertical force at the gusset-to-column interface will be increased to Vc + ΔVb, and a moment Mb will result on the gusset-to-beam connection, where Mb = (ΔVb)α

(13-13)

If ΔVb is taken equal to Vb, none of the vertical component of the brace force is transmitted to the beam; the resulting procedure is that presented by AISC (1984) for concentric gravity axes, extended to connections to column flanges. This method was also recommended by the AISC/ASCE task group (Thornton, 1991). Design by this method may be uneconomical. It is very punishing to the gusset and beam because of the moment, Mb , induced on the gusset-to-beam connection. This moment will require a larger connection and a thicker gusset. Additionally, the limit state of local web yielding may limit the strength of the beam. This special case interrupts the natural flow of forces assumed in the Uniform Force Method and thus is best used when the beam-tocolumn interface is already highly loaded, independently of the brace, by a high shear, R b, in the beam-to-column connection.

Special Case 3, No Gusset-to-Column Web Connection When the connection is to a column web and the brace is shallow (as for large θ) or the beam is deep, it may be more economical to eliminate the gusset-to-column connection entirely and connect the gusset to the beam only. The Uniform Force Method can be applied to this situation by setting β and ec equal to zero as illustrated in Figure 13-5. Since there is to be no gusset-to-column connection, Vc and Hc also equal zero. Thus, Vb = V and Hb = H. – = α = e tanθ, there is no moment on the gusset-to-beam interface and the gusset-toIf α b beam connection can be designed for the required shear force, Hb, and the required axial – ≠ α = e tanθ, the gusset-to-beam interface must be designed for the moment, force, Vb. If α b Mb, in addition to Hb and Vb, where – M = V (α − α) (13-14) b

b

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(a) Diagonal bracing connection

(b) Gusset free-body diagram

(c) Column free-body diagram

(d) Beam free-body diagram

Rb = Rub or Rua, required end reaction of the beam Rc = Ruc or Rac, required column axial load above the connection Ab = Aub or Aab, required transverse force from adjacent bay H = horizontal component of the required axial force Hb = Hub or Hab, required shear force on the gusset-to-beam connection Hc = Huc or Hac, required axial force on the gusset-to-column connection Vb = Vub or Vab, required axial force on the gusset-to-beam connection Vc = Vuc or Vac, required shear force on the gusset-to-column connection P = Pu or Pa, required axial force V = vertical component of the required axial force Fig. 13-4. Force transfer, Uniform Force Method special case 2. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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(a) Diagonal bracing connection

(b) Gusset free-body diagram

(c) Column free-body diagram

(d) Beam free-body diagram

Rb = Rub or Rua, required end reaction of the beam Rc = Ruc or Rac, required column axial load above the connection Ab = Aub or Aab, required transverse force from adjacent bay H = horizontal component of the required axial force Hb = Hub or Hab, required shear force on the gusset-to-beam connection Vb = Vub or Vab, required axial force on the gusset-to-beam connection P = Pu or Pa, required axial force V = vertical component of the required axial force Fig. 13-5. Force transfer, Uniform Force Method special case 3.

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The beam-to-column connection must be designed for the required shear force, Rb + Vb. Note that, since the connection is to a column web, ec is zero and hence Hc is also zero. For a connection to a column flange, if the gusset-to-column-flange connection is eliminated, the beam-to-column connection must be a moment connection designed for the moment, Vec, in addition to the shear, V. Thus, uniform forces on all interfaces are no longer possible.

Analysis of Existing Diagonal Bracing Connections A combination of α and β which provides for no moments on the three interfaces can usually be achieved when a connection is being designed. However, when analyzing an existing connection or when other constraints exist on gusset dimensions, the values of α and β may not satisfy the basic relationship α − β tanθ = eb tanθ − ec

(13-1)

When this happens, uniform interface forces will not satisfy equilibrium and moments will exist on one or both gusset edges or at the beam-to-column interface. To illustrate this point, consider an existing design where the actual centroids of the gusset– – and β, to-beam and gusset-to-column connections are at α respectively. If the connection at one edge of the gusset is more rigid than the other, it is logical to assume that the more rigid edge takes all of the moment necessary for equilibrium. For instance, the gusset of Figure 13-2 is shown welded to the beam and bolted with double angles to the column. For this configuration, the gusset-to-beam connection will be much more rigid than the gusset-tocolumn connection. Take α and β as the ideal centroids of the gusset-to-beam and gusset-to-column connec– tions, respectively. Setting β = β, the α required for no moment on the gusset-to-beam connection may be calculated as – α = K + β tanθ (13-15) where K = eb tanθ − ec – If α ≠ α, a moment, Mb , will exist on the gusset-to-beam connection where – M = V (α − α) b

b

(13-16)

(13-17)

Conversely, suppose the gusset-to-column connection were judged to be more rigid. Setting – the β required for no moment on the gusset-to-column connection may be calculated α = α, as –−K α tanθ

β= ᎏ – If β ≠ β, a moment, Mc, will exist on the gusset-to-column connection where – Mc = Hc(β − β)

(13-18)

(13-19)

If both connections were equally rigid and no obvious allocation of moment could be made, – and β − β– by minthe moment could be distributed based on minimized eccentricities α − α imizing the objective function, ξ, where

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2

2

⎛ α −α⎞ ⎛ β−β⎞ ξ=⎜ ⎟ − λ α − βtanθ − K ⎟ +⎜ ⎝ α ⎠ ⎝ β ⎠

(

)

(13-20)

In the preceding equation, λ is a Lagrange multiplier. The values of α and β that minimize ξ are ⎛ α⎞ K ′tanθ + K ⎜ ⎟ ⎝ β⎠ α= D

2

(13-21)

and β=

K ′ − K tan θ D

(13-22)

where ⎛ α⎞ K ′ = α ⎜ tan θ + ⎟ β⎠ ⎝ ⎛ α⎞ D = tan 2 θ + ⎜ ⎟ ⎝ β⎠

(13-23)

2

(13-24)

Available Strength The available strength of a diagonal bracing connection is determined from the applicable limit states for the bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). In all cases, the available strength, φRn or Rn/Ω, must equal or exceed the required strength, Ru or Ra. Note that when the gusset is directly welded to the beam or column, the connection should be designed for the larger of the peak stress and 1.25 times the average stress, but the weld size need not be larger than that required to develop the strength of the gusset. This 25% increase is recommended to provide ductility to allow adequate force redistribution in the weld group (Hewitt and Thornton, 2004).

TRUSS CONNECTIONS Members in Trusses For light loads, trusses are commonly composed of tees for the top and bottom chords with single-angle or double-angle web members. In welded construction, the single-angle and double-angle web members may, in many cases, be welded to the stem of the tee, thus, eliminating the need for gussets. When single-angle web members are used, all web members should be placed on the same side of the chord; staggering the web members causes a torque on the chord, as illustrated in Figure 13-6. Also see “Design Considerations for HSS-to-HSS Truss Connections” at the end of Part 13.

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Double-angle truss members are usually designed to act as a unit. When unequal-leg angles are used, long legs are normally assembled back-to-back. A simple notation for the angle assembly is LLBB (long legs back-to-back) and SLBB (short legs back-to-back). Alternatively, the notation might be graphical in nature as and . For large loads, W-shapes may be used with the web vertical and gussets welded to the flange for the truss connections. Web members may be single angles or double angles, although W-shapes are sometimes used for both chord and web members as shown in Figure 13-7. Heavy shapes in trusses must meet the design and fabrication restrictions and special requirements in AISC Specification Sections A3.1c and A3.1d. With member orientation as shown for the field-welded truss joint in Figure 13-7(a), connections usually are made by groove welding flanges to flanges and fillet welding webs directly or indirectly by the use of gussets. Fit-up of joints in this type of construction are very sensitive to dimensional variations in the rolled shapes; fabricators sometimes prefer to use built-up shapes in these cases. The web connection plate in Figure 13-7(a) is a typical detail. While the diagonal member could theoretically be cut so that the diagonal web would be extended into the web of the chord for a direct connection, such a detail is difficult to fabricate. Additionally, welding access becomes very limited; note the obvious difficulty of welding the gusset or diagonal directly to the chord web. As illustrated, this weld is usually omitted. When stiffeners and doubler plates are required for concentrated flange forces, the designer should consider selecting a heavier section to eliminate the need for stiffening. Although this will increase the material cost of the member, the heavier section will likely provide a more economical solution due to the reduction in labor cost associated with the elimination of stiffening (Ricker, 1992; Thornton, 1992).

Minimum Connection Strength In the absence of defined design loads, a minimum required strength of 10 kips for LRFD or 6 kips for ASD should be considered, as noted in AISC Specification Commentary

Fig. 13-6. Staggered web members result in a torque on the truss chord. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Section J1.1. For smaller elements, a required strength more appropriate to the size and use of the part should be used. Additionally, when trusses are shop-assembled or fieldassembled on the ground for subsequent erection, consideration should be given to loads induced during handling, shipping and erection.

Panel-Point Connections A panel-point connection connects diagonal and/or vertical web members to the chord member of a truss. These web members deliver axial forces, tensile or compressive, to the truss chord. In bolted construction, a gusset is usually required because of bolt spacing and edge distance requirements. In welded construction, it is sometimes possible to eliminate the need for a gusset.

(a) Shop and field welding

Note: Check vertical and chord for reinforcing requirements

(b) Shop welding Fig. 13-7. Truss panel-point connections for W-shape truss members. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Design Checks The available strength of a panel-point connection is determined from the applicable limit states for the bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). In all cases, the available strength, φRn or Rn/Ω, must exceed the required strength, Ru or Ra. In the panel-point connection of Figure 13-8, the neutral axes of the vertical and diagonal truss members intersect on the neutral axis of the truss chord. As a result, the forces in all members of the truss are axial. It is common practice, however, to modify working lines slightly from the gravity axes to establish repetitive panels and avoid fractional dimensions less than 1/8 in. or to accommodate a larger panel-point connection or a connection for bottom-chord lateral bracing, a purlin, or a sway-frame. This eccentricity and the resulting moment should be considered in the design of the truss chord. In contrast, for the design of the truss web members, AISC Specification Section J1.7 permits that the center of gravity of the end connection of a statically loaded truss member need not coincide with the gravity axis of the connected member. This is because tests have shown that there is no appreciable difference in the available strength between balanced and unbalanced connections subjected to static loading. Accordingly, the truss web members and their end connections may be designed for the axial load, neglecting the effect of this minor eccentricity.

Shop and Field Practices In bolted construction, it is convenient to use standard gage lines of the angles as truss working lines; where wider angles with two gage lines are used, the gage line nearest the heel of the angle is the one which is substituted for the gravity axis. To provide for stiffness in the finished truss, the web members of the truss are extended to near the edge of the fillet of the tee (k-distance). If welded, the required welds are then applied along the heel and toe of each angle, beginning at their ends rather than at the edge of the tee stem.

Support Connections A truss support connection connects the ends of trusses to supporting members.

Fig. 13-8. Truss panel-point connection. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Design Checks The available strength of a support connection is determined from the applicable limit states for the bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). Additionally, truss support connections produce tensile or compressive single concentrated forces at the beam end; the limit states of the available flange strength in local bending and the limit states of the available web strength in local yielding, crippling, and compression buckling may have to be checked. In all cases, the available strength, φRn or Rn/Ω, must exceed the required strength, Ru or Ra. At the end of a truss supported by a column, all member axes may not intersect at a common point. When this is the case, an eccentricity results. Typically, it is the neutral axis of the column that does not meet at the working point. If trusses with similar reactions line up on opposite sides of the column, consideration of eccentricity would not be required since any moment would be transferred through the column and into the other truss. However, if there is little or no load on the opposite side of the column, the resulting eccentricity must be considered. In Figure 13-9, the truss chord and diagonal intersect at a common working point on the face of the column flange. In this detail, there is no eccentricity in the gusset, gusset-tocolumn connection, truss chord, or diagonal. However, the column must be designed for the moment due to the eccentricity of the truss reaction from the neutral axis of the column. For the truss support connection illustrated in Figure 13-10, this eccentricity results in a moment. Assuming the connection between the members is adequate, joint rotation is resisted by the combined flexural strength of the column, the truss top chord, and the truss diagonal. However, the distribution of moment between these members will be proportional to the stiffness of the members. Thus, when the stiffness of the column is much greater than the stiffness of the other elements of the truss support connection, it is good practice to design the column and gusset-to-column connection for the full eccentricity.

Fig. 13-9. Truss support connection, working point (w.p.) on column face. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Due to its importance, the truss support connection is frequently shown in detail on the design drawing.

Shop and Field Practices When a truss is erected in place and loaded, truss members in tension will lengthen and truss members in compression will shorten. At the support connection, this may cause the tension chord of a “square-ended” truss to encroach on its connection to the supporting column. When the connection is shop-attached to the truss, erection clearance must be provided with shims to fill out whatever space remains after the truss is erected and loaded. In field erected connections, however, provision must be made for the necessary adjustment in the connection. When the tension chord delivers no calculated force to the connection, adjustment can usually be provided with slotted holes. For short spans with relatively light loads, the comparatively small deflections can be absorbed by the normal hole clearances provided for bolted construction. Slightly greater misalignment can be corrected in the field by reaming the holes. If appreciable deflection is expected, the connection may be welded. Alternatively, bolt holes may be field-drilled, but this is an expensive operation which should be avoided if at all possible. An approximation of the elongation, Δ, can be determined as Δ=

Pl AE

(13-25)

Fig. 13-10. Truss-support connection, working point (w.p.) at column centerline.

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where Δ = elongation in inches P = axial force due to service loads, kips A = gross area of the truss chord, in.2 l = length, in.2 The total change in length of the truss chord is ΣΔi, the sum of the changes in the lengths of the individual panel segments of the truss chord. The misalignment at each support connection of the tension chord is one-half the total elongation.

Truss Chord Splices Truss chord splices are expensive to fabricate and should be avoided whenever possible. In general, chord splices in ordinary building trusses are confined to cases where: 1. 2. 3. 4.

the finished truss is too large to be shipped in one piece; the truss chord exceeds the available material length; the reduction in member size of the chord justifies the added cost of a splice; or a sharp change in direction occurs in the working line of the chord and bending does not provide a satisfactory alternative.

Splices at truss chord ends that are finished to bear should be designed in accordance with AISC Specification Section J1.4.

Design Considerations for HSS-to-HSS Truss Connections HSS member sizes are often critical in connection design. Connection design should be performed during main member selection as the connection limit states may force an increase in the member wall thickness over the main member design thickness. At initial design, Packer, et al. (2010b) recommends that chords should have thick walls rather than thin walls; web members should have thin walls rather than thick walls; web members should be wide relative to the chord members, but still able to sit on the “flat” face of the chord section if possible; and gap connections (for K and N situations) are preferred to overlap connections because the members are easier to prepare, fit and weld. The connection types covered in Chapter K of the AISC Specification and in AISC Design Guide 24, Hollow Structural Section Connections (Packer et al., 2010a), are only some of the potential configurations of HSS-to-HSS connections. For reinforced connections and connections not covered in these publications, refer to CIDECT Design Guide 3, Design Guide for Rectangular Hollow Section (RHS) Joints under Predominantly Static Loading (Packer et al., 2010b).

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PART 13 REFERENCES AISC (1984), Engineering for Steel Construction, pp. 7.55–7.62, AISC, Chicago, IL. Bjorhovde, R. and Chakrabarti, S.K. (1985), “Tests of Full-Size Gusset Plate Connections,” Journal of Structural Engineering, Vol. 111, No. 3, pp. 667–684, ASCE, New York, NY. Gross, J.L. and Cheok, G. (1988), Experimental Study of Gusseted Connections for Laterally Braced Steel Buildings, National Institute of Standards and Technology Report NISTIR 88-3849, NIST, Gaithersburg, MD. Gross, J.L. (1990), “Experimental Study of Gusseted Connections,” Engineering Journal, Vol. 27, No. 3, 3rd Quarter, pp. 89–97, AISC, Chicago, IL. Hewitt, C.M. and Thornton, W.A. (2004), “Rationale Behind and Proper Application of the Ductility Factor for Bracing Connections Subjected to Shear and Transverse Loading,” Engineering Journal, Vol. 41, No. 1, 1st Quarter, pp. 3–6, AISC, Chicago, IL.

Packer, J., Sherman, D. and Leece, M. (2010a), Hollow Structural Section Connections, Design Guide 24, AISC, Chicago, IL. Packer, J.A., Wardenier, J., Zhao, X.-L., van der Vegte, G.J. and Y. Kurobane (2010b), Design Guide for Rectangular Hollow Section (RHS) Joints Under Predominantly Static Loading, Design Guide 3, CIDECT, 2nd Ed., LSS Verlag, Kőln, Germany. Richard, R.M. (1986), “Analysis of Large Bracing Connection Designs for Heavy Construction,” National Steel Construction Conference Proceedings, pp. 31.1–31.24, AISC, Chicago, IL. Ricker, D.T. (1992), “Value Engineering and Steel Economy,” Modern Steel Construction, Vol. 32, No. 2 February, AISC, Chicago, IL. Thornton, W.A. (1991), “On the Analysis and Design of Bracing Connections,” National Steel Construction Conference Proceedings, pp. 26.1–26.33, AISC, Chicago, IL. Thornton, W.A. (1992), “Designing for Cost Efficient Fabrication and Construction,” Constructional Steel Design—An International Guide, Chapter 7, pp. 845–854, Elsevier, London, UK.

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PART 14 DESIGN OF BEAM BEARING PLATES, COLUMN BASE PLATES, ANCHOR RODS AND COLUMN SPLICES

SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–3 BEAM BEARING PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–3 Force Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–3 Recommended Bearing Plate Dimensions and Thickness . . . . . . . . . . . . . . . . . . . . 14–3 Available Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–4 COLUMN BASE PLATES FOR AXIAL COMPRESSION . . . . . . . . . . . . . . . . . . . . . 14–4 Force Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–4 Recommended Base Plate Dimensions and Thickness . . . . . . . . . . . . . . . . . . . . . . . 14–5 Available Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–6 Finishing Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–6 Holes for Anchor Rods and Grouting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–6 Grouting and Leveling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–6 COLUMN BASE PLATES FOR AXIAL TENSION, SHEAR OR MOMENT . . . . . . 14–8 ANCHOR RODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–9 Minimum Edge Distance and Embedment Length . . . . . . . . . . . . . . . . . . . . . . . . . 14–10 Washer Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–10 Hooked Anchor Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–10 Headed or Threaded and Nutted Anchor Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–10 Anchor Rod Nut Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–10 COLUMN SPLICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–12 Fit-Up of Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–12 Lifting Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–12 Column Alignment and Stability During Erection . . . . . . . . . . . . . . . . . . . . . . . . . 14–14 Force Transfer in Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–14 Flange-Plated Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–16 Directly Welded Flange Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–17 Butt-Plated Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–18

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DESIGN CONSIDERATIONS FOR HSS CAP PLATES . . . . . . . . . . . . . . . . . . . . . . 14–18 Flexural Strength of the Cap Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–18 Compression Yielding and Crippling of the HSS Wall . . . . . . . . . . . . . . . . . . . . . 14–19 PART 14 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–20 DESIGN TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–21 Table 14-1. Finish Allowances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–21 Table 14-2. Recommended Maximum Sizes for Anchor-Rod Holes in Base Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–21 Table 14-3. Typical Column Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–22

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SCOPE The specification requirements and other design considerations summarized in this Part apply to the design of beam bearing plates, column base plates, anchor rods and column splices. For complete coverage of column base plate connections, see AISC Design Guide 1, Base Plate and Anchor Rod Design (Fisher and Kloiber, 2006).

BEAM BEARING PLATES A beam bearing plate is made with a plate as illustrated in Figure 14-1.

Force Transfer The required strength (beam end reaction), Ru or Ra , is distributed from the beam bottom flange to the bearing plate over an area equal to lb × 2k, where lb is the bearing length (length of contact between the beam bottom flange and the bearing plate), in. The bearing plate is then assumed to distribute the beam end reaction to the concrete or masonry as a uniform bearing pressure by cantilevered bending of the plate. The bearing plate cantilever dimension is taken as n=

B −k 2

(14-1)

where B is the bearing plate width, in. In the rare case where a bearing plate is not required, the beam end reaction, Ru or Ra , is assumed to be uniformly distributed from the beam bottom flange to the concrete or masonry as a uniform bearing pressure by cantilevered bending of the beam flanges. The beam-flange cantilever dimension is calculated as for a bearing plate, but using the beam flange width, bf , in place of B.

Recommended Bearing Plate Dimensions and Thickness The length of bearing, lb , may be established by available wall thickness, clearance requirements, or by the minimum requirements based on local web yielding or web crippling. The

Fig. 14-1. Beam bearing plate variables. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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selected dimensions of the bearing plate, B and lb , should preferably be in full inches. Bearing plate thickness should be specified in multiples of 1/8 in. up to 11/4-in. thickness and in multiples of 1/4 in. thereafter.

Available Strength The available strength of a beam bearing plate is determined from the applicable limit states for connecting elements (see Part 9). In all cases, the available strength, φRn or Rn/Ω, must exceed the required strength, Ru or Ra. The stability of the beam end must also be addressed as discussed in “Stability Bracing” in Part 2.

COLUMN BASE PLATES FOR AXIAL COMPRESSION A column base plate is made with a plate and a minimum of four anchor rods as illustrated in Figure 14-2. The base plate is often attached to the bottom of the column in the shop. Large heavy columns can be difficult to handle and set plumb with the base plate attached in the shop. When the column is over a certain weight, it may be better to detail the base plate loose for setting and leveling before the column is set. The weight where loose base plates should be considered varies by field practice but it should be considered where the assembly weighs more than 4 tons.

Force Transfer In Figure 14-3, the required strength (column axial force), Pu or Pa, is distributed from the column end to the column base plate in direct bearing. The column base plate is then assumed to distribute the column axial force to the concrete or masonry as a uniform bearing pressure by cantilevered bending of the plate. The critical base plate cantilever dimension, l, is determined as the larger of m, n and λn′ where

Fig. 14-2. Typical column base for axial compressive loads.

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m=

N − 0.95 d 2

(14-2)

n=

B − 0.8 b f 2

(14-3)

n′ = λ=

db f

(14-4)

4

2 X ≤1 1+ 1− X

LRFD

(14-5)

ASD

⎛ 4 db ⎞ P f u X =⎜ ⎟ ⎜⎝ ( d + b f )2 ⎟⎠ φc Pp

(14-6a)

⎛ 4 db ⎞ Ω P f c a X =⎜ ⎟ ⎜⎝ ( d + b f )2 ⎟⎠ Pp

(14-6b)

Note that, because both the term in parentheses and the ratio of the required strength, Pu or Pa, to the available strength, φcPp or Pp /Ωc, are always less than or equal to 1, the value of X will always be less than or equal to 1. Note also that λ can always be taken conservatively as 1. For further information, see Thornton (1990a), Thornton (1990b), and AISC Design Guide 1, Base Plate and Anchor Rod Design (Fisher and Kloiber, 2006).

Recommended Base Plate Dimensions and Thickness The selected dimensions of the base plate, B and N, should preferably be in full inches. Base plate thickness should be specified in multiples of 1/8 in. up to 11/4-in. thickness and in multiples of 1/4 in. thereafter.

Fig. 14-3. Column base plate design variables.

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Available Strength The available strength of an axially loaded column base plate is determined from the applicable limit states for connecting elements (see Part 9). From Thornton (1990a), the minimum base plate thickness can be calculated as LRFD tmin = l

ASD

2 Pu 0.9 Fy BN

(14-7a)

tmin = l

3.33Pa Fy BN

(14-7b)

The length, l, the critical base plate cantilever dimension, is determined as the larger of m, n and λn′. In all cases, the available strength, φRn or Rn/Ω, must exceed the required strength, Ru or Ra.

Finishing Requirements Base plate finishing requirements are given in AISC Specification Section M2.8. When finishing is required, the plate material must be ordered thicker than the specified base plate thickness to allow for the material removed in finishing. Finishing allowances are given in Table 14-1 per ASTM A6 flatness tolerances for steel base plates with Fu equal to or less than 60 ksi based upon the width, thickness, and whether one or both sides are to be finished. Finishing allowances for steel base plates with Fu greater than 60 ksi should be increased by 50%. The criteria for fit-up of column splices given in AISC Specification Section M4.4 are also applicable to column base plates.

Holes for Anchor Rods and Grouting Recommended maximum anchor rod hole sizes are given in Table 14-2. These hole sizes will accommodate reasonable misalignments in the setting of the anchor rods and allow better adjustment of the column base to the correct centerlines. It is normally unnecessary to deduct the area of holes when determining the required base plate area. An adequate washer should be provided for each anchor rod. When base plates with large areas are used, at least one grout hole should be provided near the center of the base plate through which grout may be placed. This will provide for a more even distribution of the grout and also prevent air pockets. Note that a grout hole may not be required when the grout is dry-packed. Grout holes do not require the same accuracy for size and location as anchor rod holes. Holes in base plates for anchor rods and grouting often must be flame-cut, because drill sizes and punching capabilities may be limited to smaller diameters. Flame-cut holes may have a slight taper and should be inspected to assure proper clearances for anchor rods.

Grouting and Leveling High-strength, non-shrink grout is placed between the column base plate and the supporting foundation. When base plates are shipped attached to the column, three methods of column support are: AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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1. The use of leveling nuts and, in some cases, washers on the anchor rods beneath the base plate, as illustrated in Figure 14-4. 2. The use of shim stacks between the base plate and the supporting foundation. 3. The use of a steel leveling plate (normally 1/4 in. thick), set to elevation and grouted prior to the setting of the column. The leveling plate should meet the flatness tolerances specified in ASTM A6. It may be larger than the base plate to accommodate anchor rod placement tolerances and can be used as a setting template for the anchor rods. For further information on grouting and leveling of column base plates, see AISC Design Guide 10, Erection Bracing of Low-Rise Structural Steel Frames (Fisher and West, 1997). When base plates are shipped loose, the base plates are usually grouted after the base plate has been aligned and leveled with one of the preceding methods. For heavy loose base plates, three-point leveling bolts, illustrated in Figure 14-5, are commonly used. These threaded attachments may consist of a nut or an angle and nut welded to the base plate. Leveling bolts must be of sufficient length to compensate for the space provided for grouting. Rounding the point of the leveling bolt will prevent it from “walking” or moving laterally as it is turned. Additionally, a small steel pad under the point reduces friction and prevents damage to the concrete. Heavy loose base plates should be provided with some means of handling at the erection site. Lifting holes can be provided in the vertical legs of shop-attached connection angles. Lifting lugs can also be used and can remain in place after erection, unless they create an interference or removal is required in the contract documents. Leveling bolts or nuts should not be used to support the column during erection. If grouting is delayed until after steel erection, the base plate must be shimmed to properly distribute loads to the foundation without overstressing either the base plate or the concrete. This difficulty of supporting columns while leveling and grouting their bases makes it advisable that footings be finished to near the proper elevation (Ricker, 1989). The top of the rough footing should be set approximately 1 to 2 in. below the bottom of the base plate to provide for adjustment. Alternatively, an angle frame as illustrated in Figure 14-6 could be constructed to the proper elevation and filled with grout prior to erection.

Fig. 14-4. Leveling nuts and washers. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COLUMN BASE PLATES FOR AXIAL TENSION, SHEAR OR MOMENT For anchor rod diameters not greater than 11/4 in., angles bolted or welded to the column as shown in Figure 14-7(a) are generally adequate to transfer uplift forces resulting from axial loads and moments. When greater resistance is required, stiffeners may be used with horizontal plates or angles as illustrated in Figure 14-7(b). These stiffeners are not usually considered to be part of the column area in bearing on the base plate. The angles preferably should be set back from the column end about 1/8 in. Stiffeners preferably should be set back about 1 in. from the base plate to eliminate a pocket that might prevent drainage and, thus, protect the column and column base plate from corrosion.

Fig. 14-5. Three-point leveling.

Fig. 14-6. Angle-frame leveling. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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For further information, see AISC Design Guide 1, Base Plate and Anchor Rod Design (Fisher and Kloiber, 2006).

ANCHOR RODS Cast-in-place anchor rods, illustrated in Figure 14-8, are generally made from unheaded rod material or headed bolt material. Drilled-in (post-set) anchors can be used for corrective work or in new work as determined by the owner’s designated representative for design and as permitted in the applicable building code. The design of post-set anchors is governed by manufacturers’ specifications; see also ACI 349 Appendix D (ACI, 2006). Post-set anchors that rely upon torque or tension to develop anchorage by wedging action should not be used

(a)

(b)

Fig. 14-7. Typical column bases for uplift.

(a) Hooked

(b) Headed

(c) Threaded with nut

Fig. 14-8. Cast-in-place anchor rods. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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unless the stability of the column during erection is provided by means other than the postset anchors.

Minimum Edge Distance and Embedment Length In general, minimum edge distances, embedment lengths, and the design of anchorages into concrete are covered by ACI 318 (ACI, 2008). These provisions include methods to account for edge distance and group action, as does ACI 349. AISC Design Guides 1, 7 and 10 provide additional material on the design of anchor rods in concrete (Fisher and Kloiber, 2006; Fisher, 2004; Fisher and West, 1997). In addition to providing the recommended minimum embedment length, anchor rods must extend a distance above the foundation that is sufficient to permit adequate thread engagement of the nut. Adequate thread engagement for anchor rods is identical to the condition described in the RCSC Specification as adequate for steel-to-steel structural joints using high-strength bolts: having the end of the (anchor rod) flush with or outside the face of the nut.

Washer Requirements Because base plates typically have holes larger than oversized holes to allow for tolerances on the location of the anchor rod, washers are usually furnished from ASTM A36 steel plate. They may be round, square or rectangular, and generally have holes that are 1/16 in. larger than the anchor rod diameter. The thickness must be suitable for the forces to be transferred. Minimum washer sizes are given in Table 14-2.

Hooked Anchor Rods Hooked anchor rods should be used only for axially loaded members subject to compression only to locate and prevent the displacement or overturning of columns due to erection loads or accidental collisions during erection. Additionally, high-strength steels are not recommended for use in hooked rods since bending with heat may materially affect their strength.

Headed or Threaded and Nutted Anchor Rods When anchor rods are required for a calculated tensile force, T, a more positive anchorage is formed when headed anchor rods, illustrated in Figure 14-8(b), are used. With adequate embedment and edge distance, the limit state is either a tensile failure of the anchor rod or the pull-out of a cone of concrete radiating outward from the head (Marsh and Burdette, 1985a, 1985b) as illustrated in Figure 14-9. Marsh and Burdette (1985a, 1985b) showed that the head of the anchor rod usually provides sufficient anchorage and the use of an additional washer or plate does not add significantly to the anchorage. The nut and threading shown in Figure 14-8(c) is acceptable in lieu of a bolt head. The nut should be welded to the rod to prevent the rod from turning out when the top nut is tightened.

Anchor Rod Nut Installation The majority of anchorage applications in buildings do not require special anchor rod nut installation procedures or pretension in the anchor rod. The anchor rod nuts should be “drawn down tight” as columns and bases are erected, per ANSI/ASSE A10.13 Section 9.6 (ASSE, 2001). This condition can be achieved by following the same practices as recommended for AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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snug-tightened installation in steel-to-steel bolted joints in the RCSC Specification. Snugtight is the condition that exists when all plies in a connection have been pulled into firm contact by the bolts in the joint and all the bolts in the joint have been tightened sufficiently to prevent the removal of the nuts without the use of a wrench. When, in the judgment of the owner’s designated representative for design, the performance of the structure will be compromised by excessive elongation of the anchor rods under tensile loads, pretension may be required. Some examples of applications that may require pretension include structures that cantilever from concrete foundations, moment-resisting column bases with significant tensile forces in the anchor rods, or where load reversal might result in the progressive loosening of the nuts on the anchor rods. When pretensioning of anchor rods is specified, care must be taken in the design of the column base and the embedment of the anchor rod. The shaft of the anchor rod must be free of bond to the encasing concrete so that the rod is free to elongate as it is pretensioned. Also, loss of pretension due to creep in the concrete must be taken into account. Although the design of pretensioned anchorage devices is beyond the scope of this Manual, it should be noted that pretension should not be specified for anchorage devices that have not been properly designed and configured to be pretensioned.

Fig. 14-9. Concrete cone subject to pull-out. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COLUMN SPLICES When the height of a building exceeds the available length of column sections, or when it is economically advantageous to change the column size at a given floor level, it becomes necessary to splice two columns together. Column splices at the final exterior and interior perimeter and at interior openings must be located a minimum of 48 in. above the finished floor to accommodate the attachment of safety cables, except when constructability does not allow. For simplicity and uniformity, other column splices should be located at the same height. Note that column splices placed significantly higher than this are impractical in terms of field assembly.

Fit-Up of Column Splices From AISC Specification Section M2.6, the ends of columns in a column splice which depend upon contact bearing for the transfer of axial forces must be finished to a common plane by milling, sawing, or other suitable means. In theory, if this were done and the pieces were erected truly plumb, there would be full-contact bearing across the entire surface; this is true in most cases. However, AISC Specification Section M4.4 recognizes that a perfect fit on the entire available surface will not exist in all cases. A 1/16-in. gap is permissible with no requirements for repair or shimming. During erection, at the time of tightening the bolts or depositing the welds, columns will usually be subjected to loads which are significantly less than the design loads. Full-scale tests (Popov and Stephen, 1977) which progressed to column failure have demonstrated that subsequent loading to the design loads does not result in distress in the bolts or welds of the splice. If the gap exceeds 1/16 in. but is equal to or less than 1/4 in., and if an engineering investigation shows that sufficient contact area does not exist, nontapered steel shims are required. Mild steel shims are acceptable regardless of the steel grade of the column or bearing material. If required, these shims must be contained, usually with a tack weld, so that they cannot be worked out of the joint. There is no provision in the AISC Specification for gaps larger than 1/4 in. When such a gap exists, an engineering evaluation should be made of this condition based upon the type of loading transferred by the column splice. Tightly driven tapered shims may be required or the required strength may be developed through flange and web splice plates. Alternatively, the gap may be ground or gouged to a suitable profile and filled with weld metal.

Lifting Devices As illustrated in Figure 14-10, lifting devices are typically used to facilitate the handling and erection of columns. When flange-plated or web-plated column splices are used for W-shape columns, it is convenient to place lifting holes in these flange plates as illustrated in Figure 14-10(a). When butt-plated column splices are used, additional temporary plates with lifting holes may be required as illustrated in Figure 14-10(b). W-shape column splices which do not utilize web-plated or butt-plated column splices (i.e., groove-welded column splices) may be provided with a lifting hole in the column web as illustrated in Figure 14-10(c). While a hole in the column web reduces the cross-sectional area of the column, this reduction will seldom be critical since the column is sized for the loads at the floor below and the splice is located above the floor. Alternatively, auxiliary plates with lifting holes may be connected to the column so that they do not interfere with the welding. Typical column splices for tubes and box-columns are illustrated in Figure 14-10(d). Holes in lifting devices AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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may be drilled, reamed or flame-cut with a mechanically guided torch. In the latter case, the bearing surface of the hole in the direction of the lift must be smooth. The lifting device and its attachment to the column must be of sufficient strength to support the weight of the column as it is brought from the horizontal position (as delivered) to the vertical position (as erected); the lifting device and its attachment to the column must be adequate for the tensile forces, shear forces and moments induced during handling and erection. A suitable shackle and pin are connected to the lifting device while the column is on the ground. The steel erector usually establishes the size and type of shackle and pin to be used in erection and this information must be transmitted to the fabricator prior to detailing. Except for excessively heavy lifting pieces, it is customary to select a single pin and pinhole diameter to accommodate the majority of structural steel members, whether they are columns or other heavy structural steel members. The pin is attached to the lifting

(a) W-shape columns, flange-plated column splices with lifting holes

(b) W-shape and box-shaped columns. butt-plated column splices with auxiliary lifting plates

(c) W-shape columns, no splice plates, lifting hole in column web

(d) Tubular and box-shape columns, auxiliary lifting plates

Fig. 14-10. Lifting devices for columns. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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hook and a lanyard trails to the ground or floor level. After the column is erected and connected, the pin is removed from the device by means of the lanyard, eliminating the need for an ironworker to climb the column. The shackle pin, as assembled with the column, must be free and clear, so that it may be withdrawn laterally after the column has been landed and stabilized. The safety of the structure, equipment and personnel is of utmost importance during the erection period. It is recommended that all welds that are used on the lifting devices and stability devices be inspected very carefully, both in the shop and later in the field, for any damage that may have occurred in handling and shipping. Groove welds frequently are inspected with ultrasonic methods (UT) and fillet welds are inspected with magnetic particle (MT) or liquid dye penetrant (PT) methods.

Column Alignment and Stability During Erection Column splices should provide for safety and stability during erection when the columns might be subjected to wind, construction, and/or accidental loading prior to the placing of the floor system. The nominal flange-plated, web-plated, and butt-plated column splices developed here consider this type of loading. In other splices, column alignment and stability during erection are achieved by the addition of temporary lugs for field bolting as illustrated in Figure 14-11. The material thickness, weld size, and bolt diameter required are a function of the loading. A conservative resisting moment arm is normally taken as the distance from the compressive toe or flange face to the gage line of the temporary lug. The overturning moment should be checked about both axes of the column. The recommended minimum plate or angle thickness is 1/2 in.; the recommended minimum weld size is 5/16 in.; additionally, high-strength bolts are normally used as stability devices. Temporary lugs are not normally used as lifting devices. Unless required to be removed in the contract documents, these temporary lugs may remain. Column alignment is provided with centerpunch marks that are useful in centering the columns in two directions.

Force Transfer in Column Splices As illustrated in Figure 14-12, for the W-shapes most frequently used as columns, the distance between the inner faces of the flanges is constant throughout any given nominal depth group; as the nominal weight per foot increases for each nominal depth, the flange and web thicknesses increase. From AISC Specification Section J7, the available bearing strength, φRn or Rn/Ω, of the contact area of a finished surface is determined with Rn = 1.8Fy Apb φ = 0.75

(14-8)

Ω = 2.00

where Apb = projected bearing area, in.2 Fy = specified mimimum yield stress of the column, ksi This bearing strength is much greater than the axial strength of the column and will seldom prove critical in the member design. For column splices transferring only axial forces, complete axial force transfer may be achieved through bearing on finished surfaces; bolts or AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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welds are required by AISC Specification Section J1.4 to be sufficient to hold all parts securely in place. In addition to axial forces, from AISC Specification Section J1.4, column splices must be proportioned to achieve the required strength in tension, due to the combination of dead load and lateral loads. Note that it is not permissible to use forces due to live load to offset the tensile forces from wind or seismic loads. Additional column splice requirements are provided in the AISC Seismic Provisions.

Fig. 14-11. Column stability and alignment devices. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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For dead and wind loads, if the required strength due to the effect of the dead load is greater than the required strength due to the wind load, the splice is not subjected to tension and a nominal splice may be selected from those in Table 14-3. When the required strength due to dead load is less than the required strength due to the wind load, the splice will be subjected to tension and the nominal splices from Table 14-3 are acceptable if the available tensile strength of the splice is greater than or equal to the required strength. Otherwise, a splice must be designed with sufficient area and attachment. When shear from lateral loads is divided among several columns, the force on any single column is relatively small and can usually be resisted by friction on the contact bearing surfaces and/or by the flange plates, web plates or butt plates. If the required shear strength exceeds the available shear strength of the column splice selected from Table 14-3, a column splice must be designed with sufficient area and attachment. The column splices shown in Table 14-3 meet the OSHA requirement for 300 lb located 18 in. from the column face.

Flange-Plated Column Splices Table 14-3 gives typical flange-plated column splice details for W-shape columns. These details are not splice requirements, but rather, typical column splices in accordance with AISC Specification provisions and typical erection requirements. Other splice designs may also be developed. It is assumed in all cases that the lower shaft will be the heavier, although not necessarily the deeper, section. Full-contact bearing is always achieved when lighter sections are centered over heavier sections of the same nominal depth group. If the upper column is not centered on the lower column, or if columns of different nominal depths must bear on each other, some areas of the upper column will not be in contact with the lower column. These areas are hatched in Figure 14-13. When additional bearing area is not required, unfinished fillers may be used. These fillers are intended for “pack-out” of thickness and are usually set back 1/4 in. or more from the finished column end. Since no force is transferred by these fillers, only nominal attachment to the column is required. When additional bearing area is required, fillers finished to bear on the larger column may be provided. Such fillers are proportioned to carry bearing loads at the bearing strength calculated from AISC Specification Section J7 and must be connected to the column to transfer this calculated force. In Table 14-3, Cases I and II are for all-bolted flange-plated column splices for W-shape columns. Bolts in column splices are usually the same size and type as for other bolts on the

Fig. 14-12. Distance between flanges for typical W-shape columns. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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column. Bolt spacing, end distance and edge distances resulting from the plate sizes shown permit the use of 3/ 4-in.- and 7/8-in.-diameter bolts in the splice details shown. Larger diameter bolts may require an increase in edge or end distances. Refer to AISC Specification Chapter J. The use of high-strength bolts in bearing-type connections is assumed in all field and shop splices. However, when slotted or oversized holes are utilized, or in splices employing undeveloped fillers over 1/4 in. thick, slip-critical connections may be required; refer to AISC Specification Section J5.2. For ease of erection, field clearances for lap splices fastened by bolts range from 1/8 in. to 3/ 16 in. under each plate. Cases IV and V are for all-welded flange-plated column splices for W-shape columns. Splice welds are assumed to be made with E70XX electrodes and are proportioned as required by the AISC Specification provisions. The GMAW and FCAW equivalents to E70XX electrodes may be substituted if desired. Field clearance for welded splices are limited to 1/16 in. to control the expense of building up welds to close openings. Note that the fillet weld lengths, Y, as compared to the lengths L/2, provide 2-in. unwelded distance below and above the column shaft finish line. This provides a degree of flexibility in the splice plates to assist the erector. Cases VI and VII apply to combination bolted and welded column splices. Since the available strength of the welds will, in most cases, exceed the strength of the bolts, the weld and splice lengths shown may be reduced, if desired, to balance the strength of the fasteners to the upper or lower column, provided that the available strength of the splice is still greater than the required strength of the splice, including erection loading.

Directly Welded Flange Column Splices Table 14-3 also includes typical directly welded flange column splice details for W-shape and HSS or box-shaped columns. These details are not splice requirements, but rather, typical column splices in accordance with AISC Specification provisions and typical erection requirements. Other splice designs may also be developed. It is assumed in all cases that the lower shaft will be the heavier, although not necessarily the deeper, section. Case VIII applies to W-shape columns spliced with either partial-joint-penetration or complete-joint-penetration groove welds. Case X applies to HSS or box-shaped columns spliced with partial-joint-penetration or complete-joint-penetration groove welds.

Fig. 14-13. Columns not centered or of different nominal depth. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Butt-Plated Column Splices Table 14-3 further includes typical butt-plated column splice details for W-shape and HSS or box-shaped columns. These details are not splice requirements, but rather, present typical column splices in accordance with AISC Specification provisions and typical erection requirements. Other splice designs may also be developed. It is assumed in all cases that the lower shaft will be the heavier, although not necessarily the deeper, section. Butt plates are used frequently on welded splices where the upper and lower columns are of different nominal depths, but may not be economical for bolted splices since fillers cannot be eliminated. Typical butt plates are 11/2 in. thick for a W8 over W10 splice, and 2 in. thick for other W-shape combinations such as W10 over W12 and W12 over W14. Butt plates which are subjected to substantial bending stresses, such as required on boxed columns, will require a more careful review and analysis. One common method is to assume forces are transferred through the butt plate on a 45° angle and check the thickness obtained for shear and bearing strength. Finishing requirements for butt plates are specified in AISC Specification Section M2.8. Case III is a combination flange-plated and butt-plated column splice for W-shape columns. Case IX applies to welded butt-plated column splices for W-shape columns. Case XI applies to welded butt-plated column splices for HSS or box-shaped columns. Case XII applies to welded butt-plated column splices between W-shape and HSS or box-shaped columns.

DESIGN CONSIDERATIONS FOR HSS CAP PLATES The simplest form of attachment to an HSS is to connect the framing member to the top of an HSS. The cap plate serves as a bearing device to transfer the reactions from the framing member into the HSS. The cap plate may also be used to transfer moment into the HSS column. The moment transfer is through a force couple that consists of both compressive and tensile reactions delivered to the cap plate.

Flexural Strength of the Cap Plate The available strength of the cap plate, in terms of reaction resistance, is determined as φRn or Rn/Ω with Rn =

Bt12 H⎞ ⎛l 4 ⎜ br + a − ⎟ ⎝ 2 2⎠

φ = 0.90

Fyc

Ω = 1.67

where B = HSS width, in. Fyc = specified minimum yield stress of the cap plate, ksi H = HSS depth, in. a = distance from the HSS centroid to the end of the attached member, in. lbr = required bearing length for the attached member, in. t1 = cap plate thickness, in.

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This equation applies only if the cap plate is subjected to cantilever bending, as shown in Figure 14-14. This occurs when the beam or joist reaction point is outside of the HSS face. If a stiffener is used in the beam and is positioned over the HSS wall, then the equation does not apply, since the cap plate is not subjected to bending. Also if the denominator of the equation results in a negative number, bending of the cap plate can be disregarded.

Compression Yielding and Crippling of the HSS Wall The available strength of the HSS wall due to compression yielding and compression crippling is determined in accordance with AISC Specification Section K1.

Fig. 14-14. Cap plate subject to cantilever bending.

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PART 14 REFERENCES ACI (2006), Code Requirements for Nuclear Safety Related Concrete Structures, ACI 34906, American Concrete Institute, Farmington Hills, MI. ACI (2008), Building Code Requirements for Structural Concrete, ACI 318-08 and ACI 318M-08, American Concrete Institute, Farmington Hills, MI. ASSE (2001), Safety Requirements for Steel Erection, ANSI/ASSE 10.13-01, American Society of Safety Engineers, Des Plaines, IL. Fisher, J.M. (2004), Industrial Buildings—Roofs to Anchor Rods, Design Guide 7, 2nd Ed., AISC, Chicago, IL. Fisher, J.M. and Kloiber, L.A. (2006), Base Plate and Anchor Rod Design, 2nd Ed., Design Guide 1, AISC, Chicago, IL. Fisher, J.M. and West, M.A. (1997), Erection Bracing of Low-Rise Structural Steel Frames, Design Guide 10, AISC, Chicago, IL. Marsh, M.L. and Burdette, E.G. (1985a), “Anchorage of Steel Building Components to Concrete,” Engineering Journal, Vol. 15, No. 4, 4th Quarter, pp. 33–39, AISC, Chicago, IL. Marsh, M.L. and Burdette, E.G. (1985b), “Multiple Bolt Anchorages: Method for Determining the Effective Projected Area of Overlapping Stress Cones,” Engineering Journal, Vol. 15, No. 4, 4th Quarter, pp. 29–32, AISC, Chicago, IL. Popov, E.P. and Stephen, R.M. (1977), “Capacity of Columns with Splice Imperfections,” Engineering Journal, Vol. 14, No. 1, 1st Quarter, pp. 16–23, AISC Chicago, IL. Ricker, D.T. (1989), “Some Practical Aspects of Column Base Selection,” Engineering Journal, Vol. 26, No. 3, 3rd Quarter, AISC, Chicago, IL. Thornton, W.A. (1990a), “Design of Small Base Plates for Wide-Flange Columns,” Engineering Journal, Vol. 27, No. 3, 3rd Quarter, pp. 108–110, AISC, Chicago, IL. Thornton, W.A. (1990b), “Design of Small Base Plates for Wide-Flange Columns—A Concatenation of Methods,” Engineering Journal, Vol. 27, No. 4, 4th Quarter, pp. 173–174, AISC, Chicago, IL.

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Table 14-1

Finish Allowances Add to Finish One Side, in.

Add to Finish Two Sides, in.

11/4 or less over 11/4 to 2, incl.

1/16

1/8 1/4

Maximum dimension over 24 in.

11/4 or less over 11/4 to 2, incl.

1/8 3/16

1/4

56 in. wide or less

over 2 to 71/2, incl. over 71/2 to 10, incl. over 10 to 15, incl.

1/4

3/8

1/2

5/8

3/4

7/8

over 2 to 6, incl. over 6 to 10, incl. over 10 to 15, incl.

1/4

3/8

1/2

5/8

3/4

7/8

Size

Thickness, in.

Maximum dimension 24 in. or less

Over 56 in. wide to 72 in. wide

1/8

3/8

Note: These allowances apply for material with Fu ≤ 60 ksi.

Table 14-2

Recommended Maximum Sizes for Anchor-Rod Holes in Base Plates Anchor Rod Diameter, in. 3/4 7/8

1 11/4

Max. Hole Diameter, in.

Min. Washer Size, in.

Min. Washer Thickness

Anchor Rod Diameter, in.

Hole Diameter, in.

Min. Washer Size, in.

Min. Washer Thickness

15/16 19/16 113/16 21/16

2 21/2 3 3

1/4 5/16

11/2 13/4 2 21/2

25/16 23/4 31/4 33/4

31/2 4 5 51/2

1/2

3/8 1/2

5/8 3/4 7/8

Notes: 1. Circular or square washers meeting the washer size are acceptible. 2. Clearance must be considered when choosing an appropriate anchor rod hole location, noting effects such as the position of the rod in the hole with respect to the column, weld size and other interferences. 3. When base plates are less than 11/4 in. thick, punching of holes may be an economical option. In this case, 3/4-in. anchor rods and 11/16-in.-diameter punched holes may be used with ASTM F844 (USS Standard) washers in place of fabricated plate washers.

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Table 14-3

Typical Column Splices Case I: All-bolted flange-plated column splices between columns with depth du and dl nominally the same.

For lifting devices, see Figure 14-10. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Table 14-3 (continued)

Typical Column Splices Case I: All-bolted flange-plated column splices between columns with depth du and dl nominally the same.

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Table 14-3 (continued)

Typical Column Splices Case II: All-bolted flange-plated column splices between columns with depth du nominally 2 in. less than depth dl.

Table 14-3 (continued)

Typical Column Splices Case III: All-bolted flange-plated and butt-plated column splices between columns with depth du nominally 2 in. less than depth dl.

For lifting devices, see Figure 14-10. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Table 14-3 (continued)

Typical Column Splices Case II and III: All-bolted flange-plated column splices between columns with depth du nominally 2 in. less than depth dl.

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Table 14-3 (continued)

Typical Column Splices Case IV: All-welded flange-plated column splices between columns with depths du and dl nominally the same.

For lifting devices, see Figure 14-10.

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Table 14-3 (continued)

Typical Column Splices Case IV: All-welded flange-plated column splices between columns with depth du nominally 2 in. less than depth dl.

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Table 14-3 (continued)

Typical Column Splices Case IV: All-welded flange-plated column splices between columns with depths du and dl nominally the same.

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Table 14-3 (continued)

Typical Column Splices Case IV: All-welded flange-plated column splices between columns with depths du and dl nominally the same.

Placing this additional increment of (X + Y) can be done by making weld lengths X continuous across the end of the splice plate and by increasing Y (and therefore the plate Length) if required.

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Table 14-3 (continued)

Typical Column Splices Case V: All-welded flange-plated column splices between columns with depth du nominally 2 in. less than depth dl.

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Table 14-3 (continued)

Typical Column Splices Case V: All-welded flange-plated column splices between columns with depth du nominally 2 in. less than depth dl.

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Table 14-3 (continued)

Typical Column Splices Case VI: Combination bolted and welded column splices between columns with depths du and dl nominally the same.

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Table 14-3 (continued)

Typical Column Splices Case VI: Combination bolted and welded column splices between columns with depths du and dl nominally the same.

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Table 14-3 (continued)

Typical Column Splices Case VII: Combination bolted and welded flange-plated column splices between columns with depth du nominally 2 in. less than depth dl. Fillers developed for bearing.

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Table 14-3 (continued)

Typical Column Splices Case VII: Combination bolted and welded flange-plated column splices between columns with depth du nominally 2 in. less than depth dl. Fillers developed for bearing.

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Table 14-3 (continued)

Typical Column Splices Case VIII: Directly welded flange column splices between columns with depths du and dl nominally the same.

(a) Partial-joint-penetration groove welds

(b) Complete-joint-penetration groove welds

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Table 14-3 (continued)

Typical Column Splices Case VIII: Directly welded flange column splices between columns with depths du and dl nominally the same.

Note: User to verify weld accessibility of channel to lower column shaft, or consider the use of a bolted-bolted connection.

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Table 14-3 (continued)

Typical Column Splices Case VIII: Directly welded flange column splices between columns with depths du and dl nominally the same.

Note: User to verify weld accessibility of channel to lower column shaft, or consider the use of a bolted-bolted connection.

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Table 14-3 (continued)

Typical Column Splices Case VIII: Directly welded flange column splices between columns with depths du and dl nominally the same.

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Table 14-3 (continued)

Typical Column Splices Case IX: Butt-plated column splices between columns with depth du nominally 2 in. less than depth dl.

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Table 14-3 (continued)

Typical Column Splices Case IX: Butt-plated column splices between columns with depth du nominally 2 in. less than depth dl.

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Table 14-3 (continued)

Typical Column Splices Cases X, XI, XII Special column splices.

lifting and alignment devices. For lifting devices see Figure 14-10. For alignment devices see Figure 14-11.

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Table 14-3 (continued)

Typical Column Splices Cases X, XI, XII Special column splices.

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AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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PART 15 DESIGN OF HANGER CONNECTIONS, BRACKET PLATES, AND CRANE-RAIL CONNECTIONS

SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–2 HANGER CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–2 BRACKET PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–3 CRANE-RAIL CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–6 Bolted Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–6 Table 15-1. Crane Rail Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–7 Welded Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–7 Hook Bolt Fastenings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–8 Rail Clip Fastenings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–8 Rail Clamp Fastenings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–8 Patented Rail Clip Fastenings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–9 DESIGN TABLE DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–9 PART 15 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–11 DESIGN TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–12 Table 15-2. Preliminary Hanger Connection Selection Table . . . . . . . . . . . . . . . . 15–12 Table 15-3. Net Plastic Section Modulus, Znet . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–14 Table 15-4. Dimensions and Weights of Clevises . . . . . . . . . . . . . . . . . . . . . . . . . 15–16 Table 15-5. Clevis Numbers Compatible with Various Rods and Pins . . . . . . . . . 15–17 Table 15-6. Dimensions and Weights of Turnbuckles . . . . . . . . . . . . . . . . . . . . . . 15–18 Table 15-7. Dimensions and Weights of Sleeve Nuts . . . . . . . . . . . . . . . . . . . . . . 15–19 Table 15-8. Dimensions and Weights of Recessed-Pin Nuts . . . . . . . . . . . . . . . . . 15–20 Table 15-9. Dimensions and Weights of Clevis and Cotter Pins . . . . . . . . . . . . . . 15–21

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SCOPE The specification requirements and other design considerations summarized in this Part apply to the design of hanger connections, bracket plates, and crane-rail connections. For the design of similar connections for HSS and pipe, see the AISC Specification Chapter K.

HANGER CONNECTIONS Hanger connections, illustrated in Figure 15-1, are usually made with a plate, tee, angle, or pair of angles. The available strength of a hanger connection is determined from the applicable limit states for the bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). In all cases, the available strength, φRn or Rn/Ω, must exceed the required strength, Ru or Ra.

(a) Tee hanger

(b) Plate hanger Fig. 15-1. Typical hanger connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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BRACKET PLATES

BRACKET PLATES A bracket plate, illustrated in Figure 15-2, acts as a cantilevered beam. The available strength of a bracket plate is determined from the applicable limit states for the bolts (see Part 7), welds (see Part 8), and connecting elements (see Part 9). Additionally the following checks must be considered: flexural yielding at Sections a-a in Figure 15-2; flexural rupture through Sections a-a in Figure 15-2; and shear yielding, local yielding and local buckling through Sections b-b in Figure 15-2 (Muir and Thornton, 2004). The following procedures are for a single bracket plate with the applied load Pr, where Pr is the required strength using LRFD load combinations, Pu, or the required strength using ASD load combinations, Pa. In all cases, the available strength must equal or exceed the required strength. The seat plate of Figure 15-2 should be attached to the column and to the bracket plate(s) to prevent sidesway. The required flexural strength at Sections a-a in Figure 15-2 is LRFD

ASD

Mu = Pu e

Ma = Pa e

(15-1a)

where e = distance shown in Figure 15-2, in.

(b) welded

(a) bolted

Nr = Pr cosθ Vr = Pr sinθ Mr = Pr e − Nr (b′/2) Fig. 15-2. Bracket-plate connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(15-1b)

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For flexural yielding, the available strength, φMn or Mn/Ω, of the bracket plate is Mn = Fy Z φ = 0.90

(15-2)

Ω = 1.67

where Z = gross plastic section modulus of the bracket plate at Sections a-a in Figure 15-2, in.3 For flexural rupture, the available strength, φMn or Mn /Ω, of the bracket plate is Mn = Fu Znet φ = 0.75

(15-3)

Ω = 2.00

where Znet = net plastic section modulus of the bracket plate at Sections a-a in Figure 15-2, in.3 See Table 15-3 for the determination of Znet for standard holes. General equations for determination of Znet follow (Mohr and Murray, 2008). For an odd number of bolt rows Z net =

1 t (s − d h′ )(n 2 s + d h′ ) 4

(15-4)

1 t (s − d h′ )n 2 s 4

(15-5)

For an even number of bolt rows Z net = where d h′ = hole diameter + 1/16, in. n = number of bolt rows s = vertical bolt row spacing, in. In both cases, the vertical edge distances are assumed to be s/2 with plate depth of a = ns. The required shear strength at Sections b-b in Figure 15-2 is LRFD

ASD

Vu = Pu sinθ

Va = Pa sinθ

(15-6a)

(15-6b)

For shear yielding, the available strength, φVn or Vn /Ω, of the bracket plate is Vn = 0.6Fy tb′ φ = 1.00

Ω = 1.50

where b′ = a sinθ, in. a = depth of bracket plate, in. t = thickness of bracket plate, in. θ = angle shown in Figure 15-2, degrees AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(15-7)

AISC_PART 15:14th Ed.

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Page 5

15–5

BRACKET PLATES

The required normal and flexural strength at Sections b-b in Figure 15-2 is LRFD

ASD

b′ Mu = Pue − N u ⎛ ⎞ ⎝ 2⎠

(15-8a)

b′ M a = Pae − N a ⎛ ⎞ ⎝ 2⎠

(15-8b)

Nu = Pu cosθ

(15-9a)

Na = Pa cosθ

(15-9b)

For interaction of normal and flexural strengths, the following interaction equation must be satisfied: N r Mr + ≤ 1.0 N c Mc

(15-10)

The nominal normal strength of the bracket plate for the limit states of local yielding and local buckling is Nn = Fcr tb′, kips

(15-11)

and the nominal flexural strength of the bracket plate for the limit states of local yielding and local buckling is Mn =

Fcr tb ′ 2 , kip-in. 4

(15-12)

For design by LRFD Mc = φM n Mr = Mu N c = φN n Nr = Nu φ = 0.90 For design by ASD M Mc = n Ω Mr = M a N Nc = n Ω Nr = N a Ω = 1.67 For the limit state of local yielding of the bracket plate, Fcr = Fy

(15-13)

For the limit state of local buckling of the bracket plate, Fcr = QFy

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(15-14)

AISC_PART 15:14th Ed.

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15–6

8:11 AM

Page 6

DESIGN OF HANGER CONNECTIONS, BRACKET PLATES, AND…

When λ ≤ 0.70, the limit state of local buckling need not be considered (that is, Q = 1). When 0.70 < λ ≤ 1.41 Q = 1.34 − 0.486λ

(15-15)

When 1.41 < λ Q= where λ =

( ) b′ t

1.30 λ2

(15-16)

Fy

( )

2

b′ 5 475 + 1,120 a′ a a′ = = length of freee edge, in. cosθ

(15-17)

(15-18)

CRANE-RAIL CONNECTIONS Bolted Splices It is desirable to use properly installed and maintained bolted splice bars in crane-rail connections rather than welded splice bars, which are frequently subject to failure in service. Standard rail drilling and joint-bar punching, as furnished by manufacturers of light standard rails for track work, include round holes in rail ends and slotted holes in joint bars to receive standard oval-neck track bolts. Holes in rails are oversized and punching in joint bars is spaced to allow 1/16-in. to 1/8-in. clearance between rail ends (see manufacturers’ catalogs for spacing and dimensions of holes and slots). Although this construction is satisfactory for track and light crane service, its use in general crane service may lead to high maintenance and joint failure. Welded splices are therefore preferable. For best service in bolted splices, it is recommended that tight joints be required for all rails for crane service. This will require rail ends to be finished, and the special rail drilling and joint-bar punching tabulated in Table 15-1 and shown in Figure 15-3. Special rail drilling is accepted by some mills, or rails may be ordered blank for shop drilling. End finishing of standard rails can be done at the mill. However, light rails often must be endfinished in the shop or ground at the site prior to erection. In the crane rail range from 104 to 175 lb per yard, rails and joint bars are manufactured to obtain a tight fit and no further special end finishing, drilling or punching is required. Because of cumulative tolerance variations in holes, bolt diameters and rail ends, a slight gap may sometimes occur. It may sometimes be necessary to ream holes through joined bar and rail to permit entry of bolts. Joint bars for crane service are provided in various sections to match the rails. Joint bars for light and standard rails can be purchased blank for special shop punching to obtain tight joints. See manufacturer data for dimensions, material specifications, and the identification necessary to match the crane-rail section. Joint-bar bolts, as distinguished from oval-neck track bolts, have straight shanks to the head and are manufactured to ASTM A449 specifications. Nuts are manufactured to ASTM A563 Grade B specifications. Alternatively, ASTM A325 bolts and compatible ASTM A563 nuts can be used. Bolt assembly includes an alloy steel spring washer, furnished to American AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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15–7

CRANE-RAIL CONNECTIONS

Table 15-1

Crane Rail Splices Rail Drilling Wt. per Yard

g

lb

in.

40 60 85 104 135 171 175

171/128

Hole Dia.

A

Joint Bar

Bolt

Washer

Punching

B

C

Hole Dia.

in.

in. in. in. in.

13/16*

21/2

1115/128 13/16* 217/64 15/16* 27/16 11/16 215/32 13/16 25/8 13/16 221/32 13/16

21/2 21/2 4 4 4 4

5 5 5 5 5 5 5

– – – 6 6 6 6

13/16* 13/16*

D

B

in.

in. in. in.

415/16*

415/16* 15/16* 415/16* 11/16 715/16 13/16 715/16 13/16 715/16 13/16 715/16

5 5 5 5 5 5 5

C

– – – 6 6 6 6

L

20 24 24 34 34 34 34

H

in.

in.

G

Dia. Grip

in.

in.

in.

in.

in.

3/4

115/16

31/2

21/2

3/16

I

Inside Dia.

Thickness and Width

× × 3/8 × 3/8 × 1/2 × 1/2 × 1/2 7/16 × 1/2

13/16 7/16 2 211/16 3/4 219/32 4 211/16 13/16 7/16 311/32 7/8 35/32 43/4 33/16 15/16 7/16 31/2 1 31/2 51/4 31/2 11/16 7/16 – 11/8 35/8 51/2 311/16 13/16 7/16 – 11/8 47/16 61/4 41/16 13/16 7/16

–

11/8 41/8

61/4 315/16 13/16

3/8

Wt. 2 Bars Bolts, Nuts, Washers With Ftg.

W/O Ftg.

lb

lb

20.0 36.5 56.6 73.5 – – –

16.5 29.6 45.3 55.4 75.3 90.8 87.7

*Special rail drilling and joint bar punching. Ftg. = fitting

Railway Engineering and Maintenance of Way Association (AREMA) specifications. After installation, bolts should be retightened within 30 days and every three months thereafter.

Welded Splices When welded splices are specified, consult the manufacturer for recommended rail-end preparation, welding procedure, and method of ordering. Although the joint continuity made possible by this method of splicing is desirable, the careful control required in all stages of the welding operation may be difficult to meet during crane-rail installation. Rails should not be attached to structural supports by welding. Rails with holes for joint bar bolts should not be used in making welded splices.

Fig. 15-3. Special rail drilling and joint-bar punching. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 15:14th Ed.

15–8

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DESIGN OF HANGER CONNECTIONS, BRACKET PLATES, AND…

Hook Bolt Fastenings Hook bolts (Figure 15-4) are used primarily with light rails when attached to beams that are too narrow for clamps. Rail adjustment to ±1/2 in. is inherent in the threaded shank. Hook bolts are paired alternately 3 to 4 in. apart, spaced at about 24 in. on center. The special rail drilling required must be done in the fabricator’s shop. Hook bolts are not recommended for use with heavy-duty cycle cranes [Crane Manufacturers Association of America (CMAA) Classes, D, E, and F]. It is generally recommended that hook bolts should not be used in runway systems that are longer than 500 ft because the bolts do not allow for longitudinal movement of the rail.

Rail Clip Fastenings Rail clips are forged or cast devices that are shaped to match specific rail profiles. They are usually bolted to the runway girder flange with one bolt or are sometimes welded. Rail clips have been used satisfactorily with all classes of cranes. However, one drawback is that when a single bolt is used, the clip can rotate in response to rail longitudinal movement. This clip rotation can cause cam action that might force the rail out of alignment. Because of this limitation, rail clips should only be used in crane systems subject to infrequent use, and for runways less than 500 ft in length.

Rail Clamp Fastenings Rail clamps are a common method of attachment for heavy-duty cycle cranes. Rail clamps are detailed to provide two types: tight and floating (see Figure 15-5). Each clamp consists of two plates: an upper clamp plate and a lower filler plate. Dimensions shown are suggested. See manufacturers’ catalogs for recommended gages, bolt sizes and detail dimensions not shown. The lower plate is flat and nominally matches the height of the toe of the rail flange. The upper plate covers the lower plate and extends over the top of the lower rail flange. In the tight clamp, the upper plate is detailed to fit tightly to the lower tail flange top, thus “clamping” it tightly in place when the fasteners are tightened. In the past, the tight clamp had been illustrated with the filler plates fitted tightly against the rail flange toe. This tight fit-up was rarely achieved in practice and is not considered to be necessary to achieve a tight type clamp. In the floating type clamp, the pieces are detailed to provide a clearance both alongside the rail flange toe and below the upper plate. The floating type does not, in reality, clamp the rail but merely holds the rail within the limits of the clamp clearances.

Fig. 15-4. Hook bolts. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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8:11 AM

Page 9

15–9

DESIGN TABLE DISCUSSION

High-strength bolts are recommended for both clamp types. Both types should be spaced 3 ft or less apart.

Patented Rail Clip Fastenings Each manufacturer’s literature presents in detail the desirable aspects of the various designs. In general, patented rail clips are easy to install due to their range of adjustment and provide both limitation of lateral movement and allowance for longitudinal movement. Patented rail clips should be considered as a viable alternative to conventional hook bolts, clips or clamps. Because of their desirable characteristics, patented rail clips can be used without restriction except as limited by the specific manufacturer’s recommendations. Installations using patented rail clips sometimes incorporate pads beneath the rail. When this is done, the lateral float of the rail should be limited as in the case of the tight rail clamps.

DESIGN TABLE DISCUSSION Table 15-2. Preliminary Hanger Connection Selection Table Values are given for the available tensile strength per in. of fitting length in bending of a tee fitting flange or angle leg with Fu = 58 ksi and Fu = 65 ksi. The bending strength is calculated in terms of Fu, which provides good correlation with available test data (Thornton, 1992; Swanson, 2002). Table 15-2 can be used to select a trial fitting once the number and size of bolts required is known. The number of bolts required must be selected such that the available tensile strength of one bolt, φrn or rn/Ω, exceeds the required tensile force per bolt, rut or rat .

Fig. 15-5. Rail clamps. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 15:14th Ed.

15–10

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8:11 AM

Page 10

DESIGN OF HANGER CONNECTIONS, BRACKET PLATES, AND…

In this table, it is assumed that equal moments exist at the face of the tee stem or angle leg and at the bolt line. The available flexural strength of the tee flange, φb Mn or Mn/Ωb, is determined with Mn = Mp = Fu Z φb = 0.90

(15-19)

Ωb = 1.67

In the above equation, the plastic section modulus, Z, per unit length of the angle or tee flange is Z=

t2 4

(15-20)

where t is the thickness of the angle or tee flange, in. Thus, for a unit length of the angle or tee flange the available flexural strength, φb Mn or Mn/Ωb, is determined with Mn = φb = 0.90

Fu t 2 4

(15-21)

Ωb = 1.67

The tensile force on the fitting per bolt row, 2rut or 2rat, must be less than the appropriate (LRFD or ASD) value shown in Table 15-2 times the tributary length per pair of bolts, p (length perpendicular to the elevation shown in Table 15-2).

Table 15-3. Net Plastic Section Modulus, Z net Values of the net plastic section modulus Znet are given in Table 15-3 for standard holes and numbers of fasteners spaced 3 in. on center, the usual spacing for these connections. The values are determined using Equations 15-4 and 15-5.

Forged Steel Structural Hardware Table 15-4. Dimensions and Weights of Clevises Dimensions, weights and available strengths of clevises are listed in Table 15-4.

Table 15-5. Clevis Numbers Compatible with Various Rods and Pins Compatibility of clevises with various rods and pins is given in Table 15-5.

Table 15-6. Dimensions and Weights of Turnbuckles Dimensions, weights and available strengths of turnbuckles are listed in Table 15-6.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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PART 15 REFERENCES

PART 15 REFERENCES Mohr, B.A. and Murray, T.M. (2008), “Bending Strength of Steel Bracket and Splice Plates,” Engineering Journal, AISC, Vol. 45, No. 2, 2nd Quarter, pp. 97–106. Muir, L.S. and Thornton, W.A. (2004), “A Direct Method for Obtaining the Plate Buckling Coefficient for Double Coped Beams,” Engineering Journal, AISC, Vol. 41, No. 3, 3rd Quarter, pp. 133–134. Swanson, J.A. (2002), “Ultimate Strength Prying Models for Bolted T-Stub Connections,” Engineering Journal, Vol. 39, No. 3, 3rd Quarter, pp. 136–147, AISC, Chicago, IL. Thornton, W.A. (1992), “Strength and Serviceability of Hanger Connections,” Engineering Journal, AISC, Vol. 29, No. 4, 4th Quarter, pp. 145–149, Chicago, IL. See also ERRATA, Engineering Journal, Vol. 33, No. 1, 1st Quarter, 1996, pp. 39, 40.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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15–12

8:11 AM

Page 12

DESIGN OF HANGER CONNECTIONS, BRACKET PLATES, AND…

Table 15-2a Fu = 58 ksi

Preliminary Hanger Connection Selection Table

Available tensile strength, kips per linear in., limited by bending of the flange

b, in. t, in. 5/16 3/8 7/16 1/2 9/16 5/8 11/16 3/4 13/16 7/8 15/16

1 11/16 11/8 13/16 11/4

11/4

1

3/8 7/16 1/2 9/16 5/8 11/16 3/4 13/16 7/8 15/16

1 11/16 11/8 13/16 11/4

13/4

2

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

3.39 4.88 6.65 8.68 11.0 13.6 16.4 19.5 22.9 26.6 30.5 34.7 39.2 44.0 49.0 54.3

5.10 7.34 9.99 13.1 16.5 20.4 24.7 29.4 34.5 40.0 45.9 52.2 58.9 66.1 73.6 81.6

2.71 3.91 5.32 6.95 8.79 10.9 13.1 15.6 18.3 21.3 24.4 27.8 31.4 35.2 39.2 43.4

4.08 5.87 7.99 10.4 13.2 16.3 19.7 23.5 27.6 32.0 36.7 41.8 47.1 52.9 58.9 65.3

2.26 3.26 4.43 5.79 7.33 9.04 10.9 13.0 15.3 17.7 20.3 23.2 26.1 29.3 32.6 36.2

3.40 4.89 6.66 8.70 11.0 13.6 16.4 19.6 23.0 26.6 30.6 34.8 39.3 44.0 49.1 54.4

1.94 2.79 3.80 4.96 6.28 7.75 9.38 11.2 13.1 15.2 17.4 19.8 22.4 25.1 28.0 31.0

2.91 4.19 5.71 7.46 9.44 11.7 14.1 16.8 19.7 22.8 26.2 29.8 33.7 37.8 42.1 46.6

1.70 2.44 3.32 4.34 5.49 6.78 8.21 9.77 11.5 13.3 15.3 17.4 19.6 22.0 24.5 27.1

2.55 3.67 5.00 6.53 8.26 10.2 12.3 14.7 17.2 20.0 22.9 26.1 29.5 33.0 36.8 40.8

21/4 5/16

11/2

ASD

1.51 2.17 2.95 3.86 4.88 6.03 7.30 8.68 10.2 11.8 13.6 15.4 17.4 19.5 21.8 24.1

21/2 2.27 3.26 4.44 5.80 7.34 9.06 11.0 13.1 15.3 17.8 20.4 23.2 26.2 29.4 32.7 36.3

1.36 1.95 2.66 3.47 4.40 5.43 6.57 7.81 9.17 10.6 12.2 13.9 15.7 17.6 19.6 21.7

23/4 2.04 2.94 4.00 5.22 6.61 8.16 9.87 11.7 13.8 16.0 18.4 20.9 23.6 26.4 29.4 32.6

1.23 1.78 2.42 3.16 4.00 4.93 5.97 7.10 8.34 9.67 11.1 12.6 14.3 16.0 17.8 19.7

31/4

3 1.85 2.67 3.63 4.75 6.01 7.41 8.97 10.7 12.5 14.5 16.7 19.0 21.4 24.0 26.8 29.7

1.13 1.63 2.22 2.89 3.66 4.52 5.47 6.51 7.64 8.86 10.2 11.6 13.1 14.7 16.3 18.1

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.70 2.45 3.33 4.35 5.51 6.80 8.22 9.79 11.5 13.3 15.3 17.4 19.6 22.0 24.5 27.2

1.04 1.50 2.05 2.67 3.38 4.17 5.05 6.01 7.05 8.18 9.39 10.7 12.1 13.5 15.1 16.7

1.57 2.26 3.07 4.02 5.08 6.27 7.59 9.03 10.6 12.3 14.1 16.1 18.1 20.3 22.6 25.1

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15–13

DESIGN TABLES

Table 15-2b Fu = 65 ksi

Preliminary Hanger Connection Selection Table

Available tensile strength, kips per linear in., limited by bending of the flange

b, in. t, in. 5/16 3/8 7/16 1/2 9/16 5/8 11/16 3/4 13/16 7/8 15/16

1 11/16 11/8 13/16 11/4

11/4

1

3/8 7/16 1/2 9/16 5/8 11/16 3/4 13/16 7/8 15/16

1 11/16 11/8 13/16 11/4

13/4

2

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

ASD

LRFD

3.80 5.47 7.45 9.73 12.3 15.2 18.4 21.9 25.7 29.8 34.2 38.9 43.9 49.3 54.9 60.8

5.71 8.23 11.2 14.6 18.5 22.9 27.7 32.9 38.6 44.8 51.4 58.5 66.0 74.0 82.5 91.4

3.04 4.38 5.96 7.78 9.85 12.2 14.7 17.5 20.6 23.8 27.4 31.1 35.2 39.4 43.9 48.7

4.57 6.58 8.96 11.7 14.8 18.3 22.1 26.3 30.9 35.8 41.1 46.8 52.8 59.2 66.0 73.1

2.53 3.65 4.97 6.49 8.21 10.1 12.3 14.6 17.1 19.9 22.8 25.9 29.3 32.8 36.6 40.5

3.81 5.48 7.46 9.75 12.3 15.2 18.4 21.9 25.7 29.9 34.3 39.0 44.0 49.4 55.0 60.9

2.17 3.13 4.26 5.56 7.04 8.69 10.5 12.5 14.7 17.0 19.5 22.2 25.1 28.1 31.4 34.8

3.26 4.70 6.40 8.36 10.6 13.1 15.8 18.8 22.1 25.6 29.4 33.4 37.7 42.3 47.1 52.2

1.90 2.74 3.72 4.87 6.16 7.60 9.20 10.9 12.8 14.9 17.1 19.5 22.0 24.6 27.4 30.4

2.86 4.11 5.60 7.31 9.25 11.4 13.8 16.5 19.3 22.4 25.7 29.3 33.0 37.0 41.2 45.7

21/2

21/4 5/16

11/2

ASD

1.69 2.43 3.31 4.32 5.47 6.76 8.18 9.73 11.4 13.2 15.2 17.3 19.5 21.9 24.4 27.0

2.54 3.66 4.98 6.50 8.23 10.2 12.3 14.6 17.2 19.9 22.9 26.0 29.4 32.9 36.7 40.6

1.52 2.19 2.98 3.89 4.93 6.08 7.36 8.76 10.3 11.9 13.7 15.6 17.6 19.7 22.0 24.3

23/4 2.29 3.29 4.48 5.85 7.40 9.14 11.1 13.2 15.4 17.9 20.6 23.4 26.4 29.6 33.0 36.6

1.38 1.99 2.71 3.54 4.48 5.53 6.69 7.96 9.34 10.8 12.4 14.2 16.0 17.9 20.0 22.1

31/4

3 2.08 2.99 4.07 5.32 6.73 8.31 10.1 12.0 14.0 16.3 18.7 21.3 24.0 26.9 30.0 33.2

1.27 1.82 2.48 3.24 4.11 5.07 6.13 7.30 8.56 9.93 11.4 13.0 14.6 16.4 18.3 20.3

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.90 2.74 3.73 4.88 6.17 7.62 9.22 11.0 12.9 14.9 17.1 19.5 22.0 24.7 27.5 30.5

1.17 1.68 2.29 2.99 3.79 4.68 5.66 6.74 7.91 9.17 10.5 12.0 13.5 15.2 16.9 18.7

1.76 2.53 3.45 4.50 5.70 7.03 8.51 10.1 11.9 13.8 15.8 18.0 20.3 22.8 25.4 28.1

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DESIGN OF HANGER CONNECTIONS, BRACKET PLATES, AND…

Table 15-3

Net Plastic Section Modulus, Znet, in.3 (Standard Holes)

Nominal Bolt Diameter, d , in.

# Bolts in One Vertical Row, n

Bracket Plate Depth, d , in.

2 3 4 5

6 9 12 15

1.59 3.70 6.38 10.1

2.39 5.55 9.56 15.1

6 7 8 9 10

18 21 24 27 30

14.3 19.6 25.5 32.4 39.8

21.5 29.5 38.3 48.6 59.8

12 14 16 18 20

36 42 48 54 60

57.4 78.1 102 129 159

86.1 117 153 194 239

115 156 204 258 319

143 195 255 323 398

172 234 306 387 478

22 24 26 28 30

66 72 78 84 90

193 230 269 312 359

289 344 404 469 538

386 459 539 625 717

482 574 673 781 896

32 34 36

96 102 108

408 461 516

612 691 775

816 921 1030

1020 1150 1290

3

1

/4

3

/8

7

/4 Bracket Plate Thickness, t , in.

1

5

3

3.19 7.40 12.8 20.2

3.98 9.26 15.9 25.2

4.78 11.1 19.1 30.2

28.7 39.3 51.0 64.8 79.7

35.9 49.1 63.8 81.0 99.6

/2

/8

/4

43.0 58.9 76.5 97.2 120

3

/8

/8

1

/2

5

/8

2.25 5.25 9.00 14.3

3.00 7.00 12.0 19.0

3.75 8.75 15.0 23.8

20.3 27.8 36.0 45.8 56.3

27.0 37.0 48.0 61.0 75.0

33.8 46.3 60.0 76.3 93.8

81.0 110 144 182 225

108 147 192 243 300

135 184 240 304 375

579 689 808 937 1080

272 324 380 441 506

363 432 507 588 675

454 540 634 735 844

1220 1380 1550

576 650 729

768 867 972

960 1080 1220

Notes: The area reduction per hole is assumed to be dh + 1/16 in. Bolts spaced 3 in. vertically with 11/2-in. edge distance at top and bottom. Interpolate for intermediate plate thicknesses. Values are based on Equations 15-4 and 15-5.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN TABLES

Table 15-3 (continued)

Net Plastic Section Modulus, Znet, in.3 (Standard Holes)

Nominal Bolt Diameter, d , in.

# Bolts in One Vertical Row, n

Bracket Plate Depth, d , in.

2 3 4 5

6 9 12 15

6 7 8 9 10

18 21 24 27 30

40.5 55.5 72.0 91.5 113

47.3 64.8 84.0 107 131

12 14 16 18 20

36 42 48 54 60

162 221 288 365 450

189 257 336 425 525

101 138 180 228 281

22 24 26 28 30

66 72 78 84 90

545 648 761 882 1010

635 756 887 1030 1180

32 34 36

96 102 108

1150 1300 1460

1340 1520 1700

7

1 Bracket Plate Thickness, t , in.

/8

3

/4

4.50 10.5 18.0 28.5

7

/8

5.25 12.3 21.0 33.3

1

5

3

2.81 6.59 11.3 17.8

3.52 8.24 14.1 22.3

4.22 9.89 16.9 26.8

25.3 34.7 45.0 57.2 70.3

31.6 43.4 56.3 71.5 87.9

/2

/8

/4

7

/8

4.92 11.5 19.7 31.2

1 5.63 13.2 22.5 35.7

38.0 52.1 67.5 85.8 105

44.3 60.8 78.8 100 123

50.6 69.4 90.0 114 141

127 172 225 285 352

152 207 270 342 422

177 241 315 399 492

203 276 360 456 563

340 405 475 551 633

425 506 594 689 791

510 608 713 827 949

596 709 832 965 1110

681 810 951 1100 1270

720 813 911

900 1020 1140

1080 1220 1370

1260 1420 1590

1440 1630 1820

Notes: The area reduction per hole is assumed to be dh + 1/16 in. Bolts spaced 3 in. vertically with 11/2-in. edge distance at top and bottom. Interpolate for intermediate plate thicknesses. Values are based on Equations 15-4 and 15-5.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DESIGN OF HANGER CONNECTIONS, BRACKET PLATES, AND…

Table 15-4

Dimensions and Weights of Clevises

Clevis Number

Dimensions, in. Max. p

b

2

Max. D 5/8

3/4

17/16

21/2

7/8

11/2

21/2

3

13/8

13/4

31/2

11/2

4

n

Weight, lb

a

w

39/16

11/16

5/16

(+1/32, -0)

1

1

4

11/4

5/16

(+1/32, -0)

2.5

12.5

18.8

3

11/4

51/16

11/2

1/2

(+1/16, -1/32)

4

25.0

37.5

2

31/2

11/2

6

13/4

1/2

(+1/16, -1/16)

6

30.0

45.0

13/4

21/4

4

13/4

515/16

2

1/2

(+1/16, -1/16)

9

35.0

52.5

5

21/8

21/2

5

21/4

7

21/2

5/8

(+3/32, -0)

16

62.5

93.8

6

21/2

3

6

23/4

8

3

3/4

(+3/32,

-0)

26

7

3

33/4

7

3

9

31/2

7/8

(+1/8, -1/16)

36

114

171

8

4

41/4

8

4

101/8

11/2 (+1/8, -1/16)

90

225

338

5/8

4

t

Available Strength, kips* ASD 5.83

90.0

LRFD 8.75

135

Notes: Weights and dimensions of clevises are typical; products of all suppliers are essentially similar. User shall verify with the manufacturer that product meets available strength specifications above. * Tabulated available strengths are based on φ = 0.50, Ω = 3.00. Strength at service load corresponds to a 3:1 safety factor using maximum pin diameter.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 15:14th Ed.

2/24/11

8:12 AM

Page 17

15–17

DESIGN TABLES

Table 15-5

Clevis Numbers Compatible with Various Rods and Pins Dia. of Tap, in.

Diameter of Pin, in. 1

/2

5

/8

3

/4

3

/8

2

2

2

1

/2

2

2

2

5

/8

2

2

2

3

/4

7

/8

7

/8

1

1

1

1 /4 1 /2 13/4

2

21/2 21/2 21/2 21/2 3

3

3

3

3

3

31/2

1

3

3

3

3

31/2

1

3

1 /8

3

3

1

1

1

4

4

4

4

4

5

5

5

13/4

4

5

5

5

5

17/8

5

5

5

5

5

2

5

3 /2 3 /2

3 /2 31/2

8

8

4 5

5

5

5

5

6

6

5

5

6

6

6

6

21/4

6

6

6

6

6

7

7

23/8

6

6

6

6

7

7

7

1

6

6

2 /2

41/4

3

3

21/8

4

2 /2 21/2 21/2 21/2 21/2

3

15/8

31/4 31/2 33/4

21/2 21/2 21/2 21/2

11/8

1 /2

3

1

1 1 /4

21/4 21/2 23/4

7

6

7

7

7

7

7

25/8

7

7

7

7

7

8

23/4

7

7

7

7

8

8

27/8

7

8

8

8

8

8

3

7

8

8

8

8

8

8

8

31/8

8

8

8

8

8

8

8

31/4

8

8

8

8

8

8

8

33/8

8

8

8

8

8

8

8

31/2

8

8

8

8

8

8

35/8

8

8

8

8

8

33/4

8

8

8

8

8

37/8

8

8

8

4

8

8

Notes: Tabular values assume that the net area of the clevis through the pin hole is greater than or equal to 125% of the net area of the rod, and is applicable to round rods without upset ends. For other net area ratios, the required clevis size may be calculated by referring to the dimensions tabulated in Tables 15-4 and 7-17.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 15:14th Ed.

2/24/11

15–18

8:12 AM

Page 18

DESIGN OF HANGER CONNECTIONS, BRACKET PLATES, AND…

Table 15-6

Dimensions and Weights of Turnbuckles

Weight (lb) for Length a, in.

Dimensions, in.

Available Strength, kips

Diameter D, in.

a

n

c

e

g

6

6

9/16

71/8

9/16

11/32

0.42

79/16

11/16

15/16

15/16

11/16 15/16

77/8 81/8 85/8

13/16

7/8

6 6 6 6

25/32

15/16 13/32

11/2 123/32 17/8

0.65 0.98 1.45 1.85

1 11/8 11/4 13/8

6 6 6 6

17/16 19/16 19/16 113/16

87/8 91/8 91/8 95/8

19/32 113/32 19/16 111/16

21/32 29/32 217/32 23/4

11/2 15/8 13/4 17/8

6 6 6 6

17/8 93/4 21/2 11 21/2 11 213/16 115/8

2 21/4

6 6

21/2 23/4

3/8 1/2

9

12

18

24

26

ASD LRFD Rn /Ω* φRn* 2.00

1.20 1.58 2.35 3.02

2.43 3.06 4.20

2.60 4.06 4.00 6.15

4.02 4.70 6.49

4.40 6.85 10.0 6.10 7.13 11.3 13.1

15.5 19.3 25.3 29.0

23.3 29.0 38.0 43.5

127/32 131/32 21/8 23/8

31/32 6.15 39/32 9.80 39/16 9.80 4 14.0

9.70

9.13 16.8

15.3 15.3

35.0 40.9 47.2 62.0

52.5 61.3 70.8 93.0

213/16 115/8 35/16 125/8

23/8 211/16

4 45/8

14.0 19.6

15.3 30.9

27.5 43.5

6 6

33/4 43/16

131/2 143/8

3 31/4

5 55/8

23.3 31.5

30.9

42.4 54.0

3 31/4

6 6

45/16 57/16

145/8 167/8

35/8 37/8

61/8 63/4

39.5 60.5

31/2 33/4

6 6

57/16 6

167/8 18

37/8 45/8

63/4 81/2

60.5 95.0

4 41/4

6 9

6 63/4

18 221/2

45/8 51/4

81/2 93/4

95.0

41/2 43/4

9 9

63/4 63/4

221/2 221/2

51/4 51/4

93/4 93/4

5

9

71/2

24

6

5/8 3/4

10

0.90 1.35 1.84

3.00

16.0

3.67 5.50 5.83 8.75 8.67 13.0 12.0 18.0

4.25 5.43

19.5

19.4

62.0 93.0 80.0 120 100 125

150 188

161 203

242 305

203 280

305 420

152

280 390

420 585

152 152

390 390

585 585

200

491

737

79.5 70.0

79.5

Notes: Weights and dimensions of turnbuckles are typical; products of all suppliers are essentially similar. Users shall verify with the manufacturer that product meets strength specifications above. * Tabulated available strengths are based on φ = 0.50, Ω = 3.00.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 15:14th Ed.

2/24/11

8:12 AM

Page 19

15–19

DESIGN TABLES

Table 15-7

Dimensions and Weights of Sleeve Nuts

Screw Dia., D, in.

Short Dia.

Long Dia.

3/8

11/16

25/32

7/16

25/32

7/8

1/2

7/8 15/16

1 11/16 17/32 17/16 15/8 113/16 21/16 21/4 21/2 211/16 215/16 31/8 35/16 31/2 315/16 43/8 413/16 51/4 55/8 6 63/8 67/8 71/2 715/16 83/8 87/8 91/4 93/4 101/8 105/8

9/16 5/8 3/4 7/8

1 11/8 11/4 13/8 11/2 15/8 13/4 17/8 2 21/4 21/2 23/4 3 31/4 31/2 33/4 4 41/4 41/2 43/4 5 51/4 51/2 53/4 6

11/16 11/4 17/16 15/8 113/16 2 23/16 23/8 29/16 23/4 215/16 31/8 31/2 37/8 41/4 45/8 5 53/8 53/4 61/8 61/2 67/8 71/4 75/8 8 83/8 83/4 91/8

Dimensions, in. Length l 4 4 4 5 5 5 7 7 71/2 71/2 8 8 81/2 81/2 9 9 91/2 10 101/2 11 111/2 12 121/2 13 131/2 14 141/2 15 151/2 16 161/2 17

Nut n

Clear c

—

—

—

—

—

—

—

—

—

—

—

—

17/16 17/16 15/8 15/8 17/8 17/8 21/16 21/16 25/16 25/16 21/2 23/4 215/16 33/16 33/8 35/8 313/16 41/16 43/4 5 51/4 51/2 53/4 6 61/4 61/2

1 11/8 11/4 13/8 11/2 15/8 13/4 17/8 2 21/8 23/8 25/8 27/8 31/8 33/8 35/8 37/8 41/8 43/8 43/4 5 51/4 51/2 53/4 6 61/4

Weight, lb

0.27 0.34 0.43 0.64 0.93 1.12 1.75 2.46 3.10 4.04 4.97 6.16 7.36 8.87 10.4 12.2 16.2 21.1 26.7 33.2 40.6 49.1 58.6 69.2 75.0 90.0 98.0 110 122 142 157 176

Notes: Weights and dimensions of sleeve nuts are typical; products of all suppliers are essentially similar. User shall verify with the manufacturer that strengths of sleeve nut are greater than the corresponding connecting rod when the same material is used.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 15:14th Ed.

2/24/11

15–20

8:12 AM

Page 20

DESIGN OF HANGER CONNECTIONS, BRACKET PLATES, AND…

Table 15-8

Dimensions and Weights of Recessed-Pin Nuts

Pin Dimensions, in. Pin Dia. d, in.

D 21/4

2, 21/2, 23/4 3, 31/4, 31/2 33/4, 4 41/4, 41/2, 43/4 5, 51/4 51/2, 53/4, 6 61/4, 61/2 63/4, 7 71/4, 71/2 73/4, 8, 81/4 81/2, 83/4, 9 91/4, 91/2 93/4, 10

Nut Dimensions, in.

Thread

11/2 2 21/2 3 31/2 4 41/2 5 51/2 51/2 6 6 6 6

Diameter Thickness t

T

c

1 11/8 11/4 13/8 11/2 15/8 13/4 17/8 2 2 21/4 21/4 23/8 23/8

1/8

7/8

1/8

1 11/8 11/4 13/8 11/2 15/8 13/4 17/8 17/8 21/8 21/8 21/4 21/4

1/8 1/4 1/4 1/4 1/4 3/8 3/8 3/8 3/8 3/8 3/8 3/8

Short Dia. 3 35/8 43/8 47/8 53/4 61/4 7 75/8 81/8 85/8 93/8 101/4 111/4 111/4

Recess

Weight, lb

Long Dia.

Rough Dia.

33/8

25/8

1/4

41/8 5 55/8 65/8 71/4 81/8 87/8 93/8 10 107/8 117/8 13 13

31/8 37/8 43/8 51/4 53/4 61/2 7 71/2 8 83/4 95/8 105/8 105/8

1/4

s

3/8 3/8 1/2 1/2 5/8 5/8 3/4 3/4 3/4 3/4 3/4 3/4

1 2 3 4 5 6 8 10 12 14 19 24 32 32

Notes: Although nuts may be used on all sizes of pins as shown above, a detail similar to that shown at the left is preferable for pin diameters over 10 in. In this detail, the pin is held in place by a recessed cap at each end and secured by a bolt passing completely through the caps and pin. Suitable provisions must be made for attaching pilots and driving nuts.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 15:14th Ed.

2/24/11

8:12 AM

Page 21

15–21

DESIGN TABLES

Table 15-9

Dimensions and Weights of Clevis and Cotter Pins

c

Pins with Heads Pin Diameter d, in.

11/4 11/2 13/4 2 21/4 21/2 23/4 3 31/4 31/2 33/4

Cotter

Head Diameter h, in.

Weight of One, lb

Length c, in.

Diameter p, in.

Weight per 100, lb

11/2 13/4 2 23/8 25/8 27/8 31/8 31/2 33/4 4 41/4

0.19 + 0.35l 0.26 + 0.50l 0.33 + 0.68l 0.47 + 0.89l 0.58 + 1.13l 0.70 + 1.39l 0.82 + 1.68l 1.02 + 2.00l 1.17 + 2.35l 1.34 + 2.73l 1.51 + 3.13l

2 21/2 23/4 3 31/4 33/4 4 5 5 6 6

1/4

2.64 3.10 3.50 9.00 9.40 10.9 11.4 28.5 28.5 33.8 33.8

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1/4 1/4 3/8 3/8 3/8 3/8 1/2 1/2 1/2 1/2

AISC_PART 15:14th Ed.

15–22

2/24/11

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Page 22

DESIGN OF HANGER CONNECTIONS, BRACKET PLATES, AND…

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

4/1/11

9:15 AM

Page 1

16–1

PART 16 SPECIFICATIONS AND CODES

SPECIFICATION FOR STRUCTURAL STEEL BUILDINGS, JUNE 22, 2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.1–i Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.1–iii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.1–v Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.1–xxvii Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.1–xliii Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.1–1 Commentary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.1–241 SPECIFICATION FOR STRUCTURAL JOINTS USING HIGH-STRENGTH BOLTS, DECEMBER 31, 2009 . . . . . . . . . . . . . . . . . . . . . . . . . 16.2–i Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16.2–iii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2–v Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2–vii Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2–ix Specification and Commentary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2–1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2–80 CODE OF STANDARD PRACTICE FOR STEEL BUILDINGS AND BRIDGES, APRIL 14, 2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.3–i Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.3–iii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.3–v Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.3–vii Specification and Commentary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.3–1

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

16.1–2

1/20/11

7:56 AM

Page 2

SPECIFICATIONS AND CODES

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

2/24/11

3:34 PM

Page i

ANSI/AISC 360-10 An American National Standard

Specification for Structural Steel Buildings June 22, 2010 Supersedes the Specification for Structural Steel Buildings dated March 9, 2005 and all previous versions of this specification Approved by the AISC Committee on Specifications

AMERICAN INSTITUTE OF STEEL CONSTRUCTION One East Wacker Drive, Suite 700 Chicago, Illinois 60601-1802

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A_14th Ed._February 25, 2013 14-11-22 12:44 PM Page ii

(Black plate)

AISC © 2010 by American Institute of Steel Construction All rights reserved. This book or any part thereof must not be reproduced in any form without the written permission of the publisher. The AISC logo is a registered trademark of AISC. The information presented in this publication has been prepared in accordance with recognized engineering principles and is for general information only. While it is believed to be accurate, this information should not be used or relied upon for any specific application without competent professional examination and verification of its accuracy, suitability and applicability by a licensed professional engineer, designer or architect. The publication of the material contained herein is not intended as a representation or warranty on the part of the American Institute of Steel Construction or of any other person named herein, that this information is suitable for any general or particular use or of freedom from infringement of any patent or patents. Anyone making use of this information assumes all liability arising from such use. Caution must be exercised when relying upon other specifications and codes developed by other bodies and incorporated by reference herein since such material may be modified or amended from time to time subsequent to the printing of this edition. The Institute bears no responsibility for such material other than to refer to it and incorporate it by reference at the time of the initial publication of this edition. Printed in the United States of America Second Printing: February 2012 Third Printing: February 2013 Fourth Printing: February 2015

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

1/20/11

7:56 AM

Page iii

16.1–iii

PREFACE (This Preface is not part of ANSI/AISC 360-10, Specification for Structural Steel Buildings, but is included for informational purposes only.) This Specification is based upon past successful usage, advances in the state of knowledge, and changes in design practice. The 2010 American Institute of Steel Construction’s Specification for Structural Steel Buildings provides an integrated treatment of allowable stress design (ASD) and load and resistance factor design (LRFD), and replaces earlier Specifications. As indicated in Chapter B of the Specification, designs can be made according to either ASD or LRFD provisions. This Specification has been developed as a consensus document to provide a uniform practice in the design of steel-framed buildings and other structures. The intention is to provide design criteria for routine use and not to provide specific criteria for infrequently encountered problems, which occur in the full range of structural design. This Specification is the result of the consensus deliberations of a committee of structural engineers with wide experience and high professional standing, representing a wide geographical distribution throughout the United States. The committee includes approximately equal numbers of engineers in private practice and code agencies, engineers involved in research and teaching, and engineers employed by steel fabricating and producing companies. The contributions and assistance of more than 50 additional professional volunteers working in ten task committees are also hereby acknowledged. The Symbols, Glossary and Appendices to this Specification are an integral part of the Specification. A non-mandatory Commentary has been prepared to provide background for the Specification provisions and the user is encouraged to consult it. Additionally, nonmandatory User Notes are interspersed throughout the Specification to provide concise and practical guidance in the application of the provisions. The reader is cautioned that professional judgment must be exercised when data or recommendations in the Specification are applied, as described more fully in the disclaimer notice preceding this Preface. This Specification was approved by the Committee on Specifications: James M. Fisher, Chairman Edward E. Garvin, Vice Chairman Hansraj G. Ashar William F. Baker John M. Barsom William D. Bast Reidar Bjorhovde Roger L. Brockenbrough Gregory G. Deierlein Bruce R. Ellingwood Michael D. Engelhardt Shu-Jin Fang Steven J. Fenves John W. Fisher Theodore V. Galambos

Louis F. Geschwindner Lawrence G. Griffis John L. Gross Jerome F. Hajjar Patrick M. Hassett Tony C. Hazel Mark V. Holland Ronald J. Janowiak Richard C. Kaehler Lawrence A. Kloiber Lawrence F. Kruth Jay W. Larson Roberto T. Leon James O. Malley Sanjeev R. Malushte

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

16.1–iv

1/20/11

7:56 AM

Page iv

PREFACE

David L. McKenzie Duane K. Miller Larry S. Muir Thomas M. Murray R. Shankar Nair Jack E. Petersen Douglas A. Rees-Evans Thomas A. Sabol

Robert E. Shaw, Jr. Donald R. Sherman W. Lee Shoemaker William A. Thornton Raymond H. R. Tide Chia-Ming Uang Donald W. White Cynthia J. Duncan, Secretary

The Committee gratefully acknowledges the following task committee members and staff for their contribution to this document: Allen Adams Farid Alfawakhiri Susan Burmeister Bruce M. Butler Charles J. Carter Helen Chen Bernard Cvijanovic Robert Disque Carol Drucker W. Samuel Easterling Duane Ellifritt Marshall T. Ferrell Christopher M. Foley Steven Freed Fernando Frias Nancy Gavlin Amanuel Gebremeskel Rodney D. Gibble Subhash Goel Arvind Goverdhan Kurt Gustafson Tom Harrington Todd Helwig Richard Henige Stephen Herlache Steve Herth Keith Hjelmstad Nestor Iwankiw William P. Jacobs, V Matthew Johann Daniel Kaufman Keith Landwehr Barbara Lane Michael Lederle Roberto Leon Andres Lepage

Brent Leu J. Walter Lewis William Lindley Stanley Lindsey LeRoy Lutz Bonnie Manley Peter Marshall Margaret Matthew Curtis L. Mayes William McGuire Saul Mednick James Milke Heath Mitchell Patrick Newman Jeffrey Packer Frederick Palmer Dhiren Panda Teoman Pekoz Clarkson Pinkham Thomas Poulos Christopher Raebel Thomas D. Reed Clinton Rex Benjamin Schafer Thomas Schlafly Monica Stockmann James Swanson Steven J. Thomas Emile Troup Brian Uy Amit H. Varma Sriramulu Vinnakota Ralph Vosters Robert Weber Michael A. West Ronald D. Ziemian

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

1/20/11

7:56 AM

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TABLE OF CONTENTS SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii GLOSSARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xliii SPECIFICATION A. GENERAL PROVISIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A1. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Seismic Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2. Nuclear Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 A2. Referenced Specifications, Codes and Standards . . . . . . . . . . . . . . . . . . . . . . . 2 A3. Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. Structural Steel Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1a. ASTM Designations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1b. Unidentified Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1c. Rolled Heavy Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1d. Built-Up Heavy Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2. Steel Castings and Forgings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3. Bolts, Washers and Nuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4. Anchor Rods and Threaded Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5. Consumables for Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 6. Headed Stud Anchors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 A4. Structural Design Drawings and Specifications . . . . . . . . . . . . . . . . . . . . . . . . 9 B. DESIGN REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 B1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 B2. Loads and Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 B3. Design Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1. Required Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2. Limit States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3. Design for Strength Using Load and Resistance Factor Design (LRFD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4. Design for Strength Using Allowable Strength Design (ASD) . . . . . . . . 11 5. Design for Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6. Design of Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6a. Simple Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6b. Moment Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 7. Moment Redistribution in Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 8. Diaphragms and Collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 9. Design for Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 10. Design for Ponding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 11. Design for Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 12. Design for Fire Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Specification for Structural Steel Buildings, June 22, 2010

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13. Design for Corrosion Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 14. Anchorage to Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Member Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1. Classification of Sections for Local Buckling . . . . . . . . . . . . . . . . . . . . . 14 1a. Unstiffened Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1b. Stiffened Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2. Design Wall Thickness for HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3. Gross and Net Area Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3a. Gross Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3b. Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Fabrication and Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Quality Control and Quality Assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Evaluation of Existing Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

C. DESIGN FOR STABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 C1. General Stability Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1. Direct Analysis Method of Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2. Alternative Methods of Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 C2. Calculation of Required Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1. General Analysis Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2. Consideration of Initial Imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2a. Direct Modeling of Imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2b. Use of Notional Loads to Represent Imperfections . . . . . . . . . . . . . . . . . 22 3. Adjustments to Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 C3. Calculation of Available Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 D. DESIGN OF MEMBERS FOR TENSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 D1. Slenderness Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 D2. Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 D3. Effective Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 D4. Built-Up Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 D5. Pin-Connected Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1. Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2. Dimensional Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 D6. Eyebars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1. Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2. Dimensional Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 E. DESIGN OF MEMBERS FOR COMPRESSION . . . . . . . . . . . . . . . . . . . . . . . . 31 E1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 E2. Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 E3. Flexural Buckling of Members without Slender Elements . . . . . . . . . . . . . . . 33 E4. Torsional and Flexural-Torsional Buckling of Members Without Slender Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 E5. Single Angle Compression Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Specification for Structural Steel Buildings, June 22, 2010

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E6.

E7.

F.

16.1–vii

Built-Up Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1. Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2. Dimensional Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Members with Slender Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 1. Slender Unstiffened Elements, Qs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2. Slender Stiffened Elements, Qa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

DESIGN OF MEMBERS FOR FLEXURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 F1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 F2. Doubly Symmetric Compact I-Shaped Members and Channels Bent About Their Major Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 1. Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2. Lateral-Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 F3. Doubly Symmetric I-Shaped Members With Compact Webs and Noncompact or Slender Flanges Bent About Their Major Axis . . . . . . . . . . . 49 1. Lateral-Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2. Compression Flange Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 F4. Other I-Shaped Members With Compact or Noncompact Webs Bent About Their Major Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 1. Compression Flange Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2. Lateral-Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3. Compression Flange Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4. Tension Flange Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 F5. Doubly Symmetric and Singly Symmetric I-Shaped Members With Slender Webs Bent About Their Major Axis . . . . . . . . . . . . . . . . . . . . . . . . . . 54 1. Compression Flange Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2. Lateral-Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3. Compression Flange Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4. Tension Flange Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 F6. I-Shaped Members and Channels Bent About Their Minor Axis . . . . . . . . . . 55 1. Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2. Flange Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 F7. Square and Rectangular HSS and Box-Shaped Members . . . . . . . . . . . . . . . . 56 1. Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2. Flange Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3. Web Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 F8. Round HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 1. Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2. Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 F9. Tees and Double Angles Loaded in the Plane of Symmetry . . . . . . . . . . . . . . 58 1. Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2. Lateral-Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3. Flange Local Buckling of Tees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4. Local Buckling of Tee Stems in Flexural Compression . . . . . . . . . . . . . 59 Specification for Structural Steel Buildings, June 22, 2010

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F10. Single Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 1. Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2. Lateral-Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3. Leg Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 F11. Rectangular Bars and Rounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 1. Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2. Lateral-Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 F12. Unsymmetrical Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 1. Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2. Lateral-Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3. Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 F13. Proportions of Beams and Girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 1. Strength Reductions for Members With Holes in the Tension Flange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2. Proportioning Limits for I-Shaped Members . . . . . . . . . . . . . . . . . . . . . . 64 3. Cover Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4. Built-Up Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5. Unbraced Length for Moment Redistribution . . . . . . . . . . . . . . . . . . . . . 66 G. DESIGN OF MEMBERS FOR SHEAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 G1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 G2. Members With Unstiffened or Stiffened Webs . . . . . . . . . . . . . . . . . . . . . . . . 67 1. Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2. Transverse Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 G3. Tension Field Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 1. Limits on the Use of Tension Field Action . . . . . . . . . . . . . . . . . . . . . . . 70 2. Shear Strength With Tension Field Action . . . . . . . . . . . . . . . . . . . . . . . 70 3. Transverse Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 G4. Single Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 G5. Rectangular HSS and Box-Shaped Members . . . . . . . . . . . . . . . . . . . . . . . . . .71 G6. Round HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 G7. Weak Axis Shear in Doubly Symmetric and Singly Symmetric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 G8. Beams and Girders with Web Openings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 H. DESIGN OF MEMBERS FOR COMBINED FORCES AND TORSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 H1. Doubly and Singly Symmetric Members Subject to Flexure and Axial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 1. Doubly and Singly Symmetric Members Subject to Flexure and Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2. Doubly and Singly Symmetric Members Subject to Flexure and Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3. Doubly Symmetric Rolled Compact Members Subject to Single Axis Flexure and Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Specification for Structural Steel Buildings, June 22, 2010

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H4. I.

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Unsymmetric and Other Members Subject to Flexure and Axial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Members Subject to Torsion and Combined Torsion, Flexure, Shear and/or Axial force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 1. Round and Rectangular HSS Subject to Torsion . . . . . . . . . . . . . . . . . . . 77 2. HSS Subject to Combined Torsion, Shear, Flexure and Axial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3. Non-HSS Members Subject to Torsion and Combined Stress . . . . . . . . 79 Rupture of Flanges With Holes Subject to Tension . . . . . . . . . . . . . . . . . . . . . 79

DESIGN OF COMPOSITE MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 I1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 1. Concrete and Steel Reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2. Nominal Strength of Composite Sections . . . . . . . . . . . . . . . . . . . . . . . . 82 2a. Plastic Stress Distribution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 2b. Strain Compatibility Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3. Material Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4. Classification of Filled Composite Sections for Local Buckling . . . . . . 83 I2. Axial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 1. Encased Composite Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 1a. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 1b. Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 1c. Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 1d. Load Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 1e. Detailing Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 2. Filled Composite Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 2a. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 2b. Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 2c. Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 2d. Load Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 I3. Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 1a. Effective Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 1b. Strength During Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 2. Composite Beams With Steel Headed Stud or Steel Channel Anchors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 2a. Positive Flexural Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 2b. Negative Flexural Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 2c. Composite Beams With Formed Steel Deck . . . . . . . . . . . . . . . . . . . . . . 90 2d. Load Transfer Between Steel Beam and Concrete Slab . . . . . . . . . . . . . 90 3. Encased Composite Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4. Filled Composite Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4a. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4b. Flexural Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Specification for Structural Steel Buildings, June 22, 2010

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Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 1. Filled and Encased Composite Members . . . . . . . . . . . . . . . . . . . . . . . . . 93 2. Composite Beams With Formed Steel Deck . . . . . . . . . . . . . . . . . . . . . . 93 Combined Flexure and Axial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Load Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 1. General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 2. Force Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 2a. External Force Applied to Steel Section . . . . . . . . . . . . . . . . . . . . . . . . . 94 2b. External Force Applied to Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 2c. External Force Applied Concurrently to Steel and Concrete . . . . . . . . . 94 3. Force Transfer Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3a. Direct Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3b. Shear Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3c. Direct Bond Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4. Detailing Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4a. Encased Composite Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4b. Filled Composite Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Composite Diaphragms and Collector Beams . . . . . . . . . . . . . . . . . . . . . . . . . 96 Steel Anchors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 2. Steel Anchors in Composite Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 2a. Strength of Steel Headed Stud Anchors . . . . . . . . . . . . . . . . . . . . . . . . . . 97 2b. Strength of Steel Channel Anchors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 2c. Required Number of Steel Anchors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 2d. Detailing Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3. Steel Anchors in Composite Components . . . . . . . . . . . . . . . . . . . . . . . .100 3a. Shear Strength of Steel Headed Stud Anchors in Composite Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3b. Tensile Strength of Steel Headed Stud Anchors in Composite Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 3c. Strength of Steel Headed Stud Anchors for Interaction of Shear and Tension in Composite Components . . . . . . . . . . . . . . . . . . . . . . . . 102 3d. Shear Strength of Steel Channel Anchors in Composite Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 3e. Detailing Requirements in Composite Components . . . . . . . . . . . . . . . 104 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

DESIGN OF CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 J1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 1. Design Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 2. Simple Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3. Moment Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4. Compression Members With Bearing Joints . . . . . . . . . . . . . . . . . . . . . 106 5. Splices in Heavy Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Specification for Structural Steel Buildings, June 22, 2010

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6. Weld Access Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7. Placement of Welds and Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 8. Bolts in Combination With Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 9. High-Strength Bolts in Combination With Rivets . . . . . . . . . . . . . . . . . 108 10. Limitations on Bolted and Welded Connections . . . . . . . . . . . . . . . . . . 108 Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 1. Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 1a. Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 1b. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 2. Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 2a. Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 2b. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 3. Plug and Slot Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3a. Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3b. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4. Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5. Combination of Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 6. Filler Metal Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7. Mixed Weld Metal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 Bolts and Threaded Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 1. High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 2. Size and Use of Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 3. Minimum Spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 4. Minimum Edge Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5. Maximum Spacing and Edge Distance . . . . . . . . . . . . . . . . . . . . . . . . . 122 6. Tensile and Shear Strength of Bolts and Threaded Parts . . . . . . . . . . . . 124 7. Combined Tension and Shear in Bearing-Type Connections . . . . . . . . 125 8. High-Strength Bolts in Slip-Critical Connections . . . . . . . . . . . . . . . . . 126 9. Combined Tension and Shear in Slip-Critical Connections . . . . . . . . . 127 10. Bearing Strength at Bolt Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 11. Special Fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 12. Tension Fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Affected Elements of Members and Connecting Elements . . . . . . . . . . . . . . 128 1. Strength of Elements in Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 2. Strength of Elements in Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129 3. Block Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129 4. Strength of Elements in Compression . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5. Strength of Elements in Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 1. Fillers in Welded Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 1a. Thin Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 1b. Thick Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130 2. Fillers in Bolted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Specification for Structural Steel Buildings, June 22, 2010

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Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Bearing Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Column Bases and Bearing on Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Anchor Rods and Embedments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Flanges and Webs with Concentrated Forces . . . . . . . . . . . . . . . . . . . . . . . . 133 1. Flange Local Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 2. Web Local Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 3. Web Local Crippling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 4. Web Sidesway Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5. Web Compression Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 6. Web Panel Zone Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 7. Unframed Ends of Beams and Girders . . . . . . . . . . . . . . . . . . . . . . . . . 138 8. Additional Stiffener Requirements for Concentrated Forces . . . . . . . . . 138 9. Additional Doubler Plate Requirements for Concentrated Forces . . . . 138

K. DESIGN OF HSS AND BOX MEMBER CONNECTIONS . . . . . . . . . . . . . . . 140 K1. Concentrated Forces on HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 1. Definitions of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 2. Round HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 3. Rectangular HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 K2. HSS-to-HSS Truss Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 1. Definitions of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 2. Round HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 3. Rectangular HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 K3. HSS-to-HSS Moment Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 1. Definitions of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 2. Round HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 3. Rectangular HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 K4. Welds of Plates and Branches to Rectangular HSS . . . . . . . . . . . . . . . . . . . . 154 L. DESIGN FOR SERVICEABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 L1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 L2. Camber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 L3. Deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 L4. Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 L5. Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 L6. Wind-Induced Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 L7. Expansion and Contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 L8. Connection Slip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 M. FABRICATION AND ERECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 M1. Shop and Erection Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 M2. Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 1. Cambering, Curving and Straightening . . . . . . . . . . . . . . . . . . . . . . . . . 165 2. Thermal Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Specification for Structural Steel Buildings, June 22, 2010

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3. Planing of Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 4. Welded Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 5. Bolted Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 6. Compression Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 7. Dimensional Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 8. Finish of Column Bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 9. Holes for Anchor Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 10. Drain Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 11. Requirements for Galvanized Members . . . . . . . . . . . . . . . . . . . . . . . . 168 Shop Painting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 1. General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 2. Inaccessible Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 3. Contact Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 4. Finished Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 5. Surfaces Adjacent to Field Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 1. Column Base Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 2. Stability and Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 3. Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 4. Fit of Column Compression Joints and Base Plates . . . . . . . . . . . . . . . 169 5. Field Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 6. Field Painting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

N. QUALITY CONTROL AND QUALITY ASSURANCE . . . . . . . . . . . . . . . . . . 170 N1. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 N2. Fabricator and Erector Quality Control Program . . . . . . . . . . . . . . . . . . . . . 171 N3. Fabricator and Erector Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 1. Submittals for Steel Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 2. Available Documents for Steel Construction . . . . . . . . . . . . . . . . . . . . . 171 N4. Inspection and Nondestructive Testing Personnel . . . . . . . . . . . . . . . . . . . . . 172 1. Quality Control Inspector Qualifications . . . . . . . . . . . . . . . . . . . . . . . . 172 2. Quality Assurance Inspector Qualifications . . . . . . . . . . . . . . . . . . . . . . 173 3. NDT Personnel Qualifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 N5. Minimum Requirements for Inspection of Structural Steel Buildings . . . . . 173 1. Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 2. Quality Assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 3. Coordinated Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 4. Inspection of Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 5. Nondestructive Testing of Welded Joints . . . . . . . . . . . . . . . . . . . . . . . . 177 5a. Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 5b. CJP Groove Weld NDT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 5c. Access Hole NDT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 5d. Welded Joints Subjected to Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 5e. Reduction of Rate of Ultrasonic Testing . . . . . . . . . . . . . . . . . . . . . . . . 178 Specification for Structural Steel Buildings, June 22, 2010

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5f. Increase in Rate of Ultrasonic Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 178 5g. Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 6. Inspection of High-Strength Bolting . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 7. Other Inspection Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Minimum Requirements for Inspection of Composite Construction . . . . . . 181 Approved Fabricators and Erectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 Nonconforming Material and Workmanship . . . . . . . . . . . . . . . . . . . . . . . . . 182

APPENDIX 1. DESIGN BY INELASTIC ANALYSIS . . . . . . . . . . . . . . . . . . . . . . 183 1.1. General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 1.2. Ductility Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 1. Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 2. Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 3. Unbraced Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 4. Axial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 1.3. Analysis Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 1. Material Properties and Yield Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . 186 2. Geometric Imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 3. Residual Stress and Partial Yielding Effects . . . . . . . . . . . . . . . . . . . . . 187 APPENDIX 2. DESIGN FOR PONDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 2.1. Simplified Design for Ponding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 2.2. Improved Design for Ponding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 APPENDIX 3. DESIGN FOR FATIGUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 3.1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 3.2. Calculation of Maximum Stresses and Stress Ranges . . . . . . . . . . . . . . . . . . 193 3.3. Plain Material and Welded Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 3.4. Bolts and Threaded Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 3.5. Special Fabrication and Erection Requirements . . . . . . . . . . . . . . . . . . . . . . 197 APPENDIX 4. STRUCTURAL DESIGN FOR FIRE CONDITIONS . . . . . . . . . 214 4.1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 4.1.1. Performance Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 4.1.2. Design by Engineering Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 214 4.1.3. Design by Qualification Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 215 4.1.4. Load Combinations and Required Strength . . . . . . . . . . . . . . . . . . 215 4.2. Structural Design for Fire Conditions by Analysis . . . . . . . . . . . . . . . . . . . . 215 4.2.1. Design-Basis Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 4.2.1.1. Localized Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 4.2.1.2. Post-Flashover Compartment Fires . . . . . . . . . . . . . . . . . . . . . . . . 216 4.2.1.3. Exterior Fires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 4.2.1.4. Active Fire Protection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 4.2.2. Temperatures in Structural Systems under Fire Conditions . . . . . 216 4.2.3. Material Strengths at Elevated Temperatures . . . . . . . . . . . . . . . . 216 Specification for Structural Steel Buildings, June 22, 2010

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4.2.3.1. Thermal Elongation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 4.2.3.2. Mechanical Properties at Elevated Temperatures . . . . . . . . . . . . . 217 4.2.4. Structural Design Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . 218 4.2.4.1. General Structural Integrity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 4.2.4.2. Strength Requirements and Deformation Limits . . . . . . . . . . . . . . 218 4.2.4.3. Methods of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 4.2.4.3a. Advanced Methods of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 4.2.4.3b. Simple Methods of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 4.2.4.4. Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Design by Qualification Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 4.3.1. Qualification Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 4.3.2. Restrained Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 4.3.3. Unrestrained Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

APPENDIX 5. EVALUATION OF EXISTING STRUCTURES . . . . . . . . . . . . . . 223 5.1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 5.2. Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 1. Determination of Required Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 2. Tensile Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 3. Chemical Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 4. Base Metal Notch Toughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 5. Weld Metal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 6. Bolts and Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 5.3. Evaluation by Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 1. Dimensional Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 2. Strength Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 3. Serviceability Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 5.4. Evaluation by Load Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 1. Determination of Load Rating by Testing . . . . . . . . . . . . . . . . . . . . . . . 225 2. Serviceability Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 5.5. Evaluation Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 APPENDIX 6. STABILITY BRACING FOR COLUMNS AND BEAMS . . . . . . 227 6.1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 6.2. Column Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 1. Relative Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 2. Nodal Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 6.3. Beam Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 1. Lateral Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 1a. Relative Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 1b. Nodal Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 2. Torsional Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 2a. Nodal Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 2b. Continuous Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Specification for Structural Steel Buildings, June 22, 2010

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Beam-Column Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

APPENDIX 7. 7.1. 7.2.

7.3

ALTERNATIVE METHODS OF DESIGN FOR STABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 General Stability Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Effective Length Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 1. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 2. Required Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 3. Available Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 First-Order Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 1. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 2. Required Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 3. Available Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

APPENDIX 8. APPROXIMATE SECOND-ORDER ANALYSIS . . . . . . . . . . . . . 237 8.1. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 8.2. Calculation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 1. Multiplier B1 for P-δ Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 2. Multiplier B2 for P-Δ Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 COMMENTARY INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 COMMENTARY SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 COMMENTARY GLOSSARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 A. GENERAL PROVISIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 A1. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 A2. Referenced Specifications, Codes and Standards . . . . . . . . . . . . . . . . . . . . . 247 A3. Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 1. Structural Steel Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 1a. ASTM Designations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 1c. Rolled Heavy Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 2. Steel Castings and Forgings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 3. Bolts, Washers and Nuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 4. Anchor Rods and Threaded Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 5. Consumables for Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 A4. Structural Design Drawings and Specifications . . . . . . . . . . . . . . . . . . . . . . 252 B. DESIGN REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 B1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 B2. Loads and Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 B3. Design Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 1. Required Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 2. Limit States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Specification for Structural Steel Buildings, June 22, 2010

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3.

B4.

Design for Strength Using Load and Resistance Factor Design (LRFD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 4. Design for Strength Using Allowable Strength Design (ASD) . . . . . . . 260 5. Design for Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 6. Design of Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 7. Moment Redistribution in Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 8. Diaphragms and Collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 10. Design for Ponding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 12. Design for Fire Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 13. Design for Corrosion Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Member Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 1. Classifications of Sections for Local Buckling . . . . . . . . . . . . . . . . . . . 268 2. Design Wall Thickness for HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 3. Gross and Net Area Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 3a. Gross Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 3b. Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

C. DESIGN FOR STABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 C1. General Stability Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 C2. Calculation of Required Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 1. General Analysis Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 2. Consideration of Initial Imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . 279 3. Adjustments to Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 C3. Calculation of Available Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 D. DESIGN OF MEMBERS FOR TENSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 D1. Slenderness Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 D2. Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 D3. Effective Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 D4. Built-Up Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 D5. Pin-Connected Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 1. Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 2. Dimensional Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 D6. Eyebars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .288 1. Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 2. Dimensional Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .288 E. DESIGN OF MEMBERS FOR COMPRESSION . . . . . . . . . . . . . . . . . . . . . . . 290 E1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 E2. Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 E3. Flexural Buckling of Members Without Slender Elements . . . . . . . . . . . . . . 292 E4. Torsional and Flexural-Torsional Buckling of Members Without Slender Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 E5. Single Angle Compression Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 E6. Built-Up Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Specification for Structural Steel Buildings, June 22, 2010

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1. Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 2. Dimensional Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Members with Slender Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 1. Slender Unstiffened Elements, Qs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 2. Slender Stiffened Elements, Qa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

DESIGN OF MEMBERS FOR FLEXURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 F1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 F2. Doubly Symmetric Compact I-Shaped Members and Channels Bent About Their Major Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 F3. Doubly Symmetric I-Shaped Members With Compact Webs and Noncompact or Slender Flanges Bent About Their Major Axis . . . . . . . . . . 310 F4. Other I-Shaped Members with Compact or Noncompact Webs Bent About Their Major Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 F5. Doubly Symmetric and Singly Symmetric I-Shaped Members with Slender Webs Bent About Their Major Axis . . . . . . . . . . . . . . . . . . . . . 312 F6. I-Shaped Members and Channels Bent About Their Minor Axis . . . . . . . . . 312 F7. Square and Rectangular HSS and Box-Shaped Members . . . . . . . . . . . . . . . 312 F8. Round HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 F9. Tees and Double Angles Loaded in the Plane of Symmetry . . . . . . . . . . . . . 314 F10. Single Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 1. Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 2. Lateral-Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 3. Leg Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 F11. Rectangular Bars and Rounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 F12. Unsymmetrical Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 F13. Proportions of Beams and Girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 1. Strength Reductions for Members With Holes in the Tension Flange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 2. Proportioning Limits for I-Shaped Members . . . . . . . . . . . . . . . . . . . . . 323 3. Cover Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 5. Unbraced Length for Moment Redistribution . . . . . . . . . . . . . . . . . . . . 324

G. DESIGN OF MEMBERS FOR SHEAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 G1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 G2. Members With Unstiffened or Stiffened Webs . . . . . . . . . . . . . . . . . . . . . . . 325 1. Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 2. Transverse Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 G3. Tension Field Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 1. Limits on the Use of Tension Field Action . . . . . . . . . . . . . . . . . . . . . . 327 2. Shear Strength With Tension Field Action . . . . . . . . . . . . . . . . . . . . . . 328 3. Transverse Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 G4. Single Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 G5. Rectangular HSS and Box-Shaped Members . . . . . . . . . . . . . . . . . . . . . . . . 329 Specification for Structural Steel Buildings, June 22, 2010

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G6. G7. G8.

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Round HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 Weak Axis Shear in Doubly and Singly Symmetric Shapes . . . . . . . . . . . . . 330 Beams and Girders with Web Openings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330

H. DESIGN OF MEMBERS FOR COMBINED FORCES AND TORSION . . . . 331 H1. Doubly and Singly Symmetric Members Subject to Flexure and Axial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 1. Doubly and Singly Symmetric Members Subject to Flexure and Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 2. Doubly and Singly Symmetric Members in Flexure and Tension . . . . . 335 3. Doubly Symmetric Rolled Compact Members Subject to Single Axis Flexure and Compression . . . . . . . . . . . . . . . . . . . . . . . . . . 335 H2. Unsymmetric and Other Members Subject to Flexure and Axial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 H3. Members Subject to Torsion and Combined Torsion, Flexure, Shear and/or Axial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 1. Round and Rectangular HSS Subject to Torsion . . . . . . . . . . . . . . . . . . 341 2. HSS Subject to Combined Torsion, Shear, Flexure and Axial Force . . 342 3. Non-HSS Members Subject to Torsion and Combined Stress . . . . . . . 343 H4. Rupture of Flanges With Holes Subject to Tension . . . . . . . . . . . . . . . . . . . . 343 I.

DESIGN OF COMPOSITE MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 I1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 1. Concrete and Steel Reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 2. Nominal Strength of Composite Sections . . . . . . . . . . . . . . . . . . . . . . . 346 2a. Plastic Stress Distribution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 2b. Strain-Compatibility Aproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 3. Material Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 4. Classification of Filled Composite Sections for Local Buckling . . . . . 348 I2. Axial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 1. Encased Composite Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 1a. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 1b. Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 1c. Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 2. Filled Composite Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 2a. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 2b. Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 2c. Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 I3. Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 1a. Effective Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 1b. Strength During Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 2. Composite Beams With Steel Headed Stud or Steel Channel Anchors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 Specification for Structural Steel Buildings, June 22, 2010

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2a. Positive Flexural Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 2b. Negative Flexural Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 2c. Composite Beams With Formed Steel Deck . . . . . . . . . . . . . . . . . . . . . 360 2d. Load Transfer Between Steel Beam and Concrete Slab . . . . . . . . . . . . 360 3. Encased Composite Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 4. Filled Composite Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 1. Filled and Encased Composite Members . . . . . . . . . . . . . . . . . . . . . . . . 365 2. Composite Beams With Formed Steel Deck . . . . . . . . . . . . . . . . . . . . . 365 Combined Flexure and Axial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 Load Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 1. General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 2. Force Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 3. Force Transfer Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 3a. Direct Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 3b. Shear Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 3c. Direct Bond Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 4. Detailing Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 Composite Diaphragms and Collector Beams . . . . . . . . . . . . . . . . . . . . . . . . 374 Steel Anchors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 2. Steel Anchors in Composite Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 2a. Strength of Steel Headed Stud Anchors . . . . . . . . . . . . . . . . . . . . . . . . . 377 2b. Strength of Steel Channel Anchors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 2d. Detailing Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 3. Steel Anchors in Composite Components . . . . . . . . . . . . . . . . . . . . . . . 380 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382

DESIGN OF CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 J1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 1. Design Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 2. Simple Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 3. Moment Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 4. Compression Members With Bearing Joints . . . . . . . . . . . . . . . . . . . . . 384 5. Splices in Heavy Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 6. Weld Access Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 7. Placement of Welds and Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 8. Bolts in Combination With Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 9. High-Strength Bolts in Combination With Rivets . . . . . . . . . . . . . . . . . 388 10. Limitations on Bolted and Welded Connections . . . . . . . . . . . . . . . . . . 388 J2. Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 1. Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 1a. Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

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1b. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 2. Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 2a. Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 2b. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 3. Plug and Slot Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 3a. Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 3b. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 4. Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 5. Combination of Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 6. Filler Metal Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 7. Mixed Weld Metal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 J3. Bolts and Threaded Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 1. High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 2. Size and Use of Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 3. Minimum Spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 4. Minimum Edge Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 5. Maximum Spacing and Edge Distance . . . . . . . . . . . . . . . . . . . . . . . . . 402 6. Tension and Shear Strength of Bolts and Threaded Parts . . . . . . . . . . . 402 7. Combined Tension and Shear in Bearing-Type Connections . . . . . . . . 404 8. High-Strength Bolts in Slip-Critical Connections . . . . . . . . . . . . . . . . . 406 9. Combined Tension and Shear in Slip-Critical Connections . . . . . . . . . 410 10. Bearing Strength at Bolt Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410 12. Tension Fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 J4. Affected Elements of Members and Connecting Elements . . . . . . . . . . . . . . 411 1. Strength of Elements in Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 2. Strength of Elements in Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 3. Block Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 4. Strength of Elements in Compression . . . . . . . . . . . . . . . . . . . . . . . . . . 413 J5. Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 J7. Bearing Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 J8. Column Bases and Bearing on Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 J9. Anchor Rods and Embedments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 J10. Flanges and Webs with Concentrated Forces . . . . . . . . . . . . . . . . . . . . . . . . 415 1. Flange Local Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 2. Web Local Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 3. Web Local Crippling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 4. Web Sidesway Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 5. Web Compression Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 6. Web Panel-Zone Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 7. Unframed Ends of Beams and Girders . . . . . . . . . . . . . . . . . . . . . . . . . 421 8. Additional Stiffener Requirements for Concentrated Forces . . . . . . . . 422 9. Additional Doubler Plate Requirements for Concentrated Forces . . . . 423

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K. DESIGN OF HSS AND BOX MEMBER CONNECTIONS . . . . . . . . . . . . . . . 425 K1. Concentrated Forces on HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 1. Definitions of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 2. Round HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 3. Rectangular HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 K2. HSS-to-HSS Truss Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 1. Definitions of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 2. Round HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 3. Rectangular HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 K3. HSS-to-HSS Moment Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436 K4. Welds of Plates and Branches to Rectangular HSS . . . . . . . . . . . . . . . . . . . . 437 L. DESIGN FOR SERVICEABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 L1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 L2. Camber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 L3. Deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 L4. Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 L5. Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 L6. Wind-Induced Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 L7. Expansion and Contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 L8. Connection Slip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 M. FABRICATION AND ERECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 M1. Shop and Erection Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 M2. Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 1. Cambering, Curving and Straightening . . . . . . . . . . . . . . . . . . . . . . . . . 445 2. Thermal Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 4. Welded Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 5. Bolted Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 10. Drain Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 11. Requirements for Galvanized Members . . . . . . . . . . . . . . . . . . . . . . . . 447 M3. Shop Painting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 1. General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 3. Contact Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 5. Surfaces Adjacent to Field Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 M4. Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 2. Stability and Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 4. Fit of Column Compression Joints and Base Plates . . . . . . . . . . . . . . . 448 5. Field Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 N. QUALITY CONTROL AND QUALITY ASSURANCE . . . . . . . . . . . . . . . . . . 450 N1. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450 N2. Fabricator and Erector Quality Control Program . . . . . . . . . . . . . . . . . . . . . 451 N3. Fabricator and Erector Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452 1. Submittals for Steel Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452 Specification for Structural Steel Buildings, June 22, 2010

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N5.

N6. N7.

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2. Available Documents for Steel Construction . . . . . . . . . . . . . . . . . . . . . 452 Inspection and Nondestructive Testing Personnel . . . . . . . . . . . . . . . . . . . . . 453 1. Quality Control Inspector Qualifications . . . . . . . . . . . . . . . . . . . . . . . . 453 2. Quality Assurance Inspector Qualifications . . . . . . . . . . . . . . . . . . . . . . 453 3. NDT Personnel Qualifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Minimum Requirements for Inspection of Structural Steel Buildings . . . . . 454 1. Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454 2. Quality Assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454 3. Coordinated Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 4. Inspection of Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .456 5. Nondestructive Testing of Welded Joints . . . . . . . . . . . . . . . . . . . . . . . . 460 5a. Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 5b. CJP Groove Weld NDT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 5c. Access Hole NDT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462 5d. Welded Joints Subjected to Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462 5e. Reduction of Rate of Ultrasonic Testing . . . . . . . . . . . . . . . . . . . . . . . . 462 5f. Increase in Rate of Ultrasonic Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 463 6. Inspection of High-Strength Bolting . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 7. Other Inspection Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464 Minimum Requirements for Inspection of Composite Construction . . . . . . 466 Approved Fabricators and Erectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466

APPENDIX 1. DESIGN BY INELASTIC ANALYSIS . . . . . . . . . . . . . . . . . . . . . . 468 1.1. General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 1.2. Ductility Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 1. Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 2. Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 3. Unbraced Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472 4. Axial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 1.3. Analysis Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 1. Material Properties and Yield Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . 474 2. Geometric Imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 3. Residual Stresses and Partial Yielding Effects . . . . . . . . . . . . . . . . . . . 474 APPENDIX 2.

DESIGN FOR PONDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476

APPENDIX 3. 3.1. 3.2. 3.3. 3.4. 3.5.

DESIGN FOR FATIGUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Calculation of Maximum Stresses and Stress Ranges . . . . . . . . . . . . . . 479 Plain Material and Welded Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 Bolts and Threaded Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 Special Fabrication and Erection Requirements . . . . . . . . . . . . . . . . . . 482

APPENDIX 4. STRUCTURAL DESIGN FOR FIRE CONDITIONS . . . . . . . . . 483 4.1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 Specification for Structural Steel Buildings, June 22, 2010

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4.1.1. Performance Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 4.1.2. Design by Engineering Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 483 4.1.4. Load Combinations and Required Strength . . . . . . . . . . . . . . . . . . 484 Structural Design for Fire Conditions by Analysis . . . . . . . . . . . . . . . . . . . . 485 4.2.1. Design-Basis Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 4.2.1.1. Localized Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 4.2.1.2. Post-Flashover Compartment Fires . . . . . . . . . . . . . . . . . . . . . . . . 485 4.2.1.3. Exterior Fires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 4.2.1.4. Active Fire Protection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 4.2.2. Temperatures in Structural Systems Under Fire Conditions . . . . . 486 4.2.3. Material Strengths at Elevated Temperatures . . . . . . . . . . . . . . . . 490 4.2.4. Structural Design Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . 491 4.2.4.1. General Structural Integrity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 4.2.4.2. Strength Requirements and Deformation Limits . . . . . . . . . . . . . . 491 4.2.4.3. Methods of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 4.2.4.3a. Advanced Methods of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 4.2.4.3b. Simple Methods of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492 4.2.4.4. Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492 Design by Qualification Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 4.3.1. Qualification Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 4.3.2. Restrained Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 4.3.3. Unrestrained Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

APPENDIX 5. EVALUATION OF EXISTING STRUCTURES . . . . . . . . . . . . . . 497 5.1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 5.2. Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 1. Determination of Required Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 2. Tensile Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 4. Base Metal Notch Toughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 5. Weld Metal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 6. Bolts and Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 5.3. Evaluation by Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 2. Strength Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 5.4. Evaluation by Load Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499 1. Determination of Load Rating by Testing . . . . . . . . . . . . . . . . . . . . . . . 499 2. Serviceability Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499 5.5. Evaluation Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500 APPENDIX 6. STABILITY BRACING FOR COLUMNS AND BEAMS . . . . . . 501 6.1. General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501 6.2. Column Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504 6.3. Beam Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 1. Lateral Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506 2. Torsional Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506 Specification for Structural Steel Buildings, June 22, 2010

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Beam-Column Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

APPENDIX 7. ALTERNATIVE METHODS OF DESIGN FOR STABILITY . . 509 7.2. Effective Length Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 7.3. First-Order Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518 APPENDIX 8.

APPROXIMATE SECOND-ORDER ANALYSIS . . . . . . . . . . . . . 520

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

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16.1–xxvii

SYMBOLS

Some definitions in the list below have been simplified in the interest of brevity. In all cases, the definitions given in the body of the Specification govern. Symbols without text definitions, used only in one location and defined at that location are omitted in some cases. The section or table number in the right-hand column refers to the Section where the symbol is first used. Symbol ABM Ab Abi Abj Ac Ac Ae Ae Afc Afg Afn Aft Ag Ag Agv An An Ant Anv Apb As Asa Asf Asr Asr At Aw Awe Awei A1 A1

Definition Section Cross-sectional area of the base metal, in.2 (mm2) . . . . . . . . . . . . . . . . . . . J2.4 Nominal unthreaded body area of bolt or threaded part, in.2 (mm2) . . . . . J3.6 Cross-sectional area of the overlapping branch, in.2 (mm2) . . . . . . . . . . . K2.3 Cross-sectional area of the overlapped branch, in.2 (mm2) . . . . . . . . . . . . K2.3 Area of concrete, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I2.1b Area of concrete slab within effective width, in.2 (mm2) . . . . . . . . . . . . . I3.2d Effective net area, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D2 Summation of the effective areas of the cross section based on the reduced effective width, be, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . E7.2 Area of compression flange, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . G3.1 Gross area of tension flange, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . F13.1 Net area of tension flange, in. 2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . F13.1 Area of tension flange, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G3.1 Gross cross-sectional area of member, in.2 (mm2) . . . . . . . . . . . . . . . . . . . B3.7 Gross area of composite member, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . I2.1 Gross area subject to shear, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . J4.3 Net area of member, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B4.3 Area of the directly connected elements, in.2 (mm2) . . . . . . . . . . . . Table D3.1 Net area subject to tension, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . J4.3 Net area subject to shear, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J4.3 Projected area in bearing, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J7 Cross-sectional area of steel section, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . I2.1b Cross-sectional area of steel headed stud anchor, in.2 (mm2) . . . . . . . . . . I8.2a Area on the shear failure path, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . D5.1 Area of continuous reinforcing bars, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . I2.1 Area of adequately developed longitudinal reinforcing steel within the effective width of the concrete slab, in.2 (mm2) . . . . . . . . . . . . . . . . . I3.2d Net area in tension, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 3.4 Area of web, the overall depth times the web thickness, dtw, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G2.1 Effective area of the weld, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J2.4 Effective area of weld throat of any ith weld element, in.2 (mm2) . . . . . . . J2.4 Loaded area of concrete, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I6.3a Area of steel concentrically bearing on a concrete support, in.2 (mm2) . . . . J8

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

16.1–xxviii

Symbol A2 B B Bb Bbi Bbj Bp B1 B2 C Cb Cd Cf Cm Cp Cr Cs Cv Cw C2 D D D Db Du

E Ec Ec (T) Es E(T)

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SYMBOLS

Definition Section Maximum area of the portion of the supporting surface that is geometrically similar to and concentric with the loaded area, in.2 (mm2) . . . J8 Overall width of rectangular HSS member, measured 90 ° to the plane of the connection, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . Table D3.1 Overall width of rectangular steel section along face transferring load, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I6.3c Overall width of rectangular HSS branch member, measured 90 ° to the plane of the connection, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . K2.1 Overall width of the overlapping branch, in. (mm) . . . . . . . . . . . . . . . . . . K2.3 Overall width of the overlapped branch, in. (mm) . . . . . . . . . . . . . . . . . . K2.3 Width of plate, measured 90 ° to the plane of the connection, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K1.1 Multiplier to account for P-δ effects . . . . . . . . . . . . . . . . . . . . . . . . . . . App.8.2 Multiplier to account for P-Δ effects . . . . . . . . . . . . . . . . . . . . . . . . . . App.8.2 HSS torsional constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H3.1 Lateral-torsional buckling modification factor for nonuniform moment diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F1 Coefficient accounting for increased required bracing stiffness at inflection point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 6.3.1 Constant from Table A-3.1 for the fatigue category . . . . . . . . . . . . . . App. 3.3 Coefficient accounting for nonuniform moment . . . . . . . . . . . . . . . App. 8.2.1 Ponding flexibility coefficient for primary member in a flat roof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 2.1 Coefficient for web sidesway buckling . . . . . . . . . . . . . . . . . . . . . . . . . . J10.4 Ponding flexibility coefficient for secondary member in a flat roof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 2.1 Web shear coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G2.1 Warping constant, in.6 (mm6) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E4 Edge distance increment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table J3.5 Outside diameter of round HSS, in. (mm) . . . . . . . . . . . . . . . . . . . . Table B4.1 Outside diameter of round HSS main member, in. (mm) . . . . . . . . . . . . . K2.1 Nominal dead load, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 2.2 Outside diameter of round HSS branch member, in. (mm) . . . . . . . . . . . . K2.1 In slip-critical connections, a multiplier that reflects the ratio of the mean installed bolt pretension to the specified minimum bolt pretension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J3.8 Modulus of elasticity of steel = 29,000 ksi (200 000 MPa) . . . . . . Table B4.1 Modulus of elasticity of concrete = wc1.5 fc′ , ksi (0.043wc1.5 fc′ , MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I2.1b Modulus of elasticity of concrete at elevated temperature, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 4.2.3.2 Modulus of elasticity of steel = 29,000 ksi (200 000 MPa) . . . . . . . . . . . I2.1b Elastic modulus of elasticity of steel at elevated temperature, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 4.2.4.3

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

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SYMBOLS

Symbol EIeff Fc Fca Fcbw , Fcbz Fcr Fcry Fcrz Fe Fe (T) Fex FEXX Fey Fez Fin FL

Fn Fn FnBM Fnt F′nt Fnv Fnw Fnw Fnwi Fnwix Fnwiy Fp (T) FSR FTH Fu Fu (T) Fy

16.1–xxix

Definition Section Effective stiffness of composite section, kip-in.2 (N-mm2) . . . . . . . . . . . . I2.1b Available stress, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K1.1 Available axial stress at the point of consideration, ksi (MPa) . . . . . . . . . . H2 Available flexural stress at the point of consideration, ksi (MPa) . . . . . . . . H2 Critical stress, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E3 Critical stress about the y-axis of symmetry, ksi (MPa) . . . . . . . . . . . . . . . . E4 Critical torsional buckling stress, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . E4 Elastic buckling stress, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E3 Critical elastic buckling stress with the elastic modulus E(T) at elevated temperature, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . App. 4.2.4.3 Flexural elastic buckling stress about the major principal axis, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E4 Filler metal classification strength, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . J2.4 Flexural elastic buckling stress about the major principal axis, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E4 Torsional elastic buckling stress, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . E4 Nominal bond stress, 0.06 ksi (0.40 MPa) . . . . . . . . . . . . . . . . . . . . . . . . I6.3c Magnitude of flexural stress in compression flange at which flange local buckling or lateral-torsional buckling is influenced by yielding, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table B4.1 Nominal stress, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H3.3 Nominal tensile stress, Fnt, or shear stress, Fnv, from Table J3.2, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J3.6 Nominal stress of the base metal, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . J2.4 Nominal tensile stress from Table J3.2, ksi (MPa) . . . . . . . . . . . . . . . . . . . J3.7 Nominal tensile stress modified to include the effects of shear stress, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J3.7 Nominal shear stress from Table J3.2, ksi (MPa) . . . . . . . . . . . . . . . . . . . . J3.7 Nominal stress of the weld metal, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . J2.4 Nominal stress of the weld metal (Chapter J) with no increase in strength due to directionality of load, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . K4 Nominal stress in ith weld element, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . J2.4 x component of nominal stress, Fnwi, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . J2.4 y component of nominal stress, Fnwi, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . J2.4 Proportional limit at elevated temperatures, ksi (MPa) . . . . . . . . . App. 4.2.3.2 Allowable stress range, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 3.3 Threshold allowable stress range, maximum stress range for indefinite design life from Table A-3.1, ksi (MPa) . . . . . . . . . . . . . . . App. 3.1 Specified minimum tensile strength, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . D2 Minimum tensile strength at elevated temperature, ksi (MPa) . . . App. 4.2.3.2 Specified minimum yield stress, ksi (MPa). As used in this Specification, “yield stress” denotes either the specified minimum yield point (for those steels that have a yield point) or specified yield strength (for those steels that do not have a yield point) . . . . . . . . . B3.7

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

16.1–xxx

Symbol Fyb Fybi Fybj Fyf Fyp Fysr Fyst Fy (T) Fyw G G(T) H H H Hb Hbi I Ic Id Ip Is Is Isr Ist

Ist1

Ist2

Ix, Iy

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SYMBOLS

Definition Section Specified minimum yield stress of HSS branch member material, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.1 Specified minimum yield stress of the overlapping branch material, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.3 Specified minimum yield stress of the overlapped branch material, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.3 Specified minimum yield stress of the flange, ksi (MPa) . . . . . . . . . . . . . J10.1 Specified minimum yield stress of plate, ksi (MPa) . . . . . . . . . . . . . . . . K1.1 Specified minimum yield stress of reinforcing bars, ksi (MPa) . . . . . . . I2.1b Specified minimum yield stress of the stiffener material, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G3.3 Yield stress at elevated temperature, ksi (MPa) . . . . . . . . . . . . . . . App. 4.2.4.3 Specified minimum yield stress of the web material, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G3.3 Shear modulus of elasticity of steel = 11,200 ksi (77 200 MPa) . . . . . . . . . E4 Shear modulus of elasticity of steel at elevated temperature, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 4.2.3.2 Flexural constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E4 Story shear, in the direction of translation being considered, produced by the lateral forces used to compute ΔH, kips (N) . . . . . App. 8.2.2 Overall height of rectangular HSS member, measured in the plane of the connection, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . Table D3.1 Overall height of rectangular HSS branch member, measured in the plane of the connection, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . K2.1 Overall depth of the overlapping branch, in. (mm) . . . . . . . . . . . . . . . . . . K2.3 Moment of inertia in the plane of bending, in.4 (mm4) . . . . . . . . . . App. 8.2.1 Moment of inertia of the concrete section about the elastic neutral axis of the composite section, in.4 (mm4) . . . . . . . . . . . . . . . . . . . I2.1b Moment of inertia of the steel deck supported on secondary members, in.4 (mm4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 2.1 Moment of inertia of primary members, in.4 (mm4) . . . . . . . . . . . . . . App. 2.1 Moment of inertia of secondary members, in.4 (mm4) . . . . . . . . . . . . App. 2.1 Moment of inertia of steel shape about the elastic neutral axis of the composite section, in.4 (mm4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I2.1b Moment of inertia of reinforcing bars about the elastic neutral axis of the composite section, in.4 (mm4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I2.1b Moment of inertia of transverse stiffeners about an axis in the web center for stiffener pairs, or about the face in contact with the web plate for single stiffeners, in.4 (mm4) . . . . . . . . . . . . . . . . . . . . . . G3.3 Minimum moment of inertia of transverse stiffeners required for development of the web shear buckling resistance in Section G2.2, in.4 (mm4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G3.3 Minimum moment of inertia of transverse stiffeners required for development of the full web shear buckling plus the web tension field resistance, Vr = Vc2, in.4 (mm4) . . . . . . . . . . . . . . . . . . . . . . . G3.3 Moment of inertia about the principal axes, in.4 (mm4) . . . . . . . . . . . . . . . . E4 Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

1/20/11

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SYMBOLS

Symbol Iy Iyc Iz J K Kx Ky Kz K1

L L L L L L Lb

Lb Lb Lm Lp Lp Lpd Lr Ls Lv MA Ma MB MC Mcx , Mcy

16.1–xxxi

Definition Section Out-of-plane moment of inertia, in.4 (mm4) . . . . . . . . . . . . . . . . . . App. 6.3.2a Moment of inertia of the compression flange about the y-axis, in.4 (mm4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F4.2 Minor principal axis moment of inertia, in.4 (mm4) . . . . . . . . . . . . . . . . . F10.2 Torsional constant, in.4 (mm4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E4 Effective length factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C3, E2 Effective length factor for flexural buckling about x-axis . . . . . . . . . . . . . . E4 Effective length factor for flexural buckling about y-axis . . . . . . . . . . . . . . E4 Effective length factor for torsional buckling . . . . . . . . . . . . . . . . . . . . . . . . E4 Effective length factor in the plane of bending, calculated based on the assumption of no lateral translation at the member ends, set equal to 1.0 unless analysis justifies a smaller value . . . . . . . . . . . . App. 8.2.1 Height of story, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 7.3.2 Length of member, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H3.1 Nominal occupancy live load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 4.1.4 Laterally unbraced length of member, in. (mm) . . . . . . . . . . . . . . . . . . . . . . E2 Length of span, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 6.3.2a Length of member between work points at truss chord centerlines, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E5 Length between points that are either braced against lateral displacement of compression flange or braced against twist of the cross section, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F2.2 Distance between braces, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 6.2 Largest laterally unbraced length along either flange at the point of load, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J10.4 Limiting laterally unbraced length for eligibility for moment redistribution in beams according to Section B3.7 . . . . . . . . . . . . . . . . . F13.5 Limiting laterally unbraced length for the limit state of yielding, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F2.2 Length of primary members, ft (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 2.1 Limiting laterally unbraced length for plastic analysis, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 1.2.3 Limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F2.2 Length of secondary members, ft (m) . . . . . . . . . . . . . . . . . . . . . . . . . App. 2.1 Distance from maximum to zero shear force, in. (mm) . . . . . . . . . . . . . . . . G6 Absolute value of moment at quarter point of the unbraced segment, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F1 Required flexural strength using ASD load combinations, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J10.4 Absolute value of moment at centerline of the unbraced segment, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F1 Absolute value of moment at three-quarter point of the unbraced segment, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F1 Available flexural strength determined in accordance with Chapter F, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H1.1 Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

16.1–xxxii

Symbol Mcx

Mcx Me Mlt Mmax Mmid Mn Mnt

Mp Mp Mr Mr Mrb Mr-ip Mr-op Mrx,Mry Mrx

Mu My My Myc Myt M1′ M1 M2

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SYMBOLS

Definition Section Available lateral-torsional strength for strong axis flexure determined in accordance with Chapter F using Cb = 1.0, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H1.3 Available flexural strength about the x-axis for the limit state of tensile rupture of the flange, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . H4 Elastic lateral-torsional buckling moment, kip-in. (N-mm) . . . . . . . . . . F10.2 First-order moment using LRFD or ASD load combinations, due to lateral translation of the structure only, kip-in. (N-mm) . . . . . . App. 8.2 Absolute value of maximum moment in the unbraced segment, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F1 Moment at the middle of the unbraced length, kip-in. (N-mm) . . . . App. 1.2.3 Nominal flexural strength, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . F1 First-order moment using LRFD or ASD load combinations, with the structure restrained against lateral translation, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 8.2 Plastic bending moment, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . Table B4.1 Moment corresponding to plastic stress distribution over the composite cross section, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . I3.4b Required second-order flexural strength under LRFD or ASD load combinations, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 8.2 Required flexural strength using LRFD or ASD load combinations, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H1.1 Required bracing moment using LRFD or ASD load combinations, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 6.3.2 Required in-plane flexural strength in branch using LRFD or ASD load combinations, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . K3.2 Required out-of-plane flexural strength in branch using LRFD or ASD load combinations, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . K3.2 Required flexural strength, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . H1.1 Required flexural strength at the location of the bolt holes; positive for tension in the flange under consideration, negative for compression, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H4 Required flexural strength using LRFD load combinations, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J10.4 Moment at yielding of the extreme fiber, kip-in. (N-mm) . . . . . . . . Table B4.1 Yield moment about the axis of bending, kip-in. (N-mm) . . . . . . . . . . . . F10.1 Moment at yielding of the extreme fiber in the compression flange, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F4.2 Moment at yielding of the extreme fiber in the tension flange, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F4.4 Effective moment at the end of the unbraced length opposite from M2, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 1.2.3 Smaller moment at end of unbraced length, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F13.5, App. 1.2.3 Larger moment at end of unbraced length, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F13.5, App. 1.2.3 Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

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SYMBOLS

Symbol Ni Ni Ov Pc Pcy Pe Pe story Pey Pe1 Plt Pmf

Pn Pn Pno Pnt Pp Pr Pr Pr Pr Pr Prb Pro Pstory

Pu Pu Py Q

16.1–xxxiii

Definition Section Notional load applied at level i, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . C2.2b Additional lateral load, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 7.3 Overlap connection coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.2 Available axial strength, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H1.1 Available compressive strength out of the plane of bending, kips (N) . . . H1.3 Elastic critical buckling load determined in accordance with Chapter C or Appendix 7, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I2.1b Elastic critical buckling strength for the story in the direction of translation being considered, kips (N) . . . . . . . . . . . . . . . . . . . . . . App 8.2.2 Elastic critical buckling load for buckling about the weak axis, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H1.2 Elastic critical buckling strength of the member in the plane of bending, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 8.2.1 First-order axial force using LRFD or ASD load combinations, due to lateral translation of the structure only, kips (N) . . . . . . . . . . . App. 8.2 Total vertical load in columns in the story that are part of moment frames, if any, in the direction of translation being considered, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 8.2.2 Nominal axial strength, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D2 Nominal compressive strength, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . E1 Nominal compressive strength of zero length, doubly symmetric, axially loaded composite member, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . I2 First-order axial force using LRFD and ASD load combinations, with the structure restrained against lateral translation, kips (N) . . . . App. 8.2 Nominal bearing strength, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J8 Required second-order axial strength using LRFD or ASD load combinations, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 8.2 Required axial compressive strength using LRFD or ASD load combinations, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C2.3 Required axial strength using LRFD or ASD load combinations, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H1.1 Required axial strength of the member at the location of the bolt holes; positive in tension, negative in compression, kips (N) . . . . . . . . . . . H4 Required external force applied to the composite member, kips (N) . . . . I6.2a Required brace strength using LRFD or ASD load combinations, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 6.2 Required axial strength in chord at a joint, on the side of joint with lower compression stress, kips (N) . . . . . . . . . . . . . . . . . . . . . Table K1.1 Total vertical load supported by the story using LRFD or ASD load combinations, as applicable, including loads in columns that are not part of the lateral force resisting system, kips (N) . . . . App. 8.2.2 Required axial strength in chord using LRFD load combinations, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K1.1 Required axial strength in compression, kips (N) . . . . . . . . . . . . . . App. 1.2.2 Axial yield strength, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C2.3 Net reduction factor accounting for all slender compression elements . . . . E7 Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

16.1–xxxiv

Symbol Qa Qct Qcv Qf Qn Qnt Qnv Qrt Qrv Qs R R R Ra RFIL Rg RM Rn Rn Rn Rnwl Rnwt

Rnx Rny Rp Rpc Rpg RPJP Rpt Ru S S S Sc

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SYMBOLS

Definition Section Reduction factor for slender stiffened elements . . . . . . . . . . . . . . . . . . . . . E7.2 Available tensile strength, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I8.3c Available shear strength, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I8.3c Chord-stress interaction parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.2 Nominal strength of one steel headed stud or steel channel anchor, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I3.2 Nominal tensile strength of steel headed stud anchor, kips (N) . . . . . . . . I8.3b Nominal shear strength of steel headed stud anchor, kips (N) . . . . . . . . . I8.3a Required tensile strength, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I8.3c Required shear strength, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I8.3c Reduction factor for slender unstiffened elements . . . . . . . . . . . . . . . . . . . E7.1 Radius of joint surface, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . Table J2.2 Nominal load due to rainwater or snow, exclusive of the ponding contribution, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 2.2 Seismic response modification coefficient . . . . . . . . . . . . . . . . . . . . . . . . A1.1 Required strength using ASD load combinations . . . . . . . . . . . . . . . . . . . B3.4 Reduction factor for joints using a pair of transverse fillet welds only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 3.3 Coefficient to account for group effect . . . . . . . . . . . . . . . . . . . . . . . . . . . I8.2a Coefficient to account for influence of P-δ on P-Δ . . . . . . . . . . . . . App. 8.2.2 Nominal strength, specified in Chapters B through K . . . . . . . . . . . . . . . B3.3 Nominal slip resistance, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J3.8 Nominal strength of the applicable force transfer mechanism, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I6.3 Total nominal strength of longitudinally loaded fillet welds, as determined in accordance with Table J2.5, kips (N) . . . . . . . . . . . . . . . J2.4 Total nominal strength of transversely loaded fillet welds, as determined in accordance with Table J2.5 without the alternate in Section J2.4(a), kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J2.4 Horizontal component of the nominal strength of a weld group, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J2.4 Vertical component of the nominal strength of a weld group, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J2.4 Position effect factor for shear studs . . . . . . . . . . . . . . . . . . . . . . . . . . . . I8.2a Web plastification factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F4.1 Bending strength reduction factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F5.2 Reduction factor for reinforced or nonreinforced transverse partial-joint-penetration (PJP) groove welds . . . . . . . . . . . . . . . . . . . App. 3.3 Web plastification factor corresponding to the tension flange yielding limit state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F4.4 Required strength using LRFD load combinations . . . . . . . . . . . . . . . . . . B3.3 Elastic section modulus, in.3 (mm3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F8.2 Spacing of secondary members, ft (m) . . . . . . . . . . . . . . . . . . . . . . . . App. 2.1 Nominal snow load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 4.1.4 Elastic section modulus to the toe in compression relative to the axis of bending, in.3 (mm3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F10.3 Specification for Structural Steel Buildings, June 22, 2010

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SYMBOLS

Symbol Se Sip Smin Sop Sxc, Sxt Sx Sy T Ta Tb Tc Tn Tr Tu U U Ubs Up Us V′ Vc Vc1 Vc2 Vn Vr Vr V′r Yi

Z

16–xxxv

Definition Section Effective section modulus about major axis, in.3 (mm3) . . . . . . . . . . . . . . F7.2 Effective elastic section modulus of welds for in-plane bending (Table K4.1), in.3 (mm3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K4 Lowest elastic section modulus relative to the axis of bending, in.3 (mm3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F12 Effective elastic section modulus of welds for out-of-plane bending (Table K4.1), in.3 (mm3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K4 Elastic section modulus referred to compression and tension flanges, respectively, in.3 (mm3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table B4.1 Elastic section modulus taken about the x-axis, in.3 (mm3) . . . . . . . . . . . . F2.2 Elastic section modulus taken about the y-axis. For a channel, the minimum section modulus, in.3 (mm3) . . . . . . . . . . . . . . . . . . . . . . . . . F6.2 Nominal forces and deformations due to the design-basis fire defined in Appendix Section 4.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . App. 4.1.4 Required tension force using ASD load combinations, kips (N) . . . . . . . . J3.9 Minimum fastener tension given in Table J3.1 or J3.1M, kips (N) . . . . . . J3.8 Available torsional strength, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . H3.2 Nominal torsional strength, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . H3.1 Required torsional strength using LRFD or ASD load combinations, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H3.2 Required tension force using LRFD load combinations, kips (N) . . . . . . . J3.9 Shear lag factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D3 Utilization ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.2 Reduction coefficient, used in calculating block shear rupture strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J4.3 Stress index for primary members . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 2.2 Stress index for secondary members . . . . . . . . . . . . . . . . . . . . . . . . . . App. 2.2 Nominal shear force between the steel beam and the concrete slab transferred by steel anchors, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . I3.2d Available shear strength, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H3.2 Smaller of the available shear strengths in the adjacent web panels with Vn as defined in Section G2.1, kips (N) . . . . . . . . . . . . . . . . . G3.3 Smaller of the available shear strengths in the adjacent web panels with Vn as defined in Section G3.2, kips (N) . . . . . . . . . . . . . . . . . . . . . . G3.3 Nominal shear strength, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G1 Larger of the required shear strengths in the adjacent web panels using LRFD or ASD load combinations, kips (N) . . . . . . . . . . . . . . . . . . G3.3 Required shear strength using LRFD or ASD load combinations, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H3.2 Required longitudinal shear force to be transferred to the steel or concrete, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I6.2 Gravity load applied at level i from the LRFD load combination or ASD load combination, as applicable, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C2.2b, App. 7.3.2 Plastic section modulus about the axis of bending, in.3 (mm3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F7.1 Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

16.1–xxxvi

Symbol Zb Zx Zy a a a a a′ aw

b b

b b b bcf be be beoi beov bf bfc bft bl bs bs d d d d d d db db dc

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SYMBOLS

Definition Section Plastic section modulus of branch about the axis of bending, in.3 (mm3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K3.1 Plastic section modulus about the x-axis, in.3 (mm3) . . . . . . . . . . . . . . . . . F2.1 Plastic section modulus about the y-axis, in.3 (mm3) . . . . . . . . . . . . . . . . . F6.1 Clear distance between transverse stiffeners, in. (mm) . . . . . . . . . . . . . . F13.2 Distance between connectors, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . E6.1 Shortest distance from edge of pin hole to edge of member measured parallel to the direction of force, in. (mm) . . . . . . . . . . . . . . . . D5.1 Half the length of the nonwelded root face in the direction of the thickness of the tension-loaded plate, in. (mm) . . . . . . . . . . . . . App. 3.3 Weld length along both edges of the cover plate termination to the beam or girder, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F13.3 Ratio of two times the web area in compression due to application of major axis bending moment alone to the area of the compression flange components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F4.2 Full width of leg in compression, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . F10.3 For flanges of I-shaped members, half the full-flange width, bf ; for flanges of channels, the full nominal dimension of the flange, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F6.2 Full width of longest leg, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E7.1 Width of unstiffened compression element; width of stiffened compression element, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B4.1 Width of the leg resisting the shear force, in. (mm) . . . . . . . . . . . . . . . . . . . G4 Width of column flange, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J10.6 Reduced effective width, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E7.2 Effective edge distance for calculation of tensile rupture strength of pin-connected member, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D5.1 Effective width of the branch face welded to the chord, in. (mm) . . . . . . K2.3 Effective width of the branch face welded to the overlapped brace, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.3 Width of flange, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B4.1 Width of compression flange, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . F4.2 Width of tension flange, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G3.1 Length of longer leg of angle, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . E5 Length of shorter leg of angle, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . E5 Stiffener width for one-sided stiffeners, in. (mm) . . . . . . . . . . . . . . App. 6.3.2 Nominal fastener diameter, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J3.3 Nominal bolt diameter, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J3.10 Full nominal depth of the section, in. (mm) . . . . . . . . . . . . . . . . . . B4.1, J10.3 Depth of rectangular bar, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F11.2 Diameter, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J7 Diameter of pin, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D5.1 Depth of beam, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J10.6 Nominal diameter (body or shank diameter), in. (mm) . . . . . . . . . . . . App. 3.4 Depth of column, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J10.6

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

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SYMBOLS

Symbol e emid-ht fc′ fc′(T) fo

fra frbw, frbz frv g g h h h

hc

ho hp

hr k kc ksc kv l l lb lc

16–xxxvii

Definition Section Eccentricity in a truss connection, positive being away from the branches, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.1 Distance from the edge of steel headed stud anchor shank to the steel deck web, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I8.2a Specified compressive strength of concrete, ksi (MPa) . . . . . . . . . . . . . . I1.2b Compressive strength of concrete at elevated temperature, ksi (MPa) . . . I1.2b Stress due to D + R (D = nominal dead load, R = nominal load due to rainwater or snow exclusive of the ponding contribution), ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 2.2 Required axial stress at the point of consideration using LRFD or ASD load combinations, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H2 Required flexural stress at the point of consideration using LRFD or ASD load combinations, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H2 Required shear stress using LRFD or ASD load combinations, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J3.7 Transverse center-to-center spacing (gage) between fastener gage lines, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B4.3 Gap between toes of branch members in a gapped K-connection, neglecting the welds, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.1 Width of stiffened compression element, in. (mm) . . . . . . . . . . . . . . . . . . B4.1 Height of shear element, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G2.1b Clear distance between flanges less the fillet or corner radius for rolled shapes; distance between adjacent lines of fasteners or the clear distance between flanges when welds are used for built-up shapes, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J10.4 Twice the distance from the center of gravity to the following: the inside face of the compression flange less the fillet or corner radius, for rolled shapes; the nearest line of fasteners at the compression flange or the inside faces of the compression flange when welds are used, for built-up sections, in. (mm) . . . . . . . . . . . . . . . . B4.1 Distance between the flange centroids, in. (mm) . . . . . . . . . . . . . . . . . . . . F2.2 Twice the distance from the plastic neutral axis to the nearest line of fasteners at the compression flange or the inside face of the compression flange when welds are used, in. (mm) . . . . . . . . . . . . . . . . . B4.1 Nominal height of rib, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I8.2a Distance from outer face of flange to the web toe of fillet, in. (mm) . . . J10.2 Coefficient for slender unstiffened elements . . . . . . . . . . . . . . . . . . Table B4.1 Slip-critical combined tension and shear coefficient . . . . . . . . . . . . . . . . . J3.9 Web plate shear buckling coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . G2.1 Actual length of end-loaded weld, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . J2.2 Length of connection, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table D3.1 Length of bearing, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J7 Clear distance, in the direction of the force, between the edge of the hole and the edge of the adjacent hole or edge of the material, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J3.10

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

16.1–xxxviii

Symbol lca le lov lp n n nb ns nSR p pi r rcr ri ri r—o rt

rts rx rx ry rz s t t t t t t t t tb tbi tbj tcf tf tf

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Definition Section Length of channel anchor, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I8.2b Total effective weld length of groove and fillet welds to rectangular HSS for weld strength calculations, in. (mm) . . . . . . . . . . . . . . K4 Overlap length measured along the connecting face of the chord beneath the two branches, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.1 Projected length of the overlapping branch on the chord, in. (mm) . . . . . K2.1 Number of nodal braced points within the span . . . . . . . . . . . . . . . . . App. 6.3 Threads per inch (per mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 3.4 Number of bolts carrying the applied tension . . . . . . . . . . . . . . . . . . . . . . . J3.9 Number of slip planes required to permit the connection to slip . . . . . . . . J3.8 Number of stress range fluctuations in design life . . . . . . . . . . . . . . . App. 3.3 Pitch, in. per thread (mm per thread) . . . . . . . . . . . . . . . . . . . . . . . . . . App. 3.4 Ratio of element i deformation to its deformation at maximum stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J2.4 Radius of gyration, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E2 Distance from instantaneous center of rotation to weld element with minimum Δu /ri ratio, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J2.4 Minimum radius of gyration of individual component, in. (mm) . . . . . . . E6.1 Distance from instantaneous center of rotation to ith weld element, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J2.4 Polar radius of gyration about the shear center, in. (mm) . . . . . . . . . . . . . . . E4 Radius of gyration of the flange components in flexural compression plus one-third of the web area in compression due to application of major axis bending moment alone, in. (mm) . . . . . . . . . . . . . . . . . . . . . F4.2 Effective radius of gyration, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . F2.2 Radius of gyration about the x-axis, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . E4 Radius of gyration about the geometric axis parallel to the connected leg, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E5 Radius of gyration about y-axis, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . E4 Radius of gyration about the minor principal axis, in. (mm) . . . . . . . . . . . . E5 Longitudinal center-to-center spacing (pitch) of any two consecutive holes, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B4.3 Thickness of element, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E7.1 Thickness of wall, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E7.2 Thickness of angle leg, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F10.2 Width of rectangular bar parallel to axis of bending, in. (mm) . . . . . . . . F11.2 Thickness of connected material, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . J3.10 Thickness of plate, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D5.1 Total thickness of fillers, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J5.2 Design wall thickness of HSS member, in. (mm) . . . . . . . . . . . . . . B4.1, K1.1 Design wall thickness of HSS branch member, in. (mm) . . . . . . . . . . . . . K2.1 Thickness of overlapping branch, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . K2.3 Thickness of overlapped branch, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . K2.3 Thickness of column flange, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . J10.6 Thickness of flange, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F6.2 Thickness of loaded flange, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . J10.1 Specification for Structural Steel Buildings, June 22, 2010

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Symbol tf tfc tp tp tst tw tw tw w w w w w wc wr x xi xo, yo x– y yi z α β β βT βbr βeff βeop βsec βTb βw Δ ΔH

16–xxxix

Definition Section Thickness of flange of channel anchor, in. (mm) . . . . . . . . . . . . . . . . . . . I8.2b Thickness of compression flange, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . F4.2 Thickness of plate, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K1.1 Thickness of tension loaded plate, in. (mm) . . . . . . . . . . . . . . . . . . . . App. 3.3 Thickness of web stiffener, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . App. 6.3.2a Thickness of web, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table B4.1 Smallest effective weld throat thickness around the perimeter of branch or plate, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K4 Thickness of channel anchor web, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . I8.2b Width of cover plate, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F13.3 Size of weld leg, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J2.2 Subscript relating symbol to major principal axis bending . . . . . . . . . . . . . H2 Width of plate, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table D3.1 Leg size of the reinforcing or contouring fillet, if any, in the direction of the thickness of the tension-loaded plate, in. (mm) . . . . . App. 3.3 Weight of concrete per unit volume (90 ≤ wc ≤ 155 lbs/ft3 or 1500 ≤ wc ≤ 2500 kg/m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I2.1 Average width of concrete rib or haunch, in. (mm) . . . . . . . . . . . . . . . . . . I3.2 Subscript relating symbol to strong axis bending . . . . . . . . . . . . . . . . . . . .H1.1 x component of ri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J2.4 Coordinates of the shear center with respect to the centroid, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E4 Eccentricity of connection, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . Table D3.1 Subscript relating symbol to weak axis bending . . . . . . . . . . . . . . . . . . . . H1.1 y component of ri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .J2.4 Subscript relating symbol to minor principal axis bending . . . . . . . . . . . . . H2 ASD/LRFD force level adjustment factor . . . . . . . . . . . . . . . . . . . . . . . . . C2.3 Reduction factor given by Equation J2-1 . . . . . . . . . . . . . . . . . . . . . . . . . . J2.2 Width ratio; the ratio of branch diameter to chord diameter for round HSS; the ratio of overall branch width to chord width for rectangular HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.1 Overall brace system stiffness, kip-in./rad (N-mm/rad) . . . . . . . . App. 6.3.2a Required brace stiffness, kips/in. (N/mm) . . . . . . . . . . . . . . . . . . . . .App. 6.2.1 Effective width ratio; the sum of the perimeters of the two branch members in a K-connection divided by eight times the chord width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.1 Effective outside punching parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.3 Web distortional stiffness, including the effect of web transverse stiffeners, if any, kip-in./rad (N-mm/rad) . . . . . . . . . . . . . . . . . . . . App. 6.3.2a Required torsional stiffness for nodal bracing, kip-in./rad (N-mm/rad) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 6.3.2a Section property for unequal leg angles, positive for short legs in compression and negative for long legs in compression . . . . . . . . . . . F10.2 First-order interstory drift due to the LRFD or ASD load combinations, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 7.3.2 First-order interstory drift due to lateral forces, in. (mm) . . . . . . . . App. 8.2.2 Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

16.1–xl

Symbol Δi Δ mi Δ ui εcu (T) γ ζ η λ λp λpd λpf λpw λr λrf λrw μ φ φB φb φc φc φsf φT φt φt φv φv Ω ΩB Ωb Ωc Ωc Ωsf ΩT Ωt

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Definition Section Deformation of weld elements at intermediate stress levels, linearly proportioned to the critical deformation based on distance from the instantaneous center of rotation, ri, in. (mm) . . . . . . . . . J2.4 Deformation of weld element at maximum stress, in. (mm) . . . . . . . . . . . J2.4 Deformation of weld element at ultimate stress (rupture), usually in element furthest from instantaneous center of rotation, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J2.4 Maximum concrete strain at elevated temperature, % . . . . . . . . . . App. 4.2.3.2 Chord slenderness ratio; the ratio of one-half the diameter to the wall thickness for round HSS; the ratio of one-half the width to wall thickness for rectangular HSS . . . . . . . . . . . . . . . . . . . K2.1 Gap ratio; the ratio of the gap between the branches of a gapped K-connection to the width of the chord for rectangular HSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K2.1 Load length parameter, applicable only to rectangular HSS; the ratio of the length of contact of the branch with the chord in the plane of the connection to the chord width . . . . . . . . . . . . . K2.1 Slenderness parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F3.2 Limiting slenderness parameter for compact element . . . . . . . . . . . . . . . . . B4 Limiting slenderness parameter for plastic design . . . . . . . . . . . . . . . App. 1.2 Limiting slenderness parameter for compact flange . . . . . . . . . . . . . . . . . F3.2 Limiting slenderness parameter for compact web . . . . . . . . . . . . . . . . . . . . . F4 Limiting slenderness parameter for noncompact element . . . . . . . . . . . . . . B4 Limiting slenderness parameter for noncompact flange . . . . . . . . . . . . . . F3.2 Limiting slenderness parameter for noncompact web . . . . . . . . . . . . . . . . F4.2 Mean slip coefficient for Class A or B surfaces, as applicable, or as established by tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J3.8 Resistance factor, specified in Chapters B through K . . . . . . . . . . . . . . . . B3.3 Resistance factor for bearing on concrete . . . . . . . . . . . . . . . . . . . . . . . . . I6.3a Resistance factor for flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F1 Resistance factor for compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B3.7 Resistance factor for axially loaded composite columns . . . . . . . . . . . . . I2.1b Resistance factor for shear on the failure path . . . . . . . . . . . . . . . . . . . . . D5.1 Resistance factor for torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H3.1 Resistance factor for tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D2 Resistance factor for steel headed stud anchor in tension . . . . . . . . . . . . . I8.3b Resistance factor for shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G1 Resistance factor for steel headed stud anchor in shear . . . . . . . . . . . . . . I8.3a Safety factor, specified in Chapters B through K . . . . . . . . . . . . . . . . . . . B3.4 Safety factor for bearing on concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I6.1 Safety factor for flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F1 Safety factor for compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B3.7 Safety factor for axially loaded composite columns . . . . . . . . . . . . . . . . . I2.1b Safety factor for shear on the failure path . . . . . . . . . . . . . . . . . . . . . . . . D5.1 Safety factor for torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H3.1 Safety factor for tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D2 Specification for Structural Steel Buildings, June 22, 2010

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SYMBOLS

Symbol Ωt Ωv Ωv ρsr ρst θ θ θi τb

16–xli

Definition Section Safety factor for steel headed stud anchor in tension . . . . . . . . . . . . . . . . I8.3b Safety factor for shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G1 Safety factor for steel headed stud anchor in shear . . . . . . . . . . . . . . . . . I8.3a Minimum reinforcement ratio for longitudinal reinforcing . . . . . . . . . . . . I2.1 The larger of Fyw /Fyst and 1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G3.3 Angle of loading measured from the weld longitudinal axis, degrees . . . . J2.4 Acute angle between the branch and chord, degrees . . . . . . . . . . . . . . . . . K2.1 Αngle of loading measured from the longitudinal axis of ith weld element, degrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J2.4 Stiffness reduction parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C2.3

Specification for Structural Steel Buildings, June 22, 2010

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Specification for Structural Steel Buildings, June 22, 2010

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GLOSSARY

Terms defined in this Glossary are italicized in the Glossary and where they first appear within a section or long paragraph throughout the Specification. Notes: (1) Terms designated with † are common AISI-AISC terms that are coordinated between the two standards development organizations. (2) Terms designated with * are usually qualified by the type of load effect; for example, nominal tensile strength, available compressive strength, and design flexural strength. (3) Terms designated with ** are usually qualified by the type of component; for example, web local buckling and flange local bending. Active fire protection. Building materials and systems that are activated by a fire to mitigate adverse effects or to notify people to take some action to mitigate adverse effects. Allowable strength*†. Nominal strength divided by the safety factor, Rn/Ω. Allowable stress*. Allowable strength divided by the appropriate section property, such as section modulus or cross-section area. Applicable building code†. Building code under which the structure is designed. ASD (allowable strength design)†. Method of proportioning structural components such that the allowable strength equals or exceeds the required strength of the component under the action of the ASD load combinations. ASD load combination†. Load combination in the applicable building code intended for allowable strength design (allowable stress design). Authority having jurisdiction (AHJ). Organization, political subdivision, office or individual charged with the responsibility of administering and enforcing the provisions of the applicable building code. Available strength*†. Design strength or allowable strength, as appropriate. Available stress*. Design stress or allowable stress, as appropriate. Average rib width. In a formed steel deck, average width of the rib of a corrugation. Batten plate. Plate rigidly connected to two parallel components of a built-up column or beam designed to transmit shear between the components. Beam. Nominally horizontal structural member that has the primary function of resisting bending moments. Beam-column. Structural member that resists both axial force and bending moment. Bearing†. In a connection, limit state of shear forces transmitted by the mechanical fastener to the connection elements. Bearing (local compressive yielding)†. Limit state of local compressive yielding due to the action of a member bearing against another member or surface. Bearing-type connection. Bolted connection where shear forces are transmitted by the bolt bearing against the connection elements. Specification for Structural Steel Buildings, June 22, 2010

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GLOSSARY

Block shear rupture†. In a connection, limit state of tension rupture along one path and shear yielding or shear rupture along another path. Braced frame†. Essentially vertical truss system that provides resistance to lateral forces and provides stability for the structural system. Bracing. Member or system that provides stiffness and strength to limit the out-of-plane movement of another member at a brace point. Branch member. In an HSS connection, member that terminates at a chord member or main member. Buckling†. Limit state of sudden change in the geometry of a structure or any of its elements under a critical loading condition. Buckling strength. Strength for instability limit states. Built-up member, cross section, section, shape. Member, cross section, section or shape fabricated from structural steel elements that are welded or bolted together. Camber. Curvature fabricated into a beam or truss so as to compensate for deflection induced by loads. Charpy V-notch impact test. Standard dynamic test measuring notch toughness of a specimen. Chord member. In an HSS connection, primary member that extends through a truss connection. Cladding. Exterior covering of structure. Cold-formed steel structural member†. Shape manufactured by press-braking blanks sheared from sheets, cut lengths of coils or plates, or by roll forming cold- or hot-rolled coils or sheets; both forming operations being performed at ambient room temperature, that is, without manifest addition of heat such as would be required for hot forming. Collector. Also known as drag strut; member that serves to transfer loads between floor diaphragms and the members of the lateral force resisting system. Column. Nominally vertical structural member that has the primary function of resisting axial compressive force. Column base. Assemblage of structural shapes, plates, connectors, bolts and rods at the base of a column used to transmit forces between the steel superstructure and the foundation. Compact section. Section capable of developing a fully plastic stress distribution and possessing a rotation capacity of approximately three before the onset of local buckling. Compartmentation. Enclosure of a building space with elements that have a specific fire endurance. Complete-joint-penetration (CJP) groove weld. Groove weld in which weld metal extends through the joint thickness, except as permitted for HSS connections. Composite. Condition in which steel and concrete elements and members work as a unit in the distribution of internal forces. Composite beam. Structural steel beam in contact with and acting compositely with a reinforced concrete slab.

Specification for Structural Steel Buildings, June 22, 2010

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16.1–xlv

Composite component. Member, connecting element or assemblage in which steel and concrete elements work as a unit in the distribution of internal forces, with the exception of the special case of composite beams where steel anchors are embedded in a solid concrete slab or in a slab cast on formed steel deck. Concrete breakout surface. The surface delineating a volume of concrete surrounding a steel headed stud anchor that separates from the remaining concrete. Concrete crushing. Limit state of compressive failure in concrete having reached the ultimate strain. Concrete haunch. In a composite floor system constructed using a formed steel deck, the section of solid concrete that results from stopping the deck on each side of the girder. Concrete-encased beam. Beam totally encased in concrete cast integrally with the slab. Connection†. Combination of structural elements and joints used to transmit forces between two or more members. Construction documents. Design drawings, specifications, shop drawings and erection drawings. Cope. Cutout made in a structural member to remove a flange and conform to the shape of an intersecting member. Cover plate. Plate welded or bolted to the flange of a member to increase cross-sectional area, section modulus or moment of inertia. Cross connection. HSS connection in which forces in branch members or connecting elements transverse to the main member are primarily equilibrated by forces in other branch members or connecting elements on the opposite side of the main member. Design-basis fire. Set of conditions that define the development of a fire and the spread of combustion products throughout a building or portion thereof. Design drawings. Graphic and pictorial documents showing the design, location and dimensions of the work. These documents generally include plans, elevations, sections, details, schedules, diagrams and notes. Design load†. Applied load determined in accordance with either LRFD load combinations or ASD load combinations, whichever is applicable. Design strength*†. Resistance factor multiplied by the nominal strength, φRn. Design wall thickness. HSS wall thickness assumed in the determination of section properties. Diagonal stiffener. Web stiffener at column panel zone oriented diagonally to the flanges, on one or both sides of the web. Diaphragm†. Roof, floor or other membrane or bracing system that transfers in-plane forces to the lateral force resisting system. Diaphragm plate. Plate possessing in-plane shear stiffness and strength, used to transfer forces to the supporting elements. Direct analysis method. Design method for stability that captures the effects of residual stresses and initial out-of-plumbness of frames by reducing stiffness and applying notional loads in a second-order analysis.

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Direct bond interaction. In a composite section, mechanism by which force is transferred between steel and concrete by bond stress. Distortional failure. Limit state of an HSS truss connection based on distortion of a rectangular HSS chord member into a rhomboidal shape. Distortional stiffness. Out-of-plane flexural stiffness of web. Double curvature. Deformed shape of a beam with one or more inflection points within the span. Double-concentrated forces. Two equal and opposite forces applied normal to the same flange, forming a couple. Doubler. Plate added to, and parallel with, a beam or column web to increase strength at locations of concentrated forces. Drift. Lateral deflection of structure. Effective length. Length of an otherwise identical column with the same strength when analyzed with pinned end conditions. Effective length factor, K. Ratio between the effective length and the unbraced length of the member. Effective net area. Net area modified to account for the effect of shear lag. Effective section modulus. Section modulus reduced to account for buckling of slender compression elements. Effective width. Reduced width of a plate or slab with an assumed uniform stress distribution which produces the same effect on the behavior of a structural member as the actual plate or slab width with its nonuniform stress distribution. Elastic analysis. Structural analysis based on the assumption that the structure returns to its original geometry on removal of the load. Elevated temperatures. Heating conditions experienced by building elements or structures as a result of fire which are in excess of the anticipated ambient conditions. Encased composite member. Composite member consisting of a structural concrete member and one or more embedded steel shapes. End panel. Web panel with an adjacent panel on one side only. End return. Length of fillet weld that continues around a corner in the same plane. Engineer of record. Licensed professional responsible for sealing the design drawings and specifications. Expansion rocker. Support with curved surface on which a member bears that can tilt to accommodate expansion. Expansion roller. Round steel bar on which a member bears that can roll to accommodate expansion. Eyebar. Pin-connected tension member of uniform thickness, with forged or thermally cut head of greater width than the body, proportioned to provide approximately equal strength in the head and body. Factored load †. Product of a load factor and the nominal load. Fastener. Generic term for bolts, rivets or other connecting devices.

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16.1–xlvii

Fatigue†. Limit state of crack initiation and growth resulting from repeated application of live loads. Faying surface. Contact surface of connection elements transmitting a shear force. Filled composite member. Composite member consisting of a shell of HSS filled with structural concrete. Filler. Plate used to build up the thickness of one component. Filler metal. Metal or alloy added in making a welded joint. Fillet weld. Weld of generally triangular cross section made between intersecting surfaces of elements. Fillet weld reinforcement. Fillet welds added to groove welds. Finished surface. Surfaces fabricated with a roughness height value measured in accordance with ANSI/ASME B46.1 that is equal to or less than 500. Fire. Destructive burning, as manifested by any or all of the following: light, flame, heat or smoke. Fire barrier. Element of construction formed of fire-resisting materials and tested in accordance with an approved standard fire resistance test, to demonstrate compliance with the applicable building code. Fire resistance. Property of assemblies that prevents or retards the passage of excessive heat, hot gases or flames under conditions of use and enables them to continue to perform a stipulated function. First-order analysis. Structural analysis in which equilibrium conditions are formulated on the undeformed structure; second-order effects are neglected. Fitted bearing stiffener. Stiffener used at a support or concentrated load that fits tightly against one or both flanges of a beam so as to transmit load through bearing. Flare bevel groove weld. Weld in a groove formed by a member with a curved surface in contact with a planar member. Flare V-groove weld. Weld in a groove formed by two members with curved surfaces. Flashover. Transition to a state of total surface involvement in a fire of combustible materials within an enclosure. Flat width. Nominal width of rectangular HSS minus twice the outside corner radius. In the absence of knowledge of the corner radius, the flat width may be taken as the total section width minus three times the thickness. Flexural buckling†. Buckling mode in which a compression member deflects laterally without twist or change in cross-sectional shape. Flexural-torsional buckling†. Buckling mode in which a compression member bends and twists simultaneously without change in cross-sectional shape. Force. Resultant of distribution of stress over a prescribed area. Formed section. See cold-formed steel structural member. Formed steel deck. In composite construction, steel cold formed into a decking profile used as a permanent concrete form.

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Fully restrained moment connection. Connection capable of transferring moment with negligible rotation between connected members. Gage. Transverse center-to-center spacing of fasteners. Gapped connection. HSS truss connection with a gap or space on the chord face between intersecting branch members. Geometric axis. Axis parallel to web, flange or angle leg. Girder. See Beam. Girder filler. In a composite floor system constructed using a formed steel deck, narrow piece of sheet steel used as a fill between the edge of a deck sheet and the flange of a girder. Gouge. Relatively smooth surface groove or cavity resulting from plastic deformation or removal of material. Gravity load. Load acting in the downward direction, such as dead and live loads. Grip (of bolt). Thickness of material through which a bolt passes. Groove weld. Weld in a groove between connection elements. See also AWS D1.1/D1.1M. Gusset plate. Plate element connecting truss members or a strut or brace to a beam or column. Heat flux. Radiant energy per unit surface area. Heat release rate. Rate at which thermal energy is generated by a burning material. High-strength bolt. Fastener in compliance with ASTM A325, A325M, A490, A490M, F1852, F2280 or an alternate fastener as permitted in Section J3.1. Horizontal shear. In a composite beam, force at the interface between steel and concrete surfaces. HSS. Square, rectangular or round hollow structural steel section produced in accordance with a pipe or tubing product specification. Inelastic analysis. Structural analysis that takes into account inelastic material behavior, including plastic analysis. In-plane instability†. Limit state involving buckling in the plane of the frame or the member. Instability†. Limit state reached in the loading of a structural component, frame or structure in which a slight disturbance in the loads or geometry produces large displacements. Introduction length. In an encased composite column, the length along which the column force is assumed to be transferred into or out of the steel shape. Joint†. Area where two or more ends, surfaces or edges are attached. Categorized by type of fastener or weld used and method of force transfer. Joint eccentricity. In an HSS truss connection, perpendicular distance from chord member center of gravity to intersection of branch member work points. k-area. The region of the web that extends from the tangent point of the web and the flangeweb fillet (AISC k dimension) a distance 11/2 in. (38 mm) into the web beyond the k dimension.

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K-connection. HSS connection in which forces in branch members or connecting elements transverse to the main member are primarily equilibriated by forces in other branch members or connecting elements on the same side of the main member. Lacing. Plate, angle or other steel shape, in a lattice configuration, that connects two steel shapes together. Lap joint. Joint between two overlapping connection elements in parallel planes. Lateral bracing. Member or system that is designed to inhibit lateral buckling or lateraltorsional buckling of structural members. Lateral force resisting system. Structural system designed to resist lateral loads and provide stability for the structure as a whole. Lateral load. Load acting in a lateral direction, such as wind or earthquake effects. Lateral-torsional buckling†. Buckling mode of a flexural member involving deflection out of the plane of bending occurring simultaneously with twist about the shear center of the cross section. Leaning column. Column designed to carry gravity loads only, with connections that are not intended to provide resistance to lateral loads. Length effects. Consideration of the reduction in strength of a member based on its unbraced length. Lightweight concrete. Structural concrete with an equilibrium density of 115 lb/ft3 (1840 kg/m3) or less as determined by ASTM C567. Limit state†. Condition in which a structure or component becomes unfit for service and is judged either to be no longer useful for its intended function (serviceability limit state) or to have reached its ultimate load-carrying capacity (strength limit state). Load†. Force or other action that results from the weight of building materials, occupants and their possessions, environmental effects, differential movement or restrained dimensional changes. Load effect†. Forces, stresses and deformations produced in a structural component by the applied loads. Load factor†. Factor that accounts for deviations of the nominal load from the actual load, for uncertainties in the analysis that transforms the load into a load effect and for the probability that more than one extreme load will occur simultaneously. Local bending** †. Limit state of large deformation of a flange under a concentrated transverse force. Local buckling**. Limit state of buckling of a compression element within a cross section. Local yielding**†. Yielding that occurs in a local area of an element. LRFD (load and resistance factor design)†. Method of proportioning structural components such that the design strength equals or exceeds the required strength of the component under the action of the LRFD load combinations. LRFD load combination†. Load combination in the applicable building code intended for strength design (load and resistance factor design).

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Main member. In an HSS connection, chord member, column or other HSS member to which branch members or other connecting elements are attached. Mechanism. Structural system that includes a sufficient number of real hinges, plastic hinges or both, so as to be able to articulate in one or more rigid body modes. Mill scale. Oxide surface coating on steel formed by the hot rolling process. Moment connection. Connection that transmits bending moment between connected members. Moment frame†. Framing system that provides resistance to lateral loads and provides stability to the structural system, primarily by shear and flexure of the framing members and their connections. Negative flexural strength. Flexural strength of a composite beam in regions with tension due to flexure on the top surface. Net area. Gross area reduced to account for removed material. Nodal brace. Brace that prevents lateral movement or twist independently of other braces at adjacent brace points (see relative brace). Nominal dimension. Designated or theoretical dimension, as in tables of section properties. Nominal load†. Magnitude of the load specified by the applicable building code. Nominal rib height. In a formed steel deck, height of deck measured from the underside of the lowest point to the top of the highest point. Nominal strength*†. Strength of a structure or component (without the resistance factor or safety factor applied) to resist load effects, as determined in accordance with this Specification. Noncompact section. Section that can develop the yield stress in its compression elements before local buckling occurs, but cannot develop a rotation capacity of three. Nondestructive testing. Inspection procedure wherein no material is destroyed and the integrity of the material or component is not affected. Notch toughness. Energy absorbed at a specified temperature as measured in the Charpy V-notch impact test. Notional load. Virtual load applied in a structural analysis to account for destabilizing effects that are not otherwise accounted for in the design provisions. Out-of-plane buckling†. Limit state of a beam, column or beam-column involving lateral or lateral-torsional buckling. Overlapped connection. HSS truss connection in which intersecting branch members overlap. Panel zone. Web area of beam-to-column connection delineated by the extension of beam and column flanges through the connection, transmitting moment through a shear panel. Partial-joint-penetration (PJP) groove weld. Groove weld in which the penetration is intentionally less than the complete thickness of the connected element. Partially restrained moment connection. Connection capable of transferring moment with rotation between connected members that is not negligible. Specification for Structural Steel Buildings, June 22, 2010

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Percent elongation. Measure of ductility, determined in a tensile test as the maximum elongation of the gage length divided by the original gage length expressed as a percentage. Pipe. See HSS. Pitch. Longitudinal center-to-center spacing of fasteners. Center-to-center spacing of bolt threads along axis of bolt. Plastic analysis. Structural analysis based on the assumption of rigid-plastic behavior, that is, that equilibrium is satisfied and the stress is at or below the yield stress throughout the structure. Plastic hinge. Fully yielded zone that forms in a structural member when the plastic moment is attained. Plastic moment. Theoretical resisting moment developed within a fully yielded cross section. Plastic stress distribution method. In a composite member, method for determining stresses assuming that the steel section and the concrete in the cross section are fully plastic. Plastification. In an HSS connection, limit state based on an out-of-plane flexural yield line mechanism in the chord at a branch member connection. Plate girder. Built-up beam. Plug weld. Weld made in a circular hole in one element of a joint fusing that element to another element. Ponding. Retention of water due solely to the deflection of flat roof framing. Positive flexural strength. Flexural strength of a composite beam in regions with compression due to flexure on the top surface. Pretensioned bolt. Bolt tightened to the specified minimum pretension. Pretensioned joint. Joint with high-strength bolts tightened to the specified minimum pretension. Properly developed. Reinforcing bars detailed to yield in a ductile manner before crushing of the concrete occurs. Bars meeting the provisions of ACI 318, insofar as development length, spacing and cover, are deemed to be properly developed. Prying action. Amplification of the tension force in a bolt caused by leverage between the point of applied load, the bolt and the reaction of the connected elements. Punching load. In an HSS connection, component of branch member force perpendicular to a chord. P-δ effect. Effect of loads acting on the deflected shape of a member between joints or nodes. P-Δ effect. Effect of loads acting on the displaced location of joints or nodes in a structure. In tiered building structures, this is the effect of loads acting on the laterally displaced location of floors and roofs. Quality assurance. Monitoring and inspection tasks performed by an agency or firm other than the fabricator or erector to ensure that the material provided and work performed by the fabricator and erector meet the requirements of the approved construction documents and referenced standards. Quality assurance includes those tasks designated “special inspection” by the applicable building code. Specification for Structural Steel Buildings, June 22, 2010

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Quality assurance inspector (QAI). Individual designated to provide quality assurance inspection for the work being performed. Quality assurance plan (QAP). Program in which the agency or firm responsible for quality assurance maintains detailed monitoring and inspection procedures to ensure conformance with the approved construction documents and referenced standards. Quality control. Controls and inspections implemented by the fabricator or erector, as applicable, to ensure that the material provided and work performed meet the requirements of the approved construction documents and referenced standards. Quality control inspector (QCI). Individual designated to perform quality control inspection tasks for the work being performed. Quality control program (QCP). Program in which the fabricator or erector, as applicable, maintains detailed fabrication or erection and inspection procedures to ensure conformance with the approved design drawings, specifications and referenced standards. Reentrant. In a cope or weld access hole, a cut at an abrupt change in direction in which the exposed surface is concave. Relative brace. Brace that controls the relative movement of two adjacent brace points along the length of a beam or column or the relative lateral displacement of two stories in a frame (see nodal brace). Required strength*†. Forces, stresses and deformations acting on a structural component, determined by either structural analysis, for the LRFD or ASD load combinations, as appropriate, or as specified by this Specification or Standard. Resistance factorφ†. Factor that accounts for unavoidable deviations of the nominal strength from the actual strength and for the manner and consequences of failure. Restrained construction. Floor and roof assemblies and individual beams in buildings where the surrounding or supporting structure is capable of resisting substantial thermal expansion throughout the range of anticipated elevated temperatures. Reverse curvature. See double curvature. Root of joint. Portion of a joint to be welded where the members are closest to each other. Rotation capacity. Incremental angular rotation that a given shape can accept prior to excessive load shedding, defined as the ratio of the inelastic rotation attained to the idealized elastic rotation at first yield.. Rupture strength†. Strength limited by breaking or tearing of members or connecting elements. Safety factor, Ω†. Factor that accounts for deviations of the actual strength from the nominal strength, deviations of the actual load from the nominal load, uncertainties in the analysis that transforms the load into a load effect, and for the manner and consequences of failure. Second-order effect. Effect of loads acting on the deformed configuration of a structure; includes P-δ effect and P-Δ effect. Seismic response modification factor. Factor that reduces seismic load effects to strength level.

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Service load†. Load under which serviceability limit states are evaluated. Service load combination. Load combination under which serviceability limit states are evaluated. Serviceability limit state†. Limiting condition affecting the ability of a structure to preserve its appearance, maintainability, durability or the comfort of its occupants or function of machinery, under normal usage. Shear buckling†. Buckling mode in which a plate element, such as the web of a beam, deforms under pure shear applied in the plane of the plate. Shear lag. Nonuniform tensile stress distribution in a member or connecting element in thevicinity of a connection. Shear wall†. Wall that provides resistance to lateral loads in the plane of the wall and provides stability for the structural system. Shear yielding (punching). In an HSS connection, limit state based on out-of-plane shear strength of the chord wall to which branch members are attached. Sheet steel. In a composite floor system, steel used for closure plates or miscellaneous trimming in a formed steel deck. Shim. Thin layer of material used to fill a space between faying or bearing surfaces. Sidesway buckling (frame). Stability limit state involving lateral sidesway instability of a frame. Simple connection. Connection that transmits negligible bending moment between connected members. Single-concentrated force. Tensile or compressive force applied normal to the flange of a member. Single curvature. Deformed shape of a beam with no inflection point within the span. Slender-element section. Cross section possessing plate components of sufficient slenderness such that local buckling in the elastic range will occur. Slip. In a bolted connection, limit state of relative motion of connected parts prior to the attainment of the available strength of the connection. Slip-critical connection. Bolted connection designed to resist movement by friction on the faying surface of the connection under the clamping force of the bolts. Slot weld. Weld made in an elongated hole fusing an element to another element. Snug-tightened joint. Joint with the connected plies in firm contact as specified in Chapter J. Specifications. Written documents containing the requirements for materials, standards and workmanship. Specified minimum tensile strength. Lower limit of tensile strength specified for a material as defined by ASTM. Specified minimum yield stress†. Lower limit of yield stress specified for a material as defined by ASTM. Splice. Connection between two structural elements joined at their ends to form a single, longer element.

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Stability. Condition in the loading of a structural component, frame or structure in which a slight disturbance in the loads or geometry does not produce large displacements. Statically loaded. Not subject to significant fatigue stresses. Gravity, wind and seismic loadings are considered to be static loadings. Steel anchor. Headed stud or hot rolled channel welded to a steel member and embodied in concrete of a composite member to transmit shear, tension or a combination of shear and tension at the interface of the two materials. Stiffened element. Flat compression element with adjoining out-of-plane elements along both edges parallel to the direction of loading. Stiffener. Structural element, usually an angle or plate, attached to a member to distribute load, transfer shear or prevent buckling. Stiffness. Resistance to deformation of a member or structure, measured by the ratio of the applied force (or moment) to the corresponding displacement (or rotation). Strain compatibility method. In a composite member, method for determining the stresses considering the stress-strain relationships of each material and its location with respect to the neutral axis of the cross section. Strength limit state†. Limiting condition in which the maximum strength of a structure or its components is reached. Stress. Force per unit area caused by axial force, moment, shear or torsion. Stress concentration. Localized stress considerably higher than average due to abrupt changes in geometry or localized loading. Strong axis. Major principal centroidal axis of a cross section. Structural analysis†. Determination of load effects on members and connections based on principles of structural mechanics. Structural component†. Member, connector, connecting element or assemblage. Structural steel. Steel elements as defined in Section 2.1 of the AISC Code of Standard Practice for Steel Buildings and Bridges. Structural system. An assemblage of load-carrying components that are joined together to provide interaction or interdependence. T-connection. HSS connection in which the branch member or connecting element is perpendicular to the main member and in which forces transverse to the main member are primarily equilibriated by shear in the main member. Tensile strength (of material)†. Maximum tensile stress that a material is capable of sustaining as defined by ASTM. Tensile strength (of member). Maximum tension force that a member is capable of sustaining. Tension and shear rupture†. In a bolt or other type of mechanical fastener, limit state of rupture due to simultaneous tension and shear force. Tension field action. Behavior of a panel under shear in which diagonal tensile forces develop in the web and compressive forces develop in the transverse stiffeners in a manner similar to a Pratt truss. Thermally cut. Cut with gas, plasma or laser. Specification for Structural Steel Buildings, June 22, 2010

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Tie plate. Plate element used to join two parallel components of a built-up column, girder or strut rigidly connected to the parallel components and designed to transmit shear between them. Toe of fillet. Junction of a fillet weld face and base metal. Tangent point of a fillet in a rolled shape. Torsional bracing. Bracing resisting twist of a beam or column. Torsional buckling†. Buckling mode in which a compression member twists about its shear center axis. Transverse reinforcement. In an encased composite column, steel reinforcement in the form of closed ties or welded wire fabric providing confinement for the concrete surrounding the steel shape. Transverse stiffener. Web stiffener oriented perpendicular to the flanges, attached to the web. Tubing. See HSS. Turn-of-nut method. Procedure whereby the specified pretension in high-strength bolts is controlled by rotating the fastener component a predetermined amount after the bolt has been snug tightened. Unbraced length. Distance between braced points of a member, measured between the centers of gravity of the bracing members. Uneven load distribution. In an HSS connection, condition in which the load is not distributed through the cross section of connected elements in a manner that can be readily determined. Unframed end. The end of a member not restrained against rotation by stiffeners or connection elements. Unrestrained construction. Floor and roof assemblies and individual beams in buildings that are assumed to be free to rotate and expand throughout the range of anticipated elevated temperatures. Unstiffened element. Flat compression element with an adjoining out-of-plane element along one edge parallel to the direction of loading. Weak axis. Minor principal centroidal axis of a cross section. Weathering steel. High-strength, low-alloy steel that, with suitable precautions, can be used in normal atmospheric exposures (not marine) without protective paint coating. Web crippling†. Limit state of local failure of web plate in the immediate vicinity of a concentrated load or reaction. Web sidesway buckling. Limit state of lateral buckling of the tension flange opposite the location of a concentrated compression force. Weld metal. Portion of a fusion weld that has been completely melted during welding. Weld metal has elements of filler metal and base metal melted in the weld thermal cycle. Weld root. See root of joint. Y-connection. HSS connection in which the branch member or connecting element is not perpendicular to the main member and in which forces transverse to the main member are primarily equilibriated by shear in the main member. Specification for Structural Steel Buildings, June 22, 2010

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Yield moment†. In a member subjected to bending, the moment at which the extreme outer fiber first attains the yield stress. Yield point†. First stress in a material at which an increase in strain occurs without an increase in stress as defined by ASTM. Yield strength†. Stress at which a material exhibits a specified limiting deviation from the proportionality of stress to strain as defined by ASTM. Yield stress†. Generic term to denote either yield point or yield strength, as appropriate for the material. Yielding†. Limit state of inelastic deformation that occurs when the yield stress is reached. Yielding (plastic moment)†. Yielding throughout the cross section of a member as the bending moment reaches the plastic moment. Yielding (yield moment)†. Yielding at the extreme fiber on the cross section of a member when the bending moment reaches the yield moment.

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CHAPTER A GENERAL PROVISIONS

This chapter states the scope of the Specification, summarizes referenced specifications, codes and standards, and provides requirements for materials and structural design documents. The chapter is organized as follows: A1. A2. A3. A4.

A1.

Scope Referenced Specifications, Codes and Standards Material Structural Design Drawings and Specifications

SCOPE The Specification for Structural Steel Buildings (ANSI/AISC 360), hereafter referred to as the Specification, shall apply to the design of the structural steel system or systems with structural steel acting compositely with reinforced concrete, where the steel elements are defined in the AISC Code of Standard Practice for Steel Buildings and Bridges, Section 2.1, hereafter referred to as the Code of Standard Practice. This Specification includes the Symbols, the Glossary, Chapters A through N, and Appendices 1 through 8. The Commentary and the User Notes interspersed throughout are not part of the Specification. User Note: User notes are intended to provide concise and practical guidance in the application of the provisions. This Specification sets forth criteria for the design, fabrication and erection of structural steel buildings and other structures, where other structures are defined as structures designed, fabricated and erected in a manner similar to buildings, with building-like vertical and lateral load resisting-elements. Wherever this Specification refers to the applicable building code and there is none, the loads, load combinations, system limitations, and general design requirements shall be those in ASCE/SEI 7. Where conditions are not covered by the Specification, designs are permitted to be based on tests or analysis, subject to the approval of the authority having jurisdiction. Alternative methods of analysis and design are permitted, provided such alternative methods or criteria are acceptable to the authority having jurisdiction.

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SCOPE

[Sect. A1.

User Note: For the design of structural members, other than hollow structural sections (HSS) that are cold-formed to shapes with elements not more than 1 in. (25 mm) in thickness, the provisions of the AISI North American Specification for the Design of Cold-Formed Steel Structural Members are recommended.

1.

Seismic Applications The Seismic Provisions for Structural Steel Buildings (ANSI/AISC 341) shall apply to the design of seismic force resisting systems of structural steel or of structural steel acting compositely with reinforced concrete, unless specifically exempted by the applicable building code. User Note: ASCE/SEI 7 (Table 12.2-1, Item H) specifically exempts structural steel systems, but not composite systems, in seismic design categories B and C if they are designed according to the Specification and the seismic loads are computed using a seismic response modification factor, R, of 3. For seismic design category A, ASCE/SEI 7 does specify lateral forces to be used as the seismic loads and effects, but these calculations do not involve the use of an R factor. Thus for seismic design category A it is not necessary to define a seismic force resisting system that meets any special requirements and the Seismic Provisions for Structural Steel Buildings do not apply. The provisions of Appendix 1 of this Specification shall not apply to the seismic design of buildings and other structures.

2.

Nuclear Applications The design, fabrication and erection of nuclear structures shall comply with the requirements of the Specification for Safety-Related Steel Structures for Nuclear Facilities (ANSI/AISC N690), in addition to the provisions of this Specification.

A2.

REFERENCED SPECIFICATIONS, CODES AND STANDARDS The following specifications, codes and standards are referenced in this Specification: ACI International (ACI) ACI 318-08 Building Code Requirements for Structural Concrete and Commentary ACI 318M-08 Metric Building Code Requirements for Structural Concrete and Commentary ACI 349-06 Code Requirements for Nuclear Safety-Related Concrete Structures and Commentary American Institute of Steel Construction (AISC) AISC 303-10 Code of Standard Practice for Steel Buildings and Bridges ANSI/AISC 341-10 Seismic Provisions for Structural Steel Buildings ANSI/AISC N690-06 Specification for Safety-Related Steel Structures for Nuclear Facilities

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REFERENCED SPECIFICATIONS, CODES AND STANDARDS

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American Society of Civil Engineers (ASCE) ASCE/SEI 7-10 Minimum Design Loads for Buildings and Other Structures ASCE/SEI/SFPE 29-05 Standard Calculation Methods for Structural Fire Protection American Society of Mechanical Engineers (ASME) ASME B18.2.6-06 Fasteners for Use in Structural Applications ASME B46.1-02 Surface Texture, Surface Roughness, Waviness, and Lay American Society for Nondestructive Testing (ASNT) ANSI/ASNT CP-189-2006 Standard for Qualification and Certification of Nondestructive Testing Personnel Recommended Practice No. SNT-TC-1A-2006 Personnel Qualification and Certification in Nondestructive Testing ASTM International (ASTM) A6/A6M-09 Standard Specification for General Requirements for Rolled Structural Steel Bars, Plates, Shapes, and Sheet Piling A36/A36M-08 Standard Specification for Carbon Structural Steel A53/A53M-07 Standard Specification for Pipe, Steel, Black and Hot-Dipped, ZincCoated, Welded and Seamless A193/A193M-08b Standard Specification for Alloy-Steel and Stainless Steel Bolting Materials for High Temperature or High Pressure Service and Other Special Purpose Applications A194/A194M-09 Standard Specification for Carbon and Alloy Steel Nuts for Bolts for High Pressure or High Temperature Service, or Both A216/A216M-08 Standard Specification for Steel Castings, Carbon, Suitable for Fusion Welding, for High Temperature Service A242/A242M-04(2009) Standard Specification for High-Strength Low-Alloy Structural Steel A283/A283M-03(2007) Standard Specification for Low and Intermediate Tensile Strength Carbon Steel Plates A307-07b Standard Specification for Carbon Steel Bolts and Studs, 60,000 PSI Tensile Strength A325-09 Standard Specification for Structural Bolts, Steel, Heat Treated, 120/105 ksi Minimum Tensile Strength A325M-09 Standard Specification for Structural Bolts, Steel, Heat Treated 830 MPa Minimum Tensile Strength (Metric) A354-07a Standard Specification for Quenched and Tempered Alloy Steel Bolts, Studs, and Other Externally Threaded Fasteners A370-09 Standard Test Methods and Definitions for Mechanical Testing of Steel Products A449-07b Standard Specification for Hex Cap Screws, Bolts and Studs, Steel, Heat Treated, 120/105/90 ksi Minimum Tensile Strength, General Use A490-08b Standard Specification for Heat-Treated Steel Structural Bolts, Alloy Steel, Heat Treated, 150 ksi Minimum Tensile Strength A490M-08 Standard Specification for High-Strength Steel Bolts, Classes 10.9 and 10.9.3, for Structural Steel Joints (Metric) Specification for Structural Steel Buildings, June 22, 2010

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[Sect. A2.

A500/A500M-07 Standard Specification for Cold-Formed Welded and Seamless Carbon Steel Structural Tubing in Rounds and Shapes A501-07 Standard Specification for Hot-Formed Welded and Seamless Carbon Steel Structural Tubing A502-03 Standard Specification for Steel Structural Rivets, Steel, Structural A514/A514M-05 Standard Specification for High-Yield Strength, Quenched and Tempered Alloy Steel Plate, Suitable for Welding A529/A529M-05 Standard Specification for High-Strength Carbon-Manganese Steel of Structural Quality A563-07a Standard Specification for Carbon and Alloy Steel Nuts A563M-07 Standard Specification for Carbon and Alloy Steel Nuts [Metric] A568/A568M-09 Standard Specification for Steel, Sheet, Carbon, Structural, and High-Strength, Low-Alloy, Hot-Rolled and Cold-Rolled, General Requirements for A572/A572M-07 Standard Specification for High-Strength Low-Alloy ColumbiumVanadium Structural Steel A588/A588M-05 Standard Specification for High-Strength Low-Alloy Structural Steel, up to 50 ksi [345 MPa] Minimum Yield Point, with Atmospheric Corrosion Resistance A606/A606M-09 Standard Specification for Steel, Sheet and Strip, High-Strength, Low-Alloy, Hot-Rolled and Cold-Rolled, with Improved Atmospheric Corrosion Resistance A618/A618M-04 Standard Specification for Hot-Formed Welded and Seamless High-Strength Low-Alloy Structural Tubing A668/A668M-04 Standard Specification for Steel Forgings, Carbon and Alloy, for General Industrial Use A673/A673M-04 Standard Specification for Sampling Procedure for Impact Testing of Structural Steel A709/A709M-09 Standard Specification for Structural Steel for Bridges A751-08 Standard Test Methods, Practices, and Terminology for Chemical Analysis of Steel Products A847/A847M-05 Standard Specification for Cold-Formed Welded and Seamless High-Strength, Low-Alloy Structural Tubing with Improved Atmospheric Corrosion Resistance A852/A852M-03(2007) Standard Specification for Quenched and Tempered LowAlloy Structural Steel Plate with 70 ksi [485 MPa] Minimum Yield Strength to 4 in. [100 mm] Thick A913/A913M-07 Standard Specification for High-Strength Low-Alloy Steel Shapes of Structural Quality, Produced by Quenching and Self-Tempering Process (QST) A992/A992M-06a Standard Specification for Structural Steel Shapes User Note: ASTM A992 is the most commonly referenced specification for W-shapes. A1011/A1011M-09a Standard Specification for Steel, Sheet and Strip, Hot-Rolled, Carbon, Structural, High-Strength Low-Alloy, High-Strength Low-Alloy with Improved Formability, and Ultra-High Strength A1043/A1043M-05 Standard Specification for Structural Steel with Low Yield to Tensile Ratio for Use in Buildings Specification for Structural Steel Buildings, June 22, 2010

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C567-05a Standard Test Method for Determining Density of Structural Lightweight Concrete E119-08a Standard Test Methods for Fire Tests of Building Construction and Materials E165-02 Standard Test Method for Liquid Penetrant Examination E709-08 Standard Guide for Magnetic Particle Examination F436-09 Standard Specification for Hardened Steel Washers F436M-09 Standard Specification for Hardened Steel Washers (Metric) F606-07 Standard Test Methods for Determining the Mechanical Properties of Externally and Internally Threaded Fasteners, Washers, Direct Tension Indicators, and Rivets F606M-07 Standard Test Methods for Determining the Mechanical Properties of Externally and Internally Threaded Fasteners, Washers, and Rivets (Metric) F844-07a Standard Specification for Washers, Steel, Plain (Flat), Unhardened for General Use F959-09 Standard Specification for Compressible-Washer-Type Direct Tension Indicators for Use with Structural Fasteners F959M-07 Standard Specification for Compressible-Washer-Type Direct Tension Indicators for Use with Structural Fasteners (Metric) F1554-07a Standard Specification for Anchor Bolts, Steel, 36, 55, and 105 ksi Yield Strength User Note: ASTM F1554 is the most commonly referenced specification for anchor rods. Grade and weldability must be specified. F1852-08 Standard Specification for “Twist-Off” Type Tension Control Structural Bolt/Nut/Washer Assemblies, Steel, Heat Treated, 120/105 ksi Minimum Tensile Strength F2280-08 Standard Specification for “Twist Off” Type Tension Control Structural Bolt/ Nut/Washer Assemblies, Steel, Heat Treated, 150 ksi Minimum Tensile Strength American Welding Society (AWS) AWS A5.1/A5.1M-2004 Specification for Carbon Steel Electrodes for Shielded Metal Arc Welding AWS A5.5/A5.5M-2004 Specification for Low-Alloy Steel Electrodes for Shielded Metal Arc Welding AWS A5.17/A5.17M-1997 (R2007) Specification for Carbon Steel Electrodes and Fluxes for Submerged Arc Welding AWS A5.18/A5.18M-2005 Specification for Carbon Steel Electrodes and Rods for Gas Shielded Arc Welding AWS A5.20/A5.20M-2005 Specification for Carbon Steel Electrodes for Flux Cored Arc Welding AWS A5.23/A5.23M-2007 Specification for Low-Alloy Steel Electrodes and Fluxes for Submerged Arc Welding AWS A5.25/A5.25M-1997 (R2009) Specification for Carbon and Low-Alloy Steel Electrodes and Fluxes for Electroslag Welding AWS A5.26/A5.26M-1997 (R2009) Specification for Carbon and Low-Alloy Steel Electrodes for Electrogas Welding Specification for Structural Steel Buildings, June 22, 2010

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AWS A5.28/A5.28M-2005 Specification for Low-Alloy Steel Electrodes and Rods for Gas Shielded Arc Welding AWS A5.29/A5.29M-2005 Specification for Low-Alloy Steel Electrodes for Flux Cored Arc Welding AWS A5.32/A5.32M-1997 (R2007) Specification for Welding Shielding Gases AWS B5.1-2003 Specification for the Qualification of Welding Inspectors AWS D1.1/D1.1M-2010 Structural Welding Code—Steel AWS D1.3 -2008 Structural Welding Code—Sheet Steel Research Council on Structural Connections (RCSC) Specification for Structural Joints Using High-Strength Bolts, 2009

A3.

MATERIAL

1.

Structural Steel Materials Material test reports or reports of tests made by the fabricator or a testing laboratory shall constitute sufficient evidence of conformity with one of the ASTM standards listed in Section A3.1a. For hot-rolled structural shapes, plates, and bars, such tests shall be made in accordance with ASTM A6/A6M; for sheets, such tests shall be made in accordance with ASTM A568/A568M; for tubing and pipe, such tests shall be made in accordance with the requirements of the applicable ASTM standards listed above for those product forms.

1a.

ASTM Designations Structural steel material conforming to one of the following ASTM specifications is approved for use under this Specification: (1) Hot-rolled structural shapes ASTM A36/A36M ASTM A529/A529M ASTM A572/A572M ASTM A588/A588M

ASTM A709/A709M ASTM A913/A913M ASTM A992/ A992M ASTM A1043/A1043M

(2) Structural tubing ASTM A500 ASTM A501

ASTM A618/A618M ASTM A847/A847M

(3) Pipe ASTM A53/A53M, Gr. B (4) Plates ASTM A36/A36M ASTM A242/A242M ASTM A283/A283M ASTM A514/A514M ASTM A529/A529M ASTM A572/A572M (5) Bars ASTM A36/A36M ASTM A529/A529M

ASTM A588/A588M ASTM A709/A709M ASTM A852/A852M ASTM A1011/A1011M ASTM A1043/A1043M

ASTM A572/A572M ASTM A709/A709M

Specification for Structural Steel Buildings, June 22, 2010

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(6) Sheets ASTM A606/A606M ASTM A1011/A1011M SS, HSLAS, AND HSLAS-F

1b.

Unidentified Steel Unidentified steel, free of injurious defects, is permitted to be used only for members or details whose failure will not reduce the strength of the structure, either locally or overall. Such use shall be subject to the approval of the engineer of record. User Note: Unidentified steel may be used for details where the precise mechanical properties and weldability are not of concern. These are commonly curb plates, shims and other similar pieces.

1c.

Rolled Heavy Shapes ASTM A6/A6M hot-rolled shapes with a flange thickness exceeding 2 in. (50 mm) are considered to be rolled heavy shapes. Rolled heavy shapes used as members subject to primary (computed) tensile forces due to tension or flexure and spliced or connected using complete-joint-penetration groove welds that fuse through the thickness of the flange or the flange and the web, shall be specified as follows. The structural design documents shall require that such shapes be supplied with Charpy V-notch (CVN) impact test results in accordance with ASTM A6/A6M, Supplementary Requirement S30, Charpy V-Notch Impact Test for Structural Shapes – Alternate Core Location. The impact test shall meet a minimum average value of 20 ft-lb (27 J) absorbed energy at a maximum temperature of +70 °F (+21 °C). The above requirements do not apply if the splices and connections are made by bolting. Where a rolled heavy shape is welded to the surface of another shape using groove welds, the requirement above applies only to the shape that has weld metal fused through the cross section. User Note: Additional requirements for joints in heavy rolled members are given in Sections J1.5, J1.6, J2.6 and M2.2.

1d.

Built-Up Heavy Shapes Built-up cross sections consisting of plates with a thickness exceeding 2 in. (50 mm) are considered built-up heavy shapes. Built-up heavy shapes used as members subject to primary (computed) tensile forces due to tension or flexure and spliced or connected to other members using complete-joint-penetration groove welds that fuse through the thickness of the plates, shall be specified as follows. The structural design documents shall require that the steel be supplied with Charpy V-notch impact test results in accordance with ASTM A6/A6M, Supplementary Requirement S5, Charpy V-Notch Impact Test. The impact test shall be conducted in accordance with ASTM A673/A673M, Frequency P, and shall meet a minimum average value of 20 ft-lb (27 J) absorbed energy at a maximum temperature of +70 °F (+21 °C). Specification for Structural Steel Buildings, June 22, 2010

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When a built-up heavy shape is welded to the face of another member using groove welds, the requirement above applies only to the shape that has weld metal fused through the cross section. User Note: Additional requirements for joints in heavy built-up members are given in Sections J1.5, J1.6, J2.6 and M2.2.

2.

Steel Castings and Forgings Steel castings shall conform to ASTM A216/A216M, Grade WCB with Supplementary Requirement S11. Steel forgings shall conform to ASTM A668/A668M. Test reports produced in accordance with the above reference standards shall constitute sufficient evidence of conformity with such standards.

3.

Bolts, Washers and Nuts Bolt, washer and nut material conforming to one of the following ASTM specifications is approved for use under this Specification: (1) Bolts ASTM A307 ASTM A325 ASTM A325M ASTM A354 ASTM A449

ASTM A490 ASTM A490M ASTM F1852 ASTM F2280

(2) Nuts ASTM A194/A194M ASTM A563

ASTM A563M

(3) Washers ASTM F436 ASTM F436M

ASTM F844

(4) Compressible-Washer-Type Direct Tension Indicators ASTM F959 ASTM F959M Manufacturer’s certification shall constitute sufficient evidence of conformity with the standards.

4.

Anchor Rods and Threaded Rods Anchor rod and threaded rod material conforming to one of the following ASTM specifications is approved for use under this Specification: ASTM A36/A36M ASTM A193/A193M ASTM A354 ASTM A449

ASTM A572/A572M ASTM A588/A588M ASTM F1554

User Note: ASTM F1554 is the preferred material specification for anchor rods. Specification for Structural Steel Buildings, June 22, 2010

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A449 material is acceptable for high-strength anchor rods and threaded rods of any diameter. Threads on anchor rods and threaded rods shall conform to the Unified Standard Series of ASME B18.2.6 and shall have Class 2A tolerances. Manufacturer’s certification shall constitute sufficient evidence of conformity with the standards.

5.

Consumables for Welding Filler metals and fluxes shall conform to one of the following specifications of the American Welding Society: AWS A5.1/A5.1M AWS A5.5/A5.5M AWS A5.17/A5.17M AWS A5.18/A5.18M AWS A5.20/A5.20M AWS A5.23/A5.23M

AWS A5.25/A5.25M AWS A5.26/A5.26M AWS A5.28/A5.28M AWS A5.29/A5.29M AWS A5.32/A5.32M

Manufacturer’s certification shall constitute sufficient evidence of conformity with the standards. Filler metals and fluxes that are suitable for the intended application shall be selected.

6.

Headed Stud Anchors Steel headed stud anchors shall conform to the requirements of the Structural Welding Code—Steel (AWS D1.1/D1.1M). Manufacturer’s certification shall constitute sufficient evidence of conformity with AWS D1.1/D1.1M.

A4.

STRUCTURAL DESIGN DRAWINGS AND SPECIFICATIONS The structural design drawings and specifications shall meet the requirements in the Code of Standard Practice. User Note: Provisions in this Specification contain information that is to be shown on design drawings. These include: Section A3.1c Rolled heavy shapes where alternate core Charpy V-notch toughness (CVN) is required Section A3.1d Built-up heavy shapes where CVN toughness is required Section J3.1 Locations of connections using pretensioned bolts Other information is needed by the fabricator or erector and should be shown on design drawings including: Fatigue details requiring nondestructive testing (Appendix 3; e.g., Table A3.1, Cases 5.1 to 5.4) Risk category (Chapter N) Indication of complete-joint-penetration (CJP) welds subject to tension (Chapter N) Specification for Structural Steel Buildings, June 22, 2010

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CHAPTER B DESIGN REQUIREMENTS

This chapter addresses general requirements for the analysis and design of steel structures applicable to all chapters of the specification. The chapter is organized as follows: B1. B2. B3. B4. B5. B6. B7.

B1.

General Provisions Loads and Load Combinations Design Basis Member Properties Fabrication and Erection Quality Control and Quality Assurance Evaluation of Existing Structures

GENERAL PROVISIONS The design of members and connections shall be consistent with the intended behavior of the framing system and the assumptions made in the structural analysis. Unless restricted by the applicable building code, lateral load resistance and stability may be provided by any combination of members and connections.

B2.

LOADS AND LOAD COMBINATIONS The loads and load combinations shall be as stipulated by the applicable building code. In the absence of a building code, the loads and load combinations shall be those stipulated in Minimum Design Loads for Buildings and Other Structures (ASCE/SEI 7). For design purposes, the nominal loads shall be taken as the loads stipulated by the applicable building code. User Note: When using ASCE/SEI 7, for design according to Section B3.3 (LRFD), the load combinations in ASCE/SEI 7, Section 2.3 apply. For design according to Section B3.4 (ASD), the load combinations in ASCE/SEI 7, Section 2.4 apply.

B3.

DESIGN BASIS Designs shall be made according to the provisions for load and resistance factor design (LRFD) or to the provisions for allowable strength design (ASD).

1.

Required Strength The required strength of structural members and connections shall be determined by structural analysis for the appropriate load combinations as stipulated in Section B2.

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Design by elastic, inelastic or plastic analysis is permitted. Provisions for inelastic and plastic analysis are as stipulated in Appendix 1, Design by Inelastic Analysis.

2.

Limit States Design shall be based on the principle that no applicable strength or serviceability limit state shall be exceeded when the structure is subjected to all appropriate load combinations. Design for structural integrity requirements of the applicable building code shall be based on nominal strength rather than design strength (LRFD) or allowable strength (ASD), unless specifically stated otherwise in the applicable building code. Limit states for connections based on limiting deformations or yielding of the connection components need not be considered for meeting structural integrity requirements. For the purpose of satisfying structural integrity provisions of the applicable building code, bearing bolts in connections with short-slotted holes parallel to the direction of the tension load are permitted, and shall be assumed to be located at the end of the slot.

3.

Design for Strength Using Load and Resistance Factor Design (LRFD) Design according to the provisions for load and resistance factor design (LRFD) satisfies the requirements of this Specification when the design strength of each structural component equals or exceeds the required strength determined on the basis of the LRFD load combinations. All provisions of this Specification, except for those in Section B3.4, shall apply. Design shall be performed in accordance with Equation B3-1: Ru ≤ φRn

(B3-1)

where Ru = required strength using LRFD load combinations Rn = nominal strength, specified in Chapters B through K φ = resistance factor, specified in Chapters B through K φRn = design strength

4.

Design for Strength Using Allowable Strength Design (ASD) Design according to the provisions for allowable strength design (ASD) satisfies the requirements of this Specification when the allowable strength of each structural component equals or exceeds the required strength determined on the basis of the ASD load combinations. All provisions of this Specification, except those of Section B3.3, shall apply. Design shall be performed in accordance with Equation B3-2: Ra ≤ Rn /Ω where Ra = required strength using ASD load combinations Rn = nominal strength, specified in Chapters B through K Ω = safety factor, specified in Chapters B through K Rn /Ω = allowable strength Specification for Structural Steel Buildings, June 22, 2010

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Design for Stability Stability of the structure and its elements shall be determined in accordance with Chapter C.

6.

Design of Connections Connection elements shall be designed in accordance with the provisions of Chapters J and K. The forces and deformations used in design shall be consistent with the intended performance of the connection and the assumptions used in the structural analysis. Self-limiting inelastic deformations of the connections are permitted. At points of support, beams, girders and trusses shall be restrained against rotation about their longitudinal axis unless it can be shown by analysis that the restraint is not required. User Note: Section 3.1.2 of the Code of Standard Practice addresses communication of necessary information for the design of connections.

6a.

Simple Connections A simple connection transmits a negligible moment. In the analysis of the structure, simple connections may be assumed to allow unrestrained relative rotation between the framing elements being connected. A simple connection shall have sufficient rotation capacity to accommodate the required rotation determined by the analysis of the structure.

6b.

Moment Connections Two types of moment connections, fully restrained and partially restrained, are permitted, as specified below. (a) Fully Restrained (FR) Moment Connections A fully restrained (FR) moment connection transfers moment with a negligible rotation between the connected members. In the analysis of the structure, the connection may be assumed to allow no relative rotation. An FR connection shall have sufficient strength and stiffness to maintain the angle between the connected members at the strength limit states. (b) Partially Restrained (PR) Moment Connections Partially restrained (PR) moment connections transfer moments, but the rotation between connected members is not negligible. In the analysis of the structure, the force-deformation response characteristics of the connection shall be included. The response characteristics of a PR connection shall be documented in the technical literature or established by analytical or experimental means. The component elements of a PR connection shall have sufficient strength, stiffness and deformation capacity at the strength limit states.

7.

Moment Redistribution in Beams The required flexural strength of beams composed of compact sections, as defined in Section B4.1, and satisfying the unbraced length requirements of Section F13.5 Specification for Structural Steel Buildings, June 22, 2010

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may be taken as nine-tenths of the negative moments at the points of support, produced by the gravity loading and determined by an elastic analysis satisfying the requirements of Chapter C, provided that the maximum positive moment is increased by one-tenth of the average negative moment determined by an elastic analysis. This reduction is not permitted for moments in members with Fy exceeding 65 ksi (450 MPa), for moments produced by loading on cantilevers, for design using partially restrained (PR) moment connections, or for design by inelastic analysis using the provisions of Appendix 1. This reduction is permitted for design according to Section B3.3 (LRFD) and for design according to Section B3.4 (ASD). The required axial strength shall not exceed 0.15φcFy Ag for LRFD or 0.15Fy Ag /Ωc for ASD where φc and Ω c are determined from Section E1, and Ag = gross area of member, in.2 (mm2), and Fy = specified minimum yield stress, ksi (MPa).

8.

Diaphragms and Collectors Diaphragms and collectors shall be designed for forces that result from loads as stipulated in Section B2. They shall be designed in conformance with the provisions of Chapters C through K, as applicable.

9.

Design for Serviceability The overall structure and the individual members and connections shall be checked for serviceability. Requirements for serviceability design are given in Chapter L.

10.

Design for Ponding The roof system shall be investigated through structural analysis to assure adequate strength and stability under ponding conditions, unless the roof surface is provided with a slope of 1/4 in. per ft (20 mm per meter) or greater toward points of free drainage or an adequate system of drainage is provided to prevent the accumulation of water. Methods of checking ponding are provided in Appendix 2, Design for Ponding.

11.

Design for Fatigue Fatigue shall be considered in accordance with Appendix 3, Design for Fatigue, for members and their connections subject to repeated loading. Fatigue need not be considered for seismic effects or for the effects of wind loading on normal building lateral force resisting systems and building enclosure components.

12.

Design for Fire Conditions Two methods of design for fire conditions are provided in Appendix 4, Structural Design for Fire Conditions: by Analysis and by Qualification Testing. Compliance with the fire protection requirements in the applicable building code shall be deemed to satisfy the requirements of this section and Appendix 4. Nothing in this section is intended to create or imply a contractual requirement for the engineer of record responsible for the structural design or any other member of the design team.

Specification for Structural Steel Buildings, June 22, 2010

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User Note: Design by qualification testing is the prescriptive method specified in most building codes. Traditionally, on most projects where the architect is the prime professional, the architect has been the responsible party to specify and coordinate fire protection requirements. Design by analysis is a new engineering approach to fire protection. Designation of the person(s) responsible for designing for fire conditions is a contractual matter to be addressed on each project.

13.

Design for Corrosion Effects Where corrosion may impair the strength or serviceability of a structure, structural components shall be designed to tolerate corrosion or shall be protected against corrosion.

14.

Anchorage to Concrete Anchorage between steel and concrete acting compositely shall be designed in accordance with Chapter I. The design of column bases and anchor rods shall be in accordance with Chapter J.

B4.

MEMBER PROPERTIES

1.

Classification of Sections for Local Buckling For compression, sections are classified as nonslender element or slender-element sections. For a nonslender element section, the width-to-thickness ratios of its compression elements shall not exceed λr from Table B4.1a. If the width-to-thickness ratio of any compression element exceeds λr, the section is a slender-element section. For flexure, sections are classified as compact, noncompact or slender-element sections. For a section to qualify as compact, its flanges must be continuously connected to the web or webs and the width-to-thickness ratios of its compression elements shall not exceed the limiting width-to-thickness ratios, λp, from Table B4.1b. If the width-to-thickness ratio of one or more compression elements exceeds λp, but does not exceed λr from Table B4.1b, the section is noncompact. If the width-to-thickness ratio of any compression element exceeds λr, the section is a slender-element section.

1a.

Unstiffened Elements For unstiffened elements supported along only one edge parallel to the direction of the compression force, the width shall be taken as follows: (a) For flanges of I-shaped members and tees, the width, b, is one-half the full-flange width, bf. (b) For legs of angles and flanges of channels and zees, the width, b, is the full nominal dimension. (c) For plates, the width, b, is the distance from the free edge to the first row of fasteners or line of welds. (d) For stems of tees, d is taken as the full nominal depth of the section.

Specification for Structural Steel Buildings, June 22, 2010

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User Note: Refer to Table B4.1 for the graphic representation of unstiffened element dimensions.

1b.

Stiffened Elements For stiffened elements supported along two edges parallel to the direction of the compression force, the width shall be taken as follows: (a) For webs of rolled or formed sections, h is the clear distance between flanges less the fillet or corner radius at each flange; hc is twice the distance from the center of gravity to the inside face of the compression flange less the fillet or corner radius. (b) For webs of built-up sections, h is the distance between adjacent lines of fasteners or the clear distance between flanges when welds are used, and hc is twice the distance from the center of gravity to the nearest line of fasteners at the compression flange or the inside face of the compression flange when welds are used; hp is twice the distance from the plastic neutral axis to the nearest line of fasteners at the compression flange or the inside face of the compression flange when welds are used. (c) For flange or diaphragm plates in built-up sections, the width, b, is the distance between adjacent lines of fasteners or lines of welds. (d) For flanges of rectangular hollow structural sections (HSS), the width, b, is the clear distance between webs less the inside corner radius on each side. For webs of rectangular HSS, h is the clear distance between the flanges less the inside corner radius on each side. If the corner radius is not known, b and h shall be taken as the corresponding outside dimension minus three times the thickness. The thickness, t, shall be taken as the design wall thickness, per Section B4.2. (e) For perforated cover plates, b is the transverse distance between the nearest line of fasteners, and the net area of the plate is taken at the widest hole. User Note: Refer to Table B4.1 for the graphic representation of stiffened element dimensions. For tapered flanges of rolled sections, the thickness is the nominal value halfway between the free edge and the corresponding face of the web.

2.

Design Wall Thickness for HSS The design wall thickness, t, shall be used in calculations involving the wall thickness of hollow structural sections (HSS). The design wall thickness, t, shall be taken equal to 0.93 times the nominal wall thickness for electric-resistance-welded (ERW) HSS and equal to the nominal thickness for submerged-arc-welded (SAW) HSS.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed._

2/17/12

16.1–16

2:34 PM

Page 16

MEMBER PROPERTIES

[Sect. B4.

Case

TABLE B4.1a Width-to-Thickness Ratios: Compression Elements Members Subject to Axial Compression Limiting Width-to- Width-to-Thickness Thickness Ratio ␭r Ratio (nonslender/slender)

Description of Element

Unstiffened Elements

1 Flanges of rolled I-shaped sections, plates projecting from rolled I-shaped sections; outstanding legs of pairs of angles connected with continuous contact, flanges of channels, and flanges of tees

b/t

0.56

E Fy

[a]

2 Flanges of built-up I-shaped sections and plates or angle legs projecting from built-up I-shaped sections

b/t

0.64

kcE Fy

3 Legs of single angles, legs of double angles with separators, and all other unstiffened elements

b/t

0.45

E Fy

d/t

0.75

E Fy

h/tw

1.49

E Fy

b/t

1.40

E Fy

b/t

1.40

E Fy

b/t

1.49

E Fy

D/t

E 0.11 Fy

4 Stems of tees

5 Webs of doublysymmetric I-shaped sections and channels

6 Walls of rectangular Stiffened Elements

HSS and boxes of uniform thickness

7 Flange cover plates and diaphragm plates between lines of fasteners or welds

8 All other stiffened elements

9 Round HSS

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Examples

AISC_PART 16_Spec.1_A:14th Ed._

2/17/12

Sect. B4.]

2:18 PM

Page 17

MEMBER PROPERTIES

16.1–17

Case

TABLE B4.1b Width-to-Thickness Ratios: Compression Elements Members Subject to Flexure Limiting Width-to-Thickness Ratio ␭r ␭p

Description of Element

Unstiffened Elements

10 Flanges of rolled I-shaped sections, channels, and tees

Width-to(compact/ (noncompact/ Thickness noncompact) slender) Ratio

E Fy

b/t

0.38

b/t

E 0.38 Fy

b/t

0.54

E Fy

0.91

E Fy

b/t

0.38

E Fy

1.0

E Fy

d/t

0.84

E Fy

1.03

E Fy

15 Webs of doublysymmetric I-shaped sections and channels

h/tw

3.76

E Fy

5.70

E Fy

16 Webs of singlysymmetric I-shaped sections

hc /tw

5.70

E Fy

11 Flanges of doubly and singly symmetric I-shaped built-up sections 12 Legs of single angles

13 Flanges of all I-shaped sections and channels in flexure about the weak axis

1.0

[a] [b]

14 Stems of tees

Stiffened Elements

E Fy

hc hp

k E 0.95 c FL

[c]

E Fy

⎛ ⎞ Mp ⎜ 0.54 M − 0.09⎟ ⎝ ⎠ y

2

≤ λr

17 Flanges of rectangular HSS and boxes of uniform thickness

b/t

1.12

E Fy

1.40

E Fy

18 Flange cover plates and diaphragm plates between lines of fasteners or welds

b/t

1.12

E Fy

1.40

E Fy

h/t

2.42

E Fy

5.70

E Fy

19 Webs of rectangular HSS and boxes

Examples

20 Round HSS

D/t

0.07

E Fy

E 0.31 Fy

[a] kc = 4兾 h / t w but shall not be taken less than 0.35 nor greater than 0.76 for calculation purposes. [b] FL = 0.7Fy for major axis bending of compact and noncompact web built-up I-shaped members with Sxt /Sxc ≥ 0.7; FL = Fy Sxt /Sxc ≥ 0.5Fy for major-axis bending of compact and noncompact web built-up I-shaped members with Sxt /Sxc < 0.7. [c] My is the moment at yielding of the extreme fiber. Mp = plastic bending moment, kip-in. (N-mm) E = modulus of elasticity of steel = 29,000 ksi (200 000 MPa) Fy = specified minimum yield stress, ksi (MPa)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

16.1–18

1/20/11

7:56 AM

Page 18

MEMBER PROPERTIES

[Sect. B4.

User Note: A pipe can be designed using the provisions of the Specification for round HSS sections as long as the pipe conforms to ASTM A53 Class B and the appropriate limitations of the Specification are used. ASTM A500 HSS and ASTM A53 Grade B pipe are produced by an ERW process. An SAW process is used for cross sections that are larger than those permitted by ASTM A500.

3.

Gross and Net Area Determination

3a.

Gross Area The gross area, Ag, of a member is the total cross-sectional area.

3b.

Net Area The net area, An, of a member is the sum of the products of the thickness and the net width of each element computed as follows: In computing net area for tension and shear, the width of a bolt hole shall be taken as 1/16 in. (2 mm) greater than the nominal dimension of the hole. For a chain of holes extending across a part in any diagonal or zigzag line, the net width of the part shall be obtained by deducting from the gross width the sum of the diameters or slot dimensions as provided in this section, of all holes in the chain, and adding, for each gage space in the chain, the quantity s2/4g, where s = longitudinal center-to-center spacing (pitch) of any two consecutive holes, in. (mm) g = transverse center-to-center spacing (gage) between fastener gage lines, in. (mm) For angles, the gage for holes in opposite adjacent legs shall be the sum of the gages from the back of the angles less the thickness. For slotted HSS welded to a gusset plate, the net area, An, is the gross area minus the product of the thickness and the total width of material that is removed to form the slot. In determining the net area across plug or slot welds, the weld metal shall not be considered as adding to the net area. For members without holes, the net area, An, is equal to the gross area, Ag. User Note: Section J4.1(b) limits An to a maximum of 0.85Ag for splice plates with holes.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

Sect. B7.]

B5.

1/20/11

7:56 AM

Page 19

EVALUATION OF EXISTING STRUCTURES

16.1–19

FABRICATION AND ERECTION Shop drawings, fabrication, shop painting and erection shall satisfy the requirements stipulated in Chapter M, Fabrication and Erection.

B6.

QUALITY CONTROL AND QUALITY ASSURANCE Quality control and quality assurance activities shall satisfy the requirements stipulated in Chapter N, Quality Control and Quality Assurance.

B7.

EVALUATION OF EXISTING STRUCTURES The evaluation of existing structures shall satisfy the requirements stipulated in Appendix 5, Evaluation of Existing Structures.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

1/20/11

7:56 AM

Page 20

16.1–20

CHAPTER C DESIGN FOR STABILITY

This chapter addresses requirements for the design of structures for stability. The direct analysis method is presented herein; alternative methods are presented in Appendix 7. The chapter is organized as follows: C1. C2. C3.

C1.

General Stability Requirements Calculation of Required Strengths Calculation of Available Strengths

GENERAL STABILITY REQUIREMENTS Stability shall be provided for the structure as a whole and for each of its elements. The effects of all of the following on the stability of the structure and its elements shall be considered: (1) flexural, shear and axial member deformations, and all other deformations that contribute to displacements of the structure; (2) second-order effects (both P-Δ and P-δ effects); (3) geometric imperfections; (4) stiffness reductions due to inelasticity; and (5) uncertainty in stiffness and strength. All load-dependent effects shall be calculated at a level of loading corresponding to LRFD load combinations or 1.6 times ASD load combinations. Any rational method of design for stability that considers all of the listed effects is permitted; this includes the methods identified in Sections C1.1 and C1.2. For structures designed by inelastic analysis, the provisions of Appendix 1 shall be satisfied. User Note: The term “design” as used in these provisions is the combination of analysis to determine the required strengths of components and the proportioning of components to have adequate available strength. See Commentary Section C1 and Table C-C1.1 for explanation of how requirements (1) through (5) of Section C1 are satisfied in the methods of design listed in Sections C1.1 and C1.2.

1.

Direct Analysis Method of Design The direct analysis method of design, which consists of the calculation of required strengths in accordance with Section C2 and the calculation of available strengths in accordance with Section C3, is permitted for all structures.

2.

Alternative Methods of Design The effective length method and the first-order analysis method, defined in Appendix 7, are permitted as alternatives to the direct analysis method for structures that satisfy the constraints specified in that appendix. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A_14th Ed._February 12, 2013 12/02/13 9:38 AM Page 21

Sect. C2.]

C2.

CALCULATION OF REQUIRED STRENGTHS

16.1–21

CALCULATION OF REQUIRED STRENGTHS For the direct analysis method of design, the required strengths of components of the structure shall be determined from an analysis conforming to Section C2.1. The analysis shall include consideration of initial imperfections in accordance with Section C2.2 and adjustments to stiffness in accordance with Section C2.3.

1.

General Analysis Requirements The analysis of the structure shall conform to the following requirements: (1) The analysis shall consider flexural, shear and axial member deformations, and all other component and connection deformations that contribute to displacements of the structure. The analysis shall incorporate reductions in all stiffnesses that are considered to contribute to the stability of the structure, as specified in Section C2.3. (2) The analysis shall be a second-order analysis that considers both P-Δ and P-δ effects, except that it is permissible to neglect the effect of P-δ on the response of the structure when the following conditions are satisfied: (a) The structure supports gravity loads primarily through nominally-vertical columns, walls or frames; (b) the ratio of maximum second-order drift to maximum first-order drift (both determined for LRFD load combinations or 1.6 times ASD load combinations, with stiffnesses adjusted as specified in Section C2.3) in all stories is equal to or less than 1.7; and (c) no more than one-third of the total gravity load on the structure is supported by columns that are part of moment-resisting frames in the direction of translation being considered. It is necessary in all cases to consider P-δ effects in the evaluation of individual members subject to compression and flexure. User Note: A P-Δ-only second-order analysis (one that neglects the effects of P-δ on the response of the structure) is permitted under the conditions listed. The requirement for considering P-δ effects in the evaluation of individual members can be satisfied by applying the B1 multiplier defined in Appendix 8. Use of the approximate method of second-order analysis provided in Appendix 8 is permitted as an alternative to a rigorous second-order analysis. (3) The analysis shall consider all gravity and other applied loads that may influence the stability of the structure. User Note: It is important to include in the analysis all gravity loads, including loads on leaning columns and other elements that are not part of the lateral force resisting system. (4) For design by LRFD, the second-order analysis shall be carried out under LRFD load combinations. For design by ASD, the second-order analysis shall be carried out under 1.6 times the ASD load combinations, and the results shall be divided by 1.6 to obtain the required strengths of components.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

16.1–22

2.

1/20/11

7:56 AM

Page 22

CALCULATION OF REQUIRED STRENGTHS

[Sect. C2.

Consideration of Initial Imperfections The effect of initial imperfections on the stability of the structure shall be taken into account either by direct modeling of imperfections in the analysis as specified in Section C2.2a or by the application of notional loads as specified in Section C2.2b. User Note: The imperfections considered in this section are imperfections in the locations of points of intersection of members. In typical building structures, the important imperfection of this type is the out-of-plumbness of columns. Initial out-of-straightness of individual members is not addressed in this section; it is accounted for in the compression member design provisions of Chapter E and need not be considered explicitly in the analysis as long as it is within the limits specified in the AISC Code of Standard Practice.

2a.

Direct Modeling of Imperfections In all cases, it is permissible to account for the effect of initial imperfections by including the imperfections directly in the analysis. The structure shall be analyzed with points of intersection of members displaced from their nominal locations. The magnitude of the initial displacements shall be the maximum amount considered in the design; the pattern of initial displacements shall be such that it provides the greatest destabilizing effect. User Note: Initial displacements similar in configuration to both displacements due to loading and anticipated buckling modes should be considered in the modeling of imperfections. The magnitude of the initial displacements should be based on permissible construction tolerances, as specified in the AISC Code of Standard Practice or other governing requirements, or on actual imperfections if known. In the analysis of structures that support gravity loads primarily through nominallyvertical columns, walls or frames, where the ratio of maximum second-order drift to maximum first-order drift (both determined for LRFD load combinations or 1.6 times ASD load combinations, with stiffnesses adjusted as specified in Section C2.3) in all stories is equal to or less than 1.7, it is permissible to include initial imperfections only in the analysis for gravity-only load combinations and not in the analysis for load combinations that include applied lateral loads.

2b.

Use of Notional Loads to Represent Imperfections For structures that support gravity loads primarily through nominally-vertical columns, walls or frames, it is permissible to use notional loads to represent the effects of initial imperfections in accordance with the requirements of this section. The notional load shall be applied to a model of the structure based on its nominal geometry. User Note: The notional load concept is applicable to all types of structures, but the specific requirements in Sections C2.2b(1) through C2.2b(4) are applicable only for the particular class of structure identified above.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

Sect. C2.]

1/20/11

7:56 AM

Page 23

CALCULATION OF REQUIRED STRENGTHS

16.1–23

(1) Notional loads shall be applied as lateral loads at all levels. The notional loads shall be additive to other lateral loads and shall be applied in all load combinations, except as indicated in (4), below. The magnitude of the notional loads shall be: Ni = 0.002αYi

(C2-1)

where α = 1.0 (LRFD); α = 1.6 (ASD) Ni = notional load applied at level i, kips (N) Yi = gravity load applied at level i from the LRFD load combination or ASD load combination, as applicable, kips (N) User Note: The notional loads can lead to additional (generally small) fictitious base shears in the structure. The correct horizontal reactions at the foundation may be obtained by applying an additional horizontal force at the base of the structure, equal and opposite in direction to the sum of all notional loads, distributed among vertical load-carrying elements in the same proportion as the gravity load supported by those elements. The notional loads can also lead to additional overturning effects, which are not fictitious. (2) The notional load at any level, Ni, shall be distributed over that level in the same manner as the gravity load at the level. The notional loads shall be applied in the direction that provides the greatest destabilizing effect. User Note: For most building structures, the requirement regarding notional load direction may be satisfied as follows: For load combinations that do not include lateral loading, consider two alternative orthogonal directions of notional load application, in a positive and a negative sense in each of the two directions, in the same direction at all levels; for load combinations that include lateral loading, apply all notional loads in the direction of the resultant of all lateral loads in the combination. (3) The notional load coefficient of 0.002 in Equation C2-1 is based on a nominal initial story out-of-plumbness ratio of 1/500; where the use of a different maximum out-of-plumbness is justified, it is permissible to adjust the notional load coefficient proportionally. User Note: An out-of-plumbness of 1/500 represents the maximum tolerance on column plumbness specified in the AISC Code of Standard Practice . In some cases, other specified tolerances such as those on plan location of columns will govern and will require a tighter plumbness tolerance. (4) For structures in which the ratio of maximum second-order drift to maximum first-order drift (both determined for LRFD load combinations or 1.6 times ASD load combinations, with stiffnesses adjusted as specified in Section C2.3) in all stories is equal to or less than 1.7, it is permissible to apply the notional load, Ni, Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A_14th Ed._February 25, 2013 14-11-26 1:58 PM Page 24

16.1–24

CALCULATION OF REQUIRED STRENGTHS

(Black plate)

[Sect. C2.

only in gravity-only load combinations and not in combinations that include other lateral loads.

3.

Adjustments to Stiffness The analysis of the structure to determine the required strengths of components shall use reduced stiffnesses, as follows: (1) A factor of 0.80 shall be applied to all stiffnesses that are considered to contribute to the stability of the structure. It is permissible to apply this reduction factor to all stiffnesses in the structure. User Note: Applying the stiffness reduction to some members and not others can, in some cases, result in artificial distortion of the structure under load and possible unintended redistribution of forces. This can be avoided by applying the reduction to all members, including those that do not contribute to the stability of the structure. (2) An additional factor, τb, shall be applied to the flexural stiffnesses of all members whose flexural stiffnesses are considered to contribute to the stability of the structure. (a) When αPr /Py ≤ 0.5 τb = 1.0

(C2-2a)

τb = 4(αPr /Py)[1− (αPr /Py)]

(C2-2b)

(b) When αPr /Py > 0.5

where α = 1.0 (LRFD); α = 1.6 (ASD) Pr = required axial compressive strength using LRFD or ASD load combinations, kips (N) Py = axial yield strength (= Fy Ag), kips (N) User Note: Taken together, sections (1) and (2) require the use of 0.8τb times the nominal elastic flexural stiffness and 0.8 times other nominal elastic stiffnesses for structural steel members in the analysis. (3) In structures to which Section C2.2b is applicable, in lieu of using τb < 1.0 where αPr /Py > 0.5, it is permissible to use τb = 1.0 for all members if a notional load of 0.001αYi [where Yi is as defined in Section C2.2b(1)] is applied at all levels, in the direction specified in Section C2.2b(2), in all load combinations. These notional loads shall be added to those, if any, used to account for imperfections and shall not be subject to Section C2.2b(4). (4) Where components comprised of materials other than structural steel are considered to contribute to the stability of the structure and the governing codes and specifications for the other materials require greater reductions in stiffness, such greater stiffness reductions shall be applied to those components. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

Sect. C3.]

C3.

1/20/11

7:56 AM

Page 25

CALCULATION OF AVAILABLE STRENGTHS

16.1–25

CALCULATION OF AVAILABLE STRENGTHS For the direct analysis method of design, the available strengths of members and connections shall be calculated in accordance with the provisions of Chapters D, E, F, G, H, I, J and K, as applicable, with no further consideration of overall structure stability. The effective length factor, K, of all members shall be taken as unity unless a smaller value can be justified by rational analysis. Bracing intended to define the unbraced lengths of members shall have sufficient stiffness and strength to control member movement at the braced points. Methods of satisfying bracing requirements for individual columns, beams and beam-columns are provided in Appendix 6. The requirements of Appendix 6 are not applicable to bracing that is included as part of the overall force-resisting system.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

1/20/11

7:56 AM

Page 26

16.1–26

CHAPTER D DESIGN OF MEMBERS FOR TENSION

This chapter applies to members subject to axial tension caused by static forces acting through the centroidal axis. The chapter is organized as follows: D1. D2. D3. D4. D5. D6.

Slenderness Limitations Tensile Strength Effective Net Area Built-Up Members Pin-Connected Members Eyebars

User Note: For cases not included in this chapter the following sections apply: • B3.11 Members subject to fatigue • Chapter H Members subject to combined axial tension and flexure • J3 Threaded rods • J4.1 Connecting elements in tension • J4.3 Block shear rupture strength at end connections of tension members

D1.

SLENDERNESS LIMITATIONS There is no maximum slenderness limit for members in tension. User Note: For members designed on the basis of tension, the slenderness ratio L /r preferably should not exceed 300. This suggestion does not apply to rods or hangers in tension.

D2.

TENSILE STRENGTH The design tensile strength, φt Pn, and the allowable tensile strength, Pn /Ωt, of tension members shall be the lower value obtained according to the limit states of tensile yielding in the gross section and tensile rupture in the net section. (a) For tensile yielding in the gross section: Pn = Fy Ag φt = 0.90 (LRFD)

(D2-1)

Ωt = 1.67 (ASD)

(b) For tensile rupture in the net section: Pn = Fu Ae φt = 0.75 (LRFD)

Ωt = 2.00 (ASD)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(D2-2)

AISC_PART 16_Spec.1_A:14th Ed.

1/20/11

Sect. D4.]

7:56 AM

Page 27

BUILT-UP MEMBERS

16.1–27

where Ae = effective net area, in.2 (mm2) Ag = gross area of member, in.2 (mm2) Fy = specified minimum yield stress, ksi (MPa) Fu = specified minimum tensile strength, ksi (MPa) When members without holes are fully connected by welds, the effective net area used in Equation D2-2 shall be as defined in Section D3. When holes are present in a member with welded end connections, or at the welded connection in the case of plug or slot welds, the effective net area through the holes shall be used in Equation D2-2.

D3.

EFFECTIVE NET AREA The gross area, Ag, and net area, An, of tension members shall be determined in accordance with the provisions of Section B4.3. The effective net area of tension members shall be determined as follows: Ae = AnU

(D3-1)

where U, the shear lag factor, is determined as shown in Table D3.1. For open cross sections such as W, M, S, C or HP shapes, WTs, STs, and single and double angles, the shear lag factor, U, need not be less than the ratio of the gross area of the connected element(s) to the member gross area. This provision does not apply to closed sections, such as HSS sections, nor to plates. User Note: For bolted splice plates Ae = An ≤ 0.85Ag, according to Section J4.1.

D4.

BUILT-UP MEMBERS For limitations on the longitudinal spacing of connectors between elements in continuous contact consisting of a plate and a shape or two plates, see Section J3.5. Either perforated cover plates or tie plates without lacing are permitted to be used on the open sides of built-up tension members. Tie plates shall have a length not less than two-thirds the distance between the lines of welds or fasteners connecting them to the components of the member. The thickness of such tie plates shall not be less than one-fiftieth of the distance between these lines. The longitudinal spacing of intermittent welds or fasteners at tie plates shall not exceed 6 in. (150 mm). User Note: The longitudinal spacing of connectors between components should preferably limit the slenderness ratio in any component between the connectors to 300.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

16.1–28

1/20/11

7:56 AM

Page 28

BUILT-UP MEMBERS

[Sect. D4.

TABLE D3.1 Shear Lag Factors for Connections to Tension Members Case 1

2

3

4

Description of Element

Shear Lag Factor, U

All tension members where the tension load is transmitted directly to each of the cross-sectional elements by fasteners or welds (except as in Cases 4, 5 and 6). All tension members, except plates and HSS, where the tension load is transmitted to some but not all of the crosssectional elements by fasteners or longitudinal welds or by longitudinal welds in combination with transverse welds. (Alternatively, for W, M, S and HP, Case 7 may be used. For angles, Case 8 may be used.) All tension members where the tension load is transmitted only by transverse welds to some but not all of the cross-sectional elements. Plates where the tension load is transmitted by longitudinal welds only.

Example

U = 1.0

U = 1− x l

U = 1.0 and An = area of the directly connected elements / ≥ 2w…U = 1.0 2w > / ≥ 1.5w…U = 0.87 1.5w > / ≥ w…U = 0.75

5

Round HSS with a single concentric gusset plate

/ ≥ 1.3D…U = 1.0

D ≤ l < 1.3D …U = 1− x l x =D π

6

Rectangular HSS

with a single concentric gusset plate

l ≥ H …U = 1− x l

with two side gusset plates

l ≥ H …U = 1− x l

x=

B 2 + 2BH 4(B + H )

x= 7

8

W, M, S or HP Shapes or Tees cut from these shapes. (If U is calculated per Case 2, the larger value is permitted to be used.)

Single and double angles (If U is calculated per Case 2, the larger value is permitted to be used.)

with flange connected with 3 or more fasteners per line in the direction of loading with web connected with 4 or more fasteners per line in the direction of loading with 4 or more fasteners per line in the direction of loading with 3 fasteners per line in the direction of loading (With fewer than 3 fasteners per line in the direction of loading, use Case 2.)

B2 4(B + H )

bf ≥ 2/3d…U = 0.90 bf < 2/3d…U = 0.85

U = 0.70

U = 0.80

U = 0.60

l = length of connection, in. (mm); w = plate width, in. (mm); x– = eccentricity of connection, in. (mm); B = overall width of rectangular HSS member, measured 90° to the plane of the connection, in. (mm); H = overall height of rectangular HSS member, measured in the plane of the connection, in. (mm)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

1/20/11

Sect. D6.]

7:56 AM

Page 29

EYEBARS

D5.

PIN-CONNECTED MEMBERS

1.

Tensile Strength

16.1–29

The design tensile strength, φt Pn, and the allowable tensile strength, Pn /Ωt, of pinconnected members, shall be the lower value determined according to the limit states of tensile rupture, shear rupture, bearing and yielding. (a) For tensile rupture on the net effective area: Pn = Fu (2tbe) φt = 0.75 (LRFD)

(D5-1)

Ωt = 2.00 (ASD)

(b) For shear rupture on the effective area: Pn = 0.6Fu Asf φsf = 0.75 (LRFD)

(D5-2)

Ωsf = 2.00 (ASD)

where Asf = area on the shear failure path = 2t(a + d / 2), in.2 (mm2) a = shortest distance from edge of the pin hole to the edge of the member measured parallel to the direction of the force, in. (mm) be = 2t + 0.63, in. (= 2t + 16, mm), but not more than the actual distance from the edge of the hole to the edge of the part measured in the direction normal to the applied force, in. (mm) d = diameter of pin, in. (mm) t = thickness of plate, in. (mm) (c) For bearing on the projected area of the pin, use Section J7. (d) For yielding on the gross section, use Section D2(a).

2.

Dimensional Requirements The pin hole shall be located midway between the edges of the member in the direction normal to the applied force. When the pin is expected to provide for relative movement between connected parts while under full load, the diameter of the pin hole shall not be more than 1/32 in. (1 mm) greater than the diameter of the pin. The width of the plate at the pin hole shall not be less than 2be + d and the minimum extension, a, beyond the bearing end of the pin hole, parallel to the axis of the member, shall not be less than 1.33be. The corners beyond the pin hole are permitted to be cut at 45° to the axis of the member, provided the net area beyond the pin hole, on a plane perpendicular to the cut, is not less than that required beyond the pin hole parallel to the axis of the member.

D6.

EYEBARS

1.

Tensile Strength The available tensile strength of eyebars shall be determined in accordance with Section D2, with Ag taken as the cross-sectional area of the body. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.1_A:14th Ed.

1/20/11

16.1–30

7:56 AM

Page 30

EYEBARS

[Sect. D6.

For calculation purposes, the width of the body of the eyebars shall not exceed eight times its thickness.

2.

Dimensional Requirements Eyebars shall be of uniform thickness, without reinforcement at the pin holes, and have circular heads with the periphery concentric with the pin hole. The radius of transition between the circular head and the eyebar body shall not be less than the head diameter. The pin diameter shall not be less than seven-eighths times the eyebar body width, and the pin hole diameter shall not be more than 1/32 in. (1 mm) greater than the pin diameter. For steels having Fy greater than 70 ksi (485 MPa), the hole diameter shall not exceed five times the plate thickness, and the width of the eyebar body shall be reduced accordingly. A thickness of less than 1/2 in. (13 mm) is permissible only if external nuts are provided to tighten pin plates and filler plates into snug contact. The width from the hole edge to the plate edge perpendicular to the direction of applied load shall be greater than two-thirds and, for the purpose of calculation, not more than three-fourths times the eyebar body width.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed._

2/17/12

11:39 AM

Page 31

16.1–31

CHAPTER E DESIGN OF MEMBERS FOR COMPRESSION

This chapter addresses members subject to axial compression through the centroidal axis. The chapter is organized as follows: E1. E2. E3. E4. E5. E6. E7.

General Provisions Effective Length Flexural Buckling of Members without Slender Elements Torsional and Flexural-Torsional Buckling of Members without Slender Elements Single Angle Compression Members Built-Up Members Members with Slender Elements

User Note: For cases not included in this chapter the following sections apply: • H1 – H2 Members subject to combined axial compression and flexure • H3 Members subject to axial compression and torsion • I2 Composite axially loaded members • J4.4 Compressive strength of connecting elements

E1.

GENERAL PROVISIONS The design compressive strength, φc Pn, and the allowable compressive strength, Pn /Ωc, are determined as follows. The nominal compressive strength, Pn, shall be the lowest value obtained based on the applicable limit states of flexural buckling, torsional buckling, and flexuraltorsional buckling. φc = 0.90 (LRFD)

Ωc = 1.67 (ASD)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–32

1/20/11

7:58 AM

Page 32

GENERAL PROVISIONS

[Sect. E1.

TABLE USER NOTE E1.1 Selection Table for the Application of Chapter E Sections Without Slender Elements

Cross Section

With Slender Elements

Sections in Chapter E

Limit States

Sections in Chapter E

Limit States

E3 E4

FB TB

E7

LB FB TB

E3 E4

FB FTB

E7

LB FB FTB

E3

FB

E7

LB FB

E3

FB

E7

LB FB

E3 E4

FB FTB

E7

LB FB FTB

E6 E3 E4

FB FTB

E6 E7

E5

Unsymmetrical shapes other than single angles

LB FB FTB

E5

E3

FB

N/A

N/A

E4

FTB

E7

LB FTB

FB = flexural buckling, TB = torsional buckling, FTB = flexural-torsional buckling, LB = local buckling

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. E3.]

E2.

1/20/11

7:58 AM

Page 33

FLEXURAL BUCKLING OF MEMBERS WITHOUT SLENDER ELEMENTS

16.1–33

EFFECTIVE LENGTH The effective length factor, K, for calculation of member slenderness, KL/r, shall be determined in accordance with Chapter C or Appendix 7, where L = laterally unbraced length of the member, in. (mm) r = radius of gyration, in. (mm) User Note: For members designed on the basis of compression, the effective slenderness ratio KL/r preferably should not exceed 200.

E3.

FLEXURAL BUCKLING OF MEMBERS WITHOUT SLENDER ELEMENTS This section applies to nonslender element compression members as defined in Section B4.1 for elements in uniform compression. User Note: When the torsional unbraced length is larger than the lateral unbraced length, Section E4 may control the design of wide flange and similarly shaped columns.

The nominal compressive strength, Pn, shall be determined based on the limit state of flexural buckling. Pn = Fcr Ag

(E3-1)

The critical stress, Fcr, is determined as follows: (a) When

KL E ≤ 4.71 r Fy

(or

Fy ≤ 2.25 ) Fe

Fy ⎤ ⎡ ⎢ Fcr = 0.658 Fe ⎥ Fy ⎢ ⎥ ⎣ ⎦

(b) When KL > 4.71 E r Fy

(or

(E3-2)

Fy > 2.25 ) Fe

Fcr = 0.877Fe

(E3-3)

where Fe = elastic buckling stress determined according to Equation E3-4, as specified in Appendix 7, Section 7.2.3(b), or through an elastic buckling analysis, as applicable, ksi (MPa) Fe =

π2E ⎛ KL ⎞ ⎟ ⎜⎝ r ⎠

2

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(E3-4)

AISC_PART 16_Spec.2_B:14th Ed.

16.1–34

1/20/11

7:58 AM

Page 34

FLEXURAL BUCKLING OF MEMBERS WITHOUT SLENDER ELEMENTS

[Sect. E3.

User Note: The two inequalities for calculating the limits and applicability of Sections E3(a) and E3(b), one based on KL/r and one based on Fy /Fe, provide the same result.

E4.

TORSIONAL AND FLEXURAL-TORSIONAL BUCKLING OF MEMBERS WITHOUT SLENDER ELEMENTS This section applies to singly symmetric and unsymmetric members and certain doubly symmetric members, such as cruciform or built-up columns without slender elements, as defined in Section B4.1 for elements in uniform compression. In addition, this section applies to all doubly symmetric members without slender elements when the torsional unbraced length exceeds the lateral unbraced length. These provisions are required for single angles with b/t > 20. The nominal compressive strength, Pn, shall be determined based on the limit states of torsional and flexural-torsional buckling, as follows: Pn = Fcr Ag

(E4-1)

The critical stress, Fcr, is determined as follows: (a) For double angle and tee-shaped compression members: ⎡ 4 Fcry Fcrz H ⎛ Fcry + Fcrz ⎞ ⎢ Fcr = ⎜ 1− 1− ⎟ ⎝ 2H ⎠ ⎢ ( Fcry + Fcrz )2 ⎣

⎤ ⎥ ⎥ ⎦

(E4-2)

where Fcry is taken as Fcr from Equation E3-2 or E3-3 for flexural buckling about KL K y L the y-axis of symmetry, and for tee-shaped compression members, = r ry KL KL and from Section E6 for double angle compression members, and = r r m

( )

Fcrz =

GJ Ag ro2

(E4-3)

(b) For all other cases, Fcr shall be determined according to Equation E3-2 or E3-3, using the torsional or flexural-torsional elastic buckling stress, Fe, determined as follows: (i) For doubly symmetric members: ⎤ 1 ⎡ π 2 ECw Fe = ⎢ + GJ ⎥ 2 ⎥⎦ I x + I y ⎢⎣ ( K z L ) (ii) For singly symmetric members where y is the axis of symmetry:

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(E4-4)

AISC_PART 16_Spec.2_B:14th Ed.

Sect. E4.]

1/20/11

7:58 AM

Page 35

TORSIONAL AND FLEXURAL-TORSIONAL BUCKLING OF MEMBERS

4 Fey Fez H ⎛ Fey + Fez ⎞ ⎡ ⎢1 − 1 − Fe = ⎜ ⎟ ⎝ 2H ⎠ ⎢ ( Fey + Fez )2 ⎣

⎤ ⎥ ⎥⎦

16.1–35

(E4-5)

(iii) For unsymmetric members, Fe is the lowest root of the cubic equation: 2

2

⎛x ⎞ ⎛y ⎞ ( Fe − Fex )( Fe − Fey )( Fe − Fez ) − Fe2 ( Fe − Fey ) ⎜ o ⎟ − Fe2 ( Fe − Fex ) ⎜ o ⎟ = 0 (E4-6) ⎝ ro ⎠ ⎝ ro ⎠ where Ag Cw

= gross cross-sectional area of member, in.2 (mm2) = warping constant, in.6 (mm6) π2E

Fex

=

Fey

=

Fez

⎛ π 2 ECw ⎞ 1 = ⎜ + GJ ⎟ 2 2 ⎝ (Kz L) ⎠ Ag ro

G

= shear modulus of elasticity of steel = 11,200 ksi (77 200 MPa)

H

= 1−

Ix, Iy J Kx Ky Kz ⫺ ro

= moment of inertia about the principal axes, in.4 (mm4) = torsional constant, in.4 (mm4) = effective length factor for flexural buckling about x-axis = effective length factor for flexural buckling about y-axis = effective length factor for torsional buckling = polar radius of gyration about the shear center, in. (mm)

⫺ ro2

= xo2 + yo2 +

⎛ Kx L ⎞ ⎜⎝ r ⎟⎠ x

2

(E4-7)

2

(E4-8)

π2E ⎛ KyL ⎞ ⎜ r ⎟ ⎝ y ⎠

xo2 + yo2 ro2

Ix + Iy Ag

(E4-9)

(E4-10)

(E4-11)

rx = radius of gyration about x-axis, in. (mm) = radius of gyration about y-axis, in. (mm) ry xo, yo = coordinates of the shear center with respect to the centroid, in. (mm) User Note: For doubly symmetric I-shaped sections, Cw may be taken as Iy ho2/4, where ho is the distance between flange centroids, in lieu of a more precise analysis. For tees and double angles, omit the term with Cw when computing Fez and take xo as 0.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–36

E5.

1/20/11

7:58 AM

Page 36

SINGLE ANGLE COMPRESSION MEMBERS

[Sect. E5.

SINGLE ANGLE COMPRESSION MEMBERS The nominal compressive strength, Pn, of single angle members shall be determined in accordance with Section E3 or Section E7, as appropriate, for axially loaded members. For single angles with b/t > 20, Section E4 shall be used. Members meeting the criteria imposed in Section E5(a) or E5(b) are permitted to be designed as axially loaded members using the specified effective slenderness ratio, KL/r. The effects of eccentricity on single angle members are permitted to be neglected when evaluated as axially loaded compression members using one of the effective slenderness ratios specified in Section E5(a) or E5(b), provided that: (1) members are loaded at the ends in compression through the same one leg; (2) members are attached by welding or by connections with a minimum of two bolts; and (3) there are no intermediate transverse loads. Single angle members with different end conditions from those described in Section E5(a) or (b), with the ratio of long leg width to short leg width greater than 1.7 or with transverse loading, shall be evaluated for combined axial load and flexure using the provisions of Chapter H. (a) For equal-leg angles or unequal-leg angles connected through the longer leg that are individual members or are web members of planar trusses with adjacent web members attached to the same side of the gusset plate or chord: (i) When

(ii) When

L ≤ 80 : rx KL L = 72 + 0.75 r rx

(E5-1)

KL L = 32 + 1.25 ≤ 200 r rx

(E5-2)

L > 80 : rx

For unequal-leg angles with leg length ratios less than 1.7 and connected through the shorter leg, KL/r from Equations E5-1 and E5-2 shall be increased by adding 4[(bl /bs)2⫺1], but KL/r of the members shall not be taken as less than 0.95L/rz. (b) For equal-leg angles or unequal-leg angles connected through the longer leg that are web members of box or space trusses with adjacent web members attached to the same side of the gusset plate or chord: (i) When L ≤ 75 : rx KL L = 60 + 0.8 r rx (ii) When L > 75 : rx Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(E5-3)

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

Sect. E6.]

7:58 AM

Page 37

BUILT-UP MEMBERS

16.1–37

KL L = 45 + ≤ 200 r rx

(E5-4)

For unequal-leg angles with leg length ratios less than 1.7 and connected through the shorter leg, KL/r from Equations E5-3 and E5-4 shall be increased by adding 6[(bl/bs)2⫺1], but KL/r of the member shall not be taken as less than 0.82L/rz where L = length of member between work points at truss chord centerlines, in. (mm) bl = length of longer leg of angle, in. (mm) bs = length of shorter leg of angle, in. (mm) rx = radius of gyration about the geometric axis parallel to the connected leg, in. (mm) rz = radius of gyration about the minor principal axis, in. (mm)

E6.

BUILT-UP MEMBERS

1.

Compressive Strength This section applies to built-up members composed of two shapes either (a) interconnected by bolts or welds, or (b) with at least one open side interconnected by perforated cover plates or lacing with tie plates. The end connection shall be welded or connected by means of pretensioned bolts with Class A or B faying surfaces. User Note: It is acceptable to design a bolted end connection of a built-up compression member for the full compressive load with bolts in bearing and bolt design based on the shear strength; however, the bolts must be pretensioned. In built-up compression members, such as double-angle struts in trusses, a small relative slip between the elements especially at the end connections can increase the effective length of the combined cross section to that of the individual components and significantly reduce the compressive strength of the strut. Therefore, the connection between the elements at the ends of built-up members should be designed to resist slip. The nominal compressive strength of built-up members composed of two shapes that are interconnected by bolts or welds shall be determined in accordance with Sections E3, E4 or E7 subject to the following modification. In lieu of more accurate analysis, if the buckling mode involves relative deformations that produce shear forces in the connectors between individual shapes, KL/r is replaced by (KL/r)m determined as follows: (a) For intermediate connectors that are bolted snug-tight: 2

⎛ KL ⎞ ⎛ KL ⎞ ⎛ a ⎞ ⎜⎝ ⎟ = ⎜⎝ ⎟ + r ⎠m r ⎠ o ⎜⎝ ri ⎟⎠

2

(E6-1)

(b) For intermediate connectors that are welded or are connected by means of pretensioned bolts: Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B_14th Ed._February 12, 2013 12/02/13 9:41 AM Page 38

16.1–38

(i) When

(ii) When

BUILT-UP MEMBERS

[Sect. E6.

⎛ KL ⎞ ⎛ KL ⎞ ⎟ ⎟ =⎜ ⎜⎝ r ⎠m ⎝ r ⎠o

(E6-2a)

a ≤ 40 ri

a > 40 ri 2

⎛ Kia ⎞ ⎛ KL ⎞ ⎛ KL ⎞ ⎜⎝ ⎟⎠ = ⎜⎝ ⎟⎠ + ⎜⎝ r m r o ri ⎟⎠

2

(E6-2b)

where

⎛ KL ⎞ ⎜⎝ ⎟ = modified slenderness ratio of built-up member r ⎠m ⎛ KL ⎞ ⎜⎝ ⎟ = slenderness ratio of built-up member acting as a unit in the r ⎠o Ki

a ri

2.

buckling direction being considered = 0.50 for angles back-to-back = 0.75 for channels back-to-back = 0.86 for all other cases = distance between connectors, in. (mm) = minimum radius of gyration of individual component, in. (mm)

Dimensional Requirements Individual components of compression members composed of two or more shapes shall be connected to one another at intervals, a, such that the effective slenderness ratio, Ka/ri , of each of the component shapes between the fasteners does not exceed three-fourths times the governing slenderness ratio of the built-up member. The least radius of gyration, ri, shall be used in computing the slenderness ratio of each component part. At the ends of built-up compression members bearing on base plates or finished surfaces, all components in contact with one another shall be connected by a weld having a length not less than the maximum width of the member or by bolts spaced longitudinally not more than four diameters apart for a distance equal to 11/2 times the maximum width of the member. Along the length of built-up compression members between the end connections required above, longitudinal spacing for intermittent welds or bolts shall be adequate to provide for the transfer of the required strength. For limitations on the longitudinal spacing of fasteners between elements in continuous contact consisting of a plate and a shape or two plates, see Section J3.5. Where a component of a built-up compression member consists of an outside plate, the maximum spacing shall not exceed the thickness of the thinner outside plate times 0.75 E /Fy nor 12 in. (305 mm), when intermittent welds are provided along the edges of the components or when fasteners are provided on all gage lines at each section. When fasteners are staggered, the maximum spacing of fasteners on each gage line shall not exceed the thickness of the thinner outside plate times 1.12 E /Fy nor 18 in. (460 mm). Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. E6.]

1/20/11

7:58 AM

Page 39

BUILT-UP MEMBERS

16.1–39

Open sides of compression members built up from plates or shapes shall be provided with continuous cover plates perforated with a succession of access holes. The unsupported width of such plates at access holes, as defined in Section B4.1, is assumed to contribute to the available strength provided the following requirements are met: (1) The width-to-thickness ratio shall conform to the limitations of Section B4.1. User Note: It is conservative to use the limiting width-to-thickness ratio for Case 7 in Table B4.1a with the width, b, taken as the transverse distance between the nearest lines of fasteners. The net area of the plate is taken at the widest hole. In lieu of this approach, the limiting width-to-thickness ratio may be determined through analysis. (2) The ratio of length (in direction of stress) to width of hole shall not exceed 2. (3) The clear distance between holes in the direction of stress shall be not less than the transverse distance between nearest lines of connecting fasteners or welds. (4) The periphery of the holes at all points shall have a minimum radius of 11/2 in. (38 mm). As an alternative to perforated cover plates, lacing with tie plates is permitted at each end and at intermediate points if the lacing is interrupted. Tie plates shall be as near the ends as practicable. In members providing available strength, the end tie plates shall have a length of not less than the distance between the lines of fasteners or welds connecting them to the components of the member. Intermediate tie plates shall have a length not less than one-half of this distance. The thickness of tie plates shall be not less than one-fiftieth of the distance between lines of welds or fasteners connecting them to the segments of the members. In welded construction, the welding on each line connecting a tie plate shall total not less than one-third the length of the plate. In bolted construction, the spacing in the direction of stress in tie plates shall be not more than six diameters and the tie plates shall be connected to each segment by at least three fasteners. Lacing, including flat bars, angles, channels or other shapes employed as lacing, shall be so spaced that the L/r ratio of the flange element included between their connections shall not exceed three-fourths times the governing slenderness ratio for the member as a whole. Lacing shall be proportioned to provide a shearing strength normal to the axis of the member equal to 2% of the available compressive strength of the member. The L/r ratio for lacing bars arranged in single systems shall not exceed 140. For double lacing this ratio shall not exceed 200. Double lacing bars shall be joined at the intersections. For lacing bars in compression, L is permitted to be taken as the unsupported length of the lacing bar between welds or fasteners connecting it to the components of the built-up member for single lacing, and 70% of that distance for double lacing. User Note: The inclination of lacing bars to the axis of the member shall preferably be not less than 60⬚ for single lacing and 45⬚ for double lacing. When the distance between the lines of welds or fasteners in the flanges is more than 15 in. (380 mm), the lacing shall preferably be double or be made of angles. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

16.1–40

7:58 AM

Page 40

BUILT-UP MEMBERS

[Sect. E6.

For additional spacing requirements, see Section J3.5.

E7.

MEMBERS WITH SLENDER ELEMENTS This section applies to slender-element compression members, as defined in Section B4.1 for elements in uniform compression. The nominal compressive strength, Pn, shall be the lowest value based on the applicable limit states of flexural buckling, torsional buckling, and flexural-torsional buckling. Pn = Fcr Ag

(E7-1)

The critical stress, Fcr, shall be determined as follows: (a) When

KL E ≤ 4.71 r QFy

⎛ QFy ⎞ ⎜⎝ or Fe ≤ 2.25 ⎟⎠ QFy ⎤ ⎡ Fcr = Q ⎢ 0.658 Fe ⎥ Fy ⎢ ⎥ ⎣ ⎦

(b) When

KL E > 4.71 r QFy

(E7-2)

⎛ QFy ⎞ ⎜⎝ or Fe > 2.25 ⎟⎠ Fcr = 0.877Fe

(E7-3)

where Fe = elastic buckling stress, calculated using Equations E3-4 and E4-4 for doubly symmetric members, Equations E3-4 and E4-5 for singly symmetric members, and Equation E4-6 for unsymmetric members, except for single angles with b/t ≤ 20, where Fe is calculated using Equation E3-4, ksi (MPa) Q = net reduction factor accounting for all slender compression elements; = 1.0 for members without slender elements, as defined in Section B4.1, for elements in uniform compression = Qs Qa for members with slender-element sections, as defined in Section B4.1, for elements in uniform compression. User Note: For cross sections composed of only unstiffened slender elements, Q = Qs (Qa = 1.0). For cross sections composed of only stiffened slender elements, Q = Qa (Qs = 1.0). For cross sections composed of both stiffened and unstiffened slender elements, Q = Qs Qa. For cross sections composed of multiple unstiffened slender elements, it is conservative to use the smaller Qs from the more slender element in determining the member strength for pure compression.

1.

Slender Unstiffened Elements, Qs The reduction factor, Qs, for slender unstiffened elements is defined as follows: (a) For flanges, angles and plates projecting from rolled columns or other compression members: Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. E7.]

1/20/11

7:58 AM

Page 41

MEMBERS WITH SLENDER ELEMENTS

(i) When

b E ≤ 0.56 t Fy Qs = 1.0

(ii) When 0.56

(E7-4)

E b E < < 1.03 Fy t Fy ⎛ b ⎞ Fy Qs = 1.415 − 0.74 ⎜ ⎟ ⎝ t⎠ E

(iii) When

16.1–41

(E7-5)

b E ≥ 1.03 t Fy Qs =

0.69 E ⎛ b⎞ Fy ⎜ ⎟ ⎝ t⎠

(E7-6)

2

(b) For flanges, angles and plates projecting from built-up I-shaped columns or other compression members: (i) When

b Ekc ≤ 0.64 t Fy Qs = 1.0

(ii) When 0.64

(E7-7)

Ekc b Ekc < ≤ 1.17 Fy t Fy ⎛ b⎞ Qs = 1.415 − 0.65 ⎜ ⎟ ⎝ t⎠

(iii) When

Fy Ekc

(E7-8)

b Ekc > 1.17 t Fy Qs =

0.90 Ekc ⎛ b⎞ Fy ⎜ ⎟ ⎝ t⎠

2

(E7-9)

where b = width of unstiffened compression element, as defined in Section B4.1, in. (mm) 4 , and shall not be taken less than 0.35 nor greater than 0.76 for kc = h t w calculation purposes t = thickness of element, in. (mm) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–42

1/20/11

7:58 AM

Page 42

MEMBERS WITH SLENDER ELEMENTS

[Sect. E7.

(c) For single angles (i) When

b E ≤ 0.45 t Fy Qs = 1.0

(ii) When 0.45

(E7-10)

E b E < ≤ 0.91 Fy t Fy ⎛ b ⎞ Fy Qs = 1.34 − 0.76 ⎜ ⎟ ⎝ t⎠ E

(iii) When

(E7-11)

b E > 0.91 t Fy Qs =

0.53E ⎛ b⎞ Fy ⎜ ⎟ ⎝ t⎠

2

(E7-12)

where b = full width of longest leg, in. (mm) (d) For stems of tees (i) When

d E ≤ 0.75 t Fy Qs = 1.0

(ii) When 0.75

(E7-13)

E d E < ≤ 1.03 Fy t Fy ⎛ d ⎞ Fy Qs = 1.908 − 1.22 ⎜ ⎟ ⎝ t⎠ E

(iii) When

(E7-14)

d E > 1.03 t Fy Qs =

0.69 E ⎛ d⎞ Fy ⎜ ⎟ ⎝ t⎠

2

where d = full nominal depth of tee, in. (mm)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(E7-15)

AISC_PART 16_Spec.2_B:14th Ed.

Sect. E7.]

2.

1/20/11

7:58 AM

Page 43

MEMBERS WITH SLENDER ELEMENTS

16.1–43

Slender Stiffened Elements, Qa The reduction factor, Qa , for slender stiffened elements is defined as follows: Qa =

Ae Ag

(E7-16)

where Ag = gross cross-sectional area of member, in.2 (mm2) Ae = summation of the effective areas of the cross section based on the reduced effective width, be, in.2 (mm2) The reduced effective width, be, is determined as follows: b E (a) For uniformly compressed slender elements, with ≥ 1.49 , except flanges of t f square and rectangular sections of uniform thickness: be = 1.92 t

E f

⎡ 0.34 E ⎤ ⎢1 − ⎥≤b ( b / t) f ⎦ ⎣

(E7-17)

where f is taken as Fcr with Fcr calculated based on Q = 1.0 (b) For flanges of square and rectangular slender-element sections of uniform thickb E ness with ≥ 1.40 : t f be = 1.92 t

E f

⎡ 0.38 E ⎤ ⎢1 − ⎥≤b ⎣ (b / t ) f ⎦

(E7-18)

where f = Pn /Ae User Note: In lieu of calculating f = Pn /Ae, which requires iteration, f may be taken equal to Fy. This will result in a slightly conservative estimate of column available strength. (c) For axially loaded circular sections: When 0.11

E D E < < 0.45 Fy t Fy Q = Qa =

0.038 E 2 + Fy ( D / t ) 3

where D = outside diameter of round HSS, in. (mm) t = thickness of wall, in. (mm)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(E7-19)

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

7:58 AM

Page 44

16.1–44

CHAPTER F DESIGN OF MEMBERS FOR FLEXURE

This chapter applies to members subject to simple bending about one principal axis. For simple bending, the member is loaded in a plane parallel to a principal axis that passes through the shear center or is restrained against twisting at load points and supports. The chapter is organized as follows: F1. F2. F3. F4. F5. F6. F7. F8. F9. F10. F11. F12. F13.

General Provisions Doubly Symmetric Compact I-Shaped Members and Channels Bent About Their Major Axis Doubly Symmetric I-Shaped Members with Compact Webs and Noncompact or Slender Flanges Bent About Their Major Axis Other I-Shaped Members With Compact or Noncompact Webs Bent About Their Major Axis Doubly Symmetric and Singly Symmetric I-Shaped Members With Slender Webs Bent About Their Major Axis I-Shaped Members and Channels Bent About Their Minor Axis Square and Rectangular HSS and Box-Shaped Members Round HSS Tees and Double Angles Loaded in the Plane of Symmetry Single Angles Rectangular Bars and Rounds Unsymmetrical Shapes Proportions of Beams and Girders

User Note: For cases not included in this chapter the following sections apply: • Chapter G Design provisions for shear • H1–H3 Members subject to biaxial flexure or to combined flexure and axial force • H3 Members subject to flexure and torsion • Appendix 3 Members subject to fatigue For guidance in determining the appropriate sections of this chapter to apply, Table User Note F1.1 may be used.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. F1.]

1/20/11

7:58 AM

Page 45

16.1–45

GENERAL PROVISIONS

TABLE USER NOTE F1.1 Selection Table for the Application of Chapter F Sections Section in Chapter F

Cross Section

Flange Web Slenderness Slenderness

Limit States

F2

C

C

Y, LTB

F3

NC, S

C

LTB, FLB

F4

C, NC, S

C, NC

Y, LTB, FLB, TFY

F5

C, NC, S

S

Y, LTB, FLB, TFY

F6

C, NC, S

N/A

Y, FLB

F7

C, NC, S

C, NC

Y, FLB, WLB

F8

N/A

N/A

Y, LB

F9

C, NC, S

N/A

Y, LTB, FLB

F10

N/A

N/A

Y, LTB, LLB

F11

N/A

N/A

Y, LTB

N/A

N/A

All limit states

F12

Unsymmetrical shapes, other than single angles

Y = yielding, LTB = lateral-torsional buckling, FLB = flange local buckling, WLB = web local buckling, TFY = tension flange yielding, LLB = leg local buckling, LB = local buckling, C = compact, NC = noncompact, S = slender Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

16.1–46

F1.

7:58 AM

Page 46

GENERAL PROVISIONS

[Sect. F1.

GENERAL PROVISIONS The design flexural strength, φb Mn, and the allowable flexural strength, Mn/Ωb, shall be determined as follows: (1) For all provisions in this chapter φb = 0.90 (LRFD)

Ωb = 1.67 (ASD)

and the nominal flexural strength, Mn, shall be determined according to Sections F2 through F13. (2) The provisions in this chapter are based on the assumption that points of support for beams and girders are restrained against rotation about their longitudinal axis. (3) For singly symmetric members in single curvature and all doubly symmetric members: Cb, the lateral-torsional buckling modification factor for nonuniform moment diagrams when both ends of the segment are braced is determined as follows: Cb =

12.5 M max 2.5 M max + 3M A + 4 M B + 3MC

(F1-1)

where Mmax = absolute value of maximum moment in the unbraced segment, kip-in. (N-mm) MA = absolute value of moment at quarter point of the unbraced segment, kip-in. (N-mm) MB = absolute value of moment at centerline of the unbraced segment, kipin. (N-mm) MC = absolute value of moment at three-quarter point of the unbraced segment, kip-in. (N-mm) For cantilevers or overhangs where the free end is unbraced, Cb = 1.0. User Note: For doubly symmetric members with no transverse loading between brace points, Equation F1-1 reduces to 1.0 for the case of equal end moments of opposite sign (uniform moment), 2.27 for the case of equal end moments of the same sign (reverse curvature bending), and to 1.67 when one end moment equals zero. For singly symmetric members, a more detailed analysis for Cb is presented in the Commentary. (4) In singly symmetric members subject to reverse curvature bending, the lateraltorsional buckling strength shall be checked for both flanges. The available flexural strength shall be greater than or equal to the maximum required moment causing compression within the flange under consideration.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. F2.]

F2.

1/20/11

7:58 AM

Page 47

DOUBLY SYMMETRIC COMPACT I-SHAPED MEMBERS AND CHANNELS

16.1–47

DOUBLY SYMMETRIC COMPACT I-SHAPED MEMBERS AND CHANNELS BENT ABOUT THEIR MAJOR AXIS This section applies to doubly symmetric I-shaped members and channels bent about their major axis, having compact webs and compact flanges as defined in Section B4.1 for flexure. User Note: All current ASTM A6 W, S, M, C and MC shapes except W21×48, W14×99, W14×90, W12×65, W10×12, W8×31, W8×10, W6×15, W6×9, W6×8.5 and M4×6 have compact flanges for Fy = 50 ksi (345 MPa); all current ASTM A6 W, S, M, HP, C and MC shapes have compact webs at Fy ≤ 65 ksi (450 MPa). The nominal flexural strength, Mn, shall be the lower value obtained according to the limit states of yielding (plastic moment) and lateral-torsional buckling.

1.

Yielding Mn = Mp = Fy Zx

(F2-1)

where Fy = specified minimum yield stress of the type of steel being used, ksi (MPa) Zx = plastic section modulus about the x-axis, in.3 (mm3)

2.

Lateral-Torsional Buckling (a) When Lb ≤ Lp, the limit state of lateral-torsional buckling does not apply. (b) When Lp < Lb ≤ Lr ⎡ ⎛ Lb − L p ⎞ ⎤ M n = Cb ⎢ M p − ( M p − 0.7 Fy S x ) ⎜ ⎥ ≤ Mp ⎝ Lr − L p ⎟⎠ ⎥⎦ ⎢⎣

(F2-2)

(c) When Lb > Lr Mn = Fcr Sx ≤ Mp

(F2-3)

where Lb = length between points that are either braced against lateral displacement of the compression flange or braced against twist of the cross section, in. (mm) Fcr =

Cb π 2 E ⎛ Lb ⎞ ⎜⎝ r ⎟⎠ ts

2

1 + 0.078

Jc ⎛ Lb ⎞ S x ho ⎜⎝ rts ⎟⎠

2

and where E = modulus of elasticity of steel = 29,000 ksi (200 000 MPa) J = torsional constant, in.4 (mm4) Sx = elastic section modulus taken about the x-axis, in.3 (mm3) ho = distance between the flange centroids, in. (mm) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(F2-4)

AISC_PART 16_Spec.2_B:14th Ed.

16.1–48

1/20/11

7:58 AM

Page 48

DOUBLY SYMMETRIC COMPACT I-SHAPED MEMBERS AND CHANNELS

[Sect. F2.

User Note: The square root term in Equation F2-4 may be conservatively taken equal to 1.0.

User Note: Equations F2-3 and F2-4 provide identical solutions to the following expression for lateral-torsional buckling of doubly symmetric sections that has been presented in past editions of the AISC LRFD Specification: 2

π ⎛ πE ⎞ EI yGJ + ⎜ I yCw ⎝ Lb ⎟⎠ Lb The advantage of Equations F2-3 and F2-4 is that the form is very similar to the expression for lateral-torsional buckling of singly symmetric sections given in Equations F4-4 and F4-5. Mcr = Cb

The limiting lengths Lp and Lr are determined as follows: L p = 1.76ry

Lr = 1.95rts

E 0.7 Fy

E Fy

(F2-5)

2

Jc ⎛ Jc ⎞ ⎛ 0.77 Fy ⎞ + 6.76 ⎜ + ⎜ ⎝ E ⎟⎠ ⎝ S x ho ⎟⎠ S x ho

2

(F2-6)

where rts2 =

I yCw

(F2-7)

Sx

and the coefficient c is determined as follows: (a) For doubly symmetric I-shapes: c = 1 (b) For channels: c =

(F2-8a)

ho I y 2 Cw

(F2-8b)

I h2 User Note: For doubly symmetric I-shapes with rectangular flanges, Cw = y o 4 and thus Equation F2-7 becomes rts2 =

I y ho 2Sx

rts may be approximated accurately and conservatively as the radius of gyration of the compression flange plus one-sixth of the web: rts =

bf ⎛ 1 ht w ⎞ 12 ⎜ 1 + ⎝ 6 b f t f ⎟⎠

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. F4.]

F3.

1/20/11

7:58 AM

Page 49

OTHER I-SHAPED MEMBERS WITH COMPACT OR NONCOMPACT WEBS

16.1–49

DOUBLY SYMMETRIC I-SHAPED MEMBERS WITH COMPACT WEBS AND NONCOMPACT OR SLENDER FLANGES BENT ABOUT THEIR MAJOR AXIS This section applies to doubly symmetric I-shaped members bent about their major axis having compact webs and noncompact or slender flanges as defined in Section B4.1 for flexure. User Note: The following shapes have noncompact flanges for Fy = 50 ksi (345 MPa): W21×48, W14×99, W14×90, W12×65, W10×12, W8×31, W8×10, W6×15, W6×9, W6×8.5 and M4×6. All other ASTM A6 W, S and M shapes have compact flanges for Fy ≤ 50 ksi (345 MPa). The nominal flexural strength, Mn, shall be the lower value obtained according to the limit states of lateral-torsional buckling and compression flange local buckling.

1.

Lateral-Torsional Buckling For lateral-torsional buckling, the provisions of Section F2.2 shall apply.

2.

Compression Flange Local Buckling (a) For sections with noncompact flanges ⎛ λ − λ pf ⎞ M n = M p − ( M p − 0.7 Fy S x ) ⎜ ⎝ λ rf − λ pf ⎟⎠

(F3-1)

(b) For sections with slender flanges Mn =

0.9 Ekc S x λ2

(F3-2)

where bf 2t f λpf = λp is the limiting slenderness for a compact flange, Table B4.1b λrf = λr is the limiting slenderness for a noncompact flange, Table B4.1b 4 kc = and shall not be taken less than 0.35 nor greater than 0.76 for calcuh t w lation purposes λ =

h = distance as defined in Section B4.1b, in. (mm)

F4.

OTHER I-SHAPED MEMBERS WITH COMPACT OR NONCOMPACT WEBS BENT ABOUT THEIR MAJOR AXIS This section applies to doubly symmetric I-shaped members bent about their major axis with noncompact webs and singly symmetric I-shaped members with webs attached to the mid-width of the flanges, bent about their major axis, with compact or noncompact webs, as defined in Section B4.1 for flexure. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–50

1/20/11

7:58 AM

Page 50

OTHER I-SHAPED MEMBERS WITH COMPACT OR NONCOMPACT WEBS

[Sect. F4.

User Note: I-shaped members for which this section is applicable may be designed conservatively using Section F5. The nominal flexural strength, Mn, shall be the lowest value obtained according to the limit states of compression flange yielding, lateral-torsional buckling, compression flange local buckling, and tension flange yielding.

1.

Compression Flange Yielding Mn = Rpc Myc = Rpc Fy Sxc

(F4-1)

where Myc = yield moment in the compression flange, kip-in. (N-mm)

2.

Lateral-Torsional Buckling (a) When Lb ≤ Lp, the limit state of lateral-torsional buckling does not apply. (b) When Lp < Lb ≤ Lr ⎡ ⎛ Lb − L p ⎞ ⎤ M n = Cb ⎢ R pc M yc − ( R pc M yc − FL S xc ) ⎜ ⎥ ≤ R pc M yc ⎝ Lr − L p ⎟⎠ ⎥⎦ ⎢⎣

(F4-2)

(c) When Lb > Lr Mn = Fcr Sxc ≤ Rpc Myc where Myc = Fy Sxc

Fcr =

Cb π 2 E ⎛ Lb ⎞ ⎜⎝ r ⎟⎠ t

2

(F4-3) (F4-4)

1 + 0.078

J ⎛ Lb ⎞ S xc ho ⎜⎝ rt ⎟⎠

2

(F4-5)

I yc ≤ 0.23, J shall be taken as zero Iy where Iyc = moment of inertia of the compression flange about the y-axis, in.4 (mm4)

For

The stress, FL, is determined as follows: (i) When

S xt ≥ 0.7 S xc FL = 0.7Fy

(ii) When

(F4-6a)

S xt < 0.7 S xc FL = Fy

S xt ≥ 0.5 Fy S xc

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(F4-6b)

AISC_PART 16_Spec.2_B:14th Ed.

Sect. F4.]

1/20/11

7:58 AM

Page 51

OTHER I-SHAPED MEMBERS WITH COMPACT OR NONCOMPACT WEBS

16.1–51

The limiting laterally unbraced length for the limit state of yielding, Lp, is determined as: L p = 1.1rt

E Fy

(F4-7)

The limiting unbraced length for the limit state of inelastic lateral-torsional buckling, Lr, is determined as: Lr = 1.95rt

E FL

2

J ⎛ J ⎞ ⎛F ⎞ + ⎜ + 6.76 ⎜ L ⎟ ⎝ E⎠ ⎝ S xc ho ⎟⎠ S xc ho

2

(F4-8)

The web plastification factor, Rpc, shall be determined as follows: (i) When Iyc /Iy > 0.23 (a) When

hc ≤ λ pw tw R pc =

(b) When

Mp M yc

(F4-9a)

hc > λ pw tw ⎡ Mp ⎛ Mp ⎞ ⎛ λ − λ pw ⎞ ⎤ M p R pc = ⎢ −⎜ − 1⎟ ⎜ ⎟⎥ ≤ ⎢⎣ M yc ⎝ M yc ⎠ ⎝ λ rw − λ pw ⎠ ⎥⎦ M yc

(F4-9b)

(ii) When Iyc /Iy ≤ 0.23 Rpc = 1.0

(F4-10)

where = Fy Zx ≤ 1.6Fy Sxc Mp Sxc, Sxt = elastic section modulus referred to compression and tension flanges, respectively, in.3 (mm3) h λ = c tw λpw = λp, the limiting slenderness for a compact web, Table B4.1b = λr, the limiting slenderness for a noncompact web, Table B4.1b λrw = twice the distance from the centroid to the following: the inside face of hc the compression flange less the fillet or corner radius, for rolled shapes; the nearest line of fasteners at the compression flange or the inside faces of the compression flange when welds are used, for built-up sections, in. (mm)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–52

1/20/11

7:58 AM

Page 52

OTHER I-SHAPED MEMBERS WITH COMPACT OR NONCOMPACT WEBS

[Sect. F4.

The effective radius of gyration for lateral-torsional buckling, rt, is determined as follows: (i) For I-shapes with a rectangular compression flange rt =

b fc ⎛h 1 h2 ⎞ 12 ⎜ o + aw ⎟ ⎝ d 6 hod ⎠

(F4-11)

where aw =

hc t w b fc t fc

(F4-12)

bfc = width of compression flange, in. (mm) tfc = compression flange thickness, in. (mm) (ii) For I-shapes with a channel cap or a cover plate attached to the compression flange rt = radius of gyration of the flange components in flexural compression plus one-third of the web area in compression due to application of major axis bending moment alone, in. (mm) aw = the ratio of two times the web area in compression due to application of major axis bending moment alone to the area of the compression flange components User Note: For I-shapes with a rectangular compression flange, rt may be approximated accurately and conservatively as the radius of gyration of the compression flange plus one-third of the compression portion of the web; in other words b fc

rt =

3.

1 ⎞ ⎛ 12 ⎜ 1 + aw ⎟ ⎝ 6 ⎠

Compression Flange Local Buckling (a) For sections with compact flanges, the limit state of local buckling does not apply. (b) For sections with noncompact flanges ⎛ λ − λ pf ⎞ M n = R pc M yc − ( R pc M yc − FL S xc ) ⎜ ⎝ λ rf − λ pf ⎟⎠

(F4-13)

(c) For sections with slender flanges Mn =

0.9 Ekc S xc λ2

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(F4-14)

AISC_PART 16_Spec.2_B:14th Ed.

Sect. F4.]

1/20/11

7:58 AM

Page 53

16.1–53

OTHER I-SHAPED MEMBERS WITH COMPACT OR NONCOMPACT WEBS

where FL is defined in Equations F4-6a and F4-6b Rpc is the web plastification factor, determined by Equations F4-9 4 kc = and shall not be taken less than 0.35 nor greater than 0.76 for calcuh t w lation purposes bfc 2 t fc λpf = λp, the limiting slenderness for a compact flange, Table B4.1b λrf = λr, the limiting slenderness for a noncompact flange, Table B4.1b λ

4.

=

Tension Flange Yielding (a) When Sxt ≥ Sxc, the limit state of tension flange yielding does not apply. (b) When Sxt < Sxc Mn = Rpt Myt

(F4-15)

where Myt = Fy Sxt The web plastification factor corresponding to the tension flange yielding limit state, Rpt, is determined as follows: (i) When

hc ≤ λ pw tw Rpt =

(ii) When

Mp Myt

(F4-16a)

hc > λ pw tw ⎡ Mp ⎛ Mp ⎞ ⎛ λ − λ pw ⎞ ⎤ Mp Rpt = ⎢ −⎜ − 1⎟ ⎜ ⎟⎥ ≤ M M ⎢⎣ yt ⎝ yt ⎠ ⎝ λrw − λ pw ⎠ ⎥⎦ Myt

(F4-16b)

where λ

=

hc tw

λpw = λp, the limiting slenderness for a compact web, defined in Table B4.1b λrw = λr, the limiting slenderness for a noncompact web, defined in Table B4.1b

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–54

F5.

1/20/11

7:58 AM

Page 54

DOUBLY SYMMETRIC AND SINGLY SYMMETRIC I-SHAPED MEMBERS

[Sect. F5.

DOUBLY SYMMETRIC AND SINGLY SYMMETRIC I-SHAPED MEMBERS WITH SLENDER WEBS BENT ABOUT THEIR MAJOR AXIS This section applies to doubly symmetric and singly symmetric I-shaped members with slender webs attached to the mid-width of the flanges and bent about their major axis as defined in Section B4.1 for flexure. The nominal flexural strength, Mn, shall be the lowest value obtained according to the limit states of compression flange yielding, lateral-torsional buckling, compression flange local buckling, and tension flange yielding.

1.

2.

Compression Flange Yielding Mn = Rpg Fy Sxc

(F5-1)

Mn = Rpg Fcr Sxc

(F5-2)

Lateral-Torsional Buckling

(a) When Lb ≤ Lp, the limit state of lateral-torsional buckling does not apply. (b) When Lp < Lb ≤ Lr ⎡ ⎛ Lb − L p ⎞ ⎤ Fcr = Cb ⎢ Fy − ( 0.3Fy ) ⎜ ⎥ ≤ Fy ⎝ Lr − L p ⎟⎠ ⎥⎦ ⎢⎣

(F5-3)

(c) When Lb > Lr Fcr =

Cb π 2 E ⎛ Lb ⎞ ⎜⎝ r ⎟⎠ t

2

≤ Fy

(F5-4)

where Lp is defined by Equation F4-7 Lr = πrt

E 0.7 Fy

(F5-5)

Rpg, the bending strength reduction factor is determined as follows: R pg = 1 −

⎛ hc aw E⎞ − 5.7 ≤ 1.0 ⎜ Fy ⎟⎠ 1, 200 + 300 aw ⎝ t w

(F5-6)

where aw is defined by Equation F4-12 but shall not exceed 10 rt is the effective radius of gyration for lateral buckling as defined in Section F4

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. F6.]

3.

1/20/11

7:58 AM

Page 55

I-SHAPED MEMBERS AND CHANNELS

16.1–55

Compression Flange Local Buckling Mn = Rpg Fcr Sxc

(F5-7)

(a) For sections with compact flanges, the limit state of compression flange local buckling does not apply. (b) For sections with noncompact flanges ⎡ ⎛ λ − λ pf ⎞ ⎤ Fcr = ⎢ Fy − ( 0.3Fy ) ⎜ ⎥ ⎝ λrf − λ pf ⎟⎠ ⎥⎦ ⎢⎣

(F5-8)

(c) For sections with slender flanges Fcr =

0.9 Ekc ⎛ bf ⎞ ⎜⎝ 2 t ⎟⎠ f

2

(F5-9)

where 4 and shall not be taken less than 0.35 nor greater than 0.76 for calcuh t w lation purposes

kc = λ

=

b fc 2 t fc

λpf = λp, the limiting slenderness for a compact flange, Table B4.1b λrf = λr, the limiting slenderness for a noncompact flange, Table B4.1b

4.

Tension Flange Yielding (a) When Sxt ≥ Sxc, the limit state of tension flange yielding does not apply. (b) When Sxt < Sxc Mn = Fy Sxt

F6.

(F5-10)

I-SHAPED MEMBERS AND CHANNELS BENT ABOUT THEIR MINOR AXIS This section applies to I-shaped members and channels bent about their minor axis. The nominal flexural strength, Mn, shall be the lower value obtained according to the limit states of yielding (plastic moment) and flange local buckling.

1.

Yielding Mn = Mp = Fy Zy ≤ 1.6Fy Sy

2.

(F6-1)

Flange Local Buckling (a) For sections with compact flanges the limit state of flange local buckling does not apply.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–56

1/20/11

7:58 AM

Page 56

I-SHAPED MEMBERS AND CHANNELS

[Sect. F6.

User Note: All current ASTM A6 W, S, M, C and MC shapes except W21×48, W14×99, W14×90, W12×65, W10×12, W8×31, W8×10, W6×15, W6×9, W6×8.5 and M4×6 have compact flanges at Fy = 50 ksi (345 MPa). (b) For sections with noncompact flanges ⎡ ⎛ λ − λ pf ⎞ ⎤ M n = ⎢ M p − ( M p − 0.7 Fy S y ) ⎜ ⎥ ⎝ λ rf − λ pf ⎟⎠ ⎦⎥ ⎢⎣

(F6-2)

(c) For sections with slender flanges Mn = Fcr Sy

(F6-3)

where Fcr =

0.69 E ⎛ b⎞ ⎜⎝ t ⎟⎠

(F6-4)

2

f

λ

=

b tf

λpf = λp, the limiting slenderness for a compact flange, Table B4.1b λrf = λr, the limiting slenderness for a noncompact flange, Table B4.1b b = for flanges of I-shaped members, half the full-flange width, bf ; for flanges of channels, the full nominal dimension of the flange, in. (mm) tf = thickness of the flange, in. (mm) Sy = elastic section modulus taken about the y-axis, in.3 (mm3); for a channel, the minimum section modulus

F7.

SQUARE AND RECTANGULAR HSS AND BOX-SHAPED MEMBERS This section applies to square and rectangular HSS, and doubly symmetric boxshaped members bent about either axis, having compact or noncompact webs and compact, noncompact or slender flanges as defined in Section B4.1 for flexure. The nominal flexural strength, Mn, shall be the lowest value obtained according to the limit states of yielding (plastic moment), flange local buckling and web local buckling under pure flexure. User Note: Very long rectangular HSS bent about the major axis are subject to lateral-torsional buckling; however, the Specification provides no strength equation for this limit state since beam deflection will control for all reasonable cases.

1.

Yielding Mn = Mp = Fy Z where Z = plastic section modulus about the axis of bending, in.3 (mm3) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(F7-1)

AISC_PART 16_Spec.2_B:14th Ed._

2/17/12

Sect. F8.]

2.

11:42 AM

Page 57

ROUND HSS

16.1–57

Flange Local Buckling (a) For compact sections, the limit state of flange local buckling does not apply. (b) For sections with noncompact flanges ⎛ b M n = M p − ( M p − Fy S ) ⎜ 3.57 tf ⎝

⎞ Fy − 4.0⎟ ≤ M p E ⎠

(F7-2)

(c) For sections with slender flanges Mn = Fy Se

(F7-3)

where Se = effective section modulus determined with the effective width, be, of the compression flange taken as: be = 1.92 t f

3.

E Fy

⎡ 0.38 ⎢1 − b / tf ⎢⎣

E Fy

⎤ ⎥≤b ⎥⎦

(F7-4)

Web Local Buckling (a) For compact sections, the limit state of web local buckling does not apply. (b) For sections with noncompact webs ⎛ h M n = M p − ( M p − Fy S ) ⎜ 0.305 tw ⎝

F8.

⎞ Fy − 0.738⎟ ≤ M p E ⎠

(F7-5)

ROUND HSS 0.45 E . Fy The nominal flexural strength, Mn, shall be the lower value obtained according to the limit states of yielding (plastic moment) and local buckling. This section applies to round HSS having D/t ratios of less than

1.

Yielding Mn = Mp = Fy Z

2.

(F8-1)

Local Buckling (a) For compact sections, the limit state of flange local buckling does not apply. (b) For noncompact sections ⎛ ⎞ ⎜ 0.021E ⎟ + Fy ⎟ S Mn = ⎜ D ⎛ ⎞ ⎜ ⎜ ⎟ ⎟ ⎝ ⎝ t⎠ ⎠

(F8-2)

(c) For sections with slender walls Mn = Fcr S Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(F8-3)

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

16.1–58

7:58 AM

Page 58

ROUND HSS

[Sect. F8.

where 0.33E ⎛ D⎞ ⎜⎝ ⎟⎠ t S = elastic section modulus, in.3 (mm3) t = thickness of wall, in. (mm)

Fcr =

F9.

(F8-4)

TEES AND DOUBLE ANGLES LOADED IN THE PLANE OF SYMMETRY This section applies to tees and double angles loaded in the plane of symmetry. The nominal flexural strength, Mn, shall be the lowest value obtained according to the limit states of yielding (plastic moment), lateral-torsional buckling, flange local buckling, and local buckling of tee stems.

1.

Yielding Mn = Mp

(F9-1)

Mp = Fy Zx ≤ 1.6My

(F9-2)

where (a) For stems in tension

(b) For stems in compression Mp = Fy Zx ≤ My

2.

(F9-3)

Lateral-Torsional Buckling M n = Mcr =

π EI yGJ Lb

(B +

1 + B2

)

(F9-4)

where ⎛ d ⎞ Iy B = ±2.3 ⎜ ⎟ ⎝ Lb ⎠ J

(F9-5)

The plus sign for B applies when the stem is in tension and the minus sign applies when the stem is in compression. If the tip of the stem is in compression anywhere along the unbraced length, the negative value of B shall be used.

3.

Flange Local Buckling of Tees (a) For sections with a compact flange in flexural compression, the limit state of flange local buckling does not apply. (b) For sections with a noncompact flange in flexural compression

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. F9.]

1/20/11

7:58 AM

Page 59

TEES AND DOUBLE ANGLES LOADED IN THE PLANE OF SYMMETRY

16.1–59

⎛ λ − λ pf ⎞ Mn = M p − ( M p − 0.7 Fy Sxc ) ⎜ ≤ 1.6 M y ⎝ λrf − λ pf ⎟⎠

(F9-6)

(c) For sections with a slender flange in flexural compression Mn =

0.7 ES xc ⎛ bf ⎞ ⎜⎝ 2 t ⎟⎠ f

(F9-7)

2

where Sxc = elastic section modulus referred to the compression flange, in.3 (mm3) bf 2t f λpf = λp, the limiting slenderness for a compact flange, Table B4.1b λrf = λr, the limiting slenderness for a noncompact flange, Table B4.1b λ =

User Note: For double angles with flange legs in compression, Mn based on local buckling is to be determined using the provisions of Section F10.3 with b/t of the flange legs and Equation F10-1 as an upper limit.

4.

Local Buckling of Tee Stems in Flexural Compression Mn = Fcr Sx

(F9-8)

where Sx = elastic section modulus, in.3 (mm3) The critical stress, Fcr, is determined as follows: (a) When

d E ≤ 0.84 tw Fy Fcr = Fy

(b) When 0.84

(F9-9)

E d E < ≤ 1.03 Fy t w Fy ⎡ d Fcr = ⎢ 2.55 − 1.84 t w ⎣

(c) When

Fy E

⎤ ⎥ Fy ⎦

(F9-10)

d E > 1.03 tw Fy Fcr =

0.69 E ⎛d⎞ ⎜⎝ t ⎟⎠ w

2

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(F9-11)

AISC_PART 16_Spec.2_B:14th Ed.

16.1–60

1/20/11

7:58 AM

Page 60

TEES AND DOUBLE ANGLES LOADED IN THE PLANE OF SYMMETRY

[Sect. F9.

User note: For double angles with web legs in compression, Mn based on local buckling is to be determined using the provisions of Section F10.3 with b/t of the web legs and Equation F10-1 as an upper limit.

F10. SINGLE ANGLES This section applies to single angles with and without continuous lateral restraint along their length. Single angles with continuous lateral-torsional restraint along the length are permitted to be designed on the basis of geometric axis (x, y) bending. Single angles without continuous lateral-torsional restraint along the length shall be designed using the provisions for principal axis bending except where the provision for bending about a geometric axis is permitted. If the moment resultant has components about both principal axes, with or without axial load, or the moment is about one principal axis and there is axial load, the combined stress ratio shall be determined using the provisions of Section H2. User Note: For geometric axis design, use section properties computed about the x- and y-axis of the angle, parallel and perpendicular to the legs. For principal axis design, use section properties computed about the major and minor principal axes of the angle. The nominal flexural strength, Mn, shall be the lowest value obtained according to the limit states of yielding (plastic moment), lateral-torsional buckling, and leg local buckling. User Note: For bending about the minor axis, only the limit states of yielding and leg local buckling apply.

1.

Yielding Mn = 1.5My

(F10-1)

where My = yield moment about the axis of bending, kip-in. (N-mm)

2.

Lateral-Torsional Buckling For single angles without continuous lateral-torsional restraint along the length (a) When Me ≤ My ⎛ 0.17 Me ⎞ M n = ⎜ 0.92 − Me M y ⎟⎠ ⎝

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(F10-2)

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

7:58 AM

Page 61

SINGLE ANGLES

16.1–61

⎛ My ⎞ M n = ⎜ 1.92 − 1.17 M y ≤ 1.5 M y Me ⎟⎠ ⎝

(F10-3)

Sect. F10.]

(b) When Me > My

where Me, the elastic lateral-torsional buckling moment, is determined as follows: (i) For bending about the major principal axis of equal-leg angles: Me =

0.46 Eb 2 t 2Cb Lb

(F10-4)

(ii) For bending about the major principal axis of unequal-leg angles:

Me =

2 ⎛ ⎞ ⎛ Lb t ⎞ 4.9 EI zCb ⎜ 2 ⎟ β . β + 0 052 + w w ⎜⎝ r ⎟⎠ ⎜ ⎟ Lb2 z ⎝ ⎠

(F10-5)

where Cb is computed using Equation F1-1 with a maximum value of 1.5 Lb = laterally unbraced length of member, in. (mm) Iz = minor principal axis moment of inertia, in.4 (mm4) rz = radius of gyration about the minor principal axis, in. (mm) t = thickness of angle leg, in. (mm) βw = section property for unequal leg angles, positive for short legs in compression and negative for long legs in compression. If the long leg is in compression anywhere along the unbraced length of the member, the negative value of βw shall be used. User Note: The equation for βw and values for common angle sizes are listed in the Commentary. (iii) For bending moment about one of the geometric axes of an equal-leg angle with no axial compression (a) And with no lateral-torsional restraint: (i) With maximum compression at the toe Me =

2 ⎛ ⎞ 0.66 Eb 4 tCb ⎛ Lb t ⎞ ⎜ 1 0 78 . + ⎜⎝ 2 ⎟⎠ − 1⎟ 2 ⎟⎠ ⎜⎝ Lb b

(F10-6a)

(ii) With maximum tension at the toe Me =

2 ⎛ ⎞ 0.66 Eb 4 tCb ⎛ Lb t ⎞ ⎟ ⎜ 1 0 78 1 . + + ⎜ ⎟ ⎝ b2 ⎠ ⎟⎠ ⎜⎝ Lb2

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(F10-6b)

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

16.1–62

7:58 AM

Page 62

SINGLE ANGLES

[Sect. F10.

My shall be taken as 0.80 times the yield moment calculated using the geometric section modulus. where b = full width of leg in compression, in. (mm) User Note: Mn may be taken as My for single angles with their vertical leg toe in compression, and having a span-to-depth ratio less than or equal to 2

Fy 1.64 E ⎛ t ⎞ ⎜⎝ ⎟⎠ − 1.4 Fy b E (b) And with lateral-torsional restraint at the point of maximum moment only: Me shall be taken as 1.25 times Me computed using Equation F10-6a or F10-6b. My shall be taken as the yield moment calculated using the geometric section modulus.

3.

Leg Local Buckling The limit state of leg local buckling applies when the toe of the leg is in compression. (a) For compact sections, the limit state of leg local buckling does not apply. (b) For sections with noncompact legs: ⎛ ⎛ b⎞ M n = Fy Sc ⎜ 2.43 − 1.72 ⎜ ⎟ ⎝ t⎠ ⎝

Fy ⎞ E ⎟⎠

(F10-7)

(c) For sections with slender legs: Mn = Fcr Sc

(F10-8)

where Fcr =

0.71E ⎛ b⎞ ⎜⎝ ⎟⎠ t

(F10-9)

2

Sc = elastic section modulus to the toe in compression relative to the axis of bending, in.3 (mm3). For bending about one of the geometric axes of an equal-leg angle with no lateral-torsional restraint, Sc shall be 0.80 of the geometric axis section modulus.

F11. RECTANGULAR BARS AND ROUNDS This section applies to rectangular bars bent about either geometric axis and rounds. The nominal flexural strength, Mn, shall be the lower value obtained according to the limit states of yielding (plastic moment) and lateral-torsional buckling. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. F12.]

1.

1/20/11

7:59 AM

Page 63

UNSYMMETRICAL SHAPES

16.1–63

Yielding Lb d 0.08 E bent about their major axis, rectangular bars ≤ Fy t2 bent about their minor axis and rounds: For rectangular bars with

Mn = Mp = Fy Z ≤ 1.6My

2.

(F11-1)

Lateral-Torsional Buckling (a) For rectangular bars with

0.08 E Lb d 1.9 E bent about their major axis: < 2 ≤ Fy Fy t

⎡ ⎛ L d ⎞ Fy ⎤ M n = Cb ⎢1.52 − 0.274 ⎜ b2 ⎟ ⎥ M y ≤ M p ⎝ t ⎠ E⎦ ⎣ (b) For rectangular bars with

(F11-2)

Lb d 1.9 E bent about their major axis: > Fy t2 Mn = Fcr Sx ≤ Mp

(F11-3)

where 1.9 ECb (F11-4) Lb d t2 Lb = length between points that are either braced against lateral displacement of the compression region, or between points braced to prevent twist of the cross section, in. (mm) d = depth of rectangular bar, in. (mm) t = width of rectangular bar parallel to axis of bending, in. (mm)

Fcr =

(c) For rounds and rectangular bars bent about their minor axis, the limit state of lateral-torsional buckling need not be considered.

F12. UNSYMMETRICAL SHAPES This section applies to all unsymmetrical shapes, except single angles. The nominal flexural strength, Mn, shall be the lowest value obtained according to the limit states of yielding (yield moment), lateral-torsional buckling, and local buckling where Mn = Fn Smin

(F12-1)

where Smin = lowest elastic section modulus relative to the axis of bending, in.3 (mm3)

1.

Yielding Fn = Fy

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(F12-2)

AISC_PART 16_Spec.2_B:14th Ed.

16.1–64

2.

1/20/11

7:59 AM

Page 64

UNSYMMETRICAL SHAPES

[Sect. F12.

Lateral-Torsional Buckling Fn = Fcr ≤ Fy

(F12-3)

where Fcr = lateral-torsional buckling stress for the section as determined by analysis, ksi (MPa) User Note: In the case of Z-shaped members, it is recommended that Fcr be taken as 0.5Fcr of a channel with the same flange and web properties.

3.

Local Buckling Fn = Fcr ≤ Fy

(F12-4)

where Fcr = local buckling stress for the section as determined by analysis, ksi (MPa)

F13. PROPORTIONS OF BEAMS AND GIRDERS 1.

Strength Reductions for Members With Holes in the Tension Flange This section applies to rolled or built-up shapes and cover-plated beams with holes, proportioned on the basis of flexural strength of the gross section. In addition to the limit states specified in other sections of this Chapter, the nominal flexural strength, Mn, shall be limited according to the limit state of tensile rupture of the tension flange. (a) When Fu Afn ≥ Yt Fy Afg, the limit state of tensile rupture does not apply. (b) When Fu Afn < Yt Fy Afg, the nominal flexural strength, Mn, at the location of the holes in the tension flange shall not be taken greater than Mn =

Fu A fn Sx A fg

(F13-1)

where Afg = gross area of tension flange, calculated in accordance with the provisions of Section B4.3a, in.2 (mm2) Afn = net area of tension flange, calculated in accordance with the provisions of Section B4.3b, in.2 (mm2) Yt = 1.0 for Fy /Fu ≤ 0.8 = 1.1 otherwise

2.

Proportioning Limits for I-Shaped Members Singly symmetric I-shaped members shall satisfy the following limit: 0.1 ≤

I yc ≤ 0.9 Iy

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(F13-2)

AISC_PART 16_Spec.2_B:14th Ed.

Sect. F13.]

1/20/11

7:59 AM

Page 65

PROPORTIONS OF BEAMS AND GIRDERS

16.1–65

I-shaped members with slender webs shall also satisfy the following limits: (a) When

(b) When

a ≤ 1.5 h E ⎛ h⎞ = 12.0 ⎜⎝ t ⎟⎠ F w max y

(F13-3)

0.40 E ⎛ h⎞ = ⎜⎝ t ⎟⎠ Fy w max

(F13-4)

a > 1.5 h

where a = clear distance between transverse stiffeners, in. (mm) In unstiffened girders h/tw shall not exceed 260. The ratio of the web area to the compression flange area shall not exceed 10.

3.

Cover Plates Flanges of welded beams or girders may be varied in thickness or width by splicing a series of plates or by the use of cover plates. The total cross-sectional area of cover plates of bolted girders shall not exceed 70% of the total flange area. High-strength bolts or welds connecting flange to web, or cover plate to flange, shall be proportioned to resist the total horizontal shear resulting from the bending forces on the girder. The longitudinal distribution of these bolts or intermittent welds shall be in proportion to the intensity of the shear. However, the longitudinal spacing shall not exceed the maximum specified for compression or tension members in Section E6 or D4, respectively. Bolts or welds connecting flange to web shall also be proportioned to transmit to the web any loads applied directly to the flange, unless provision is made to transmit such loads by direct bearing. Partial-length cover plates shall be extended beyond the theoretical cutoff point and the extended portion shall be attached to the beam or girder by high-strength bolts in a slip-critical connection or fillet welds. The attachment shall be adequate, at the applicable strength given in Sections J2.2, J3.8 or B3.11 to develop the cover plate’s portion of the flexural strength in the beam or girder at the theoretical cutoff point. For welded cover plates, the welds connecting the cover plate termination to the beam or girder shall have continuous welds along both edges of the cover plate in the length a′, defined below, and shall be adequate to develop the cover plate’s portion of the available strength of the beam or girder at the distance a′ from the end of the cover plate.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–66

1/20/11

7:59 AM

Page 66

PROPORTIONS OF BEAMS AND GIRDERS

[Sect. F13.

(a) When there is a continuous weld equal to or larger than three-fourths of the plate thickness across the end of the plate a′ = w

(F13-5)

where w = width of cover plate, in. (mm) (b) When there is a continuous weld smaller than three-fourths of the plate thickness across the end of the plate a′ = 1.5w

(F13-6)

(c) When there is no weld across the end of the plate a′ = 2w

4.

(F13-7)

Built-Up Beams Where two or more beams or channels are used side-by-side to form a flexural member, they shall be connected together in compliance with Section E6.2. When concentrated loads are carried from one beam to another or distributed between the beams, diaphragms having sufficient stiffness to distribute the load shall be welded or bolted between the beams.

5.

Unbraced Length for Moment Redistribution For moment redistribution in beams according to Section B3.7, the laterally unbraced length, Lb, of the compression flange adjacent to the redistributed end moment locations shall not exceed Lm determined as follows. (a) For doubly symmetric and singly symmetric I-shaped beams with the compression flange equal to or larger than the tension flange loaded in the plane of the web: ⎡ ⎛ M ⎞ ⎤⎛ E ⎞ Lm = ⎢ 0.12 + 0.076 ⎜ 1 ⎟ ⎥ ⎜ ⎟ ry ⎝ M 2 ⎠ ⎦ ⎝ Fy ⎠ ⎣

(F13-8)

(b) For solid rectangular bars and symmetric box beams bent about their major axis: ⎛ E⎞ ⎡ ⎛ M ⎞ ⎤⎛ E ⎞ Lm = ⎢ 0.17 + 0.10 ⎜ 1 ⎟ ⎥ ⎜ ⎟ ry ≥ 0.10 ⎜ ⎟ ry ⎠ ⎝ M F ⎠ ⎝ ⎝ Fy ⎠ 2 ⎦ y ⎣

(F13-9)

where Fy = specified minimum yield stress of the compression flange, ksi (MPa) M1 = smaller moment at end of unbraced length, kip-in. (N-mm) M2 = larger moment at end of unbraced length, kip-in. (N-mm) ry = radius of gyration about y-axis, in. (mm) (M1 /M2) is positive when moments cause reverse curvature and negative for single curvature There is no limit on Lb for members with round or square cross sections or for any beam bent about its minor axis. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

7:59 AM

Page 67

16.1–67

CHAPTER G DESIGN OF MEMBERS FOR SHEAR

This chapter addresses webs of singly or doubly symmetric members subject to shear in the plane of the web, single angles and HSS sections, and shear in the weak direction of singly or doubly symmetric shapes. The chapter is organized as follows: G1. G2. G3. G4. G5. G6. G7. G8.

General Provisions Members with Unstiffened or Stiffened Webs Tension Field Action Single Angles Rectangular HSS and Box-Shaped Members Round HSS Weak Axis Shear in Doubly Symmetric and Singly Symmetric Shapes Beams and Girders with Web Openings

User Note: For cases not included in this chapter, the following sections apply: • H3.3 Unsymmetric sections • J4.2 Shear strength of connecting elements • J10.6 Web panel zone shear

G1.

GENERAL PROVISIONS Two methods of calculating shear strength are presented below. The method presented in Section G2 does not utilize the post buckling strength of the member (tension field action). The method presented in Section G3 utilizes tension field action. The design shear strength, φvVn, and the allowable shear strength, Vn /Ωv, shall be determined as follows: For all provisions in this chapter except Section G2.1(a): φv = 0.90 (LRFD)

Ωv = 1.67 (ASD)

G2.

MEMBERS WITH UNSTIFFENED OR STIFFENED WEBS

1.

Shear Strength This section applies to webs of singly or doubly symmetric members and channels subject to shear in the plane of the web. The nominal shear strength, Vn, of unstiffened or stiffened webs according to the limit states of shear yielding and shear buckling, is Vn = 0.6Fy Aw Cv Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(G2-1)

AISC_PART 16_Spec.2_B_14th Ed._February 12, 2013 12/02/13 9:42 AM Page 68

16.1–68

MEMBERS WITH UNSTIFFENED OR STIFFENED WEBS

(a) For webs of rolled I-shaped members with φv = 1.00 (LRFD)

[Sect. G2.

h t w ≤ 2.24 E Fy :

Ω v = 1.50 (ASD)

and Cv = 1.0

(G2-2)

User Note: All current ASTM A6 W, S and HP shapes except W44×230, W40×149, W36×135, W33×118, W30×90, W24×55, W16×26 and W12×14 meet the criteria stated in Section G2.1(a) for Fy = 50 ksi (345 MPa). (b) For webs of all other doubly symmetric shapes and singly symmetric shapes and channels, except round HSS, the web shear coefficient, Cv, is determined as follows: (i) When h / t w ≤ 1.10 kv E / Fy Cv = 1.0

(G2-3)

(ii) When 1.10 kv E / Fy < h / t w ≤ 1.37 kv E / Fy

Cv =

1.10 kv E / Fy h / tw

(G2-4)

(iii) When h / t w > 1.37 kv E / Fy Cv =

1.51kv E

( h / tw )2 Fy

(G2-5)

where Aw = area of web, the overall depth times the web thickness, dtw, in.2 (mm2) h = for rolled shapes, the clear distance between flanges less the fillet or corner radii, in. (mm) = for built-up welded sections, the clear distance between flanges, in. (mm) = for built-up bolted sections, the distance between fastener lines, in. (mm) = for tees, the overall depth, in. (mm) tw = thickness of web, in. (mm) The web plate shear buckling coefficient, kv, is determined as follows: (i) For webs without transverse stiffeners and with h/tw < 260: kv = 5 except for the stem of tee shapes where kv = 1.2. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed._

Sect. G2.]

2/17/12

11:43 AM

Page 69

MEMBERS WITH UNSTIFFENED OR STIFFENED WEBS

16.1–69

(ii) For webs with transverse stiffeners: kv = 5 +

5

(G2-6)

( a / h )2

⎡ 260 ⎤ = 5 when a/h > 3.0 or a/h > ⎢ ⎥ ⎣ ( h / tw ) ⎦

2

where a = clear distance between transverse stiffeners, in. (mm) User Note: For all ASTM A6 W, S, M and HP shapes except M12.5×12.4, M12.5×11.6, M12×11.8, M12×10.8, M12×10, M10×8 and M10×7.5, when Fy = 50 ksi (345 MPa), Cv = 1.0.

2.

Transverse Stiffeners Transverse stiffeners are not required where h / t w ≤ 2.46 E / Fy , or where the available shear strength provided in accordance with Section G2.1 for kv = 5 is greater than the required shear strength. The moment of inertia, Ist, of transverse stiffeners used to develop the available web shear strength, as provided in Section G2.1, about an axis in the web center for stiffener pairs or about the face in contact with the web plate for single stiffeners, shall meet the following requirement I st ≥ bt 3w j

(G2-7)

where j=

2.5

( a / h )2

− 2 ≥ 0.5

(G2-8)

and b is the smaller of the dimensions a and h Transverse stiffeners are permitted to be stopped short of the tension flange, provided bearing is not needed to transmit a concentrated load or reaction. The weld by which transverse stiffeners are attached to the web shall be terminated not less than four times nor more than six times the web thickness from the near toe of the web-to-flange weld. When single stiffeners are used, they shall be attached to the compression flange, if it consists of a rectangular plate, to resist any uplift tendency due to torsion in the flange. Bolts connecting stiffeners to the girder web shall be spaced not more than 12 in. (305 mm) on center. If intermittent fillet welds are used, the clear distance between welds shall not be more than 16 times the web thickness nor more than 10 in. (250 mm).

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

16.1–70

7:59 AM

Page 70

TENSION FIELD ACTION

G3.

TENSION FIELD ACTION

1.

Limits on the Use of Tension Field Action

[Sect. G3.

Consideration of tension field action is permitted for flanged members when the web plate is supported on all four sides by flanges or stiffeners. Consideration of tension field action is not permitted: (a) for end panels in all members with transverse stiffeners; (b) when a兾h exceeds 3.0 or 关260兾冠h兾tw冡兴 ; 2

(c) when 2 Aw 兾冠Afc + Aft冡 > 2.5; or (d) when h兾bfc or h兾bft > 6.0. where Afc = area of compression flange, in.2 (mm2) Aft = area of tension flange, in.2 (mm2) bfc = width of compression flange, in. (mm) bft = width of tension flange, in. (mm) In these cases, the nominal shear strength, Vn, shall be determined according to the provisions of Section G2.

2.

Shear Strength With Tension Field Action When tension field action is permitted according to Section G3.1, the nominal shear strength, Vn, with tension field action, according to the limit state of tension field yielding, shall be (a) When h / t w ≤ 1.10 kv E / Fy Vn = 0.6Fy Aw

(G3-1)

(b) When h / t w > 1.10 kv E / Fy ⎛ ⎞ 1 − Cv ⎟ Vn = 0.6 Fy Aw ⎜ Cv + 2 ⎜⎝ 1.15 1 + ( a / h ) ⎟⎠

(G3-2)

where kv and Cv are as defined in Section G2.1

3.

Transverse Stiffeners Transverse stiffeners subject to tension field action shall meet the requirements of Section G2.2 and the following limitations: (1) ( b t )st ≤ 0.56

E Fyst

⎡ V − Vc1 ⎤ (2) I st ≥ I st1 + ( I st 2 − I st1 ) ⎢ r ⎥ ⎣ Vc 2 − Vc1 ⎦ Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(G3-3) (G3-4)

AISC_PART 16_Spec.2_B:14th Ed.

Sect. G5.]

1/20/11

7:59 AM

Page 71

RECTANGULAR HSS AND BOX-SHAPED MEMBERS

16.1–71

where 冇b兾t冈st = width-to-thickness ratio of the stiffener Fyst = specified minimum yield stress of the stiffener material, ksi (MPa) = moment of inertia of the transverse stiffeners about an axis in the web Ist center for stiffener pairs, or about the face in contact with the web plate for single stiffeners, in.4 (mm4) = minimum moment of inertia of the transverse stiffeners required for Ist1 development of the web shear buckling resistance in Section G2.2, in.4 (mm4) = minimum moment of inertia of the transverse stiffeners required for Ist2 development of the full web shear buckling plus the web tension field resistance, Vr = Vc2 , in.4 (mm4) = Vr Vc1 Vc2 ρst Fyw

G4.

h 4ρ1st.3 ⎛ Fyw ⎞ ⎟ ⎜ 40 ⎝ E ⎠

1.5

(G3-5)

= larger of the required shear strengths in the adjacent web panels using LRFD or ASD load combinations, kips (N) = smaller of the available shear strengths in the adjacent web panels with Vn as defined in Section G2.1, kips (N) = smaller of the available shear strengths in the adjacent web panels with Vn as defined in Section G3.2, kips (N) = the larger of Fyw/Fyst and 1.0 = specified minimum yield stress of the web material, ksi (MPa)

SINGLE ANGLES The nominal shear strength, Vn, of a single angle leg shall be determined using Equation G2-1 and Section G2.1(b) with Aw = bt where b = width of the leg resisting the shear force, in. (mm) t = thickness of angle leg, in. (mm) h/tw = b/t kv = 1.2

G5.

RECTANGULAR HSS AND BOX-SHAPED MEMBERS The nominal shear strength, Vn, of rectangular HSS and box members shall be determined using the provisions of Section G2.1 with Aw = 2ht where h = width resisting the shear force, taken as the clear distance between the flanges less the inside corner radius on each side, in. (mm) t = design wall thickness, equal to 0.93 times the nominal wall thickness for electric-resistance-welded (ERW) HSS and equal to the nominal thickness for submerged-arc-welded (SAW) HSS, in. (mm) tw = t, in. (mm) kv = 5

Specification for Structural Steel Buildings, June 22, 2010

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[Sect. G5.

If the corner radius is not known, h shall be taken as the corresponding outside dimension minus 3 times the thickness.

G6.

ROUND HSS The nominal shear strength, Vn, of round HSS, according to the limit states of shear yielding and shear buckling, shall be determined as: Vn = Fcr Ag /2

(G6-1)

where Fcr shall be the larger of Fcr =

1.60 E 5

(G6-2a)

Lv ⎛ D ⎞ 4 ⎜ ⎟ D⎝ t⎠ and Fcr =

0.78 E

(G6-2b)

3

⎛ D⎞ 2 ⎜⎝ ⎟⎠ t

but shall not exceed 0.6Fy Ag = gross cross-sectional area of member, in.2 (mm2) D = outside diameter, in. (mm) Lv = distance from maximum to zero shear force, in. (mm) t = design wall thickness, equal to 0.93 times the nominal wall thickness for ERW HSS and equal to the nominal thickness for SAW HSS, in. (mm) User Note: The shear buckling equations, Equations G6-2a and G6-2b, will control for D/t over 100, high-strength steels, and long lengths. For standard sections, shear yielding will usually control.

G7.

WEAK AXIS SHEAR IN DOUBLY SYMMETRIC AND SINGLY SYMMETRIC SHAPES For doubly and singly symmetric shapes loaded in the weak axis without torsion, the nominal shear strength, Vn, for each shear resisting element shall be determined using Equation G2-1 and Section G2.1(b) with Aw = bf tf , h/tw = b/tf, kv = 1.2, and b = for flanges of I-shaped members, half the full-flange width, bf ; for flanges of channels, the full nominal dimension of the flange, in. (mm) User Note: For all ASTM A6 W, S, M and HP shapes, when Fy ≤ 50 ksi (345 MPa), Cv = 1.0.

G8.

BEAMS AND GIRDERS WITH WEB OPENINGS The effect of all web openings on the shear strength of steel and composite beams shall be determined. Adequate reinforcement shall be provided when the required strength exceeds the available strength of the member at the opening. Specification for Structural Steel Buildings, June 22, 2010

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CHAPTER H DESIGN OF MEMBERS FOR COMBINED FORCES AND TORSION

This chapter addresses members subject to axial force and flexure about one or both axes, with or without torsion, and members subject to torsion only. The chapter is organized as follows: H1. H2. H3. H4.

Doubly and Singly Symmetric Members Subject to Flexure and Axial Force Unsymmetric and Other Members Subject to Flexure and Axial Force Members Subject to Torsion and Combined Torsion, Flexure, Shear and/or Axial Force Rupture of Flanges with Holes Subject to Tension

User Note: For composite members, see Chapter I.

H1.

DOUBLY AND SINGLY SYMMETRIC MEMBERS SUBJECT TO FLEXURE AND AXIAL FORCE

1.

Doubly and Singly Symmetric Members Subject to Flexure and Compression The interaction of flexure and compression in doubly symmetric members and singly symmetric members for which 0.1 ≤ 共Iyc兾Iy兲 ≤ 0.9, constrained to bend about a geometric axis (x and/or y) shall be limited by Equations H1-1a and H1-1b, where Iyc is the moment of inertia of the compression flange about the y-axis, in.4 (mm4). User Note: Section H2 is permitted to be used in lieu of the provisions of this section. (a) When

(b) When

Pr ≥ 0.2 Pc Pr 8 ⎛ Mrx Mry ⎞ ≤ 1.0 + + Pc 9 ⎜⎝ Mcx Mcy ⎟⎠

(H1-1a)

Pr ⎛ Mrx Mry ⎞ ≤ 1.0 + + 2 Pc ⎜⎝ Mcx Mcy ⎟⎠

(H1-1b)

Pr < 0.2 Pc

where Pr = required axial strength using LRFD or ASD load combinations, kips (N) Pc = available axial strength, kips (N) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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[Sect. H1.

Mr = required flexural strength using LRFD or ASD load combinations, kip-in. (N-mm) Mc = available flexural strength, kip-in. (N-mm) x = subscript relating symbol to strong axis bending y = subscript relating symbol to weak axis bending For design according to Section B3.3 (LRFD): Pr = required axial strength using LRFD load combinations, kips (N) Pc = φc Pn = design axial strength, determined in accordance with Chapter E, kips (N) Mr = required flexural strength using LRFD load coMbinations, kip-in. (N-mm) Mc = φb Mn = design flexural strength determined in accordance with Chapter F, kip-in. (N-mm) φc = resistance factor for compression = 0.90 φb = resistance factor for flexure = 0.90 For design according to Section B3.4 (ASD): Pr = required axial strength using ASD load combinations, kips (N) Pc = Pn /Ωc = allowable axial strength, determined in accordance with Chapter E, kips (N) Mr = required flexural strength using ASD load combinations, kip-in. (N-mm) Mc = Mn /Ωb = allowable flexural strength determined in accordance with Chapter F, kip-in. (N-mm) Ωc = safety factor for compression = 1.67 Ωb = safety factor for flexure = 1.67

2.

Doubly and Singly Symmetric Members Subject to Flexure and Tension The interaction of flexure and tension in doubly symmetric members and singly symmetric members constrained to bend about a geometric axis (x and/or y) shall be limited by Equations H1-1a and H1-1b where For design according to Section B3.3 (LRFD): Pr = required axial strength using LRFD load combinations, kips (N) Pc = φtPn = design axial strength, determined in accordance with Section D2, kips (N) Mr = required flexural strength using LRFD load combinations, kip-in. (N-mm) Mc = φb Mn = design flexural strength determined in accordance with Chapter F, kip-in. (N-mm) φt = resistance factor for tension (see Section D2) φb = resistance factor for flexure = 0.90 For design according to Section B3.4 (ASD): Pr = required axial strength using ASD load combinations, kips (N) Pc = Pn /Ω t = allowable axial strength, determined in accordance with Section D2, kips (N) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. H1.]

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DOUBLY AND SINGLY SYMMETRIC MEMBERS

Mr = required flexural strength using ASD load combinations, kip-in. (N-mm) Mc = Mn /Ωb = allowable flexural strength determined in accordance with Chapter F, kip-in. (N-mm) Ωt = safety factor for tension (see Section D2) Ωb = safety factor for flexure = 1.67 For doubly symmetric members, Cb in Chapter F may be multiplied by for axial tension that acts concurrently with flexure

1+

αPr Pey

where Pey =

π 2 EI y L2b

and α = 1.0 (LRFD); α = 1.6 (ASD) A more detailed analysis of the interaction of flexure and tension is permitted in lieu of Equations H1-1a and H1-1b.

3.

Doubly Symmetric Rolled Compact Members Subject to Single Axis Flexure and Compression For doubly symmetric rolled compact members with 共KL兲z ≤ 共KL兲y subjected to flexure and compression with moments primarily about their major axis, it is permissible to consider the two independent limit states, in-plane instability and out-of-plane buckling or lateral-torsional buckling, separately in lieu of the combined approach provided in Section H1.1. For members with Mry兾Mcy ≥ 0.05, the provisions of Section H1.1 shall be followed. (a) For the limit state of in-plane instability, Equations H1-1 shall be used with Pc, Mrx and Mcx determined in the plane of bending. (b) For the limit state of out-of-plane buckling and lateral-torsional buckling: 2 Pr ⎛ P ⎞ ⎛ Mrx ⎞ ≤ 1.0 1.5 − 0.5 r ⎟ + ⎜ ⎟ ⎜ Pcy ⎝ Pcy ⎠ ⎝ Cb Mcx ⎠

(H1-2)

where Pcy = available compressive strength out of the plane of bending, kips (N) Cb = lateral-torsional buckling modification factor determined from Section F1 Mcx = available lateral-torsional strength for strong axis flexure determined in accordance with Chapter F using Cb = 1.0, kip-in. (N-mm) User Note: In Equation H1-2, Cb Mcx may be larger than φb Mpx in LRFD or Mpx /Ωb in ASD. The yielding resistance of the beam-column is captured by Equations H1-1.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–76

H2.

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UNSYMMETRIC AND OTHER MEMBERS

[Sect. H2.

UNSYMMETRIC AND OTHER MEMBERS SUBJECT TO FLEXURE AND AXIAL FORCE This section addresses the interaction of flexure and axial stress for shapes not covered in Section H1. It is permitted to use the provisions of this Section for any shape in lieu of the provisions of Section H1. fra frbw frbz + + ≤ 1.0 Fca Fcbw Fcbz

(H2-1)

where fra

= required axial stress at the point of consideration using LRFD or ASD load combinations, ksi (MPa) = available axial stress at the point of consideration, ksi (MPa) Fca frbw, frbz = required flexural stress at the point of consideration using LRFD or ASD load combinations, ksi (MPa) Fcbw ,Fcbz = available flexural stress at the point of consideration, ksi (MPa) w = subscript relating symbol to major principal axis bending z = subscript relating symbol to minor principal axis bending For design according to Section B3.3 (LRFD): fra Fca frbw, frbz Fcbw, Fcbz

φc φt φb

= required axial stress at the point of consideration using LRFD load combinations, ksi (MPa) = φc Fcr = design axial stress, determined in accordance with Chapter E for compression or Section D2 for tension, ksi (MPa) = required flexural stress at the point of consideration using LRFD or ASD load combinations, ksi (MPa) φ M = b n = design flexural stress determined in accordance with S Chapter F, ksi (MPa). Use the section modulus for the specific location in the cross section and consider the sign of the stress. = resistance factor for compression = 0.90 = resistance factor for tension (Section D2) = resistance factor for flexure = 0.90

For design according to Section B3.4 (ASD): fra Fca frbw, frbz Fcbw, Fcbz

Ωc

= required axial stress at the point of consideration using ASD load combinations, ksi (MPa) F = cr = allowable axial stress determined in accordance with Chapter E Ωc for compression, or Section D2 for tension, ksi (MPa) = required flexural stress at the point of consideration using LRFD or ASD load combinations, ksi (MPa) Mn = = allowable flexural stress determined in accordance with ΩbS Chapter F, ksi (MPa). Use the section modulus for the specific location in the cross section and consider the sign of the stress. = safety factor for compression = 1.67 Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. H3.]

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MEMBERS SUBJECT TO TORSION AND COMBINED TORSION

Ωt Ωb

16.1–77

= safety factor for tension (see Section D2) = safety factor for flexure = 1.67

Equation H2-1 shall be evaluated using the principal bending axes by considering the sense of the flexural stresses at the critical points of the cross section. The flexural terms are either added to or subtracted from the axial term as appropriate. When the axial force is compression, second order effects shall be included according to the provisions of Chapter C. A more detailed analysis of the interaction of flexure and tension is permitted in lieu of Equation H2-1.

H3.

MEMBERS SUBJECT TO TORSION AND COMBINED TORSION, FLEXURE, SHEAR AND/OR AXIAL FORCE

1.

Round and Rectangular HSS Subject to Torsion The design torsional strength, φT Tn, and the allowable torsional strength, Tn /ΩT, for round and rectangular HSS according to the limit states of torsional yielding and torsional buckling shall be determined as follows: φT = 0.90 (LRFD)

ΩT = 1.67 (ASD)

Tn = FcrC

(H3-1)

where C is the HSS torsional constant The critical stress, Fcr, shall be determined as follows: (a) For round HSS, Fcr shall be the larger of (i)

Fcr =

1.23E

(H3-2a)

5 D⎞ 4

L⎛ ⎜ ⎟ D⎝ t ⎠ and Fcr =

(ii)

0.60 E 3 D⎞ 2

⎛ ⎜⎝ ⎟⎠ t but shall not exceed 0.6Fy, where L = length of the member, in. (mm) D = outside diameter, in. (mm) (b) For rectangular HSS (i) When h / t ≤ 2.45 E / Fy

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(H3-2b)

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MEMBERS SUBJECT TO TORSION AND COMBINED TORSION

Fcr = 0.6Fy (ii) When 2.45

(H3-3)

E E < h / t ≤ 3.07 Fy Fy Fcr =

(iii) When 3.07

[Sect. H3.

(

0.6 Fy 2.45 E / Fy ⎛ h⎞ ⎜⎝ ⎟⎠ t

)

(H3-4)

E < h / t ≤ 260 Fy Fcr =

0.458 π 2 E ⎛ h⎞ ⎜⎝ ⎟⎠ t

(H3-5)

2

where h = flat width of longer side as defined in Section B4.1b(d), in. (mm) t = design wall thickness defined in Section B4.2, in. (mm) User Note: The torsional constant, C, may be conservatively taken as: π(D − t) t 2 For rectangular HSS: C = 2共B ⫺ t兲共H ⫺ t兲t ⫺ 4.5 共4 ⫺ π兲t3 2

For round HSS: C =

2.

HSS Subject to Combined Torsion, Shear, Flexure and Axial Force When the required torsional strength, Tr, is less than or equal to 20% of the available torsional strength, Tc, the interaction of torsion, shear, flexure and/or axial force for HSS shall be determined by Section H1 and the torsional effects shall be neglected. When Tr exceeds 20% of Tc, the interaction of torsion, shear, flexure and/or axial force shall be limited, at the point of consideration, by 2

⎛ Pr Mr ⎞ ⎛ Vr Tr ⎞ ⎜⎝ P + M ⎟⎠ + ⎜⎝ V + T ⎟⎠ ≤ 1.0 c c c c

(H3-6)

where For design according to Section B3.3 (LRFD): Pr = required axial strength using LRFD load combinations, kips (N) Pc = φPn = design tensile or compressive strength in accordance with Chapter D or E, kips (N) Mr = required flexural strength using LRFD load combinations, kip-in. (N-mm) Mc = φb Mn = design flexural strength in accordance with Chapter F, kip-in. (N-mm) Vr = required shear strength using LRFD load combinations, kips (N) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. H4.]

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RUPTURE OF FLANGES WITH HOLES SUBJECT TO TENSION

16.1–79

Vc = φvVn = design shear strength in accordance with Chapter G, kips (N) Tr = required torsional strength using LRFD load combinations, kip-in. (N-mm) Tc = φT Tn = design torsional strength in accordance with Section H3.1, kip-in. (N-mm) For design according to Section B3.4 (ASD): Pr = required axial strength using ASD load combinations, kips (N) Pc = Pn /Ω = allowable tensile or compressive strength in accordance with Chapter D or E, kips (N) Mr = required flexural strength using ASD load combinations, kip-in. (N-mm) Mc = Mn /Ωb = allowable flexural strength in accordance with Chapter F, kip-in. (N-mm) Vr = required shear strength using ASD load combinations, kips (N) Vc = Vn /Ωv = allowable shear strength in accordance with Chapter G, kips (N) Tr = required torsional strength using ASD load combinations, kip-in. (N-mm) Tc = Tn /ΩT = allowable torsional strength in accordance with Section H3.1, kip-in. (N-mm)

3.

Non-HSS Members Subject to Torsion and Combined Stress The available torsional strength for non-HSS members shall be the lowest value obtained according to the limit states of yielding under normal stress, shear yielding under shear stress, or buckling, determined as follows: φT = 0.90 (LRFD)

ΩT = 1.67 (ASD)

(a) For the limit state of yielding under normal stress Fn = Fy

(H3-7)

(b) For the limit state of shear yielding under shear stress Fn = 0.6Fy

(H3-8)

(c) For the limit state of buckling Fn = Fcr

(H3-9)

where Fcr = buckling stress for the section as determined by analysis, ksi (MPa) Some constrained local yielding is permitted adjacent to areas that remain elastic.

H4.

RUPTURE OF FLANGES WITH HOLES SUBJECT TO TENSION At locations of bolt holes in flanges subject to tension under combined axial force and major axis flexure, flange tensile rupture strength shall be limited by Equation H4-1. Each flange subject to tension due to axial force and flexure shall be checked separately. Pr Mrx + ≤ 1.0 Pc Mcx Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(H4-1)

AISC_PART 16_Spec.2_B:14th Ed.

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RUPTURE OF FLANGES WITH HOLES SUBJECT TO TENSION

[Sect. H4.

where Pr = required axial strength of the member at the location of the bolt holes, positive in tension, negative in compression, kips (N) Pc = available axial strength for the limit state of tensile rupture of the net section at the location of bolt holes, kips (N) Mrx = required flexural strength at the location of the bolt holes; positive for tension in the flange under consideration, negative for compression, kip-in. (N-mm) Mcx = available flexural strength about x-axis for the limit state of tensile rupture of the flange, determined according to Section F13.1. When the limit state of tensile rupture in flexure does not apply, use the plastic bending moment, Mp, determined with bolt holes not taken into consideration, kip-in. (N-mm) For design according to Section B3.3 (LRFD): Pr = required axial strength using LRFD load combinations, kips (N) Pc = φt Pn = design axial strength for the limit state of tensile rupture, determined in accordance with Section D2(b), kips (N) Mrx = required flexural strength using LRFD load combinations, kip-in. (Nmm) Mcx = φbMn = design flexural strength determined in accordance with Section F13.1 or the plastic bending moment, Mp, determined with bolt holes not taken into consideration, as applicable, kip-in. (N-mm) φt = resistance factor for tensile rupture = 0.75 φb = resistance factor for flexure = 0.90 For design according to Section B3.4 (ASD): Pr = required axial strength using ASD load combinations, kips (N) P Pc = n = allowable axial strength for the limit state of tensile rupture, deterΩt mined in accordance with Section D2(b), kips (N) Mrx = required flexural strength using ASD load combinations, kip-in. (N-mm) M Mcx = n = allowable flexural strength determined in accordance with Section Ωb F13.1, or the plastic bending moment, Mp, determined with bolt holes not taken into consideration, as applicable, kip-in. (N-mm) Ωt = safety factor for tensile rupture = 2.00 Ωb = safety factor for flexure = 1.67

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

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CHAPTER I DESIGN OF COMPOSITE MEMBERS

This chapter addresses composite members composed of rolled or built-up structural steel shapes or HSS and structural concrete acting together, and steel beams supporting a reinforced concrete slab so interconnected that the beams and the slab act together to resist bending. Simple and continuous composite beams with steel headed stud anchors, concrete-encased, and concrete filled beams, constructed with or without temporary shores, are included. The chapter is organized as follows: I1. I2. I3. I4. I5. I6. I7. I8. I9.

I1.

General Provisions Axial Force Flexure Shear Combined Axial Force and Flexure Load Transfer Composite Diaphragms and Collector Beams Steel Anchors Special Cases

GENERAL PROVISIONS In determining load effects in members and connections of a structure that includes composite members, consideration shall be given to the effective sections at the time each increment of load is applied.

1.

Concrete and Steel Reinforcement The design, detailing and material properties related to the concrete and reinforcing steel portions of composite construction shall comply with the reinforced concrete and reinforcing bar design specifications stipulated by the applicable building code. Additionally, the provisions in ACI 318 shall apply with the following exceptions and limitations: (1) ACI 318 Sections 7.8.2 and 10.13, and Chapter 21 shall be excluded in their entirety. (2) Concrete and steel reinforcement material limitations shall be as specified in Section I1.3. (3) Transverse reinforcement limitations shall be as specified in Section I2.1a(2), in addition to those specified in ACI 318. (4) The minimum longitudinal reinforcing ratio for encased composite members shall be as specified in Section I2.1a(3). Concrete and steel reinforcement components designed in accordance with ACI 318 shall be based on a level of loading corresponding to LRFD load combinations.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B_14th Ed._February 12, 2013 12/02/13 9:43 AM Page 82

16.1–82

GENERAL PROVISIONS

[Sect. I1.

User Note: It is the intent of the Specification that the concrete and reinforcing steel portions of composite concrete members be detailed utilizing the noncomposite provisions of ACI 318 as modified by the Specification. All requirements specific to composite members are covered in the Specification. Note that the design basis for ACI 318 is strength design. Designers using ASD for steel must be conscious of the different load factors.

2.

Nominal Strength of Composite Sections The nominal strength of composite sections shall be determined in accordance with the plastic stress distribution method or the strain compatibility method as defined in this section. The tensile strength of the concrete shall be neglected in the determination of the nominal strength of composite members. Local buckling effects shall be considered for filled composite members as defined in Section I1.4. Local buckling effects need not be considered for encased composite members.

2a.

Plastic Stress Distribution Method For the plastic stress distribution method, the nominal strength shall be computed assuming that steel components have reached a stress of Fy in either tension or compression and concrete components in compression due to axial force and/or flexure have reached a stress of 0.85f ′c. For round HSS filled with concrete, a stress of 0.95f ′c is permitted to be used for concrete components in compression due to axial force and/or flexure to account for the effects of concrete confinement.

2b.

Strain Compatibility Method For the strain compatibility method, a linear distribution of strains across the section shall be assumed, with the maximum concrete compressive strain equal to 0.003 in./in. (mm/mm). The stress-strain relationships for steel and concrete shall be obtained from tests or from published results for similar materials. User Note: The strain compatibility method should be used to determine nominal strength for irregular sections and for cases where the steel does not exhibit elasto-plastic behavior. General guidelines for the strain compatibility method for encased members subjected to axial load, flexure or both are given in AISC Design Guide 6 and ACI 318.

3.

Material Limitations For concrete, structural steel, and steel reinforcing bars in composite systems, the following limitations shall be met, unless justified by testing or analysis:

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. I1.]

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GENERAL PROVISIONS

16.1–83

(1) For the determination of the available strength, concrete shall have a compressive strength, f ′c, of not less than 3 ksi (21 MPa) nor more than 10 ksi (70 MPa) for normal weight concrete and not less than 3 ksi (21 MPa) nor more than 6 ksi (42 MPa) for lightweight concrete. User Note: Higher strength concrete material properties may be used for stiffness calculations but may not be relied upon for strength calculations unless justified by testing or analysis. (2) The specified minimum yield stress of structural steel and reinforcing bars used in calculating the strength of composite members shall not exceed 75 ksi (525 MPa).

4.

Classification of Filled Composite Sections for Local Buckling For compression, filled composite sections are classified as compact, noncompact or slender. For a section to qualify as compact, the maximum width-to-thickness ratio of its compression steel elements shall not exceed the limiting width-to-thickness ratio, λp, from Table I1.1a. If the maximum width-to-thickness ratio of one or more steel compression elements exceeds λp, but does not exceed λr from Table I1.1a, the filled composite section is noncompact. If the maximum width-to-thickness ratio of any compression steel element exceeds λr, the section is slender. The maximum permitted width-to-thickness ratio shall be as specified in the table. For flexure, filled composite sections are classified as compact, noncompact or slender. For a section to qualify as compact, the maximum width-to-thickness ratio of its compression steel elements shall not exceed the limiting width-to-thickness ratio, λp, from Table I1.1b. If the maximum width-to-thickness ratio of one or more steel compression elements exceeds λp, but does not exceed λr from Table I1.1b, the section is noncompact. If the width-to-thickness ratio of any steel element exceeds λr, the section is slender. The maximum permitted width-to-thickness ratio shall be as specified in the table. Refer to Table B4.1a and Table B4.1b for definitions of width (b and D) and thickness (t) for rectangular and round HSS sections. User Note: All current ASTM A500 Grade B square HSS sections are compact according to the limits of Table I1.1a and Table I1.1b except HSS7×7×1/8, HSS8×8×1/8, HSS9×9×1/8 and HSS12×12× 3/16 which are noncompact for both axial compression and flexure. All current ASTM A500 Grade B round HSS sections are compact according to the limits of Table I1.1a and Table I1.1b for both axial compression and flexure with the exception of HSS16.0×0.25, which is noncompact for flexure.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

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GENERAL PROVISIONS

[Sect. I1.

TABLE I1.1A Limiting Width-to-Thickness Ratios for Compression Steel Elements in Composite Members Subject to Axial Compression For Use with Section I2.2 Width-toThickness Ratio

Description of Element

Walls of Rectangular HSS and Boxes of Uniform Thickness

b/t

Round HSS

D/t

λp Compact/ Noncompact

2.26

E Fy

0.15E Fy

λr Noncompact/ Slender

3.00

E Fy

0.19E Fy

Maximum Permitted

5.00

E Fy

0.31E Fy

TABLE I1.1B Limiting Width-to-Thickness Ratios for Compression Steel Elements in Composite Members Subject to Flexure For Use with Section I3.4 Width-toThickness Ratio

Description of Element

λp Compact/ Noncompact

λr Noncompact/ Slender

Maximum Permitted

Flanges of Rectangular HSS and Boxes of Uniform Thickness

b/t

2.26

E Fy

3.00

E Fy

5.00

E Fy

Webs of Rectangular HSS and Boxes of Uniform Thickness

h/t

3.00

E Fy

5.70

E Fy

5.70

E Fy

Round HSS

D/t

0.09E Fy

0.31E Fy

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

0.31E Fy

AISC_PART 16_Spec.2_B:14th Ed.

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AXIAL FORCE

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AXIAL FORCE This section applies to two types of composite members subject to axial force: encased composite members and filled composite members.

1.

Encased Composite Members

1a.

Limitations For encased composite members, the following limitations shall be met: (1) The cross-sectional area of the steel core shall comprise at least 1% of the total composite cross section. (2) Concrete encasement of the steel core shall be reinforced with continuous longitudinal bars and lateral ties or spirals. Where lateral ties are used, a minimum of either a No. 3 (10 mm) bar spaced at a maximum of 12 in. (305 mm) on center, or a No. 4 (13 mm) bar or larger spaced at a maximum of 16 in. (406 mm) on center shall be used. Deformed wire or welded wire reinforcement of equivalent area are permitted. Maximum spacing of lateral ties shall not exceed 0.5 times the least column dimension. (3) The minimum reinforcement ratio for continuous longitudinal reinforcing, ρsr, shall be 0.004, where ρsr is given by: ρsr =

Asr Ag

(I2-1)

where Ag = gross area of composite member, in.2 (mm2) Asr = area of continuous reinforcing bars, in.2 (mm2) User Note: Refer to Sections 7.10 and 10.9.3 of ACI 318 for additional tie and spiral reinforcing provisions.

1b.

Compressive Strength The design compressive strength, φc Pn, and allowable compressive strength, Pn /Ωc, of doubly symmetric axially loaded encased composite members shall be determined for the limit state of flexural buckling based on member slenderness as follows: φc = 0.75 (LRFD) (a) When

Ωc = 2.00 (ASD)

Pno ≤ 2.25 Pe Pno ⎤ ⎡ Pn = Pno ⎢ 0.658 Pe ⎥ ⎢ ⎥ ⎣ ⎦

(b) When

Pno > 2.25 Pe Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(I2-2)

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

16.1–86

7:59 AM

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AXIAL FORCE

[Sect. I2.

Pn = 0.877Pe

(I2-3)

where (I2-4) Pno = Fy As + Fysr Asr + 0.85 fc′Ac Pe = elastic critical buckling load determined in accordance with Chapter C or Appendix 7, kips (N) (I2-5) = π2(EIeff)/(KL)2 Ac = area of concrete, in.2 (mm2) As = area of the steel section, in.2 (mm2) Ec = modulus of elasticity of concrete EIeff C1

Es Fy Fysr Ic Is Isr K L fc′ wc

)

(

= wc1.5 fc′ , ksi 0.043wc1.5 fc′ , MPa = effective stiffness of composite section, kip-in.2 (N-mm2) = Es Is + 0.5Es Isr + C1Ec Ic = coefficient for calculation of effective rigidity of an encased composite compression member

(I2-6)

⎛ As ⎞ (I2-7) = 0.1 + 2 ⎜ ≤ 0.3 ⎝ Ac + As ⎟⎠ = modulus of elasticity of steel = 29,000 ksi (200 000 MPa) = specified minimum yield stress of steel section, ksi (MPa) = specified minimum yield stress of reinforcing bars, ksi (MPa) = moment of inertia of the concrete section about the elastic neutral axis of the composite section, in.4 (mm4) = moment of inertia of steel shape about the elastic neutral axis of the composite section, in.4 (mm4) = moment of inertia of reinforcing bars about the elastic neutral axis of the composite section, in.4 (mm4) = effective length factor = laterally unbraced length of the member, in. (mm) = specified compressive strength of concrete, ksi (MPa) = weight of concrete per unit volume (90 ≤ wc ≤ 155 lbs/ft3 or 1500 ≤ wc ≤ 2500 kg/m3)

The available compressive strength need not be less than that specified for the bare steel member as required by Chapter E.

1c.

Tensile Strength The available tensile strength of axially loaded encased composite members shall be determined for the limit state of yielding as follows: Pn = Fy As + Fysr Asr φt = 0.90 (LRFD)

1d.

(I2-8)

Ωt = 1.67 (ASD)

Load Transfer Load transfer requirements for encased composite members shall be determined in accordance with Section I6. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

Sect. I2.]

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7:59 AM

Page 87

16.1–87

AXIAL FORCE

Detailing Requirements Clear spacing between the steel core and longitudinal reinforcing shall be a minimum of 1.5 reinforcing bar diameters, but not less than 1.5 in. (38 mm). If the composite cross section is built up from two or more encased steel shapes, the shapes shall be interconnected with lacing, tie plates, batten plates or similar components to prevent buckling of individual shapes due to loads applied prior to hardening of the concrete.

2.

Filled Composite Members

2a.

Limitations For filled composite members, the cross-sectional area of the steel section shall comprise at least 1% of the total composite cross section. Filled composite members shall be classified for local buckling according to Section I1.4.

2b.

Compressive Strength The available compressive strength of axially loaded doubly symmetric filled composite members shall be determined for the limit state of flexural buckling in accordance with Section I2.1b with the following modifications: (a) For compact sections Pno = Pp

(I2-9a)

where

E ⎞ ⎛ Pp = Fy As + C2 fc′ ⎜ Ac + Asr s ⎟ ⎝ Ec ⎠ C2 = 0.85 for rectangular sections and 0.95 for round sections

(I2-9b)

(b) For noncompact sections Pno = Pp −

Pp − Py

( λr − λ p )

2

( λ − λ p )2

where λ, λp and λr are slenderness ratios determined from Table I1.1a Pp is determined from Equation I2-9b E ⎞ ⎛ Py = Fy As + 0.7 fc′ ⎜ Ac + Asr s ⎟ ⎝ Ec ⎠

(I2-9c)

(I2-9d)

(c) For slender sections E ⎞ ⎛ Pno = Fcr As + 0.7 fc′ ⎜ Ac + Asr s ⎟ ⎝ Ec ⎠

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(I2-9e)

AISC_PART 16_Spec.2_B:14th Ed._

2/17/12

16.1–88

11:44 AM

Page 88

AXIAL FORCE

[Sect. I2.

where (i) For rectangular filled sections Fcr =

9 Es ⎛ b⎞ ⎜⎝ ⎟⎠ t

(I2-10)

2

(ii) For round filled sections Fcr =

0.72 Fy ⎛ ⎛ D ⎞ Fy ⎞ ⎜⎝ ⎜⎝ t ⎟⎠ E ⎟⎠ s

(I2-11)

0.2

The effective stiffness of the composite section, EIeff, for all sections shall be: EIeff = Es Is + Es Isr + C3 Ec Ic

(I2-12)

where C3 = coefficient for calculation of effective rigidity of filled composite compression member ⎡ As ⎤ = 0.6 + 2 ⎢ ⎥ ≤ 0.9 ⎣ Ac + As ⎦

(I2-13)

The available compressive strength need not be less than specified for the bare steel member as required by Chapter E.

2c.

Tensile Strength The available tensile strength of axially loaded filled composite members shall be determined for the limit state of yielding as follows: Pn = As Fy + Asr Fysr φt = 0.90 (LRFD)

2d.

(I2-14)

Ωt = 1.67 (ASD)

Load Transfer Load transfer requirements for filled composite members shall be determined in accordance with Section I6.

I3.

FLEXURE This section applies to three types of composite members subject to flexure: composite beams with steel anchors consisting of steel headed stud anchors or steel channel anchors, encased composite members, and filled composite members.

1.

General

1a.

Effective Width The effective width of the concrete slab shall be the sum of the effective widths for each side of the beam centerline, each of which shall not exceed: Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

Sect. I3.]

7:59 AM

Page 89

FLEXURE

16.1–89

(1) one-eighth of the beam span, center-to-center of supports; (2) one-half the distance to the centerline of the adjacent beam; or (3) the distance to the edge of the slab.

1b.

Strength During Construction When temporary shores are not used during construction, the steel section alone shall have adequate strength to support all loads applied prior to the concrete attaining 75% of its specified strength fc′. The available flexural strength of the steel section shall be determined in accordance with Chapter F.

2.

Composite Beams With Steel Headed Stud or Steel Channel Anchors

2a.

Positive Flexural Strength The design positive flexural strength, φb Mn , and allowable positive flexural strength, Mn /Ωb, shall be determined for the limit state of yielding as follows: φb = 0.90 (LRFD)

Ωb = 1.67 (ASD)

(a) When h t w ≤ 3.76 E / Fy Mn shall be determined from the plastic stress distribution on the composite section for the limit state of yielding (plastic moment). User Note: All current ASTM A6 W, S and HP shapes satisfy the limit given in Section I3.2a(a) for Fy ≤ 50 ksi (345 MPa). (b) When h t w > 3.76 E / Fy Mn shall be determined from the superposition of elastic stresses, considering the effects of shoring, for the limit state of yielding (yield moment).

2b.

Negative Flexural Strength The available negative flexural strength shall be determined for the steel section alone, in accordance with the requirements of Chapter F. Alternatively, the available negative flexural strength shall be determined from the plastic stress distribution on the composite section, for the limit state of yielding (plastic moment), with φb = 0.90 (LRFD)

Ωb = 1.67 (ASD)

provided that the following limitations are met: (1) The steel beam is compact and is adequately braced in accordance with Chapter F. (2) Steel headed stud or steel channel anchors connect the slab to the steel beam in the negative moment region. (3) The slab reinforcement parallel to the steel beam, within the effective width of the slab, is properly developed.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–90

2c.

1/20/11

7:59 AM

Page 90

FLEXURE

[Sect. I3.

Composite Beams With Formed Steel Deck (1) General The available flexural strength of composite construction consisting of concrete slabs on formed steel deck connected to steel beams shall be determined by the applicable portions of Sections I3.2a and I3.2b, with the following requirements: (1) The nominal rib height shall not be greater than 3 in. (75 mm). The average width of concrete rib or haunch, wr, shall be not less than 2 in. (50 mm), but shall not be taken in calculations as more than the minimum clear width near the top of the steel deck. (2) The concrete slab shall be connected to the steel beam with welded steel headed stud anchors, 3/4 in. (19 mm) or less in diameter (AWS D1.1/D1.1M). Steel headed stud anchors shall be welded either through the deck or directly to the steel cross section. Steel headed stud anchors, after installation, shall extend not less than 11/2 in. (38 mm) above the top of the steel deck and there shall be at least 1/2 in. (13 mm) of specified concrete cover above the top of the steel headed stud anchors. (3) The slab thickness above the steel deck shall be not less than 2 in. (50 mm). (4) Steel deck shall be anchored to all supporting members at a spacing not to exceed 18 in. (460 mm). Such anchorage shall be provided by steel headed stud anchors, a combination of steel headed stud anchors and arc spot (puddle) welds, or other devices specified by the contract documents. (2) Deck Ribs Oriented Perpendicular to Steel Beam Concrete below the top of the steel deck shall be neglected in determining composite section properties and in calculating Ac for deck ribs oriented perpendicular to the steel beams. (3) Deck Ribs Oriented Parallel to Steel Beam Concrete below the top of the steel deck is permitted to be included in determining composite section properties and shall be included in calculating Ac. Formed steel deck ribs over supporting beams are permitted to be split longitudinally and separated to form a concrete haunch. When the nominal depth of steel deck is 11/2 in. (38 mm) or greater, the average width, wr, of the supported haunch or rib shall be not less than 2 in. (50 mm) for the first steel headed stud anchor in the transverse row plus four stud diameters for each additional steel headed stud anchor.

2d.

Load Transfer Between Steel Beam and Concrete Slab (1) Load Transfer for Positive Flexural Strength The entire horizontal shear at the interface between the steel beam and the concrete slab shall be assumed to be transferred by steel headed stud or steel channel anchors, except for concrete-encased beams as defined in Section I3.3. For composite action with concrete subject to flexural compression, the nominal shear force between the steel beam and the concrete slab transferred by steel anchors, V ′, between the point of maximum positive moment and the point of zero moment shall be determined as the lowest value in accordance with the limit Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

7:59 AM

Sect. I3.]

Page 91

FLEXURE

16.1–91

states of concrete crushing, tensile yielding of the steel section, or the shear strength of the steel anchors: (a) Concrete crushing V′ = 0.85fc′Ac

(I3-1a)

(b) Tensile yielding of the steel section V′ = Fy As

(I3-1b)

(c) Shear strength of steel headed stud or steel channel anchors V′ = ΣQn

(I3-1c)

where Ac = area of concrete slab within effective width, in.2 (mm2) As = area of steel cross section, in.2 (mm2) ΣQn = sum of nominal shear strengths of steel headed stud or steel channel anchors between the point of maximum positive moment and the point of zero moment, kips (N) (2) Load Transfer for Negative Flexural Strength In continuous composite beams where longitudinal reinforcing steel in the negative moment regions is considered to act compositely with the steel beam, the total horizontal shear between the point of maximum negative moment and the point of zero moment shall be determined as the lower value in accordance with the following limit states: (a) For the limit state of tensile yielding of the slab reinforcement V′ = Fysr Asr

(I3-2a)

where Asr = area of adequately developed longitudinal reinforcing steel within the effective width of the concrete slab, in.2 (mm2) Fysr = specified minimum yield stress of the reinforcing steel, ksi (MPa) (b) For the limit state of shear strength of steel headed stud or steel channel anchors V′ = ΣQn

3.

(I3-2b)

Encased Composite Members The available flexural strength of concrete-encased members shall be determined as follows: φb = 0.90 (LRFD)

Ωb = 1.67 (ASD)

The nominal flexural strength, Mn, shall be determined using one of the following methods: (a) The superposition of elastic stresses on the composite section, considering the effects of shoring for the limit state of yielding (yield moment). Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

16.1–92

7:59 AM

Page 92

FLEXURE

[Sect. I3.

(b) The plastic stress distribution on the steel section alone, for the limit state of yielding (plastic moment) on the steel section. (c) The plastic stress distribution on the composite section or the strain-compatibility method, for the limit state of yielding (plastic moment) on the composite section. For concrete-encased members, steel anchors shall be provided.

4.

Filled Composite Members

4a.

Limitations Filled composite sections shall be classified for local buckling according to Section I1.4.

4b.

Flexural Strength The available flexural strength of filled composite members shall be determined as follows: φb = 0.90 (LRFD)

Ωb = 1.67 (ASD)

The nominal flexural strength, Mn, shall be determined as follows: (a) For compact sections Mn = Mp

(I3-3a)

where Mp = moment corresponding to plastic stress distribution over the composite cross section, kip-in. (N-mm) (b) For noncompact sections ⎛ λ − λp ⎞ Mn = Mp − ( Mp − My ) ⎜ ⎝ λr − λ p ⎟⎠

(I3-3b)

where λ, λp and λr are slenderness ratios determined from Table I1.1b. My = yield moment corresponding to yielding of the tension flange and first yield of the compression flange, kip-in. (N-mm). The capacity at first yield shall be calculated assuming a linear elastic stress distribution with the maximum concrete compressive stress limited to 0.7fc′ and the maximum steel stress limited to Fy. (c) For slender sections, Mn, shall be determined as the first yield moment. The compression flange stress shall be limited to the local buckling stress, Fcr , determined using Equation I2-10 or I2-11. The concrete stress distribution shall be linear elastic with the maximum compressive stress limited to 0.70f ′c.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

Sect. I6.]

7:59 AM

Page 93

LOAD TRANSFER

I4.

SHEAR

1.

Filled and Encased Composite Members

16.1–93

The design shear strength, φv Vn, and allowable shear strength, Vn /Ωv, shall be determined based on one of the following: (a) The available shear strength of the steel section alone as specified in Chapter G (b) The available shear strength of the reinforced concrete portion (concrete plus steel reinforcement) alone as defined by ACI 318 with φv = 0.75 (LRFD)

Ω v = 2.00 (ASD)

(c) The nominal shear strength of the steel section as defined in Chapter G plus the nominal strength of the reinforcing steel as defined by ACI 318 with a combined resistance or safety factor of φv = 0.75 (LRFD)

2.

Ω v = 2.00 (ASD)

Composite Beams With Formed Steel Deck The available shear strength of composite beams with steel headed stud or steel channel anchors shall be determined based upon the properties of the steel section alone in accordance with Chapter G.

I5.

COMBINED FLEXURE AND AXIAL FORCE The interaction between flexure and axial forces in composite members shall account for stability as required by Chapter C. The available compressive strength and the available flexural strength shall be determined as defined in Sections I2 and I3, respectively. To account for the influence of length effects on the axial strength of the member, the nominal axial strength of the member shall be determined in accordance with Section I2. For encased composite members and for filled composite members with compact sections, the interaction between axial force and flexure shall be based on the interaction equations of Section H1.1 or one of the methods as defined in Section I1.2. For filled composite members with noncompact or slender sections, the interaction between axial forces and flexure shall be based on the interaction equations of Section H1.1. User Note: Methods for determining the capacity of composite beam-columns are discussed in the Commentary.

I6.

LOAD TRANSFER

1.

General Requirements When external forces are applied to an axially loaded encased or filled composite member, the introduction of force to the member and the transfer of longitudinal

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–94

1/20/11

7:59 AM

Page 94

LOAD TRANSFER

[Sect. I6.

shears within the member shall be assessed in accordance with the requirements for force allocation presented in this section. The design strength, φRn, or the allowable strength, Rn /Ω, of the applicable force transfer mechanisms as determined in accordance with Section I6.3 shall equal or exceed the required longitudinal shear force to be transferred, Vr′, as determined in accordance with Section I6.2.

2.

Force Allocation Force allocation shall be determined based upon the distribution of external force in accordance with the following requirements: User Note: Bearing strength provisions for externally applied forces are provided in Section J8. For filled composite members, the term

A2 A1 in Equation J8-2

may be taken equal to 2.0 due to confinement effects.

2a.

External Force Applied to Steel Section When the entire external force is applied directly to the steel section, the force required to be transferred to the concrete, Vr′, shall be determined as follows: Vr′ = Pr (1 ⫺ Fy As /Pno)

(I6-1)

where Pno = nominal axial compressive strength without consideration of length effects, determined by Equation I2-4 for encased composite members, and Equation I2-9a for filled composite members, kips (N) Pr = required external force applied to the composite member, kips (N)

2b.

External Force Applied to Concrete When the entire external force is applied directly to the concrete encasement or concrete fill, the force required to be transferred to the steel, Vr′, shall be determined as follows: Vr′ = Pr (Fy As /Pno)

(I6-2)

where Pno = nominal axial compressive strength without consideration of length effects, determined by Equation I2-4 for encased composite members, and Equation I2-9a for filled composite members, kips (N) Pr = required external force applied to the composite member, kips (N)

2c.

External Force Applied Concurrently to Steel and Concrete When the external force is applied concurrently to the steel section and concrete encasement or concrete fill, Vr′ shall be determined as the force required to establish equilibrium of the cross section.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

Sect. I6.]

7:59 AM

Page 95

LOAD TRANSFER

16.1–95

User Note: The Commentary provides an acceptable method of determining the longitudinal shear force required for equilibrium of the cross section.

3.

Force Transfer Mechanisms The nominal strength, Rn, of the force transfer mechanisms of direct bond interaction, shear connection, and direct bearing shall be determined in accordance with this section. Use of the force transfer mechanism providing the largest nominal strength is permitted. Force transfer mechanisms shall not be superimposed. The force transfer mechanism of direct bond interaction shall not be used for encased composite members.

3a.

Direct Bearing Where force is transferred in an encased or filled composite member by direct bearing from internal bearing mechanisms, the available bearing strength of the concrete for the limit state of concrete crushing shall be determined as follows: Rn = 1.7fc′A1 φB = 0.65 (LRFD)

(I6-3)

ΩB = 2.31 (ASD)

where A1 = loaded area of concrete, in.2 (mm2) User Note: An example of force transfer via an internal bearing mechanism is the use of internal steel plates within a filled composite member.

3b.

Shear Connection Where force is transferred in an encased or filled composite member by shear connection, the available shear strength of steel headed stud or steel channel anchors shall be determined as follows: Rc = ΣQcv

(I6-4)

where ΣQcv = sum of available shear strengths, φQnv or Qnv /Ω as appropriate, of steel headed stud or steel channel anchors, determined in accordance with Section I8.3a or Section I8.3d, respectively, placed within the load introduction length as defined in Section I6.4, kips (N)

3c.

Direct Bond Interaction Where force is transferred in a filled composite member by direct bond interaction, the available bond strength between the steel and concrete shall be determined as follows: φ = 0.45 (LRFD)

Ω = 3.33 (ASD)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

16.1–96

7:59 AM

Page 96

LOAD TRANSFER

[Sect. I6.

(a) For rectangular steel sections filled with concrete: Rn = B2 Cin Fin

(I6-5)

(b) For round steel sections filled with concrete: Rn = 0.25πD2 Cin Fin

(I6-6)

where Cin = 2 if the filled composite member extends to one side of the point of force transfer = 4 if the filled composite member extends on both sides of the point of force transfer Rn = nominal bond strength, kips (N) Fin = nominal bond stress= 0.06 ksi (0.40 MPa) B = overall width of rectangular steel section along face transferring load, in. (mm) D = outside diameter of round HSS, in. (mm)

4.

Detailing Requirements

4a.

Encased Composite Members Steel anchors utilized to transfer longitudinal shear shall be distributed within the load introduction length, which shall not exceed a distance of two times the minimum transverse dimension of the encased composite member above and below the load transfer region. Anchors utilized to transfer longitudinal shear shall be placed on at least two faces of the steel shape in a generally symmetric configuration about the steel shape axes. Steel anchor spacing, both within and outside of the load introduction length, shall conform to Section I8.3e.

4b.

Filled Composite Members Where required, steel anchors transferring the required longitudinal shear force shall be distributed within the load introduction length, which shall not exceed a distance of two times the minimum transverse dimension of a rectangular steel member or two times the diameter of a round steel member both above and below the load transfer region. Steel anchor spacing within the load introduction length shall conform to Section I8.3e.

I7.

COMPOSITE DIAPHRAGMS AND COLLECTOR BEAMS Composite slab diaphragms and collector beams shall be designed and detailed to transfer loads between the diaphragm, the diaphragm’s boundary members and collector elements, and elements of the lateral force resisting system. User Note: Design guidelines for composite diaphragms and collector beams can be found in the Commentary.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

Sect. I8.]

7:59 AM

Page 97

16.1–97

STEEL ANCHORS

I8.

STEEL ANCHORS

1.

General The diameter of a steel headed stud anchor shall not be greater than 2.5 times the thickness of the base metal to which it is welded, unless it is welded to a flange directly over a web. Section I8.2 applies to a composite flexural member where steel anchors are embedded in a solid concrete slab or in a slab cast on formed steel deck. Section I8.3 applies to all other cases.

2.

Steel Anchors in Composite Beams The length of steel headed stud anchors shall not be less than four stud diameters from the base of the steel headed stud anchor to the top of the stud head after installation.

2a.

Strength of Steel Headed Stud Anchors The nominal shear strength of one steel headed stud anchor embedded in a solid concrete slab or in a composite slab with decking shall be determined as follows: Qn = 0.5 Asa fc′ Ec ≤ Rg R p Asa Fu where Asa Ec

= cross-sectional area of steel headed stud anchor, in.2 (mm2) = modulus of elasticity of concrete

(

= wc1.5 fc′ , ksi 0.043wc1.5 fc′ , MPa Fu Rg

(I8-1)

)

= specified minimum tensile strength of a steel headed stud anchor, ksi (MPa) = 1.0 for: (a) one steel headed stud anchor welded in a steel deck rib with the deck oriented perpendicular to the steel shape; (b) any number of steel headed stud anchors welded in a row directly to the steel shape; (c) any number of steel headed stud anchors welded in a row through steel deck with the deck oriented parallel to the steel shape and the ratio of the average rib width to rib depth ≥ 1.5 = 0.85 for: (a) two steel headed stud anchors welded in a steel deck rib with the deck oriented perpendicular to the steel shape; (b) one steel headed stud anchor welded through steel deck with the deck oriented parallel to the steel shape and the ratio of the average rib width to rib depth < 1.5 = 0.7 for three or more steel headed stud anchors welded in a steel deck rib with the deck oriented perpendicular to the steel shape

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–98

1/20/11

7:59 AM

Page 98

STEEL ANCHORS

[Sect. I8.

= 0.75 for: (a) steel headed stud anchors welded directly to the steel shape; (b) steel headed stud anchors welded in a composite slab with the deck oriented perpendicular to the beam and emid-ht ≥ 2 in. (50 mm); (c) steel headed stud anchors welded through steel deck, or steel sheet used as girder filler material, and embedded in a composite slab with the deck oriented parallel to the beam = 0.6 for steel headed stud anchors welded in a composite slab with deck oriented perpendicular to the beam and emid-ht < 2 in. (50 mm) emid-ht = distance from the edge of steel headed stud anchor shank to the steel deck web, measured at mid-height of the deck rib, and in the load bearing direction of the steel headed stud anchor (in other words, in the direction of maximum moment for a simply supported beam), in. (mm)

Rp

User Note: The table below presents values for Rg and Rp for several cases. Capacities for steel headed stud anchors can be found in the Manual. Condition

Rg

Rp

No decking

1.0

0.75

Decking oriented parallel to the steel shape wr ≥ 1.5 hr wr < 1.5 hr

1.0

0.75

0.85**

0.75

1.0 0.85 0.7

0.6+ 0.6+ 0.6+

Decking oriented perpendicular to the steel shape Number of steel headed stud anchors occupying the same decking rib 1 2 3 or more

hr = nominal rib height, in. (mm) wr = average width of concrete rib or haunch (as defined in Section I3.2c), in. (mm) ** for a single steel headed stud anchor + this value may be increased to 0.75 when emid-ht ≥ 2 in. (51 mm)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

Sect. I8.]

2b.

7:59 AM

Page 99

STEEL ANCHORS

16.1–99

Strength of Steel Channel Anchors The nominal shear strength of one hot-rolled channel anchor embedded in a solid concrete slab shall be determined as follows: Qn = 0.3(t f + 0.5 t w )la fc′Ec

(I8-2)

where la = length of channel anchor, in. (mm) tf = thickness of flange of channel anchor, in. (mm) tw = thickness of channel anchor web, in. (mm) The strength of the channel anchor shall be developed by welding the channel to the beam flange for a force equal to Qn, considering eccentricity on the anchor.

2c.

Required Number of Steel Anchors The number of anchors required between the section of maximum bending moment, positive or negative, and the adjacent section of zero moment shall be equal to the horizontal shear as determined in Sections I3.2d(1) and I3.2d(2) divided by the nominal shear strength of one steel anchor as determined from Section I8.2a or Section I8.2b. The number of steel anchors required between any concentrated load and the nearest point of zero moment shall be sufficient to develop the maximum moment required at the concentrated load point.

2d.

Detailing Requirements Steel anchors required on each side of the point of maximum bending moment, positive or negative, shall be distributed uniformly between that point and the adjacent points of zero moment, unless specified otherwise on the contract documents. Steel anchors shall have at least 1 in. (25 mm) of lateral concrete cover in the direction perpendicular to the shear force, except for anchors installed in the ribs of formed steel decks. The minimum distance from the center of an anchor to a free edge in the direction of the shear force shall be 8 in. (203 mm) if normal weight concrete is used and 10 in. (250 mm) if lightweight concrete is used. The provisions of ACI 318, Appendix D are permitted to be used in lieu of these values. The minimum center-to-center spacing of steel headed stud anchors shall be six diameters along the longitudinal axis of the supporting composite beam and four diameters transverse to the longitudinal axis of the supporting composite beam, except that within the ribs of formed steel decks oriented perpendicular to the steel beam the minimum center-to-center spacing shall be four diameters in any direction. The maximum center-to-center spacing of steel anchors shall not exceed eight times the total slab thickness or 36 in. (900 mm).

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–100

3.

1/20/11

7:59 AM

Page 100

STEEL ANCHORS

[Sect. I8.

Steel Anchors in Composite Components This section shall apply to the design of cast-in-place steel headed stud anchors and steel channel anchors in composite components. The provisions of the applicable building code or ACI 318, Appendix D may be used in lieu of the provisions in this section. User Note: The steel headed stud anchor strength provisions in this section are applicable to anchors located primarily in the load transfer (connection) region of composite columns and beam-columns, concrete-encased and filled composite beams, composite coupling beams, and composite walls, where the steel and concrete are working compositely within a member. They are not intended for hybrid construction where the steel and concrete are not working compositely, such as with embed plates. Section I8.2 specifies the strength of steel anchors embedded in a solid concrete slab or in a concrete slab with formed steel deck in a composite beam. Limit states for the steel shank of the anchor and for concrete breakout in shear are covered directly in this Section. Additionally, the spacing and dimensional limitations provided in these provisions preclude the limit states of concrete pryout for anchors loaded in shear and concrete breakout for anchors loaded in tension as defined by ACI 318, Appendix D. For normal weight concrete: Steel headed stud anchors subjected to shear only shall not be less than five stud diameters in length from the base of the steel headed stud to the top of the stud head after installation. Steel headed stud anchors subjected to tension or interaction of shear and tension shall not be less than eight stud diameters in length from the base of the stud to the top of the stud head after installation. For lightweight concrete: Steel headed stud anchors subjected to shear only shall not be less than seven stud diameters in length from the base of the steel headed stud to the top of the stud head after installation. Steel headed stud anchors subjected to tension shall not be less than ten stud diameters in length from the base of the stud to the top of the stud head after installation. The nominal strength of steel headed stud anchors subjected to interaction of shear and tension for lightweight concrete shall be determined as stipulated by the applicable building code or ACI 318 Appendix D. Steel headed stud anchors subjected to tension or interaction of shear and tension shall have a diameter of the head greater than or equal to 1.6 times the diameter of the shank.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. I8.]

1/20/11

7:59 AM

Page 101

16.1–101

STEEL ANCHORS

User Note: The following table presents values of minimum steel headed stud anchor h/d ratios for each condition covered in the Specification: Loading Condition

Normal Weight Concrete

Lightweight Concrete

Shear

h/d ≥ 5

h/d ≥ 7

Tension

h/d ≥ 8

h/d ≥ 10

Shear and Tension

h/d ≥ 8

N/A∗

h/d = ratio of steel headed stud anchor shank length to the top of the stud head, to shank diameter ∗ Refer to ACI 318, Appendix D for the calculation of interaction effects of anchors embedded in lightweight concrete.

3a.

Shear Strength of Steel Headed Stud Anchors in Composite Components Where concrete breakout strength in shear is not an applicable limit state, the design shear strength, φv Qnv , and allowable shear strength, Qnv /Ωv, of one steel headed stud anchor shall be determined as follows: Qnv = Fu Asa φv = 0.65 (LRFD)

(I8-3)

Ωv = 2.31 (ASD)

where Qnv = nominal shear strength of steel headed stud anchor, kips (N) Asa = cross-sectional area of steel headed stud anchor, in.2 (mm2) Fu = specified minimum tensile strength of a steel headed stud anchor, ksi (MPa) Where concrete breakout strength in shear is an applicable limit state, the available shear strength of one steel headed stud anchor shall be determined by one of the following: (1) Where anchor reinforcement is developed in accordance with Chapter 12 of ACI 318 on both sides of the concrete breakout surface for the steel headed stud anchor, the minimum of the steel nominal shear strength from Equation I8-3 and the nominal strength of the anchor reinforcement shall be used for the nominal shear strength, Qnv, of the steel headed stud anchor. (2) As stipulated by the applicable building code or ACI 318, Appendix D.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–102

1/20/11

7:59 AM

Page 102

STEEL ANCHORS

[Sect. I8.

User Note: If concrete breakout strength in shear is an applicable limit state (for example, where the breakout prism is not restrained by an adjacent steel plate, flange or web), appropriate anchor reinforcement is required for the provisions of this Section to be used. Alternatively, the provisions of the applicable building code or ACI 318, Appendix D may be used.

3b.

Tensile Strength of Steel Headed Stud Anchors in Composite Components Where the distance from the center of an anchor to a free edge of concrete in the direction perpendicular to the height of the steel headed stud anchor is greater than or equal to 1.5 times the height of the steel headed stud anchor measured to the top of the stud head, and where the center-to-center spacing of steel headed stud anchors is greater than or equal to three times the height of the steel headed stud anchor measured to the top of the stud head, the available tensile strength of one steel headed stud anchor shall be determined as follows: Qnt = Fu Asa φt = 0.75 (LRFD)

(I8-4)

Ωt = 2.00 (ASD)

where Qnt = nominal tensile strength of steel headed stud anchor, kips (N) Where the distance from the center of an anchor to a free edge of concrete in the direction perpendicular to the height of the steel headed stud anchor is less than 1.5 times the height of the steel headed stud anchor measured to the top of the stud head, or where the center-to-center spacing of steel headed stud anchors is less than three times the height of the steel headed stud anchor measured to the top of the stud head, the nominal tensile strength of one steel headed stud anchor shall be determined by one of the following: (a) Where anchor reinforcement is developed in accordance with Chapter 12 of ACI 318 on both sides of the concrete breakout surface for the steel headed stud anchor, the minimum of the steel nominal tensile strength from Equation I8-4 and the nominal strength of the anchor reinforcement shall be used for the nominal tensile strength, Qnt, of the steel headed stud anchor. (b) As stipulated by the applicable building code or ACI 318, Appendix D. User Note: Supplemental confining reinforcement is recommended around the anchors for steel headed stud anchors subjected to tension or interaction of shear and tension to avoid edge effects or effects from closely spaced anchors. See the Commentary and ACI 318, Section D5.2.9 for guidelines.

3c.

Strength of Steel Headed Stud Anchors for Interaction of Shear and Tension in Composite Components Where concrete breakout strength in shear is not a governing limit state, and where the distance from the center of an anchor to a free edge of concrete in the direction Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. I8.]

1/20/11

7:59 AM

Page 103

STEEL ANCHORS

16.1–103

perpendicular to the height of the steel headed stud anchor is greater than or equal to 1.5 times the height of the steel headed stud anchor measured to the top of the stud head, and where the center-to-center spacing of steel headed stud anchors is greater than or equal to three times the height of the steel headed stud anchor measured to the top of the stud head, the nominal strength for interaction of shear and tension of one steel headed stud anchor shall be determined as follows: ⎡⎛ Qrt ⎞ 5 / 3 ⎛ Qrv ⎞ 5 / 3 ⎤ ⎢⎜ ⎟ + ⎜⎝ Q ⎟⎠ ⎥ ≤ 1.0 cv ⎥⎦ ⎢⎣⎝ Qct ⎠

(I8-5)

where Qct = available tensile strength, kips (N) Qrt = required tensile strength, kips (N) Qcv = available shear strength, kips (N) Qrv = required shear strength, kips (N) For design in accordance with Section B3.3 (LRFD): Qrt = required tensile strength using LRFD load combinations, kips (N) Qct = φt Qnt = design tensile strength, determined in accordance with Section I8.3b, kips (N) Qrv = required shear strength using LRFD load combinations, kips (N) Qcv = φvQnv = design shear strength, determined in accordance with Section I8.3a, kips (N) φt = resistance factor for tension = 0.75 φv = resistance factor for shear = 0.65 For design in accordance with Section B3.4 (ASD): Qrt = required tensile strength using ASD load combinations, kips (N) Q Qct = nt = allowable tensile strength, determined in accordance with Section Ωt I8.3b, kips (N) Qrv = required shear strength using ASD load combinations, kips (N) Q Qcv = nv = allowable shear strength, determined in accordance with Section Ωv I8.3a, kips (N) Ωt = safety factor for tension = 2.00 Ωv = safety factor for shear = 2.31 Where concrete breakout strength in shear is a governing limit state, or where the distance from the center of an anchor to a free edge of concrete in the direction perpendicular to the height of the steel headed stud anchor is less than 1.5 times the height of the steel headed stud anchor measured to the top of the stud head, or where the center-to-center spacing of steel headed stud anchors is less than three times the height of the steel headed stud anchor measured to the top of the stud head, the nominal strength for interaction of shear and tension of one steel headed stud anchor shall be determined by one of the following: (a) Where anchor reinforcement is developed in accordance with Chapter 12 of ACI 318 on both sides of the concrete breakout surface for the steel headed stud Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–104

1/20/11

7:59 AM

Page 104

STEEL ANCHORS

[Sect. I8.

anchor, the minimum of the steel nominal shear strength from Equation I8-3 and the nominal strength of the anchor reinforcement shall be used for the nominal shear strength, Qnv, of the steel headed stud anchor, and the minimum of the steel nominal tensile strength from Equation I8-4 and the nominal strength of the anchor reinforcement shall be used for the nominal tensile strength, Qnt, of the steel headed stud anchor for use in Equation I8-5. (b) As stipulated by the applicable building code or ACI 318, Appendix D.

3d.

Shear Strength of Steel Channel Anchors in Composite Components The available shear strength of steel channel anchors shall be based on the provisions of Section I8.2b with the resistance factor and safety factor as specified below. φv = 0.75 (LRFD)

3e.

Ωv = 2.00 (ASD)

Detailing Requirements in Composite Components Steel anchors shall have at least 1 in. (25 mm) of lateral clear concrete cover. The minimum center-to-center spacing of steel headed stud anchors shall be four diameters in any direction. The maximum center-to-center spacing of steel headed stud anchors shall not exceed 32 times the shank diameter. The maximum center-to-center spacing of steel channel anchors shall be 24 in. (600 mm). User Note: Detailing requirements provided in this section are absolute limits. See Sections I8.3a, I8.3b and I8.3c for additional limitations required to preclude edge and group effect considerations.

I9.

SPECIAL CASES When composite construction does not conform to the requirements of Section I1 through Section I8, the strength of steel anchors and details of construction shall be established by testing.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

7:59 AM

Page 105

16.1–105

CHAPTER J DESIGN OF CONNECTIONS

This chapter addresses connecting elements, connectors and the affected elements of connected members not subject to fatigue loads. The chapter is organized as follows: J1. J2. J3. J4. J5. J6. J7. J8. J9. J10.

General Provisions Welds Bolts and Threaded Parts Affected Elements of Members and Connecting Elements Fillers Splices Bearing Strength Column Bases and Bearing on Concrete Anchor Rods and Embedments Flanges and Webs with Concentrated Forces

User Note: For cases not included in this chapter, the following sections apply: • Chapter K Design of HSS and Box Member Connections • Appendix 3 Design for Fatigue

J1.

GENERAL PROVISIONS

1.

Design Basis The design strength, φRn, and the allowable strength Rn /Ω, of connections shall be determined in accordance with the provisions of this chapter and the provisions of Chapter B. The required strength of the connections shall be determined by structural analysis for the specified design loads, consistent with the type of construction specified, or shall be a proportion of the required strength of the connected members when so specified herein. Where the gravity axes of intersecting axially loaded members do not intersect at one point, the effects of eccentricity shall be considered.

2.

Simple Connections Simple connections of beams, girders and trusses shall be designed as flexible and are permitted to be proportioned for the reaction shears only, except as otherwise indicated in the design documents. Flexible beam connections shall accommodate end rotations of simple beams. Some inelastic but self-limiting deformation in the connection is permitted to accommodate the end rotation of a simple beam. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B_14th Ed._February 12, 2013 12/02/13 9:44 AM Page 106

16.1–106

3.

GENERAL PROVISIONS

[Sect. J1.

Moment Connections End connections of restrained beams, girders and trusses shall be designed for the combined effect of forces resulting from moment and shear induced by the rigidity of the connections. Response criteria for moment connections are provided in Section B3.6b. User Note: See Chapter C and Appendix 7 for analysis requirements to establish the required strength for the design of connections.

4.

Compression Members With Bearing Joints Compression members relying on bearing for load transfer shall meet the following requirements: (1) When columns bear on bearing plates or are finished to bear at splices, there shall be sufficient connectors to hold all parts securely in place. (2) When compression members other than columns are finished to bear, the splice material and its connectors shall be arranged to hold all parts in line and their required strength shall be the lesser of: (i) An axial tensile force of 50% of the required compressive strength of the member; or (ii) The moment and shear resulting from a transverse load equal to 2% of the required compressive strength of the member. The transverse load shall be applied at the location of the splice exclusive of other loads that act on the member. The member shall be taken as pinned for the determination of the shears and moments at the splice. User Note: All compression joints should also be proportioned to resist any tension developed by the load combinations stipulated in Section B2.

5.

Splices in Heavy Sections When tensile forces due to applied tension or flexure are to be transmitted through splices in heavy sections, as defined in Sections A3.1c and A3.1d, by complete-jointpenetration groove (CJP) welds, the following provisions apply: (1) material notch-toughness requirements as given in Sections A3.1c and A3.1d; (2) weld access hole details as given in Section J1.6; (3) filler metal requirements as given in Section J2.6; and (4) thermal cut surface preparation and inspection requirements as given in Section M2.2. The foregoing provision is not applicable to splices of elements of built-up shapes that are welded prior to assembling the shape. User Note: CJP groove welded splices of heavy sections can exhibit detrimental effects of weld shrinkage. Members that are sized for compression that are also subject to tensile forces may be less susceptible to damage from shrinkage if they are spliced using partial-joint-penetration PJP groove welds on the flanges and fillet-welded web plates, or using bolts for some or all of the splice.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. J1.]

6.

1/20/11

7:59 AM

Page 107

GENERAL PROVISIONS

16.1–107

Weld Access Holes All weld access holes required to facilitate welding operations shall be detailed to provide room for weld backing as needed. The access hole shall have a length from the toe of the weld preparation not less than 11/2 times the thickness of the material in which the hole is made, nor less than 11/2 in. (38 mm). The access hole shall have a height not less than the thickness of the material with the access hole, nor less than 3 /4 in. (19 mm), nor does it need to exceed 2 in. (50 mm). For sections that are rolled or welded prior to cutting, the edge of the web shall be sloped or curved from the surface of the flange to the reentrant surface of the access hole. In hot-rolled shapes, and built-up shapes with CJP groove welds that join the web-to-flange, weld access holes shall be free of notches and sharp reentrant corners. No arc of the weld access hole shall have a radius less than 3/8 in. (10 mm). In built-up shapes with fillet or partial-joint-penetration groove welds that join the web-to-flange, weld access holes shall be free of notches and sharp reentrant corners. The access hole shall be permitted to terminate perpendicular to the flange, providing the weld is terminated at least a distance equal to the weld size away from the access hole. For heavy sections as defined in Sections A3.1c and A3.1d, the thermally cut surfaces of weld access holes shall be ground to bright metal and inspected by either magnetic particle or dye penetrant methods prior to deposition of splice welds. If the curved transition portion of weld access holes is formed by predrilled or sawed holes, that portion of the access hole need not be ground. Weld access holes in other shapes need not be ground nor inspected by dye penetrant or magnetic particle methods.

7.

Placement of Welds and Bolts Groups of welds or bolts at the ends of any member which transmit axial force into that member shall be sized so that the center of gravity of the group coincides with the center of gravity of the member, unless provision is made for the eccentricity. The foregoing provision is not applicable to end connections of single angle, double angle and similar members.

8.

Bolts in Combination With Welds Bolts shall not be considered as sharing the load in combination with welds, except that shear connections with any grade of bolts permitted by Section A3.3, installed in standard holes or short slots transverse to the direction of the load, are permitted to be considered to share the load with longitudinally loaded fillet welds. In such connections the available strength of the bolts shall not be taken as greater than 50% of the available strength of bearing-type bolts in the connection. In making welded alterations to structures, existing rivets and high-strength bolts tightened to the requirements for slip-critical connections are permitted to be utilized for carrying loads present at the time of alteration and the welding need only provide the additional required strength.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed._

16.1–108

9.

2/17/12

11:45 AM

Page 108

GENERAL PROVISIONS

[Sect. J1.

High-Strength Bolts in Combination With Rivets In both new work and alterations, in connections designed as slip-critical connections in accordance with the provisions of Section J3, high-strength bolts are permitted to be considered as sharing the load with existing rivets.

10.

Limitations on Bolted and Welded Connections Joints with pretensioned bolts or welds shall be used for the following connections: (1) Column splices in all multi-story structures over 125 ft (38 m) in height (2) Connections of all beams and girders to columns and any other beams and girders on which the bracing of columns is dependent in structures over 125 ft (38 m) in height (3) In all structures carrying cranes of over 5 ton (50 kN) capacity: roof truss splices and connections of trusses to columns; column splices; column bracing; knee braces; and crane supports (4) Connections for the support of machinery and other live loads that produce impact or reversal of load Snug-tightened joints or joints with ASTM A307 bolts shall be permitted except where otherwise specified.

J2.

WELDS All provisions of AWS D1.1/D1.1M apply under this Specification, with the exception that the provisions of the listed AISC Specification Sections apply under this Specification in lieu of the cited AWS provisions as follows: (1) (2) (3) (4) (5) (6) (7)

Section J1.6 in lieu of AWS D1.1/D1.1M, Section 5.17.1 Section J2.2a in lieu of AWS D1.1/D1.1M, Section 2.4.2.10 Table J2.2 in lieu of AWS D1.1/D1.1M, Table 2.1 Table J2.5 in lieu of AWS D1.1/D1.1M, Table 2.3 Appendix 3, Table A-3.1 in lieu of AWS D1.1/D1.1M, Table 2.5 Section B3.11 and Appendix 3 in lieu of AWS D1.1/D1.1M, Section 2, Part C Section M2.2 in lieu of AWS D1.1/D1.1M, Sections 5.15.4.3 and 5.15.4.4

1.

Groove Welds

1a.

Effective Area The effective area of groove welds shall be considered as the length of the weld times the effective throat. The effective throat of a complete-joint-penetration (CJP) groove weld shall be the thickness of the thinner part joined. The effective throat of a partial-joint-penetration (PJP) groove weld shall be as shown in Table J2.1.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. J2.]

1/20/11

7:59 AM

Page 109

16.1–109

WELDS

TABLE J2.1 Effective Throat of Partial-Joint-Penetration Groove Welds Welding Position F (flat), H (horizontal), V (vertical), OH (overhead)

Welding Process Shielded metal arc (SMAW) Gas metal arc (GMAW) Flux cored arc (FCAW)

Groove Type (AWS D1.1/D1.1M, Figure 3.3)

Effective Throat

J or U groove All 60° V

depth of groove

J or U groove Submerged arc (SAW)

F 60° bevel or V

Gas metal arc (GMAW) Flux cored arc (FCAW)

F, H

Shielded metal arc (SMAW) Gas metal arc (GMAW) Flux cored arc (FCAW)

45° bevel

All 45° bevel V, OH

depth of groove

depth of groove minus 1/8 in. (3 mm)

User Note: The effective throat of a partial-joint-penetration groove weld is dependent on the process used and the weld position. The design drawings should either indicate the effective throat required or the weld strength required, and the fabricator should detail the joint based on the weld process and position to be used to weld the joint. The effective weld throat for flare groove welds when filled flush to the surface of a round bar or a 90° bend in a formed section or rectangular HSS, shall be as shown in Table J2.2, unless other effective throats are demonstrated by tests. The effective throat of flare groove welds filled less than flush shall be as shown in Table J2.2, less the greatest perpendicular dimension measured from a line flush to the base metal surface to the weld surface. Larger effective throats than those in Table J2.2 are permitted for a given welding procedure specification (WPS), provided the fabricator can establish by qualification the consistent production of such larger effective throat. Qualification shall consist of sectioning the weld normal to its axis, at mid-length and terminal ends. Such sectioning shall be made on a number of combinations of material sizes representative of the range to be used in the fabrication.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed._

2/17/12

16.1–110

11:47 AM

Page 110

WELDS

[Sect. J2.

TABLE J2.2 Effective Weld Throats of Flare Groove Welds Flare Bevel Groove[a]

Welding Process

Flare V-Groove

GMAW and FCAW-G

5/8

R

3/4

R

SMAW and FCAW-S

5/16

R

5/8

R

SAW

5/16

R

1/2

R

[a] For flare bevel groove with R < 3/8 in. (10 mm), use only reinforcing fillet weld on filled flush joint. General note: R = radius of joint surface (can be assumed to be 2t for HSS), in. (mm)

TABLE J2.3 Minimum Effective Throat of Partial-Joint-Penetration Groove Welds

[a]

1b.

Material Thickness of Thinner Part Joined, in. (mm)

Minimum Effective Throat, [a] in. (mm)

To 1/4 (6) inclusive Over 1/4 (6) to 1/2 (13) Over 1/2 (13) to 3/4 (19) Over 3/4 (19) to 11/2 (38) Over 11/2 (38) to 21/4 (57) Over 21/4 (57) to 6 (150) Over 6 (150)

(3) (5) 1/4 (6) 5/16 (8) 3/8 (10) 1/2 (13) 5/8 (16)

1/8

3/16

See Table J2.1.

Limitations The minimum effective throat of a partial-joint-penetration groove weld shall not be less than the size required to transmit calculated forces nor the size shown in Table J2.3. Minimum weld size is determined by the thinner of the two parts joined.

2.

Fillet Welds

2a.

Effective Area The effective area of a fillet weld shall be the effective length multiplied by the effective throat. The effective throat of a fillet weld shall be the shortest distance from the root to the face of the diagrammatic weld. An increase in effective throat

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

1/20/11

Sect. J2.]

7:59 AM

Page 111

16.1–111

WELDS

TABLE J2.4 Minimum Size of Fillet Welds Material Thickness of Thinner Part Joined, in. (mm)

Minimum Size of Fillet Weld, [a] in. (mm)

To 1/4 (6) inclusive Over 1/4 (6) to 1/2 (13) Over 1/2 (13) to 3/4 (19) Over 3/4 (19)

1/8

(3) (5) 1/4 (6) 5/16 (8) 3/16

[a]

Leg dimension of fillet welds. Single pass welds must be used. Note: See Section J2.2b for maximum size of fillet welds.

is permitted if consistent penetration beyond the root of the diagrammatic weld is demonstrated by tests using the production process and procedure variables. For fillet welds in holes and slots, the effective length shall be the length of the centerline of the weld along the center of the plane through the throat. In the case of overlapping fillets, the effective area shall not exceed the nominal cross-sectional area of the hole or slot, in the plane of the faying surface.

2b.

Limitations The minimum size of fillet welds shall be not less than the size required to transmit calculated forces, nor the size as shown in Table J2.4. These provisions do not apply to fillet weld reinforcements of partial- or complete-joint-penetration groove welds. The maximum size of fillet welds of connected parts shall be: (a) Along edges of material less than 1/4-in. (6 mm) thick; not greater than the thickness of the material. (b) Along edges of material 1/4 in. (6 mm) or more in thickness; not greater than the thickness of the material minus 1/16 in. (2 mm), unless the weld is especially designated on the drawings to be built out to obtain full-throat thickness. In the as-welded condition, the distance between the edge of the base metal and the toe of the weld is permitted to be less than 1/16 in. (2 mm) provided the weld size is clearly verifiable. The minimum length of fillet welds designed on the basis of strength shall be not less than four times the nominal weld size, or else the effective size of the weld shall be considered not to exceed one quarter of its length. If longitudinal fillet welds are used alone in end connections of flat-bar tension members, the length of each fillet weld shall be not less than the perpendicular distance between them. For the effect of longitudinal fillet weld length in end connections upon the effective area of the connected member, see Section D3.

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For end-loaded fillet welds with a length up to 100 times the weld size, it is permitted to take the effective length equal to the actual length. When the length of the end-loaded fillet weld exceeds 100 times the weld size, the effective length shall be determined by multiplying the actual length by the reduction factor, β, determined as follows: β = 1.2 ⫺ 0.002(l/w) ≤ 1.0

(J2-1)

where l = actual length of end-loaded weld, in. (mm) w = size of weld leg, in. (mm) When the length of the weld exceeds 300 times the leg size, w, the effective length shall be taken as 180w. Intermittent fillet welds are permitted to be used to transfer calculated stress across a joint or faying surfaces and to join components of built-up members. The length of any segment of intermittent fillet welding shall be not less than four times the weld size, with a minimum of 11/2 in. (38 mm). In lap joints, the minimum amount of lap shall be five times the thickness of the thinner part joined, but not less than 1 in. (25 mm). Lap joints joining plates or bars subjected to axial stress that utilize transverse fillet welds only shall be fillet welded along the end of both lapped parts, except where the deflection of the lapped parts is sufficiently restrained to prevent opening of the joint under maximum loading. Fillet weld terminations are permitted to be stopped short or extend to the ends or sides of parts or be boxed except as limited by the following: (1) For overlapping elements of members in which one connected part extends beyond an edge of another connected part that is subject to calculated tensile stress, fillet welds shall terminate not less than the size of the weld from that edge. (2) For connections where flexibility of the outstanding elements is required, when end returns are used the length of the return shall not exceed four times the nominal size of the weld nor half the width of the part. (3) Fillet welds joining transverse stiffeners to plate girder webs 3/4-in. (19 mm) thick or less shall end not less than four times nor more than six times the thickness of the web from the web toe of the web-to-flange welds, except where the ends of stiffeners are welded to the flange. (4) Fillet welds that occur on opposite sides of a common plane shall be interrupted at the corner common to both welds. User Note: Fillet weld terminations should be located approximately one weld size from the edge of the connection to minimize notches in the base metal. Fillet welds terminated at the end of the joint, other than those connecting stiffeners to girder webs, are not a cause for correction. Fillet welds in holes or slots are permitted to be used to transmit shear and resist loads perpendicular to the faying surface in lap joints or to prevent the buckling or Specification for Structural Steel Buildings, June 22, 2010

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separation of lapped parts and to join components of built-up members. Such fillet welds may overlap, subject to the provisions of Section J2. Fillet welds in holes or slots are not to be considered plug or slot welds.

3.

Plug and Slot Welds

3a.

Effective Area The effective shearing area of plug and slot welds shall be considered as the nominal cross-sectional area of the hole or slot in the plane of the faying surface.

3b.

Limitations Plug or slot welds are permitted to be used to transmit shear in lap joints or to prevent buckling or separation of lapped parts and to join component parts of built-up members. The diameter of the holes for a plug weld shall not be less than the thickness of the part containing it plus 5/16 in. (8 mm), rounded to the next larger odd 1/16 in. (even mm), nor greater than the minimum diameter plus 1/8 in. (3 mm) or 21/4 times the thickness of the weld. The minimum center-to-center spacing of plug welds shall be four times the diameter of the hole. The length of slot for a slot weld shall not exceed 10 times the thickness of the weld. The width of the slot shall be not less than the thickness of the part containing it plus 5 /16 in. (8 mm) rounded to the next larger odd 1/16 in. (even mm), nor shall it be larger than 21/4 times the thickness of the weld. The ends of the slot shall be semicircular or shall have the corners rounded to a radius of not less than the thickness of the part containing it, except those ends which extend to the edge of the part. The minimum spacing of lines of slot welds in a direction transverse to their length shall be four times the width of the slot. The minimum center-to-center spacing in a longitudinal direction on any line shall be two times the length of the slot. The thickness of plug or slot welds in material 5/8 in. (16 mm) or less in thickness shall be equal to the thickness of the material. In material over 5/8-in. (16 mm) thick, the thickness of the weld shall be at least one-half the thickness of the material but not less than 5/8 in. (16 mm).

4.

Strength The design strength, φRn and the allowable strength, Rn /Ω, of welded joints shall be the lower value of the base material strength determined according to the limit states of tensile rupture and shear rupture and the weld metal strength determined according to the limit state of rupture as follows: For the base metal Rn = FnBM ABM

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(J2-2)

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TABLE J2.5 Available Strength of Welded Joints, ksi (MPa) Load Type and Direction Relative to Weld Axis

Pertinent Metal

φ and Ω

Nominal Effective Stress Area (FnBM or (ABM or Fnw) Awe) ksi (MPa) in.2 (mm2)

Required Filler Metal Strength Level [a][b]

COMPLETE-JOINT-PENETRATION GROOVE WELDS

Tension Normal to weld axis

Strength of the joint is controlled by the base metal

Matching filler metal shall be used. For T- and corner joints with backing left in place, notch tough filler metal is required. See Section J2.6.

Compression Normal to weld axis

Strength of the joint is controlled by the base metal

Filler metal with a strength level equal to or one strength level less than matching filler metal is permitted.

Tension or compression Parallel to weld axis

Tension or compression in parts joined parallel to a weld need not be considered in design of welds joining the parts.

Filler metal with a strength level equal to or less than matching filler metal is permitted.

Shear

Strength of the joint is controlled by the base metal

Matching filler metal shall be used.[c]

PARTIAL-JOINT-PENETRATION GROOVE WELDS INCLUDING FLARE V-GROOVE AND FLARE BEVEL GROOVE WELDS Tension Normal to weld axis Compression Column to base plate and column splices designed per Section J1.4(1)

Base

φ = 0.75 Ω = 2.00

Fu

See J4

Weld

φ = 0.80 Ω = 1.88

0.60FEXX

See J2.1a

Compressive stress need not be considered in design of welds joining the parts. φ = 0.90 Ω = 1.67

Fy

Weld

φ = 0.80 Ω = 1.88

0.60FEXX

See J2.1a

Base

φ = 0.90 Ω = 1.67

Fy

See J4

Weld

φ = 0.80 Ω = 1.88

0.90FEXX

See J2.1a

Compression Connections of members designed to bear other than columns as described in Section J1.4(2)

Base

Compression Connections not finished-to-bear Tension or compression Parallel to weld axis

See J4

Tension or compression in parts joined parallel to a weld need not be considered in design of welds joining the parts. Base

Shear Weld

Governed by J4 φ = 0.75 Ω = 2.00

0.60FEXX

See J2.1a

Specification for Structural Steel Building, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Filler metal with a strength level equal to or less than matching filler metal is permitted.

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TABLE J2.5 (continued) Available Strength of Welded Joints, ksi (MPa) Load Type and Direction Relative to Weld Axis

Pertinent Metal

Nominal Effective Stress Area (FnBM or (ABM or Fnw) Awe) ksi (MPa) in.2 (mm2)

φ and Ω

Required Filler Metal Strength Level [a][b]

FILLET WELDS INCLUDING FILLETS IN HOLES AND SLOTS AND SKEWED T–JOINTS Base Shear Tension or compression Parallel to weld axis

Weld

Governed by J4 φ = 0.75 Ω = 2.00

0.60FEXX [d]

See J2.2a

Tension or compression in parts joined parallel to a weld need not be considered in design of welds joining the parts.

Filler metal with a strength level equal to or less than matching filler metal is permitted.

PLUG AND SLOT WELDS Shear Parallel to faying surface on the effective area

Base

Weld

Governed by J4 φ = 0.75 Ω = 2.00

0.60FEXX

See J2.3a

Filler metal with a strength level equal to or less than matching filler metal is permitted.

[a]

For matching weld metal see AWS D1.1/D1.1M, Section 3.3. Filler metal with a strength level one strength level greater than matching is permitted. [c] Filler metals with a strength level less than matching may be used for groove welds between the webs and flanges of built-up sections transferring shear loads, or in applications where high restraint is a concern. In these applications, the weld joint shall be detailed and the weld shall be designed using the thickness of the material as the effective throat, where φ = 0.80, Ω = 1.88 and 0.60FEXX is the nominal strength. [d] Alternatively, the provisions of Section J2.4(a) are permitted provided the deformation compatibility of the various weld elements is considered. Sections J2.4(b) and (c) are special applications of Section J2.4(a) that provide for deformation compatibility. [b]

For the weld metal Rn = Fnw Awe

(J2-3)

where FnBM = nominal stress of the base metal, ksi (MPa) Fnw = nominal stress of the weld metal, ksi (MPa) ABM = cross-sectional area of the base metal, in.2 (mm2) Awe = effective area of the weld, in.2 (mm2) The values of φ, Ω, FnBM and Fnw and limitations thereon are given in Table J2.5. Alternatively, for fillet welds the available strength is permitted to be determined as follows: φ = 0.75 (LRFD)

Ω = 2.00 (ASD)

(a) For a linear weld group with a uniform leg size, loaded through the center of gravity (J2-4) Rn = Fnw Awe where (J2-5) Fnw = 0.60FEXX 共1.0 + 0.50 sin1.5 θ兲 Specification for Structural Steel Buildings, June 22, 2010

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and FEXX = filler metal classification strength, ksi (MPa) θ = angle of loading measured from the weld longitudinal axis, degrees User Note: A linear weld group is one in which all elements are in a line or are parallel. (b) For weld elements within a weld group that are analyzed using an instantaneous center of rotation method, the components of the nominal strength, Rnx and Rny, and the nominal moment capacity, Mn, are permitted to be determined as follows:

where Awei Fnwi f共pi 兲 Fnwi Fnwix Fnwiy pi rcr ri xi yi Δi Δ mi Δucr Δ ui θi

Rnx = ∑Fnwix Awei

(J2-6a)

Rny =∑Fnwiy Awei

(J2-6b)

Mn = ∑ 关Fnwiy Awei (xi) ⫺ Fnwix Awei (yi)兴

(J2-7)

= effective area of weld throat of the ith weld element, in.2 (mm2) = 0.60FEXX 共1.0 + 0.50sin1.5 θi 兲f共pi 兲 (J2-8) = 关pi 共1.9 ⫺ 0.9pi )兴 0.3 (J2-9) = nominal stress in the ith weld element, ksi (MPa) = x-component of nominal stress, Fnwi, ksi (MPa) = y-component of nominal stress, Fnwi, ksi (MPa) = Δ i /Δ mi, ratio of element i deformation to its deformation at maximum stress = distance from instantaneous center of rotation to weld element with minimum Δui /ri ratio, in. (mm) = distance from instantaneous center of rotation to ith weld element, in. (mm) = x component of ri = y component of ri = ri Δucr /rcr = deformation of the ith weld element at an intermediate stress level, linearly proportioned to the critical deformation based on distance from the instantaneous center of rotation, ri, in. (mm) = 0.209(θi + 2)⫺0.32 w, deformation of the ith weld element at maximum stress, in. (mm) = deformation of the weld element with minimum Δui /ri ratio at ultimate stress (rupture), usually in the element furthest from instantaneous center of rotation, in. (mm) = 1.087(θi + 6)⫺0.65 w ≤ 0.17w, deformation of the ith weld element at ultimate stress (rupture), in. (mm) = angle between the longitudinal axis of ith weld element and the direction of the resultant force acting on the element, degrees

(c) For fillet weld groups concentrically loaded and consisting of elements with a uniform leg size that are oriented both longitudinally and transversely to the direction of applied load, the combined strength, Rn, of the fillet weld group shall be determined as the greater of Specification for Structural Steel Buildings, June 22, 2010

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(i) Rn = Rnwl + Rnwt

(J2-10a)

or (ii) Rn = 0.85 Rnwl + 1.5 Rnwt

(J2-10b)

where Rnwl = total nominal strength of longitudinally loaded fillet welds, as determined in accordance with Table J2.5, kips (N) Rnwt = total nominal strength of transversely loaded fillet welds, as determined in accordance with Table J2.5 without the alternate in Section J2.4(a), kips (N)

5.

Combination of Welds If two or more of the general types of welds (groove, fillet, plug, slot) are combined in a single joint, the strength of each shall be separately computed with reference to the axis of the group in order to determine the strength of the combination.

6.

Filler Metal Requirements The choice of filler metal for use with complete-joint-penetration groove welds subject to tension normal to the effective area shall comply with the requirements for matching filler metals given in AWS D1.1/D1.1M. User Note: The following User Note Table summarizes the AWS D1.1/D1.1M provisions for matching filler metals. Other restrictions exist. For a complete list of base metals and prequalified matching filler metals see AWS D1.1/D1.1M, Table 3.1. Base Metal A36 ≤ 3/4 in. thick

Matching Filler Metal 60 & 70 ksi filler metal

A36 > ¾ in. A588* A1011

A572 (Gr. 50 & 55) A913 (Gr. 50) A992 A1018

SMAW: E7015, E7016, E7018, E7028 Other processes: 70 ksi filler metal

A913

(Gr. 60 & 65)

80 ksi filler metal

*For corrosion resistance and color similar to the base metal, see AWS D1.1/D1.1M, subclause 3.7.3. Notes: Filler metals shall meet the requirements of AWS A5.1, A5.5, A5.17, A5.18, A5.20, A5.23, A5.28 or A5.29. In joints with base metals of different strengths, use either a filler metal that matches the higher strength base metal or a filler metal that matches the lower strength and produces a low hydrogen deposit.

Filler metal with a specified minimum Charpy V-notch toughness of 20 ft-lb (27 J) at 40 °F (4 °C) or lower shall be used in the following joints: (1) Complete-joint-penetration groove welded T- and corner joints with steel backing left in place, subject to tension normal to the effective area, unless the joints Specification for Structural Steel Buildings, June 22, 2010

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are designed using the nominal strength and resistance factor or safety factor as applicable for a partial-joint-penetration groove weld (2) Complete-joint-penetration groove welded splices subject to tension normal to the effective area in heavy sections as defined in Sections A3.1c and A3.1d The manufacturer’s Certificate of Conformance shall be sufficient evidence of compliance.

7.

Mixed Weld Metal When Charpy V-notch toughness is specified, the process consumables for all weld metal, tack welds, root pass and subsequent passes deposited in a joint shall be compatible to ensure notch-tough composite weld metal.

J3.

BOLTS AND THREADED PARTS

1.

High-Strength Bolts Use of high-strength bolts shall conform to the provisions of the Specification for Structural Joints Using High-Strength Bolts, hereafter referred to as the RCSC Specification, as approved by the Research Council on Structural Connections, except as otherwise provided in this Specification. High-strength bolts in this Specification are grouped according to material strength as follows: Group A—ASTM A325, A325M, F1852, A354 Grade BC, and A449 Group B—ASTM A490, A490M, F2280, and A354 Grade BD When assembled, all joint surfaces, including those adjacent to the washers, shall be free of scale, except tight mill scale. Bolts are permitted to be installed to the snug-tight condition when used in: (a) bearing-type connections except as noted in Section E6 or Section J1.10 (b) tension or combined shear and tension applications, for Group A bolts only, where loosening or fatigue due to vibration or load fluctuations are not design considerations The snug-tight condition is defined as the tightness required to bring the connected plies into firm contact. Bolts to be tightened to a condition other than snug tight shall be clearly identified on the design drawings. All high-strength bolts specified on the design drawings to be used in pretensioned or slip-critical joints shall be tightened to a bolt tension not less than that given in Table J3.1 or J3.1M. Installation shall be by any of the following methods: turn-ofnut method, a direct-tension-indicator, twist-off-type tension-control bolt, calibrated wrench, or alternative design bolt. User Note: There are no specific minimum or maximum tension requirements for snug-tight bolts. Fully pretensioned bolts such as ASTM F1852 or F2280 are permitted unless specifically prohibited on design drawings.

Specification for Structural Steel Buildings, June 22, 2010

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TABLE J3.1 Minimum Bolt Pretension, kips* Bolt Size, in.

Group A (e.g., A325 Bolts)

Group B ( e.g., A490 Bolts)

1/2

12 19 28 39 51 56 71 85 103

15 24 35 49 64 80 102 121 148

5/8 3/4 7/8

1 11/8 11/4 13/8 11/2

*Equal to 0.70 times the minimum tensile strength of bolts, rounded off to nearest kip, as specified in ASTM specifications for A325 and A490 bolts with UNC threads.

TABLE J3.1M Minimum Bolt Pretension, kN* Bolt Size, mm M16 M20 M22 M24 M27 M30 M36

Group A ( e.g., A325M Bolts) Group B ( e.g., A490M Bolts) 91 142 176 205 267 326 475

114 179 221 257 334 408 595

*Equal to 0.70 times the minimum tensile strength of bolts, rounded off to nearest kN, as specified in ASTM specifications for A325M and A490M bolts with UNC threads.

When bolt requirements cannot be provided within the RCSC Specification limitations because of requirements for lengths exceeding 12 diameters or diameters exceeding 11/2 in. (38 mm), bolts or threaded rods conforming to Group A or Group B materials are permitted to be used in accordance with the provisions for threaded parts in Table J3.2. When ASTM A354 Grade BC, A354 Grade BD, or A449 bolts and threaded rods are used in slip-critical connections, the bolt geometry including the thread pitch, thread length, head and nut(s) shall be equal to or (if larger in diameter) proportional to that required by the RCSC Specification. Installation shall comply with all applicable requirements of the RCSC Specification with modifications as required for the increased diameter and/or length to provide the design pretension.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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[Sect. J3.

TABLE J3.2 Nominal Strength of Fasteners and Threaded Parts, ksi (MPa) Nominal Tensile Strength, Fnt , ksi (MPa)[a]

Nominal Shear Strength in Bearing-Type Connections, Fnv , ksi (MPa)[b]

A307 bolts

45 (310)

27 (188) [c] [d]

Group A (e.g., A325) bolts, when threads are not excluded from shear planes

90 (620)

54 (372)

Group A (e.g., A325) bolts, when threads are excluded from shear planes

90 (620)

68 (469)

Group B (e.g., A490) bolts, when threads are not excluded from shear planes

113 (780)

68 (469)

Group B (e.g., A490) bolts, when threads are excluded from shear planes

113 (780)

84 (579)

Threaded parts meeting the requirements of Section A3.4, when threads are not excluded from shear planes

0.75Fu

0.450Fu

Threaded parts meeting the requirements of Section A3.4, when threads are excluded from shear planes

0.75Fu

0.563Fu

Description of Fasteners

[a]

For high-strength bolts subject to tensile fatigue loading, see Appendix 3. For end loaded connections with a fastener pattern length greater than 38 in. (965 mm), Fnv shall be reduced to 83.3% of the tabulated values. Fastener pattern length is the maximum distance parallel to the line of force between the centerline of the bolts connecting two parts with one faying surface. [c] For A307 bolts the tabulated values shall be reduced by 1% for each 1/16 in. (2 mm) over 5 diameters of length in the grip. [d] Threads permitted in shear planes. [b]

2.

Size and Use of Holes The maximum sizes of holes for bolts are given in Table J3.3 or Table J3.3M, except that larger holes, required for tolerance on location of anchor rods in concrete foundations, are permitted in column base details. Standard holes or short-slotted holes transverse to the direction of the load shall be provided in accordance with the provisions of this specification, unless oversized holes, short-slotted holes parallel to the load, or long-slotted holes are approved Specification for Structural Steel Buildings, June 22, 2010

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TABLE J3.3 Nominal Hole Dimensions, in. Hole Dimensions Bolt Diameter, in.

Standard (Dia.)

Oversize (Dia.)

Short-Slot (Width ⴛ Length)

Long-Slot (Width ⴛ Length)

× 11/16 × 7/8 13/16 × 1 15/16 × 11/8 11/16 × 15/16 (d + 1/16) × (d + 3/8)

× 11/4 × 19/16 13/16 × 17/8 15/16 × 23/16 11/16 × 2½ (d + 1/16) × (2.5 × d )

1/2

9/16

5/8

5/8

11/16

13/16 15/16 11/16 11/4 d + 5/16

3/4

13/16

7/8

15/16

1 ≥ 11/8

11/16 d + 1/16

9/16

11/16

9/16

11/16

TABLE J3.3M Nominal Hole Dimensions, mm Hole Dimensions Bolt Diameter, mm

Standard (Dia.)

Oversize (Dia.)

M16 M20 M22 M24 M27 M30 ≥ M36

18 22 24 27 [a] 30 33 d+3

20 24 28 30 35 38 d+8

[a]

Short-Slot Long-Slot (Width ⴛ Length) (Width ⴛ Length) 18 × 22 22 × 26 24 × 30 27 × 32 30 × 37 33 × 40 (d + 3) × (d + 10)

18 × 40 22 × 50 24 × 55 27 × 60 30 × 67 33 × 75 (d + 3) × 2.5d

Clearance provided allows the use of a 1-in. bolt if desirable.

by the engineer of record. Finger shims up to 1/4 in. (6 mm) are permitted in slipcritical connections designed on the basis of standard holes without reducing the nominal shear strength of the fastener to that specified for slotted holes. Oversized holes are permitted in any or all plies of slip-critical connections, but they shall not be used in bearing-type connections. Hardened washers shall be installed over oversized holes in an outer ply. Short-slotted holes are permitted in any or all plies of slip-critical or bearing-type connections. The slots are permitted without regard to direction of loading in slipcritical connections, but the length shall be normal to the direction of the load in bearing-type connections. Washers shall be installed over short-slotted holes in an outer ply; when high-strength bolts are used, such washers shall be hardened washers conforming to ASTM F436. Specification for Structural Steel Buildings, June 22, 2010

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[Sect. J3.

When Group B bolts over 1 in. (25 mm) in diameter are used in slotted or oversized holes in external plies, a single hardened washer conforming to ASTM F436, except with 5/16-in. (8 mm) minimum thickness, shall be used in lieu of the standard washer. User Note: Washer requirements are provided in the RCSC Specification, Section 6. Long-slotted holes are permitted in only one of the connected parts of either a slipcritical or bearing-type connection at an individual faying surface. Long-slotted holes are permitted without regard to direction of loading in slip-critical connections, but shall be normal to the direction of load in bearing-type connections. Where long-slotted holes are used in an outer ply, plate washers, or a continuous bar with standard holes, having a size sufficient to completely cover the slot after installation, shall be provided. In high-strength bolted connections, such plate washers or continuous bars shall be not less than 5/16-in. (8 mm) thick and shall be of structural grade material, but need not be hardened. If hardened washers are required for use of high-strength bolts, the hardened washers shall be placed over the outer surface of the plate washer or bar.

3.

Minimum Spacing The distance between centers of standard, oversized or slotted holes shall not be less than 22/3 times the nominal diameter, d, of the fastener; a distance of 3d is preferred.

4.

Minimum Edge Distance The distance from the center of a standard hole to an edge of a connected part in any direction shall not be less than either the applicable value from Table J3.4 or Table J3.4M, or as required in Section J3.10. The distance from the center of an oversized or slotted hole to an edge of a connected part shall be not less than that required for a standard hole to an edge of a connected part plus the applicable increment, C2, from Table J3.5 or Table J3.5M. User Note: The edge distances in Tables J3.4 and J3.4M are minimum edge distances based on standard fabrication practices and workmanship tolerances. The appropriate provisions of Sections J3.10 and J4 must be satisfied.

5.

Maximum Spacing and Edge Distance The maximum distance from the center of any bolt to the nearest edge of parts in contact shall be 12 times the thickness of the connected part under consideration, but shall not exceed 6 in. (150 mm). The longitudinal spacing of fasteners between elements consisting of a plate and a shape or two plates in continuous contact shall be as follows: (a) For painted members or unpainted members not subject to corrosion, the spacing shall not exceed 24 times the thickness of the thinner part or 12 in. (305 mm). (b) For unpainted members of weathering steel subject to atmospheric corrosion, the spacing shall not exceed 14 times the thickness of the thinner part or 7 in. (180 mm). Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Sect. J3.]

BOLTS AND THREADED PARTS

16.1–123

TABLE J3.4 Minimum Edge Distance[a] from Center of Standard Hole[b] to Edge of Connected Part, in. Bolt Diameter, in.

Minimum Edge Distance

1/2

3/4

5/8

7/8

3/4

1

7/8

11/8

1

11/4

11/8

11/2

11/4

15/8

Over 11/4

11/4 × d

[a]

If necessary, lesser edge distances are permitted provided the appropriate provisions from Sections J3.10 and J4 are satisfied, but edge distances less than one bolt diameter are not permitted without approval from the engineer of record. [b] For oversized or slotted holes, see Table J3.5.

TABLE J3.4M Minimum Edge Distance[a] from Center of Standard Hole[b] to Edge of Connected Part, mm Bolt Diameter, mm

Minimum Edge Distance

16 20

22 26

22

28

24

30

27

34

30

38

36

46

Over 36

1.25d

[a]

If necessary, lesser edge distances are permitted provided the appropriate provisions from Sections J3.10 and J4 are satisfied, but edge distances less than one bolt diameter are not permitted without approval from the engineer of record. [b] For oversized or slotted holes, see Table J3.5M.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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BOLTS AND THREADED PARTS

[Sect. J3.

TABLE J3.5 Values of Edge Distance Increment C2, in.

[a]

Slotted Holes

Nominal Diameter of Fastener, in.

Oversized Holes

Short Slots

≤ 7/8

1/16

1/8

1

1/8

1/8

≥ 11/8

1/8

3/16

Long Axis Perpendicular to Edge Long Slots[a]

Long Axis Parallel to Edge

3/4d

0

When length of slot is less than maximum allowable (see Table J3.3), C2 is permitted to be reduced by one-half the difference between the maximum and actual slot lengths.

TABLE J3.5M Values of Edge Distance Increment C2, mm

[a]

Slotted Holes

Nominal Diameter of Fastener, mm

Oversized Holes

Short Slots

≤ 22

2

3

24

3

3

≥ 27

3

5

Long Axis Perpendicular to Edge Long Slots[a]

Long Axis Parallel to Edge

0.75d

0

When length of slot is less than maximum allowable (see Table J3.3M), C2 is permitted to be reduced by one-half the difference between the maximum and actual slot lengths.

User Note: Dimensions in (a) and (b) do not apply to elements consisting of two shapes in continuous contact.

6.

Tensile and Shear Strength of Bolts and Threaded Parts The design tensile or shear strength, φRn, and the allowable tensile or shear strength, Rn /Ω, of a snug-tightened or pretensioned high-strength bolt or threaded part shall be determined according to the limit states of tension rupture and shear rupture as follows: Rn = Fn Ab φ = 0.75 (LRFD)

Ω = 2.00 (ASD)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(J3-1)

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BOLTS AND THREADED PARTS

16.1–125

where Ab = nominal unthreaded body area of bolt or threaded part, in.2 (mm2) Fn = nominal tensile stress, Fnt, or shear stress, Fnv, from Table J3.2, ksi (MPa) The required tensile strength shall include any tension resulting from prying action produced by deformation of the connected parts. User Note: The force that can be resisted by a snug-tightened or pretensioned high-strength bolt or threaded part may be limited by the bearing strength at the bolt hole per Section J3.10. The effective strength of an individual fastener may be taken as the lesser of the fastener shear strength per Section J3.6 or the bearing strength at the bolt hole per Section J3.10. The strength of the bolt group is taken as the sum of the effective strengths of the individual fasteners.

7.

Combined Tension and Shear in Bearing-Type Connections The available tensile strength of a bolt subjected to combined tension and shear shall be determined according to the limit states of tension and shear rupture as follows: Rn = F′nt Ab φ = 0.75 (LRFD)

(J3-2)

Ω = 2.00 (ASD)

where F′nt = nominal tensile stress modified to include the effects of shear stress, ksi (MPa) F′nt = 1.3Fnt −

Fnt frv ≤ Fnt φFnv

(LRFD)

(J3-3a)

F′nt = 1.3Fnt −

ΩFnt frv ≤ Fnt Fnv

(ASD)

(J3-3b)

Fnt = nominal tensile stress from Table J3.2, ksi (MPa) Fnv = nominal shear stress from Table J3.2, ksi (MPa) frv = required shear stress using LRFD or ASD load combinations, ksi (MPa) The available shear stress of the fastener shall equal or exceed the required shear stress, frv. User Note: Note that when the required stress, f, in either shear or tension, is less than or equal to 30% of the corresponding available stress, the effects of combined stress need not be investigated. Also note that Equations J3-3a and J3-3b can be rewritten so as to find a nominal shear stress, F′nv, as a function of the required tensile stress, ft.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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8.

(Black plate)

BOLTS AND THREADED PARTS

[Sect. J3.

High-Strength Bolts in Slip-Critical Connections Slip-critical connections shall be designed to prevent slip and for the limit states of bearing-type connections. When slip-critical bolts pass through fillers, all surfaces subject to slip shall be prepared to achieve design slip resistance. The available slip resistance for the limit state of slip shall be determined as follows: Rn = μDu hf Tb ns

(J3-4)

(a) For standard size and short-slotted holes perpendicular to the direction of the load φ = 1.00 (LRFD)

Ω = 1.50 (ASD)

(b) For oversized and short-slotted holes parallel to the direction of the load φ = 0.85 (LRFD)

Ω = 1.76 (ASD)

(c) For long-slotted holes φ = 0.70 (LRFD)

Ω = 2.14 (ASD)

where μ = mean slip coefficient for Class A or B surfaces, as applicable, and determined as follows, or as established by tests: (i) For Class A surfaces (unpainted clean mill scale steel surfaces or surfaces with Class A coatings on blast-cleaned steel or hot-dipped galvanized and roughened surfaces) μ = 0.30 (ii) For Class B surfaces (unpainted blast-cleaned steel surfaces or surfaces with Class B coatings on blast-cleaned steel) μ = 0.50 Du = 1.13, a multiplier that reflects the ratio of the mean installed bolt pretension to the specified minimum bolt pretension. The use of other values may be approved by the engineer of record. Tb = minimum fastener tension given in Table J3.1, kips, or Table J3.1M, kN hf = factor for fillers, determined as follows: (i) Where there are no fillers or where bolts have been added to distribute loads in the filler hf = 1.0 (ii) Where bolts have not been added to distribute the load in the filler: (a) For one filler between connected parts hf = 1.0 (b) For two or more fillers between connected parts hf = 0.85 ns = number of slip planes required to permit the connection to slip Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Sect. J3.]

9.

BOLTS AND THREADED PARTS

16.1–127

Combined Tension and Shear in Slip-Critical Connections When a slip-critical connection is subjected to an applied tension that reduces the net clamping force, the available slip resistance per bolt, from Section J3.8, shall be multiplied by the factor, ksc, as follows: ksc = 1 −

Tu DuTb nb

(LRFD)

(J3-5a)

ksc = 1 −

1.5Ta DuTb nb

(ASD)

(J3-5b)

where Ta = required tension force using ASD load combinations, kips (kN) Tu = required tension force using LRFD load combinations, kips (kN) nb = number of bolts carrying the applied tension

10.

Bearing Strength at Bolt Holes The available bearing strength, φRn and Rn/Ω, at bolt holes shall be determined for the limit state of bearing as follows: φ = 0.75 (LRFD)

Ω = 2.00 (ASD)

The nominal bearing strength of the connected material, Rn, is determined as follows: (a) For a bolt in a connection with standard, oversized and short-slotted holes, independent of the direction of loading, or a long-slotted hole with the slot parallel to the direction of the bearing force (i) When deformation at the bolt hole at service load is a design consideration Rn = 1.2lc tFu ≤ 2.4dtFu

(J3-6a)

(ii) When deformation at the bolt hole at service load is not a design consideration Rn = 1.5lc tFu ≤ 3.0dtFu

(J3-6b)

(b) For a bolt in a connection with long-slotted holes with the slot perpendicular to the direction of force Rn = 1.0lc tFu ≤ 2.0dtFu

(J3-6c)

(c) For connections made using bolts that pass completely through an unstiffened box member or HSS, see Section J7 and Equation J7-1; where Fu = specified minimum tensile strength of the connected material, ksi (MPa) d = nominal bolt diameter, in. (mm) lc = clear distance, in the direction of the force, between the edge of the hole and the edge of the adjacent hole or edge of the material, in. (mm) t = thickness of connected material, in. (mm) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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BOLTS AND THREADED PARTS

[Sect. J3.

For connections, the bearing resistance shall be taken as the sum of the bearing resistances of the individual bolts. Bearing strength shall be checked for both bearing-type and slip-critical connections. The use of oversized holes and short- and long-slotted holes parallel to the line of force is restricted to slip-critical connections per Section J3.2. User Note: The effective strength of an individual fastener is the lesser of the fastener shear strength per Section J3.6 or the bearing strength at the bolt hole per Section J3.10. The strength of the bolt group is the sum of the effective strengths of the individual fasteners.

11.

Special Fasteners The nominal strength of special fasteners other than the bolts presented in Table J3.2 shall be verified by tests.

12.

Tension Fasteners When bolts or other fasteners in tension are attached to an unstiffened box or HSS wall, the strength of the wall shall be determined by rational analysis.

J4.

AFFECTED ELEMENTS OF MEMBERS AND CONNECTING ELEMENTS This section applies to elements of members at connections and connecting elements, such as plates, gussets, angles and brackets.

1.

Strength of Elements in Tension The design strength, φRn, and the allowable strength, Rn /Ω, of affected and connecting elements loaded in tension shall be the lower value obtained according to the limit states of tensile yielding and tensile rupture. (a) For tensile yielding of connecting elements Rn = Fy Ag φ = 0.90 (LRFD)

(J4-1)

Ω = 1.67 (ASD)

(b) For tensile rupture of connecting elements Rn = Fu Ae φ = 0.75 (LRFD)

(J4-2)

Ω = 2.00 (ASD)

where Ae = effective net area as defined in Section D3, in.2 (mm2); for bolted splice plates, Ae = An ≤ 0.85Ag. User Note: The effective net area of the connection plate may be limited due to stress distribution as calculated by methods such as the Whitmore section.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Sect. J4.]

2.

AFFECTED ELEMENTS OF MEMBERS AND CONNECTING ELEMENTS

16.1–129

Strength of Elements in Shear The available shear strength of affected and connecting elements in shear shall be the lower value obtained according to the limit states of shear yielding and shear rupture: (a) For shear yielding of the element: Rn = 0.60Fy Agv φ = 1.00 (LRFD)

(J4-3)

Ω = 1.50 (ASD)

where Agv = gross area subject to shear, in.2 (mm2) (b) For shear rupture of the element: Rn = 0.60Fu Anv φ = 0.75 (LRFD)

(J4-4)

Ω = 2.00 (ASD)

where Anv = net area subject to shear, in.2 (mm2)

3.

Block Shear Strength The available strength for the limit state of block shear rupture along a shear failure path or paths and a perpendicular tension failure path shall be taken as Rn = 0.60Fu Anv + Ubs Fu Ant ≤ 0.60Fy Agv + Ubs Fu Ant φ = 0.75 (LRFD)

(J4-5)

Ω = 2.00 (ASD)

where Ant = net area subject to tension, in.2 (mm2) Where the tension stress is uniform, Ubs = 1; where the tension stress is nonuniform, Ubs = 0.5. User Note: Typical cases where Ubs should be taken equal to 0.5 are illustrated in the Commentary.

4.

Strength of Elements in Compression The available strength of connecting elements in compression for the limit states of yielding and buckling shall be determined as follows: (a) When KL/r ≤ 25 Pn = Fy Ag φ = 0.90 (LRFD)

Ω = 1.67 (ASD)

(b) When KL/r >25, the provisions of Chapter E apply.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(J4-6)

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16.1–130

5.

AFFECTED ELEMENTS OF MEMBERS AND CONNECTING ELEMENTS

[Sect. J4.

Strength of Elements in Flexure The available flexural strength of affected elements shall be the lower value obtained according to the limit states of flexural yielding, local buckling, flexural lateraltorsional buckling and flexural rupture.

J5.

FILLERS

1.

Fillers in Welded Connections Whenever it is necessary to use fillers in joints required to transfer applied force, the fillers and the connecting welds shall conform to the requirements of Section J5.1a or Section J5.1b, as applicable.

1a.

Thin Fillers Fillers less than 1/4 in. (6 mm) thick shall not be used to transfer stress. When the thickness of the fillers is less than 1/4 in. (6 mm), or when the thickness of the filler is 1/4 in. (6 mm) or greater but not adequate to transfer the applied force between the connected parts, the filler shall be kept flush with the edge of the outside connected part, and the size of the weld shall be increased over the required size by an amount equal to the thickness of the filler.

1b.

Thick Fillers When the thickness of the fillers is adequate to transfer the applied force between the connected parts, the filler shall extend beyond the edges of the outside connected base metal. The welds joining the outside connected base metal to the filler shall be sufficient to transmit the force to the filler and the area subjected to the applied force in the filler shall be adequate to avoid overstressing the filler. The welds joining the filler to the inside connected base metal shall be adequate to transmit the applied force.

2.

Fillers in Bolted Connections When a bolt that carries load passes through fillers that are equal to or less than 1/4 in. (6 mm) thick, the shear strength shall be used without reduction. When a bolt that carries load passes through fillers that are greater than 1/4 in. (6 mm) thick, one of the following requirements shall apply: (a) The shear strength of the bolts shall be multiplied by the factor 1 ⫺ 0.4(t ⫺ 0.25) [S.I.: 1 ⫺ 0.0154(t ⫺ 6)] but not less than 0.85, where t is the total thickness of the fillers; (b) The fillers shall be extended beyond the joint and the filler extension shall be secured with enough bolts to uniformly distribute the total force in the connected element over the combined cross section of the connected element and the fillers; (c) The size of the joint shall be increased to accommodate a number of bolts that is equivalent to the total number required in (b) above; or

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Sect. J8.]

COLUMN BASES AND BEARING ON CONCRETE

16.1–131

(d) The joint shall be designed to prevent slip in accordance with Section J3.8 using either Class B surfaces or Class A surfaces with turn-of-nut tightening.

J6.

SPLICES Groove-welded splices in plate girders and beams shall develop the nominal strength of the smaller spliced section. Other types of splices in cross sections of plate girders and beams shall develop the strength required by the forces at the point of the splice.

J7.

BEARING STRENGTH The design bearing strength, φRn, and the allowable bearing strength, Rn /Ω, of surfaces in contact shall be determined for the limit state of bearing (local compressive yielding) as follows: φ = 0.75 (LRFD)

Ω = 2.00 (ASD)

The nominal bearing strength, Rn, shall be determined as follows: (a) For finished surfaces, pins in reamed, drilled, or bored holes, and ends of fitted bearing stiffeners Rn = 1.8Fy Apb

(J7-1)

where Apb = projected area in bearing, in.2 (mm2) Fy = specified minimum yield stress, ksi (MPa) (b) For expansion rollers and rockers (i) When d ≤ 25 in. (635 mm) Rn = 1.2(Fy ⫺ 13)lb d / 20

(J7-2)

(S.I.: Rn = 1.2(Fy ⫺ 90)lb d / 20)

(J7-2M)

(ii) When d > 25 in. (635 mm) Rn = 6.0( Fy − 13)lb d / 20

(S.I. : Rn = 30.2(Fy − 90)lb

d / 20

(J7-3)

)

(J7-3M)

where d = diameter, in. (mm) lb = length of bearing, in. (mm)

J8.

COLUMN BASES AND BEARING ON CONCRETE Proper provision shall be made to transfer the column loads and moments to the footings and foundations.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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16.1–132

COLUMN BASES AND BEARING ON CONCRETE

[Sect. J8.

In the absence of code regulations, the design bearing strength, φc Pp, and the allowable bearing strength, Pp /Ωc, for the limit state of concrete crushing are permitted to be taken as follows: φc = 0.65 (LRFD)

Ωc = 2.31 (ASD)

The nominal bearing strength, Pp, is determined as follows: (a) On the full area of a concrete support: Pp = 0.85fc′A1

(J8-1)

(b) On less than the full area of a concrete support: Pp = 0.85 fc ′ A1 A2 / A1 ≤ 1.7 fc ′ A1

(J8-2)

where A1 = area of steel concentrically bearing on a concrete support, in.2 (mm2) A2 = maximum area of the portion of the supporting surface that is geometrically similar to and concentric with the loaded area, in.2 (mm2) f ′c = specified compressive strength of concrete, ksi (MPa)

J9.

ANCHOR RODS AND EMBEDMENTS Anchor rods shall be designed to provide the required resistance to loads on the completed structure at the base of columns including the net tensile components of any bending moment that may result from load combinations stipulated in Section B2. The anchor rods shall be designed in accordance with the requirements for threaded parts in Table J3.2. User Note: ASTM F1554 anchor rods may be furnished in accordance to product specifications with a body diameter less than the nominal diameter. Load effects such as bending and elongation should be calculated based on minimum diameters permitted by the product specification. See ASTM F1554 and the table, “Applicable ASTM Specifications for Various Types of Structural Fasteners,” in Part 2 of the AISC Steel Construction Manual. Design of column bases and anchor rods for the transfer of forces to the concrete foundation including bearing against the concrete elements shall satisfy the requirements of ACI 318 or ACI 349. User Note: When columns are required to resist a horizontal force at the base plate, bearing against the concrete elements should be considered. When anchor rods are used to resist horizontal forces, hole size, anchor rod setting tolerance, and the horizontal movement of the column shall be considered in the design. Larger oversized holes and slotted holes are permitted in base plates when adequate bearing is provided for the nut by using ASTM F844 washers or plate washers to bridge the hole. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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FLANGES AND WEBS WITH CONCENTRATED FORCES

16.1–133

User Note: The permitted hole sizes, corresponding washer dimensions and nuts are given in the AISC Steel Construction Manual and ASTM F1554.

User Note: See ACI 318 for embedment design and for shear friction design. See OSHA for special erection requirements for anchor rods.

J10. FLANGES AND WEBS WITH CONCENTRATED FORCES This section applies to single- and double-concentrated forces applied normal to the flange(s) of wide flange sections and similar built-up shapes. A single-concentrated force can be either tensile or compressive. Double-concentrated forces are one tensile and one compressive and form a couple on the same side of the loaded member. When the required strength exceeds the available strength as determined for the limit states listed in this section, stiffeners and/or doublers shall be provided and shall be sized for the difference between the required strength and the available strength for the applicable limit state. Stiffeners shall also meet the design requirements in Section J10.8. Doublers shall also meet the design requirement in Section J10.9. User Note: See Appendix 6.3 for requirements for the ends of cantilever members. Stiffeners are required at unframed ends of beams in accordance with the requirements of Section J10.7.

1.

Flange Local Bending This section applies to tensile single-concentrated forces and the tensile component of double-concentrated forces. The design strength, φRn, and the allowable strength, Rn /Ω, for the limit state of flange local bending shall be determined as follows: Rn = 6.25Fy f tf2 φ = 0.90 (LRFD)

(J10-1)

Ω = 1.67 (ASD)

where Fyf = specified minimum yield stress of the flange, ksi (MPa) tf = thickness of the loaded flange, in. (mm) If the length of loading across the member flange is less than 0.15bf, where bf is the member flange width, Equation J10-1 need not be checked. When the concentrated force to be resisted is applied at a distance from the member end that is less than 10tf, Rn shall be reduced by 50%. When required, a pair of transverse stiffeners shall be provided.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

16.1–134

2.

1/20/11

7:59 AM

Page 134

FLANGES AND WEBS WITH CONCENTRATED FORCES

[Sect. J10.

Web Local Yielding This section applies to single-concentrated forces and both components of doubleconcentrated forces. The available strength for the limit state of web local yielding shall be determined as follows: φ = 1.00 (LRFD) Ω = 1.50 (ASD) The nominal strength, Rn, shall be determined as follows: (a) When the concentrated force to be resisted is applied at a distance from the member end that is greater than the depth of the member, d, Rn = Fyw tw (5k + lb)

(J10-2)

(b) When the concentrated force to be resisted is applied at a distance from the member end that is less than or equal to the depth of the member, d, Rn = Fyw tw (2.5k + lb)

(J10-3)

where Fyw = specified minimum yield stress of the web material, ksi (MPa) k = distance from outer face of the flange to the web toe of the fillet, in. (mm) lb = length of bearing (not less than k for end beam reactions), in. (mm) tw = thickness of web, in. (mm) When required, a pair of transverse stiffeners or a doubler plate shall be provided.

3.

Web Local Crippling This section applies to compressive single-concentrated forces or the compressive component of double-concentrated forces. The available strength for the limit state of web local crippling shall be determined as follows: φ = 0.75 (LRFD)

Ω = 2.00 (ASD)

The nominal strength, Rn, shall be determined as follows: (a) When the concentrated compressive force to be resisted is applied at a distance from the member end that is greater than or equal to d/ 2: 1.5 ⎤ ⎡ EFyw t f ⎛l ⎞⎛t ⎞ Rn = 0.80t w2 ⎢1 + 3 ⎜ b ⎟ ⎜ w ⎟ ⎥ ⎝ d ⎠ ⎝ tf ⎠ ⎥ tw ⎢ ⎣ ⎦

(J10-4)

(b) When the concentrated compressive force to be resisted is applied at a distance from the member end that is less than d/ 2:

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

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FLANGES AND WEBS WITH CONCENTRATED FORCES

16.1–135

(i) For lb /d ≤ 0.2 Rn =

⎡

0.40t w2 ⎢1 + ⎢ ⎣

⎛l ⎞⎛t ⎞ 3⎜ b ⎟ ⎜ w ⎟ ⎝ d ⎠ ⎝ tf ⎠

1.5 ⎤

⎥ EFyw t f tw ⎥ ⎦

(J10-5a)

(ii) For lb /d > 0.2 Rn =

⎡

4 lb ⎞⎛t ⎞ − 0.2⎟ ⎜ w ⎟ ⎝ d ⎠ ⎝ tf ⎠

⎛ 0.40t w2 ⎢1 + ⎜ ⎢ ⎣

1.5 ⎤

⎥ EFyw t f tw ⎥ ⎦

(J10-5b)

where d = full nominal depth of the section, in. (mm) When required, a transverse stiffener, a pair of transverse stiffeners, or a doubler plate extending at least one-half the depth of the web shall be provided.

4.

Web Sidesway Buckling This section applies only to compressive single-concentrated forces applied to members where relative lateral movement between the loaded compression flange and the tension flange is not restrained at the point of application of the concentrated force. The available strength of the web for the limit state of sidesway buckling shall be determined as follows: φ = 0.85 (LRFD)

Ω = 1.76 (ASD)

The nominal strength, Rn, shall be determined as follows: (a) If the compression flange is restrained against rotation (i) When (h/tw)/(Lb /bf ) ≤ 2.3

Rn =

3 ⎛ h / tw ⎞ ⎤ Cr t w3 t f ⎡ ⎢1 + 0.4 ⎜ ⎥ h2 ⎢ ⎝ Lb / b f ⎟⎠ ⎥ ⎣ ⎦

(J10-6)

(ii) When (h/tw)/(Lb /bf ) > 2.3, the limit state of web sidesway buckling does not apply. When the required strength of the web exceeds the available strength, local lateral bracing shall be provided at the tension flange or either a pair of transverse stiffeners or a doubler plate shall be provided. (b) If the compression flange is not restrained against rotation (i) When (h/tw)/(Lb /bf ) ≤ 1.7

Rn =

3 Cr t w3 t f ⎡ ⎛ h / t w ⎞ ⎤ ⎢ 0.4 ⎜ ⎥ h 2 ⎢ ⎝ Lb / b f ⎟⎠ ⎥ ⎣ ⎦

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(J10-7)

AISC_PART 16_Spec.2_B:14th Ed.

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[Sect. J10.

(ii) When (h/tw)/(Lb /bf ) > 1.7, the limit state of web sidesway buckling does not apply. When the required strength of the web exceeds the available strength, local lateral bracing shall be provided at both flanges at the point of application of the concentrated forces. In Equations J10-6 and J10-7, the following definitions apply: Cr = 960,000 ksi (6.62 ⫻ 106 MPa) when Mu < My (LRFD) or 1.5Ma < My (ASD) at the location of the force = 480,000 ksi (3.31 ⫻ 106 MPa) when Mu ≥ My (LRFD) or 1.5Ma ≥ My (ASD) at the location of the force Lb = largest laterally unbraced length along either flange at the point of load, in. (mm) Ma = required flexural strength using ASD load combinations, kip-in. (N-mm) Mu = required flexural strength using LRFD load combinations, kip-in. (N-mm) bf = width of flange, in. (mm) h = clear distance between flanges less the fillet or corner radius for rolled shapes; distance between adjacent lines of fasteners or the clear distance between flanges when welds are used for built-up shapes, in. (mm) User Note: For determination of adequate restraint, refer to Appendix 6.

5.

Web Compression Buckling This section applies to a pair of compressive single-concentrated forces or the compressive components in a pair of double-concentrated forces, applied at both flanges of a member at the same location. The available strength for the limit state of web local buckling shall be determined as follows: Rn =

24 t w3 EFyw

φ = 0.90 (LRFD)

h

(J10-8)

Ω = 1.67 (ASD)

When the pair of concentrated compressive forces to be resisted is applied at a distance from the member end that is less than d/ 2, Rn shall be reduced by 50%. When required, a single transverse stiffener, a pair of transverse stiffeners, or a doubler plate extending the full depth of the web shall be provided.

6.

Web Panel Zone Shear This section applies to double-concentrated forces applied to one or both flanges of a member at the same location. The available strength of the web panel zone for the limit state of shear yielding shall be determined as follows: Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. J10.]

1/20/11

7:59 AM

Page 137

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φ = 0.90 (LRFD)

16.1–137

Ω = 1.67 (ASD)

The nominal strength, Rn, shall be determined as follows: (a) When the effect of panel-zone deformation on frame stability is not considered in the analysis: (i) For Pr ≤ 0.4Pc Rn = 0.60Fy dc tw

(J10-9)

⎛ P⎞ Rn = 0.60 Fy dc t w ⎜ 1.4 − r ⎟ ⎝ Pc ⎠

(J10-10)

(ii) For Pr > 0.4Pc

(b) When frame stability, including plastic panel-zone deformation, is considered in the analysis: (i) For Pr ≤ 0.75Pc ⎛ 3bcf tcf2 ⎞ Rn = 0.60 Fy dc t w ⎜ 1 + d b dc t w ⎟⎠ ⎝

(J10-11)

⎛ 3bcf tcf2 ⎞ ⎛ 1.2 Pr ⎞ Rn = 0.60 Fy dc t w ⎜ 1 + ⎟ ⎜⎝ 1.9 − P ⎟⎠ d d t b c w⎠ c ⎝

(J10-12)

(ii) For Pr > 0.75Pc

In Equations J10-9 through J10-12, the following definitions apply: Ag = gross cross-sectional area of member, in.2 (mm2) bcf = width of column flange, in. (mm) db = depth of beam, in. (mm) dc = depth of column, in. (mm) Fy = specified minimum yield stress of the column web, ksi (MPa) Pc = Py, kips (N) (LRFD) Pc = 0.60Py, kips (N) (ASD) Pr = required axial strength using LRFD or ASD load combinations, kips (N) Py = Fy Ag, axial yield strength of the column, kips (N) tcf = thickness of column flange, in. (mm) tw = thickness of column web, in. (mm) When required, doubler plate(s) or a pair of diagonal stiffeners shall be provided within the boundaries of the rigid connection whose webs lie in a common plane. See Section J10.9 for doubler plate design requirements.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed._

16.1–138

7.

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[Sect. J10.

Unframed Ends of Beams and Girders At unframed ends of beams and girders not otherwise restrained against rotation about their longitudinal axes, a pair of transverse stiffeners, extending the full depth of the web, shall be provided.

8.

Additional Stiffener Requirements for Concentrated Forces Stiffeners required to resist tensile concentrated forces shall be designed in accordance with the requirements of Section J4.1 and welded to the loaded flange and the web. The welds to the flange shall be sized for the difference between the required strength and available strength. The stiffener to web welds shall be sized to transfer to the web the algebraic difference in tensile force at the ends of the stiffener. Stiffeners required to resist compressive concentrated forces shall be designed in accordance with the requirements in Section J4.4 and shall either bear on or be welded to the loaded flange and welded to the web. The welds to the flange shall be sized for the difference between the required strength and the applicable limit state strength. The weld to the web shall be sized to transfer to the web the algebraic difference in compression force at the ends of the stiffener. For fitted bearing stiffeners, see Section J7. Transverse full depth bearing stiffeners for compressive forces applied to a beam or plate girder flange(s) shall be designed as axially compressed members (columns) in accordance with the requirements of Section E6.2 and Section J4.4. The member properties shall be determined using an effective length of 0.75h and a cross section composed of two stiffeners, and a strip of the web having a width of 25tw at interior stiffeners and 12tw at the ends of members. The weld connecting full depth bearing stiffeners to the web shall be sized to transmit the difference in compressive force at each of the stiffeners to the web. Transverse and diagonal stiffeners shall comply with the following additional requirements: (1) The width of each stiffener plus one-half the thickness of the column web shall not be less than one-third of the flange or moment connection plate width delivering the concentrated force. (2) The thickness of a stiffener shall not be less than one-half the thickness of the flange or moment connection plate delivering the concentrated load, nor less than the width divided by 16. (3) Transverse stiffeners shall extend a minimum of one-half the depth of the member except as required in Section J10.5 and Section J10.7.

9.

Additional Doubler Plate Requirements for Concentrated Forces Doubler plates required for compression strength shall be designed in accordance with the requirements of Chapter E. Doubler plates required for tensile strength shall be designed in accordance with the requirements of Chapter D. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.2_B:14th Ed.

Sect. J10.]

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16.1–139

Doubler plates required for shear strength (see Section J10.6) shall be designed in accordance with the provisions of Chapter G. Doubler plates shall comply with the following additional requirements: (1) The thickness and extent of the doubler plate shall provide the additional material necessary to equal or exceed the strength requirements. (2) The doubler plate shall be welded to develop the proportion of the total force transmitted to the doubler plate.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

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CHAPTER K DESIGN OF HSS AND BOX MEMBER CONNECTIONS

This chapter addresses connections to HSS members and box sections of uniform wall thickness. User Note: Connection strength is often governed by the size of HSS members, especially the wall thickness of truss chords, and this must be considered in the initial design. The chapter is organized as follows: K1. K2. K3. K4.

Concentrated Forces on HSS HSS-to-HSS Truss Connections HSS-to-HSS Moment Connections Welds of Plates and Branches to Rectangular HSS

User Note: See also Chapter J for additional requirements for bolting to HSS. See Section J3.10(c) for through-bolts.

User Note: Connection parameters must be within the limits of applicability. Limit states need only be checked when connection geometry or loading is within the parameters given in the description of the limit state.

K1.

CONCENTRATED FORCES ON HSS The design strength, φRn, and the allowable strength, Rn /Ω, of connections shall be determined in accordance with the provisions of this chapter and the provisions of Section B3.6.

1.

Definitions of Parameters Ag = gross cross-sectional area of member, in.2 (mm2) B = overall width of rectangular HSS member, measured 90° to the plane of the connection, in. (mm) Bp = width of plate, measured 90° to the plane of the connection, in. (mm) D = outside diameter of round HSS, in. (mm) Fc = available stress, ksi (MPa) = Fy for LRFD; 0.60Fy for ASD Fy = specified minimum yield stress of HSS member material, ksi (MPa) Fyp = specified minimum yield stress of plate material, ksi (MPa) Fu = specified minimum tensile strength of HSS member material, ksi (MPa) H = overall height of rectangular HSS member, measured in the plane of the connection, in. (mm) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

Sect. K2.]

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16.1–141

S = elastic section modulus of member, in.3 (mm3) lb = bearing length of the load, measured parallel to the axis of the HSS member (or measured across the width of the HSS in the case of loaded cap plates), in. (mm) t = design wall thickness of HSS member, in. (mm) tp = thickness of plate, in. (mm)

2.

Round HSS The available strength of connections with concentrated loads and within the limits in Table K1.1A shall be taken as shown in Table K1.1.

3.

Rectangular HSS The available strength of connections with concentrated loads and within the limits in Table K1.2A shall be taken as the lowest value of the applicable limit states shown in Table K1.2.

K2.

HSS-TO-HSS TRUSS CONNECTIONS The design strength, φPn, and the allowable strength, Pn /Ω, of connections shall be determined in accordance with the provisions of this chapter and the provisions of Section B3.6. HSS-to-HSS truss connections are defined as connections that consist of one or more branch members that are directly welded to a continuous chord that passes through the connection and shall be classified as follows: (a) When the punching load, Pr sinθ, in a branch member is equilibrated by beam shear in the chord member, the connection shall be classified as a T-connection when the branch is perpendicular to the chord, and a Y-connection otherwise. (b) When the punching load, Pr sinθ, in a branch member is essentially equilibrated (within 20%) by loads in other branch member(s) on the same side of the connection, the connection shall be classified as a K-connection. The relevant gap is between the primary branch members whose loads equilibrate. An N-connection can be considered as a type of K-connection. User Note: A K-connection with one branch perpendicular to the chord is often called an N-connection. (c) When the punching load, Pr sinθ, is transmitted through the chord member and is equilibrated by branch member(s) on the opposite side, the connection shall be classified as a cross-connection. (d) When a connection has more than two primary branch members, or branch members in more than one plane, the connection shall be classified as a general or multiplanar connection. When branch members transmit part of their load as K-connections and part of their load as T-, Y- or cross-connections, the adequacy of the connections shall be determined by interpolation on the proportion of the available strength of each in total. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–142

2/17/12

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HSS-TO-HSS TRUSS CONNECTIONS

[Sect. K2.

TABLE K1.1 Available Strengths of Plate-to-Round HSS Connections Plate Bending Connection Type

Connection Available Strength

Transverse Plate T- and Cross-Connections

Limit State: HSS Local Yielding Plate Axial Load ⎛ ⎜ 5.5 Rn sinθ = Fy t 2 ⎜ ⎜ 1− 0.81B p ⎜⎝ D

φ = 0.90 (LRFD) Longitudinal Plate T-, Yand Cross-Connections

⎞ ⎟ ⎟ Qf ⎟ ⎟⎠

In-Plane

Outof-Plane

—

Mn = 0.5BpRn

(K1-1)

Ω = 1.67 (ASD)

Limit State: HSS Plastification Plate Axial Load

⎛ l ⎞ Rn sinθ = 5.5Fy t 2 ⎜ 1+ 0.25 b ⎟ Qf (K1-2) Mn = 0.8IbRn D⎠ ⎝

φ = 0.90 (LRFD) Longitudinal Plate T-Connections

—

Ω = 1.67 (ASD)

Limit States: Plate Limit States and HSS Punching Shear Plate Shear Load For Rn , see Chapter J. Additionally, the following relationship shall be met: tp ≤

Cap Plate Connections

Fu t Fyp

—

—

—

—

(K1-3)

Limit State: Local Yielding of HSS Axial Load

(

)

Rn = 2Fy t 5t p + l b ≤ Fy A

φ = 1.00 (LRFD)

(K1-4)

Ω = 1.50 (ASD)

FUNCTIONS Qf = 1 for HSS (connecting surface) in tension = 1.0 − 0.3U (1 + U ) for HSS (connecting surface) in compression where Pro and Mro are determined on the side of the joint that Pro Mro has the lower compression stress. Pro and Mro refer to required U= + Fc Ag Fc S strengths in the HSS. Pro = Pu for LRFD; Pa for ASD. Mro = Mu for LRFD; Ma for ASD. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(K1-5) (K1-6)

AISC_PART 16_Spec.3_C:14th Ed.

Sect. K2.]

1/20/11

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HSS-TO-HSS TRUSS CONNECTIONS

TABLE K1.1A Limits of Applicability of Table K1.1 Plate load angle: HSS wall slenderness:

Width ratio: Material strength: Ductility:

θ D /t D /t D /t D /t 0.2 Fy Fy /Fu

≥ 30° ≤ 50 for T-connections under branch plate axial load or bending ≤ 40 for cross-connections under branch plate axial load or bending ≤ 0.11E /Fy under branch plate shear loading ≤ 0.11E /Fy for cap plate connections in compression < Bp /D ≤ 1.0 for transverse branch plate connections ≤ 52 ksi (360 MPa) ≤ 0.8 Note: ASTM A500 Grade C is acceptable.

TABLE K1.2 Available Strengths of Plate-to-Rectangular HSS Connections Connection Type

Connection Available Strength

Transverse Plate T- and Cross-Connections, Under Plate Axial Load

Limit State: Local Yielding of Plate, For All β Rn =

10 Fy tB p ≤ Fypt pB p Bt

φ = 0.95 (LRFD)

(K1-7)

Ω = 1.58 (ASD)

Limit State: HSS Shear Yielding (Punching), When 0.85B ≤ Bp ≤ B ⫺ 2t

(

Rn = 0.6Fy t 2t p + 2Bep φ = 0.95 (LRFD)

)

(K1-8)

Ω = 1.58 (ASD)

Limit State: Local Yielding of HSS Sidewalls, When β = 1.0 Rn = 2Fy t ( 5k + l b φ = 1.00 (LRFD)

)

(K1-9)

Ω = 1.50 (ASD)

Limit State: Local Crippling of HSS Sidewalls, When β = 1.0 and Plate is in Compression, for T-Connections ⎛ 3l b ⎞ Rn = 1.6t 2 ⎜ 1+ EFy Qf ⎝ H − 3t ⎠⎟ φ = 0.75 (LRFD)

(K1-10)

Ω = 2.00 (ASD)

Limit State: Local Crippling of HSS Sidewalls, When β = 1.0 and Plate is in Compression, for Cross-Connections ⎛ 48t 3 ⎞ Rn = ⎜ ⎟ EFy Qf ⎝ H − 3t ⎠ φ = 0.90 (LRFD) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Ω = 1.67 (ASD)

(K1-11)

AISC_PART 16_Spec.3_C:14th Ed.

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[Sect. K2.

TABLE K1.2. (continued) Available Strengths of Plate-to-Rectangular HSS Connections Connection Type

Connection Available Strength

Longitudinal Plate T-, Y- and CrossConnections, Under Plate Axial Load

Limit State: HSS Plastification

Rn sinθ =

Fy t 2 tp 1− B

⎛ 2l tp ⎞ b + 4 1− Qf ⎟ ⎜ ⎜⎝ B B ⎟⎠

φ = 1.00 (LRFD) Longitudinal Through Plate T- and Y-Connections, Under Plate Axial Load

Ω = 1.50 (ASD)

Limit State: HSS Wall Plastification

Rn sinθ =

2Fy t 2 tp 1− B

⎛ 2l tp ⎞ b + 4 1− Qf ⎟ ⎜ ⎜⎝ B B ⎟⎠

φ = 1.00 (LRFD) Longitudinal Plate T-Connections, Under Plate Shear Load

(K1-12)

(K1-13)

Ω = 1.50 (ASD)

Limit States: Plate Limit States and HSS Punching Shear For Rn , see Chapter J. Additionally, the following relationship shall be met:

tp ≤

Fu t Fyp

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(K1-3)

AISC_PART 16_Spec.3_C:14th Ed._

Sect. K2.]

2/17/12

12:09 PM

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16.1–145

TABLE K1.2 (continued) Available Strengths of Plate-to-Rectangular HSS Connections Connection Type

Connection Available Strength

Cap Plate Connections, under Axial Load

Limit State: Local Yielding of Sidewalls

(

)

)

(

Rn = 2Fy t 5t p + l b , when 5t p + l b < B

(K1-14a)

)

(

Rn = Fy A, when 5t p + l b ≥ B φ = 1.00 (LRFD)

(K1-14b)

Ω = 1.50 (ASD)

Limit State: Local Crippling of Sidewalls, When Plate is in Compression 1.5 ⎤ ⎡ tp 6l ⎛ t ⎞ Rn = 1.6t 2 ⎢1+ b ⎜ ⎟ ⎥ EFy , wh hen 5t p + l b < B (K1-15) ⎢ B ⎝ tp ⎠ ⎥ t ⎣ ⎦

(

φ = 0.75 (LRFD)

)

Ω = 2.00 (ASD)

FUNCTIONS Qf = 1 for HSS (connecting surface) in tension = 1.3 − 0.4

U ≤ 1.0 for HSS (connecting surface) in compression, for transverse β plate connections

= 1− U 2 for HSS (connecting surface) in compression, for longitudinal plate and longitudinal through plate connections

U

=

Bep =

k

Pro M ro where Pro and Mro are determined on the side of the joint that has + , the lower compression stress. Pro and Mro refer to required Fc Ag Fc S strengths in the HSS. Pro = Pu for LRFD; Pa for ASD. Mro = Mu for LRFD; Ma for ASD. 10B p ≤ Bp Bt

(K1-16)

(K1-17)

(K1-6)

(K1-18)

= outside corner radius of HSS ≥ 1.5 t

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–146

1/20/11

8:01 AM

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[Sect. K2.

TABLE K1.2A Limits of Applicability of Table K1.2 Plate load angle: θ HSS wall slenderness: B /t or H /t

≥ 30° ≤ 35 for loaded wall, for transverse branch plate connections ≤ 40 for loaded wall, for longitudinal branch plate and through plate connections

B /t or H /t

(B − 3t ) t

Width ratio: Material strength: Ductility:

)

or (H − 3t t ≤ 1.40 E Fy for loaded wall, for branch plate shear loading ≤ 1.0 for transverse branch plate connections 0.25 ≤ Bp /B Fy ≤ 52 ksi (360 MPa) Fy /Fu ≤ 0.8 Note: ASTM A500 Grade C is acceptable.

For the purposes of this Specification, the centerlines of branch members and chord members shall lie in a common plane. Rectangular HSS connections are further limited to have all members oriented with walls parallel to the plane. For trusses that are made with HSS that are connected by welding branch members to chord members, eccentricities within the limits of applicability are permitted without consideration of the resulting moments for the design of the connection.

1.

Definitions of Parameters Ag = gross cross-sectional area of member, in.2 (mm2) B = overall width of rectangular HSS main member, measured 90° to the plane of the connection, in. (mm) Bb = overall width of rectangular HSS branch member, measured 90° to the plane of the connection, in. (mm) D = outside diameter of round HSS main member, in. (mm) Db = outside diameter of round HSS branch member, in. (mm) Fc = available stress in chord, ksi (MPa) = Fy for LRFD; 0.60Fy for ASD Fy = specified minimum yield stress of HSS main member material, ksi (MPa) Fyb = specified minimum yield stress of HSS branch member material, ksi (MPa) Fu = specified minimum tensile strength of HSS material, ksi (MPa) H = overall height of rectangular HSS main member, measured in the plane of the connection, in. (mm) Hb = overall height of rectangular HSS branch member, measured in the plane of the connection, in. (mm) Ov = lov /lp × 100, % S = elastic section modulus of member, in.3 (mm3) e = eccentricity in a truss connection, positive being away from the branches, in. (mm) g = gap between toes of branch members in a gapped K-connection, neglecting the welds, in. (mm) lb = Hb /sinθ, in. (mm) lov = overlap length measured along the connecting face of the chord beneath the two branches, in. (mm) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

Sect. K3.]

lp t tb β

βeff γ

η

θ ζ

2.

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= projected length of the overlapping branch on the chord, in. (mm) = design wall thickness of HSS main member, in. (mm) = design wall thickness of HSS branch member, in. (mm) = width ratio; the ratio of branch diameter to chord diameter = Db /D for round HSS; the ratio of overall branch width to chord width = Bb /B for rectangular HSS = effective width ratio; the sum of the perimeters of the two branch members in a K-connection divided by eight times the chord width = chord slenderness ratio; the ratio of one-half the diameter to the wall thickness = D/2t for round HSS; the ratio of one-half the width to wall thickness = B/2t for rectangular HSS = load length parameter, applicable only to rectangular HSS; the ratio of the length of contact of the branch with the chord in the plane of the connection to the chord width = lb /B = acute angle between the branch and chord (degrees) = gap ratio; the ratio of the gap between the branches of a gapped K-connection to the width of the chord = g/B for rectangular HSS

Round HSS The available strength of HSS-to-HSS truss connections within the limits in Table K2.1A shall be taken as the lowest value of the applicable limit states shown in Table K2.1.

3.

Rectangular HSS The available strength of HSS-to-HSS truss connections within the limits in Table K2.2A shall be taken as the lowest value of the applicable limit states shown in Table K2.2.

K3. HSS-TO-HSS MOMENT CONNECTIONS The design strength, φMn, and the allowable strength, Mn /Ω, of connections shall be determined in accordance with the provisions of this chapter and the provisions of Section B3.6. HSS-to-HSS moment connections are defined as connections that consist of one or two branch members that are directly welded to a continuous chord that passes through the connection, with the branch or branches loaded by bending moments. A connection shall be classified as: (a) A T-connection when there is one branch and it is perpendicular to the chord and as a Y-connection when there is one branch but not perpendicular to the chord (b) A cross-connection when there is a branch on each (opposite) side of the chord For the purposes of this Specification, the centerlines of the branch member(s) and the chord member shall lie in a common plane.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–148

1/20/11

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[Sect. K3.

TABLE K2.1 Available Strengths of Round HSS-to-HSS Truss Connections Connection Type

Connection Available Axial Strength

General Check For T-, Y-, Cross- and K-Connections With Gap, When Db (tens/comp) < (D ⫺ 2t)

Limit State: Shear Yielding (Punching) ⎛ 1+ sin θ ⎞ Pn = 0 . 6Fy t π Db ⎜ ⎟ ⎝ 2sin2θ ⎠ φ = 0.95 (LRFD)

T- and Y-Connections

(K2-1)

Ω = 1.58 (ASD)

Limit State: Chord Plastification

)

(

Pn sinθ = Fy t 2 3 . 1+ 15 . 6β 2 γ 0.2Qf

φ = 0.90 (LRFD) Cross-Connections

(K2-2)

Ω = 1.67 (ASD)

Limit State: Chord Plastification

⎛ 5 .7 ⎞ Pn sinθ = Fy t 2 ⎜ Qf ⎝ 1− 0 . 81β ⎟⎠

φ = 0.90 (LRFD) K-Connections With Gap or Overlap

(K2-3)

Ω = 1.67 (ASD)

Limit State: Chord Plastification ⎛

(Pn sinθ)compression branch = Fy t 2 ⎜⎝ 2.0 + 11.33

Db comp ⎞ Q g Qf D ⎟⎠

(K2-4)

(Pn sinθ)tension branch = (Pn sinθ)compression branch φ = 0.90 (LRFD)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Ω = 1.67 (ASD)

(K2-5)

AISC_PART 16_Spec.3_C_14th Ed._February 25, 2013 14-11-10 11:51 AM Page 149

Sect. K3.]

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HSS-TO-HSS MOMENT CONNECTIONS

16.1–149

TABLE K2.1 (continued) Available Strengths of Round HSS-to-HSS Truss Connections FUNCTIONS Qf = 1 for chord (connecting surface) in tension ⫽ 1.0 ⫺ 0.3U (1 ⫹ U ) for HSS (connecting surface) in compression U =

Pro M ro where Pro and Mro are determined on the side of the joint that has + , the lower compression stress. Pro and Mro refer to required Fc Ag Fc S strengths in the HSS. Pro = Pu for LRFD; Pa for ASD. Mro = Mu for LRFD; Ma for ASD.

⎡ ⎤ ⎢ ⎥ 1.2 0.024 γ ⎥ Q g = γ 0.2 ⎢1+ ⎢ ⎥ ⎛ 0.5g ⎞ − 1.33⎟ + 1⎥ ⎢ exp ⎜ t ⎝ ⎠ ⎢⎣ ⎥⎦ [a]

(K1-5a) (K1-5b)

(K1-6)

[a]

(K2-6)

Note that exp(x) is equal to ex, where e = 2.71828 is the base of the natural logarithm.

TABLE K2.1A Limits of Applicability of Table K2.1 Joint eccentricity: Branch angle: Chord wall slenderness:

≤ e/D ≤ 0.25 for K-connections ≥ 30° ≤ 50 for T-, Y- and K-connections ≤ 40 for cross-connections ≤ 50 for tension branch ≤ 0.05E /Fyb for compression branch < Db /D ≤ 1.0 for T-, Y-, cross- and overlapped K-connections 0.4 ≤ Db /D ≤ 1.0 for gapped K-connections g ≥ tb comp + tb tens for gapped K-connections 25% ≤ Ov ≤ 100% for overlapped K-connections tb overlapping ≤ tb overlapped for branches in overlapped K-connections Fy and Fyb ≤ 52 ksi (360 MPa) Fy /Fu and Fyb /Fub ≤ 0.8 Note: ASTM A500 Grade C is acceptable.

-0.55 θ D/t D/t Branch wall slenderness: Db /tb Db /tb Width ratio: 0.2

Gap: Overlap: Branch thickness: Material strength: Ductility:

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

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HSS-TO-HSS MOMENT CONNECTIONS

[Sect. K3.

TABLE K2.2 Available Strengths of Rectangular HSS-to-HSS Truss Connections Connection Type

Connection Available Axial Strength

T-, Y- and Cross-Connections

Limit State: Chord Wall Plastification, When β ≤ 0.85 ⎡ 2η 4 ⎤ ⎥ Qf Pn sinθ = Fy t 2 ⎢ + 1 β − ⎢⎣ ( 1− β ⎥⎦

)

φ = 1.00 (LRFD)

(K2-7)

Ω = 1.50 (ASD)

Limit State: Shear Yielding (Punching), When 0.85 < β ≤ 1− 1 γ or B t < 10

(

Pn sinθ = 0.6Fy tB 2 η + 2βeop φ = 0.95 (LRFD)

)

(K2-8)

Ω = 1.58 (ASD)

Limit State: Local Yielding of Chord Sidewalls, When β = 1.0 Pn sinθ = 2Fy t ( 5k + l b φ = 1.00 (LRFD) Case for checking limit state of shear of chord side walls

)

(K2-9)

Ω = 1.50 (ASD)

Limit State: Local Crippling of Chord Sidewalls, When β = 1.0 and Branch is in Compression, for T- or Y-Connections ⎛ 3l b ⎞ Pn sinθ = 1.6t 2 ⎜ 1+ EFy Qf ⎝ H − 3t ⎟⎠ φ = 0.75 (LRFD)

(K2-10)

Ω = 2.00 (ASD)

Limit State: Local Crippling of Chord Sidewalls, When β = 1.0 and Branches are in Compression, for Cross-Connections ⎛ 48t 3 ⎞ Pn sinθ = ⎜ ⎟ EFy Qf ⎝ H − 3t ⎠ φ = 0.90 (LRFD)

(K2-11)

Ω = 1.67 (ASD)

Limit State: Local Yielding of Branch/Branches Due to Uneven Load Distribution, When β > 0.85 Pn = Fybt b ( 2H b + 2beoi − 4t b φ = 0.95 (LRFD)

)

(K2-12)

Ω = 1.58 (ASD)

where beoi =

10 Bt

⎛ Fy t ⎞ ⎜ ⎟ Bb ≤ Bb ⎝ Fybt b ⎠

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(K2-13)

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HSS-TO-HSS MOMENT CONNECTIONS

TABLE K2.2 (continued) Available Strengths of Rectangular HSS-to-HSS Truss Connections Connection Type

Connection Available Axial Strength

T-, Y- and Cross-Connections

Limit State: Shear of Chord Sidewalls For Cross-Connections With θ < 90° and Where a Projected Gap is Created (See Figure). Determine Pn sinθ in accordance with Section G5.

Gapped K-Connections

Limit State: Chord Wall Plastification, for All β

)

(

Pn sinθ = Fy t 2 9.8βeff γ 0.5 Qf φ = 0.90 (LRFD)

(K2-14)

Ω = 1.67 (ASD)

Limit State: Shear Yielding (Punching), when Bb < B ⫺ 2t Do not check for square branches.

(

Pn sinθ = 0.6Fy tB 2 η + β + βeop φ = 0.95 (LRFD)

)

(K2-15)

Ω = 1.58 (ASD)

Limit State: Shear of Chord Sidewalls, in the Gap Region Determine Pn sinθ in accordance with Section G5. Do not check for square chords. Limit State: Local Yielding of Branch/Branches Due to Uneven Load Distribution. Do not check for square branches or if B /t ≥ 15. Pn = Fybt b ( 2H b + Bb + beoi − 4t b φ = 0.95 (LRFD)

)

(K2-16)

Ω = 1.58 (ASD)

where beoi =

10 ⎛ Fy t ⎞ ⎜ ⎟ Bb ≤ Bb B t ⎝ Fybt b ⎠

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(K2-13)

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HSS-TO-HSS MOMENT CONNECTIONS

[Sect. K3.

TABLE K2.2 (continued) Available Strengths of Rectangular HSS-to-HSS Truss Connections Connection Type

Connection Available Axial Strength

Overlapped K-Connections

Limit State: Local Yielding of Branch/Branches Due to Uneven Load Distribution φ = 0.95 (LRFD)

Ω = 1.58 (ASD)

When 25% ≤ Ov < 50%: ⎡O ⎤ Pn,i = Fybi t bi ⎢ v ( 2H bi − 4t bi + beoi + beov ⎥ 50 ⎣ ⎦

)

(K2-17)

When 50% ≤ Ov < 80%:

(

Pn,i = Fybi t bi 2H bi − 4t bi + beoi + beov Note that the force arrows shown for overlapped K-connections may be reversed; i and j control member identification.

)

(K2-18)

)

(K2-19)

When 80% ≤ Ov < 100%:

(

Pn,i = Fybi t bi 2H bi − 4t bi + Bbi + beov beoi =

beov =

10 Bt

⎛ Fy t ⎞ ⎜ ⎟ Bbi ≤ Bbi ⎝ Fybi t bi ⎠

10 ⎛ Fybj t bj ⎜ Bbj t bj ⎝ Fybi t bi

⎞ ⎟ Bbi ≤ Bbi ⎠

(K2-20)

(K2-21)

Subscript i refers to the overlapping branch Subscript j refers to the overlapped branch ⎛ Fybj Abj ⎞ Pn,j = Pn,i ⎜ ⎟ ⎝ Fybi Abi ⎠

(K2-22)

FUNCTIONS Qf = 1 for chord (connecting surface) in tension

(K1-5a)

U ≤ 1 for chord (connecting surface) in compression, for T-, Y- and β cross-connections U = 1.3 − 0.4 ≤ 1.0 for chord (connecting surface) in compression, for gapped βeff K-connections = 1.3 − 0.4

U

=

where Pro and Mro are determined on the side of the joint that has Pro M ro + , the higher compression stress. Pro and Mro refer to required Fc Ag Fc S strengths in the HSS. Pro = Pu for LRFD; Pa for ASD. Mro = Mu for LRFD; Ma for ASD.

βeff = ⎡(Bb + H b ⎢⎣ βeop =

)compression branch + (Bb + Hb )tensioon branch ⎤⎥⎦

4B

5β ≤β γ

(K1-16) (K2-23)

(K1-6)

(K2-24) (K2-25)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C_14th Ed._ 22/02/12 2:54 PM Page 153

Sect. K3.]

HSS-TO-HSS MOMENT CONNECTIONS

16.1–153

TABLE K2.2A Limits of Applicability of Table K2.2 Joint eccentricity: -0.55 Branch angle: θ Chord wall slenderness: B /t and H /t

B /t H /t Branch wall slenderness: Bb /tb and H b /tb

≤ e /H ≤ 0.25 for K-connections ≥ 30° ≤ 35 for gapped K-connections and T-, Yand cross-connections ≤ 30 for overlapped K-connections ≤ 35 for overlapped K-connections ≤ 35 for tension branch ≤ 1.25

E for compression branch of gapped Fyb K-, T-, Y- and cross-connections

≤ 35 for compression branch of gapped K-, T-, Yand cross-connections ≤ 1.1 Width ratio:

Bb /B and H b /B

Aspect ratio: Overlap: Branch width ratio:

0.5 25% Bbi /Bbj

Branch thickness ratio:

tbi /tbj

Material strength: Ductility:

Fy and Fyb Fy /Fu and Fyb /Fub

E Fyb

for compression branch of overlapped K-connections

≥ 0.25 for T-, Y- cross- and overlapped K-connections ≤ H b /Bb ≤ 2.0 and 0.5 ≤ H /B ≤ 2.0 ≤ Ov ≤ 100% for overlapped K-connections ≥ 0.75 for overlapped K-connections, where subscript i refers to the overlapping branch and subscript j refers to the overlapped branch ≤ 1.0 for overlapped K-connections, where subscript i refers to the overlapping branch and subscript j refers to the overlapped branch ≤ 52 ksi (360 MPa) ≤ 0.8 Note: ASTM A500 Grade C is acceptable.

ADDITIONAL LIMITS FOR GAPPED K-CONNECTIONS

Width ratio:

Gap ratio: Gap: Branch size:

Bb H and b B B βeff ζ = g /B g smaller Bb

≥ 0.1+ ≥ ≥ ≥ ≥

γ 50

0.35 0.5 (1 ⫺ βeff ) tb compression branch + tb tension branch 0.63 (larger Bb ), if both branches are square

Note: Maximum gap size will be controlled by the e /H limit. If gap is large, treat as two Y-connections.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–154

1.

1/20/11

8:01 AM

Page 154

HSS-TO-HSS MOMENT CONNECTIONS

[Sect. K3.

Definitions of Parameters Ag = gross cross-sectional area of member, in.2 (mm2) B = overall width of rectangular HSS main member, measured 90 ° to the plane of the connection, in. (mm) Bb = overall width of rectangular HSS branch member, measured 90 ° to the plane of the connection, in. (mm) D = outside diameter of round HSS main member, in. (mm) Db = outside diameter of round HSS branch member, in. (mm) Fc = available stress, ksi (MPa) = Fy for LRFD; 0.60Fy for ASD Fy = specified minimum yield stress of HSS main member material, ksi (MPa) Fyb = specified minimum yield stress of HSS branch member material, ksi (MPa) Fu = specified minimum tensile strength of HSS member material, ksi (MPa) H = overall height of rectangular HSS main member, measured in the plane of the connection, in. (mm) Hb = overall height of rectangular HSS branch member, measured in the plane of the connection, in. (mm) S = elastic section modulus of member, in.3 (mm3) Zb = Plastic section modulus of branch about the axis of bending, in.3 (mm3) t = design wall thickness of HSS main member, in. (mm) tb = design wall thickness of HSS branch member, in. (mm) β = width ratio = Db/D for round HSS; ratio of branch diameter to chord diameter = Bb/B for rectangular HSS; ratio of overall branch width to chord width γ = chord slenderness ratio = D/2t for round HSS; ratio of one-half the diameter to the wall thickness = B/2t for rectangular HSS; ratio of one-half the width to the wall thickness η = load length parameter, applicable only to rectangular HSS = lb/B; the ratio of the length of contact of the branch with the chord in the plane of the connection to the chord width, where lb=Hb /sin θ θ = acute angle between the branch and chord (degrees)

2.

Round HSS The available strength of moment connections within the limits of Table K3.1A shall be taken as the lowest value of the applicable limit states shown in Table K3.1.

3.

Rectangular HSS The available strength of moment connections within the limits of Table K3.2A shall be taken as the lowest value of the applicable limit states shown in Table K3.2.

K4.

WELDS OF PLATES AND BRANCHES TO RECTANGULAR HSS The design strength, φRn, φMn and φPn, and the allowable strength, Rn /Ω, Mn /Ω and Pn /Ω, of connections shall be determined in accordance with the provisions of this chapter and the provisions of Section B3.6.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

Sect. K4.]

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WELDS OF PLATES AND BRANCHES TO RECTANGULAR HSS

16.1–155

TABLE K3.1 Available Strengths of Round HSS-to-HSS Moment Connections Connection Type

Connection Available Flexural Strength

Branch(es) under In-Plane Bending T-, Y- and Cross-Connections

Limit State: Chord Plastification M n sinθ = 5.39Fy t 2 γ 0.5βDbQf φ = 0.90 (LRFD)

(K3-1)

Ω = 1.67 (ASD)

Limit State: Shear Yielding (Punching), When Db < (D ⫺ 2t ) ⎛ 1+ 3sinθ ⎞ M n = 0.6Fy tDb2 ⎜ ⎟ ⎝ 4 sin2θ ⎠ φ = 0.95 (LRFD) Branch(es) under Out-of-Plane Bending T-, Y- and Cross-Connections

(K3-2)

Ω = 1.58 (ASD)

Limit State: Chord Plastification ⎛ 3.0 ⎞ M n sinθ = Fy t 2Db ⎜ Qf ⎝ 1− 0.81β ⎟⎠ φ = 0.90 (LRFD)

(K3-3)

Ω = 1.67 (ASD)

Limit State: Shear Yielding (Punching), When Db < (D ⫺ 2t ) ⎛ 3 + sinθ ⎞ M n = 0.6Fy tDb2 ⎜ ⎟ ⎝ 4 sin2θ ⎠ φ = 0.95 (LRFD)

(K3-4)

Ω = 1.58 (ASD)

For T-, Y- and cross-connections, with branch(es) under combined axial load, in-plane bending and out-of-plane bending, or any combination of these load effects: 2

⎛ M r −op ⎞ Pr ⎛ M r −ip ⎞ +⎜ ⎟ +⎜ ⎟ ≤ 1.0 Pc ⎝ M c-ip ⎠ ⎝ M c-op ⎠

(K3-5)

Mc-ip = φMn = design flexural strength for in-plane bending from Table K3.1, kip-in. (N-mm) = Mn /Ω = allowable flexural strength for in-plane bending from Table K3.1, kip-in. (N-mm) Mc-op = φMn = design flexural strength for out-of-plane bending from Table K3.1, kip-in. (N-mm) = Mn /Ω = allowable flexural strength for out-of-plane bending from Table K3.1, kip-in. (N-mm) Mr-ip = required flexural strength for in-plane bending, using LRFD or ASD load combinations, as applicable, kip-in. (N-mm) Mr-op = required flexural strength for out-of-plane bending, using LRFD or ASD load combinations, as applicable, kip-in. (N-mm) Pc = φPn = design axial strength from Table K2.1, kips (N) = Pn /Ω = allowable axial strength from Table K2.1, kips (N) Pr = required axial strength using LRFD or ASD load combinations, as applicable, kips (N) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C_14th Ed._February 12, 2013 12/02/13 9:48 AM Page 156

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WELDS OF PLATES AND BRANCHES TO RECTANGULAR HSS

[Sect. K4.

TABLE K3.1 (continued) Available Strengths of Round HSS-to-HSS Moment Connections FUNCTIONS Qf = 1 for chord (connecting surface) in tension = 1.0 ⫺ 0.3U (1 + U ) for HSS (connecting surface) in compression

U =

where Pro and Mro are determined on the side of the joint that has Pro M ro + , the lower compression stress. Pro and Mro refer to required Fc Ag Fc S strengths in the HSS. Pro = Pu for LRFD; Pa for ASD. Mro = Mu for LRFD; Ma for ASD.

(K1-5)

(K1-6)

TABLE K3.1A Limits of Applicability of Table K3.1 Branch angle: θ Chord wall slenderness: D/t D/t Branch wall slenderness: Db /t b Db /t b Width ratio: 0.2 Fy and Fyb Material strength: Ductility: Fy /Fu and Fyb /Fub

≥ ≤ ≤ ≤ ≤ < ≤ ≤

30° 50 for T- and Y-connections 40 for cross-connections 50 0.05E /Fyb Db /D ≤ 1.0 52 ksi (360 MPa) 0.8 Note: ASTM A500 Grade C is acceptable.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C_14th Ed._February 12, 2013 12/02/13 9:57 AM Page 157

Sect. K4.]

WELDS OF PLATES AND BRANCHES TO RECTANGULAR HSS

16.1–157

TABLE K3.2 Available Strengths of Rectangular HSS-to-HSS Moment Connections Connection Type

Connection Available Flexural Strength

Branch(es) under In-Plane Bending T- and Cross-Connections

Limit State: Chord Wall Plastification, When β ≤ 0.85 ⎡ 1 η 2 M n = Fy t 2H b ⎢ + + ⎢⎣ 2 η 1− β ( 1− β φ = 1.00 (LRFD)

)

⎤ ⎥ Qf ⎥⎦

(K3-6)

Ω = 1.50 (ASD)

Limit State: Sidewall Local Yielding, When β > 0.85

Mn = 0.5 F y*t (Hb + 5t )2 φ = 1.00 (LRFD)

(K3-7)

Ω = 1.50 (ASD)

Limit State: Local Yielding of Branch/Branches Due to Uneven Load Distribution, When β > 0.85 ⎡ ⎛ b M n = Fyb ⎢ Z b − ⎜ 1− eoi Bb ⎝ ⎢⎣ φ = 0.95 (LRFD) Branch(es) under Out-of-Plane Bending T- and Cross-Connections

⎤ ⎞ ⎟⎠ BbH bt b ⎥ ⎥⎦

(K3-8)

Ω = 1.58 (ASD)

Limit State: Chord Wall Plastification, When β ≤ 0.85

)

⎡ 0.5H (1+ β 2BBb (1+ β b M n = Fy t 2 ⎢ + ⎢ (1− β (1− β ⎣

)

φ = 1.00 (LRFD)

)

) ⎥⎤Q ⎥ ⎦

f

(K3-9)

Ω = 1.50 (ASD)

Limit State: Sidewall Local Yielding, When β > 0.85

Mn = F y*t (B − t )(Hb + 5t ) φ = 1.00 (LRFD)

(K3-10)

Ω = 1.50 (ASD)

Limit State: Local Yielding of Branch/Branches Due to Uneven Load Distribution, When β > 0.85 2 ⎡ ⎤ ⎛ b ⎞ M n = Fyb ⎢ Z b − 0.5 ⎜ 1− eoi ⎟ Bb2 t b ⎥ ⎢ ⎥ Bb ⎠ ⎝ ⎣ ⎦

φ = 0.95 (LRFD)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Ω = 1.58 (ASD)

(K3-11)

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WELDS OF PLATES AND BRANCHES TO RECTANGULAR HSS

[Sect. K4.

TABLE K3.2 (continued) Available Strengths of Rectangular HSS-to-HSS Moment Connections Connection Type

Connection Available Flexural Strength

Branch(es) under Out-of-Plane Bending T- and Cross-Connections (continued)

Limit State: Chord Distortional Failure, for T-Connections and Unbalanced Cross-Connections

)

M n = 2Fy t ⎡⎢H bt + BHt (B + H ⎤⎥ ⎣ ⎦ φ = 1.00 (LRFD)

(K3-12)

Ω = 1.50 (ASD)

For T- and cross-connections, with branch(es) under combined axial load, in-plane bending and out-of-plane bending, or any combination of these load effects: Pr ⎛ M r -ip ⎞ ⎛ M r -op ⎞ +⎜ ⎟ +⎜ ⎟ ≤ 1 .0 Pc ⎝ M c-ip ⎠ ⎝ M c-op ⎠

(K3-13)

Mc-ip = φMn = design flexural strength for in-plane bending from Table K3.2, kip-in. (N-mm) = Mn /Ω = allowable flexural strength for in-plane bending from Table K3.2, kip-in. (N-mm) Mc-op = φMn = design flexural strength for out-of-plane bending from Table K3.2, kip-in. (N-mm) = Mn /Ω = allowable flexural strength for out-of-plane bending from Table K3.2, kip-in. (N-mm) Mr-ip = required flexural strength for in-plane bending, using LRFD or ASD load combinations, as applicable, kip-in. (N-mm) Mr-op = required flexural strength for out-of-plane bending, using LRFD or ASD load combinations, as applicable, kip-in. (N-mm) Pc = φPn = design axial strength from Table K2.2, kips (N) = Pn /Ω = allowable axial strength from Table K2.2, kips (N) Pr = required axial strength using LRFD or ASD load combinations, as applicable, kips (N) FUNCTIONS Qf = 1 for chord (connecting surface) in tension = 1.3 − 0.4

U

=

U ≤ 1.0 for chord (connecting surface) in compression β

where Pro and Mro are determined on the side of the joint that Pro M ro + , has the lower compression stress. Pro and Mro refer to required Fc Ag Fc S strengths in the HSS. Pro = Pu for LRFD; Pa for ASD. Mro = Mu for LRFD; Ma for ASD.

(K1-15) (K1-16)

(K1-6)

F y* = Fy for T-connections and = 0.8Fy for cross-connections beoi =

10 ⎛ Fy t ⎞ ⎜ ⎟ Bb ≤ Bb B / t ⎝ Fybt b ⎠

(K2-13)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

Sect. K4.]

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16.1–159

TABLE K3.2A Limits of Applicability of Table K3.2 Branch angle: θ Chord wall slenderness: B /t and H /t Branch wall slenderness: B b /tb and Hb /tb

≅ 90° ≤ 35 ≤ 35 ≤ 1.25

B b /B 0.5 Fy and Fyb Fy /Fu and Fyb /Fub

Width ratio: Aspect ratio: Material strength: Ductility:

≥ ≤ ≤ ≤

E Fyb

0.25 Hb /Bb ≤ 2.0 and 0.5 ≤ H/B ≤ 2.0 52 ksi (360 MPa) 0.8 Note: ASTM A500 Grade C is acceptable.

The available strength of branch connections shall be determined for the limit state of nonuniformity of load transfer along the line of weld, due to differences in relative stiffness of HSS walls in HSS-to-HSS connections and between elements in transverse plate-to-HSS connections, as follows: Rn or Pn = Fnwtwle

(K4-1)

Mn-ip = FnwSip

(K4-2)

Mn-op = FnwSop

(K4-3)

For interaction, see Equation K3-13. (a) For fillet welds φ = 0.75 (LRFD)

Ω = 2.00 (ASD)

(b) For partial-joint-penetration groove welds φ = 0.80 (LRFD)

Ω = 1.88 (ASD)

where Fnw = nominal stress of weld metal (Chapter J) with no increase in strength due to directionality of load, ksi (MPa) Sip = effective elastic section modulus of welds for in-plane bending (Table K4.1), in.3 (mm3) Sop = effective elastic section modulus of welds for out-of-plane bending (Table K4.1), in.3 (mm3) le = total effective weld length of groove and fillet welds to rectangular HSS for weld strength calculations, in. (mm) tw = smallest effective weld throat around the perimeter of branch or plate, in. (mm)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

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WELDS OF PLATES AND BRANCHES TO RECTANGULAR HSS

[Sect. K4.

TABLE K4.1 Effective Weld Properties for Connections to Rectangular HSS Connection Type

Connection Weld Strength

Transverse Plate T- and CrossConnections Under Plate Axial Load

Effective Weld Properties ⎛ 10 ⎞ ⎛ Fy t ⎞ le = 2 ⎜ ⎜ ⎟ B p ≤ 2B p ⎝ B t ⎟⎠ ⎝ Fypt p ⎠

(K4-4)

where le = total effective weld length for welds on both sides of the transverse plate T-, Y- and Cross-Connections Under Branch Axial Load or Bending

Effective Weld Properties le =

2H b + 2beoi sinθ

(K4-5)

2

Sip =

tw ⎛ H b ⎞ ⎛ H ⎞ + tw beoi ⎜ b ⎟ ⎝ sin θ ⎠ 3 ⎜⎝ sin θ ⎟⎠

(tw 3)(Bb − beoi ) t ⎛ H ⎞ Sop = tw ⎜ b ⎟ Bb + w Bb2 − ⎝ sinθ ⎠ 3 Bb

( )

beoi =

10 ⎛ Fy t ⎞ ⎜ ⎟ Bb ≤ Bb B t ⎝ Fybt b ⎠

(K4-6) 3

(K4-7)

(K2-13)

When β > 0.85 or θ > 50°, beoi /2 shall not exceed 2t.

Gapped K-Connections Under Branch Axial Load

Effective Weld Properties When θ ≤ 50°: le =

2 (H b − 1.2t b sinθ

) + 2 (B

b

− 1.2t b

)

(K4-8)

When θ ≥ 60°: le =

2 (H b − 1.2t b sinθ

) + (B

b

− 1.2t b

)

(K4-9)

When 50° < θ < 60°, linear interpolation shall be used to determine le .

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

Sect. K4.]

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WELDS OF PLATES AND BRANCHES TO RECTANGULAR HSS

TABLE K4.1 (continued) Effective Weld Properties for Connections to Rectangular HSS Connection Type

Connection Weld Strength

Overlapped K-Connections under Branch Axial Load

Overlapping Member Effective Weld Properties (all dimensions are for the overlapping branch, i ) When 25% ≤ Ov < 50%:

l e,i =

⎡ 2Ov ⎢⎛ O ⎞ ⎛ H bi 1− v 50 ⎢⎜⎝ 100 ⎟⎠ ⎜⎝ sinθi ⎣

⎞ Ov ⎛ H bi ⎟⎠ + 100 ⎜⎜ sin θ + θ i j ⎝

(

)

⎞⎤ ⎟ ⎥+ beoi + beov ⎟⎠ ⎥ ⎦

(K4-10)

When 50% ≤ Ov < 80%:

Note that the force arrows shown for overlapped K-connections may be reversed; i and j control member identification

⎡⎛ O ⎞⎛ H ⎞ O ⎛ H bi l e,i = 2 ⎢⎜ 1− v ⎟ ⎜ bi ⎟ + v ⎜ ⎢⎝ 100 ⎠ ⎝ sinθi ⎠ 100 ⎜⎝ sin θi + θ j ⎣

(

)

⎞⎤ ⎟ ⎥+ beoi + beov ⎟⎠ ⎥ ⎦

(K4-11)

When 80% ≤ Ov ≤ 100%: ⎡⎛ O ⎞⎛ H l e,i = 2 ⎢⎜ 1− v ⎟ ⎜ bi ⎢⎝ 100 ⎠ ⎝ sinθi ⎣

beoi =

beov =

⎞⎤ ⎞ Ov ⎛ H bi ⎥ ⎟⎠ + 100 ⎜⎜ sin θ + θ ⎟⎟ ⎥+ Bbi + beov i j ⎠ ⎝ ⎦ (K4-12)

10 ⎛ Fy t ⎜ B t ⎝ Fybi t bi

(

⎞ ⎟ Bbi ≤ Bbi ⎠

10 ⎛ Fybj t bj ⎜ Bbj t bj ⎝ Fybi t bi

⎞ ⎟ Bbi ≤ Bbi ⎠

)

(K2-20)

(K2-21)

when Bbi /Bb > 0.85 or θi > 50°, beoi /2 shall not exceed 2t and when Bbi /Bbj > 0.85 or (180 ⫺ θi ⫺ θj ) > 50°, beov /2 shall not exceed 2t bj Subscript i refers to the overlapping branch Subscript j refers to the overlapped branch le,j =

beoj =

10 Bt

2H bj + 2beoj sinθ j

(K4-13)

⎛ Fy t ⎞ ⎜ ⎟ Bbj ≤ Bbj ⎝ Fybj t bj ⎠

(K4-14)

When Bbj /B > 0.85 or θj > 50°, le,j = 2 (Hbj ⫺ 1.2tbj )/sinθj

Specification for Structural Steel Buildings, June 22, 2010

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AISC_PART 16_Spec.3_C:14th Ed.

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WELDS OF PLATES AND BRANCHES TO RECTANGULAR HSS

[Sect. K4.

When an overlapped K-connection has been designed in accordance with Table K2.2 of this chapter, and the branch member component forces normal to the chord are 80% “balanced” (i.e., the branch member forces normal to the chord face differ by no more than 20%), the “hidden” weld under an overlapping branch may be omitted if the remaining welds to the overlapped branch everywhere develop the full capacity of the overlapped branch member walls. The weld checks in Table K4.1 are not required if the welds are capable of developing the full strength of the branch member wall along its entire perimeter (or a plate along its entire length). User Note: The approach used here to allow down-sizing of welds assumes a constant weld size around the full perimeter of the HSS branch. Special attention is required for equal width (or near-equal width) connections which combine partial-joint-penetration groove welds along the matched edges of the connection, with fillet welds generally across the main member face.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

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8:01 AM

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CHAPTER L DESIGN FOR SERVICEABILITY

This chapter addresses serviceability design requirements. The chapter is organized as follows: L1. L2. L3. L4. L5. L6. L7. L8.

L1.

General Provisions Camber Deflections Drift Vibration Wind-Induced Motion Expansion and Contraction Connection Slip

GENERAL PROVISIONS Serviceability is a state in which the function of a building, its appearance, maintainability, durability and comfort of its occupants are preserved under normal usage. Limiting values of structural behavior for serviceability (such as maximum deflections and accelerations) shall be chosen with due regard to the intended function of the structure. Serviceability shall be evaluated using appropriate load combinations for the serviceability limit states identified. User Note: Serviceability limit states, service loads, and appropriate load combinations for serviceability requirements can be found in ASCE/SEI 7, Appendix C and Commentary to Appendix C. The performance requirements for serviceability in this chapter are consistent with those requirements. Service loads, as stipulated herein, are those that act on the structure at an arbitrary point in time and are not usually taken as the nominal loads.

L2.

CAMBER Where camber is used to achieve proper position and location of the structure, the magnitude, direction and location of camber shall be specified in the structural drawings.

L3.

DEFLECTIONS Deflections in structural members and structural systems under appropriate service load combinations shall not impair the serviceability of the structure.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

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8:01 AM

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DEFLECTIONS

[Sect. L3.

User Note: Conditions to be considered include levelness of floors, alignment of structural members, integrity of building finishes, and other factors that affect the normal usage and function of the structure. For composite members, the additional deflections due to the shrinkage and creep of the concrete should be considered.

L4.

DRIFT Drift of a structure shall be evaluated under service loads to provide for serviceability of the structure, including the integrity of interior partitions and exterior cladding. Drift under strength load combinations shall not cause collision with adjacent structures or exceed the limiting values of such drifts that may be specified by the applicable building code.

L5.

VIBRATION The effect of vibration on the comfort of the occupants and the function of the structure shall be considered. The sources of vibration to be considered include pedestrian loading, vibrating machinery and others identified for the structure.

L6.

WIND-INDUCED MOTION The effect of wind-induced motion of buildings on the comfort of occupants shall be considered.

L7.

EXPANSION AND CONTRACTION The effects of thermal expansion and contraction of a building shall be considered. Damage to building cladding can cause water penetration and may lead to corrosion.

L8.

CONNECTION SLIP The effects of connection slip shall be included in the design where slip at bolted connections may cause deformations that impair the serviceability of the structure. Where appropriate, the connection shall be designed to preclude slip. User Note: For the design of slip-critical connections, see Sections J3.8 and J3.9. For more information on connection slip, refer to the RCSC Specification for Structural Joints Using High-Strength Bolts.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

8:01 AM

Page 165

16.1–165

CHAPTER M FABRICATION AND ERECTION

This chapter addresses requirements for shop drawings, fabrication, shop painting and erection. The chapter is organized as follows: M1. M2. M3. M4.

M1.

Shop and Erection Drawings Fabrication Shop Painting Erection

SHOP AND ERECTION DRAWINGS Shop and erection drawings are permitted to be prepared in stages. Shop drawings shall be prepared in advance of fabrication and give complete information necessary for the fabrication of the component parts of the structure, including the location, type and size of welds and bolts. Erection drawings shall be prepared in advance of erection and give information necessary for erection of the structure. Shop and erection drawings shall clearly distinguish between shop and field welds and bolts and shall clearly identify pretensioned and slip-critical high-strength bolted connections. Shop and erection drawings shall be made with due regard to speed and economy in fabrication and erection.

M2.

FABRICATION

1.

Cambering, Curving and Straightening Local application of heat or mechanical means is permitted to be used to introduce or correct camber, curvature and straightness. The temperature of heated areas shall not exceed 1,100 °F (593 °C) for ASTM A514/A514M and ASTM A852/A852M steel nor 1,200 °F (649 °C) for other steels.

2.

Thermal Cutting Thermally cut edges shall meet the requirements of AWS D1.1/D1.1M, subclauses 5.15.1.2, 5.15.4.3 and 5.15.4.4 with the exception that thermally cut free edges that will not be subject to fatigue shall be free of round-bottom gouges greater than 3/16 in. (5 mm) deep and sharp V-shaped notches. Gouges deeper than 3/16 in. (5 mm) and notches shall be removed by grinding or repaired by welding. Reentrant corners shall be formed with a curved transition. The radius need not exceed that required to fit the connection. The surface resulting from two straight torch cuts meeting at a point is not considered to be curved. Discontinuous corners are permitted where the material on both sides of the discontinuous reentrant corner are connected to a mating piece to prevent deformation and associated stress concentration at the corner. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

16.1–166

8:01 AM

Page 166

FABRICATION

[Sect. M2.

User Note: Reentrant corners with a radius of 1/2 to 3/8 in. (13 to 10 mm) are acceptable for statically loaded work. Where pieces need to fit tightly together, a discontinuous reentrant corner is acceptable if the pieces are connected close to the corner on both sides of the discontinuous corner. Slots in HSS for gussets may be made with semicircular ends or with curved corners. Square ends are acceptable provided the edge of the gusset is welded to the HSS. Weld access holes shall meet the geometrical requirements of Section J1.6. Beam copes and weld access holes in shapes that are to be galvanized shall be ground to bright metal. For shapes with a flange thickness not exceeding 2 in. (50 mm), the roughness of thermally cut surfaces of copes shall be no greater than a surface roughness value of 2,000 μin. (50 μm) as defined in ASME B46.1. For beam copes and weld access holes in which the curved part of the access hole is thermally cut in ASTM A6/A6M hot-rolled shapes with a flange thickness exceeding 2 in. (50 mm) and welded built-up shapes with material thickness greater than 2 in. (50 mm), a preheat temperature of not less than 150 °F (66 °C) shall be applied prior to thermal cutting. The thermally cut surface of access holes in ASTM A6/A6M hot-rolled shapes with a flange thickness exceeding 2 in. (50 mm) and built-up shapes with a material thickness greater than 2 in. (50 mm) shall be ground. User Note: The AWS Surface Roughness Guide for Oxygen Cutting (AWS C4.177) sample 2 may be used as a guide for evaluating the surface roughness of copes in shapes with flanges not exceeding 2 in. (50 mm) thick.

3.

Planing of Edges Planing or finishing of sheared or thermally cut edges of plates or shapes is not required unless specifically called for in the construction documents or included in a stipulated edge preparation for welding.

4.

Welded Construction The technique of welding, the workmanship, appearance, and quality of welds, and the methods used in correcting nonconforming work shall be in accordance with AWS D1.1/D1.1M except as modified in Section J2.

5.

Bolted Construction Parts of bolted members shall be pinned or bolted and rigidly held together during assembly. Use of a drift pin in bolt holes during assembly shall not distort the metal or enlarge the holes. Poor matching of holes shall be cause for rejection. Bolt holes shall comply with the provisions of the RCSC Specification for Structural Joints Using High-Strength Bolts, hereafter referred to as the RCSC Specification, Section 3.3 except that thermally cut holes are permitted with a surface roughness profile not exceeding 1,000 μin. (25 μm) as defined in ASME B46.1. Gouges shall not exceed a depth of 1/16 in. (2 mm). Water jet cut holes are also permitted.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

Sect. M2.]

8:01 AM

Page 167

FABRICATION

16.1–167

User Note: The AWS Surface Roughness Guide for Oxygen Cutting (AWS C4.177) sample 3 may be used as a guide for evaluating the surface roughness of thermally cut holes. Fully inserted finger shims, with a total thickness of not more than 1/4 in. (6 mm) within a joint, are permitted without changing the strength (based upon hole type) for the design of connections. The orientation of such shims is independent of the direction of application of the load. The use of high-strength bolts shall conform to the requirements of the RCSC Specification, except as modified in Section J3.

6.

Compression Joints Compression joints that depend on contact bearing as part of the splice strength shall have the bearing surfaces of individual fabricated pieces prepared by milling, sawing or other suitable means.

7.

Dimensional Tolerances Dimensional tolerances shall be in accordance with Chapter 6 of the AISC Code of Standard Practice for Steel Buildings and Bridges, hereafter referred to as the Code of Standard Practice.

8.

Finish of Column Bases Column bases and base plates shall be finished in accordance with the following requirements: (1) Steel bearing plates 2 in. (50 mm) or less in thickness are permitted without milling provided a satisfactory contact bearing is obtained. Steel bearing plates over 2 in. (50 mm) but not over 4 in. (100 mm) in thickness are permitted to be straightened by pressing or, if presses are not available, by milling for bearing surfaces, except as noted in subparagraphs 2 and 3 of this section, to obtain a satisfactory contact bearing. Steel bearing plates over 4 in. (100 mm) in thickness shall be milled for bearing surfaces, except as noted in subparagraphs 2 and 3 of this section. (2) Bottom surfaces of bearing plates and column bases that are grouted to ensure full bearing contact on foundations need not be milled. (3) Top surfaces of bearing plates need not be milled when complete-joint-penetration groove welds are provided between the column and the bearing plate.

9.

Holes for Anchor Rods Holes for anchor rods are permitted to be thermally cut in accordance with the provisions of Section M2.2.

10.

Drain Holes When water can collect inside HSS or box members, either during construction or during service, the member shall be sealed, provided with a drain hole at the base, or protected by other suitable means. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

16.1–168

11.

8:01 AM

Page 168

FABRICATION

[Sect. M2.

Requirements for Galvanized Members Members and parts to be galvanized shall be designed, detailed and fabricated to provide for flow and drainage of pickling fluids and zinc and to prevent pressure buildup in enclosed parts. User Note: See The Design of Products to be Hot-Dip Galvanized After Fabrication, American Galvanizer’s Association, and ASTM A123, A153, A384 and A780 for useful information on design and detailing of galvanized members. See Section M2.2 for requirements for copes of members to be galvanized.

M3.

SHOP PAINTING

1.

General Requirements Shop painting and surface preparation shall be in accordance with the provisions in Chapter 6 of the Code of Standard Practice. Shop paint is not required unless specified by the contract documents.

2.

Inaccessible Surfaces Except for contact surfaces, surfaces inaccessible after shop assembly shall be cleaned and painted prior to assembly, if required by the construction documents.

3.

Contact Surfaces Paint is permitted in bearing-type connections. For slip-critical connections, the faying surface requirements shall be in accordance with the RCSC Specification, Section 3.2.2(b).

4.

Finished Surfaces Machine-finished surfaces shall be protected against corrosion by a rust inhibitive coating that can be removed prior to erection, or which has characteristics that make removal prior to erection unnecessary.

5.

Surfaces Adjacent to Field Welds Unless otherwise specified in the design documents, surfaces within 2 in. (50 mm) of any field weld location shall be free of materials that would prevent proper welding or produce objectionable fumes during welding.

M4.

ERECTION

1.

Column Base Setting Column bases shall be set level and to correct elevation with full bearing on concrete or masonry as defined in Chapter 7 of the Code of Standard Practice.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

Sect. M4.]

2.

8:01 AM

Page 169

ERECTION

16.1–169

Stability and Connections The frame of structural steel buildings shall be carried up true and plumb within the limits defined in Chapter 7 of the Code of Standard Practice. As erection progresses, the structure shall be secured to support dead, erection and other loads anticipated to occur during the period of erection. Temporary bracing shall be provided, in accordance with the requirements of the Code of Standard Practice, wherever necessary to support the loads to which the structure may be subjected, including equipment and the operation of same. Such bracing shall be left in place as long as required for safety.

3.

Alignment No permanent bolting or welding shall be performed until the adjacent affected portions of the structure have been properly aligned.

4.

Fit of Column Compression Joints and Base Plates Lack of contact bearing not exceeding a gap of 1/16 in. (2 mm), regardless of the type of splice used (partial-joint-penetration groove welded or bolted), is permitted. If the gap exceeds 1/16 in. (2 mm), but is equal to or less than 1/4 in. (6 mm), and if an engineering investigation shows that sufficient contact area does not exist, the gap shall be packed out with nontapered steel shims. Shims need not be other than mild steel, regardless of the grade of the main material.

5.

Field Welding Surfaces in and adjacent to joints to be field welded shall be prepared as necessary to assure weld quality. This preparation shall include surface preparation necessary to correct for damage or contamination occurring subsequent to fabrication.

6.

Field Painting Responsibility for touch-up painting, cleaning and field painting shall be allocated in accordance with accepted local practices, and this allocation shall be set forth explicitly in the contract documents.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

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8:01 AM

Page 170

16.1–170

CHAPTER N QUALITY CONTROL AND QUALITY ASSURANCE

This chapter addresses minimum requirements for quality control, quality assurance and nondestructive testing for structural steel systems and steel elements of composite members for buildings and other structures. User Note: This chapter does not address quality control or quality assurance for concrete reinforcing bars, concrete materials or placement of concrete for composite members. This chapter does not address quality control or quality assurance for surface preparation or coatings.

User Note: The inspection of steel (open-web) joists and joist girders, tanks, pressure vessels, cables, cold-formed steel products, or gage metal products is not addressed in this Specification. The Chapter is organized as follows: N1. N2. N3. N4. N5. N6. N7. N8.

N1.

Scope Fabricator and Erector Quality Control Program Fabricator and Erector Documents Inspection and Nondestructive Testing Personnel Minimum Requirements for Inspection of Structural Steel Buildings Minimum Requirements for Inspection of Composite Construction Approved Fabricators and Erectors Nonconforming Material and Workmanship

SCOPE Quality control (QC) as specified in this chapter shall be provided by the fabricator and erector. Quality assurance (QA) as specified in this chapter shall be provided by others when required by the authority having jurisdiction (AHJ), applicable building code (ABC), purchaser, owner, or engineer of record (EOR). Nondestructive testing (NDT) shall be performed by the agency or firm responsible for quality assurance, except as permitted in accordance with Section N7. User Note: The QA/QC requirements in Chapter N are considered adequate and effective for most steel structures and are strongly encouraged without modification. When the ABC and AHJ requires the use of a quality assurance plan, this chapter outlines the minimum requirements deemed effective to provide satisfactory results in steel building construction. There may be cases where supplemental inspections are advisable. Additionally, where the contractor’s quality control program has demonstrated the capability to perform some tasks this plan has assigned to quality assurance, modification of the plan could be considered. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

Sect. N3.]

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FABRICATOR AND ERECTOR DOCUMENTS

16.1–171

User Note: The producers of materials manufactured in accordance with standard specifications referenced in Section A3 in this Specification, and steel deck manufacturers, are not considered to be fabricators or erectors.

N2.

FABRICATOR AND ERECTOR QUALITY CONTROL PROGRAM The fabricator and erector shall establish and maintain quality control procedures and perform inspections to ensure that their work is performed in accordance with this Specification and the construction documents. Material identification procedures shall comply with the requirements of Section 6.1 of the Code of Standard Practice, and shall be monitored by the fabricator’s quality control inspector (QCI). The fabricator’s QCI shall inspect the following as a minimum, as applicable: (1) Shop welding, high-strength bolting, and details in accordance with Section N5 (2) Shop cut and finished surfaces in accordance with Section M2 (3) Shop heating for straightening, cambering and curving in accordance with Section M2.1 (4) Tolerances for shop fabrication in accordance with Section 6 of the Code of Standard Practice The erector’s QCI shall inspect the following as a minimum, as applicable: (1) Field welding, high-strength bolting, and details in accordance with Section N5 (2) Steel deck and headed steel stud anchor placement and attachment in accordance with Section N6 (3) Field cut surfaces in accordance with Section M2.2 (4) Field heating for straightening in accordance with Section M2.1 (5) Tolerances for field erection in accordance with Section 7.13 of the Code of Standard Practice.

N3.

FABRICATOR AND ERECTOR DOCUMENTS

1.

Submittals for Steel Construction The fabricator or erector shall submit the following documents for review by the engineer of record (EOR) or the EOR’s designee, in accordance with Section 4 or A4.4 of the Code of Standard Practice, prior to fabrication or erection, as applicable: (1) Shop drawings, unless shop drawings have been furnished by others (2) Erection drawings, unless erection drawings have been furnished by others

2.

Available Documents for Steel Construction The following documents shall be available in electronic or printed form for review by the EOR or the EOR’s designee prior to fabrication or erection, as applicable, unless otherwise required in the contract documents to be submitted:

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

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FABRICATOR AND ERECTOR DOCUMENTS

[Sect. N3.

(1) For main structural steel elements, copies of material test reports in accordance with Section A3.1. (2) For steel castings and forgings, copies of material test reports in accordance with Section A3.2. (3) For fasteners, copies of manufacturer’s certifications in accordance with Section A3.3. (4) For deck fasteners, copies of manufacturer’s product data sheets or catalog data. The data sheets shall describe the product, limitations of use, and recommended or typical installation instructions. (5) For anchor rods and threaded rods, copies of material test reports in accordance with Section A3.4. (6) For welding consumables, copies of manufacturer’s certifications in accordance with Section A3.5. (7) For headed stud anchors, copies of manufacturer’s certifications in accordance with Section A3.6. (8) Manufacturer’s product data sheets or catalog data for welding filler metals and fluxes to be used. The data sheets shall describe the product, limitations of use, recommended or typical welding parameters, and storage and exposure requirements, including baking, if applicable. (9) Welding procedure specifications (WPSs). (10) Procedure qualification records (PQRs) for WPSs that are not prequalified in accordance with AWS D1.1/D1.1M or AWS D1.3/D1.3M, as applicable. (11) Welding personnel performance qualification records (WPQR) and continuity records. (12) Fabricator’s or erector’s, as applicable, written quality control manual that shall include, as a minimum: (i) Material control procedures (ii) Inspection procedures (iii) Nonconformance procedures (13) Fabricator’s or erector’s, as applicable, QC inspector qualifications.

N4.

INSPECTION AND NONDESTRUCTIVE TESTING PERSONNEL

1.

Quality Control Inspector Qualifications Quality control (QC) welding inspection personnel shall be qualified to the satisfaction of the fabricator’s or erector’s QC program, as applicable, and in accordance with either of the following: (a) Associate welding inspectors (AWI) or higher as defined in AWS B5.1, Standard for the Qualification of Welding Inspectors, or (b) Qualified under the provisions of AWS D1.1/D1.1M subclause 6.1.4 QC bolting inspection personnel shall be qualified on the basis of documented training and experience in structural bolting inspection.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

Sect. N5.]

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MINIMUM REQUIREMENTS FOR INSPECTION

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Quality Assurance Inspector Qualifications Quality assurance (QA) welding inspectors shall be qualified to the satisfaction of the QA agency’s written practice, and in accordance with either of the following: (a) Welding inspectors (WIs) or senior welding inspectors (SWIs), as defined in AWS B5.1, Standard for the Qualification of Welding Inspectors, except associate welding inspectors (AWIs) are permitted to be used under the direct supervision of WIs, who are on the premises and available when weld inspection is being conducted, or (b) Qualified under the provisions of AWS D1.1/D1.1M, subclause 6.1.4 QA bolting inspection personnel shall be qualified on the basis of documented training and experience in structural bolting inspection.

3.

NDT Personnel Qualifications Nondestructive testing personnel, for NDT other than visual, shall be qualified in accordance with their employer’s written practice, which shall meet or exceed the criteria of AWS D1.1/D1.1M Structural Welding Code—Steel, subclause 6.14.6, and: (a) American Society for Nondestructive Testing (ASNT) SNT-TC-1A, Recommended Practice for the Qualification and Certification of Nondestructive Testing Personnel, or (b) ASNT CP-189, Standard for the Qualification and Certification of Nondestructive Testing Personnel.

N5.

MINIMUM REQUIREMENTS FOR INSPECTION OF STRUCTURAL STEEL BUILDINGS

1.

Quality Control QC inspection tasks shall be performed by the fabricator’s or erector’s quality control inspector (QCI), as applicable, in accordance with Sections N5.4, N5.6 and N5.7. Tasks in Tables N5.4-1 through N5.4-3 and Tables N5.6-1 through N5.6-3 listed for QC are those inspections performed by the QCI to ensure that the work is performed in accordance with the construction documents. For QC inspection, the applicable construction documents are the shop drawings and the erection drawings, and the applicable referenced specifications, codes and standards. User Note: The QCI need not refer to the design drawings and project specifications. The Code of Standard Practice, Section 4.2(a), requires the transfer of information from the Contract Documents (design drawings and project specification) into accurate and complete shop and erection drawings, allowing QC inspection to be based upon shop and erection drawings alone.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–174

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MINIMUM REQUIREMENTS FOR INSPECTION

[Sect. N5.

Quality Assurance Quality assurance (QA) inspection of fabricated items shall be made at the fabricator’s plant. The quality assurance inspector (QAI) shall schedule this work to minimize interruption to the work of the fabricator. QA inspection of the erected steel system shall be made at the project site. The QAI shall schedule this work to minimize interruption to the work of the erector. The QAI shall review the material test reports and certifications as listed in Section N3.2 for compliance with the construction documents. QA inspection tasks shall be performed by the QAI, in accordance with Sections N5.4, N5.6 and N5.7. Tasks in Tables N5.4-1 through N5.4-3 and N5.6-1 through N5.6-3 listed for QA are those inspections performed by the QAI to ensure that the work is performed in accordance with the construction documents. Concurrent with the submittal of such reports to the AHJ, EOR or owner, the QA agency shall submit to the fabricator and erector: (1) Inspection reports (2) Nondestructive testing reports

3.

Coordinated Inspection Where a task is noted to be performed by both QC and QA, it is permitted to coordinate the inspection function between the QCI and QAI so that the inspection functions are performed by only one party. Where QA relies upon inspection functions performed by QC, the approval of the engineer of record and the authority having jurisdiction is required.

4.

Inspection of Welding Observation of welding operations and visual inspection of in-process and completed welds shall be the primary method to confirm that the materials, procedures and workmanship are in conformance with the construction documents. For structural steel, all provisions of AWS D1.1/D1.1M Structural Welding Code—Steel for statically loaded structures shall apply. User Note: Section J2 of this Specification contains exceptions to AWS D1.1/D1.1M.

As a minimum, welding inspection tasks shall be in accordance with Tables N5.41, N5.4-2 and N5.4-3. In these tables, the inspection tasks are as follows: O – Observe these items on a random basis. Operations need not be delayed pending these inspections. P – Perform these tasks for each welded joint or member.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

Sect. N5.]

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MINIMUM REQUIREMENTS FOR INSPECTION

TABLE N5.4-1 Inspection Tasks Prior to Welding Inspection Tasks Prior to Welding

QC

QA

Welding procedure specifications (WPSs) available

P

P

Manufacturer certifications for welding consumables available

P

P

Material identification (type/grade)

O

O

Welder identification system1

O

O

Fit-up of groove welds (including joint geometry) • Joint preparation • Dimensions (alignment, root opening, root face, bevel) • Cleanliness (condition of steel surfaces) • Tacking (tack weld quality and location) • Backing type and fit (if applicable)

O

O

Configuration and finish of access holes

O

O

Fit-up of fillet welds • Dimensions (alignment, gaps at root) • Cleanliness (condition of steel surfaces) • Tacking (tack weld quality and location)

O

O

Check welding equipment

O

—

1

The fabricator or erector, as applicable, shall maintain a system by which a welder who has welded a joint or member can be identified. Stamps, if used, shall be the low-stress type.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

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[Sect. N5.

TABLE N5.4-2 Inspection Tasks During Welding Inspection Tasks During Welding

QC

QA

Use of qualified welders

O

O

Control and handling of welding consumables • Packaging • Exposure control

O

O

No welding over cracked tack welds

O

O

Environmental conditions • Wind speed within limits • Precipitation and temperature

O

O

WPS followed • Settings on welding equipment • Travel speed • Selected welding materials • Shielding gas type/flow rate • Preheat applied • Interpass temperature maintained (min./max.) • Proper position (F, V, H, OH)

O

O

Welding techniques • Interpass and final cleaning • Each pass within profile limitations • Each pass meets quality requirements

O

O

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed._

Sect. N5.]

2/17/12

12:14 PM

Page 177

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16.1–177

TABLE N5.4-3 Inspection Tasks After Welding Inspection Tasks After Welding

QC

QA

Welds cleaned

O

O

Size, length and location of welds

P

P

Welds meet visual acceptance criteria • Crack prohibition • Weld/base-metal fusion • Crater cross section • Weld profiles • Weld size • Undercut • Porosity

P

P

Arc strikes

P

P

k-area1

P

P

Backing removed and weld tabs removed (if required)

P

P

Repair activities

P

P

Document acceptance or rejection of welded joint or member

P

P

1

When welding of doubler plates, continuity plates or stiffeners has been performed in the k-area, visually inspect the web k-area for cracks within 3 in. (75 mm) of the weld.

5.

Nondestructive Testing of Welded Joints

5a.

Procedures Ultrasonic testing (UT), magnetic particle testing (MT), penetrant testing (PT) and radiographic testing (RT), where required, shall be performed by QA in accordance with AWS D1.1/D1.1M. Acceptance criteria shall be in accordance with AWS D1.1/D1.1M for statically loaded structures, unless otherwise designated in the design drawings or project specifications.

5b.

CJP Groove Weld NDT For structures in Risk Category III or IV of Table 1.5-1, Risk Category of Buildings and Other Structures for Flood, Wind, Snow, Earthquake and Ice Loads, of ASCE/ SEI 7, Minimum Design Loads for Buildings and Other Structures, UT shall be performed by QA on all CJP groove welds subject to transversely applied tension loading in butt, T- and corner joints, in materials 5/16 in. (8 mm) thick or greater. For structures in Risk Category II, UT shall be performed by QA on 10% of CJP groove welds in butt, T- and corner joints subject to transversely applied tension loading, in materials 5/16 in. (8 mm) thick or greater. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–178

1/20/11

8:01 AM

Page 178

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[Sect. N5.

User Note: For structures in Risk Category I, NDT of CJP groove welds is not required. For all structures in all Risk Categories, NDT of CJP groove welds in materials less than 5/16 in. (8 mm) thick is not required.

5c.

Access Hole NDT Thermally cut surfaces of access holes shall be tested by QA using MT or PT, when the flange thickness exceeds 2 in. (50 mm) for rolled shapes, or when the web thickness exceeds 2 in. (50 mm) for built-up shapes. Any crack shall be deemed unacceptable regardless of size or location. User Note: See Section M2.2.

5d.

Welded Joints Subjected to Fatigue When required by Appendix 3, Table A-3.1, welded joints requiring weld soundness to be established by radiographic or ultrasonic inspection shall be tested by QA as prescribed. Reduction in the rate of UT is prohibited.

5e.

Reduction of Rate of Ultrasonic Testing The rate of UT is permitted to be reduced if approved by the EOR and the AHJ. Where the initial rate for UT is 100%, the NDT rate for an individual welder or welding operator is permitted to be reduced to 25%, provided the reject rate, the number of welds containing unacceptable defects divided by the number of welds completed, is demonstrated to be 5% or less of the welds tested for the welder or welding operator. A sampling of at least 40 completed welds for a job shall be made for such reduction evaluation. For evaluating the reject rate of continuous welds over 3 ft (1 m) in length where the effective throat is 1 in. (25 mm) or less, each 12 in. (300 mm) increment or fraction thereof shall be considered as one weld. For evaluating the reject rate on continuous welds over 3 ft (1 m) in length where the effective throat is greater than 1 in. (25 mm), each 6 in. (150 mm) of length or fraction thereof shall be considered one weld.

5f.

Increase in Rate of Ultrasonic Testing For structures in Risk Category II, where the initial rate for UT is 10%, the NDT rate for an individual welder or welding operator shall be increased to 100% should the reject rate, the number of welds containing unacceptable defects divided by the number of welds completed, exceeds 5% of the welds tested for the welder or welding operator. A sampling of at least 20 completed welds for a job shall be made prior to implementing such an increase. When the reject rate for the welder or welding operator, after a sampling of at least 40 completed welds, has fallen to 5% or less, the rate of UT shall be returned to 10%. For evaluating the reject rate of continuous welds over 3 ft (1 m) in length where the effective throat is 1 in. (25 mm) or less,

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

Sect. N5.]

1/20/11

8:01 AM

Page 179

MINIMUM REQUIREMENTS FOR INSPECTION

16.1–179

each 12-in. (300 mm) increment or fraction thereof shall be considered as one weld. For evaluating the reject rate on continuous welds over 3 ft (1 m) in length where the effective throat is greater than 1 in. (25 mm), each 6 in. (150 mm) of length or fraction thereof shall be considered one weld.

5g.

Documentation All NDT performed shall be documented. For shop fabrication, the NDT report shall identify the tested weld by piece mark and location in the piece. For field work, the NDT report shall identify the tested weld by location in the structure, piece mark, and location in the piece. When a weld is rejected on the basis of NDT, the NDT record shall indicate the location of the defect and the basis of rejection.

6.

Inspection of High-Strength Bolting Observation of bolting operations shall be the primary method used to confirm that the materials, procedures and workmanship incorporated in construction are in conformance with the construction documents and the provisions of the RCSC Specification. (1) For snug-tight joints, pre-installation verification testing as specified in Table N5.6-1 and monitoring of the installation procedures as specified in Table N5.6-2 are not applicable. The QCI and QAI need not be present during the installation of fasteners in snug-tight joints. (2) For pretensioned joints and slip-critical joints, when the installer is using the turn-of-nut method with matchmarking techniques, the direct-tension-indicator method, or the twist-off-type tension control bolt method, monitoring of bolt pretensioning procedures shall be as specified in Table N5.6-2. The QCI and QAI need not be present during the installation of fasteners when these methods are used by the installer. (3) For pretensioned joints and slip-critical joints, when the installer is using the calibrated wrench method or the turn-of-nut method without matchmarking, monitoring of bolt pretensioning procedures shall be as specified in Table N5.6-2. The QCI and QAI shall be engaged in their assigned inspection duties during installation of fasteners when these methods are used by the installer. As a minimum, bolting inspection tasks shall be in accordance with Tables N5.6-1, N5.6-2 and N5.6-3. In these tables, the inspection tasks are as follows: O – Observe these items on a random basis. Operations need not be delayed pending these inspections. P – Perform these tasks for each bolted connection.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–180

1/20/11

8:01 AM

Page 180

MINIMUM REQUIREMENTS FOR INSPECTION

[Sect. N5.

TABLE N5.6-1 Inspection Tasks Prior to Bolting Inspection Tasks Prior to Bolting

QC

QA

Manufacturer’s certifications available for fastener materials

O

P

Fasteners marked in accordance with ASTM requirements

O

O

Proper fasteners selected for the joint detail (grade, type, bolt length if threads are to be excluded from shear plane)

O

O

Proper bolting procedure selected for joint detail

O

O

Connecting elements, including the appropriate faying surface condition and hole preparation, if specified, meet applicable requirements

O

O

Pre-installation verification testing by installation personnel observed and documented for fastener assemblies and methods used

P

O

Proper storage provided for bolts, nuts, washers and other fastener components

O

O

QC

QA

Fastener assemblies, of suitable condition, placed in all holes and washers (if required) are positioned as required

O

O

Joint brought to the snug-tight condition prior to the pretensioning operation

O

O

Fastener component not turned by the wrench prevented from rotating

O

O

Fasteners are pretensioned in accordance with the RCSC Specification, progressing systematically from the most rigid point toward the free edges

O

O

QC

QA

P

P

TABLE N5.6-2 Inspection Tasks During Bolting Inspection Tasks During Bolting

TABLE N5.6-3 Inspection Tasks After Bolting Inspection Tasks After Bolting Document acceptance or rejection of bolted connections

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

Sect. N6.]

7.

1/20/11

8:01 AM

Page 181

MINIMUM REQUIREMENTS FOR INSPECTION

16.1–181

Other Inspection Tasks The fabricator’s QCI shall inspect the fabricated steel to verify compliance with the details shown on the shop drawings, such as proper application of joint details at each connection. The erector’s QCI shall inspect the erected steel frame to verify compliance with the details shown on the erection drawings, such as braces, stiffeners, member locations and proper application of joint details at each connection. The QAI shall be on the premises for inspection during the placement of anchor rods and other embedments supporting structural steel for compliance with the construction documents. As a minimum, the diameter, grade, type and length of the anchor rod or embedded item, and the extent or depth of embedment into the concrete, shall be verified prior to placement of concrete. The QAI shall inspect the fabricated steel or erected steel frame, as appropriate, to verify compliance with the details shown on the construction documents, such as braces, stiffeners, member locations and proper application of joint details at each connection.

N6.

MINIMUM REQUIREMENTS FOR INSPECTION OF COMPOSITE CONSTRUCTION Inspection of structural steel and steel deck used in composite construction shall comply with the requirements of this Chapter. For welding of steel headed stud anchors, the provisions of AWS D1.1/D1.1M, Structural Welding Code—Steel, apply. For welding of steel deck, observation of welding operations and visual inspection of in-process and completed welds shall be the primary method to confirm that the materials, procedures and workmanship are in conformance with the construction documents. All applicable provisions of AWS D1.3/D1.3M, Structural Welding Code—Sheet Steel, shall apply. Deck welding inspection shall include verification of the welding consumables, welding procedure specifications and qualifications of welding personnel prior to the start of the work, observations of the work in progress, and a visual inspection of all completed welds. For steel deck attached by fastening systems other than welding, inspection shall include verification of the fasteners to be used prior to the start of the work, observations of the work in progress to confirm installation in conformance with the manufacturer’s recommendations, and a visual inspection of the completed installation. For those items for quality control (QC) in Table N6.1 that contain an observe designation, the QC inspection shall be performed by the erector’s quality control inspector (QCI). In Table N6.1, the inspection tasks are as follows: O – Observe these items on a random basis. Operations need not be delayed pending these inspections. P – Perform these tasks for each steel element.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–182

1/20/11

8:01 AM

Page 182

MINIMUM REQUIREMENTS FOR INSPECTION

[Sect. N6.

TABLE N6.1 Inspection of Steel Elements of Composite Construction Prior to Concrete Placement Inspection of Steel Elements of Composite Construction Prior to Concrete Placement

QC

QA

Placement and installation of steel deck

P

P

Placement and installation of steel headed stud anchors

P

P

Document acceptance or rejection of steel elements

P

P

N7.

APPROVED FABRICATORS AND ERECTORS Quality assurance (QA) inspections, except nondestructive testing (NDT), may be waived when the work is performed in a fabricating shop or by an erector approved by the authority having jurisdiction (AHJ) to perform the work without QA. NDT of welds completed in an approved fabricator’s shop may be performed by that fabricator when approved by the AHJ. When the fabricator performs the NDT, the QA agency shall review the fabricator’s NDT reports. At completion of fabrication, the approved fabricator shall submit a certificate of compliance to the AHJ stating that the materials supplied and work performed by the fabricator are in accordance with the construction documents. At completion of erection, the approved erector shall submit a certificate of compliance to the AHJ stating that the materials supplied and work performed by the erector are in accordance with the construction documents.

N8.

NONCONFORMING MATERIAL AND WORKMANSHIP Identification and rejection of material or workmanship that is not in conformance with the construction documents shall be permitted at any time during the progress of the work. However, this provision shall not relieve the owner or the inspector of the obligation for timely, in-sequence inspections. Nonconforming material and workmanship shall be brought to the immediate attention of the fabricator or erector, as applicable. Nonconforming material or workmanship shall be brought into conformance, or made suitable for its intended purpose as determined by the engineer of record. Concurrent with the submittal of such reports to the AHJ, EOR or owner, the QA agency shall submit to the fabricator and erector: (1) Nonconformance reports (2) Reports of repair, replacement or acceptance of nonconforming items

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

8:01 AM

Page 183

16.1–183

APPENDIX 1 DESIGN BY INELASTIC ANALYSIS

This appendix addresses design by inelastic analysis, in which consideration of the redistribution of member and connection forces and moments as a result of localized yielding is permitted. The appendix is organized as follows: 1.1. 1.2. 1.3.

1.1.

General Requirements Ductility Requirements Analysis Requirements

GENERAL REQUIREMENTS Design by inelastic analysis shall be conducted in accordance with Section B3.3, using load and resistance factor design (LRFD). The design strength of the structural system and its members and connections shall equal or exceed the required strength as determined by the inelastic analysis. The provisions of this Appendix do not apply to seismic design. The inelastic analysis shall take into account: (1) flexural, shear and axial member deformations, and all other component and connection deformations that contribute to the displacements of the structure; (2) second-order effects (including P-Δ and P-δ effects); (3) geometric imperfections; (4) stiffness reductions due to inelasticity, including the effect of residual stresses and partial yielding of the cross section; and (5) uncertainty in system, member, and connection strength and stiffness. Strength limit states detected by an inelastic analysis that incorporates all of the above requirements are not subject to the corresponding provisions of the Specification when a comparable or higher level of reliability is provided by the analysis. Strength limit states not detected by the inelastic analysis shall be evaluated using the corresponding provisions of Chapters D, E, F, G, H, I, J and K. Connections shall meet the requirements of Section B3.6. Members and connections subject to inelastic deformations shall be shown to have adequate ductility consistent with the intended behavior of the structural system. Force redistribution due to rupture of a member or connection is not permitted. Any method that uses inelastic analysis to proportion members and connections to satisfy these general requirements is permitted. A design method based on inelastic analysis that meets the above strength requirements, the ductility requirements of Section 1.2, and the analysis requirements of Section 1.3 satisfies these general requirements.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–184

1.2.

1/20/11

8:01 AM

Page 184

DUCTILITY REQUIREMENTS

[App. 1.2.

DUCTILITY REQUIREMENTS Members and connections with elements subject to yielding shall be proportioned such that all inelastic deformation demands are less than or equal to their inelastic deformation capacities. In lieu of explicitly ensuring that the inelastic deformation demands are less than or equal to their inelastic deformation capacities, the following requirements shall be satisfied for steel members subject to plastic hinging.

1.

Material The specified minimum yield stress, Fy, of members subject to plastic hinging shall not exceed 65 ksi (450 MPa).

2.

Cross Section The cross section of members at plastic hinge locations shall be doubly symmetric with width-to-thickness ratios of their compression elements not exceeding λpd, where λpd is equal to λp from Table B4.1b except as modified below: (a) For the width-to-thickness ratio, h/tw, of webs of I-shaped sections, rectangular HSS, and box-shaped sections subject to combined flexure and compression (i) When Pu /φc Py ≤ 0.125 ⎛ 2.75 Pu ⎞ ⎜⎝ 1 − φ P ⎟⎠

(A-1-1)

⎛ Pu ⎞ E ⎜⎝ 2.33 − φ P ⎟⎠ ≥ 1.49 F c y y

(A-1-2)

λ pd = 3.76

E Fy

c y

(ii) When Pu /φc Py > 0.125 λ pd = 1.12

E Fy

where h = as defined in Section B4.1, in. (mm) tw = web thickness, in. (mm) Pu = required axial strength in compression, kips (N) Py = FyAg = axial yield strength, kips (N) φc = resistance factor for compression = 0.90 (b) For the width-to-thickness ratio, b/t, of flanges of rectangular HSS and boxshaped sections, and for flange cover plates, and diaphragm plates between lines of fasteners or welds λ pd = 0 . 94 E / Fy where b = as defined in Section B4.1, in. (mm) t = as defined in Section B4.1, in. (mm)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(A-1-3)

AISC_PART 16_Spec.3_C:14th Ed.

App. 1.2.]

1/20/11

8:01 AM

Page 185

DUCTILITY REQUIREMENTS

16.1–185

(c) For the diameter-to-thickness ratio, D/t, of circular HSS in flexure λpd = 0.045E/Fy

(A-1-4)

where D = outside diameter of round HSS, in. (mm)

3.

Unbraced Length In prismatic member segments that contain plastic hinges, the laterally unbraced length, Lb, shall not exceed Lpd, determined as follows. For members subject to flexure only, or to flexure and axial tension, Lb shall be taken as the length between points braced against lateral displacement of the compression flange, or between points braced to prevent twist of the cross section. For members subject to flexure and axial compression, Lb shall be taken as the length between points braced against both lateral displacement in the minor axis direction and twist of the cross section. (a) For I-shaped members bent about their major axis: ⎡ M ′⎤ E L pd = ⎢ 0.12 − 0.076 1 ⎥ ry M 2 ⎥ Fy ⎢⎣ ⎦

(A-1-5)

where ry = radius of gyration about minor axis, in. (mm) (i) When the magnitude of the bending moment at any location within the unbraced length exceeds M2 M1′ / M 2 = +1

(A-1-6a)

Otherwise: (ii) When Mmid ≤ (M1 + M2)/2 M1′ = M1

(A-1-6b)

(iii) When Mmid > (M1 + M2)/2 M1′ = 2 M mid − M 2 < M 2

(A-1-6c)

where M1 = smaller moment at end of unbraced length, kip-in. (N-mm) M2 = larger moment at end of unbraced length, kip-in. (N-mm). M2 shall be taken as positive in all cases. Mmid = moment at middle of unbraced length, kip-in. (N-mm) M1′ = effective moment at end of unbraced length opposite from M2, kip-in. (N-mm) The moments M1 and Mmid are individually taken as positive when they cause compression in the same flange as the moment M2 and negative otherwise.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–186

1/20/11

8:01 AM

Page 186

DUCTILITY REQUIREMENTS

[App. 1.2.

(b) For solid rectangular bars and for rectangular HSS and box-shaped members bent about their major axis ⎡ M ′⎤ E E L pd = ⎢ 0.17 − 0.10 1 ⎥ ry ≥ 0.10 ry M 2 ⎥ Fy Fy ⎢⎣ ⎦

(A-1-7)

For all types of members subject to axial compression and containing plastic hinges, the laterally unbraced lengths about the cross section major and minor axes shall not exceed 4.71rx E Fy and 4.71ry E Fy , respectively. There is no Lpd limit for member segments containing plastic hinges in the following cases: (1) Members with circular or square cross sections subject only to flexure or to combined flexure and tension (2) Members subject only to flexure about their minor axis or combined tension and flexure about their minor axis (3) Members subject only to tension

4.

Axial Force To assure adequate ductility in compression members with plastic hinges, the design strength in compression shall not exceed 0.75Fy Ag.

1.3.

ANALYSIS REQUIREMENTS The structural analysis shall satisfy the general requirements of Section 1.1. These requirements are permitted to be satisfied by a second-order inelastic analysis meeting the requirements of this Section. Exception: For continuous beams not subject to axial compression, a first-order inelastic or plastic analysis is permitted and the requirements of Sections 1.3.2 and 1.3.3 are waived. User Note: Refer to the Commentary for guidance in conducting a traditional plastic analysis and design in conformance with these provisions.

1.

Material Properties and Yield Criteria The specified minimum yield stress, Fy, and the stiffness of all steel members and connections shall be reduced by a factor of 0.90 for the analysis, except as noted below in Section 1.3.3. The influence of axial force, major axis bending moment, and minor axis bending moment shall be included in the calculation of the inelastic response. The plastic strength of the member cross section shall be represented in the analysis either by an elastic-perfectly-plastic yield criterion expressed in terms of the axial

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 1.3.]

1/20/11

8:01 AM

Page 187

ANALYSIS REQUIREMENTS

16.1–187

force, major axis bending moment, and minor axis bending moment, or by explicit modeling of the material stress-strain response as elastic-perfectly-plastic.

2.

Geometric Imperfections The analysis shall include the effects of initial geometric imperfections. This shall be done by explicitly modeling the imperfections as specified in Section C2.2a or by the application of equivalent notional loads as specified in Section C2.2b.

3.

Residual Stress and Partial Yielding Effects The analysis shall include the influence of residual stresses and partial yielding. This shall be done by explicitly modeling these effects in the analysis or by reducing the stiffness of all structural components as specified in Section C2.3. If the provisions of Section C2.3 are used, then: (1) The 0.9 stiffness reduction factor specified in Section 1.3.1 shall be replaced by the reduction of the elastic modulus E by 0.8 as specified in Section C2.3, and (2) The elastic-perfectly-plastic yield criterion, expressed in terms of the axial force, major axis bending moment, and minor axis bending moment, shall satisfy the cross section strength limit defined by Equations H1-1a and H1-1b using Pc = 0.9Py, Mcx = 0.9Mpx and Mcy = 0.9Mpy.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

8:01 AM

Page 188

16.1–188

APPENDIX 2 DESIGN FOR PONDING

This appendix provides methods for determining whether a roof system has adequate strength and stiffness to resist ponding. The appendix is organized as follows: 2.1. 2.2.

2.1.

Simplified Design for Ponding Improved Design for Ponding

SIMPLIFIED DESIGN FOR PONDING The roof system shall be considered stable for ponding and no further investigation is needed if both of the following two conditions are met: Cp + 0.9Cs ≤ 0.25 Id ≥ 25(S )10 4

–6

(S.I.: Id ≥ 3 940 S4 )

(A-2-1) (A-2-2) (A-2-2M)

where Cp =

32 Ls L4p

(A-2-3)

10 7 I p

Cp =

504 Ls L4p (S.I.) Ip

Cs =

32 SL4s 10 7 I s

Cs =

504 SL4s (S.I.) Is

(A-2-3M)

(A-2-4)

(A-2-4M)

Id = moment of inertia of the steel deck supported on secondary members, in.4 per ft (mm4 per m) Ip = moment of inertia of primary members, in.4 (mm4) Is = moment of inertia of secondary members, in.4 (mm4) Lp = length of primary members, ft (m) Ls = length of secondary members, ft (m) S = spacing of secondary members, ft (m)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 2.2.]

1/20/11

8:01 AM

Page 189

IMPROVED DESIGN FOR PONDING

16.1–189

For trusses and steel joists, the calculation of the moments of inertia, Ip and Is, shall include the effects of web member strain when used in the above equation. User Note: When the moment of inertia is calculated using only the truss or joist chord areas, the reduction in the moment of inertia due to web strain can typically be taken as 15%. A steel deck shall be considered a secondary member when it is directly supported by the primary members.

2.2.

IMPROVED DESIGN FOR PONDING The provisions given below are to be used when a more accurate evaluation of framing stiffness is needed than that given by Equations A-2-1 and A-2-2. Define the stress indexes ⎛ 0.8 Fy − fo ⎞ Up = ⎜ ⎟⎠ for the primary member ⎝ fo p

(A-2-5)

⎛ 0.8 Fy − fo ⎞ Us = ⎜ ⎟⎠ for the secondary member ⎝ fo s

(A-2-6)

where fo = stress due to D + R (D = nominal dead load, R = nominal load due to rainwater or snow exclusive of the ponding contribution), ksi (MPa) For roof framing consisting of primary and secondary members, evaluate the combined stiffness as follows. Enter Figure A-2.1 at the level of the computed stress index, Up , determined for the primary beam; move horizontally to the computed Cs value of the secondary beams and then downward to the abscissa scale. The combined stiffness of the primary and secondary framing is sufficient to prevent ponding if the flexibility coefficient read from this latter scale is more than the value of Cp computed for the given primary member; if not, a stiffer primary or secondary beam, or combination of both, is required. A similar procedure must be followed using Figure A-2.2.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–190

1/20/11

8:01 AM

Page 190

IMPROVED DESIGN FOR PONDING

[App. 2.2.

For roof framing consisting of a series of equally spaced wall bearing beams, evaluate the stiffness as follows. The beams are considered as secondary members supported on an infinitely stiff primary member. For this case, enter Figure A-2.2 with the computed stress index, Us. The limiting value of Cs is determined by the intercept of a horizontal line representing the Us value and the curve for Cp = 0. User Note: The ponding deflection contributed by a metal deck is usually such a small part of the total ponding deflection of a roof panel that it is sufficient merely to limit its moment of inertia [per foot (meter) of width normal to its span] to 0.000025 (3 940) times the fourth power of its span length.

Upper Limit of Flexibility Coefficient Cp Fig. A-2.1. Limiting flexibility coefficient for the primary systems.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 2.2.]

1/20/11

8:01 AM

Page 191

IMPROVED DESIGN FOR PONDING

16.1–191

Evaluate the stability against ponding of a roof consisting of a metal roof deck of relatively slender depth-to-span ratio, spanning between beams supported directly on columns, as follows. Use Figure A-2.1 or A-2.2, using as Cs the flexibility coefficient for a one-foot (one-meter) width of the roof deck (S = 1.0).

Upper Limit of Flexibility Coefficient Cs Fig. A-2.2. Limiting flexibility coefficient for the secondary systems.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

8:01 AM

Page 192

16.1–192

APPENDIX 3 DESIGN FOR FATIGUE

This appendix applies to members and connections subject to high cycle loading within the elastic range of stresses of frequency and magnitude sufficient to initiate cracking and progressive failure, which defines the limit state of fatigue. User Note: See AISC Seismic Provisions for Structural Steel Buildings for structures subject to seismic loads. The appendix is organized as follows: 3.1. 3.2. 3.3. 3.4. 3.5.

3.1.

General Provisions Calculation of Maximum Stresses and Allowable Stress Ranges Plain Material and Welded Joints Bolts and Threaded Parts Special Fabrication and Erection Requirements

GENERAL PROVISIONS The provisions of this Appendix apply to stresses calculated on the basis of service loads. The maximum permitted stress due to service loads is 0.66Fy . Stress range is defined as the magnitude of the change in stress due to the application or removal of the service live load. In the case of a stress reversal, the stress range shall be computed as the numerical sum of maximum repeated tensile and compressive stresses or the numerical sum of maximum shearing stresses of opposite direction at the point of probable crack initiation. In the case of complete-joint-penetration groove welds, the maximum allowable stress range calculated by Equation A-3-1 applies only to welds that have been ultrasonically or radiographically tested and meet the acceptance requirements of Sections 6.12.2 or 6.13.2 of AWS D1.1/D1.1M. No evaluation of fatigue resistance is required if the live load stress range is less than the threshold allowable stress range, FTH. See Table A-3.1. No evaluation of fatigue resistance of members consisting of shapes or plate is required if the number of cycles of application of live load is less than 20,000. No evaluation of fatigue resistance of members consisting of HSS in building-type structures subject to code mandated wind loads is required. The cyclic load resistance determined by the provisions of this Appendix is applicable to structures with suitable corrosion protection or subject only to mildly corrosive atmospheres, such as normal atmospheric conditions.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 3.3.]

1/20/11

8:01 AM

Page 193

PLAIN MATERIAL AND WELDED JOINTS

16.1–193

The cyclic load resistance determined by the provisions of this Appendix is applicable only to structures subject to temperatures not exceeding 300 °F (150 °C). The engineer of record shall provide either complete details including weld sizes or shall specify the planned cycle life and the maximum range of moments, shears and reactions for the connections.

3.2.

CALCULATION OF MAXIMUM STRESSES AND STRESS RANGES Calculated stresses shall be based upon elastic analysis. Stresses shall not be amplified by stress concentration factors for geometrical discontinuities. For bolts and threaded rods subject to axial tension, the calculated stresses shall include the effects of prying action, if any. In the case of axial stress combined with bending, the maximum stresses, of each kind, shall be those determined for concurrent arrangements of the applied load. For members having symmetric cross sections, the fasteners and welds shall be arranged symmetrically about the axis of the member, or the total stresses including those due to eccentricity shall be included in the calculation of the stress range. For axially loaded angle members where the center of gravity of the connecting welds lies between the line of the center of gravity of the angle cross section and the center of the connected leg, the effects of eccentricity shall be ignored. If the center of gravity of the connecting welds lies outside this zone, the total stresses, including those due to joint eccentricity, shall be included in the calculation of stress range.

3.3.

PLAIN MATERIAL AND WELDED JOINTS In plain material and welded joints the range of stress at service loads shall not exceed the allowable stress range computed as follows. (a) For stress categories A, B, B′, C, D, E and E′ the allowable stress range, FSR, shall be determined by Equation A-3-1 or A-3-1M, as follows: ⎛ Cf ⎞ FSR = ⎜ ⎝ nSR ⎟⎠ ⎛ C f × 329 ⎞ FSR = ⎜ ⎝ nSR ⎟⎠

0.333

≥ FTH

0.333

≥ FTH

(A-3-1)

(S.I.)

where Cf = constant from Table A-3.1 for the fatigue category FSR = allowable stress range, ksi (MPa) FTH = threshold allowable stress range, maximum stress range for indefinite design life from Table A-3.1, ksi (MPa) nSR = number of stress range fluctuations in design life = number of stress range fluctuations per day × 365 × years of design life Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(A-3-1M)

AISC_PART 16_Spec.3_C:14th Ed.

16.1–194

1/20/11

8:01 AM

Page 194

PLAIN MATERIAL AND WELDED JOINTS

[App. 3.3.

(b) For stress category F, the allowable stress range, FSR, shall be determined by Equation A-3-2 or A-3-2M as follows: ⎛ Cf ⎞ FSR = ⎜ ⎝ nSR ⎟⎠

FSR

(

⎛ C f 11 × 10 4 =⎜ nSR ⎜ ⎝

0.167

) ⎞⎟

≥ FTH

(A-3-2)

0.167

≥ FTH

⎟ ⎠

(S.I.)

(A-3-2M)

(c) For tension-loaded plate elements connected at their end by cruciform, T or corner details with complete-joint-penetration (CJP) groove welds or partialjoint-penetration (PJP) groove welds, fillet welds, or combinations of the preceding, transverse to the direction of stress, the allowable stress range on the cross section of the tension-loaded plate element at the toe of the weld shall be determined as follows: (i) Based upon crack initiation from the toe of the weld on the tension loaded plate element the allowable stress range, FSR, shall be determined by Equation A-3-3 or A-3-3M, for stress category C as follows: ⎛ 44 × 10 8 ⎞ FSR = ⎜ ⎟ ⎝ nSR ⎠ ⎛ 14.4 × 1011 ⎞ FSR = ⎜ ⎟ nSR ⎝ ⎠

0.333

≥ 10

(A-3-3)

0.333

(S.I.)

≥ 68.9

(A-3-3M)

(ii) Based upon crack initiation from the root of the weld the allowable stress range, FSR, on the tension loaded plate element using transverse PJP groove welds, with or without reinforcing or contouring fillet welds, the allowable stress range on the cross section at the toe of the weld shall be determined by Equation A-3-4 or A-3-4M, for stress category C′ as follows: ⎛ 44 × 10 8 ⎞ FSR = RPJP ⎜ ⎟ ⎝ nSR ⎠ ⎛ 14.4 × 1011 ⎞ FSR = RPJP ⎜ ⎟ nSR ⎝ ⎠

0.333

(A-3-4)

0.333

(S.I.)

(A-3-4M)

where RPJP, the reduction factor for reinforced or nonreinforced transverse PJP groove welds, is determined as follows:

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 3.3.]

1/20/11

8:01 AM

Page 195

PLAIN MATERIAL AND WELDED JOINTS

RPJP

⎛ ⎛ 2a ⎞ ⎛ w⎞⎞ ⎜ 0.65 − 0.59 ⎜ t ⎟ + 0.72 ⎜ t ⎟ ⎟ ⎝ p⎠ ⎝ p⎠⎟ =⎜ ≤ 1.0 ⎜ ⎟ t 0p.167 ⎜ ⎟ ⎝ ⎠

RPJP

⎛ ⎛ 2a ⎞ ⎛ w⎞⎞ ⎜ 1.12 − 1.01⎜ t ⎟ + 1.24 ⎜ t ⎟ ⎟ ⎝ p⎠ ⎝ p⎠⎟ =⎜ ≤ 1.0 ⎜ ⎟ t 0p.167 ⎜ ⎟ ⎝ ⎠

16.1–195

(A-3-5)

(S.I.)

(A-3-5M)

If RPJP = 1.0, use stress category C. 2a = length of the nonwelded root face in the direction of the thickness of the tension-loaded plate, in. (mm) w = leg size of the reinforcing or contouring fillet, if any, in the direction of the thickness of the tension-loaded plate, in. (mm) tp = thickness of tension loaded plate, in. (mm) (iii) Based upon crack initiation from the roots of a pair of transverse fillet welds on opposite sides of the tension loaded plate element, the allowable stress range, FSR, on the cross section at the toe of the welds shall be determined by Equation A-3-6 or A-3-6M, for stress category C′′ as follows: FSR

⎛ 44 × 10 8 ⎞ = RFIL ⎜ ⎟ ⎝ nSR ⎠

⎛ 14.4 × 1011 ⎞ FSR = RFIL ⎜ ⎟ nSR ⎝ ⎠

0.333

(A-3-6)

0.333

(S.I.)

(A-3-6M)

where RFIL is the reduction factor for joints using a pair of transverse fillet welds only. ⎛ 0.06 + 0.72 ( w / t p ) ⎞ RFIL = ⎜ ⎟ ≤ 1.0 t 0p.167 ⎝ ⎠ ⎛ 0.10 + 1.24 ( w / t p ) ⎞ RFIL = ⎜ ⎟ ≤ 1.0 t 0p.167 ⎝ ⎠

(A-3-7)

(S.I..)

If RFIL = 1.0, use stress category C.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(A-3-7M)

AISC_PART 16_Spec.3_C:14th Ed.

16.1–196

3.4.

1/20/11

8:01 AM

Page 196

BOLTS AND THREADED PARTS

[App. 3.4.

BOLTS AND THREADED PARTS In bolts and threaded parts, the range of stress at service loads shall not exceed the allowable stress range computed as follows. (a) For mechanically fastened connections loaded in shear, the maximum range of stress in the connected material at service loads shall not exceed the allowable stress range computed using Equation A-3-1 where Cf and FTH are taken from Section 2 of Table A-3.1. (b) For high-strength bolts, common bolts and threaded anchor rods with cut, ground or rolled threads, the maximum range of tensile stress on the net tensile area from applied axial load and moment plus load due to prying action shall not exceed the allowable stress range computed using Equation A-3-8 or A-3-8M (stress category G). The net area in tension, At, is given by Equation A-3-9 or A-3-9M. ⎛ 3.9 × 10 8 ⎞ FSR = ⎜ ⎝ nSR ⎟⎠ ⎛ 1.28 × 1011 ⎞ FSR = ⎜ ⎟⎠ nSR ⎝ At =

At =

0.333

≥7

(A-3-8)

0.333

≥ 48

π⎛ 0.9743⎞ ⎟ ⎜⎝ d b − 4 n ⎠

π ( db − 0.9382 p)2 4

( S.I. )

(A-3-8M)

2

(A-3-9)

(S.I.)

(A-3-9M)

where db = the nominal diameter (body or shank diameter), in. (mm) n = threads per in. (threads per mm) p = pitch, in. per thread (mm per thread) For joints in which the material within the grip is not limited to steel or joints which are not tensioned to the requirements of Table J3.1 or J3.1M, all axial load and moment applied to the joint plus effects of any prying action shall be assumed to be carried exclusively by the bolts or rods. For joints in which the material within the grip is limited to steel and which are pretensioned to the requirements of Table J3.1 or J3.1M, an analysis of the relative stiffness of the connected parts and bolts shall be permitted to be used to determine the tensile stress range in the pretensioned bolts due to the total service live load and moment plus effects of any prying action. Alternatively, the stress range in the bolts shall be assumed to be equal to the stress on the net tensile area due to 20% of the absolute value of the service load axial load and moment from dead, live and other loads.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 3.5.]

3.5.

1/20/11

8:01 AM

Page 197

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

16.1–197

SPECIAL FABRICATION AND ERECTION REQUIREMENTS Longitudinal backing bars are permitted to remain in place, and if used, shall be continuous. If splicing is necessary for long joints, the bar shall be joined with complete penetration butt joints and the reinforcement ground prior to assembly in the joint. Longitudinal backing, if left in place, shall be attached with continuous fillet welds. In transverse joints subject to tension, backing bars, if used, shall be removed and the joint back gouged and welded. In transverse complete-joint-penetration T and corner joints, a reinforcing fillet weld, not less than 1/4 in. (6 mm) in size shall be added at reentrant corners. The surface roughness of thermally cut edges subject to cyclic stress ranges, that include tension, shall not exceed 1,000 μin. (25 μm), where ASME B46.1 is the reference standard. User Note: AWS C4.1 Sample 3 may be used to evaluate compliance with this requirement.

Reentrant corners at cuts, copes and weld access holes shall form a radius of not less than 3/8 in. (10 mm) by predrilling or subpunching and reaming a hole, or by thermal cutting to form the radius of the cut. If the radius portion is formed by thermal cutting, the cut surface shall be ground to a bright metal surface. For transverse butt joints in regions of tensile stress, weld tabs shall be used to provide for cascading the weld termination outside the finished joint. End dams shall not be used. Run-off tabs shall be removed and the end of the weld finished flush with the edge of the member. See Section J2.2b for requirements for end returns on certain fillet welds subject to cyclic service loading.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–198

1/20/11

8:01 AM

Page 198

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

[App. 3.5.

TABLE A-3.1 Fatigue Design Parameters Stress Category

Description

Constant Cf

Threshold FTH ksi Potential Crack (MPa) Initiation Point

SECTION 1 – PLAIN MATERIAL AWAY FROM ANY WELDING 1.1 Base metal, except noncoated weathering steel, with rolled or cleaned surface. Flame-cut edges with surface roughness value of 1,000 μin. (25 μm) or less, but without reentrant corners.

A

250 x 108

24 (165)

Away from all welds or structural connections

1.2 Noncoated weathering steel base metal with rolled or cleaned surface. Flame-cut edges with surface roughness value of 1,000 μin. (25 μm) or less, but without reentrant corners.

B

120 x 108

16 (110)

Away from all welds or structural connections

1.3 Member with drilled or reamed holes. Member with re-entrant corners at copes, cuts, block-outs or other geometrical discontinuities made to requirements of Appendix 3, Section 3.5, except weld access holes.

B

120 x 108

16 (110)

At any external edge or at hole perimeter

1.4 Rolled cross sections with weld access holes made to requirements of Section J1.6 and Appendix 3, Section 3.5. Members with drilled or reamed holes containing bolts for attachment of light bracing where there is a small longitudinal component of brace force.

C

44 x 108

10 (69)

At reentrant corner of weld access hole or at any small hole (may contain bolt for minor connections)

SECTION 2 – CONNECTED MATERIAL IN MECHANICALLY FASTENED JOINTS 2.1 Gross area of base metal in lap joints connected by high-strength bolts in joints satisfying all requirements for slip-critical connections.

B

120 x 108

16 (110)

Through gross section near hole

2.2 Base metal at net section of highstrength bolted joints, designed on the basis of bearing resistance, but fabricated and installed to all requirements for slip-critical connections.

B

120 x 108

16 (110)

In net section originating at side of hole

2.3 Base metal at the net section of other mechanically fastened joints except eye bars and pin plates.

D

22 x 108

7 (48)

In net section originating at side of hole

2.4 Base metal at net section of eyebar head or pin plate.

E

11 x 108

4.5 (31)

In net section originating at side of hole

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 3.5.]

1/20/11

8:01 AM

Page 199

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

16.1–199

TABLE A-3.1 (continued) Fatigue Design Parameters

Illustrative Typical Examples

SECTION 1 – PLAIN MATERIAL AWAY FROM ANY WELDING 1.1 and 1.2

1.3

1.4

SECTION 2 – CONNECTED MATERIAL IN MECHANICALLY FASTENED JOINTS 2.1

(Note: figures are for slip-critical bolted connections)

2.2

(Note: figures are for bolted connections designed to bear, meeting the requirements of slip-critical connections)

2.3

(Note: figures are for snug-tightened bolts, rivets, or other mechanical fasteners)

2.4

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–200

1/20/11

8:01 AM

Page 200

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

[App. 3.5.

TABLE A-3.1 (continued) Fatigue Design Parameters Stress Category

Description

Constant Cf

Threshold FTH ksi Potential Crack (MPa) Initiation Point

SECTION 3 – WELDED JOINTS JOINING COMPONENTS OF BUILT-UP MEMBERS 3.1 Base metal and weld metal in members without attachments built up of plates or shapes connected by continuous longitudinal complete-joint-penetration groove welds, back gouged and welded from second side, or by continuous fillet welds.

B

120 x 108

16 (110)

From surface or internal discontinuities in weld away from end of weld

3.2 Base metal and weld metal in members without attachments built up of plates or shapes, connected by continuous longitudinal complete-joint-penetration groove welds with backing bars not removed, or by continuous partialjoint-penetration groove welds.

B′

61 x 108

12 (83)

From surface or internal discontinuities in weld, including weld attaching backing bars

3.3 Base metal at weld metal terminations of longitudinal welds at weld access holes in connected built-up members.

D

22 x 108

7 (48)

From the weld termination into the web or flange

3.4 Base metal at ends of longitudinal intermittent fillet weld segments.

E

11 x 108

4.5 (31)

In connected material at start and stop locations of any weld deposit

3.5 Base metal at ends of partial length welded coverplates narrower than the flange having square or tapered ends, with or without welds across the ends; and coverplates wider than the flange with welds across the ends. Flange thickness (tf ) ≤ 0.8 in. (20 mm)

E

11 x 108

Flange thickness (tf ) > 0.8 in. (20 mm)

E′

3.9 x 108

3.6 Base metal at ends of partial length welded coverplates wider than the flange without welds across the ends.

E′

3.9 x 108

4.5 (31) 2.6 (18) 2.6 (18)

In flange at toe of end weld or in flange at termination of longitudinal weld or in edge of flange with wide coverplates

In edge of flange at end of coverplate weld

SECTION 4 – LONGITUDINAL FILLET WELDED END CONNECTIONS Initiating from end of any weld termination extending into the base metal

4.1 Base metal at junction of axially loaded members with longitudinally welded end connections. Welds shall be on each side of the axis of the member to balance weld stresses. t ≤ 0.5 in. (12 mm)

E

11 x 108

t > 0.5 in. (12 mm)

E′

3.9 x 108

4.5 (31) 2.6 (18)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 3.5.]

1/20/11

8:01 AM

Page 201

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

16.1–201

TABLE A-3.1 (continued) Fatigue Design Parameters

Illustrative Typical Examples

SECTION 3 – WELDED JOINTS JOINING COMPONENTS OF BUILT-UP MEMBERS 3.1

3.2

3.3

(a)

(b)

3.4

3.5

3.6

SECTION 4 – LONGITUDINAL FILLET WELDED END CONNECTIONS 4.1

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–202

1/20/11

8:01 AM

Page 202

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

[App. 3.5.

TABLE A-3.1 (continued) Fatigue Design Parameters Stress Category

Description

Constant Cf

Threshold FTH ksi Potential Crack (MPa) Initiation Point

SECTION 5 – WELDED JOINTS TRANSVERSE TO DIRECTION OF STRESS 5.1 Weld metal and base metal in or adjacent to complete-joint-penetration groove welded splices in rolled or welded cross sections with welds ground essentially parallel to the direction of stress and with soundness established by radiographic or ultrasonic inspection in accordance with the requirements of subclauses 6.12 or 6.13 of AWS D1.1/D1.1M.

B

120 x 108

16 (110)

From internal discontinuities in weld metal or along the fusion boundary

5.2 Weld metal and base metal in or adjacent to complete-joint-penetration groove welded splices with welds ground essentially parallel to the direction of stress at transitions in thickness or width made on a slope no greater than 1:21/2 and with weld soundness established by radiographic or ultrasonic inspection in accordance with the requirements of subclauses 6.12 or 6.13 of AWS D1.1/D1.1M. Fy < 90 ksi (620 MPa)

B

120 x 108

Fy ≥ 90 ksi (620 MPa)

B′

61 x 108

5.3 Base metal with Fy equal to or greater than 90 ksi (620 MPa) and weld metal in or adjacent to complete-jointpenetration groove welded splices with welds ground essentially parallel to the direction of stress at transitions in width made on a radius of not less than 2 ft (600 mm) with the point of tangency at the end of the groove weld and with weld soundness established by radiographic or ultrasonic inspection in accordance with the requirements of subclauses 6.12 or 6.13 of AWS D1.1/D1.1M.

B

120 x 108

16 (110)

From internal discontinuities in filler metal or discontinuities along the fusion boundary

5.4 Weld metal and base metal in or adjacent to the toe of complete-jointpenetration groove welds in T or corner joints or splices, with or without transitions in thickness having slopes no greater than 1:21/2 , when weld reinforcement is not removed and with weld soundness established by radiographic or ultrasonic inspection in accordance with the requirements of subclauses 6.12 or 6.13 of AWS D1.1/D1.1M.

C

44 x 108

10 (69)

From surface discontinuity at toe of weld extending into base metal or into weld metal.

From internal discontinuities in filler metal or along fusion boundary or at start of transition when Fy ≥ 90 ksi (620 MPa)

16 (110) 12 (83)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 3.5.]

1/20/11

8:01 AM

Page 203

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

TABLE A-3.1 (continued) Fatigue Design Parameters

Illustrative Typical Examples

SECTION 5 – WELDED JOINTS TRANSVERSE TO DIRECTION OF STRESS 5.1

5.2

5.3

5.4

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

16.1–203

AISC_PART 16_Spec.3_C_14th Ed._February 12, 2013 12/02/13 9:52 AM Page 204

16.1–204

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

[App. 3.5.

TABLE A-3.1 (continued) Fatigue Design Parameters Stress Category

Description

Constant Cf

Threshold FTH ksi (MPa)

Potential Crack Initiation Point

SECTION 5 – WELDED JOINTS TRANSVERSE TO DIRECTION OF STRESS (continued) 5.5 Base metal and weld metal at transverse end connections of tension-loaded plate elements using partial-joint-penetration groove welds in butt or T- or corner joints, with reinforcing or contouring fillets, FSR shall be the smaller of the toe crack or root crack allowable stress range. Crack initiating from weld toe:

C

44 x 108

10 (69)

Initiating from geometrical discontinuity at toe of weld extending into base metal.

Crack initiating from weld root:

C′

Eqn. A-3-4 or A-3-4M

None provided

Initiating at weld root subject to tension extending into and through weld

5.6 Base metal and weld metal at transverse end connections of tensionloaded plate elements using a pair of fillet welds on opposite sides of the plate. FSR shall be the smaller of the toe crack or root crack allowable stress range. Crack initiating from weld toe:

C

44 x 108

10 (69)

Initiating from geometrical discontinuity at toe of weld extending into base metal.

Crack initiating from weld root:

C′′

Eqn. A-3-6 or A-3-6M

None provided

Initiating at weld root subject to tension extending into and through weld

5.7 Base metal of tension loaded plate elements and on girders and rolled beam webs or flanges at toe of transverse fillet welds adjacent to welded transverse stiffeners.

C

44 x 108

10 (69)

From geometrical discontinuity at toe of fillet extending into base metal

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 3.5.]

1/20/11

8:01 AM

Page 205

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

TABLE A-3.1 (continued) Fatigue Design Parameters

Illustrative Typical Examples

SECTION 5 – WELDED JOINTS TRANSVERSE TO DIRECTION OF STRESS 5.5

5.6

5.7

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

16.1–205

AISC_PART 16_Spec.3_C:14th Ed.

16.1–206

1/20/11

8:01 AM

Page 206

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

[App. 3.5.

TABLE A-3.1 (continued) Fatigue Design Parameters Stress Category

Description

Constant Cf

Threshold FTH ksi Potential Crack (MPa) Initiation Point

SECTION 6 – BASE METAL AT WELDED TRANSVERSE MEMBER CONNECTIONS 6.1 Base metal at details attached by complete-joint-penetration groove welds subject to longitudinal loading only when the detail embodies a transition radius, R, with the weld termination ground smooth and with weld soundness established by radiographic or ultrasonic inspection in accordance with the requirements of subclauses 6.12 or 6.13 of AWS D1.1/D1.1M. R ≥ 24 in. (600 mm) 24 in. > R ≥ 6 in. (600 mm > R ≥ 150 mm) 6 in. > R ≥ 2 in. (150 mm > R ≥ 50 mm) 2 in. (50 mm) > R

Near point of tangency of radius at edge of member

B

120 x 108

C

44 x 108

D

22 x 108

E

11 x 108

B

120 x 108

C

44 x 108

D

22 x 108

E

11 x 108

C

44 x 108

C

44 x 108

D

22 x 108

E

11 x 108

16 (110) 10 (69) 7 (48) 4.5 (31)

6.2 Base metal at details of equal thickness attached by complete-jointpenetration groove welds subject to transverse loading with or without longitudinal loading when the detail embodies a transition radius, R, with the weld termination ground smooth and with weld soundness established by radiographic or ultrasonic inspection in accordance with the requirements of subclauses 6.12 or 6.13 of AWS D1.1/D1.1M: When weld reinforcement is removed: R ≥ 24 in. (600 mm) 24 in. > R ≥ 6 in. (600 mm > R ≥ 150 mm) 6 in. > R ≥ 2 in. (150 mm > R ≥ 50 mm) 2 in. (50 mm) > R When weld reinforcement is not removed: R ≥ 24 in. (600 mm) 24 in. > R ≥ 6 in. (600 mm > R ≥ 150 mm) 6 in. > R ≥ 2 in. (150 mm > R ≥ 50 mm) 2 in. (50 mm) > R

16 (110) 10 (69) 7 (48) 4.5 (31) 10 (69) 10 (69) 7 (48) 4.5 (31)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Near points of tangency of radius or in the weld or at fusion boundary or member or attachment At toe of the weld either along edge of member or the attachment

AISC_PART 16_Spec.3_C:14th Ed.

App. 3.5.]

1/20/11

8:01 AM

Page 207

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

16.1–207

TABLE A-3.1 (continued) Fatigue Design Parameters

Illustrative Typical Examples

SECTION 6 – BASE METAL AT WELDED TRANSVERSE MEMBER CONNECTIONS 6.1

6.2

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–208

1/20/11

8:01 AM

Page 208

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

[App. 3.5.

TABLE A-3.1 (continued) Fatigue Design Parameters Stress Category

Description

Constant Cf

Threshold FTH ksi Potential Crack (MPa) Initiation Point

SECTION 6 – BASE METAL AT WELDED TRANSVERSE MEMBER CONNECTIONS (cont’d) 6.3 Base metal at details of unequal thickness attached by complete-jointpenetration groove welds subject to transverse loading with or without longitudinal loading when the detail embodies a transition radius, R, with the weld termination ground smooth and with weld soundness established by radiographic or ultrasonic inspection in accordance with the requirements of subclauses 6.12 or 6.13 of AWS D1.1/D1.1M. When weld reinforcement is removed: R > 2 in. (50 mm)

D

22 x 108

7 (48)

At toe of weld along edge of thinner material

R ≤ 2 in. (50 mm)

E

11 x 108

4.5 (31)

In weld termination in small radius

When reinforcement is not removed: Any radius

E

11 x 108

4.5 (31)

At toe of weld along edge of thinner material Initiating in base metal at the weld termination or at the toe of the weld extending into the base metal

6.4 Base metal subject to longitudinal stress at transverse members, with or without transverse stress, attached by fillet or partial-joint-penetration groove welds parallel to direction of stress when the detail embodies a transition radius, R, with weld termination ground smooth: R > 2 in. (50 mm)

D

22 x 108

R ≤ 2 in. (50 mm)

E

11 x 108

7 (48) 4.5 (31)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 3.5.]

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16.1–209

TABLE A-3.1 (continued) Fatigue Design Parameters

Illustrative Typical Examples

SECTION 6 – BASE METAL AT WELDED TRANSVERSE MEMBER CONNECTIONS (cont’d) 6.3

6.4

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–210

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SPECIAL FABRICATION AND ERECTION REQUIREMENTS

[App. 3.5.

TABLE A-3.1 (continued) Fatigue Design Parameters Stress Category

Description

Constant Cf

Threshold FTH ksi Potential Crack (MPa) Initiation Point

SECTION 7 – BASE METAL AT SHORT ATTACHMENTS1 7.1 Base metal subject to longitudinal loading at details with welds parallel or transverse to the direction of stress where the detail embodies no transition radius and with detail length in direction of stress, a, and thickness of the attachment, b : a < 2 in. (50 mm) 2 in. (50 mm) ≤ a ≤ lesser of 12b or 4 in. (100 mm) a > 4 in. (100 mm) when b > 0.8 in. (20 mm) a > lesser of 12b or 4 in. (100 mm) when b ≤ 0.8 in. (20 mm)

Initiating in base metal at the weld termination or at the toe of the weld extending into the base metal C

44 x 108

D

22 x 108

E

11 x 108

E′

3.9 x 108

Initiating in base metal at the weld termination, extending into the base metal

7.2 Base metal subject to longitudinal stress at details attached by fillet or partial-joint-penetration groove welds, with or without transverse load on detail, when the detail embodies a transition radius, R, with weld termination ground smooth: R > 2 in. (50 mm)

D

22 x 108

R ≤ 2 in. (50 mm)

E

11 x 108

1

10 (69) 7 (48) 4.5 (31) 2.6 (18)

7 (48) 4.5 (31)

“Attachment” as used herein is defined as any steel detail welded to a member which, by its mere presence and independent of its loading, causes a discontinuity in the stress flow in the member and thus reduces the fatigue resistance.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 3.5.]

1/20/11

8:02 AM

Page 211

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

TABLE A-3.1 (continued) Fatigue Design Parameters

Illustrative Typical Examples

SECTION 7 – BASE METAL AT SHORT ATTACHMENTS1 7.1

7.2

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

16.1–211

AISC_PART 16_Spec.3_C:14th Ed.

16.1–212

1/20/11

8:02 AM

Page 212

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

[App. 3.5.

TABLE A-3.1 (continued) Fatigue Design Parameters Stress Category

Description

Constant Cf

Threshold FTH ksi Potential Crack (MPa) Initiation Point

SECTION 8 - MISCELLANEOUS 8.1 Base metal at steel headed stud anchors attached by fillet or automatic stud welding.

C

44 x 108

10 (69)

At toe of weld in base metal

8.2 Shear on throat of continuous or intermittent longitudinal or transverse fillet welds.

F

150 x 1010 (Eqn. A-3-2 or A-3-2M)

8 (55)

Initiating at the root of the fillet weld, extending into the weld

8.3 Base metal at plug or slot welds.

E

11 x 108

4.5 (31)

Initiating in the base metal at the end of the plug or slot weld, extending into the base metal

8.4 Shear on plug or slot welds.

F

150 x 1010 (Eqn. A-3-2 or A-3-2M)

8 (55)

Initiating in the weld at the faying surface, extending into the weld

8.5 Snug-tightened high-strength bolts, common bolts, threaded anchor rods, and hanger rods with cut, ground or rolled threads. Stress range on tensile stress area due to live load plus prying action when applicable.

G

3.9 x 108

7 (48)

Initiating at the root of the threads, extending into the fastener

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 3.5.]

1/20/11

8:02 AM

Page 213

SPECIAL FABRICATION AND ERECTION REQUIREMENTS

TABLE A-3.1 (continued) Fatigue Design Parameters

Illustrative Typical Examples

SECTION 8 - MISCELLANEOUS 8.1

8.2

8.3

8.4

8.5

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

16.1–213

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16.1–214

APPENDIX 4 STRUCTURAL DESIGN FOR FIRE CONDITIONS

This appendix provides criteria for the design and evaluation of structural steel components, systems and frames for fire conditions. These criteria provide for the determination of the heat input, thermal expansion and degradation in mechanical properties of materials at elevated temperatures that cause progressive decrease in strength and stiffness of structural components and systems at elevated temperatures. The appendix is organized as follows: 4.1. 4.2. 4.3.

4.1.

General Provisions Structural Design for Fire Conditions by Analysis Design by Qualification Testing

GENERAL PROVISIONS The methods contained in this appendix provide regulatory evidence of compliance in accordance with the design applications outlined in this section.

4.1.1.

Performance Objective Structural components, members and building frame systems shall be designed so as to maintain their load-bearing function during the design-basis fire and to satisfy other performance requirements specified for the building occupancy. Deformation criteria shall be applied where the means of providing structural fire resistance, or the design criteria for fire barriers, requires consideration of the deformation of the load-carrying structure. Within the compartment of fire origin, forces and deformations from the designbasis fire shall not cause a breach of horizontal or vertical compartmentation.

4.1.2.

Design by Engineering Analysis The analysis methods in Section 4.2 are permitted to be used to document the anticipated performance of steel framing when subjected to design-basis fire scenarios. Methods in Section 4.2 provide evidence of compliance with performance objectives established in Section 4.1.1. The analysis methods in Section 4.2 are permitted to be used to demonstrate an equivalency for an alternative material or method, as permitted by the applicable building code. Structural design for fire conditions using Appendix 4.2 shall be performed using the load and resistance factor design method in accordance with the provisions of Section B3.3 (LRFD).

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 4.2.]

4.1.3.

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STRUCTURAL DESIGN FOR FIRE CONDITIONS BY ANALYSIS

16.1–215

Design by Qualification Testing The qualification testing methods in Section 4.3 are permitted to be used to document the fire resistance of steel framing subject to the standardized fire testing protocols required by the applicable building code.

4.1.4.

Load Combinations and Required Strength The required strength of the structure and its elements shall be determined from the gravity load combination as follows: [0.9 or 1.2] D + T + 0.5L + 0.2S

(A-4-1)

where D = nominal dead load L = nominal occupancy live load S = nominal snow load T = nominal forces and deformations due to the design-basis fire defined in Section 4.2.1 A notional load, Ni = 0.002Yi, as defined in Section C2.2, where Ni = notional load applied at framing level i and Yi = gravity load from combination A-4-1 acting on framing level i, shall be applied in combination with the loads stipulated in Equation A-4-1. Unless otherwise stipulated by the applicable building code, D, L and S shall be the nominal loads specified in ASCE/SEI 7.

4.2.

STRUCTURAL DESIGN FOR FIRE CONDITIONS BY ANALYSIS It is permitted to design structural members, components and building frames for elevated temperatures in accordance with the requirements of this section.

4.2.1.

Design-Basis Fire A design-basis fire shall be identified to describe the heating conditions for the structure. These heating conditions shall relate to the fuel commodities and compartment characteristics present in the assumed fire area. The fuel load density based on the occupancy of the space shall be considered when determining the total fuel load. Heating conditions shall be specified either in terms of a heat flux or temperature of the upper gas layer created by the fire. The variation of the heating conditions with time shall be determined for the duration of the fire. When the analysis methods in Section 4.2 are used to demonstrate an equivalency as an alternative material or method as permitted by the applicable building code, the design-basis fire shall be determined in accordance with ASTM E119.

4.2.1.1. Localized Fire Where the heat release rate from the fire is insufficient to cause flashover, a localized fire exposure shall be assumed. In such cases, the fuel composition, arrangement of the fuel array and floor area occupied by the fuel shall be used to determine the radiant heat flux from the flame and smoke plume to the structure.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–216

1/20/11

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Page 216

STRUCTURAL DESIGN FOR FIRE CONDITIONS BY ANALYSIS

[App. 4.2.

4.2.1.2. Post-Flashover Compartment Fires Where the heat release rate from the fire is sufficient to cause flashover, a post-flashover compartment fire shall be assumed. The determination of the temperature versus time profile resulting from the fire shall include fuel load, ventilation characteristics of the space (natural and mechanical), compartment dimensions and thermal characteristics of the compartment boundary. The fire duration in a particular area shall be determined by considering the total combustible mass, or fuel load available in the space. In the case of either a localized fire or a post-flashover compartment fire, the fire duration shall be determined as the total combustible mass divided by the mass loss rate.

4.2.1.3. Exterior Fires The exposure of exterior structure to flames projecting from windows or other wall openings as a result of a post-flashover compartment fire shall be considered along with the radiation from the interior fire through the opening. The shape and length of the flame projection shall be used along with the distance between the flame and the exterior steelwork to determine the heat flux to the steel. The method identified in Section 4.2.1.2 shall be used for describing the characteristics of the interior compartment fire.

4.2.1.4. Active Fire Protection Systems The effects of active fire protection systems shall be considered when describing the design-basis fire. Where automatic smoke and heat vents are installed in nonsprinklered spaces, the resulting smoke temperature shall be determined from calculation.

4.2.2.

Temperatures in Structural Systems under Fire Conditions Temperatures within structural members, components and frames due to the heating conditions posed by the design-basis fire shall be determined by a heat transfer analysis.

4.2.3.

Material Strengths at Elevated Temperatures Material properties at elevated temperatures shall be determined from test data. In the absence of such data, it is permitted to use the material properties stipulated in this section. These relationships do not apply for steels with yield strengths in excess of 65 ksi (448 MPa) or concretes with specified compression strength in excess of 8,000 psi (55 MPa).

4.2.3.1. Thermal Elongation The coefficients of expansion shall be taken as follows: (a) For structural and reinforcing steels: For calculations at temperatures above 150 °F (65 °C), the coefficient of thermal expansion shall be 7.8 × 10−6/°F (1.4 × 10−5/oC).

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 4.2.]

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8:02 AM

Page 217

16.1–217

STRUCTURAL DESIGN FOR FIRE CONDITIONS BY ANALYSIS

TABLE A-4.2.1 Properties of Steel at Elevated Temperatures Steel Temperature, °F (°C)

k E ⴝ E ( T )/E ⴝ G ( T )/G

kp ⴝ Fp ( T )/Fy

ky ⴝ Fy ( T )/Fy

ku ⴝ Fu ( T )/Fy

68 (20)

1.00

1.00

1.00

1.00

200 (93)

1.00

1.00

1.00

1.00

400 (204)

0.90

0.80

1.00

1.00

600 (316)

0.78

0.58

1.00

1.00

750 (399)

0.70

0.42

1.00

1.00

800 (427)

0.67

0.40

0.94

0.94

1000 (538)

0.49

0.29

0.66

0.66

1200 (649)

0.22

0.13

0.35

0.35

1400 (760)

0.11

0.06

0.16

0.16

1600 (871)

0.07

0.04

0.07

0.07

1800 (982)

0.05

0.03

0.04

0.04

2000 (1093)

0.02

0.01

0.02

0.02

2200 (1204)

0.00

0.00

0.00

0.00

(b) For normal weight concrete: For calculations at temperatures above 150 °F (65 °C), the coefficient of thermal expansion shall be 1.0 × 10−5/°F (1.8 × 10−5/oC). (c) For lightweight concrete: For calculations at temperatures above 150 °F (65 °C), the coefficient of thermal expansion shall be 4.4 × 10−6/°F (7.9 × 10−6/oC).

4.2.3.2. Mechanical Properties at Elevated Temperatures The deterioration in strength and stiffness of structural members, components and systems shall be taken into account in the structural analysis of the frame. The values Fy (T), Fp (T), Fu (T), E(T), G(T), fc′(T), Ec (T) and εcu (T) at elevated temperature to be used in structural analysis, expressed as the ratio with respect to the property at ambient, assumed to be 68 °F (20 °C), shall be defined as in Tables A-4.2.1 and A-4.2.2. Fp(T) is the proportional limit at elevated temperatures, which is calculated as a ratio to yield strength as specified in Table A-4.2.1. It is permitted to interpolate between these values. For lightweight concrete, values of εcu shall be obtained from tests.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–218

1/20/11

8:02 AM

Page 218

STRUCTURAL DESIGN FOR FIRE CONDITIONS BY ANALYSIS

[App. 4.2.

TABLE A-4.2.2 Properties of Concrete at Elevated Temperatures Concrete Temperature °F (°C)

4.2.4.

kc ⴝ fc′ (T )/fc′ Normal weight concrete

Lightweight concrete

Ec (T )/Ec

εcu (T ), % Normal weight concrete

68 (20)

1.00

1.00

1.00

0.25

200 (93)

0.95

1.00

0.93

0.34

400 (204)

0.90

1.00

0.75

0.46

550 (288)

0.86

1.00

0.61

0.58

600 (316)

0.83

0.98

0.57

0.62

800 (427)

0.71

0.85

0.38

0.80

1000 (538)

0.54

0.71

0.20

1.06

1200 (649)

0.38

0.58

0.092

1.32

1400 (760)

0.21

0.45

0.073

1.43

1600 (871)

0.10

0.31

0.055

1.49

1800 (982)

0.05

0.18

0.036

1.50

2000 (1093)

0.01

0.05

0.018

1.50

2200 (1204)

0.00

0.00

0.000

0.00

Structural Design Requirements

4.2.4.1. General Structural Integrity The structural frame shall be capable of providing adequate strength and deformation capacity to withstand, as a system, the structural actions developed during the fire within the prescribed limits of deformation. The structural system shall be designed to sustain local damage with the structural system as a whole remaining stable. Continuous load paths shall be provided to transfer all forces from the exposed region to the final point of resistance. The foundation shall be designed to resist the forces and to accommodate the deformations developed during the designbasis fire.

4.2.4.2. Strength Requirements and Deformation Limits Conformance of the structural system to these requirements shall be demonstrated by constructing a mathematical model of the structure based on principles of structural mechanics and evaluating this model for the internal forces and deformations in the members of the structure developed by the temperatures from the design-basis fire.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 4.2.]

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Page 219

STRUCTURAL DESIGN FOR FIRE CONDITIONS BY ANALYSIS

16.1–219

Individual members shall be provided with adequate strength to resist the shears, axial forces and moments determined in accordance with these provisions. Connections shall develop the strength of the connected members or the forces indicated above. Where the means of providing fire resistance requires the consideration of deformation criteria, the deformation of the structural system, or members thereof, under the design-basis fire shall not exceed the prescribed limits.

4.2.4.3. Methods of Analysis 4.2.4.3a. Advanced Methods of Analysis The methods of analysis in this section are permitted for the design of all steel building structures for fire conditions. The design-basis fire exposure shall be that determined in Section 4.2.1. The analysis shall include both a thermal response and the mechanical response to the design-basis fire. The thermal response shall produce a temperature field in each structural element as a result of the design-basis fire and shall incorporate temperaturedependent thermal properties of the structural elements and fire-resistive materials, as per Section 4.2.2. The mechanical response results in forces and deformations in the structural system subjected to the thermal response calculated from the design-basis fire. The mechanical response shall take into account explicitly the deterioration in strength and stiffness with increasing temperature, the effects of thermal expansions, and large deformations. Boundary conditions and connection fixity must represent the proposed structural design. Material properties shall be defined as per Section 4.2.3. The resulting analysis shall consider all relevant limit states, such as excessive deflections, connection fractures, and overall or local buckling.

4.2.4.3b. Simple Methods of Analysis The methods of analysis in this section are permitted to be used for the evaluation of the performance of individual members at elevated temperatures during exposure to fire. The support and restraint conditions (forces, moments and boundary conditions) applicable at normal temperatures are permitted to be assumed to remain unchanged throughout the fire exposure. For steel temperatures less than or equal to 400 °F (204 °C), the member and connection design strengths shall be determined without consideration of temperature effects. User Note: At temperatures below 400 °F (204 °C), the degradation in steel properties need not be considered in calculating member strengths for the simple method of analysis; however, forces and deformations induced by elevated temperatures must be considered. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–220

1/20/11

8:02 AM

Page 220

STRUCTURAL DESIGN FOR FIRE CONDITIONS BY ANALYSIS

[App. 4.2.

(1) Tension Members It is permitted to model the thermal response of a tension element using a onedimensional heat transfer equation with heat input as determined by the design-basis fire defined in Section 4.2.1. The design strength of a tension member shall be determined using the provisions of Chapter D, with steel properties as stipulated in Section 4.2.3 and assuming a uniform temperature over the cross section using the temperature equal to the maximum steel temperature. (2) Compression Members It is permitted to model the thermal response of a compression element using a one-dimensional heat transfer equation with heat input as determined by the design-basis fire defined in Section 4.2.1. The design strength of a compression member shall be determined using the provisions of Chapter E with steel properties as stipulated in Section 4.2.3 and Equation A-4-2 used in lieu of Equations E3-2 and E3-3 to calculate the nominal compressive strength for flexural buckling: ⎡ Fcr (T ) = ⎢ 0.42 ⎢ ⎣

Fy (T )

⎤

Fe (T ) ⎥

⎥ ⎦

Fy (T )

(A-4-2)

where Fy (T ) is the yield stress at elevated temperature and Fe (T ) is the critical elastic buckling stress calculated from Equation E3-4 with the elastic modulus E(T ) at elevated temperature. Fy (T ) and E(T ) are obtained using coefficients from Table A-4.2.1. (3) Flexural Members It is permitted to model the thermal response of flexural elements using a one-dimensional heat transfer equation to calculate bottom flange temperature and to assume that this bottom flange temperature is constant over the depth of the member. The design strength of a flexural member shall be determined using the provisions of Chapter F with steel properties as stipulated in Section 4.2.3 and Equations A-4-3 through A-4-10 used in lieu of Equations F2-2 through F26 to calculate the nominal flexural strength for lateral-torsional buckling of laterally unbraced doubly symmetric members: (a) When Lb ≤ Lr (T) cx ⎡ Lb ⎤ ⎤ ⎡ ⎢ 1 − M n (T ) = Cb Mr (T ) + ⎡⎣ M p (T ) − Mr (T ) ⎤⎦ ⎢ ⎥ ⎥ ⎢⎣ ⎣ Lr (T ) ⎦ ⎥⎦

(A-4-3)

(b) When Lb > Lr (T) M n (T ) = Fcr (T )S x

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(A-4-4)

AISC_PART 16_Spec.3_C:14th Ed.

App. 4.3.]

1/20/11

8:02 AM

Page 221

16.1–221

DESIGN BY QUALIFICATION TESTING

where Fcr (T) =

Cb π 2 E (T ) ⎛ Lb ⎞ ⎜⎝ r ⎟⎠ ts

2

1 + 0.078

Jc ⎛ Lb ⎞ S x ho ⎝⎜ rts ⎟⎠

2

2

L r (T) = 1.95rts

(A-4-5)

E (T ) Jc ⎡ F (T ) ⎤ ⎛ Jc ⎞ + 6.76 ⎢ L + ⎜ ⎥ ⎝ S x ho ⎟⎠ FL (T ) S x ho ⎣ E (T ) ⎦

2

(A-4-6)

Mr (T) = S x FL (T )

(A-4-7)

FL (T) = Fy ( k p − 0.3k y )

(A-4-8)

Mp (T) = Z x Fy (T )

(A-4-9)

cx

= 0.53 +

cx

= 0.6 +

T ≤ 3.0 where T is in °F 450

T ≤ 3.0 where T is in °C 250

(A-4-10)

(S.I.)

(A-4-10M)

The material properties at elevated temperatures, E(T ) and Fy (T ), and the kp and ky coefficients are calculated in accordance with Table A-4.2.1, and other terms are as defined in Chapter F. (4) Composite Floor Members It is permitted to model the thermal response of flexural elements supporting a concrete slab using a one-dimensional heat transfer equation to calculate bottom flange temperature. That temperature shall be taken as constant between the bottom flange and mid-depth of the web and shall decrease linearly by no more than 25% from the mid-depth of the web to the top flange of the beam. The design strength of a composite flexural member shall be determined using the provisions of Chapter I, with reduced yield stresses in the steel consistent with the temperature variation described under thermal response.

4.2.4.4. Design Strength The design strength shall be determined as in Section B3.3. The nominal strength, Rn, shall be calculated using material properties, as provided in Section 4.2.3, at the temperature developed by the design-basis fire, and as stipulated in this appendix.

4.3.

DESIGN BY QUALIFICATION TESTING

4.3.1.

Qualification Standards Structural members and components in steel buildings shall be qualified for the rating period in conformance with ASTM E119. Demonstration of compliance Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–222

1/20/11

8:02 AM

Page 222

DESIGN BY QUALIFICATION TESTING

[App. 4.3.

with these requirements using the procedures specified for steel construction in Section 5 of SEI/ASCE/SFPE Standard 29-05, Standard Calculation Methods for Structural Fire Protection, is permitted.

4.3.2.

Restrained Construction For floor and roof assemblies and individual beams in buildings, a restrained condition exists when the surrounding or supporting structure is capable of resisting forces and accommodating deformations caused by thermal expansion throughout the range of anticipated elevated temperatures. Steel beams, girders and frames supporting concrete slabs that are welded or bolted to integral framing members shall be considered restrained construction.

4.3.3.

Unrestrained Construction Steel beams, girders and frames that do not support a concrete slab shall be considered unrestrained unless the members are bolted or welded to surrounding construction that has been specifically designed and detailed to resist effects of elevated temperatures. A steel member bearing on a wall in a single span or at the end span of multiple spans shall be considered unrestrained unless the wall has been designed and detailed to resist effects of thermal expansion.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

8:02 AM

Page 223

16.1–223

APPENDIX 5 EVALUATION OF EXISTING STRUCTURES

This appendix applies to the evaluation of the strength and stiffness under static vertical (gravity) loads of existing structures by structural analysis, by load tests or by a combination of structural analysis and load tests when specified by the engineer of record or in the contract documents. For such evaluation, the steel grades are not limited to those listed in Section A3.1. This appendix does not address load testing for the effects of seismic loads or moving loads (vibrations). The Appendix is organized as follows: 5.1. 5.2. 5.3. 5.4. 5.5.

5.1.

General Provisions Material Properties Evaluation by Structural Analysis Evaluation by Load Tests Evaluation Report

GENERAL PROVISIONS These provisions shall be applicable when the evaluation of an existing steel structure is specified for (a) verification of a specific set of design loadings or (b) determination of the available strength of a force resisting member or system. The evaluation shall be performed by structural analysis (Section 5.3), by load tests (Section 5.4), or by a combination of structural analysis and load tests, as specified in the contract documents. Where load tests are used, the engineer of record shall first analyze the applicable parts of the structure, prepare a testing plan, and develop a written procedure to prevent excessive permanent deformation or catastrophic collapse during testing.

5.2.

MATERIAL PROPERTIES

1.

Determination of Required Tests The engineer of record shall determine the specific tests that are required from Sections 5.2.2 through 5.2.6 and specify the locations where they are required. Where available, the use of applicable project records shall be permitted to reduce or eliminate the need for testing.

2.

Tensile Properties Tensile properties of members shall be considered in evaluation by structural analysis (Section 5.3) or load tests (Section 5.4). Such properties shall include the yield stress, tensile strength and percent elongation. Where available, certified material test reports or certified reports of tests made by the fabricator or a testing laboratory in accordance with ASTM A6/A6M or A568/A568M, as applicable, shall be permit-

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

16.1–224

8:02 AM

Page 224

MATERIAL PROPERTIES

[App. 5.2.

ted for this purpose. Otherwise, tensile tests shall be conducted in accordance with ASTM A370 from samples cut from components of the structure.

3.

Chemical Composition Where welding is anticipated for repair or modification of existing structures, the chemical composition of the steel shall be determined for use in preparing a welding procedure specification (WPS). Where available, results from certified material test reports or certified reports of tests made by the fabricator or a testing laboratory in accordance with ASTM procedures shall be permitted for this purpose. Otherwise, analyses shall be conducted in accordance with ASTM A751 from the samples used to determine tensile properties, or from samples taken from the same locations.

4.

Base Metal Notch Toughness Where welded tension splices in heavy shapes and plates as defined in Section A3.1d are critical to the performance of the structure, the Charpy V-notch toughness shall be determined in accordance with the provisions of Section A3.1d. If the notch toughness so determined does not meet the provisions of Section A3.1d, the engineer of record shall determine if remedial actions are required.

5.

Weld Metal Where structural performance is dependent on existing welded connections, representative samples of weld metal shall be obtained. Chemical analysis and mechanical tests shall be made to characterize the weld metal. A determination shall be made of the magnitude and consequences of imperfections. If the requirements of AWS D1.1/D1.1M are not met, the engineer of record shall determine if remedial actions are required.

6.

Bolts and Rivets Representative samples of bolts shall be inspected to determine markings and classifications. Where bolts cannot be properly identified visually, representative samples shall be removed and tested to determine tensile strength in accordance with ASTM F606 or ASTM F606M and the bolt classified accordingly. Alternatively, the assumption that the bolts are ASTM A307 shall be permitted. Rivets shall be assumed to be ASTM A502, Grade 1, unless a higher grade is established through documentation or testing.

5.3.

EVALUATION BY STRUCTURAL ANALYSIS

1.

Dimensional Data All dimensions used in the evaluation, such as spans, column heights, member spacings, bracing locations, cross section dimensions, thicknesses, and connection details, shall be determined from a field survey. Alternatively, when available, it shall be permitted to determine such dimensions from applicable project design or shop drawings with field verification of critical values.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 5.4.]

2.

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EVALUATION BY LOAD TESTS

16.1–225

Strength Evaluation Forces (load effects) in members and connections shall be determined by structural analysis applicable to the type of structure evaluated. The load effects shall be determined for the static vertical (gravity) loads and factored load combinations stipulated in Section B2. The available strength of members and connections shall be determined from applicable provisions of Chapters B through K of this Specification.

3.

Serviceability Evaluation Where required, the deformations at service loads shall be calculated and reported.

5.4.

EVALUATION BY LOAD TESTS

1.

Determination of Load Rating by Testing To determine the load rating of an existing floor or roof structure by testing, a test load shall be applied incrementally in accordance with the engineer of record’s plan. The structure shall be visually inspected for signs of distress or imminent failure at each load level. Appropriate measures shall be taken if these or any other unusual conditions are encountered. The tested strength of the structure shall be taken as the maximum applied test load plus the in-situ dead load. The live load rating of a floor structure shall be determined by setting the tested strength equal to 1.2D + 1.6L, where D is the nominal dead load and L is the nominal live load rating for the structure. The nominal live load rating of the floor structure shall not exceed that which can be calculated using applicable provisions of the specification. For roof structures, Lr, S or R as defined in ASCE/SEI 7, shall be substituted for L. More severe load combinations shall be used where required by applicable building codes. Periodic unloading shall be considered once the service load level is attained and after the onset of inelastic structural behavior is identified to document the amount of permanent set and the magnitude of the inelastic deformations. Deformations of the structure, such as member deflections, shall be monitored at critical locations during the test, referenced to the initial position before loading. It shall be demonstrated that the deformation of the structure does not increase by more than 10% during a one-hour holding period under sustained, maximum test load. It is permissible to repeat the sequence if necessary to demonstrate compliance. Deformations of the structure shall also be recorded 24 hours after the test loading is removed to determine the amount of permanent set. Because the amount of acceptable permanent deformation depends on the specific structure, no limit is specified for permanent deformation at maximum loading. Where it is not feasible to load test the entire structure, a segment or zone of not less than one complete bay, representative of the most critical conditions, shall be selected.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–226

2.

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EVALUATION BY LOAD TESTS

[App. 5.4.

Serviceability Evaluation When load tests are prescribed, the structure shall be loaded incrementally to the service load level. Deformations shall be monitored during a one hour holding period under sustained service test load. The structure shall then be unloaded and the deformation recorded.

5.5.

EVALUATION REPORT After the evaluation of an existing structure has been completed, the engineer of record shall prepare a report documenting the evaluation. The report shall indicate whether the evaluation was performed by structural analysis, by load testing, or by a combination of structural analysis and load testing. Furthermore, when testing is performed, the report shall include the loads and load combination used and the loaddeformation and time-deformation relationships observed. All relevant information obtained from design drawings, material test reports, and auxiliary material testing shall also be reported. Finally, the report shall indicate whether the structure, including all members and connections, is adequate to withstand the load effects.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

8:02 AM

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16.1–227

APPENDIX 6 STABILITY BRACING FOR COLUMNS AND BEAMS

This appendix addresses the minimum strength and stiffness necessary to provide a braced point in a column, beam or beam-column. The appendix is organized as follows: 6.1. 6.2. 6.3. 6.4.

General Provisions Column Bracing Beam Bracing Beam-Column Bracing

User Note: The stability requirements for braced-frame systems are provided in Chapter C. The provisions in this appendix apply to bracing that is provided to stabilize individual columns, beams and beam-columns.

6.1.

GENERAL PROVISIONS Columns with end and intermediate braced points designed to meet the requirements in Section 6.2 are permitted to be designed based on the unbraced length, L, between the braced points with an effective length factor, K = 1.0. Beams with intermediate braced points designed to meet the requirements in Section 6.3 are permitted to be designed based on the unbraced length, Lb, between the braced points. When bracing is perpendicular to the members to be braced, the equations in Sections 6.2 and 6.3 shall be used directly. When bracing is oriented at an angle to the member to be braced, these equations shall be adjusted for the angle of inclination. The evaluation of the stiffness furnished by a brace shall include its member and geometric properties, as well as the effects of connections and anchoring details. User Note: In this appendix, relative and nodal bracing systems are addressed for columns and for beams with lateral bracing. For beams with torsional bracing, nodal and continuous bracing systems are addressed. A relative brace controls the movement of the braced point with respect to adjacent braced points. A nodal brace controls the movement at the braced point without direct interaction with adjacent braced points. A continuous bracing system consists of bracing that is attached along the entire member length; however, nodal bracing systems with a regular spacing can also be modeled as a continuous system.

The available strength and stiffness of the bracing members and connections shall equal or exceed the required strength and stiffness, respectively, unless analysis indicates that smaller values are justified. A second-order analysis that includes the Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

16.1–228

8:02 AM

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GENERAL PROVISIONS

[App. 6.1.

initial out-of-straightness of the member to obtain brace strength and stiffness requirements is permitted in lieu of the requirements of this appendix.

6.2.

COLUMN BRACING It is permitted to brace an individual column at end and intermediate points along the length using either relative or nodal bracing.

1.

Relative Bracing The required strength is Prb = 0.004Pr

(A-6-1)

The required stiffness is β br =

1 ⎛ 2 Pr ⎞ (LRFD) φ ⎜⎝ Lb ⎟⎠

⎛ 2P ⎞ β br = Ω ⎜ r ⎟ (ASD) ⎝ Lb ⎠

φ = 0.75 (LRFD)

Ω = 2.00 (ASD)

(A-6-2)

where Lb = unbraced length, in. (mm) For design according to Section B3.3 (LRFD) Pr = required strength in axial compression using LRFD load combinations, kips (N) For design according to Section B3.4 (ASD) Pr = required strength in axial compression using ASD load combinations, kips (N)

2.

Nodal Bracing The required strength is Prb = 0.01Pr

(A-6-3)

The required stiffness is β br =

1 ⎛ 8 Pr ⎞ (LRFD) φ ⎜⎝ Lb ⎟⎠

⎛ 8P ⎞ β br = Ω ⎜ r ⎟ (ASD) ⎝ Lb ⎠

(A-6-4)

User Note: These equations correspond to the assumption that nodal braces are equally spaced along the column. where φ = 0.75 (LRFD)

Ω = 2.00 (ASD)

For design according to Section B3.3 (LRFD) Pr = required strength in axial compression using LRFD load combinations, kips (N) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

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8:02 AM

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BEAM BRACING

16.1–229

For design according to Section B3.4 (ASD) Pr = required strength in axial compression using ASD load combinations, kips (N) In Equation A-6-4, Lb need not be taken less than the maximum effective length, KL, permitted for the column based upon the required axial strength, Pr .

6.3.

BEAM BRACING Beams and trusses shall be restrained against rotation about their longitudinal axis at points of support. When a braced point is assumed in the design between points of support, lateral bracing, torsional bracing, or a combination of the two shall be provided to prevent the relative displacement of the top and bottom flanges (i.e., to prevent twist). In members subject to double curvature bending, the inflection point shall not be considered a braced point unless bracing is provided at that location.

1.

Lateral Bracing Lateral bracing shall be attached at or near the beam compression flange, except as follows: (1) At the free end of a cantilevered beam, lateral bracing shall be attached at or near the top (tension) flange. (2) For braced beams subject to double curvature bending, lateral bracing shall be attached to both flanges at the braced point nearest the inflection point.

1a.

Relative Bracing The required strength is Prb = 0.008Mr Cd /ho

(A-6-5)

The required stiffness is β br =

1 ⎛ 4 M r Cd ⎞ (LRFD) φ ⎜⎝ Lb ho ⎟⎠

⎛ 4 M r Cd ⎞ (ASD) β br = Ω ⎜ ⎝ Lb ho ⎟⎠

(A-6-6)

where φ = 0.75 (LRFD)

Ω = 2.00 (ASD)

Cd = 1.0 except in the following case; = 2.0 for the brace closest to the inflection point in a beam subject to double curvature bending ho = distance between flange centroids, in. (mm) For design according to Section B3.3 (LRFD) Mr = required flexural strength using LRFD load combinations, kip-in. (N-mm) For design according to Section B3.4 (ASD) Mr = required flexural strength using ASD load combinations, kip-in. (N-mm)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

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1b.

8:02 AM

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BEAM BRACING

[App. 6.3.

Prb = 0.02Mr Cd /ho

(A-6-7)

Nodal Bracing The required strength is

The required stiffness is β br =

1 ⎛ 10 Mr Cd ⎞ (LRFD) φ ⎜⎝ Lb ho ⎟⎠

⎛ 10 Mr Cd ⎞ ( ASD) β br = Ω ⎜ ⎝ Lb ho ⎟⎠

(A-6-8)

where φ = 0.75 (LRFD)

Ω = 2.00 (ASD)

For design according to Section B3.3 (LRFD) Mr = required flexural strength using LRFD load combinations, kip-in. (N-mm) For design according to Section B3.4 (ASD) Mr = required flexural strength using ASD load combinations, kip-in. (N-mm) In Equation A-6-8, Lb need not be taken less than the maximum unbraced length permitted for the beam based upon the flexural required strength, Mr.

2.

Torsional Bracing It is permitted to attach torsional bracing at any cross-sectional location, and it need not be attached near the compression flange. User Note: Torsional bracing can be provided with a moment-connected beam, cross-frame, or other diaphragm element.

2a.

Nodal Bracing The required strength is Mrb =

0.024 Mr L nCb Lb

(A-6-9)

The required stiffness of the brace is βTb =

βT ⎛ βT ⎞ ⎜⎝ 1 − β ⎟⎠ sec

(A-6-10)

where

βT =

1 ⎛ 2 . 4 LMr2 ⎞ (LRFD) φ ⎜⎝ nEI yCb2 ⎟⎠

⎛ 2 . 4 LMr2 ⎞ ( ASD) βT = Ω ⎜ 2 ⎟ ⎝ nEI yCb ⎠

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(A-6-11)

AISC_PART 16_Spec.3_C:14th Ed.

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BEAM BRACING

β sec =

3.3E ⎛ 1.5 hot w3 tst bs3 ⎞ + ho ⎜⎝ 12 12 ⎟⎠

16.1–231

(A-6-12)

where φ = 0.75 (LRFD)

Ω = 3.00 (ASD)

User Note: Ω = 1.52/φ = 3.00 in Equation A-6-11 because the moment term is squared. = modification factor defined in Chapter F = modulus of elasticity of steel = 29,000 ksi (200 000 MPa) = out-of-plane moment of inertia, in.4 (mm4) = length of span, in. (mm) = stiffener width for one-sided stiffeners, in. (mm) = twice the individual stiffener width for pairs of stiffeners, in. (mm) n = number of nodal braced points within the span tw = thickness of beam web, in. (mm) tst = thickness of web stiffener, in. (mm) βT = overall brace system stiffness, kip-in./rad (N-mm/rad) βsec = web distortional stiffness, including the effect of web transverse stiffeners, if any, kip-in./rad (N-mm/rad) Cb E Iy L bs

User Note: If βsec < βT, Equation A-6-10 is negative, which indicates that torsional beam bracing will not be effective due to inadequate web distortional stiffness. For design according to Section B3.3 (LRFD) Mr = required flexural strength using LRFD load combinations, kip-in. (N-mm) For design according to Section B3.4 (ASD) Mr = required flexural strength using ASD load combinations, kip-in. (N-mm) When required, the web stiffener shall extend the full depth of the braced member and shall be attached to the flange if the torsional brace is also attached to the flange. Alternatively, it shall be permissible to stop the stiffener short by a distance equal to 4tw from any beam flange that is not directly attached to the torsional brace. In Equation A-6-9, Lb need not be taken less than the maximum unbraced length permitted for the beam based upon the required flexural strength, Mr .

2b.

Continuous Bracing For continuous bracing, Equations A-6-9 and A-6-10 shall be used with the following modifications: (1) L/n = 1.0 (2) Lb shall be taken equal to the maximum unbraced length permitted for the beam based upon the required flexural strength, Mr

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–232

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Page 232

BEAM BRACING

[App. 6.3.

(3) The web distortional stiffness shall be taken as: β sec =

6.4.

3.3Et w3 12 ho

(A-6-13)

BEAM-COLUMN BRACING For bracing of beam-columns, the required strength and stiffness for the axial force shall be determined as specified in Section 6.2, and the required strength and stiffness for the flexure shall be determined as specified in Section 6.3. The values so determined shall be combined as follows: (a) When relative lateral bracing is used, the required strength shall be taken as the sum of the values determined using Equations A-6-1 and A-6-5, and the required stiffness shall be taken as the sum of the values determined using Equations A-6-2 and A-6-6. (b) When nodal lateral bracing is used, the required strength shall be taken as the sum of the values determined using Equations A-6-3 and A-6-7, and the required stiffness shall be taken as the sum of the values determined using Equations A-6-4 and A-6-8. In Equations A-6-4 and A-6-8, Lb for beamcolumns shall be taken as the actual unbraced length; the provisions in Sections 6.2.2 and 6.3.1b that Lb need not be taken less than the maximum permitted effective length based upon Pr and Mr shall not be applied. (c) When torsional bracing is provided for flexure in combination with relative or nodal bracing for the axial force, the required strength and stiffness shall be combined or distributed in a manner that is consistent with the resistance provided by the element(s) of the actual bracing details.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

8:02 AM

Page 233

16.1–233

APPENDIX 7 ALTERNATIVE METHODS OF DESIGN FOR STABILITY

This appendix presents alternatives to the direct analysis method of design for stability defined in Chapter C. The two alternative methods covered are the effective length method and the first-order analysis method. The appendix is organized as follows: 7.1. 7.2. 7.3.

7.1.

General Stability Requirements Effective Length Method First-Order Analysis Method

GENERAL STABILITY REQUIREMENTS The general requirements of Section C1 shall apply. As an alternative to the direct analysis method (defined in Sections C1 and C2), it is permissible to design structures for stability in accordance with either the effective length method, specified in Section 7.2, or the first-order analysis method, specified in Section 7.3, subject to the limitations indicated in those sections.

7.2.

EFFECTIVE LENGTH METHOD

1.

Limitations The use of the effective length method shall be limited to the following conditions: (1) The structure supports gravity loads primarily through nominally vertical columns, walls or frames. (2) The ratio of maximum second-order drift to maximum first-order drift (both determined for LRFD load combinations or 1.6 times ASD load combinations) in all stories is equal to or less than 1.5. User Note: The ratio of second-order drift to first-order drift in a story may be taken as the B2 multiplier, calculated as specified in Appendix 8.

2.

Required Strengths The required strengths of components shall be determined from analysis conforming to the requirements of Section C2.1, except that the stiffness reduction indicated in Section C2.3 shall not be applied; the nominal stiffnesses of all structural steel components shall be used. Notional loads shall be applied in the analysis in accordance with Section C2.2b.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–234

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EFFECTIVE LENGTH METHOD

[App. 7.2.

User Note: Since the condition specified in Section C2.2b(4) will be satisfied in all cases where the effective length method is applicable, the notional load need only be applied in gravity-only load cases.

3.

Available Strengths The available strengths of members and connections shall be calculated in accordance with the provisions of Chapters D, E, F, G, H, I, J and K, as applicable. The effective length factor, K, of members subject to compression shall be taken as specified in (a) or (b), below, as applicable. (a) In braced frame systems, shear wall systems, and other structural systems where lateral stability and resistance to lateral loads does not rely on the flexural stiffness of columns, the effective length factor, K, of members subject to compression shall be taken as 1.0, unless rational analysis indicates that a lower value is appropriate. (b) In moment frame systems and other structural systems in which the flexural stiffnesses of columns are considered to contribute to lateral stability and resistance to lateral loads, the effective length factor, K, or elastic critical buckling stress, Fe, of those columns whose flexural stiffnesses are considered to contribute to lateral stability and resistance to lateral loads shall be determined from a sidesway buckling analysis of the structure; K shall be taken as 1.0 for columns whose flexural stiffnesses are not considered to contribute to lateral stability and resistance to lateral loads. Exception: It is permitted to use K = 1.0 in the design of all columns if the ratio of maximum second-order drift to maximum first-order drift (both determined for LRFD load combinations or 1.6 times ASD load combinations) in all stories is equal to or less than 1.1. User Note: Methods of calculating the effective length factor, K, are discussed in the Commentary.

Bracing intended to define the unbraced lengths of members shall have sufficient stiffness and strength to control member movement at the braced points. User Note: Methods of satisfying the bracing requirement are provided in Appendix 6. The requirements of Appendix 6 are not applicable to bracing that is included in the analysis of the overall structure as part of the overall force-resisting system.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 7.3.]

1/20/11

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Page 235

FIRST-ORDER ANALYSIS METHOD

7.3.

FIRST-ORDER ANALYSIS METHOD

1.

Limitations

16.1–235

The use of the first-order analysis method shall be limited to the following conditions: (1) The structure supports gravity loads primarily through nominally vertical columns, walls or frames. (2) The ratio of maximum second-order drift to maximum first-order drift (both determined for LRFD load combinations or 1.6 times ASD load combinations) in all stories is equal to or less than 1.5. User Note: The ratio of second-order drift to first-order drift in a story may be taken as the B2 multiplier, calculated as specified in Appendix 8. (3) The required axial compressive strengths of all members whose flexural stiffnesses are considered to contribute to the lateral stability of the structure satisfy the limitation: αPr ≤ 0.5Py

(A-7-1)

where α = 1.0 (LRFD); α = 1.6 (ASD) Pr = required axial compressive strength under LRFD or ASD load combinations, kips (N) Py = Fy A = axial yield strength, kips (N)

2.

Required Strengths The required strengths of components shall be determined from a first-order analysis, with additional requirements (1) and (2) below. The analysis shall consider flexural, shear and axial member deformations, and all other deformations that contribute to displacements of the structure. (1) All load combinations shall include an additional lateral load, Ni, applied in combination with other loads at each level of the structure: Ni = 2.1α (Δ /L)Yi ≥ 0.0042Yi

(A-7-2)

where α = 1.0 (LRFD); α = 1.6 (ASD) Yi = gravity load applied at level i from the LRFD load combination or ASD load combination, as applicable, kips (N) Δ /L = maximum ratio of Δ to L for all stories in the structure Δ = first-order interstory drift due to the LRFD or ASD load combination, as applicable, in. (mm). Where Δ varies over the plan area of the structure, Δ shall be the average drift weighted in proportion to vertical load or, alternatively, the maximum drift. L = height of story, in. (mm)

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–236

1/20/11

8:02 AM

Page 236

FIRST-ORDER ANALYSIS METHOD

[App. 7.3.

The additional lateral load at any level, Ni, shall be distributed over that level in the same manner as the gravity load at the level. The additional lateral loads shall be applied in the direction that provides the greatest destabilizing effect. User Note: For most building structures, the requirement regarding the direction of Ni may be satisfied as follows: For load combinations that do not include lateral loading, consider two alternative orthogonal directions for the additional lateral load, in a positive and a negative sense in each of the two directions, same direction at all levels; for load combinations that include lateral loading, apply all the additional lateral loads in the direction of the resultant of all lateral loads in the combination. (2) The nonsway amplification of beam-column moments shall be considered by applying the B1 amplifier of Appendix 8 to the total member moments. User Note: Since there is no second-order analysis involved in the first-order analysis method for design by ASD, it is not necessary to amplify ASD load combinations by 1.6 before performing the analysis, as required in the direct analysis method and the effective length method.

3.

Available Strengths The available strengths of members and connections shall be calculated in accordance with the provisions of Chapters D, E, F, G, H, I, J and K, as applicable. The effective length factor, K, of all members shall be taken as unity. Bracing intended to define the unbraced lengths of members shall have sufficient stiffness and strength to control member movement at the braced points. User Note: Methods of satisfying this requirement are provided in Appendix 6. The requirements of Appendix 6 are not applicable to bracing that is included in the analysis of the overall structure as part of the overall force-resisting system.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

1/20/11

8:02 AM

Page 237

16.1–237

APPENDIX 8 APPROXIMATE SECOND-ORDER ANALYSIS

This appendix provides, as an alternative to a rigorous second-order analysis, a procedure to account for second-order effects in structures by amplifying the required strengths indicated by a first-order analysis. The appendix is organized as follows: 8.1. 8.2.

8.1.

Limitations Calculation Procedure

LIMITATIONS The use of this procedure is limited to structures that support gravity loads primarily through nominally vertical columns, walls or frames, except that it is permissible to use the procedure specified for determining P-δ effects for any individual compression member.

8.2.

CALCULATION PROCEDURE The required second-order flexural strength, Mr, and axial strength, Pr, of all members shall be determined as follows: Mr = B1 Mnt + B2 Mlt

(A-8-1)

Pr = Pnt + B2 Plt

(A-8-2)

where B1 = multiplier to account for P-δ effects, determined for each member subject to compression and flexure, and each direction of bending of the member in accordance with Section 8.2.1. B1 shall be taken as 1.0 for members not subject to compression. B2 = multiplier to account for P-Δ effects, determined for each story of the structure and each direction of lateral translation of the story in accordance with Section 8.2.2 Mlt = first-order moment using LRFD or ASD load combinations, due to lateral translation of the structure only, kip-in. (N-mm) Mnt = first-order moment using LRFD or ASD load combinations, with the structure restrained against lateral translation, kip-in. (N-mm) Mr = required second-order flexural strength using LRFD or ASD load combinations, kip-in. (N-mm) Plt = first-order axial force using LRFD or ASD load combinations, due to lateral translation of the structure only, kips (N) Pnt = first-order axial force using LRFD or ASD load combinations, with the structure restrained against lateral translation, kips (N) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

16.1–238

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CALCULATION PROCEDURE

[App. 8.2.

Pr = required second-order axial strength using LRFD or ASD load combinations, kips (N) User Note: Equations A-8-1 and A-8-2 are applicable to all members in all structures. Note, however, that B1 values other than unity apply only to moments in beam-columns; B2 applies to moments and axial forces in components of the lateral force resisting system (including columns, beams, bracing members and shear walls). See Commentary for more on the application of Equations A-81and A-8-2.

1.

Multiplier B1 for P-δ Effects The B1 multiplier for each member subject to compression and each direction of bending of the member is calculated as follows: B1 =

Cm ≥1 1 − αPr / Pe1

(A-8-3)

where α = 1.00 (LRFD); α = 1.60 (ASD) Cm = coefficient assuming no lateral translation of the frame determined as follows: (a) For beam-columns not subject to transverse loading between supports in the plane of bending Cm = 0.6 ⫺ 0.4(M1 /M2)

(A-8-4)

where M1 and M2, calculated from a first-order analysis, are the smaller and larger moments, respectively, at the ends of that portion of the member unbraced in the plane of bending under consideration. M1/M2 is positive when the member is bent in reverse curvature, negative when bent in single curvature. (b) For beam-columns subject to transverse loading between supports, the value of Cm shall be determined either by analysis or conservatively taken as 1.0 for all cases. Pe1 = elastic critical buckling strength of the member in the plane of bending, calculated based on the assumption of no lateral translation at the member ends, kips (N) Pe1 =

π 2 EI *

( K1L )2

(A-8-5)

where EI* = flexural rigidity required to be used in the analysis (= 0.8τb EI when used in the direct analysis method where τb is as defined in Chapter C; = EI for the effective length and first-order analysis methods) E = modulus of elasticity of steel = 29,000 ksi (200 000 MPa) Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Spec.3_C:14th Ed.

App. 8.2.]

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CALCULATION PROCEDURE

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I = moment of inertia in the plane of bending, in.4 (mm4) L = length of member, in. (mm) K1 = effective length factor in the plane of bending, calculated based on the assumption of no lateral translation at the member ends, set equal to 1.0 unless analysis justifies a smaller value It is permitted to use the first-order estimate of Pr (i.e., Pr = Pnt + Plt) in Equation A-8-3.

2.

Multiplier B2 for P-Δ Effects The B2 multiplier for each story and each direction of lateral translation is calculated as follows: B2 =

1 ≥1 αPstory 1− Pe story

(A-8-6)

where α = 1.00 (LRFD); α = 1.60 (ASD) Pstory = total vertical load supported by the story using LRFD or ASD load combinations, as applicable, including loads in columns that are not part of the lateral force resisting system, kips (N) Pe story = elastic critical buckling strength for the story in the direction of translation being considered, kips (N), determined by sidesway buckling analysis or as: Pe story = RM

HL ΔH

(A-8-7)

where (A-8-8) RM = 1 ⫺ 0.15 (Pmf /Pstory) L = height of story, in. (mm) Pmf = total vertical load in columns in the story that are part of moment frames, if any, in the direction of translation being considered (= 0 for braced frame systems), kips (N) Δ H = first-order interstory drift, in the direction of translation being considered, due to lateral forces, in. (mm), computed using the stiffness required to be used in the analysis (stiffness reduced as provided in Section C2.3 when the direct analysis method is used). Where Δ H varies over the plan area of the structure, it shall be the average drift weighted in proportion to vertical load or, alternatively, the maximum drift. H = story shear, in the direction of translation being considered, produced by the lateral forces used to compute Δ H, kips (N) User Note: H and Δ H in Equation A-8-7 may be based on any lateral loading that provides a representative value of story lateral stiffness, H/Δ H.

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COMMENTARY on the Specification for Structural Steel Buildings June 22, 2010

(The Commentary is not a part of ANSI/AISC 360-10, Specification for Structural Steel Buildings, but is included for informational purposes only.)

INTRODUCTION The Specification is intended to be complete for normal design usage. The Commentary furnishes background information and references for the benefit of the design professional seeking further understanding of the basis, derivations and limits of the Specification. The Specification and Commentary are intended for use by design professionals with demonstrated engineering competence.

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COMMENTARY SYMBOLS

The Commentary uses the following symbols in addition to the symbols defined in the Specification. The section number in the right-hand column refers to the Commentary section where the symbol is first used. Symbol A B Cf Fy Fys H H Ig ILB Ipos Ineg Is Itr Iy Top Iy KS MCL MS MT Mo N Qm Rcap Rm Sr Ss Str

VQ

Definition Section Angle cross-sectional area, in.2 (mm2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G4 Overall width of rectangular HSS, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . I3 Compression force in concrete slab for fully composite beam; smaller of Fy As and 0.85fc′Ac, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I3.2 Reported yield stress, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 5.2.2 Static yield stress, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 5.2.2 Overall height of rectangular HSS, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . I3 Anchor height, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I8.2b Moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement, in.4 (mm4) . . . . . . . . . . . . . . . . . . . . . . . . . I2.1b Lower bound moment of inertia, in.4 (mm4) . . . . . . . . . . . . . . . . . . . . . . . . I3.2 Effective moment of inertia for positive moment, in.4 (mm4) . . . . . . . . . . . I3.2 Effective moment of inertia for negative moment, in.4 (mm4) . . . . . . . . . . I3.2 Moment of inertia for the structural steel section, in.4 (mm4) . . . . . . . . . . . I3.2 Moment of inertia for the fully composite uncracked transformed section, in.4 (mm4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .I3.2 Moment of inertia of the top flange about an axis through the web, in.4 (mm4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F1 Moment of inertia of the entire section about an axis through the web, in.4 (mm4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F1 Secant stiffness, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B3.6 Moment at the middle of the unbraced length, kip-in. (N-mm) . . . . . . . . . . . F1 Moment at service loads, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . B3.6 Torsional moment, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G4 Maximum first-order moment within the member due to the transverse loading, kip-in. (N-mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 8 Number of cycles to failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 3.3 Mean value of the load effect Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B3.3 Minimum rotation capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 1.2.2 Mean value of the resistance R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B3.3 Stress range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 3.3 Section modulus for the structural steel section, referred to the tension flange, in.3 (mm3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I3.2 Section modulus for the fully composite uncracked transformed section, referred to the tension flange of the steel section, in.3 (mm3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I3.2 Coefficient of variation of the load effect Q . . . . . . . . . . . . . . . . . . . . . . . . B3.3 Specification for Structural Steel Buildings, June 22, 2010

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COMMENTARY SYMBOLS

VR Vb acr ap ay fv k β βact δo ν θS

16.1–243

Coefficient of variation of the resistance R . . . . . . . . . . . . . . . . . . . . . . . . . B3.3 Component of the shear force parallel to the angle leg with width b and thickness t, kips (N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G4 Distance from the compression face to the neutral axis for a slender section, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I3 Distance from the compression face to the neutral axis for a compact section, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I3 Distance from the compression face to the neutral axis for a noncompact section, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I3 Shear stress in angle, ksi (MPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G4 Plate buckling coefficient characteristic of the type of plate edge-restraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E7.1 Reliability index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B3.3 Actual bracing stiffness provided . . . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 6.1 Maximum deflection due to transverse loading, in. (mm) . . . . . . . . . . . . App. 8 Poisson’s ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E7.1 Rotation at service loads, rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B3.6

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COMMENTARY GLOSSARY

The Commentary uses the following terms in addition to the terms defined in the Glossary of the Specification. The terms listed below are italicized where they first appear in a chapter in the Commentary text. Alignment chart. Nomograph for determining the effective length factor, K, for some types of columns. Biaxial bending. Simultaneous bending of a member about two perpendicular axes. Brittle fracture. Abrupt cleavage with little or no prior ductile deformation. Column curve. Curve expressing the relationship between axial column strength and slenderness ratio. Critical load. Load at which a perfectly straight member under compression may either assume a deflected position or may remain undeflected, or a beam under flexure may either deflect and twist out of plane or remain in its in-plane deflected position, as determined by a theoretical stability analysis. Cyclic load. Repeatedly applied external load that may subject the structure to fatigue. Drift damage index. Parameter used to measure the potential damage caused by interstory drift. Effective moment of inertia. Moment of inertia of the cross section of a member that remains elastic when partial plastification of the cross section takes place, usually under the combination of residual stress and applied stress; also, the moment of inertia based on effective widths of elements that buckle locally; also, the moment of inertia used in the design of partially composite members. Effective stiffness. Stiffness of a member computed using the effective moment of inertia of its cross section. Fatigue threshold. Stress range at which fatigue cracking will not initiate regardless of the number of cycles of loading. First-order plastic analysis. Structural analysis based on the assumption of rigid-plastic behavior—in other words, that equilibrium is satisfied throughout the structure and the stress is at or below the yield stress—and in which equilibrium conditions are formulated on the undeformed structure. Flexible connection. Connection permitting a portion, but not all, of the simple beam rotation of a member end. Inelastic action. Material deformation that does not disappear on removal of the force that produced it. Interstory drift. Lateral deflection of a floor relative to the lateral deflection of the floor immediately below, divided by the distance between floors, (δn – δn-1)/h. Permanent load. Load in which variations over time are rare or of small magnitude. All other loads are variable loads.

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Plastic plateau. Portion of the stress-strain curve for uniaxial tension or compression in which the stress remains essentially constant during a period of substantially increased strain. Primary member. For ponding analysis, beam or girder that supports the concentrated reactions from the secondary members framing into it. Residual stress. Stress that remains in an unloaded member after it has been formed into a finished product. (Examples of such stresses include, but are not limited to, those induced by cold bending, cooling after rolling, or welding). Rigid frame. Structure in which connections maintain the angular relationship between beam and column members under load. Secondary member. For ponding analysis, beam or joist that directly supports the distributed ponding loads on the roof of the structure. Sidesway. Lateral movement of a structure under the action of lateral loads, unsymmetrical vertical loads or unsymmetrical properties of the structure. Sidesway buckling. Buckling mode of a multistory frame precipitated by the relative lateral displacements of joints, leading to failure by sidesway of the frame. St. Venant torsion. Portion of the torsion in a member that induces only shear stresses in the member. Strain hardening. Phenomenon wherein ductile steel, after undergoing considerable deformation at or just above yield point, exhibits the capacity to resist substantially higher loading than that which caused initial yielding. Stub-column. A short compression test specimen utilizing the complete cross section, sufficiently long to provide a valid measure of the stress-strain relationship as averaged over the cross section, but short enough so that it will not buckle as a column in the elastic or plastic range. Total building drift. Lateral frame deflection at the top of the most occupied floor divided by the height of the building to that level, Δ /H. Undercut. Notch resulting from the melting and removal of base metal at the edge of a weld. Variable load. Load with substantial variation over time. Warping torsion. Portion of the total resistance to torsion that is provided by resistance to warping of the cross section.

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CHAPTER A GENERAL PROVISIONS

A1.

SCOPE The scope of this Specification is essentially the same as the 2005 Specification for Structural Steel Buildings that it replaces, with the exception of a new Chapter N, Quality Control and Quality Assurance. The basic purpose of the provisions in this Specification is the determination of the nominal and available strengths of the members, connections and other components of steel building structures. This Specification provides two methods of design: (1) Load and Resistance Factor Design (LRFD): The nominal strength is multiplied by a resistance factor, φ, and the resulting design strength is then required to equal or exceed the required strength determined by structural analysis for the appropriate LRFD load combinations specified by the applicable building code. (2) Allowable Strength Design (ASD): The nominal strength is divided by a safety factor, Ω, and the resulting allowable strength is then required to equal or exceed the required strength determined by structural analysis for the appropriate ASD load combinations specified by the applicable building code. This Specification gives provisions for determining the values of the nominal strengths according to the applicable limit states and lists the corresponding values of the resistance factor, φ, and the safety factor, Ω. Nominal strength is usually defined in terms of resistance to a load effect, such as axial force, bending moment, shear or torque, but in some instances it is expressed in terms of a stress. The ASD safety factors are calibrated to give the same structural reliability and the same component size as the LRFD method at a live-to-dead load ratio of 3. The term available strength is used throughout the Specification to denote design strength and allowable strength, as applicable. This Specification is applicable to both buildings and other structures. Many structures found in petrochemical plants, power plants, and other industrial applications are designed, fabricated and erected in a manner similar to buildings. It is not intended that this Specification address steel structures with vertical and lateral load-resisting systems that are not similar to buildings, such as those constructed of shells or catenary cables. The Specification may be used for the design of structural steel elements, as defined in the AISC Code of Standard Practice for Steel Buildings and Bridges (AISC, 2010a), hereafter referred to as the Code of Standard Practice, when used as components of nonbuilding structures or other structures. Engineering judgment must be applied to the Specification requirements when the structural steel elements Specification for Structural Steel Buildings, June 22, 2010

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are exposed to environmental or service conditions and/or loads not usually applicable to building structures. The Code of Standard Practice defines the practices that are the commonly accepted standards of custom and usage for structural steel fabrication and erection. As such, the Code of Standard Practice is primarily intended to serve as a contractual document to be incorporated into the contract between the buyer and seller of fabricated structural steel. Some parts of the Code of Standard Practice, however, form the basis for some of the provisions in this Specification. Therefore, the Code of Standard Practice is referenced in selected locations in this Specification to maintain the ties between these documents, where appropriate. The Specification disallows seismic design of buildings and other structures using the provisions of Appendix 1. The R-factor specified in ASCE/SEI 7-10 (ASCE, 2010) used to determine the seismic loads is based on a nominal value of system overstrength and ductility that is inherent in steel structures designed by elastic analysis using this Specification. Therefore, it would be inappropriate to take advantage of the additional strength afforded by the inelastic design approach presented in Appendix 1 while simultaneously using the code specified R-factor. In addition, the provisions for ductility in Appendix 1 are not fully consistent with the intended levels for seismic design.

A2.

REFERENCED SPECIFICATIONS, CODES AND STANDARDS Section A2 provides references to documents cited in this Specification. Note that not all grades of a particular material specification are necessarily approved for use according to this Specification. For a list of approved materials and grades, see Section A3.

A3.

MATERIAL

1.

Structural Steel Materials

1a.

ASTM Designations There are hundreds of steel materials and products. This Specification lists those products/materials that are commonly useful to structural engineers and those that have a history of satisfactory performance. Other materials may be suitable for specific applications, but the evaluation of those materials is the responsibility of the engineer specifying them. In addition to typical strength properties, considerations for materials may include but are not limited to strength properties in transverse directions, ductility, formability, soundness, weldability including sensitivity to thermal cycles, notch toughness, and other forms of crack sensitivity, coatings, and corrosivity. Consideration for product form may include material considerations in addition to effects of production, tolerances, testing, reporting and surface profiles. Hot-Rolled Structural Shapes. The grades of steel approved for use under this Specification, covered by ASTM specifications, extend to a yield stress of 100 ksi (690 MPa). Some of the ASTM specifications specify a minimum yield point, while Specification for Structural Steel Buildings, June 22, 2010

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others specify a minimum yield strength. The term “yield stress” is used in this Specification as a generic term to denote either the yield point or the yield strength. It is important to be aware of limitations of availability that may exist for some combinations of strength and size. Not all structural section sizes are included in the various material specifications. For example, the 60 ksi (415 MPa) yield stress steel in the A572/A572M specification includes plate only up to 11/4 in. (32 mm) in thickness. Another limitation on availability is that even when a product is included in this Specification, it may be infrequently produced by the mills. Specifying these products may result in procurement delays or require ordering large quantities directly from the producing mills. Consequently, it is prudent to check availability before completing the details of a design. The AISC web site provides this information (www.aisc.org). Properties in the direction of rolling are of principal interest in the design of steel structures. Hence, yield stress as determined by the standard tensile test is the principal mechanical property recognized in the selection of the steels approved for use under this Specification. It must be recognized that other mechanical and physical properties of rolled steel, such as anisotropy, ductility, notch toughness, formability, corrosion resistance, etc., may also be important to the satisfactory performance of a structure. It is not possible to incorporate in the Commentary adequate information to impart full understanding of all factors that might merit consideration in the selection and specification of materials for unique or especially demanding applications. In such a situation the user of the Specification is advised to make use of reference material contained in the literature on the specific properties of concern and to specify supplementary material production or quality requirements as provided for in ASTM material specifications. One such case is the design of highly restrained welded connections (AISC, 1973). Rolled steel is anisotropic, especially insofar as ductility is concerned; therefore, weld contraction strains in the region of highly restrained welded connections may exceed the strength of the material if special attention is not given to material selection, details, workmanship and inspection. Another special situation is that of fracture control design for certain types of service conditions (AASHTO, 2010). For especially demanding service conditions such as structures exposed to low temperatures, particularly those with impact loading, the specification of steels with superior notch toughness may be warranted. However, for most buildings, the steel is relatively warm, strain rates are essentially static, and the stress intensity and number of cycles of full design stress are low. Accordingly, the probability of fracture in most building structures is low. Good workmanship and good design details incorporating joint geometry that avoids severe stress concentrations are generally the most effective means of providing fracture-resistant construction. Hollow Structural Sections (HSS). Specified minimum tensile properties are summarized in Table C-A3.1 for various HSS and pipe material specifications and grades. ASTM A53 Grade B is included as an approved pipe material specification because it is the most readily available round product in the United States. Other Specification for Structural Steel Buildings, June 22, 2010

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MATERIAL

TABLE C-A3.1 Minimum Tensile Properties of HSS and Pipe Steels Grade

Fy , ksi (MPa)

Fu , ksi (MPa)

ASTM A53

B

35 (240)

60 (415)

ASTM A500 (round)

B C

42 (290) 46 (315)

58 (400) 62 (425)

ASTM A500 (rectangular)

B C

46 (315) 50 (345)

58 (400) 62 (425)

ASTM A501

A B

36 (250) 50 (345)

58 (400) 70 (485)

ASTM A618 (round)

I and II (t ≤ 3/4 in.) III

50 (345)

70 (485)

50 (345)

65 (450)

—

50 (345)

70 (485)

350W

51 (350)

65 (450)

Specification

ASTM A847 CAN/CSA-G40.20/G40.21

North American HSS products that have properties and characteristics that are similar to the approved ASTM products are produced in Canada under the General Requirements for Rolled or Welded Structural Quality Steel (CSA, 2004). In addition, pipe is produced to other specifications that meet the strength, ductility and weldability requirements of the materials in Section A3, but may have additional requirements for notch toughness or pressure testing. Pipe can be readily obtained in ASTM A53 material and round HSS in ASTM A500 Grade B is also common. For rectangular HSS, ASTM A500 Grade B is the most commonly available material and a special order would be required for any other material. Depending upon size, either welded or seamless round HSS can be obtained. In North America, however, all ASTM A500 rectangular HSS for structural purposes are welded. Rectangular HSS differ from box sections in that they have uniform thickness except for some thickening in the rounded corners. Nominal strengths of direct welded (T, Y & K) connections of HSS have been developed analytically and empirically. Connection deformation is anticipated and is an acceptance limit for connection tests. Ductility is necessary to achieve the expected deformations. The ratio of the specified yield strength to the specified tensile strength (yield/tensile ratio) is one measure of material ductility. Materials in HSS used in connection tests have had a yield/tensile ratio of up to 0.80 and therefore that ratio has been adopted as a limit of applicability for direct welded HSS connections. ASTM A500 Grade A material does not meet this ductility “limit of applicability” for direct connections in Chapter K. ASTM A500 Grade C has a yield/tensile ratio of 0.807 but it is reasonable to use the rounding method described in ASTM E29 and find this material acceptable for use. Specification for Structural Steel Buildings, June 22, 2010

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Even though ASTM A501 includes rectangular HSS, hot-formed rectangular HSS are not currently produced in the United States. The General Requirements for Rolled or Welded Structural Quality Steel (CSA, 2004) includes Class C (cold-formed) and Class H (cold-formed and stress relieved) HSS. Class H HSS have relatively low levels of residual stress, which enhances their performance in compression and may provide better ductility in the corners of rectangular HSS.

1c.

Rolled Heavy Shapes The web-to-flange intersection and the web center of heavy hot-rolled shapes, as well as the interior portions of heavy plates, may contain a more coarse grain structure and/or lower notch toughness material than other areas of these products. This is probably caused by ingot segregation, the somewhat lesser deformation during hot rolling, higher finishing temperature, and the slower cooling rate after rolling for these heavy sections. This characteristic is not detrimental to suitability for compression members or for nonwelded members. However, when heavy cross sections are joined by splices or connections using complete-joint-penetration groove welds that extend through the coarser and/or lower notch-tough interior portions, tensile strains induced by weld shrinkage may result in cracking. An example is a completejoint-penetration groove welded connection of a heavy cross section beam to any column section. When members of lesser thickness are joined by complete-joint-penetration groove welds, which induce smaller weld shrinkage strains, to the finer grained and/or more notch-tough surface material of ASTM A6/A6M shapes and heavy built-up cross sections, the potential for cracking is significantly lower. An example is a complete-joint-penetration groove welded connection of a nonheavy cross section beam to a heavy cross section column. For critical applications such as primary tension members, material should be specified to provide adequate notch toughness at service temperatures. Because of differences in the strain rate between the Charpy V-notch (CVN) impact test and the strain rate experienced in actual structures, the CVN test is conducted at a temperature higher than the anticipated service temperature for the structure. The location of the CVN test specimens (“alternate core location”) is specified in ASTM A6/A6M, Supplemental Requirement S30. The notch toughness requirements of Section A3.1c are intended only to provide material of reasonable notch toughness for ordinary service applications. For unusual applications and/or low temperature service, more restrictive requirements and/or notch toughness requirements for other section sizes and thicknesses may be appropriate. To minimize the potential for fracture, the notch toughness requirements of Section A3.1c must be used in conjunction with good design and fabrication procedures. Specific requirements are given in Sections J1.5, J1.6, J2.6 and J2.7. For rotary-straightened W-shapes, an area of reduced notch toughness has been documented in a limited region of the web immediately adjacent to the flange. This region may exist in W-shapes of all weights, not just heavy shapes. Considerations in design and detailing that recognize this situation are presented in Chapter J.

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Steel Castings and Forgings There are a number of ASTM specifications for steel castings. The SFSA Steel Castings Handbook (SFSA, 1995) recommends ASTM A216 as a product useful for steel structures. In addition to the requirements of this Specification, SFSA recommends that various other requirements be considered for cast steel products. It may be appropriate to inspect the first piece cast using magnetic particle inspection in accordance with ASTM E125, degree 1a, b or c. Radiographic inspection level III may be desirable for critical sections of the first piece cast. Ultrasonic testing (UT) in compliance with ASTM A609/A609M (ASTM, 2007b) may be appropriate for the first cast piece over 6 in. thick. Design approval, sample approval, periodic nondestructive testing of the mechanical properties, chemical testing, and selection of the correct welding specification should be among the issues defined in the selection and procurement of cast steel products. Refer to SFSA (1995) for design information about cast steel products.

3.

Bolts, Washers and Nuts The ASTM standard specification for A307 bolts covers two grades of fasteners (ASTM, 2007c). Either grade may be used under this Specification; however, it should be noted that Grade B is intended for pipe flange bolting and Grade A is the grade long in use for structural applications.

4.

Anchor Rods and Threaded Rods ASTM F1554 is the primary specification for anchor rods. Since there is a limit on the maximum available length of ASTM A325/A325M and ASTM A490/ A490M bolts, the attempt to use these bolts for anchor rods with design lengths longer than the maximum available lengths has presented problems in the past. The inclusion of ASTM A449 and A354 materials in this Specification allows the use of higher strength material for bolts longer than ASTM A325/A325M and ASTM A490/A490M bolts. The engineer of record should specify the required strength for threaded rods used as load-carrying members.

5.

Consumables for Welding The AWS filler metal specifications listed in Section A3.5 are general specifications that include filler metal classifications suitable for building construction, as well as classifications that may not be suitable for building construction. The AWS D1.1/D1.1M, Structural Welding Code—Steel (AWS, 2010) lists in Table 3.1 various electrodes that may be used for prequalified welding procedure specifications, for the various steels that are to be joined. This list specifically does not include various classifications of filler metals that are not suitable for structural steel applications. Filler metals listed under the various AWS A5 specifications may or may not have specified notch toughness properties, depending on the specific electrode classification. Section J2.6 identifies certain welded joints where notch toughness of filler metal is needed in building construction. There may be other situations where the

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engineer of record may elect to specify the use of filler metals with specified notch toughness properties, such as for structures subject to high loading rate, cyclic loading, or seismic loading. Since AWS D1.1/D1.1M does not automatically require that the filler metal used have specified notch toughness properties, it is important that filler metals used for such applications be of an AWS classification where such properties are required. This information can be found in the AWS Filler Metal Specifications and is often contained on the filler metal manufacturer’s certificate of conformance or product specification sheets. When specifying filler metal and/or flux by AWS designation, the applicable standard specifications should be carefully reviewed to assure a complete understanding of the designation reference. This is necessary because the AWS designation systems are not consistent. For example, in the case of electrodes for shielded metal arc welding (AWS A5.1), the first two or three digits indicate the nominal tensile strength classification, in ksi, of the filler metal and the final two digits indicate the type of coating. For metric designations, the first two digits times 10 indicate the nominal tensile strength classification in MPa. In the case of mild steel electrodes for submerged arc welding (AWS A5.17/A5.17M), the first one or two digits times 10 indicate the nominal tensile strength classification for both U.S. customary and metric units, while the final digit or digits times 10 indicate the testing temperature in °F, for filler metal impact tests. In the case of low-alloy steel covered arc welding electrodes (AWS A5.5), certain portions of the designation indicate a requirement for stress relief, while others indicate no stress relief requirement. Engineers do not, in general, specify the exact filler metal to be employed on a particular structure. Rather, the decision as to which welding process and which filler metal is to be utilized is usually left with the fabricator or erector. Codes restrict the usage of certain filler materials, or impose qualification testing to prove the suitability of the specific electrode, so as to make certain that the proper filler metals are used.

A4.

STRUCTURAL DESIGN DRAWINGS AND SPECIFICATIONS The abbreviated list of requirements in this Specification is intended to be compatible with and a summary of the more extensive requirements in Section 3 of the Code of Standard Practice. The user should refer to Section 3 of the Code of Standard Practice for further information.

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CHAPTER B DESIGN REQUIREMENTS

B1.

GENERAL PROVISIONS Previous to the 2005 edition, the Specification contained a section entitled “Types of Construction”; for example, Section A2 in the 1999 Load and Resistance Factor Design Specification for Structural Steel Buildings (AISC, 2000b), hereafter referred to as the 1999 LRFD Specification. In this Specification there is no such section and the requirements related to “types of construction” have been divided between Section B1, Section B3.6 and Section J1. Historically, “Types of Construction” was the section that established what type of structures the Specification covers. The preface to the 1999 LRFD Specification suggested that the purpose of the Specification was “to provide design criteria for routine use and not to provide specific criteria for infrequently encountered problems.” The preface to the 1978 Specification for the Design, Fabrication, and Erection of Structural Steel for Buildings (AISC, 1978) contained similar language. While “routine use” may be difficult to describe, the contents of “Types of Construction” have been clearly directed at ordinary building frames with beams, columns and connections. The 1969 Specification for the Design, Fabrication, and Erection of Structural Steel for Buildings (AISC, 1969) classified “types of construction” as Type 1, 2 or 3. The primary distinction among these three types of construction was the nature of the connections of the beams to the columns. Type 1 construction referred to “rigid frames,” now called moment-resisting frames, which had connections capable of transmitting moment. Type 2 construction referred to “simple frames” with no moment transfer between beams and columns. Type 3 construction utilized “semirigid frames” with partially restrained connections. This system was allowed if a predictable and reliable amount of connection flexibility and moment transfer could be documented. The 1986 Load and Resistance Factor Design Specification for Structural Steel Buildings (AISC, 1986) changed the designations from Type 1, 2 or 3 to the designations FR (fully restrained) and PR (partially restrained). In these designations, the term “restraint” refers to the degree of moment transfer and the associated deformation in the connections. The 1986 LRFD Specification also used the term “simple framing” to refer to structures with “simple connections,” that is, connections with negligible moment transfer. In essence, FR was equivalent to Type 1, “simple framing” was equivalent to Type 2, and PR was equivalent to Type 3 construction. Type 2 construction of earlier Specifications and “simple framing” of the 1986 LRFD Specification had additional provisions that allowed the wind loads to be carried by moment resistance of selected joints of the frame, provided that: Specification for Structural Steel Buildings, June 22, 2010

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(1) The connections and connected members have capacity to resist the wind moments. (2) The girders are adequate to carry the full gravity load as “simple beams.” (3) The connections have adequate inelastic rotation capacity to avoid overstress of the fasteners or welds under combined gravity and wind loading. The concept of “wind connections” as both simple (for gravity loads) and moment resisting (for wind loads) was proposed by Sourochnikoff (1950) and further examined by Disque (1964). The basic proposal asserted that such connections have some moment resistance but that this resistance is low enough under wind load such that the connections would sustain inelastic deformations. Under repeated (cyclic) wind loads, the connection response would appear to reach a condition where the gravity load moments would be very small. The proposal postulated that the elastic resistance of the connections to wind moments would remain the same as the initial resistance, although it is known that many connections do not exhibit a linear elastic initial response. Additional recommendations have been provided by Geschwindner and Disque (2005). More recent research has shown that the AISC direct analysis method, as defined in the 2005 Specification for Structural Steel Buildings (AISC, 2005a) and this Specification, is the best approach to cover all relevant response effects (White and Goverdhan, 2008). Section B1 widens the purview of this Specification to a broader class of construction types. It recognizes that a structural system is a combination of members connected in such a way that the structure can respond in different ways to meet different design objectives under different loads. Even within the purview of ordinary buildings, there can be enormous variety in the design details. This Specification is meant to be primarily applicable to the common types of building frames with gravity loads carried by beams and girders and lateral loads carried by moment frames, braced frames or shear walls. However, there are many unusual buildings or building-like structures for which this Specification is also applicable. Rather than attempt to establish the purview of the Specification with an exhaustive classification of construction types, Section B1 requires that the design of members and their connections be consistent with the intended use of the structure and the assumptions made in the analysis of the structure.

B2.

LOADS AND LOAD COMBINATIONS The loads and load combinations for use with this Specification are given in the applicable building code. In the absence of an applicable specific local, regional or national building code, the nominal loads (for example, D, L, Lr, S, R, W and E), load factors and load combinations are as specified in ASCE/SEI 7, Minimum Design Loads for Buildings and Other Structures (ASCE, 2010). This edition of ASCE/SEI 7 has adopted the seismic design provisions of the NEHRP Recommended Seismic Provisions for New Buildings and Other Structures (BSSC, 2009), as have the AISC Seismic Provisions for Structural Steel Buildings (AISC, 2010b). The reader is referred to the commentaries of these documents for an expanded discussion on loads, load factors and seismic design. Specification for Structural Steel Buildings, June 22, 2010

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This Specification is based on strength limit states that apply to structural steel design in general. The Specification permits design for strength using either load and resistance factor design (LRFD) or allowable strength design (ASD). It should be noted that the terms strength and stress reflect whether the appropriate section property has been applied in the calculation of the limit state available strength. In most instances, the Specification uses strength rather than stress in the safety check. In all cases it is a simple matter to recast the provisions in a stress format. The terminology used to describe load combinations in ASCE/SEI 7 is somewhat different from that used by this Specification. Section 2.3 of ASCE/SEI 7 defines Combining Factored Loads Using Strength Design; these combinations are applicable to design using the LRFD approach. Section 2.4 of ASCE/SEI 7 defines Combining Nominal Loads Using Allowable Stress Design; these combinations are applicable to design using the ASD load approach. Both the LRFD and ASD load combinations in the current edition of ASCE/SEI 7 (ASCE, 2010) have been changed from those of previous editions as has the overall treatment of wind loads. LRFD load combinations. If the LRFD approach is selected, the load combination requirements are defined in Section 2.3 of ASCE/SEI 7. The load combinations in Section 2.3 of ASCE/SEI 7 are based on modern probabilistic load modeling and a comprehensive survey of reliabilities inherent in traditional design practice (Galambos et al., 1982; Ellingwood et al., 1982). These load combinations utilize a “principal action-companion action format,” which is based on the notion that the maximum combined load effect occurs when one of the time-varying loads takes on its maximum lifetime value (principal action) while the other variable loads are at “arbitrary point-in-time” values (companion actions), the latter being loads that would be measured in a load survey at any arbitrary time. The dead load, which is considered to be permanent, is the same for all combinations in which the load effects are additive. Research has shown that this approach to load combination analysis is consistent with the manner in which loads actually combine on structural elements and systems in situations in which strength limit states may be approached. The load factors reflect uncertainty in individual load magnitudes and in the analysis that transforms load to load effect. The nominal loads in ASCE/SEI 7 are substantially in excess of the arbitrary point-in-time values. The nominal live, wind and snow loads historically have been associated with mean return periods of approximately 50 years. Wind loads historically have been adjusted upward by a high load factor in previous editions to approximate a longer return period; in the 2010 edition of ASCE/SEI 7 the load factor is 1.0 and the wind-speed maps correspond to return periods deemed appropriate for the design of each occupancy type (approximately 700 years for common occupancies). The return period associated with earthquake loads has been more complex historically and the approach has been revised in both the 2003 and 2009 editions of the NEHRP Recommended Seismic Provisions for New Buildings and Other Structures (BSSC, 2003, 2009). In the 2009 edition, adopted as the basis for ASCE/SEI 7-10, the earthquake loads calculated at most locations are intended to produce a uniform maximum collapse probability of 1% in a 50 year period by integrating the collapse probability (a product of hazard amplitude and an assumed structural fragility) across Specification for Structural Steel Buildings, June 22, 2010

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all return periods. At some sites in regions of high seismic activity, where high intensity events occur frequently, deterministic limits on the ground motion result in somewhat higher collapse probabilities. Commentary to Chapter 1 of ASCE/SEI 710 provides information on the intended maximum probability of structural failure under earthquake and other loads. Load combinations of ASCE/SEI 7, Section 2.3, which apply specifically to cases in which the structural actions due to lateral forces and gravity loads counteract one another and the dead load stabilizes the structure, incorporate a load factor on dead load of 0.9. ASD Load Combinations. If the ASD approach is selected, the load combination requirements are defined in Section 2.4 of ASCE/SEI 7. The load combinations in Section 2.4 of ASCE/SEI 7 are similar to those traditionally used in allowable stress design. In ASD, safety is provided by the safety factor, Ω, and the nominal loads in the basic combinations involving gravity loads, earth pressure or fluid pressure are not factored. The reduction in the combined time-varying load effect in combinations incorporating wind or earthquake load is achieved by the load combination factor 0.75. This load combination factor dates back to the 1972 edition of ANSI Standard A58.1, the predecessor of ASCE/SEI 7. It should be noted that in ASCE/SEI 7, the 0.75 factor applies only to combinations of variable loads; it is irrational to reduce the dead load because it is always present and does not fluctuate in time. It should also be noted that certain ASD load combinations may actually result in a higher required strength than similar load combinations for LRFD. Load combinations that apply specifically to cases in which the structural actions due to lateral forces and gravity loads counteract one another, where the dead load stabilizes the structure, incorporate a load factor on dead load of 0.6. This eliminates a deficiency in the traditional treatment of counteracting loads in allowable stress design and emphasizes the importance of checking stability. The earthquake load effect is multiplied by 0.7 in applicable combinations involving that load to align allowable strength design for earthquake effects with the definition of E in the sections of ASCE/SEI 7 defining Seismic Load Effects and Combinations. The load combinations in Sections 2.3 and 2.4 of ASCE/SEI 7 apply to design for strength limit states. They do not account for gross error or negligence. Loads and load combinations for nonbuilding structures and other structures may be defined in ASCE/SEI 7 or other applicable industry standards and practices.

B3.

DESIGN BASIS Load and resistance factor design (LRFD) and allowable strength design (ASD) are distinct methods. They are equally acceptable by this Specification, but their provisions are not identical and not interchangeable. Indiscriminate use of combinations of the two methods could result in unpredictable performance or unsafe design. Thus, the LRFD and ASD methods are specified as alternatives. There are, however, circumstances in which the two methods could be used in the design, modification or renovation of a structural system without conflict, such as providing modifications to a structural floor system of an older building after assessing the as-built conditions. Specification for Structural Steel Buildings, June 22, 2010

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Required Strength This Specification permits the use of elastic, inelastic or plastic structural analysis. Generally, design is performed by elastic analysis. Provisions for inelastic and plastic analysis are given in Appendix 1. The required strength is determined by the appropriate methods of structural analysis. In some circumstances, as in the proportioning of stability bracing members that carry no calculated forces (see, for example, Appendix 6), the required strength is explicitly stated in this Specification.

2.

Limit States A limit state is a condition in which a structural system or component becomes unfit for its intended purpose (serviceability limit state), or has reached its ultimate loadcarrying capacity (strength limit state). Limit states may be dictated by functional requirements, such as maximum deflections or drift; they may be related to structural behavior, such as the formation of a plastic hinge or mechanism; or they may represent the collapse of the whole or part of the structure, such as by instability or fracture. The design provisions in the Specification ensure that the probability of exceeding a limit state is acceptably small by stipulating the combination of load factors, resistance or safety factors, nominal loads and nominal strengths consistent with the design assumptions. Two kinds of limit states apply to structures: (1) strength limit states, which define safety against local or overall failure conditions during the intended life of the structure; and (2) serviceability limit states, which define functional requirements. This Specification, like other structural design codes, focuses primarily on strength limit states because of overriding considerations of public safety. This does not mean that limit states of serviceability (see Chapter L) are not important to the designer, who must provide for functional performance and economy of design. However, serviceability considerations permit more exercise of judgment on the part of the designer. Strength limit states vary from element to element, and several limit states may apply to a given element. The most common strength limit states are yielding, buckling and rupture. The most common serviceability limit states include deflections or drift, and vibrations. Structural integrity provisions that establish minimum requirements for connectivity have been introduced into various building codes. The intent of those provisions is to provide a minimum level of robustness for the structure to enhance its performance under an extraordinary event. The requirements are prescriptive in nature, as the forces generated by the undefined extraordinary event may exceed those due to the minimum nominal loads stipulated by the building code. Unless specifically prohibited by the applicable building code, the full ductile load-deformation (stress-strain) response of steel may be used to calculate the nominal capacity to satisfy nominal strength requirements prescribed for structural integrity. The performance criteria for structural integrity are different from the traditional design methodology where serviceability and strength limit states, such as limiting Specification for Structural Steel Buildings, June 22, 2010

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deformation and preventing yielding, often control connection design. Thus, Section B3.2 establishes that limit states checked during design for traditional loads and load combinations involving limiting deformations or yielding of connection components are not necessary for the structural integrity checks. Thus, as examples of the application of these provisions, this section removes the limitation on inelastic yielding of double angles in a beam connection as they tend to straighten when subjected to high axial tension forces or the substantial deformation of bolt holes that might be restricted in traditional connection design. In addition, this section permits the use of short-slots parallel to the direction of the specified tension force without triggering the slip-critical requirements, contrary to traditional connection design, since movement of the bolt in the slot during an extraordinary event is not detrimental to overall structural performance. In this case, bolts are assumed to be located at the critical end of the slot for all applicable limit states. Single-plate shear connection design to meet structural integrity requirements is discussed in Geschwindner and Gustafson (2010).

3.

Design for Strength Using Load and Resistance Factor Design (LRFD) Design for strength by LRFD is performed in accordance with Equation B3-1. The left side of Equation B3-1, Ru, represents the required strength computed by structural analysis based on load combinations stipulated in ASCE/SEI 7 (ASCE, 2010), Section 2.3 (or their equivalent), while the right side, φRn, represents the limiting structural resistance, or design strength, provided by the member or element. The resistance factor, φ, in this Specification is equal to or less than 1.0. When compared to the nominal strength, Rn, computed according to the methods given in Chapters D through K, a φ of less than 1.0 accounts for approximations in the theory and variations in mechanical properties and dimensions of members and frames. For limit states where φ = 1.00, the nominal strength is judged to be sufficiently conservative when compared to the actual strength that no reduction is needed. The LRFD provisions are based on: (1) probabilistic models of loads and resistance; (2) a calibration of the LRFD provisions to the 1978 edition of the ASD Specification for selected members; and (3) the evaluation of the resulting provisions by judgment and past experience aided by comparative design office studies of representative structures. In the probabilistic basis for LRFD (Ravindra and Galambos, 1978; Ellingwood et al., 1982), the load effects, Q, and the resistances, R, are modeled as statistically independent random variables. In Figure C-B3.1, relative frequency distributions for Q and R are portrayed as separate curves on a common plot for a hypothetical case. As long as the resistance, R, is greater than (to the right of) the effects of the loads, Q, a margin of safety for the particular limit state exists. However, because Q and R are random variables, there is a small probability that R may be less than Q. The probability of this limit state is related to the degree of overlap of the frequency distributions in Figure C-B3.1, which depends on the positioning of their mean values (Rm versus Qm) and their dispersions. Specification for Structural Steel Buildings, June 22, 2010

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The probability that R is less than Q depends on the distributions of the many variables (material, loads, etc.) that determine resistance and total load effect. Often, only the means and the standard deviations or coefficients of variation of the variables involved in the determination of R and Q can be estimated. However, this information is sufficient to build an approximate design provision that is independent of the knowledge of these distributions, by stipulating the following design condition: β VR2 + VQ2 ≤ ln ( Rm Qm )

(C-B3-1)

where Rm = mean value of the resistance R Qm = mean value of the load effect Q VR = coefficient of variation of the resistance R VQ = coefficient of variation of the load effect Q For structural elements and the usual loading, Rm, Qm, and the coefficients of variation, VR and VQ, can be estimated, so a calculation of β=

1n ( Rm / Qm ) VR2 + VQ2

(C-B3-2)

will give a comparative measure of reliability of a structure or component. The parameter β is denoted the reliability index. Extensions to the determination of β in Equation C-B3-2 to accommodate additional probabilistic information and more complex design situations are described in Ellingwood et al. (1982) and have been used in the development of the recommended load combinations in ASCE/SEI 7. The original studies that determined the statistical properties (mean values and coefficients of variation) for the basic material properties and for steel beams, columns, composite beams, plate girders, beam-columns and connection elements that were

Fig. C-B3.1. Frequency distribution of load effect Q and resistance R.

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used to develop the LRFD provisions are presented in a series of eight articles in the September 1978 issue of the Journal of the Structural Division (ASCE, Vol. 104, ST9). The corresponding load statistics are given in Galambos et al. (1982). Based on these statistics, the values of β inherent in the 1978 Specification for the Design, Fabrication, and Erection of Structural Steel for Buildings (AISC, 1978) were evaluated under different load combinations (live/dead, wind/dead, etc.) and for various tributary areas for typical members (beams, columns, beam-columns, structural components, etc.). As might be expected, there was a considerable variation in the range of β-values. For example, compact rolled beams (flexure) and tension members (yielding) had β-values that decreased from about 3.1 at L /D = 0.50 to 2.4 at L /D = 4. This decrease is a result of ASD applying the same factor to dead load, which is relatively predictable, and live load, which is more variable. For bolted or welded connections, β was in the range of 4 to 5. The variation in β that was inherent to ASD is reduced substantially in LRFD by specifying several target β-values and selecting load and resistance factors to meet these targets. The Committee on Specifications set the point at which LRFD is calibrated to ASD at L/D = 3.0 for braced compact beams in flexure and tension members at yield. The resistance factor, φ, for these limit states is 0.90, and the implied β is approximately 2.6 for members and 4.0 for connections. The larger βvalue for connections reflects the complexity in modeling their behavior, effects of workmanship, and the benefit provided by additional strength. Limit states for other members are handled similarly. The databases on steel strength used in previous editions of the LRFD Specification for Structural Steel Buildings were based mainly on research conducted prior to 1970. An important recent study of the material properties of structural shapes (Bartlett et al., 2003) reflected changes in steel production methods and steel materials that have occurred over the past 15 years. This study indicated that the new steel material characteristics did not warrant changes in the φ-values.

4.

Design for Strength Using Allowable Strength Design (ASD) The ASD method is provided in this Specification as an alternative to LRFD for use by engineers who prefer to deal with ASD load combinations and allowable stresses in the traditional ASD format. The term “allowable strength” has been introduced to emphasize that the basic equations of structural mechanics that underlie the provisions are the same for LRFD and ASD. Traditional ASD is based on the concept that the maximum stress in a component shall not exceed a specified allowable stress under normal service conditions. The load effects are determined on the basis of an elastic analysis of the structure, while the allowable stress is the limiting stress (at yielding, instability, rupture, etc.) divided by a safety factor. The magnitude of the safety factor and the resulting allowable stress depend on the particular governing limit state against which the design must produce a certain margin of safety. For any single element, there may be a number of different allowable stresses that must be checked.

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The safety factor in traditional ASD provisions was a function of both the material and the component being considered. It may have been influenced by factors such as member length, member behavior, load source and anticipated quality of workmanship. The traditional safety factors were based solely on experience and have remained unchanged for over 50 years. Although ASD-designed structures have performed adequately over the years, the actual level of safety provided was never known. This was a principal drawback of the traditional ASD approach. An illustration of typical performance data is provided in Bjorhovde (1978), where theoretical and actual safety factors for columns are examined. Design for strength by ASD is performed in accordance with Equation B3-2. The ASD method provided in the Specification recognizes that the controlling modes of failure are the same for structures designed by ASD and LRFD. Thus, the nominal strength that forms the foundation of LRFD is the same nominal strength that provides the foundation for ASD. When considering available strength, the only difference between the two methods is the resistance factor in LRFD, φ, and the safety factor in ASD, Ω. In developing appropriate values of Ω for use in this Specification, the aim was to ensure similar levels of safety and reliability for the two methods. A straightforward approach for relating the resistance factor and the safety factor was developed. As already mentioned, the original LRFD Specification was calibrated to the 1978 ASD Specification at a live load to dead load ratio of 3. Thus, by equating the designs for the two methods at a ratio of live-to-dead load of 3, the relationship between φ and Ω can be determined. Using the live plus dead load combinations, with L = 3D, yields the following relationships. For design according to Section B3.3 (LRFD): φRn = 1.2 D + 1.6 L = 1.2 D + 1.6( 3D ) = 6 D Rn =

(C-B3-3)

6D φ

For design according to Section B3.4 (ASD): Rn = D + L = D + 3D = 4 D Ω

(C-B3-4)

Rn = Ω (4D) Equating Rn from the LRFD and ASD formulations and solving for Ω yields Ω=

6 D ⎛ 1 ⎞ 1.5 ⎟= ⎜ φ ⎝ 4D⎠ φ

(C-B3-5)

Throughout the Specification, the values of Ω were obtained from the values of φ by Equation C-B3-5.

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Design for Stability Section B3.5 provides the charging language for Chapter C on design for stability.

6.

Design of Connections Section B3.6 provides the charging language for Chapter J and Chapter K on the design of connections. Chapter J covers the proportioning of the individual elements of a connection (angles, welds, bolts, etc.) once the load effects on the connection are known. Section B3.6 establishes that the modeling assumptions associated with the structural analysis must be consistent with the conditions used in Chapter J to proportion the connecting elements. In many situations, it is not necessary to include the connection elements as part of the analysis of the structural system. For example, simple and FR connections may often be idealized as pinned or fixed, respectively, for the purposes of structural analysis. Once the analysis has been completed, the deformations or forces computed at the joints may be used to proportion the connection elements. The classifications of FR (fully restrained) and simple connections are meant to justify these idealizations for analysis with the provision that if, for example, one assumes a connection to be FR for the purposes of analysis, the actual connection must meet the FR conditions. In other words, it must have adequate strength and stiffness, as described in the provisions and discussed below. In certain cases, the deformation of the connection elements affects the way the structure resists load and hence the connections must be included in the analysis of the structural system. These connections are referred to as partially restrained (PR) moment connections. For structures with PR connections, the connection flexibility must be estimated and included in the structural analysis, as described in the following sections. Once the analysis is complete, the load effects and deformations computed for the connection can be used to check the adequacy of the connecting elements. For simple and FR connections, the connection proportions are established after the final analysis of the structural design is completed, thereby greatly simplifying the design cycle. In contrast, the design of PR connections (like member selection) is inherently iterative because one must assume values of the connection proportions in order to establish the force-deformation characteristics of the connection needed to perform the structural analysis. The life-cycle performance characteristics must also be considered. The adequacy of the assumed proportions of the connection elements can be verified once the outcome of the structural analysis is known. If the connection elements are inadequate, then the values must be revised and the structural analysis repeated. The potential benefits of using PR connections for various types of framing systems are discussed in the literature. Connection Classification. The basic assumption made in classifying connections is that the most important behavioral characteristics of the connection can be modeled by a moment-rotation (M-θ) curve. Figure C-B3.2 shows a typical M-θ curve. Implicit in the moment-rotation curve is the definition of the connection as being a region of the column and beam along with the connecting elements. The connection Specification for Structural Steel Buildings, June 22, 2010

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response is defined this way because the rotation of the member in a physical test is generally measured over a length that incorporates the contributions of not only the connecting elements, but also the ends of the members being connected and the column panel zone. Examples of connection classification schemes include those in Bjorhovde et al. (1990) and Eurocode 3 (CEN, 2005). These classifications account directly for the stiffness, strength and ductility of the connections. Connection Stiffness. Because the nonlinear behavior of the connection manifests itself even at low moment-rotation levels, the initial stiffness of the connection (shown in Figure C-B3.2) does not adequately characterize connection response at service levels. Furthermore, many connection types do not exhibit a reliable initial stiffness, or it exists only for a very small moment-rotation range. The secant stiffness, KS, at service loads is taken as an index property of connection stiffness. Specifically, KS = MS /θS

(C-B3-6)

where MS = moment at service loads, kip-in. (N-mm) θS = rotation at service loads, rad In the discussion below, L and EI are the length and bending rigidity, respectively, of the beam. If KS L /EI ≥ 20, it is acceptable to consider the connection to be fully restrained (in other words, able to maintain the angles between members). If KS L/EI ≤ 2, it is acceptable to consider the connection to be simple (in other words, it rotates without developing moment). Connections with stiffnesses between these two limits are partially restrained and the stiffness, strength and ductility of the connection must be

Fig. C-B3.2. Definition of stiffness, strength and ductility characteristics of the moment-rotation response of a partially restrained connection. Specification for Structural Steel Buildings, June 22, 2010

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considered in the design (Leon, 1994). Examples of FR, PR and simple connection response curves are shown in Figure C-B3.3. The points marked θS indicate the service load states for the example connections and thereby define the secant stiffnesses for those connections. Connection Strength. The strength of a connection is the maximum moment that it is capable of carrying, Mn, as shown in Figure C-B3.2. The strength of a connection can be determined on the basis of an ultimate limit-state model of the connection, or from a physical test. If the moment-rotation response does not exhibit a peak load then the strength can be taken as the moment at a rotation of 0.02 rad (Hsieh and Deierlein, 1991; Leon et al., 1996). It is also useful to define a lower limit on strength below which the connection may be treated as a simple connection. Connections that transmit less than 20% of the fully plastic moment of the beam at a rotation of 0.02 rad may be considered to have no flexural strength for design. However, it should be recognized that the aggregate strength of many weak connections can be important when compared to that of a few strong connections (FEMA, 1997). In Figure C-B3.3, the points marked Mn indicate the maximum strength states of the example connections. The points marked θu indicate the maximum rotation states of the example connections. Note that it is possible for an FR connection to have a strength less than the strength of the beam. It is also possible for a PR connection to have a strength greater than the strength of the beam. The strength of the connection must be adequate to resist the moment demands implied by the design loads.

Fig. C-B3.3. Classification of moment-rotation response of fully restrained (FR), partially restrained (PR) and simple connections. Specification for Structural Steel Buildings, June 22, 2010

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Connection Ductility. If the connection strength substantially exceeds the fully plastic moment of the beam, then the ductility of the structural system is controlled by the beam and the connection can be considered elastic. If the connection strength only marginally exceeds the fully plastic moment of the beam, then the connection may experience substantial inelastic deformation before the beam reaches its full strength. If the beam strength exceeds the connection strength, then deformations can concentrate in the connection. The ductility required of a connection will depend upon the particular application. For example, the ductility requirement for a braced frame in a nonseismic area will generally be less than the ductility required in a high seismic area. The rotation ductility requirements for seismic design depend upon the structural system (AISC, 2010b). In Figure C-B3.2, the rotation capacity, θu, can be defined as the value of the connection rotation at the point where either (a) the resisting strength of the connection has dropped to 0.8Mn or (b) the connection has deformed beyond 0.03 rad. This second criterion is intended to apply to connections where there is no loss in strength until very large rotations occur. It is not prudent to rely on these large rotations in design. The available rotation capacity, θu, should be compared with the rotation required at the strength limit state, as determined by an analysis that takes into account the nonlinear behavior of the connection. (Note that for design by ASD, the rotation required at the strength limit state should be assessed using analyses conducted at 1.6 times the ASD load combinations.) In the absence of an accurate analysis, a rotation capacity of 0.03 rad is considered adequate. This rotation is equal to the minimum beam-to-column connection capacity as specified in the seismic provisions for special moment frames (AISC, 2010b). Many types of PR connections, such as top and seat-angle connections, meet this criterion. Structural Analysis and Design. When a connection is classified as PR, the relevant response characteristics of the connection must be included in the analysis of the structure to determine the member and connection forces, displacements and the frame stability. Therefore, PR construction requires, first, that the moment-rotation characteristics of the connection be known and, second, that these characteristics be incorporated in the analysis and member design. Typical moment-rotation curves for many PR connections are available from one of several databases [for example, Goverdhan (1983); Ang and Morris (1984); Nethercot (1985); and Kishi and Chen (1986)]. Care should be exercised when utilizing tabulated moment-rotation curves not to extrapolate to sizes or conditions beyond those used to develop the database since other failure modes may control (ASCE Task Committee on Effective Length, 1997). When the connections to be modeled do not fall within the range of the databases, it may be possible to determine the response characteristics from tests, simple component modeling, or finite element studies (FEMA, 1995). Examples of procedures to model connection behavior are given in the literature (Bjorhovde et al., 1988; Chen and Lui, 1991; Bjorhovde et al., 1992; Lorenz et al., 1993; Chen and Toma, 1994; Chen et al., 1995; Bjorhovde et al., 1996; Leon et al., 1996; Leon and Easterling, 2002; Bijlaard et al., 2005; Bjorhovde et al., 2008). Specification for Structural Steel Buildings, June 22, 2010

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The degree of sophistication of the analysis depends on the problem at hand. Design for PR construction usually requires separate analyses for the serviceability and strength limit states. For serviceability, an analysis using linear springs with a stiffness given by Ks (see Figure C-B3.2) is sufficient if the resistance demanded of the connection is well below the strength. When subjected to strength load combinations, a procedure is needed whereby the characteristics assumed in the analysis are consistent with those of the connection response. The response is especially nonlinear as the applied moment approaches the connection strength. In particular, the effect of the connection nonlinearity on second-order moments and other stability checks needs to be considered (ASCE Task Committee on Effective Length, 1997).

7.

Moment Redistribution in Beams A beam that is reliably restrained at one or both ends (either by connection to other members or by a support) will have reserve capacity past yielding at the point with the greatest moment predicted by an elastic analysis. The additional capacity is the result of inelastic redistribution of moments. This Specification bases the design of the member on providing a resisting moment greater than the demand represented by the greatest moment predicted by the elastic analysis. This approach ignores the reserve capacity associated with inelastic redistribution. The 10% reduction of the greatest moment predicted by elastic analysis (with the accompanying 10% increase in the moment on the reverse side of the moment diagram) is an attempt to account approximately for the reserve capacity. This adjustment is appropriate only for cases where the inelastic redistribution of moments is possible. For statically determinate spans (e.g., beams that are simply supported at both ends or for cantilevers), redistribution is not possible. Therefore the adjustment is not allowable in these cases. Members with fixed ends or beams continuous over a support can sustain redistribution. Member sections that are unable to accommodate the inelastic rotation associated with the redistribution (e.g., because of local buckling) are also not permitted the reduction. Thus, only compact sections qualify for redistribution in this Specification. An inelastic analysis will automatically account for any redistribution. Therefore, the redistribution of moments only applies to moments computed from an elastic analysis. The 10% reduction rule applies only to beams. Inelastic redistribution is possible in more complicated structures, but the 10% amount is only verified, at present, for beams. For other structures, the provisions of Appendix 1 should be used.

8.

Diaphragms and Collectors This section provides charging language for the design of structural steel components (members and their connections) of diaphragms and collector systems. Diaphragms transfer in-plane lateral loads to the lateral force resisting system. Typical diaphragm elements in a building structure are the floor and roof systems which accumulate lateral forces due to gravity, wind and/or seismic loads and distribute these forces to individual elements (braced frames, moment frames, shear

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walls, etc.) of the vertically oriented lateral force resisting system of the building structure. Collectors (also known as drag struts) are often used to collect and deliver diaphragm forces to the lateral force resisting system. Diaphragms are classified into one of three categories: rigid, semi-rigid or flexible. Rigid diaphragms distribute the in-plane forces to the lateral load resisting system with negligible in-plane deformation of the diaphragm. A rigid diaphragm may be assumed to distribute the lateral loads in proportion to the relative stiffness of the individual elements of the lateral force resisting system. A semi-rigid diaphragm distributes the lateral loads in proportion to the in-plane stiffness of the diaphragm and the relative stiffness of the individual elements of the lateral force resisting system. The in-plane stiffness of a flexible diaphragm is negligible compared to the stiffness of the lateral load resisting system and, therefore, the distribution of lateral forces is independent of the relative stiffness of the individual elements of the lateral force resisting system. In this case, the distribution of lateral forces may be computed in a manner analogous to a series of simple beams spanning between the lateral force resisting system elements. Diaphragms should be designed for the shear, moment and axial forces resulting from the design loads. The diaphragm response may be considered analogous to a deep beam where the flanges (often referred to as chords of the diaphragm) develop tension and compression forces, and the web resists the shear. The component elements of the diaphragm need to have strength and deformation capacity consistent with assumptions and intended behavior.

10.

Design for Ponding As used in this Specification, ponding refers to the retention of water due solely to the deflection of flat roof framing. The amount of this water is dependent on the flexibility of the framing. Lacking sufficient framing stiffness, the accumulated weight of the water can result in the collapse of the roof. The problem becomes catastrophic when more water causes more deflection, resulting in more room for more water until the roof collapses. Detailed provisions for determining ponding stability and strength are given in Appendix 2.

12.

Design for Fire Conditions Section B3.12 provides the charging language for Appendix 4 on structural design for fire resistance. Qualification testing is an acceptable alternative to design by analysis for providing fire resistance. Qualification testing is addressed in ASCE/SFPE Standard 29 (ASCE, 2008), ASTM E119, and similar documents.

13.

Design for Corrosion Effects Steel members may deteriorate in some service environments. This deterioration may appear either as external corrosion, which would be visible upon inspection, or in undetected changes that would reduce member strength. The designer should recognize these problems by either factoring a specific amount of tolerance for damage into the design or providing adequate protection (for example, coatings or

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cathodic protection) and/or planned maintenance programs so that such problems do not occur. Because the interior of an HSS is difficult to inspect, some concern has been expressed regarding internal corrosion. However, good design practice can eliminate the concern and the need for expensive protection. Corrosion occurs in the presence of oxygen and water. In an enclosed building, it is improbable that there would be sufficient reintroduction of moisture to cause severe corrosion. Therefore, internal corrosion protection is a consideration only in HSS exposed to weather. In a sealed HSS, internal corrosion cannot progress beyond the point where the oxygen or moisture necessary for chemical oxidation is consumed (AISI, 1970). The oxidation depth is insignificant when the corrosion process must stop, even when a corrosive atmosphere exists at the time of sealing. If fine openings exist at connections, moisture and air can enter the HSS through capillary action or by aspiration due to the partial vacuum that is created if the HSS is cooled rapidly (Blodgett, 1967). This can be prevented by providing pressure-equalizing holes in locations that make it impossible for water to flow into the HSS by gravity. Situations where conservative practice would recommend an internal protective coating include: (1) open HSS where changes in the air volume by ventilation or direct flow of water is possible; and (2) open HSS subject to a temperature gradient that would cause condensation. HSS that are filled or partially filled with concrete should not be sealed. In the event of fire, water in the concrete will vaporize and may create pressure sufficient to burst a sealed HSS. Care should be taken to keep water from remaining in the HSS during or after construction, since the expansion caused by freezing can create pressure that is sufficient to burst an HSS. Galvanized HSS assemblies should not be completely sealed because rapid pressure changes during the galvanizing process tend to burst sealed assemblies.

B4.

MEMBER PROPERTIES

1.

Classification of Sections for Local Buckling Cross sections with a limiting width-to-thickness ratio, λ, greater than those provided in Table B4.1 are subject to local buckling limit states. For the 2010 Specification for Structural Steel Buildings, Table B4.1 was separated into two parts: B4.1a for compression members and B4.1b for flexural members. Separation of Table B4.1 into two parts reflects the fact that compression members are only categorized as either slender or nonslender, while flexural members may be slender, noncompact or compact. In addition, separation of Table B4.1 into two parts clarifies ambiguities in λr. The width-to-thickness ratio, λr, may be different for columns and beams, even for the same element in a cross section, reflecting both the underlying stress state of the connected elements, and the different design methodologies between columns (Chapter E and Appendix 1) and beams (Chapter F and Appendix 1). Limiting Width-to-Thickness Ratios for Compression Elements in Members Subject to Axial Compression. Compression members containing any elements Specification for Structural Steel Buildings, June 22, 2010

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with width-to-thickness ratios greater than λr provided in Table B4.1a are designated as slender and are subject to the local buckling reductions detailed in Section E7 of the Specification. Nonslender compression members (all elements having width-to-thickness ratio ≤ λr) are not subject to local buckling reductions. Flanges of Built-Up I-Shaped Sections. In the 1993 LRFD Specification for Structural Steel Buildings (AISC, 1993) , for built-up I-shaped sections under axial compression (Case 2 in Table B4.1a), modifications were made to the flange local buckling criterion to include web-flange interaction. The kc in the λr limit is the same as that used for flexural members. Theory indicates that the web-flange interaction in axial compression is at least as severe as in flexure. Rolled shapes are excluded from this provision because there are no standard sections with proportions where the interaction would occur at commonly available yield stresses. In built-up sections where the interaction causes a reduction in the flange local buckling strength, it is likely that the web is also a thin stiffened element. The kc factor accounts for the interaction of flange and web local buckling demonstrated in experiments reported in Johnson (1985). The maximum limit of 0.76 corresponds to Fcr = 0.69E/λ2 which was used as the local buckling strength in earlier editions of both the ASD and LRFD Specifications. An h/tw = 27.5 is required to reach kc = 0.76. Fully fixed restraint for an unstiffened compression element corresponds to kc = 1.3 while zero restraint gives kc = 0.42. Because of web-flange interactions it is possible to get kc < 0.42 from the kc formula. If h t w > 5.70 E Fy , use h/tw = 5.70 E / Fy in the kc equation, which corresponds to the 0.35 limit. Rectangular HSS in Compression. The limits for rectangular HSS walls in uniform compression (Case 6 in Table B4.1a) have been used in AISC Specifications since 1969. They are based on Winter (1968), where adjacent stiffened compression elements in box sections of uniform thickness were observed to provide negligible torsional restraint for one another along their corner edges. Round HSS in Compression. The λr limit for round HSS in compression (Case 9 in Table B4.1a) was first used in the 1978 Specification for the Design, Fabrication, and Erection of Structural Steel for Buildings (AISC, 1978). It was recommended in Schilling (1965) based upon research reported in Winter (1968). The same limit was also used to define a compact shape in bending in the 1978 Specification. Excluding the use of round HSS with D/t > 0.45E/Fy was also recommended in Schilling (1965). However, following the SSRC recommendations (Ziemian, 2010) and the approach used for other shapes with slender compression elements, a Q factor is used in Section E7 for round sections to account for interaction between local and column buckling. The Q factor is the ratio between the local buckling stress and the yield stress. The local buckling stress for the round section is taken from AISI provisions based on inelastic action (Winter, 1970) and is based on tests conducted on fabricated and manufactured cylinders. Subsequent tests on fabricated cylinders (Ziemian, 2010) confirm that this equation is conservative. Limiting Width-to-Thickness Ratios for Compression Elements in Members Subject to Flexure. Flexural members containing compression elements, all with width-to-thickness ratios less than or equal to λp as provided in Table B4.1b, are designated as compact. Compact sections are capable of developing a fully plastic stress Specification for Structural Steel Buildings, June 22, 2010

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distribution and they possess a rotation capacity of approximately 3 before the onset of local buckling (Yura et al., 1978). Flexural members containing any compression element with width-to-thickness ratios greater than λp, but still with all compression elements having width-to-thickness ratios less than or equal to λr, are designated as noncompact. Noncompact sections can develop partial yielding in compression elements before local buckling occurs, but will not resist inelastic local buckling at the strain levels required for a fully plastic stress distribution. Flexural members containing any compression elements with width-to-thickness ratios greater than λr are designated as slender. Slender-element sections have one or more compression elements that will buckle elastically before the yield stress is achieved. Noncompact and slender-element sections are subject to flange local buckling and/or web local buckling reductions as provided in Chapter F and summarized in Table User Note F1.1, or in Appendix 1. The values of the limiting ratios, λp and λr, specified in Table B4.1b are similar to those in the 1989 Specification for Structural Steel Buildings—Allowable Stress Design and Plastic Design (AISC, 1989) and Table 2.3.3.3 of Galambos (1978), except that λ p = 0.38 E / Fy , limited in Galambos (1978) to determinate beams and to indeterminate beams when moments are determined by elastic analysis, was adopted for all conditions on the basis of Yura et al. (1978). For greater inelastic rotation capacities than provided by the limiting value of λp given in Table B4.1b, and/or for structures in areas of high seismicity, see Chapter D and Table D1.1 of the AISC Seismic Provisions for Structural Steel Buildings (AISC, 2010b). Webs in Flexure. In the 2010 Specification for Structural Steel Buildings, formulas for λp were added as Case 16 in Table B4.1b for I-shaped beams with unequal flanges based on White (2003). Rectangular HSS in Flexure. The λp limit for compact sections is adopted from the Limit States Design of Steel Structures (CSA, 2009). Lower values of λp are specified for high-seismic design in the Seismic Provisions for Structural Steel Buildings based upon tests (Lui and Goel, 1987) that have shown that rectangular HSS braces subjected to reversed axial load fracture catastrophically under relatively few cycles if a local buckle forms. This was confirmed in tests (Sherman, 1995a) where rectangular HSS braces sustained over 500 cycles when a local buckle did not form, even though general column buckling had occurred, but failed in less than 40 cycles when a local buckle developed. Since 2005, the λp limit for webs in rectangular HSS flexural members (Case 19 in Table B4.1b) has been reduced from λp = 3.76 E / Fy to λp = 2.42 E / Fy based on the work of Wilkinson and Hancock (1998, 2002). Round HSS in Flexure. The λp values for round HSS in flexure (Case 20, Table B4.1b) are based on Sherman (1976), Sherman and Tanavde (1984) and Ziemian (2010). Section F8 also limits the D/t ratio for any round section to 0.45E/Fy. Beyond this, the local buckling strength decreases rapidly, making it impractical to use these sections in building construction.

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Design Wall Thickness for HSS ASTM A500/A500M (ASTM, 2007d) tolerances allow for a wall thickness that is not greater than ± 10% of the nominal value. Because the plate and strip from which electric-resistance-welded (ERW) HSS are made are produced to a much smaller thickness tolerance, manufacturers in the United States consistently produce ERW HSS with a wall thickness that is near the lower-bound wall thickness limit. Consequently, AISC and the Steel Tube Institute of North America (STI) recommend that 0.93 times the nominal wall thickness be used for calculations involving engineering design properties of ERW HSS. This results in a weight (mass) variation that is similar to that found in other structural shapes. Submerged-arc-welded (SAW) HSS are produced with a wall thickness that is near the nominal thickness and require no such reduction. The design wall thickness and section properties based upon this reduced thickness have been tabulated in AISC and STI publications since 1997.

3.

Gross and Net Area Determination

3a.

Gross Area Gross area is the total area of the cross section without deductions for holes or ineffective portions of elements subject to local buckling.

3b.

Net Area The net area is based on net width and load transfer at a particular chain. Because of possible damage around a hole during drilling or punching operations, 1/16 in. (1.5 mm) is added to the nominal hole diameter when computing the net area.

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CHAPTER C DESIGN FOR STABILITY

Design for stability is the combination of analysis to determine the required strengths of components and proportioning of components to have adequate available strengths. Various methods are available to provide for stability (Ziemian, 2010). Chapter C addresses the stability design requirements for steel buildings and other structures. It is based upon the direct analysis method, which can be used in all cases. The effective length method and first-order analysis method are addressed in Appendix 7 as alternative methods of design for stability, and can be used when the limits in Appendix Sections 7.2.1 and 7.3.1, respectively, are satisfied. Other approaches, including design using second-order inelastic or plastic analysis are permitted provided the general requirements in Section C1 are met. Additional provisions for design by inelastic analysis are provided in Appendix 1. Elastic structural analysis by itself is not sufficient to assess stability because the analysis and the equations for component strengths are inextricably interdependent.

C1.

GENERAL STABILITY REQUIREMENTS There are many parameters and behavioral effects that influence the stability of steelframed structures (Birnstiel and Iffland, 1980; McGuire, 1992; White and Chen, 1993; ASCE Task Committee on Effective Length, 1997; Ziemian, 2010). The stability of structures and individual elements must be considered from the standpoint of the structure as a whole, including not only the compression members, but also the beams, bracing systems and connections. Stiffness requirements for control of seismic drift are included in many building codes that prohibit sidesway amplification (Δ2nd-order /Δ1st-order or B2), calculated with nominal stiffness, from exceeding approximately 1.5 to 1.6 (ICC, 2009). This limit usually is well within the more general recommendation that sidesway amplification, calculated with reduced stiffness, should be equal to or less than 2.5. The latter recommendation is made because at larger levels of amplification, small changes in gravity loads and/or structural stiffness can result in relatively larger changes in sidesway deflections and second-order effects, due to large geometric nonlinearities. Table C-C1.1 shows how the five general requirements provided in Section C1 are addressed in the direct analysis method (Sections C2 and C3) and the effective length method (Appendix 7, Section 7.2). The first-order analysis method (Appendix 7, Section 7.3) is not included in Table C-C1.1 because it addresses these requirements in an indirect manner using a mathematical manipulation of the direct analysis method. The additional lateral load required in Appendix 7, Section 7.3.2(1) is calibrated to achieve roughly the same result as the collective effects of the notional load required in Section C2.2b, a B2 multiplier for P-Δ effects required in Section C2.1(2), and the stiffness reduction required in Section C2.3. Additionally, a B1 multiplier addresses P-δ effects as required in Appendix 7, Section 7.3.2(2). Specification for Structural Steel Buildings, June 22, 2010

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TABLE C-C1.1 Comparison of Basic Stability Requirements with Specific Provisions Basic Requirement in Section C1

Provision in Direct Analysis Method (DM)

Provision in Effective Length Method (ELM)

(1) Consider all deformations

C2.1(1). Consider all deformations

Same as DM (by reference to C2.1)

(2) Consider second-order effects (both P-Δ and P-δ)

C2.1(2). Consider second-order effects (P-Δ and P-δ)**

Same as DM (by reference to C2.1)

(3) Consider geometric imperfections This includes jointposition imperfections* (which affect structure response) and member imperfections (which affect structure response and member strength)

Effect of joint-position imperfections* on structure response

C2.2a. Direct modeling or C2.2b. Notional loads

Same as DM, second option only (by reference to C2.2b)

Effect of member imperfections on structure response

Included in the stiffness reduction specified in C2.3

Effect of member imperfections on member strength

Included in member strength formulas, with KL = L

(4) Consider stiffness reduction due to inelasticity This affects structure response and member strength

Effect of stiffness reduction on structure response

Included in the stiffness reduction specified in C2.3

All these effects are considered by using KL from a sidesway buckling analysis in the member strength check. Note that the only difference between DM and ELM is that:

Effect of stiffness reduction on member strength

Included in member strength formulas, with KL = L

Effect of stiffness/ strength uncertainty on structure response

Included in the stiffness reduction specified in C2.3

Effect of stiffness/ strength uncertainty on member strength

Included in member strength formulas, with KL = L

(5) Consider uncertainty in strength and stiffness This affects structure response and member strength

• DM uses reduced stiffness in the analysis; KL = L in the member strength check • ELM uses full stiffness in the analysis; KL from sidesway buckling analysis in the member strength check for frame members

* In typical building structures, the “joint-position imperfections” refers to column out-of-plumbness. ** Second-order effects may be considered either by rigorous second-order analysis or by the approximate technique (using B1 and B2) specified in Appendix 8.

C2.

CALCULATION OF REQUIRED STRENGTHS Analysis to determine required strengths in accordance with this Section and the assessment of member and connection available strengths in accordance with Section C3 form the basis of the direct analysis method of design for stability. This method is useful for the stability design of all structural steel systems, including moment frames, braced frames, shear walls, and combinations of these and similar systems (AISC-SSRC, 2003b). While the precise formulation of this method is Specification for Structural Steel Buildings, June 22, 2010

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unique to the AISC Specification, some of its features have similarities to other major design specifications around the world, including the Eurocodes, the Australian standard, the Canadian standard, and ACI 318 (ACI, 2008). The direct analysis method allows a more accurate determination of the load effects in the structure through the inclusion of the effects of geometric imperfections and stiffness reductions directly within the structural analysis. This also allows the use of K = 1.0 in calculating the in-plane column strength, Pc, within the beam-column interaction equations of Chapter H. This is a significant simplification in the design of steel moment frames and combined systems.

1.

General Analysis Requirements Deformations to be Considered in the Analysis. It is required that the analysis consider flexural, shear and axial deformations, and all other component and connection deformations that contribute to the displacement of the structure. However, it is important to note that “consider” is not synonymous with “include,” and some deformations can be neglected after rational consideration of their likely effect. For example, the in-plane deformation of a concrete-on-steel deck floor diaphragm in an office building usually can be neglected, but that of a cold-formed steel roof deck in a large warehouse with widely spaced lateral-load-resisting elements usually cannot. As another example, shear deformations in beams and columns in a low-rise moment frame usually can be neglected, but this may not be true in a highrise framed-tube system. Second-Order Effects. The direct analysis method includes the basic requirement to calculate the internal load effects using a second-order analysis that accounts for both P-Δ and P-δ effects (see Figure C-C2.1). P-Δ effects are the effects of loads acting on the displaced location of joints or nodes in a structure. P-δ effects are the effect of loads acting on the deflected shape of a member between joints or nodes.

Fig. C-C2.1. P-Δ and P-δ effects in beam-columns. Specification for Structural Steel Buildings, June 22, 2010

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Rigorous second-order analyses are those that accurately model all significant second-order effects. One such approach is the solution of the governing differential equation, either through stability functions or computer frame analysis programs that model these effects (McGuire et al., 2000; Ziemian, 2010). Some—but not all, and possibly not even most—modern commercial computer programs are capable of performing a rigorous second-order analysis, although this should be verified by the user for each particular program. The effect of neglecting P-δ in the analysis of the structure, a common approximation that is permitted under certain conditions, is discussed at the end of this section. Methods that modify first-order analysis results through second-order amplifiers are permitted as an alternative to a rigorous analysis. The use of the B1 and B2 amplifiers provided in Appendix 8 is one such method. The accuracy of other methods should be verified. Analysis Benchmark Problems. The following benchmark problems are recommended as a first-level check to determine whether an analysis procedure meets the requirements of a rigorous second-order analysis adequate for use in the direct analysis method (and the effective length method in Appendix 7). Some second-order analysis procedures may not include the effects of P-δ on the overall response of the structure. These benchmark problems are intended to reveal whether or not these effects are included in the analysis. It should be noted that per the requirements of Section C2.1(2), it is not always necessary to include P-δ effects in the second-order analysis (additional discussion of the consequences of neglecting these effects appears below). The benchmark problem descriptions and solutions are shown in Figures C-C2.2 and C-C2.3. Case 1 is a simply supported beam-column subjected to an axial load concurrent with a uniformly distributed transverse load between supports. This problem contains only P-δ effects because there is no translation of one end of the member relative to the other. Case 2 is a fixed-base cantilevered beam-column subjected to an axial load concurrent with a lateral load at its top. This problem contains both P-Δ and P-δ effects. In confirming the accuracy of the analysis method, both moments and deflections should be checked at the locations shown for the various levels of axial load on the member and in all cases should agree within 3% and 5%, respectively. Given that there are many attributes that must be studied to confirm the accuracy of a given analysis method for routine use in the design of general framing systems, a wide range of benchmark problems should be employed. Several other targeted analysis benchmark problems can be found in Kaehler et al. (2010), Chen and Lui (1987), and McGuire et al. (2000). When using benchmark problems to assess the correctness of a second-order procedure, the details of the analysis used in the benchmark study, such as the number of elements used to represent the member and the numerical solution scheme employed, should be replicated in the analysis used to design the actual structure. Because the ratio of design load to elastic buckling load is a strong indicator of the influence of second-order effects, benchmark problems with such ratios on the order of 0.6 to 0.7 should be included. Specification for Structural Steel Buildings, June 22, 2010

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Effect of Neglecting P-δ . A common type of approximate analysis is one that captures only P-Δ effects due to member end translations (for example, interstory drift) but fails to capture P-δ effects due to curvature of the member relative to its chord. This type of analysis is referred to as a P-Δ analysis. Where P-δ effects are significant, errors arise in approximate methods that do not accurately account for the effect of P-δ moments on amplification of both local (δ) and global (Δ) displacements and corresponding internal moments. These errors can occur both with second-order computer analysis programs and with the B1 and B2 amplifiers. For instance, the RM modifier in Equation A-8-7 is an adjustment factor that approximates the effects of P-δ (due to column curvature) on the overall sidesway displacements, Δ, and the corresponding moments. For regular rectangular moment frames, a single-elementper-member P-Δ analysis is equivalent to using the B2 amplifier of Equation A-8-6 with RM = 1, and hence, such an analysis neglects the effect of P-δ on the response of the structure.

Fig. C-C2.2. Benchmark problem Case 1.

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Fig. C-C2.3. Benchmark problem Case 2. Specification for Structural Steel Buildings, June 22, 2010

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Section C2.1(2) indicates that a P-Δ-only analysis (one that neglects the effect of P-δ deformations on the response of the structure) is permissible for typical building structures when the ratio of second-order drift to first-order drift is less than 1.7 and no more than one-third of the total gravity load on the building is on columns that are part of moment-resisting frames. The latter condition is equivalent to an RM value of 0.95 or greater. When these conditions are satisfied, the error in lateral displacement from a P-Δ-only analysis typically will be less than 3%. However, when the P-δ effect in one or more members is large (corresponding to a B1 multiplier of more than about 1.2), use of a P-Δ-only analysis may lead to larger errors in the nonsway moments in components connected to the high-P-δ members. The engineer should be aware of this possible error before using a P-Δ-only analysis in such cases. For example, consider the evaluation of the fixed-base cantilevered beam-column shown in Figure C-C2.4 using the direct analysis method. The sidesway displacement amplification factor is 3.83 and the base moment amplifier is 3.32, giving Mu = 1,394 kip-in. For the loads shown, the beam-column strength interaction according to Equation H1-1a is equal to 1.0. The sidesway displacement and base moment amplification determined by a single-element P-Δ analysis, which ignores the effect of P-δ on the response of the structure, is 2.55, resulting in an estimated Mu = 1,070 kip-in.—an error of 23.2% relative to the more accurate value of Mu—and a beam-column interaction value of 0.91. P-δ effects can be captured in some (but not all) P-Δ-only analysis methods by subdividing the members into multiple elements. For this example, three equal-length P-Δ analysis elements are required to reduce the errors in the second-order base moment and sidesway displacement to less than 3% and 5%, respectively. It should be noted that in this case the unconservative error that results from ignoring the effect of P-δ on the response of the structure is removed through the use of Equation A-8-8. For the loads shown in Figure C-C2.4, Equations A-8-6 and A-8-7

Fig. C-C2.4. Illustration of potential errors associated with the use of a single-element-per-member P-Δ analysis. Specification for Structural Steel Buildings, June 22, 2010

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with RM = 0.85 gives a B2 amplifier of 3.52. This corresponds to Mu = 1,476 kip-in. (166 × 106 N-mm) in the preceding example, approximately 6% over that determined from a rigorous second order analysis. For sway columns with nominally simply supported base conditions, the errors in the second-order internal moment and in the second-order displacements from a P-Δ-only analysis are generally smaller than 3% and 5%, respectively, when αPr /PeL ≤ 0.05, where α = 1.00 (LRFD) = 1.60 (ASD) Pr = required axial force, ASD or LRFD, kips (N) PeL = π2EI/L2 if the analysis uses nominal stiffness, kips (N) PeL = 0.8τb π2EI/L2, kips (N), if the analysis uses a flexural stiffness reduction of 0.8τb For sway columns with rotational restraint at both ends of at least 1.5(EI/L) if the analysis uses nominal stiffness or 1.5(0.8τb EI/L) if the analysis uses a flexural stiffness reduction of 0.8τb, the errors in the second-order internal moments and displacements from a P-Δ-only analysis are generally smaller than 3% and 5%, respectively, when αPr /PeL ≤ 0.12. For members subjected predominantly to nonsway end conditions, the errors in the second-order internal moments and displacements from a P-Δ-only analysis are generally smaller than 3% and 5%, respectively, when αPr /PeL ≤ 0.05. In meeting the above limitations for use of a P-Δ-only analysis, it is important to note that per Section C2.1(2) the moments along the length of member (i.e., the moments between the member-end nodal locations) should be amplified as necessary to include P-δ effects. One device for achieving this is the use of a B1 factor. Kaehler et al. (2010) provide further guidelines for the appropriate number of P-Δ analysis elements in cases where the above limits are exceeded, as well as guidelines for calculating internal element second-order moments. They also provide relaxed guidelines for the number of elements required per member when using typical second-order analysis capabilities that include both P-Δ and P-δ effects. As previously indicated, the engineer should verify the accuracy of second-order analysis software by comparisons to known solutions for a range of representative loadings. In addition to the examples presented in Chen and Lui (1987) and McGuire et al. (2000), Kaehler et al. (2010) provides five useful benchmark problems for testing second-order analysis of frames composed of prismatic members. In addition, they provide benchmarks for evaluation of second-order analysis capabilities for web-tapered members. Analysis at Strength Level. It is essential that the analysis of the frame be made at the strength level because of the nonlinearity associated with second-order effects. For design by ASD, this load level is estimated as 1.6 times the ASD load combinations, and the analysis must be conducted at this elevated load to capture second-order effects at the strength level. Specification for Structural Steel Buildings, June 22, 2010

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Consideration of Initial Imperfections Modern stability design provisions are based on the premise that the member forces are calculated by second-order elastic analysis, where equilibrium is satisfied on the deformed geometry of the structure. Initial imperfections in the structure, such as outof-plumbness and material and fabrication tolerances, create destabilizing effects. In the development and calibration of the direct analysis method, initial geometric imperfections are conservatively assumed equal to the maximum material, fabrication and erection tolerances permitted in the AISC Code of Standard Practice for Steel Buildings and Bridges (AISC, 2010a): a member out-of-straightness equal to L /1000, where L is the member length between brace or framing points, and a frame out-of-plumbness equal to H/500, where H is the story height. The permitted outof-plumbness may be smaller in some cases, as specified in the AISC Code of Standard Practice for Steel Buildings and Bridges. Initial imperfections can be accounted for in the direct analysis method through direct modeling (Section C2.2a) or the inclusion of notional loads (Section C2.2b). When second-order effects are such that the maximum sidesway amplification Δ 2nd order /Δ 1st order or B2 ≤ 1.7 using the reduced elastic stiffness (or 1.5 using the unreduced elastic stiffness) for all lateral load combinations, it is permitted to apply the notional loads only in the gravity load-only combinations and not in combination with other lateral loads. At this low range of sidesway amplification or B2 , the errors in internal forces caused by not applying the notional loads in combination with other lateral loads are relatively small. When B2 is above the threshold, the notional loads must also be applied in combination with other lateral loads. The Specification requirements for consideration of initial imperfections are intended to apply only to analyses for strength limit states. It is not necessary, in most cases, to consider initial imperfections in analyses for serviceability conditions such as drift, deflection and vibration.

3.

Adjustments to Stiffness Partial yielding accentuated by residual stresses in members can produce a general softening of the structure at the strength limit state that further creates destabilizing effects. The direct analysis method is also calibrated against inelastic distributedplasticity analyses that account for the spread of plasticity through the member cross section and along the member length. The residual stresses in W-shapes are assumed to have a maximum value of 0.3Fy in compression at the flange tips, and a distribution matching the so-called Lehigh pattern—a linear variation across the flanges and uniform tension in the web (Ziemian, 2010). Reduced stiffness (EI* = 0.8τb EI and EA* = 0.8EA) is used in the direct analysis method for two reasons. First, for frames with slender members, where the limit state is governed by elastic stability, the 0.8 factor on stiffness results in a system available strength equal to 0.8 times the elastic stability limit. This is roughly equivalent to the margin of safety implied in the design provisions for slender columns by the effective length procedure where from Equation E3-3, φPn = 0.9(0.877Pe) = 0.79Pe. Second, for frames with intermediate or stocky columns, the 0.8τb factor reduces the Specification for Structural Steel Buildings, June 22, 2010

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stiffness to account for inelastic softening prior to the members reaching their design strength. The τb factor is similar to the inelastic stiffness reduction factor implied in the column curve to account for loss of stiffness under high compression loads (αPr > 0.5Py ), and the 0.8 factor accounts for additional softening under combined axial compression and bending. It is a fortuitous coincidence that the reduction coefficients for both slender and stocky columns are close enough, such that the single reduction factor of 0.8τb works over the full range of slenderness. The use of reduced stiffness only pertains to analyses for strength and stability limit states. It does not apply to analyses for other stiffness-based conditions and criteria, such as for drift, deflection, vibration and period determination. For ease of application in design practice, where τb = 1, the reduction on EI and EA can be applied by modifying E in the analysis. However, for computer programs that do semi-automated design, one should ensure that the reduced E is applied only for the second-order analysis. The elastic modulus should not be reduced in nominal strength equations that include E (for example, Mn for lateral-torsional buckling in an unbraced beam). As shown in Figure C-C2.5, the net effect of modifying the analysis in the manner just described is to amplify the second-order forces such that they are closer to the

(a) Effective length method

(b) Direct analysis method Fig. C-C2.5. Comparison of in-plane beam-column interaction checks for (a) the effective length method and (b) the direct analysis method. Specification for Structural Steel Buildings, June 22, 2010

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actual internal forces in the structure. It is for this reason that the beam-column interaction for in-plane flexural buckling is checked using an axial strength, PnL, calculated from the column curve using the actual unbraced member length, L, in other words, with K = 1.0. In cases where the flexibility of other structural components (connections, column base details, horizontal trusses acting as diaphragms) is modeled explicitly in the analysis, the stiffness of these components also should be reduced. The stiffness reduction may be taken conservatively as EA* = 0.8EA and/or EI* = 0.8EI for all cases. Surovek-Maleck et al. (2004) discusses the appropriate reduction of connection stiffness in the analysis of PR frames. Where concrete shear walls or other nonsteel components contribute to the stability of the structure and the governing codes or standards for those elements specify a greater stiffness reduction, the greater reduction should be applied.

C3.

CALCULATION OF AVAILABLE STRENGTHS Section C3 provides that when the analysis meets the requirements in Section C2, the member provisions for available strength in Chapters E through I and connection provisions in Chapters J and K complete the process of design by the direct analysis method. The effective length factor, K, can be taken as unity for all members in the strength checks. Where beams and columns rely upon braces that are not part of the lateral-loadresisting system to define their unbraced length, the braces themselves must have sufficient strength and stiffness to control member movement at the brace points (see Appendix 6). Design requirements for braces that are part of the lateral-load-resisting system (that is, braces that are included within the analysis of the structure) are addressed within Chapter C. For beam-columns in single-axis flexure and compression, the analysis results from the direct analysis method may be used directly with the interaction equations in Section H1.3, which address in-plane flexural buckling and out-of-plane lateral-torsional instability separately. These separated interaction equations reduce the conservatism of the Section H1.1 provisions, which combine the two limit state checks into one equation that uses the most severe combination of in-plane and outof-plane limits for Pr /Pc and Mr /Mc. A significant advantage of the direct analysis method is that the in-plane check with Pc in the interaction equation is determined using K = 1.0.

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CHAPTER D DESIGN OF MEMBERS FOR TENSION

The provisions of Chapter D do not account for eccentricities between the lines of action of connected assemblies.

D1.

SLENDERNESS LIMITATIONS The advisory upper limit on slenderness in the User Note is based on professional judgment and practical considerations of economics, ease of handling, and care required so as to minimize inadvertent damage during fabrication, transport and erection. This slenderness limit is not essential to the structural integrity of tension members; it merely assures a degree of stiffness such that undesirable lateral movement (“slapping” or vibration) will be unlikely. Out-of-straightness within reasonable tolerances does not affect the strength of tension members. Applied tension tends to reduce, whereas compression tends to amplify, out-of-straightness. For single angles, the radius of gyration about the z-axis produces the maximum L/r and, except for very unusual support conditions, the maximum KL/r.

D2.

TENSILE STRENGTH Because of strain hardening, a ductile steel bar loaded in axial tension can resist without rupture a force greater than the product of its gross area and its specified minimum yield stress. However, excessive elongation of a tension member due to uncontrolled yielding of its gross area not only marks the limit of its usefulness but can precipitate failure of the structural system of which it is a part. On the other hand, depending upon the reduction of area and other mechanical properties of the steel, the member can fail by rupture of the net area at a load smaller than required to yield the gross area. Hence, general yielding of the gross area and rupture of the net area both constitute limit states. The length of the member in the net area is generally negligible relative to the total length of the member. Strain hardening is easily reached in the vicinity of holes and yielding of the net area at fastener holes does not constitute a limit state of practical significance. Except for HSS that are subjected to cyclic load reversals, there is no information that the factors governing the strength of HSS in tension differ from those for other structural shapes, and the provisions in Section D2 apply. Because the number of different end connection types that are practical for HSS is limited, the determination of the effective net area, Ae, can be simplified using the provisions in Chapter K.

D3.

EFFECTIVE NET AREA Section D3 deals with the effect of shear lag, applicable to both welded and bolted tension members. Shear lag is a concept used to account for uneven stress distribuSpecification for Structural Steel Buildings, June 22, 2010

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tion in connected members where some but not all of their elements (flange, web, leg, etc.) are connected. The reduction coefficient, U, is applied to the net area, An, of bolted members and to the gross area, Ag, of welded members. As the length of the connection, l, is increased, the shear lag effect diminishes. This concept is expressed empirically by the equation for U. Using this expression to compute the effective area, the estimated strength of some 1,000 bolted and riveted connection test specimens, with few exceptions, correlated with observed test results within a scatterband of ±10% (Munse and Chesson, 1963). Newer research provides further justification for the current provisions (Easterling and Gonzales, 1993). For any given profile and configuration of connected elements, x– is the perpendicular distance from the connection plane, or face of the member, to the centroid of the member section resisting the connection force, as shown in Figure C-D3.1. The length, l, is a function of the number of rows of fasteners or the length of weld. The length, l, is illustrated as the distance, parallel to the line of force, between the first and last row of fasteners in a line for bolted connections. The number of bolts in a line, for the purpose of the determination of l, is determined by the line with the maximum number of bolts in the connection. For staggered bolts, the out-to-out dimension is used for l, as shown in Figure C-D3.2.

Fig. C-D3.1. Determination of x– for U. Specification for Structural Steel Buildings, June 22, 2010

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From the definition of the plastic section modulus, Z = ∑| Ai di |, where Ai is the area of a cross-sectional element and di is the perpendicular distance from the plastic neutral axis to the center of gravity of the element; x– for cases like that shown on the right hand side of Figure C-D3.1(c) is Zy /A. Because the section shown is symmetric about the vertical axis and that axis is also the plastic neutral axis, the first moment of the area to the left is Zy /2, where Zy is the plastic section modulus of the entire section. The area of the left side is A/2; therefore, by definition ⫺ x = Zy /A. For the case shown on the right hand side of Figure C-D3.1(b), ⫺ x = d/2 ⫺ Zx /A. Note that the plastic neutral axis must be an axis of symmetry for this relationship to apply. There is insufficient data for establishing a value of U if all lines have only one bolt, but it is probably conservative to use Ae equal to the net area of the connected element. The limit states of block shear (Section J4.3) and bearing (Section J3.10), which must be checked, will probably control the design. The ratio of the area of the connected element to the gross area is a reasonable lower bound for U and allows for cases where the calculated U based on (1–x– / l ) is very small, or nonexistent, such as when a single bolt per gage line is used and l = 0. This lower bound is similar to other design specifications, for example the AASHTO Standard Specifications for Highway Bridges (AASHTO, 2002), which allow a U based on the area of the connected portion plus half the gross area of the unconnected portion. The effect of connection eccentricity is a function of connection and member stiffness and may sometimes need to be considered in the design of the tension connection or member. Historically, engineers have neglected the effect of eccentricity in both the member and the connection when designing tension-only bracing. In Cases 1a and 1b shown in Figure C-D3.3, the length of the connection required to resist the axial loads will usually reduce the applied axial load on the bolts to a negligible value. For Case 2, the flexibility of the member and the connections will allow the member to deform such that the resulting eccentricity is relieved to a considerable extent.

Fig. C-D3.2. Determination of l for U of bolted connections with staggered holes.

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For welded connections, l is the length of the weld parallel to the line of force as shown in Figure C-D3.4 for longitudinal and longitudinal plus transverse welds. For welds with unequal lengths, use the average length. End connections for HSS in tension are commonly made by welding around the perimeter of the HSS; in this case, there is no shear lag or reduction in the gross area.

Case 1a. End Rotation Restrained by Connection to Rigid Abutments

Case 1b. End Rotation Restrained by Symmetry

Case 2. End Rotation Not Restrained—Connection to Thin Plate Fig. C-D3.3. The effect of connection restraint on eccentricity.

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Alternatively, an end connection with gusset plates can be used. Single gusset plates may be welded in longitudinal slots that are located at the centerline of the cross section. Welding around the end of the gusset plate may be omitted for statically loaded connections to prevent possible undercutting of the gusset and having to bridge the gap at the end of the slot. In such cases, the net area at the end of the slot is the critical area as illustrated in Figure C-D3.5. Alternatively, a pair of gusset plates can be welded to opposite sides of a rectangular HSS with flare bevel groove welds with no reduction in the gross area. For end connections with gusset plates, the general provisions for shear lag in Case 2 of Table D3.1 can be simplified and the connection eccentricity can be explicitly defined as in Cases 5 and 6. In Cases 5 and 6 it is implied that the weld length, l, should not be less than the depth of the HSS. This is consistent with the weld length requirements in Case 4. In Case 5, the use of U = 1 when l ≥ 1.3D is based on research (Cheng and Kulak, 2000) that shows rupture occurs only in short connections and in long connections the round HSS tension member necks within its length and failure is by member yielding and eventual rupture. The shear lag factors given in Cases 7 and 8 of Table D3.1 are given as alternate U values to the value determined from 1 ⫺ ⫺ x /l given for Case 2 in Table D3.1. It is permissible to use the larger of the two values.

Fig. C-D3.4. Determination of l for calculation of U for connections with longitudinal and transverse welds.

Fig. C-D3.5. Net area through slot for a single gusset plate. Specification for Structural Steel Buildings, June 22, 2010

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BUILT-UP MEMBERS Although not commonly used, built-up member configurations using lacing, tie plates and perforated cover plates are permitted by this Specification. The length and thickness of tie plates are limited by the distance between the lines of fasteners, h, which may be either bolts or welds.

D5.

PIN-CONNECTED MEMBERS Pin-connected members are occasionally used as tension members with very large dead loads. Pin-connected members are not recommended when there is sufficient variation in live loading to cause wearing of the pins in the holes. The dimensional requirements presented in Specification Section D5.2 must be met to provide for the proper functioning of the pin.

1.

Tensile Strength The tensile strength requirements for pin-connected members use the same φ and Ω values as elsewhere in this Specification for similar limit states. However, the definitions of effective net area for tension and shear are different.

2.

Dimensional Requirements Dimensional requirements for pin-connected members are illustrated in Figure C-D5.1.

Dimensional Requirements 1. a ≥ 1.33 be 2. w ≥ 2be + d 3. c ≥ a where

be = 2t + 0.63 in. (16 mm) ≤ b Fig. C-D5.1. Dimensional requirements for pin-connected members.

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EYEBARS Forged eyebars have generally been replaced by pin-connected plates or eyebars thermally cut from plates. Provisions for the proportioning of eyebars contained in this Specification are based upon standards evolved from long experience with forged eyebars. Through extensive destructive testing, eyebars have been found to provide balanced designs when they are thermally cut instead of forged. The more conservative rules for pin-connected members of nonuniform cross section and for members not having enlarged “circular” heads are likewise based on the results of experimental research (Johnston, 1939). Stockier proportions are required for eyebars fabricated from steel having a yield stress greater than 70 ksi (485 MPa) to eliminate any possibility of their “dishing” under the higher design stress.

1.

Tensile Strength The tensile strength of eyebars is determined as for general tension members, except that, for calculation purposes, the width of the body of the eyebar is limited to eight times its thickness.

2.

Dimensional Requirements Dimensional limitations for eyebars are illustrated in Figure C-D6.1. Adherence to these limits assures that the controlling limit state will be tensile yielding of the body; thus, additional limit state checks are unnecessary.

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Dimensional Requirements

t ≥ 1/2 in. (13 mm) (Exception is provided in Section D6.2)

w ≤ 8t d ≥ 7/8w dh ≤ d + 1/32 in. (1 mm) R ≥ dh + 2b ≤ b ≤ 3/4w (Upper limit is for calculation purposes only) 2/3w

Fig. C-D6.1. Dimensional limitations for eyebars.

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CHAPTER E DESIGN OF MEMBERS FOR COMPRESSION

E1.

GENERAL PROVISIONS The column equations in Section E3 are based on a conversion of the research data into strength equations (Ziemian, 2010; Tide, 1985, 2001). These equations are the same as those in the 2005 AISC Specification for Structural Steel Buildings (AISC, 2005a) and are essentially the same as those in the previous editions of the LRFD Specification (AISC, 1986, 1993, 2000b). The resistance factor, φ, was increased from 0.85 to 0.90 in the 2005 Specification, recognizing substantial numbers of additional column strength analyses and test results, combined with the changes in industry practice that had taken place since the original calibrations were performed in the 1970s and 1980s. In the original research on the probability-based strength of steel columns (Bjorhovde, 1972, 1978, 1988), three column curves were recommended. The three column curves were the approximate means of bands of strength curves for columns of similar manufacture, based on extensive analyses and confirmed by full-scale tests (Bjorhovde, 1972). For example, hot-formed and cold-formed heat treated HSS columns fell into the data band of highest strength [SSRC Column Category 1P (Bjorhovde, 1972, 1988; Bjorhovde and Birkemoe, 1979; Ziemian, 2010)], while welded built-up wide-flange columns made from universal mill plates were included in the data band of lowest strength (SSRC Column Category 3P). The largest group of data clustered around SSRC Column Category 2P. Had the original LRFD Specification opted for using all three column curves for the respective column categories, probabilistic analysis would have resulted in a resistance factor φ = 0.90 or even slightly higher (Galambos, 1983; Bjorhovde, 1988; Ziemian, 2010). However, it was decided to use only one column curve, SSRC Column Category 2P, for all column types. This resulted in a larger data spread and thus a larger coefficient of variation, and so a resistance factor φ = 0.85 was adopted for the column equations to achieve a level of reliability comparable to that of beams. Since that time, significant additional analyses and tests, as well as changes in practice, have demonstrated that the increase to 0.90 was warranted, indeed even somewhat conservative (Bjorhovde, 1988). The single column curve and the resistance factor of 0.85 were selected by the AISC Committee on Specifications in 1981 when the first draft of the LRFD Specification was developed (AISC, 1986). Since then a number of changes in industry practice have taken place: (1) welded built-up shapes are no longer manufactured from universal mill plates; (2) the most commonly used structural steel is now ASTM A992, with a specified minimum yield stress of 50 ksi (345 MPa); and (3) changes in steelmaking practice have resulted in materials of higher quality and much better defined properties. The level and variability of the yield stress thus have led to a reduced coefficient of variation for the relevant material properties (Bartlett et al., 2003). Specification for Structural Steel Buildings, June 22, 2010

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An examination of the SSRC Column Curve Selection Table (Bjorhovde, 1988; Ziemian, 2010) shows that the SSRC 3P Column Curve Category is no longer needed. It is now possible to use only the statistical data for SSRC Column Category 2P for the probabilistic determination of the reliability of columns. The curves in Figures C-E1.1 and C-E1.2 show the variation of the reliability index β with the liveto-dead load ratio, L/D, in the range of 1 to 5 for LRFD with φ = 0.90 and ASD with

Fig. C-E1.1. Reliability of columns (LRFD).

Fig. C-E1.2. Reliability of columns (ASD). Specification for Structural Steel Buildings, June 22, 2010

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Ω = 1.67, respectively, for Fy = 50 ksi (345 MPa). The reliability index does not fall below β = 2.6. This is comparable to the reliability of beams.

E2.

EFFECTIVE LENGTH The concept of a maximum limiting slenderness ratio has experienced an evolutionary change from a mandatory “…The slenderness ratio, KL /r, of compression members shall not exceed 200…” in the 1978 Specification to no restriction at all in the 2005 Specification (AISC, 2005a). The 1978 ASD and the 1999 LRFD Specifications (AISC, 1978; AISC, 2000b) provided a transition from the mandatory limit to a limit that was defined in the 2005 Specification by a User Note, with the observation that “…the slenderness ratio, KL/r, preferably should not exceed 200….” However, the designer should keep in mind that columns with a slenderness ratio of more than 200 will have an elastic buckling stress (Equation E3-4) less than 6.3 ksi (43.5 MPa). The traditional upper limit of 200 was based on professional judgment and practical construction economics, ease of handling, and care required to minimize inadvertent damage during fabrication, transport and erection. These criteria are still valid and it is not recommended to exceed this limit for compression members except for cases where special care is exercised by the fabricator and erector.

E3.

FLEXURAL BUCKLING OF MEMBERS WITHOUT SLENDER ELEMENTS Section E3 applies to compression members with all nonslender elements, as defined in Section B4. The column strength equations in Section E3 are the same as those in the previous editions of the LRFD Specification, with the exception of the cosmetic replacement in KL Fy 2005 of the slenderness term, λ c = , by the more familiar slenderness ratio, πr E KL . For the convenience of those calculating the elastic buckling stress directly, r without first calculating K, the limits on the use of Equations E3-2 and E3-3 are also provided in terms of the ratio Fy /Fe, as shown in the following discussion. Comparisons between the previous column design curves and those introduced in the 2005 Specification and continued in this Specification are shown in Figures C-E3.1 and C-E3.2 for the case of Fy = 50 ksi (345 MPa). The curves show the variation of the available column strength with the slenderness ratio for LRFD and ASD, respectively. The LRFD curves reflect the change of the resistance factor, φ, from 0.85 to 0.90, as was explained in Commentary Section E1. These column equations provide improved economy in comparison with the previous editions of the Specification. KL E The limit between elastic and inelastic buckling is defined to be = 4.71 or r Fy Fy = 2.25 . These are the same as Fe = 0.44Fy that was used in the 2005 Specification. Fe Specification for Structural Steel Buildings, June 22, 2010

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For convenience, these limits are defined in Table C-E3.1 for the common values of Fy. One of the key parameters in the column strength equations is the elastic critical stress, Fe. Equation E3-4 presents the familiar Euler form for Fe. However, Fe can also be determined by other means, including a direct frame buckling analysis or a torsional or flexural-torsional buckling analysis as addressed in Section E4. The column strength equations of Section E3 can also be used for frame buckling and for torsional or flexural-torsional buckling (Section E4); they can also be entered

Fig. C-E3.1. LRFD column curves compared.

Fig. C-E3.2. ASD column curves compared. Specification for Structural Steel Buildings, June 22, 2010

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TABLE C-E3.1 Limiting values of KL /r and Fe Fy ksi (MPa)

Limiting

KL r

Fe ksi (MPa)

36 (250)

134

16.0 (111)

50 (345)

113

22.2 (153)

60 (415)

104

26.7 (184)

70 (485)

96

31.1 (215)

with a modified slenderness ratio for single-angle members (Section E5); and they can be modified by the Q-factor for columns with slender elements (Section E7).

E4.

TORSIONAL AND FLEXURAL-TORSIONAL BUCKLING OF MEMBERS WITHOUT SLENDER ELEMENTS Section E4 applies to singly symmetric and unsymmetric members, and certain doubly symmetric members, such as cruciform or built-up columns, with all nonslender elements, as defined in Section B4 for uniformly compressed elements. It also applies to doubly symmetric members when the torsional buckling length is greater than the flexural buckling length of the member. The equations in Section E4 for determining the torsional and flexural-torsional elastic buckling loads of columns are derived in textbooks and monographs on structural stability [for example, Bleich (1952); Timoshenko and Gere (1961); Galambos (1968a); Chen and Atsuta (1977); Galambos and Surovek (2008), Ziemian (2010)]. Since these equations apply only to elastic buckling, they must be modified for inelastic buckling by using the torsional and flexural-torsional critical stress, Fcr, in the column equations of Section E3. Torsional buckling of symmetric shapes and flexural-torsional buckling of unsymmetrical shapes are failure modes usually not considered in the design of hot-rolled columns. They generally do not govern, or the critical load differs very little from the weak-axis flexural buckling load. Torsional and flexural-torsional buckling modes may, however, control the strength of symmetric columns manufactured from relatively thin plate elements and unsymmetric columns and symmetric columns having torsional unbraced lengths significantly larger than the weak-axis flexural unbraced lengths. Equations for determining the elastic critical stress for such columns are given in Section E4. Table C-E4.1 serves as a guide for selecting the appropriate equations. The simpler method of calculating the buckling strength of double-angle and teeshaped members (Equation E4-2) uses directly the y-axis flexural strength from the column equations of Section E3 (Galambos, 1991). Specification for Structural Steel Buildings, June 22, 2010

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TABLE C-E4.1 Selection of Equations for Torsional and FlexuralTorsional Buckling Type of Cross Section

Applicable Equations in Section E4

Double angle and tee-shaped members Case (a) in Section E4

E4-2

All doubly symmetric shapes and Z-shapes Case (b) (i) in Section E4

E4-4

Singly symmetric members except double angles and tee-shaped members Case (b)(ii) in Section E4

E4-5

Unsymmetric shapes Case (b)(iii) in Section E4

E4-6

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Equations E4-4 and E4-9 contain a torsional buckling effective length factor, Kz. This factor may be conservatively taken as Kz =1.0. For greater accuracy, Kz = 0.5 if both ends of the column have a connection that restrains warping, say by boxing the end over a length at least equal to the depth of the member. If one end of the member is restrained from warping and the other end is free to warp, then Kz = 0.7. At points of bracing both lateral and/or torsional bracing shall be provided, as required in Appendix 6. AISC Design Guide 9 (Seaburg and Carter, 1997) provides an overview of the fundamentals of torsional loading for structural steel members. Design examples are also included.

E5.

SINGLE ANGLE COMPRESSION MEMBERS The axial load capacity of single angles is to be determined in accordance with Section E3 or E7. However, as noted in Section E4 and E7, single angles with b/t ≤ 20 do not require the computation of Fe using Equations E4-5 or E4-6. This applies to all currently produced hot rolled angles; use Section E4 to compute Fe for fabricated angles with b/t > 20. Section E5 also provides a simplified procedure for the design of single angles subjected to an axial compressive load introduced through one connected leg. The angle is treated as an axially loaded member by adjusting the member slenderness. The attached leg is to be fixed to a gusset plate or the projecting leg of another member by welding or by a bolted connection with at least two bolts. The equivalent slenderness expressions in this section presume significant restraint about the y-axis, which is perpendicular to the connected leg. This leads to the angle member tending to bend and buckle primarily about the x-axis. For this reason, L /rx is the slenderness parameter used. The modified slenderness ratios indirectly account for bending in the angles due to the eccentricity of loading and for the effects of end restraint from the truss chords. The equivalent slenderness expressions also presume a degree of rotational restraint. Equations E5-3 and E5-4 [Case (b)] assume a higher degree of x-axis rotational restraint than do Equations E5-1 and E5-2 [Case (a)]. Equations E5-3 and E5-4 are essentially equivalent to those employed for equal-leg angles as web members in latticed transmission towers in ASCE 10-97 (ASCE, 2000). In space trusses, the web members framing in from one face typically restrain the twist of the chord at the panel points and thus provide significant x-axis restraint of the angles under consideration. It is possible that the chords of a planar truss well restrained against twist justify use of Case (b), in other words, Equations E53 and E5-4. Similarly, simple single-angle diagonal braces in braced frames could be considered to have enough end restraint such that Case (a), in other words, Equations E5-1 and E5-2, could be employed for their design. This procedure, however, is not intended for the evaluation of the compressive strength of x-braced single angles. The procedure in Section E5 permits use of unequal-leg angles attached by the smaller leg provided that the equivalent slenderness is increased by an amount that Specification for Structural Steel Buildings, June 22, 2010

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is a function of the ratio of the longer to the shorter leg lengths, and has an upper limit on L/rz. If the single-angle compression members cannot be evaluated using the procedures in this section, use the provisions of Section H2. In evaluating Pn, the effective length due to end restraint should be considered. With values of effective length factors about the geometric axes, one can use the procedure in Lutz (1992) to compute an effective radius of gyration for the column. To obtain results that are not too conservative, one must also consider that end restraint reduces the eccentricity of the axial load of single-angle struts and thus the value of frbw or frbz used in the flexural term(s) in Equation H2-1.

E6.

BUILT-UP MEMBERS Section E6 addresses the strength and dimensional requirements of built-up members composed of two or more shapes interconnected by stitch bolts or welds.

1.

Compressive Strength This section applies to built-up members such as double-angle or double-channel members with closely spaced individual components. The longitudinal spacing of connectors connecting components of built-up compression members must be such that the slenderness ratio, L/r, of individual shapes does not exceed three-fourths of the slenderness ratio of the entire member. However, this requirement does not necessarily ensure that the effective slenderness ratio of the built-up member is equal to that of a built-up member acting as a single unit. For a built-up member to be effective as a structural member, the end connection must be welded or pretensioned bolted with Class A or B faying surfaces. Even so, the compressive strength will be affected by the shearing deformation of the intermediate connectors. The Specification uses the effective slenderness ratio to consider this effect. Based mainly on the test data of Zandonini (1985), Zahn and Haaijer (1987) developed an empirical formulation of the effective slenderness ratio for the 1986 AISC Load and Resistance Factor Design Specification for Structural Steel Buildings (AISC, 1986). When pretensioned bolted or welded intermediate connectors are used, Aslani and Goel (1991) developed a semi-analytical formula for use in the 1993, 1999 and 2005 AISC Specifications (AISC, 1993, 2000b, 2005a). As more test data became available, a statistical evaluation (Sato and Uang, 2007) showed that the simplified expressions used in this Specification achieve the same level of accuracy. Fastener spacing less than the maximum required for strength may be needed to ensure a close fit over the entire faying surface of components in continuous contact. Special requirements for weathering steel members exposed to atmospheric corrosion are given in Brockenbrough (1983).

2.

Dimensional Requirements Section E6.2 provides additional requirements on connector spacing and end connection for built-up member design. Design requirements for laced built-up members Specification for Structural Steel Buildings, June 22, 2010

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where the individual components are widely spaced are also provided. Some dimensioning requirements are based upon judgment and experience. The provisions governing the proportioning of perforated cover plates are based upon extensive experimental research (Stang and Jaffe, 1948).

E7.

MEMBERS WITH SLENDER ELEMENTS The structural engineer designing with hot-rolled shapes will seldom find an occasion to turn to Section E7 of the Specification. Among rolled shapes, the most frequently encountered cases requiring the application of this section are beam shapes used as columns, columns containing angles with thin legs, and tee-shaped columns having slender stems. Special attention to the determination of Q must be given when columns are made by welding or bolting thin plates together. The provisions of Section E7 address the modifications to be made when one or more plate elements in the column cross section are slender. A plate element is considered to be slender if its width-to-thickness ratio exceeds the limiting value, λr, defined in Table B4.1a. As long as the plate element is not slender, it can support the full yield stress without local buckling. When the cross section contains slender elements, the slenderness reduction factor, Q, defines the ratio of the stress at local buckling to the yield stress, Fy. The yield stress, Fy, is replaced by the value QFy in the column equations of Section E3. These modified equations are repeated as Equations E7-2 and E7-3. This approach to dealing with columns with slender elements has been used since the 1969 AISC Specification for the Design, Fabrication, and Erection of Structural Steel for Buildings (AISC, 1969), emulating the 1969 AISI Specification for the Design of Cold-Formed Steel Structural Members (AISI, 1969). Prior to 1969, the AISC practice was to remove the width of the plate that exceeded the λr limit and check the remaining cross section for conformance with the allowable stress, which proved inefficient and uneconomical. The equations in Section E7 are almost identical to the original 1969 equations. This Specification makes a distinction between columns having unstiffened and stiffened elements. Two separate philosophies are used: Unstiffened elements are considered to have attained their limit state when they reach the theoretical local buckling stress. Stiffened elements, on the other hand, make use of the post-buckling strength inherent in a plate that is supported on both of its longitudinal edges, such as in HSS columns. The effective width concept is used to obtain the added post-buckling strength. This dual philosophy reflects the 1969 practice in the design of cold-formed columns. Subsequent editions of the AISI Specifications, in particular, the North American Specification for the Design of Cold-Formed Steel Structural Members (AISI, 2001, 2007), hereafter referred to as the AISI North American Specification, adopted the effective width concept for both stiffened and unstiffened elements. Subsequent editions of the AISC Specification (including this Specification) did not follow the example set by AISI for unstiffened plates because the advantages of the post-buckling strength do not become available unless the plate elements are very slender. Such dimensions are common for cold-formed columns, but are rarely encountered in structures made from hot-rolled plates.

Specification for Structural Steel Buildings, June 22, 2010

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Slender Unstiffened Elements, Qs Equations for the slender element reduction factor, Qs, are given in Section E7.1 for outstanding elements in rolled shapes (Case a), built-up shapes (Case b), single angles (Case c), and stems of tees (Case d). The underlying scheme for these provisions is illustrated in Figure C-E7.1. The curves show the relationship between the b Fy 12(1 – v 2 ) . The width, b, t E π2k and thickness, t, are defined for the applicable cross sections in Section B4; v = 0.3 (Poisson’s ratio), and k is the plate buckling coefficient characteristic of the type of plate edge-restraint. For single angles, k = 0.425 (no restraint is assumed from the other leg), and for outstanding flange elements and stems of tees, k equals approximately 0.7, reflecting an estimated restraint from the part of the cross section to which the plate is attached on one of its edges, the other edge being free. Q-factor and a nondimensional slenderness ratio

The curve relating Q to the plate slenderness ratio has three components: (i) a part where Q = 1 when the slenderness factor is less than or equal to 0.7 (the plate can be stressed up to its yield stress), (ii) the elastic plate buckling portion when buckling is governed by Fcr =

π 2 Ek

, and (iii) a transition range that empirically 2 ⎛ b⎞ 12 1 – v ⎜ ⎟ ⎝t⎠ accountsfor the effect of early yielding due to residual stresses in the shape. Generally this transition range is taken as a straight line. The development of the provisions for unstiffened elements is due to the research of Winter and his co-work-

(

2

)

Fig. C-E7.1. Definition of Qs for unstiffened slender elements.

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ers, and a full listing of references is provided in the Commentary to the AISI North American Specification (AISI, 2001, 2007). The slenderness provisions are illustrated for the example of slender flanges of rolled shapes in Figure C-E7.2. The equations for the unstiffened projecting flanges, angles and plates in built-up cross sections (Equations E7-7 through E7-9) have a history that starts with the research reported in Johnson (1985). It was noted in tests of beams with slender flanges and slender webs that there was an interaction between the buckling of the flanges and the distortions in the web causing an unconservative prediction of strength. A modification based on the equations recommended in Johnson (1985) appeared first in the 1989 Specification for Structural Steel Buildings—Allowable Stress Design and Plastic Design (AISC, 1989). Modifications to simplify the original equations were introduced in the 1993 Load and Resistance Factor Design Specification for Structural Steel Buildings (AISC, 1993), and these equations have remained unchanged in the present Specification. The influence of web slenderness is accounted for by the introduction of the factor kc =

4 h tw

(C-E7-1)

into the equations for λr and Q, where kc is not taken as less than 0.35 nor greater than 0.76 for calculation purposes.

2.

Slender Stiffened Elements, Qa While for slender unstiffened elements the Specification for local buckling is based on the limit state of the onset of plate buckling, an improved approach based on the

Fig. C-E7.2. Q for rolled wide-flange columns with Fy = 50 ksi (345 MPa). Specification for Structural Steel Buildings, June 22, 2010

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effective width concept is used for the compressive strength of stiffened elements in columns. This method was first proposed in von Kármán et al. (1932). It was later modified by Winter (1947) to provide a transition between very slender elements and stockier elements shown by tests to be fully effective. As modified for the AISI North American Specification (AISI, 2001, 2007), the ratio of effective width to actual width increases as the level of compressive stress applied to a stiffened element in a member is decreased, and takes the form be E⎡ C E⎤ = 1.9 ⎢1 – ⎥ t f ⎣ (b / t ) f ⎦

(C-E7-2)

where f is taken as Fcr of the column based on Q = 1.0, and C is a constant based on test results (Winter, 1947). The basis for cold-formed steel columns in the AISI North American Specification editions since the 1970s is C = 0.415. The original AISI coefficient 1.9 in Equation C-E7-2 is changed to 1.92 in the Specification to reflect the fact that the modulus of elasticity E is taken as 29,500 ksi (203 400 MPa) for cold-formed steel, and 29,000 ksi (200 000 MPa) for hot-rolled steel. For the case of square and rectangular box-sections of uniform thickness, where the sides provide negligible rotational restraint to one another, the value of C = 0.38 in Equation E7-18 is higher than the value of C = 0.34 in Equation E7-17. Equation E7-17 applies to the general case of stiffened plates in uniform compression where there is substantial restraint from the adjacent flange or web elements. The coefficients C = 0.38 and C = 0.34 are smaller than the corresponding value of C = 0.415 in the AISI North American Specification (AISI, 2001, 2007), reflecting the fact that hot-rolled steel sections have stiffer connections between plates due to welding or fillets in rolled shapes than do cold-formed shapes. The classical theory of longitudinally compressed cylinders overestimates the actual buckling strength, often by 200% or more. Inevitable imperfections of shape and the eccentricity of the load are responsible for the reduction in actual strength below the theoretical strength. The limits in Section E7.2(c) are based upon test evidence (Sherman, 1976), rather than theoretical calculations, that local buckling will not D 0.11E 0.45E occur if . When D/t exceeds this value but is less than , Equation ≤ t Fy Fy E7-19 provides a reduction in the local buckling reduction factor Q. This Specification D 0.45E does not recommend the use of round HSS or pipe columns with . > t Fy

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CHAPTER F DESIGN OF MEMBERS FOR FLEXURE

F1.

GENERAL PROVISIONS Chapter F applies to members subject to simple bending about one principal axis of the cross section. Section F2 gives the provisions for the flexural strength of doubly symmetric compact I-shaped and channel members subject to bending about their major axis. For most designers, the provisions in this section will be sufficient to perform their everyday designs. The remaining sections of Chapter F address less frequently occurring cases encountered by structural engineers. Since there are many such cases, many equations and many pages in the Specification, the table in User Note F1.1 is provided as a map for navigating through the cases considered in Chapter F. The coverage of the chapter is extensive and there are many equations that appear formidable; however, it is stressed again that for most designs, the engineer need seldom go beyond Section F2. For all sections covered in Chapter F, the highest possible nominal flexural strength is the plastic moment, Mn = Mp. Being able to use this value in design represents the optimum use of the steel. In order to attain Mp the beam cross section must be compact and the member must be laterally braced. Compactness depends on the flange and web width-to-thickness ratios, as defined in Section B4. When these conditions are not met, the nominal flexural strength diminishes. All sections in Chapter F treat this reduction in the same way. For laterally braced beams, the plastic moment region extends over the range of width-to-thickness ratios, λ, terminating at λp. This is the compact condition. Beyond these limits the nominal flexural strength reduces linearly until λ reaches λr. This is the range where the section is noncompact. Beyond λr the section is a slender-element section. These three ranges are illustrated in Figure C-F1.1 for the case of rolled wide-flange members for the limit state of flange local buckling. AISC Design Guide 25, Frame Design Using Web-Tapered Members (Kaehler et al., 2010), addresses flexural strength for web-tapered members. The curve in Figure C-F1.1 shows the relationship between the flange width-to-thickness ratio, bf /2tf, and the nominal flexural strength, Mn. The basic relationship between the nominal flexural strength, Mn, and the unbraced length, Lb, for the limit state of lateral-torsional buckling is shown in Figure C-F1.2 for a compact section that is simply supported and subjected to uniform bending with Cb = 1.0. There are four principal zones defined on the basic curve by the lengths Lpd, Lp and Lr. Equation F2-5 defines the maximum unbraced length, Lp, to reach Mp with uniform moment. Elastic lateral-torsional buckling will occur when the unbraced length is greater than Lr given by Equation F2-6. Equation F2-2 defines the range Specification for Structural Steel Buildings, June 22, 2010

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of inelastic lateral-torsional buckling as a straight line between the defined limits Mp at Lp and 0.7Fy Sx at Lr. Buckling strength in the elastic region is given by Equation F2-3. The length Lpd is defined in Appendix 1 as the limiting unbraced length needed for plastic design. Although plastic design methods generally require more stringent limits on the unbraced length compared to elastic design, the magnitude of Lpd is often larger than Lp. The reason for this is because the Lpd expression

Fig. C-F1.1. Nominal flexural strength as a function of the flange width-to-thickness ratio of rolled I-shapes.

Fig. C-F1.2. Nominal flexural strength as a function of unbraced length and moment gradient. Specification for Structural Steel Buildings, June 22, 2010

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accounts for moment gradient directly, while designs based upon an elastic analysis rely on Cb factors to account for the benefits of moment gradient as outlined in the following paragraphs. For moment along the member other than uniform moment, the lateral buckling strength is obtained by multiplying the basic strength in the elastic and inelastic region by Cb as shown in Figure C-F1.2. However, in no case can the maximum moment capacity exceed the plastic moment, Mp. Note that Lp given by Equation F2-5 is merely a definition that has physical meaning only when Cb = 1.0. For Cb greater than 1.0, members with larger unbraced lengths can reach Mp, as shown by the curve for Cb > 1.0 in Figure C-F1.2. This length is calculated by setting Equation F2-2 equal to Mp and solving for Lb using the actual value of Cb. Since 1961, the following equation has been used in AISC Specifications to adjust the lateral-torsional buckling equations for variations in the moment diagram within the unbraced length. ⎛M ⎞ ⎛M ⎞ Cb = 1.75 + 1.05 ⎜ 1 ⎟ + 0.3 ⎜ 1 ⎟ ⎝ M2 ⎠ ⎝ M2 ⎠

2

(C-F1-1)

where M1 = smaller moment at end of unbraced length, kip-in. (N-mm) M2 = larger moment at end of unbraced length, kip-in. (N-mm) (M1/M2) is positive when moments cause reverse curvature and negative for single curvature This equation is only applicable to moment diagrams that consist of straight lines between braced points—a condition that is rare in beam design. The equation provides a lower bound to the solutions developed in Salvadori (1956). Equation C-F1-1 can be easily misinterpreted and misapplied to moment diagrams that are not linear within the unbraced segment. Kirby and Nethercot (1979) present an equation that applies to various shapes of moment diagrams within the unbraced segment. Their original equation has been slightly adjusted to give Equation C-F1-2 (Equation F1-1 in the body of the Specification): Cb =

12.5M max 2.5M max + 3M A + 4M B + 3M C

(C-F1-2)

This equation gives a more accurate solution for a fixed-end beam, and gives approximately the same answers as Equation C-F1-1 for moment diagrams with straight lines between points of bracing. Cb computed by Equation C-F1-2 for moment diagrams with other shapes shows good comparison with the more precise but also more complex equations (Ziemian, 2010). The absolute values of the three quarter-point moments and the maximum moment regardless of its location are used in Equation CF1-2. The maximum moment in the unbraced segment is always used for comparison with the nominal moment, Mn. The length between braces, not the distance to inflection points is used. It is still satisfactory to use Cb from Equation C-F1-1 for straight-line moment diagrams within the unbraced length.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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16.1–305

The lateral-torsional buckling modification factor given by Equation C-F1-2 is applicable for doubly symmetric sections and should be modified for application with singly symmetric sections. Previous work considered the behavior of singly-symmetric I-shaped beams subjected to gravity loading (Helwig et al., 1997). The study resulted in the following expression: 12.5 M max ⎡ ⎤ Cb = ⎢ ⎥ Rm ≤ 3.0 2 . 5 M + 3 M + 4 M + 3 M max A B C⎦ ⎣

(C-F1-3)

For single curvature bending: Rm = 1.0 For reverse curvature bending: ⎛ I y Top ⎞ Rm = 0.5 + 2 ⎜ ⎝ I y ⎟⎠

2

(C-F1-4)

where Iy Top = moment of inertia of the top flange about an axis through the web, in.4 (mm4) Iy = moment of inertia of the entire section about an axis through the web, in.4 (mm4) Since Equation C-F1-3 was developed for gravity loading on beams with a horizontal orientation of the longitudinal axis, the top flange is defined as the flange above the geometric centroid of the section. The term in the brackets of Equation C-F1-3 is identical to Equation C-F1-2 while the factor Rm is a modifier for singly-symmetric sections that is greater than unity when the top flange is the larger flange and less than unity when the top flange is the smaller flange. For singly-symmetric sections subjected to reverse curvature bending, the lateral-torsional buckling strength should be evaluated by separately treating each flange as the compression flange and comparing the available flexural strength with the required moment that causes compression in the flange under consideration. The Cb factors discussed above are defined as a function of the spacing between braced points. However, many situations arise where a beam may be subjected to reverse curvature bending and have one of the flanges continuously braced laterally by closely spaced joists and/or light gauge decking normally used for roofing or flooring systems. Although the lateral bracing provides significant restraint to one of the flanges, the other flange can still buckle laterally due to the compression caused by the reverse curvature bending. A variety of Cb expressions have been developed that are a function of the type of loading, distribution of the moment, and the support conditions. For gravity loaded beams with the top flange laterally restrained, the following expression is applicable (Yura, 1995; Yura and Helwig, 2009): ⎤ 2⎛ M ⎞ 8⎡ MCL Cb = 3.0 − ⎜ 1 ⎟ − ⎢ ⎥ * 3 ⎝ M o ⎠ 3 ⎢⎣ ( M o + M1 ) ⎥⎦

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(C-F1-5)

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GENERAL PROVISIONS

[Comm. F1.

where Mo

= moment at the end of the unbraced length that gives the largest compressive stress in the bottom flange, kip-in. (N-mm) = moment at other end of the unbraced length, kip-in. (N-mm) M1 = moment at the middle of the unbraced length, kip-in. (N-mm) MCL (Mo + M1)* = Mo if M1 is positive

The unbraced length is defined as the spacing between locations where twist is restrained. The sign convention for the moments are shown in Figure C-F1.3. Mo and M1 are negative as shown in the figure, while MCL is positive. The asterisk on the last term in Equation C-F1-5 indicates that M1 is taken as zero in the last term if it is positive. For example, considering the distribution of moment shown in Figure C-F1.4, the Cb value would be: 2 ⎛ +200 ⎞ 8 ⎛ +50 ⎞ Cb = 3.0 − ⎜ ⎟ = 5.67 ⎟− ⎜ 3 ⎝ −100 ⎠ 3 ⎝ −100 ⎠

Fig. C-F1.3. Sign convention for moments in Equation C-F1-5.

Fig. C-F1.4. Moment diagram for numerical example of application of Equation C-F1-5. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Note that (Mo + M1)* is taken as Mo since M1 is positive. In this case, the Cb = 5.67 would be used with the lateral-torsional buckling strength for the beam using an unbraced length of 20 ft which is defined by locations where twist or lateral movement of both flanges is restrained. A similar buckling problem occurs with roofing beams subjected to uplift from wind loading. The light gauge metal decking that is used for the roofing system usually provides continuous restraint to the top flange of the beam; however, the uplift can be large enough to cause the bottom flange to be in compression. The sign convention for the moment is the same as indicated in Figure C-F1.3. The moment must cause compression in the bottom flange (MCL negative) for the beam to buckle. Three different expressions are given in Figure C-F1.5 depending on whether the end moments are positive or negative (Yura and Helwig, 2009). As outlined above, the unbraced length is defined as the spacing between points where both the top and bottom flange are restrained from lateral movement or between points restrained from twist. The equations for the limit state of lateral-torsional buckling in Chapter F assume that the loads are applied along the beam centroidal axis. Cb may be conservatively

Fig. C-F1.5. Cb factors for uplift loading on beams with the top flange continuously restrained laterally. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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GENERAL PROVISIONS

[Comm. F1.

taken equal to 1.0, with the exception of some cases involving unbraced overhangs or members with no bracing within the span and with significant loading applied to the top flange. If the load is placed on the top flange and the flange is not braced, there is a tipping effect that reduces the critical moment; conversely, if the load is suspended from an unbraced bottom flange, there is a stabilizing effect that increases the critical moment (Ziemian, 2010). For unbraced top flange loading on compact Ishaped members, the reduced critical moment may be conservatively approximated by setting the square root expression in Equation F2-4 equal to unity. An effective length factor of unity is implied in the critical moment equations to represent the worst-case simply supported unbraced segment. Consideration of any end restraint due to adjacent unbuckled segments on the critical segment can increase its strength. The effects of beam continuity on lateral-torsional buckling have been studied, and a simple conservative design method, based on the analogy to end-restrained nonsway columns with an effective length less than unity, has been proposed (Ziemian, 2010).

F2.

DOUBLY SYMMETRIC COMPACT I-SHAPED MEMBERS AND CHANNELS BENT ABOUT THEIR MAJOR AXIS Section F2 applies to members with compact I-shaped or channel cross sections subject to bending about their major axis; hence, the only limit state to consider is lateral-torsional buckling. Almost all rolled wide-flange shapes listed in the AISC Steel Construction Manual (AISC, 2005b) are eligible to be designed by the provisions of this section, as indicated in the User Note in the Specification. The equations in Section F2 are identical to the corresponding equations in Section F1 of the 1999 Specification for Structural Steel Buildings—Load and Resistance Factor Design, hereafter referred to as the 1999 LRFD Specification, (AISC, 2000b) and to the provisions in the 2005 Specification for Structural Steel Buildings (AISC, 2005a), hereafter referred to as the 2005 Specification, although they are presented in different form. Table C-F2.1 gives the list of equivalent equations. The only difference between the 1999 LRFD Specification (AISC, 2000b) and this Specification is that the stress at the interface between inelastic and elastic buckling has been changed from Fy ⫺ Fr in the 1999 edition to 0.7Fy. In the specifications prior to the 2005 Specification the residual stress, Fr, for rolled and welded shapes was different, namely 10 ksi (69 MPa) and 16.5 ksi (114 MPa), respectively, while in the 2005 Specification and in this Specification the residual stress is taken as 0.3Fy so that the value of Fy ⫺ Fr = 0.7Fy is adopted. This change was made in the interest of simplicity with negligible effect on economy. The elastic lateral-torsional buckling stress, Fcr, of Equation F2-4:

Fcr =

Cb π 2 E ⎛ Lb ⎞ ⎜⎝ r ⎟⎠ ts

2

1 + 0.078

Jc ⎛ Lb ⎞ S x ho ⎜⎝ rts ⎟⎠

2

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(C-F2-1)

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DOUBLY SYMMETRIC COMPACT I-SHAPED MEMBERS

TABLE C-F2.1 Comparison of Equations for Nominal Flexural Strength 1999 AISC LRFD Specification Equations

2005 and 2010 Specification Equations

F1-1

F2-1

F1-2

F2-2

F1-13

F2-3

is identical to Equation F1-13 in the 1999 LRFD Specification:

Fcr =

Mcr Cb π = Sx Lb S x

2

⎛ πE ⎞ EI yGJ + ⎜ I yCw ⎝ Lb ⎟⎠

(C-F2-2)

if c = 1 (see Section F2 for definition): rts2 =

I yCw Sx

; ho = d – t f ; and

2G = 0.0779 π2 E

Equation F2-5 is the same as Equation F1-4 in the 1999 LRFD Specification, and Equation F2-6 corresponds to Equation F1-6. It is obtained by setting Fcr = 0.7Fy in Equation F2-4 and solving for Lb. The format of Equation F2-6 has changed in the 2010 Specification so that it is not undefined at the limit when J = 0; otherwise it gives identical results. The term rts can conservatively be calculated as the radius of gyration of the compression flange plus one-sixth of the web. These provisions have been simplified when compared to the previous ASD provisions based on a more informed understanding of beam limit states behavior. The maximum allowable stress obtained in these provisions may be slightly higher than the previous limit of 0.66Fy, since the true plastic strength of the member is reflected by use of the plastic section modulus in Equation F2-1. The Section F2 provisions for unbraced length are satisfied through the use of two equations, one for inelastic lateral-torsional buckling (Equation F2-2), and one for elastic lateral-torsional buckling (Equation F2-3). Previous ASD provisions placed an arbitrary stress limit of 0.6Fy when a beam was not fully braced and required that three equations be checked with the selection of the largest stress to determine the strength of a laterally unbraced beam. With the current provisions, once the unbraced length is determined, the member strength can be obtained directly from these equations.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Comm.1_A copy:14Ed._

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DOUBLY SYMMETRIC I-SHAPED MEMBERS

[Comm. F3.

DOUBLY SYMMETRIC I-SHAPED MEMBERS WITH COMPACT WEBS AND NONCOMPACT OR SLENDER FLANGES BENT ABOUT THEIR MAJOR AXIS Section F3 is a supplement to Section F2 for the case where the flange of the section is noncompact or slender (see Figure C-F1.1, linear variation of Mn between λpf and λrf ). As pointed out in the User Note of Section F2, very few rolled wide-flange shapes are subject to this criterion.

F4.

OTHER I-SHAPED MEMBERS WITH COMPACT OR NONCOMPACT WEBS BENT ABOUT THEIR MAJOR AXIS The provisions of Section F4 are applicable to doubly symmetric I-shaped beams with noncompact webs and to singly symmetric I-shaped members with compact or noncompact webs (see the Table in User Note F1.1). This section deals with welded I-shaped beams where the webs are not slender. Flanges may be compact, noncompact or slender. The following section, F5, considers welded I-shapes with slender webs. The contents of Section F4 are based on White (2004). Four limit states are considered: (a) compression flange yielding; (b) lateraltorsional buckling (LTB); (c) flange local buckling (FLB); and (d) tension flange yielding (TFY). The effect of inelastic buckling of the web is taken care of indirectly by multiplying the moment causing yielding in the compression flange by a factor, Rpc, and the moment causing yielding in the tension flange by a factor, Rpt. These two factors can vary from unity to as high as 1.6. Conservatively, they can be assumed to equal 1.0. The following steps are provided as a guide to the determination of Rpc and Rpt. Step 1. Calculate hp and hc, as defined in Figure C-F4.1. Step 2. Determine web slenderness and yield moments in compression and tension:

Fig. C-F4.1. Elastic and plastic stress distributions.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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OTHER I-SHAPED MEMBERS

16.1–311

hc ⎫ ⎧ ⎪ ⎪λ = t w ⎪ ⎪ Ix Ix ⎪ ⎪ ⎬ ⎨ S xc = ; S xt = d – y y ⎪ ⎪ ⎪ M yc = Fy S xc ; M yt = Fy S xt ⎪ ⎪ ⎪ ⎭ ⎩

(C-F4-1)

Step 3. Determine λpw and λrw : ⎫ ⎧ hc E ⎪ ⎪ h F E ⎪ p y ⎪λ pw = ≤ 5.70 2 ⎪ Fy ⎪⎪ ⎡ 0.54M p ⎤ ⎪ – 0.09 ⎬ ⎨ ⎢ ⎥ ⎣ My ⎦ ⎪ ⎪ ⎪ ⎪ E ⎪ ⎪λ rw = 5.70 Fy ⎪⎭ ⎪⎩

(C-F4-2)

If λ > λrw , then the web is slender and the design is governed by Section F5. Step 4. Calculate Rpc and Rpt using Section F4. The basic maximum nominal moment is Rpc Myc = Rpc Fy Sxc if the flange is in compression, and Rpt Myt = Rpt Fy Sxt if it is in tension. Thereafter, the provisions are the same as for doubly symmetric members in Sections F2 and F3. For the limit state of lateral-torsional buckling, I-shaped members with cross sections that have unequal flanges are treated as if they were doubly symmetric I-shapes. That is, Equations F2-4 and F2-6 are the same as Equations F4-5 and F4-8, except the former use Sx and the latter use Sxc, the elastic section moduli of the entire section and of the compression side, respectively. This is a simplification that tends to be somewhat conservative if the compression flange is smaller than the tension flange, and it is somewhat unconservative when the reverse is true. It is also required to check for tension flange yielding if the tension flange is smaller than the compression flange (Section F4.4). For a more accurate solution, especially when the loads are not applied at the centroid of the member, the designer is directed to Chapter 5 of the SSRC Guide and other references (Galambos, 2001; White and Jung, 2003; Ziemian, 2010). The following alternative equations in lieu of Equations F4-4, F4-5 and F4-8 are provided by White and Jung:

M n = Cb

Lr =

1.38E I y J S xc FL

2 π 2 EI y ⎧⎪ β x C ⎡ J 2 ⎤ ⎫⎪ ⎛β ⎞ + ⎜ x ⎟ + w ⎢1 + 0.0390 Lb ⎬ 2 ⎨ ⎝ 2⎠ Iy ⎣ C w ⎥⎦ ⎪ Lb ⎪ 2 ⎭ ⎩ 2

27.0C w ⎛ FL S xc ⎞ 2.6β x FL S xc ⎤ ⎡ 2.6β x FL S xc +1+ ⎢ + 1⎥ + ⎜ ⎟ EJ EJ I y ⎝ EJ ⎠ ⎦ ⎣

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(C-F4-3)

2

(C-F4-4)

AISC_PART 16_Comm.1_A copy:14Ed._

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OTHER I-SHAPED MEMBERS

[Comm. F4.

⎛ I yc ⎞ where the coefficient of monosymmetry, β x = 0.9 hα ⎜ − 1⎟ , ⎠ ⎝ I yt the warping constant, Cw = h2Iyc α, and α =

F5.

1 . I yc +1 I yt

DOUBLY SYMMETRIC AND SINGLY SYMMETRIC I-SHAPED MEMBERS WITH SLENDER WEBS BENT ABOUT THEIR MAJOR AXIS This section applies to doubly and singly symmetric I-shaped welded plate girders with a slender web, that is,

hc E > λ r = 5.70 . The applicable limit states are comtw Fy

pression flange yielding, lateral-torsional buckling, compression flange local buckling, and tension flange yielding. The provisions in this section have changed little since 1963. The provisions for plate girders are based on research reported in Basler and Thürlimann (1963). There is no seamless transition between the equations in Section F4 and F5. Thus the bending strength of a girder with Fy = 50 ksi (345 MPa) and a web slenderness h/tw =137 is not close to that of a girder with h/tw = 138. These two slenderness ratios are on either side of the limiting ratio. This gap is caused by the discontinuity between the lateral-torsional buckling resistances predicted by Section F4 and those predicted by Section F5 due to the implicit use of J = 0 in Section F5. However, for typical noncompact web section members close to the noncompact web limit, the influence of J on the lateral-torsional buckling resistance is relatively small (for example, the calculated Lr values including J versus using J = 0 typically differ by less than 10%). The implicit use of J = 0 in Section F5 is intended to account for the influence of web distortional flexibility on the lateral-torsional buckling resistance for slender-web I-section members.

F6.

I-SHAPED MEMBERS AND CHANNELS BENT ABOUT THEIR MINOR AXIS I-shaped members and channels bent about their minor axis do not experience lateral-torsional buckling or web buckling. The only limit states to consider are yielding and flange local buckling. The user note informs the designer of the few rolled shapes that need to be checked for flange local buckling.

F7.

SQUARE AND RECTANGULAR HSS AND BOX-SHAPED MEMBERS The provisions for the nominal flexural strength of HSS include the limit states of yielding and local buckling. Square and rectangular HSS are typically not subject to lateral-torsional buckling.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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SQUARE AND RECTANGULAR HSS AND BOX-SHAPED MEMBERS

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Because of the high torsional resistance of the closed cross section, the critical unbraced lengths, Lp and Lr, that correspond to the development of the plastic moment and the yield moment, respectively, are very large. For example, as shown in Figure C-F7.1, an HSS20×4×5/16 (HSS508×101.6×7.9), which has one of the largest depth-to-width ratios among standard HSS, has Lp of 6.7 ft (2.0 m) and Lr of 137 ft (42 m) as determined in accordance with the 1993 Load and Resistance Factor Design Specification for Structural Steel Buildings (AISC, 1993). An extreme deflection limit might correspond to a length-to-depth ratio of 24 or a length of 40 ft (12 m) for this member. Using the specified linear reduction between the plastic moment and the yield moment for lateral-torsional buckling, the plastic moment is reduced by only 7% for the 40-ft (12-m) length. In most practical designs where there is a moment gradient and the lateral-torsional buckling modification factor, Cb, is larger than unity, the reduction will be nonexistent or insignificant. The provisions for local buckling of noncompact rectangular HSS are also the same as those in the previous sections of this chapter: Mn = Mp for b/t ≤ λp, and a linear transition from Mp to Fy Sx when λp < b/t ≤ λr. The equation for the effective width of the compression flange when b/t exceeds λr is the same as that used for rectangular HSS in axial compression except that the stress is taken as the yield stress. This implies that the stress in the corners of the compression flange is at yield when the ultimate post-buckling strength of the flange is reached. When using the effective width, the nominal flexural strength is determined from the effective section modulus to the compression flange using the distance from the shifted neutral axis. A slightly conservative estimate of the nominal flexural strength can be obtained by using the effective width for both the compression and tension flange, thereby maintaining the symmetry of the cross section and simplifying the calculations.

Fig. C-F7.1. Lateral-torsional buckling of rectangular HSS.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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ROUND HSS

[Comm. F8.

ROUND HSS Round HSS are not subject to lateral-torsional buckling. The failure modes and postbuckling behavior of round HSS can be grouped into three categories (Sherman, 1992; Ziemian, 2010): (a) For low values of D/t, a long plastic plateau occurs in the moment-rotation curve. The cross section gradually ovalizes, local wave buckles eventually form, and the moment resistance subsequently decays slowly. Flexural strength may exceed the theoretical plastic moment due to strain hardening. (b) For intermediate values of D/t, the plastic moment is nearly achieved but a single local buckle develops and the flexural strength decays slowly with little or no plastic plateau region. (c) For high values of D/t, multiple buckles form suddenly with very little ovalization and the flexural strength drops quickly. The flexural strength provisions for round HSS reflect these three regions of behavior and are based upon five experimental programs involving hot-formed seamless pipe, electric-resistance-welded pipe, and fabricated tubing (Ziemian, 2010).

F9.

TEES AND DOUBLE ANGLES LOADED IN THE PLANE OF SYMMETRY The lateral-torsional buckling (LTB) strength of singly symmetric tee beams is given by a fairly complex formula (Ziemian, 2010). Equation F9-4 is a simplified formulation based on Kitipornchai and Trahair (1980). See also Ellifritt et al. (1992). The Cb factor used for I-shaped beams is unconservative for tee beams with the stem in compression. For such cases, Cb = 1.0 is appropriate. When beams are bent in reverse curvature, the portion with the stem in compression may control the LTB resistance even though the moments may be small relative to other portions of the unbraced length with Cb ≈ 1.0. This is because the LTB strength of a tee with the stem in compression may be only about one-fourth of the strength for the stem in tension. Since the buckling strength is sensitive to the moment diagram, Cb has been conservatively taken as 1.0. In cases where the stem is in tension, connection details should be designed to minimize any end restraining moments that might cause the stem to be in compression. The 2005 Specification did not have provisions for the local buckling strength of the stems of tee sections and the legs of double angle sections under flexural compressive stress gradient. The Commentary to this Section in the 2005 Specification explained that the local buckling strength was accounted for in the equation for the lateral-torsional buckling limit state, Equation F9-4, when the unbraced length, Lb, approached zero. While this is a correct procedure, it led to confusion and to many questions by users of the Specification. For this reason, Section F9.4, “Local Buckling of Tee Stems in Flexural Compression,” was added to provide an explicit set of formulas for the 2010 Specification. The derivation of the formulas is provided here to explain the changes. The classical formula for the elastic buckling of a rectangular plate is (Ziemian, 2010): Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Comm.1_A copy:14Ed._

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Comm. F9.] TEES AND DOUBLE ANGLES LOADED IN THE PLANE OF SYMMETRY

Fcr =

π 2 Ek

(

)

⎛ b⎞ 12 1 − ν ⎜ ⎟ ⎝ t⎠ 2

2

16.1–315

(C-F9-1)

where ν = 0.3 (Poisson’s ratio) b/t = plate width-to-thickness ratio k = plate buckling coefficient For the stem of tee sections, the width-to-thickness ratio is equal to d/tw. The two rectangular plates in Figure C-F9.1 are fixed at the top, free at the bottom and loaded, respectively, with a uniform and a linearly varying compressive stress. The corresponding plate buckling coefficients, k, are 1.33 and 1.61 (Figure 4.4, Ziemian, 2010). The graph in Figure C-F9.2 shows the general scheme used historically in developing the local buckling criteria in AISC Specifications. The ordinate is the critical stress divided by the yield stress, and the abscissa is a nondimensional width-to-thickness ratio, λ=

(

2 b Fy 12 1 − ν t E π2k

)

(C-F9-2)

In the traditional scheme it is assumed the critical stress is the yield stress, Fy, – as long as λ ≤ 0.7. Elastic buckling, governed by Equation C-F9-1 commences when

Fig.C-F9.1 Plate buckling coefficients for uniform compression and for linearly varying compressive stresses. Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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TEES AND DOUBLE ANGLES LOADED IN THE PLANE OF SYMMETRY [Comm. F9.

Fig. C-F9.2. General scheme for plate local buckling limit states.

Fig. C-F9.3. Local buckling of tee stem in flexural compression.

Specification for Structural Steel Buildings, June 22, 2010

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

AISC_PART 16_Comm.1_A copy:14Ed._

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SINGLE ANGLES

16.1–317

– λ = 1.24 and Fcr = 0.65Fy. Between these two points the transition is assumed linear to account for initial deflections and residual stresses. While these assumptions are arbitrary empirical values, they have proven satisfactory. The curve in Figure C-F9.3 shows the graph of the formulas adopted for the stem of tee sections and the legs of double angle sections when these elements are subject to flexural compression. The limiting width-to-thickness ratio up to which Fcr = Fy is (using v = 0.3 and k = 1.61):

λ = 0.7 =

)

(

2 b Fy 12 1 − ν b d E → = = 0.84 t E t tw Fy π2k

The elastic buckling range was assumed to be governed by the same equation as the local buckling of the flanges of a wide-flange beam bent about its minor axis (Equation F6-4): Fcr =

0.69 E ⎛d⎞ ⎜⎝ t ⎟⎠ w

2

The underlying plate buckling coefficient for this equation is k = 0.76, which is a conservative assumption for tee stems in flexural compression. The straight-line transition between the end of the yield limit and the onset of the elastic buckling range is also indicated in Figure C-F9.3. Flexure about the y-axis of tees and double angles does not occur frequently and is not covered in this Specification. However, guidance is given here to address this condition. The yield limit state and the local buckling limit state of the flange can be checked by using Equations F6-1 through F6-3. Lateral-torsional buckling can conservatively be calculated by assuming the flange acts alone as a rectangular beam, using Equations F11-2 through F11-4. Alternately, an elastic critical moment given as Me =

π EI x GJ Lb

(C-F9-3)

may be used in Equations F10-2 or F10-3 to obtain the nominal flexural strength.

F10. SINGLE ANGLES Flexural strength limits are established for the limit states of yielding, lateraltorsional buckling, and leg local buckling of single-angle beams. In addition to addressing the general case of unequal-leg single angles, the equal-leg angle is treated as a special case. Furthermore, bending of equal-leg angles about a geometric axis, an axis parallel to one of the legs, is addressed separately as it is a common case of angle bending. The tips of an angle refer to the free edges of the two legs. In most cases of unrestrained bending, the flexural stresses at the two tips will have the same sign (tension or compression). For constrained bending about a geometric axis, the tip stresses will Specification for Structural Steel Buildings, June 22, 2010

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differ in sign. Provisions for both tension and compression at the tip should be checked as appropriate, but in most cases it will be evident which controls. Appropriate serviceability limits for single-angle beams need also to be considered. In particular, for longer members subjected to unrestrained bending, deflections are likely to control rather than lateral-torsional buckling or leg local buckling strength. The provisions in this section follow the general format for nominal flexural resistance (see Figure C-F1.2). There is a region of full plastification, a linear transition to the yield moment, and a region of local buckling.

1.

Yielding The strength at full yielding is limited to a shape factor of 1.50 applied to the yield moment. This leads to a lower bound plastic moment for an angle that could be bent about any axis, inasmuch as these provisions are applicable to all flexural conditions. The 1.25 factor originally used was known to be a conservative value. Research work (Earls and Galambos, 1997) has indicated that the 1.50 factor represents a better lower bound value. Since the shape factor for angles is in excess of 1.50, the nominal design strength, Mn = 1.5My, for compact members is justified provided that instability does not control.

2.

Lateral-Torsional Buckling Lateral-torsional buckling may limit the flexural strength of an unbraced single-angle beam. As illustrated in Figure C-F10.1, Equation F10-2 represents the elastic buckling portion with the maximum nominal flexural strength, Mn, equal to 75% of the theoretical buckling moment, Me. Equation F10-3 represents the inelastic buckling transition expression between 0.75My and 1.5My. The maximum beam flexural strength Mn = 1.5My will occur when the theoretical buckling moment, Me, reaches or exceeds 7.7My. My is the moment at first yield in Equations F10-2 and F10-3, the

Fig. C-F10.1. Lateral-torsional buckling limits of a single-angle beam. Specification for Structural Steel Buildings, June 22, 2010

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same as the My in Equation F10-1. These equations are modifications of those developed from the results of Australian research on single angles in flexure and on an analytical model consisting of two rectangular elements of length equal to the actual angle leg width minus one-half the thickness (AISC, 1975; Leigh and Lay, 1978, 1984; Madugula and Kennedy, 1985). When bending is applied about one leg of a laterally unrestrained single angle, the angle will deflect laterally as well as in the bending direction. Its behavior can be evaluated by resolving the load and/or moments into principal axis components and determining the sum of these principal axis flexural effects. Subsection (a) of Section F10.2(iii) is provided to simplify and expedite the calculations for this common situation with equal-leg angles. For such unrestrained bending of an equal-leg angle, the resulting maximum normal stress at the angle tip (in the direction of bending) will be approximately 25% greater than the calculated stress using the geometric axis section modulus. The value of Me given by Equations F10-6a and F10-6b and the evaluation of My using 0.80 of the geometric axis section modulus reflect bending about the inclined axis shown in Figure C-F10.2. The deflection calculated using the geometric axis moment of inertia has to be increased 82% to approximate the total deflection. Deflection has two components: a vertical component (in the direction of applied load) of 1.56 times the calculated value and a horizontal component of 0.94 times the calculated value. The resultant total deflection is in the general direction of the weak principal axis bending of the angle (see Figure C-F10.2). These unrestrained bending deflections should be considered in evaluating serviceability and will often control the design over lateraltorsional buckling. The horizontal component of deflection being approximately 60% of the vertical deflection means that the lateral restraining force required to achieve purely vertical

Fig. C-F10.2. Geometric axis bending of laterally unrestrained equal-leg angles. Specification for Structural Steel Buildings, June 22, 2010

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deflection must be 60% of the applied load value (or produce a moment 60% of the applied value), which is very significant. Lateral-torsional buckling is limited by Me (Leigh and Lay, 1978, 1984) as defined in Equation F10-6a, which is based on Mcr =

⎡ ⎤ 2.33Eb 4 t 0.156(1 + 3 cos2 θ))( KL )2 t 2 ⎢ sin 2 θ + + sin θ ⎥ 2 2 4 (1 + 3 cos θ)( KL ) ⎢⎣ b ⎥⎦

(C-F10-1)

(the general expression for the critical moment of an equal-leg angle) with θ = ⫺45° for the condition where the angle tip stress is compressive (see Figure C-F10.3). Lateral-torsional buckling can also limit the flexural strength of the cross section when the maximum angle tip stress is tensile from geometric axis flexure, especially with use of the flexural strength limits in Section F10.2. Using θ = 45° in Equation C-F10-1, the resulting expression is Equation F10-6b with a +1 instead of −1 as the last term. Stress at the tip of the angle leg parallel to the applied bending axis is of the same sign as the maximum stress at the tip of the other leg when the single angle is unrestrained. For an equal-leg angle this stress is about one-third of the maximum stress. It is only necessary to check the nominal bending strength based on the tip of the angle leg with the maximum stress when evaluating such an angle. If an angle is subjected to an axial compressive load, the flexural limits obtained from Section F10.2(iii) cannot be used due to the inability to calculate a proper moment magnification factor for use in the interaction equations. For unequal-leg angles and for equal-leg angles in compression without lateral-torsional restraint, the applied load or moment must be resolved into components along the two principal axes in all cases and design must be for biaxial bending using the interaction equations in Chapter H.

Fig. C-F10.3. Equal-leg angle with general moment loading. Specification for Structural Steel Buildings, June 22, 2010

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Under major axis bending of equal-leg angles, Equation F10-4 in combination with Equations F10-2 and F10-3 controls the available moment against overall lateraltorsional buckling of the angle. This is based on Mcr given in Equation C-F10-1 with θ = 0°. Lateral-torsional buckling for this case will reduce the stress below 1.5My only for L/t ≥ 3,675Cb /Fy (Me = 7.7My). If the Lt/b2 parameter is small (less than approximately 0.87Cb for this case), local buckling will control the available moment and Mn based on lateral-torsional buckling need not be evaluated. Local buckling must be checked using Section F10.3. Lateral-torsional buckling about the major principal w-axis of an unequal-leg angle is controlled by Me in Equation F10-5. The section property, βw, reflects the location of the shear center relative to the principal axis of the section and the bending direction under uniform bending. Positive βw and maximum Me occur when the shear center is in flexural compression while negative βw and minimum Me occur when the shear center is in flexural tension (see Figure C-F10.4). This βw effect is consistent with behavior of singly symmetric I-shaped beams, which are more stable when the compression flange is larger than the tension flange. For principal w-axis bending of equal-leg angles, βw is equal to zero due to symmetry and Equation F10-5 reduces to Equation F10-4 for this special case. For reverse curvature bending, part of the unbraced length has positive βw, while the remainder has negative βw; conservatively, the negative value is assigned for that entire unbraced segment. The factor βw is essentially independent of angle thickness (less than 1% variation from mean value) and is primarily a function of the leg widths. The average values shown in Table C-F10.1 may be used for design.

3.

Leg Local Buckling The b/t limits have been modified to be more representative of flexural limits rather than using those for single angles under uniform compression. Typically the flexural

(a) +βw

(b) −βw Fig. C-F10.4. Unequal-leg angle in bending. Specification for Structural Steel Buildings, June 22, 2010

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TABLE C-F10.1 βw Values for Angles Angle size in. (mm)

βw in. (mm)*

8 ⫻ 6 (203 ⫻ 152) 8 ⫻ 4 (203 ⫻ 102)

3.31 (84.1) 5.48 (139)

7 ⫻ 4 (178 ⫻ 102)

4.37 (111)

6 ⫻ 4 (152 ⫻ 102) 6 ⫻ 31/2 (152 ⫻ 89)

3.14 (79.8) 3.69 (93.7)

5 ⫻ 31/2 (127 ⫻ 89) 5 ⫻ 3 (127 ⫻ 76)

2.40 (61.0) 2.99 (75.9)

4 ⫻ 31/2 (102 ⫻ 89) 4 ⫻ 3 (102 ⫻ 76)

0.87 (22.1) 1.65 (41.9)

31/2 ⫻ 3 (89 ⫻ 76) 31/2 ⫻ 21/2 (89 ⫻ 64)

0.87 (22.1) 1.62 (41.1)

3 ⫻ 21/2 (76 ⫻ 64) 3 ⫻ 2 (76 ⫻ 51)

0.86 (21.8) 1.56 (39.6)

21/2 ⫻ 2 (64 ⫻ 51)

0.85 (21.6)

21/2

⫻

11/2

(64 ⫻ 38)

1.49 (37.8)

Equal legs *βw =

1 Iw

∫ z (w

A

2

+z

2

)dA − 2z

0.00

o

where zo = coordinate along the z-axis of the shear center with respect to the centroid, in. (mm) Iw = moment of inertia for the major principal axis, in.4 (mm4) βw has a positive or negative value depending on the direction of bending (see Figure C-F10.4).

stresses will vary along the leg length permitting the use of the stress limits given. Even for the geometric axis flexure case, which produces uniform compression along one leg, use of these limits will provide a conservative value when compared to the results reported in Earls and Galambos (1997).

F11. RECTANGULAR BARS AND ROUNDS The provisions in Section F11 apply to solid bars with round and rectangular cross section. The prevalent limit state for such members is the attainment of the full plastic moment, Mp. The exception is the lateral-torsional buckling of rectangular bars where the depth is larger than the width. The requirements for design are identical to those given previously in Table A-F1.1 in the 1999 LRFD Specification and the same as those given in the 2005 Specification for Structural Steel Buildings (AISC, 2005a). Since the shape factor for a rectangular cross section is 1.5 and for a round section is 1.7, consideration must be given to serviceability issues such as excessive deflection or permanent deformation under service-load conditions. Specification for Structural Steel Buildings, June 22, 2010

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F12. UNSYMMETRICAL SHAPES When the design engineer encounters beams that do not contain an axis of symmetry, or any other shape for which there are no provisions in the other sections of Chapter F, the stresses are to be limited by the yield stress or the elastic buckling stress. The stress distribution and/or the elastic buckling stress must be determined from principles of structural mechanics, textbooks or handbooks, such as the SSRC Guide (Ziemian, 2010), papers in journals, or finite element analyses. Alternatively, the designer can avoid the problem by selecting cross sections from among the many choices given in the previous sections of Chapter F.

F13. PROPORTIONS OF BEAMS AND GIRDERS 1.

Strength Reductions for Members with Holes in the Tension Flange Historically, provisions for proportions of rolled beams and girders with holes in the tension flange were based upon either a percentage reduction independent of material strength or a calculated relationship between the tension rupture and tension yield strengths of the flange, with resistance factors or safety factors included in the calculation. In both cases, the provisions were developed based upon tests of steel with a specified minimum yield stress of 36 ksi (250 MPa) or less. More recent tests (Dexter and Altstadt, 2004; Yuan et al., 2004) indicate that the flexural strength on the net section is better predicted by comparison of the quantities Fy Afg and Fu Afn, with slight adjustment when the ratio of Fy to Fu exceeds 0.8. If the holes remove enough material to affect the member strength, the critical stress is adjusted from Fy to (Fu Afn /Afg) and this value is conservatively applied to the elastic section modulus, Sx. The resistance factor and safety factor used throughout this chapter, φ = 0.90 and Ω = 1.67, are those normally applied for the limit state of yielding. In the case of rupture of the tension flange due to the presence of holes, the provisions of this chapter continue to apply the same resistance and safety factors. Since the effect of Equation F13-1 is to multiply the elastic section modulus by a stress that is always less than the yield stress, it can be shown that this resistance and safety factor always give conservative results when Z/S ≤ 1.2. It can also be shown to be conservative when Z/S > 1.2 and a more accurate model for the rupture strength is used (Geschwindner, 2010a).

2.

Proportioning Limits for I-Shaped Members The provisions of this section were taken directly from Appendix G Section G1 of the 1999 LRFD Specification and are the same as the 2005 Specification for Structural Steel Buildings (AISC, 2005a). They have been part of the plate-girder design requirements since 1963 and are derived from Basler and Thürlimann (1963). The web depth-to-thickness limitations are provided so as to prevent the flange from buckling into the web. Equation F13-4 was slightly modified from the corresponding Equation A-G1-2 in the 1999 LRFD Specification to recognize the change in the definition of residual stress from a constant 16.5 ksi (114 MPa) to 30% of the yield stress in the 2005 Specification, as shown by the following derivation: Specification for Structural Steel Buildings, June 22, 2010

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(C-F13-1)

Cover Plates Cover plates need not extend the entire length of the beam or girder. The end connection between the cover plate and beam must be designed to resist the full force in the cover plate at the theoretical cutoff point. The end force in a cover plate on a beam whose required strength exceeds the available yield strength, φMy = φFy Sx (LFRD) or My /Ω = Fy Sx /Ω (ASD), of the combined shape can be determined by an elastic-plastic analysis of the cross section but can conservatively be taken as the full yield strength of the cover plate for LRFD or the full yield strength of the cover plate divided by 1.5 for ASD. The forces in a cover plate on a beam whose required strength does not exceed the available yield strength of the combined section can be determined using the elastic distribution, MQ/I. The requirements for minimum weld lengths on the sides of cover plates at each end reflect uneven stress distribution in the welds due to shear lag in short connections.

5.

Unbraced Length for Moment Redistribution The moment redistribution provisions of Section B3.7 refer to this section for setting the maximum unbraced length when moments are to be redistributed. These provisions have been a part of the Specification since the 1949 edition. Portions of members that would be required to rotate inelastically while the moments are redistributed need more closely spaced bracing than similar parts of a continuous beam. Equations F13-8 and F13-9 define the maximum permitted unbraced length in the vicinity of redistributed moment for doubly symmetric and singly symmetric I-shaped members with a compression flange equal to or larger than the tension flange bent about their major axis, and for solid rectangular bars and symmetric box beams bent about their major axis, respectively. These equations are identical to those in Appendix 1 of the 2005 Specification for Structural Steel Buildings (AISC, 2005a) and the 1999 LRFD Specification, and are based on research reported in Yura et al. (1978). They are different from the corresponding equations in Chapter N of the 1989 Specification for Structural Steel Buildings—Allowable Stress Design and Plastic Design (AISC, 1989).

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CHAPTER G DESIGN OF MEMBERS FOR SHEAR

G1.

GENERAL PROVISIONS Chapter G applies to webs of singly or doubly symmetric members subject to shear in the plane of the web, single angles and HSS, and shear in the weak direction of singly or doubly symmetric shapes. Two methods for determining the shear strength of singly or doubly symmetric I-shaped beams and built-up sections are presented. The method of Section G2 does not utilize the post-buckling strength of the web, while the method of Section G3 utilizes the post-buckling strength.

G2.

MEMBERS WITH UNSTIFFENED OR STIFFENED WEBS Section G2 deals with the shear strength of webs of wide-flange or I-shaped members, as well as webs of tee-shapes, that are subject to shear and bending in the plane of the web. The provisions in Section G2 apply to the general case when an increase of strength due to tension field action is not permitted. Conservatively, these provisions may be applied also when it is not desired to use the tension field action enhancement for convenience in design. Consideration of the effect of bending on the shear strength is not required because the effect is deemed negligible.

1.

Shear Strength The nominal shear strength of a web is defined by Equation G2-1, a product of the shear yield force, 0.6Fy Aw, and the shear-buckling reduction factor, Cv. The provisions of Case (a) in Section G2.1 for rolled I-shaped members with h t w ≤ 2.24 E Fy are similar to the 1999 and earlier LRFD provisions, with the exception that φ has been increased from 0.90 to 1.00 (with a corresponding decrease of the safety factor from 1.67 to 1.50), thus making these provisions consistent with the 1989 provisions for allowable stress design (AISC, 1989). The value of φ of 1.00 is justified by comparison with experimental test data and recognizes the minor consequences of shear yielding, as compared to those associated with tension and compression yielding, on the overall performance of rolled I-shaped members. This increase is applicable only to the shear yielding limit state of rolled I-shaped members. Case (b) in Section G2.1 uses the shear buckling reduction factor, Cv, shown in Figure C-G2.1.The curve for Cv has three segments. For webs with h / t w ≤ 1.10 kv E / Fyw , the nominal shear strength, Vn, is based on shear yielding of the web, with Cv given by Equation G2-3. This h /tw limit was

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determined by setting the critical stress causing shear buckling, Fcr, equal to the yield stress of the web, Fyw = Fy, in Equation 35 of Cooper et al. (1978). When h / t w > 1.10 kv E / Fyw , the web shear strength is based on buckling. It has been suggested to take the proportional limit as 80% of the yield stress of the web (Basler, 1961). This corresponds to h / t w = (1.10 / 0.8 )

(

)

kv E / Fyw .

When h / t w > 1.37 kv E / Fyw , the web strength is determined from the elastic buckling stress given by Equation 6 of Cooper at al. (1978) and Equation 9-7 in Timoshenko and Gere (1961): Fcr =

(

π 2 Ekv

)

12 1 − v 2 ( h / t w )

2

(C-G2-1)

Cv in Equation G2-5 was obtained by dividing Fcr from Equation C-G2-1 by 0.6Fy and using v = 0.3. The inelastic buckling transition for Cv (Equation G2-4) is used between the limits given by 1.10 kv E / Fy < h / t w ≤ 1.37 kv E /. Fy The plate buckling coefficient, kv, for panels subject to pure shear having simple supports on all four sides is given by Equation 4.3 in Ziemian (2010). 5.34 ⎫ ⎧ ⎪ 4.00 + a / h 2 for a / h ≤ 1 ⎪ ( ) ⎪ ⎪ kv = ⎨ ⎬ 4.00 ⎪ ⎪5.34 + 1 for a / h > 2 ⎪⎭ ⎪ a h / ( ) ⎩

Fig. C-G2.1. Shear buckling coefficient Cv for Fy = 50 ksi (345 MPa) and kv = 5.0. Specification for Structural Steel Buildings, June 22, 2010

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For practical purposes and without loss of accuracy, these equations have been simplified herein and in AASHTO (2010) to kv = 5 +

5

( a / h )2

(C-G2-3)

When the panel ratio, a/h, becomes large, as in the case of webs without transverse stiffeners, then kv = 5. Equation C-G2-3 applies as long as there are flanges on both edges of the web. For tee-shaped beams, the free edge is unrestrained and for this situation kv = 1.2 (JCRC, 1971). The provisions of Section G2.1 assume monotonically increasing loads. If a flexural member is subjected to load reversals causing cyclic yielding over large portions of a web, such as may occur during a major earthquake, special design considerations may apply (Popov, 1980).

2.

Transverse Stiffeners When transverse stiffeners are needed, they must be rigid enough to cause a buckling node line to form at the stiffener. This requirement applies whether or not tension field action is counted upon. The required moment of inertia of the stiffener is the same as in AASHTO (2010), but it is different from the formula in the 1989 Specification for Structural Steel Buildings—Allowable Stress Design (AISC, 1989). Equation G2-7 is derived in Chapter 11 of Salmon and Johnson (1996). The origin of the formula can be traced to Bleich (1952).

G3.

TENSION FIELD ACTION The provisions of Section G3 apply when it is intended to account for the enhanced strength of webs of built-up members due to tension field action.

1.

Limits on the Use of Tension Field Action The panels of the web of a built-up member, bounded on the top and bottom by the flanges and on each side by the transverse stiffeners, are capable of carrying loads far in excess of their “web buckling” load. Upon reaching the theoretical web buckling limit, slight lateral web displacements will have developed. These deformations are of no structural significance, because other means are still present to provide further strength. When transverse stiffeners are properly spaced and are stiff enough to resist out-ofplane movement of the postbuckled web, significant diagonal tension fields form in the web panels prior to the shear resistance limit. The web in effect acts like a Pratt truss composed of tension diagonals and compresson verticals that are stabilized by the transverse stiffeners. This effective Pratt truss furnishes the strength to resist applied shear forces unaccounted for by the linear buckling theory. The key requirement in the development of tension field action in the web of plate girders is the ability of the stiffeners to provide sufficient flexural rigidity to stabilize the web along their length. In the case of end panels there is a panel only on one side. The anchorage of the tension field is limited in many situations at these locations and Specification for Structural Steel Buildings, June 22, 2010

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is thus neglected. In addition, the enhanced resistance due to tension field forces is reduced when the panel aspect ratio becomes large. For this reason the inclusion of tension field action is not permitted when a/h exceeds 3.0 or [260/(h/tw)]2. AISC Specifications prior to 2005 have required explicit consideration of the interaction between the flexural and shear strengths when the web is designed using tension field action. White et al. (2008) show that the interaction between the shear and flexural resistances is negligible when the requirements 2Aw /(Afc + Aft) ≤ 2.5 and h/bf ≤ 6 are satisfied. Section G3.1 disallows the use of tension field action for I-section members with relatively small flange-to-web proportions identified by these limits. Similar limits are specified in AASHTO (2010); furthermore, AASHTO (2010) allows the use of a reduced “true Basler” tension field resistance for cases where these limits are violated.

2.

Shear Strength with Tension Field Action Analytical methods based on tension field action have been developed (Basler and Thürlimann, 1963; Basler, 1961) and corroborated in an extensive program of tests (Basler et al., 1960). Equation G3-2 is based on this research. The second term in the bracket represents the relative increase of the panel shear strength due to tension field action. The merits of Equation G3-2 relative to various alternative representations of web shear resistance are evaluated and Equation G3-2 is recommended in White and Barker (2008).

3.

Transverse Stiffeners The vertical component of the tension field force that is developed in the web panel must be resisted by the transverse stiffener. In addition to the rigidity required to keep the line of the stiffener as a nonmoving point for the buckled panel, as provided for in Section G2.2, the stiffener must also have a large enough area to resist the tension field reaction. Numerous studies (Horne and Grayson, 1983; Rahal and Harding, 1990a, 1990b, 1991; Stanway et al., 1993, 1996; Lee et al., 2002b; Xie and Chapman, 2003; Kim et al., 2007) have shown that transverse stiffeners in I-girders designed for tension field action are loaded predominantly in bending due to the restraint they provide to lateral deflection of the web. Generally, there is evidence of some axial compression in the transverse stiffeners due to the tension field, but even in the most slender web plates permitted by this Specification; the effect of the axial compression transmitted from the postbuckled web plate is typically minor compared to the lateral loading effect. Therefore, the transverse stiffener area requirement from prior Specifications is no longer specified. Rather, the demands on the stiffener flexural rigidity are increased in situations where the tension field action of the web is developed. Equation G3-4 is the same requirement as specified in AASHTO (2010).

G4.

SINGLE ANGLES Shear stresses in single-angle members are the result of the gradient of the bending moment along the length (flexural shear) and the torsional moment.

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The maximum elastic stress due to flexural shear is fv =

1.5Vb bt

(C-G4-1)

where Vb is the component of the shear force parallel to the angle leg with width b and thickness t. The stress is constant throughout the thickness, and it should be calculated for both legs to determine the maximum. The coefficient 1.5 is the calculated value for equal leg angles loaded along one of the principal axes. For equal leg angles loaded along one of the geometric axes, this factor is 1.35. Factors between these limits may be calculated conservatively from VbQ/It to determine the maximum stress at the neutral axis. Alternatively, if only flexural shear is considered, a uniform flexural shear stress in the leg of Vb /bt may be used due to inelastic material behavior and stress redistribution. If the angle is not laterally braced against twist, a torsional moment is produced equal to the applied transverse load times the perpendicular distance, e, to the shear center, which is at the point of intersection of the centerlines of the two legs. Torsional moments are resisted by two types of shear behavior: pure torsion (St. Venant torsion) and warping torsion [see Seaburg and Carter (1997)]. The shear stresses due to restrained warping are small compared to the St. Venant torsion (typically less than 20%) and they can be neglected for practical purposes. The applied torsional moment is then resisted by pure shear stresses that are constant along the width of the leg (except for localized regions at the toe of the leg), and the maximum value can be approximated by fv =

M T t 3M T = J At

(C-G4-2)

where A = angle cross-sectional area, in.2 (mm2) J = torsional constant [approximated by Σ(bt3/3) when precomputed value is unavailable], in.4 (mm4) MT = torsional moment, kip-in. (N-mm) For a study of the effects of warping, see Gjelsvik (1981). Torsional moments from laterally unrestrained transverse loads also produce warping normal stresses that are superimposed on the bending stresses. However, since the warping strength of single angles is relatively small, this additional bending effect, just like the warping shear effect, can be neglected for practical purposes.

G5.

RECTANGULAR HSS AND BOX-SHAPED MEMBERS The two webs of a closed rectangular cross section resist shear the same way as the single web of an I-shaped plate girder or wide-flange beam, and therefore, the provisions of Section G2 apply.

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ROUND HSS

[Comm. G6.

ROUND HSS Little information is available on round HSS subjected to transverse shear and the recommendations are based on provisions for local buckling of cylinders due to torsion. However, since torsion is generally constant along the member length and transverse shear usually has a gradient; it is recommended to take the critical stress for transverse shear as 1.3 times the critical stress for torsion (Brockenbrough and Johnston, 1981; Ziemian, 2010). The torsion equations apply over the full length of the member, but for transverse shear it is reasonable to use the length between the points of maximum and zero shear force. Only thin HSS may require a reduction in the shear strength based upon first shear yield. Even in this case, shear will only govern the design of round HSS for the case of thin sections with short spans. In the equation for the nominal shear strength, Vn, of round HSS, it is assumed that the shear stress at the neutral axis, calculated as VQ/lb, is at Fcr. For a thin round section with radius R and thickness t, I = πR3t, Q = 2R2t and b = 2t. This gives the stress at the centroid as V/πRt, in which the denominator is recognized as half the area of the round HSS.

G7.

WEAK AXIS SHEAR IN DOUBLY SYMMETRIC AND SINGLY SYMMETRIC SHAPES The nominal weak axis shear strength of doubly and singly symmetric I-shapes is governed by the equations of Section G2 with the plate buckling coefficient equal to kv = 1.2, the same as the web of a tee-shape. The maximum plate slenderness of all rolled shapes is b/tf = bf /2tf = 13.8, and for Fy = 100 ksi (690 MPa) the value of

1.10 kv E / Fy = 1.10 (1.2 ) ( 29, 000 ksi) / 100

=

20.5. Thus Cv = 1.0, except for built-

up shapes with very slender flanges.

G8.

BEAMS AND GIRDERS WITH WEB OPENINGS Web openings in structural floor members may be used to accommodate various mechanical, electrical and other systems. Strength limit states, including local buckling of the compression flange or of the web, local buckling or yielding of the tee-shaped compression zone above or below the opening, lateral buckling and moment-shear interaction, or serviceability may control the design of a flexural member with web openings. The location, size and number of openings are important and empirical limits for them have been identified. One general procedure for assessing these effects and the design of any needed reinforcement for both steel and composite beams is given in the ASCE Specification for Structural Steel Beams with Web Openings (ASCE, 1999), with background information provided in AISC Design Guide 2 by Darwin (1990) and in ASCE Task Committee on Design Criteria for Composite Structures in Steel and Concrete (1992a, 1992b).

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CHAPTER H DESIGN OF MEMBERS FOR COMBINED FORCES AND TORSION

Chapters D, E, F and G of this Specification address members subject to only one type of force: axial tension, axial compression, flexure and shear, respectively. Chapter H addresses members subject to a combination of two or more of the individual forces defined above, as well as possibly by additional forces due to torsion. The provisions fall into two categories: (a) the majority of the cases that can be handled by an interaction equation involving sums of ratios of required strengths to the available strengths; and (b) cases where the stresses due to the applied forces are added and compared to limiting buckling or yield stresses. Designers will have to consult the provisions of Sections H2 and H3 only in rarely occurring cases.

H1.

DOUBLY AND SINGLY SYMMETRIC MEMBERS SUBJECT TO FLEXURE AND AXIAL FORCE

1.

Doubly and Singly Symmetric Members Subject to Flexure and Compression Section H1 contains design provisions for doubly symmetric and singly symmetric members under combined flexure and compression and under combined flexure and tension. The provisions of Section H1 apply typically to rolled wide-flange shapes, channels, tee-shapes, round, square and rectangular HSS, solid rounds, squares, rectangles or diamonds, and any of the many possible combinations of doubly or singly symmetric shapes fabricated from plates and/or shapes by welding or bolting. The interaction equations accommodate flexure about one or both principal axes as well as axial compression or tension. In 1923, the first AISC Specification required that the stresses due to flexure and compression be added and that the sum not exceed the allowable value. An interaction equation appeared first in the 1936 Specification, stating “Members subject to f f both axial and bending stresses shall be so proportioned that the quantity a + b Fa Fb shall not exceed unity,” in which Fa and Fb are, respectively, the axial and flexural allowable stresses permitted by this Specification, and fa and fb are the corresponding stresses due to the axial force and the bending moment, respectively. This linear interaction equation was in force until the 1961 Specification, when it was modified to account for frame stability and for the P-δ effect, that is, the secondary bending between the ends of the members (Equation C-H1-1). The P-Δ effect, that is, the second-order bending moment due to story sway, was not accommodated. fa Cm f b ≤ 1.0 + fa ⎞ Fa ⎛ 1 – F b ⎜⎝ Fe′ ⎟⎠ Specification for Structural Steel Buildings, June 22, 2010

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(Black plate)

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The allowable axial stress, Fa, was determined for an effective length that is larger 1 than unity for moment frames. The term is the amplification of the interspan f 1– a Fe′ moment due to member deflection multiplied by the axial force (the P-δ effect). Cm accounts for the effect of the moment gradient. This interaction equation was part of all the subsequent editions of the AISC ASD Specifications from 1961 through 1989. A new approach to the interaction of flexural and axial forces was introduced in the 1986 AISC Load and Resistance Factor Design Specification for Structural Steel Buildings (AISC, 1986). The following is an explanation of the thinking behind the interaction curves used. The equations P 8 M pc P + = 1 for ≥ 0.2 Py 9 M p Py

(C-H1-2a)

M pc P P + = 1 for < 0.2 Py 2Py M p

(C-H1-2b)

define the lower-bound curve for the interaction of the nondimensional axial strength, P/Py, and flexural strength, Mpc /Mp, for compact wide-flange stub-columns bent about their x-axis. The cross section is assumed to be fully yielded in tension and compression. The symbol Mpc is the plastic moment strength of the cross section in the presence of an axial force, P. The curve representing Equations C-H1-2 almost overlaps the analytically exact curve for the major-axis bending of a W8×31 cross section (see Figure C-H1.1). The equations for the exact yield capacity of a wide-flange shape are (ASCE, 1971): For 0 ≤

P tw ( d − 2t f ) ≤ Py A 2⎛

P⎞ A ⎜ ⎟ P ⎝ y⎠

2

M pc =1− Mp 4 tw Zx For

t w ( d − 2t f ) A


5.1D2/t) where the edges are not fixed at the ends against rotation is given in Schilling (1965) and Ziemian (2010) as Fcr =

1.23E 5 D⎞ 4

⎛ ⎜⎝ ⎟⎠ t

(C-H3-5) L D

This equation includes a 15% reduction to account for initial imperfections. The length effect is included in this equation for simple end conditions, and the approximately 10% increase in buckling strength is neglected for edges fixed at the end. A limitation is provided so that the shear yield strength, 0.6Fy, is not exceeded. The critical stress provisions for rectangular HSS are identical to the flexural shear provisions of Section G2 with the shear buckling coefficient equal to kv = 5.0. The shear distribution due to torsion is uniform in the longest sides of a rectangular HSS, and this is the same distribution that is assumed to exist in the web of a W-shape beam. Therefore, it is reasonable that the provisions for buckling are the same in both cases.

2.

HSS Subject to Combined Torsion, Shear, Flexure and Axial Force Several interaction equation forms have been proposed in the literature for load combinations that produce both normal and shear stresses. In one common form, the normal and shear stresses are combined elliptically with the sum of the squares (Felton and Dobbs, 1967): 2

2

⎛ fv ⎞ ⎛ f ⎞ ⎜⎝ F ⎟⎠ + ⎜⎝ F ⎟⎠ ≤ 1 cr vcr

(C-H3-6)

In a second form, the first power of the ratio of the normal stresses is used: 2

⎛ f ⎞ ⎛ fv ⎞ ⎜⎝ F ⎟⎠ + ⎜⎝ F ⎟⎠ ≤ 1 cr vcr

(C-H3-7)

The latter form is somewhat more conservative, but not overly so (Schilling, 1965), and this is the form used in this Specification: 2

⎛ Pr M r ⎞ ⎛ Vr Tr ⎞ ⎜⎝ P + M ⎟⎠ + ⎜⎝ V + T ⎟⎠ ≤ 1.0 c c c c Specification for Structural Steel Buildings, June 22, 2010

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where the terms with the subscript r represent the required strengths, and the ones with the subscript c are the corresponding available strengths. Normal effects due to flexural and axial load effects are combined linearly and then combined with the square of the linear combination of flexural and torsional shear effects. When an axial compressive load effect is present, the required flexural strength, Mc, is to be determined by second-order analysis. When normal effects due to flexural and axial load effects are not present, the square of the linear combination of flexural and torsional shear effects underestimates the actual interaction. A more accurate measure is obtained without squaring this combination.

3.

Non-HSS Members Subject to Torsion and Combined Stress This section covers all the cases not previously covered. Examples are built-up unsymmetric crane girders and many other types of odd-shaped built-up cross sections. The required stresses are determined by elastic stress analysis based on established theories of structural mechanics. The three limit states to consider and the corresponding available stresses are: 1. Yielding under normal stress—Fy 2. Yielding under shear stress—0.6Fy 3. Buckling—Fcr In most cases it is sufficient to consider normal stresses and shear stresses separately because maximum values rarely occur in the same place in the cross section or at the same place in the span. AISC Design Guide 9, Torsional Analysis of Structural Steel Members (Seaburg and Carter, 1997), provides a complete discussion on torsional analysis of open shapes.

H4.

RUPTURE OF FLANGES WITH HOLES SUBJECT TO TENSION Equation H4-1 is provided to evaluate the limit state of tensile rupture of the flanges of beam-columns. This provision is only applicable in cases where there are one or more holes in the flange in net tension under the combined effect of flexure and axial forces. When both the axial and flexural stresses are tensile, their effects are additive. When the stresses are of opposite sign, the tensile effect is reduced by the compression effect.

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CHAPTER I DESIGN OF COMPOSITE MEMBERS

Chapter I includes the following major changes and additions in this edition of the Specification: 1. Concrete and Steel Reinforcement Detailing (Sections I1, I2 and I8): References to ACI 318 (ACI, 2008) are made in Sections I1.1 and I2.1 to invoke requirements for concrete and steel reinforcement requirements. References to ACI 318 are also made in Section I8.3 to invoke requirements for concrete strength of steel headed stud anchors. 2. Local Buckling Provisions (Section I1.2 and I1.4): New provisions are added for local buckling in Sections I1.2 and I1.4. These requirements also lead to new provisions for axial compression and flexural design of filled composite members that are compact, noncompact and slender as addressed in Sections I2.2 and I3.4. 3. Minimum Axial Strength for Composite Compression Members (Sections I2.1 and I2.2): These sections specify that the axial strength of an encased composite compression member and a filled composite compression member need not be less than the strength of a bare steel compression member according to the provisions of Chapter E using the same steel section as the composite member. 4. Load Transfer in Composite Members (Sections I3 and I6): New material is added and revisions are made to the load transfer requirements in composite components. The expanded scope of this section has warranted the creation of a new dedicated section for load transfer in composite members. 5. Reliability of Strength for Encased and Filled Composite Beams (Sections I3.3 and I3.4): The resistance factor and safety factor for encased and filled composite beams were adjusted based upon assessment of new data. 6. Design for Shear (Section I4): All provisions for shear design of composite members are consolidated in a new Section I4. 7. Design of Composite Beam-Columns (Section I5): Clarification of composite beamcolumn design methods is covered in Section I5. 8. Diaphragms and Collector Beams (Section I7): Performance language has been added in a new Section I7 that covers the design and detailing of composite diaphragms and collector beams. Supplemental information is provided in the Commentary as guidance to designers. 9. Steel Anchors (Section I8): New provisions covering the design of steel anchors (both headed studs and hot rolled channels) are included in Section I8. Provisions for composite beams with slabs remain essentially unchanged except for edits that were made for consistency with the new provisions. Provisions are added in Section I8.2 for edge distances of stud anchors along the axis of a composite beam for normal and lightweight concrete. New steel anchor provisions for shear, tension, and interaction of shear and tension are also provided for other forms of composite construction. These changes propose new terminology to be consistent with the more general provisions on anchorage in ACI 318 Appendix D (ACI, 2008). Specifically, the term “shear Specification for Structural Steel Buildings, June 22, 2010

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connector” is replaced by the generic term “steel anchor.” Steel anchors in the Specification can refer either to steel “headed stud anchors” or hot-rolled steel “channel anchors.”

I1.

GENERAL PROVISIONS Design of composite sections requires consideration of both steel and concrete behavior. These provisions were developed with the intent both to minimize conflicts between current steel and concrete design and detailing provisions and to give proper recognition to the advantages of composite design. As a result of the attempt to minimize design conflicts, this Specification uses a cross-sectional strength approach for compression member design consistent with that used in reinforced concrete design (ACI, 2008). This approach, in addition, results in a consistent treatment of cross-sectional strengths for both composite columns and beams. The provisions in Chapter I address strength design of the composite sections only. The designer needs to consider the loads resisted by the steel section alone when determining load effects during the construction phase. The designer also needs to consider deformations throughout the life of the structure and the appropriate cross section for those deformations. When considering these latter limit states, due allowance should be made for the additional long-term changes in stresses and deformations due to creep and shrinkage of the concrete.

1.

Concrete and Steel Reinforcement Reference is made to ACI 318 (ACI, 2008) for provisions related to the concrete and reinforcing steel portion of composite design and detailing, such as anchorage and splice lengths, intermediate column ties, reinforcing spirals, and shear and torsion provisions. Exceptions and limitations are provided as follows: (1) The composite design procedures of ACI 318 have remained unchanged for many years. It was therefore decided to exclude the composite design sections of ACI 318 to take advantage of recent research (Ziemian, 2010; Hajjar, 2000; Shanmugam and Lakshmi, 2001; Leon et al., 2007; Varma and Zhang, 2009; Jacobs and Goverdhan, 2010) into composite behavior that is reflected in the Specification. (2) Concrete limitations in addition to those given in ACI 318 are provided to reflect the applicable range of test data on composite members. See also Commentary Section I1.3. (3) ACI provisions for tie reinforcing of noncomposite reinforced concrete compression members shall be followed in addition to the provisions specified in Section I2.1a(2). See also Commentary Section I2.1a(2). (4) The limitation of 0.01Ag in ACI 318 for the minimum longitudinal reinforcing ratio of reinforced concrete compression members is based upon the phenomena of stress transfer under service load levels from the concrete to the reinforcement due to creep and shrinkage. The inclusion of an encased structural steel section Specification for Structural Steel Buildings, June 22, 2010

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meeting the requirements of Section I2.1a aids in mitigating this effect and consequently allows a reduction in minimum longitudinal reinforcing requirements. See also Commentary Section I2.1a(3). The design basis for ACI 318 is strength design. Designers using allowable stress design for steel design must be conscious of the different load factors between the two specifications.

2.

Nominal Strength of Composite Sections The strength of composite sections shall be computed based on either of the two approaches presented in this Specification. One is the strain compatibility approach, which provides a general calculation method. The other is the plastic stress distribution approach, which is a subset of the strain compatibility approach. The plastic stress distribution method provides a simple and convenient calculation method for the most common design situations, and is thus treated first. Limited use of the elastic stress distribution method is retained for calculation of composite beams with noncompact webs.

2a.

Plastic Stress Distribution Method The plastic stress distribution method is based on the assumption of linear strain across the cross section and elasto-plastic behavior. It assumes that the concrete has reached its crushing strength in compression at a strain of 0.003 and a corresponding stress (typically 0.85f ′c ) on a rectangular stress block, and that the steel has exceeded its yield strain, taken as Fy /Es. Based on these simple assumptions, the cross-sectional strength for different combinations of axial force and bending moment may be approximated for typical composite compression member cross sections. The actual interaction diagram for moment and axial force for a composite section based on a plastic stress distribution is similar to that of a reinforced concrete section as shown in Figure C-I1.1. As a simplification, for concrete-encased sections a conservative linear interaction between

(a) Strong axis

(b) Weak axis

Fig. C-I1.1. Comparison between exact and simplified moment-axial compressive force envelopes. Specification for Structural Steel Buildings, June 22, 2010

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four or five anchor points, depending on axis of bending, can be used (Roik and Bergmann, 1992; Ziemian, 2010). These points are identified as A, B, C, D and E in Figure C-I1.1. The plastic stress approach for compression members assumes that no slip has occurred between the steel and concrete portions and that the required width-tothickness ratios prevent local buckling from occurring until some yielding and concrete crushing have taken place. Tests and analyses have shown that these are reasonable assumptions for both concrete-encased steel sections with steel anchors and for HSS sections that comply with these provisions (Ziemian, 2010; Hajjar, 2000; Shanmugam and Lakshmi, 2001; Varma et al. 2002; Leon et al., 2007). For round HSS, these provisions allow for the increase of the usable concrete stress to 0.95fc′ for calculating both axial compressive and flexural strengths to account for the beneficial effects of the restraining hoop action arising from transverse confinement (Leon et al., 2007). Based on similar assumptions, but allowing for slip between the steel beam and the composite slab, simplified expressions can also be derived for typical composite beam sections. Strictly speaking, these distributions are not based on slip, but on the strength of the shear connection. Full interaction is assumed if the shear connection strength exceeds that of either (a) the tensile yield strength of the steel section or the compressive strength of the concrete slab when the composite beam is loaded in positive moment, or (b) the tensile yield strength of the longitudinal reinforcing bars in the slab or the compressive strength of the steel section when loaded in negative moment. When steel anchors are provided in sufficient numbers to fully develop this flexural strength, any slip that occurs prior to yielding has a negligible affect on behavior. When full interaction is not present, the beam is said to be partially composite. The effects of slip on the elastic properties of a partially composite beam can be significant and should be accounted for, if significant, in calculations of deflections and stresses at service loads. Approximate elastic properties of partially composite beams are given in Commentary Section I3.

2b.

Strain Compatibility Method The principles used to calculate cross-sectional strength in Section I1.2a may not be applicable to all design situations or possible cross sections. As an alternative, Section I1.2b permits the use of a generalized strain-compatibility approach that allows the use of any reasonable strain-stress model for the steel and concrete.

3.

Material Limitations The material limitations given in Section I1.3 reflect the range of material properties available from experimental testing (Ziemian, 2010; Hajjar, 2000; Shanmugam and Lakshmi, 2001; Varma et al., 2002; Leon et al., 2007). As for reinforced concrete design, a limit of 10 ksi (70 MPa) is imposed for strength calculations, both to reflect the scant data available above this strength and the changes in behavior observed (Varma et al., 2002). A lower limit of 3 ksi (21 MPa) is specified for both normal and lightweight concrete and an upper limit of 6 ksi (42 MPa) is specified for lightweight concrete to encourage the use of good quality, yet readily available, grades of strucSpecification for Structural Steel Buildings, June 22, 2010

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tural concrete. The use of higher strengths in computing the modulus of elasticity is permitted, and the limits given can be extended for strength calculations if appropriate testing and analyses are carried out.

4.

Classification of Filled Composite Sections for Local Buckling The behavior of filled composite members is fundamentally different from the behavior of hollow steel members. The concrete infill has a significant influence on the stiffness, strength and ductility of composite members. As the steel section area decreases, the concrete contribution becomes even more significant. The elastic local buckling of the steel tube is influenced significantly by the presence of the concrete infill. The concrete infill changes the buckling mode of the steel tube (both within the cross section and along the length of the member) by preventing it from deforming inwards. For example, see Figures C-I1.2 and C-I1.3. Bradford et al. (1998) analyzed the elastic local buckling behavior of filled composite compression members, showing that for rectangular steel tubes, the plate buckling coefficient (i.e., k-factor) in the elastic plate buckling equation (Ziemian,

Fig. C-I1.2. Change in cross-sectional buckling mode due to concrete infill.

Fig. C-I1.3. Changes in buckling mode with length due to the presence of infill. Specification for Structural Steel Buildings, June 22, 2010

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2010) changes from 4.00 (for hollow tubes) to 10.6 (for filled sections). As a result, the elastic plate buckling stress increases by a factor of 2.65 for filled sections as compared to hollow structural sections. Similarly, Bradford et al. (2002) showed that the elastic local buckling stress for filled round sections is 1.73 times that for hollow round sections. For rectangular filled sections, the elastic local buckling stress, Fcr, from the plate buckling equation simplifies to Equation I2-10. This equation indicates that yielding will occur for plates with b/t less than or equal to 3.00 Es / Fy , which designates the limit between noncompact and slender sections, λr. This limit does not account for the effects of residual stresses or geometric imperfections because the concrete contribution governs for these larger b/t ratios and the effects of reducing steel stresses is small. The maximum permitted b/t value for λp is based on the lack of experimental data above the limit of 5.00 Es / Fy , and the potential effects (plate deflections and locked-in stresses) of concrete placement in extremely slender filled HSS cross sections. For flexure, the b/t limits for the flanges are the same as those for walls in axial compression due to the similarities in loading and behavior. The compact/noncompact limit, λp, for webs in flexure was established conservatively as 3.00 Es / Fy . The noncompact/slender limit, λr, for the web was established conservatively as 5.70 Es / Fy , which is also the maximum permitted for hollow structural sections. This was also established as the maximum permitted value due to the lack of experimental data and concrete placement concerns for thinner filled HSS cross sections (Varma and Zhang, 2009). For round filled sections in axial compression, the noncompact/slender limit, λr, was established as 0.19E/Fy, which is 1.73 times the limit (0.11E/Fy) for hollow round sections. This was based on the findings of Bradford et al. (2002) mentioned earlier, and it compares well with experimental data. The maximum permitted D/t equal to 0.31E/Fy is based on the lack of experimental data and the potential effects of concrete placement in extremely slender filled HSS cross sections. For round filled sections in flexure, the compact/noncompact limit, λp, in Table I1.1b was developed conservatively as 1.25 times the limit (0.07E/Fy) for round hollow structural sections. The noncompact/slender limit, λr, was assumed conservatively to be the same for round hollow structural sections (0.31E/Fy). This was also established as the maximum permitted value due to lack of experimental data and concrete placement concerns for thinner filled HSS cross sections (Varma and Zhang, 2009).

I2.

AXIAL FORCE In Section I2, the design of concrete-encased and concrete-filled composite members is treated separately, although they have much in common. The intent is to facilitate design by keeping the general principles and detailing requirements for each type of compression member separate. An ultimate strength cross section model is used to determine the section strength (Leon et al., 2007; Leon and Hajjar, 2008). This model is similar to that used in previous LRFD Specifications. The major difference is that the full strength of the reinforcing steel and concrete are accounted for rather than the 70% that was used in those previous Specifications. In addition, these provisions give the strength of the Specification for Structural Steel Buildings, June 22, 2010

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composite section as a force, while the previous approach had converted that force to an equivalent stress. Since the reinforcing steel and concrete had been arbitrarily discounted, the previous provisions did not accurately predict strength for compression members with a low percentage of steel. The design for length effects is consistent with that for steel compression members. The equations used are the same as those in Chapter E, albeit in a different format, and as the percent of concrete in the section decreases, the design defaults to that of a steel section (although with different resistance and safety factors). Comparisons between the provisions in the Specification and experimental data show that the method is generally conservative but that the coefficient of variation obtained is large (Leon et al., 2007).

1.

Encased Composite Members

1a.

Limitations (1) In this Specification, the use of composite compression members is applicable to a minimum steel ratio (area of steel shape divided by the gross area of the member) equal to or greater than 1%. (2) The specified minimum quantity for transverse reinforcement is intended to provide good confinement to the concrete. It is the intent of the Specification that the transverse tie provisions of ACI 318 Chapter 7 be followed in addition to the limits provided. (3) A minimum amount of longitudinal reinforcing steel is prescribed to ensure that unreinforced concrete encasements are not designed with these provisions. Continuous longitudinal bars should be placed at each corner of the cross section. Additional provisions for minimum number of longitudinal bars are provided in ACI 318 Section 10.9.2. Other longitudinal bars may be needed to provide the required restraint to the cross-ties, but that longitudinal steel cannot be counted towards the minimum area of longitudinal reinforcing nor the cross-sectional strength unless it is continuous and properly anchored.

1b.

Compressive Strength The compressive strength of the cross section is given as the sum of the ultimate strengths of the components. The strength is not capped as in reinforced concrete compression member design for a combination of the following reasons: (1) the resistance factor is 0.75 (lower than some older Specifications); (2) the required transverse steel provides better performance than a typical reinforced concrete compression member; (3) the presence of a steel section near the center of the section reduces the possibility of a sudden failure due to buckling of the longitudinal reinforcing steel; and (4) there will typically be moment present due to the manner in which stability is addressed in the Specification through the use of a minimum notional load and the size of the member and the typical force introduction mechanisms. For application of encased composite members using the direct analysis method as defined in Chapter C, and pending the results of ongoing research on composite compression members, it is suggested that the reduced flexural stiffness EI* be based on Specification for Structural Steel Buildings, June 22, 2010

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the use of the 0.8τb reduction applied to the EIeff (from Equation I2-6) unless a more comprehensive study is undertaken. Alternatively, designers are referred to ACI 318 Chapter 10 for appropriate EcIg values to use with the 0.8τb stiffness reduction in performing frame analysis using encased composite compression members whose stiffness may be evaluated in a similar way to conventional reinforced concrete compression members. Refer to Commentary Section I3.2 for recommendations on appropriate stiffness for composite beams.

1c.

Tensile Strength Section I2.1c clarifies the tensile strength to be used in situations where uplift is a concern and for computations related to beam-column interaction. The provision focuses on the limit state of yield on gross area. Where appropriate for the structural configuration, consideration should also be given to other tensile strength and connection strength limit states as specified in Chapters D and J.

2.

Filled Composite Members

2a.

Limitations (1) As discussed for encased compression members, it is permissible to design filled composite compression members with a steel ratio as low as 1%. (2) Filled composite sections are classified as compact, noncompact or slender depending on the tube slenderness, b/t or D/t, and the limits in Table I1.1a.

2b.

Compressive Strength A compact hollow structural section (HSS) has sufficient thickness to develop yielding of the steel HSS in longitudinal compression, and to provide confinement to the concrete infill to develop its compressive strength (0.85 or 0.95f ′c ). A noncompact section has sufficient tube thickness to develop yielding of the steel tube in the longitudinal direction, but it cannot adequately confine the concrete infill after it reaches 0.70fc′ compressive stress in the concrete and starts undergoing significant inelasticity and volumetric dilation, thus pushing against the steel HSS. A slender section can neither develop yielding of the steel HSS in the longitudinal direction, nor confine the concrete after it reaches 0.70f ′c compressive stress in the concrete and starts undergoing inelastic strains and significant volumetric dilation pushing against the HSS (Varma and Zhang, 2009). Figure C-I2.1 shows the variation of the nominal axial compressive strength, Pno, of the composite section with respect to the HSS slenderness. As shown, compact sections can develop the full plastic strength, Pp, in compression. The nominal axial strength, Pno, of noncompact sections can be determined using a quadratic interpolation between the plastic strength, Pp, and the yield strength, Py, with respect to the tube slenderness. This interpolation is quadratic because the ability of the steel tube to confine the concrete infill undergoing inelasticity and volumetric dilation decreases rapidly with HSS slenderness. Slender sections are limited to developing the critical buckling stress, Fcr, of the steel HSS and 0.70f ′c of the concrete infill (Varma and Zhang, 2009). Specification for Structural Steel Buildings, June 22, 2010

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The nominal axial strength, Pn, of composite compression members including length effects may be determined using Equations I2-2 and I2-3, while using EIeff (from Equation I2-12) to account for composite section rigidity and Pno to account for the effects of local buckling as described above. This approach is slightly different than the one used for hollow structural sections found in Section E7, where the effective local buckling stress, f, for slender sections has an influence on the column buckling stress, Fcr, and vice versa. This approach was not implemented for filled compression members because: (i) their axial strength is governed significantly by the contribution of the concrete infill, (ii) concrete inelasticity occurs within the compression member failure segment irrespective of the buckling load, and (iii) the calculated nominal strengths compare conservatively with experimental results (Varma and Zhang, 2009). For application of filled composite members in the direct analysis method as defined in Chapter C and pending the results of ongoing research on composite compression members, it is suggested that the reduced flexural stiffness, EI*, be based on the use of the 0.8τb reduction applied to the EIeff from Equation I2-12 unless a more comprehensive study is undertaken.

2c.

Tensile Strength As for encased compression members, Section I2.2c specifies the tensile strength for filled composite members. Similarly, while the provision focuses on the limit state of yield on gross area, where appropriate, consideration should also be given to other tensile strength and connection strength limit states as specified in Chapters D and J.

I3.

FLEXURE

1.

General Three types of composite flexural members are addressed in this section: fully encased steel beams, concrete-filled HSS, and steel beams with mechanical anchorage to a concrete slab which are generally referred to as composite beams.

Fig. C-I2.1. Nominal axial strength, Pno, vs. HSS slenderness. Specification for Structural Steel Buildings, June 22, 2010

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Effective Width The same effective width rules apply to composite beams with a slab on either one side or both sides of the beam. In cases where the effective stiffness of a beam with a one-sided slab is important, special care should be exercised since this model can substantially overestimate stiffness (Brosnan and Uang, 1995). To simplify design, the effective width is based on the full span, center-to-center of supports, for both simple and continuous beams.

1b.

Strength During Construction Composite beam design requires care in considering the loading history. Loads applied to an unshored beam before the concrete has cured are resisted by the steel section alone; total loads applied before and after the concrete has cured are considered to be resisted by the composite section. It is usually assumed for design purposes that concrete has hardened when it attains 75% of its design strength. Unshored beam deflection caused by fresh concrete tends to increase slab thickness and dead load. For longer spans this may lead to instability analogous to roof ponding. Excessive increase of slab thickness may be avoided by beam camber. Pouring the slab to a constant thickness will also help eliminate the possibility of ponding instability (Ruddy, 1986). When forms are not attached to the top flange, lateral bracing of the steel beam during construction may not be continuous and the unbraced length may control flexural strength, as defined in Chapter F. This Specification does not include special requirements for strength during construction. For these noncomposite beams, the provisions of Chapter F apply. Load combinations for construction loads should be determined for individual projects according to local conditions, using ASCE (2010) as a guide.

2.

Composite Beams with Steel Headed Stud or Steel Channel Anchors Section I3.2 applies to simple and continuous composite beams with steel anchors, constructed with or without temporary shores. When a composite beam is controlled by deflection, the design should limit the behavior of the beam to the elastic range under serviceability load combinations. Alternatively, the amplification effects of inelastic behavior should be considered when deflection is checked. It is often not practical to make accurate stiffness calculations of composite flexural members. Comparisons to short-term deflection tests indicate that the effective moment of inertia, Ieff, is 15 to 30% lower than that calculated based on linear elastic theory, Iequiv. Therefore, for realistic deflection calculations, Ieff should be taken as 0.75Iequiv (Leon, 1990; Leon and Alsamsam, 1993). As an alternative, one may use a lower bound moment of inertia, ILB, as defined below: I LB = I s + As (YENA − d 3 )2 + ( ΣQn / Fy )(2 d 3 + d1 − YENA )2 Specification for Structural Steel Buildings, June 22, 2010

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where As = area of steel cross section, in.2 (mm2) d1 = distance from the compression force in the concrete to the top of the steel section, in. (mm) d3 = distance from the resultant steel tension force for full section tension yield to the top of the steel, in. (mm) ILB = lower bound moment of inertia, in.4 (mm4) Is = moment of inertia for the structural steel section, in.4 (mm4) ΣQn = sum of the nominal strengths of steel anchors between the point of maximum positive moment and the point of zero moment to either side, kips (kN) (C-I3-2) YENA = [As d3 + (ΣQn /Fy) (2d3 + d1)]/ [As + (ΣQn /Fy)], in. (mm) The use of constant stiffness in elastic analyses of continuous beams is analogous to the practice in reinforced concrete design. The stiffness calculated using a weighted average of moments of inertia in the positive moment region and negative moment regions may take the following form: It = aIpos + bIneg

(C-I3-3)

where Ipos = effective moment of inertia for positive moment, in.4 (mm4) Ineg = effective moment of inertia for negative moment, in.4 (mm4) The effective moment of inertia is based on the cracked transformed section considering the degree of composite action. For continuous beams subjected to gravity loads only, the value of a may be taken as 0.6 and the value of b may be taken as 0.4. For composite beams used as part of a lateral force resisting system in moment frames, the value of a and b may be taken as 0.5 for calculations related to drift. In cases where elastic behavior is desired, the cross-sectional strength of composite members is based on the superposition of elastic stresses including consideration of the effective section modulus at the time each increment of load is applied. For cases where elastic properties of partially composite beams are needed, the elastic moment of inertia may be approximated by I equiv = I s +

( ΣQn / C f ) ( I tr − I s )

(C-I3-4)

where Is = moment of inertia for the structural steel section, in.4 (mm4) Itr = moment of inertia for the fully composite uncracked transformed section, in.4 (mm4) ΣQn = strength of steel anchors between the point of maximum positive moment and the point of zero moment to either side, kips (N) Cf = compression force in concrete slab for fully composite beam; smaller of AsFy and 0.85fc′Ac, kips (N) Ac = area of concrete slab within the effective width, in.2 (mm2) The effective section modulus, Seff, referred to the tension flange of the steel section for a partially composite beam, may be approximated by Specification for Structural Steel Buildings, June 22, 2010

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Seff = Ss +

( ΣQn

C f ) ( Str − Ss )

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(C-I3-5)

where Ss = section modulus for the structural steel section, referred to the tension flange, in.3 (mm3) Str = section modulus for the fully composite uncracked transformed section, referred to the tension flange of the steel section, in.3 (mm3) Equations C-I3-4 and C-I3-5 should not be used for ratios, ΣQn /Cf, less than 0.25. This restriction is to prevent excessive slip, as well as substantial loss in beam stiffness. Studies indicate that Equations C-I3-4 and C-I3-5 adequately reflect the reduction in beam stiffness and strength, respectively, when fewer anchors are used than required for full composite action (Grant et al., 1977). U.S. practice does not generally require the following items to be considered. They are highlighted here for a designer who chooses to construct something for which these items might apply. 1. Horizontal shear strength of the slab: For the case of girders with decks with narrow troughs or thin slabs, shear strength of the slab may govern the design (for example, see Figure C-I3.1). Although the configuration of decks built in the U.S. tends to preclude this mode of failure, it is important that it be checked if the force in the slab is large or an unconventional assembly is chosen. The shear strength of the slab may be calculated as the superposition of the shear strength of the concrete plus the contribution of any slab steel crossing the shear plane. The required shear strength, as shown in the figure, is given by the difference in the force between the regions inside and outside the potential failure surface. Where experience has shown that longitudinal cracking detrimental to serviceability is likely to occur, the slab should be reinforced in the direction transverse to the supporting steel section. It is recommended that the area of such reinforcement be at least 0.002 times the concrete area in the longitudinal direction of the beam and that it be uniformly distributed. 2. Rotational capacity of hinging zones: There is no required rotational capacity for hinging zones. Where plastic redistribution to collapse is allowed, the moments

Fig. C-I3.1. Longitudinal shear in the slab [after Chien and Ritchie (1984)]. Specification for Structural Steel Buildings, June 22, 2010

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at a cross section may be as much as 30% lower than those given by a corresponding elastic analysis. This reduction in load effects is predicated, however, on the ability of the system to deform through very large rotations. To achieve these rotations, very strict local buckling and lateral-torsional buckling requirements must be fulfilled (Dekker et al., 1995). For cases in which a 10% redistribution is utilized, as permitted in Section B3.7, the required rotation capacity is within the limits provided by the local and lateral-torsional buckling provisions of Chapter F. Therefore, a rotational capacity check is not normally required for designs using this provision. 3. Minimum amount of shear connection: There is no minimum requirement for the amount of shear connection. Design aids in the U.S. often limit partial composite action to a minimum of 25% for practical reasons, but two issues arise with the use of low degrees of partial composite action. First, less than 50% composite action requires large rotations to reach the available flexural strength of the member and can result in very limited ductility after the nominal strength is reached. Second, low composite action results in an early departure from elastic behavior in both the beam and the studs. The current provisions, which are based on ultimate strength concepts, have eliminated checks for ensuring elastic behavior under service load combinations, and this can be an issue if low degrees of partial composite action are used. 4. Long-term deformations due to shrinkage and creep: There is no direct guidance in the computation of the long-term deformations of composite beams due to creep and shrinkage. The long-term deformation due to shrinkage can be calculated with the simplified model shown in Figure C-I3.2, in which the effect of shrinkage is taken as an equivalent set of end moments given by the shrinkage force (long-term restrained shrinkage strain times modulus of concrete times effective area of concrete) times the eccentricity between the center of the slab and the elastic neutral

Fig. C-I3.2. Calculation of shrinkage effects [from Chien and Ritchie (1984)].

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axis. If the restrained shrinkage coefficient for the aggregates is not known, the shrinkage strain for these calculations may be taken as 0.02%. The long-term deformations due to creep, which can be quantified using a model similar to that shown in the figure, are small unless the spans are long and the permanent live loads large. For shrinkage and creep effects, special attention should be given to lightweight aggregates, which tend to have higher creep coefficients and moisture absorption and lower modulus of elasticity than conventional aggregates, exacerbating any potential deflection problems. Engineering judgment is required, as calculations for long-term deformations require consideration of the many variables involved and because linear superposition of these effects is not strictly correct (ACI, 1997; Viest et al., 1997).

2a.

Positive Flexural Strength The flexural strength of a composite beam in the positive moment region may be controlled by the strength of the steel section, the concrete slab or the steel anchors. In addition, web buckling may limit flexural strength if the web is slender and a large portion of the web is in compression. Plastic Stress Distribution for Positive Moment. When flexural strength is determined from the plastic stress distribution shown in Figure C-I3.3, the compression force, C, in the concrete slab is the smallest of: C = Asw Fy + 2Asf Fy

(C-I3-6)

C = 0.85fc′Ac

(C-I3-7)

C = ΣQn

(C-I3-8)

where fc′ = specified compressive strength of concrete, ksi (MPa) Ac = area of concrete slab within effective width, in.2 (mm2) As = area of steel cross section, in.2 (mm2) Asw = area of steel web, in.2 (mm2) Asf = area of steel flange, in.2 (mm2) Fy = minimum specified yield stress of steel, ksi (MPa) ΣQn = sum of nominal strengths of steel headed stud anchors between the point of maximum positive moment and the point of zero moment to either side, kips (N) Longitudinal slab reinforcement makes a negligible contribution to the compression force, except when Equation C-I3-7 governs. In this case, the area of longitudinal reinforcement within the effective width of the concrete slab times the yield stress of the reinforcement may be added in determining C. The depth of the compression block is a=

C 0.85 fc ′ b

Specification for Structural Steel Buildings, June 22, 2010

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where b = effective width of concrete slab, in. (mm) A fully composite beam corresponds to the case of C governed by the yield strength of the steel beam or the compressive strength of the concrete slab, as in Equation C-I3-6 or C-I3-7. The number and strength of steel headed stud anchors govern C for a partially composite beam as in Equation C-I3-8. The plastic stress distribution may have the plastic neutral axis, PNA, in the web, in the top flange of the steel section, or in the slab, depending on the value of C. The nominal plastic moment resistance of a composite section in positive bending is given by the following equation and Figure C-I3.3: Mn = C(d1 + d2) + Py (d3 ⫺ d2)

(C-I3-10)

where Py = tensile strength of the steel section; Py =Fy As, kips (N) d1 = distance from the centroid of the compression force, C, in the concrete to the top of the steel section, in. (mm) d2 = distance from the centroid of the compression force in the steel section to the top of the steel section, in. (mm). For the case of no compression in the steel section, d2 = 0. d3 = distance from Py to the top of the steel section, in. (mm) Equation C-I3-10 is applicable for steel sections symmetrical about one or two axes. According to Table B4.1b, local web buckling does not reduce the plastic strength of a bare steel beam if the beam depth-to-web thickness ratio is not larger than 3.76 E / Fy . In the absence of web buckling research on composite beams, the same ratio is conservatively applied to composite beams. For beams with more slender webs, this Specification conservatively adopts first yield as the flexural strength limit. In this case, stresses on the steel section from permanent loads applied to unshored beams before the concrete has cured must be superimposed on stresses on the composite section from loads applied to the beams

Fig. C-I3.3. Plastic stress distribution for positive moment in composite beams. Specification for Structural Steel Buildings, June 22, 2010

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after hardening of concrete. For shored beams, all loads may be assumed to be resisted by the composite section. When first yield is the flexural strength limit, the elastic transformed section is used to calculate stresses on the composite section. The modular ratio, n = Es /Ec, used to determine the transformed section, depends on the specified unit weight and strength of concrete.

2b.

Negative Flexural Strength Plastic Stress Distribution for Negative Moment. When an adequately braced compact steel section and adequately developed longitudinal reinforcing bars act compositely in the negative moment region, the nominal flexural strength is determined from the plastic stress distributions as shown in Figure C-I3.4. Loads applied to a continuous composite beam with steel anchors throughout its length, after the slab is cracked in the negative moment region, are resisted in that region by the steel section and by properly anchored longitudinal slab reinforcement. The tensile force, T, in the reinforcing bars is the smaller of: T = Fyr Ar

(C-I3-11)

T = ΣQn

(C-I3-12)

where Ar = area of properly developed slab reinforcement parallel to the steel beam and within the effective width of the slab, in.2 (mm2) Fyr = specified yield stress of the slab reinforcement, ksi (MPa) ΣQn = sum of the nominal strengths of steel headed stud anchors between the point of maximum negative moment and the point of zero moment to either side, kips (N) A third theoretical limit on T is the product of the area and yield stress of the steel section. However, this limit is redundant in view of practical limitations for slab reinforcement. The nominal plastic moment resistance of a composite section in negative bending is given by the following equation:

Fig. C-I3.4. Plastic stress distribution for negative moment. Specification for Structural Steel Buildings, June 22, 2010

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Mn = T(d1 + d2) + Pyc (d3 ⫺ d2)

(C-I3-13)

where Pyc = the compressive strength of the steel section; Pyc = AsFy, kips (N) d1 = distance from the centroid of the longitudinal slab reinforcement to the top of the steel section, in. (mm) d2 = distance from the centroid of the tension force in the steel section to the top of the steel section, in. (mm) d3 = distance from Pyc to the top of the steel section, in. (mm)

2c.

Composite Beams with Formed Steel Deck Figure C-I3.5 is a graphic presentation of the terminology used in Section I3.2c. The design rules for composite construction with formed steel deck are based upon a study (Grant et al., 1977) of the then-available test results. The limiting parameters listed in Section I3.2c were established to keep composite construction with formed steel deck within the available research data. The Specification requires steel headed stud anchors to project a minimum of 11/2 in. (38 mm) above the deck flutes. This is intended to be the minimum in-place projection, and stud lengths prior to installation should account for any shortening of the stud that could occur during the welding process. The minimum specified cover over a steel headed stud anchor of 1/2 in. (13 mm) after installation is intended to prevent the anchor from being exposed after construction is complete. In achieving this requirement the designer should carefully consider tolerances on steel beam camber, concrete placement and finishing tolerances, and the accuracy with which steel beam deflections can be calculated. In order to minimize the possibility of exposed anchors in the final construction, the designer should consider increasing the bare steel beam size to reduce or eliminate camber requirements (this also improves floor vibration performance), checking beam camber tolerances in the fabrication shop and monitoring concrete placement operations in the field. Wherever possible, the designer should also consider providing for anchor cover requirements above the 1/2 in. (13 mm) minimum by increasing the slab thickness while maintaining the 11/2 in. (38 mm) requirement for anchor projection above the top of the steel deck as required by the Specification. The maximum spacing of 18 in. (450 mm) for connecting composite decking to the support is intended to address a minimum uplift requirement during the construction phase prior to placing concrete.

2d.

Load Transfer between Steel Beam and Concrete Slab (1) Load Transfer for Positive Flexural strength When studs are used on beams with formed steel deck, they may be welded directly through the deck or through prepunched or cut-in-place holes in the deck. The usual procedure is to install studs by welding directly through the deck; however, when the deck thickness is greater than 16 gage (1.5 mm) for single thickness, or 18 gage (1.2 mm) for each sheet of double thickness, or when the total thickness of galvanized coating is greater than 1.25 ounces/ft2 (0.38 Specification for Structural Steel Buildings, June 22, 2010

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kg/m2), special precautions and procedures recommended by the stud manufacturer should be followed. Composite beam tests in which the longitudinal spacing of steel anchors was varied according to the intensity of the static shear, and duplicate beams in which the anchors were uniformly spaced, exhibited approximately the same ultimate strength and approximately the same amount of deflection at nominal loads. Under distributed load conditions, only a slight deformation in the concrete near the more heavily stressed anchors is needed to redistribute the horizontal shear

Fig. C-I3.5. Steel deck limits. Specification for Structural Steel Buildings, June 22, 2010

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to other less heavily stressed anchors. The important consideration is that the total number of anchors be sufficient to develop the shear on either side of the point of maximum moment. The provisions of this Specification are based upon this concept of composite action. (2) Load Transfer for Negative Flexural strength In computing the available flexural strength at points of maximum negative bending, reinforcement parallel to the steel beam within the effective width of the slab may be included, provided such reinforcement is properly anchored beyond the region of negative moment. However, steel anchors are required to transfer the ultimate tensile force in the reinforcement from the slab to the steel beam. When steel deck includes units for carrying electrical wiring, crossover headers are commonly installed over the cellular deck perpendicular to the ribs. These create trenches that completely or partially replace sections of the concrete slab above the deck. These trenches, running parallel to or transverse to a composite beam, may reduce the effectiveness of the concrete flange. Without special provisions to replace the concrete displaced by the trench, the trench should be considered as a complete structural discontinuity in the concrete flange. When trenches are parallel to the composite beam, the effective flange width should be determined from the known position of the trench. Trenches oriented transverse to composite beams should, if possible, be located in areas of low bending moment and the full required number of studs should be placed between the trench and the point of maximum positive moment. Where the trench cannot be located in an area of low moment, the beam should be designed as noncomposite.

3.

Encased Composite Members Tests of concrete-encased beams demonstrate that: (1) the encasement drastically reduces the possibility of lateral-torsional instability and prevents local buckling of the encased steel; (2) the restrictions imposed on the encasement practically prevent bond failure prior to first yielding of the steel section; and (3) bond failure does not necessarily limit the moment strength of an encased steel beam (ASCE, 1979). Accordingly, this Specification permits three alternative design methods for determination of the nominal flexural strength: (a) based on the first yield in the tension flange of the composite section; (b) based on the plastic flexural strength of the steel section alone; and (c) based on the strength of the composite section obtained from the plastic stress distribution method or the strain-compatibility method. An assessment of the data indicates that the same resistance and safety factors may be used for all three approaches (Leon et al., 2007). For concrete-encased composite beams, method (c) is applicable only when shear anchors are provided along the steel section and reinforcement of the concrete encasement meets the specified detailing requirements. For concrete-encased composite beams, no limitations are placed on the slenderness of either the composite beam or the elements of the steel section, since the encasement effectively inhibits both local and lateral buckling. In method (a), stresses on the steel section from permanent loads applied to unshored beams before the concrete has hardened must be superimposed on stresses on the Specification for Structural Steel Buildings, June 22, 2010

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composite section from loads applied to the beams after hardening of the concrete. In this superposition, all permanent loads should be multiplied by the dead load factor and all live loads should be multiplied by the live load factor. For shored beams, all loads may be assumed as resisted by the composite section. Complete interaction (no slip) between the concrete and steel is assumed. Insufficient research is available to warrant coverage of partially composite encased or filled sections subjected to flexure.

4.

Filled Composite Members Tests of concrete-filled composite beams indicate that: (1) the steel tube drastically reduces the possibility of lateral-torsional instability; (2) the concrete infill changes the buckling mode of the steel HSS; and (3) bond failure does not necessarily limit the moment strength of a filled composite beam (Leon et al., 2007). Figure C-I3.6 shows the variation of the nominal flexural strength, Mn, of the filled section with respect to the HSS slenderness. As shown, compact sections can develop the full plastic strength, Mp, in flexure. The nominal flexural strength, Mn, of noncompact sections can be determined using a linear interpolation between the plastic strength, Mp, and the yield strength, My, with respect to the HSS slenderness. Slender sections are limited to developing the first yield moment, Mcr, of the composite section where the tension flange reaches first yielding, while the compression flange is limited to the critical buckling stress, Fcr, and the concrete is limited to linear elastic behavior with maximum compressive stress equal to 0.70f ′c (Varma and Zhang, 2009). The nominal flexural strengths calculated using the Specification compare conservatively with experimental results (Varma and Zhang, 2009). Figure C-I3.7

Fig. C-I3.6. Nominal flexural strength of filled beam vs. HSS slenderness. Specification for Structural Steel Buildings, June 22, 2010

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(a) Compact section—stress blocks for calculating Mp

(b) Noncompact section—stress blocks for calculating My

(c) Slender section—stress blocks for calculating first yield moment, Mcr Fig. C-I3.7. Stress blocks for calculating nominal flexural strengths of filled rectangular box sections. Specification for Structural Steel Buildings, June 22, 2010

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shows typical stress blocks for determining the nominal flexural strengths of compact, noncompact and slender filled rectangular box sections.

I4.

SHEAR Shear provisions for filled and encased composite members have been revised from the 2005 Specification, and all shear provisions are now consolidated in Section I4.

1.

Filled and Encased Composite Members Three methods for determining the shear strength of filled and encased composite members are now offered: (1) The available shear strength of the steel alone as specified in Chapter G. The intent of this method is to allow the designer to ignore the concrete contribution entirely and simply use the provisions of Chapter G with their associated resistance or safety factors. (2) The strength of the reinforced concrete portion (concrete plus transverse reinforcing bars) alone as defined by ACI 318. For this method, a resistance factor of 0.75 or the corresponding safety factor of 1.5 is to be applied which is consistent with ACI 318. (3) The strength of the steel section in combination with the contribution of the transverse reinforcing bars. For this method, the nominal shear strength (without a resistance or safety factor) of the steel section alone should be determined according to the provisions of Chapter G and then combined with the nominal shear strength of the transverse reinforcing as determined by ACI 318. These two nominal strengths should then be combined, and an overall resistance factor of 0.75 or the corresponding safety factor of 1.5 applied to the sum to determine the overall available shear strength of the member. Though it would be logical to suggest provisions where both the contributions of the steel section and reinforced concrete are superimposed, there is insufficient research available to justify such a combination.

2.

Composite Beams with Formed Steel Deck A conservative approach to shear provisions for composite beams with steel headed stud or steel channel anchors is adopted by assigning all shear to the steel section in accordance with Chapter G. This method neglects any concrete contribution and serves to simplify design.

I5.

COMBINED FLEXURE AND AXIAL FORCE As with all frame analyses in this Specification, required strengths for composite beam-columns should be obtained from second-order analysis or amplified firstorder analysis as specified in Chapter C and Appendix 7. Sections I2.1 and I2.2 suggest appropriate reduced stiffness, EI*, for composite compression members to be used with the direct analysis method of Chapter C. For the assessment of the available strength, the Specification provisions for interaction between axial force and flexure in composite members are the same as for bare steel members as covered in Specification for Structural Steel Buildings, June 22, 2010

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Section H1.1. The provisions also permit an analysis based on the strength provisions of Section I1.2 which would lead to an interaction diagram similar to those used in reinforced concrete design. This latter approach is discussed here. For encased composite members, the available axial strength, including the effects of buckling, and the available flexural strength can be calculated using either the plastic stress distribution method or the strain-compatibility method (Leon et al., 2007; Leon and Hajjar, 2008). For filled composite members, the available axial and flexural strengths can be calculated using Sections I2.2 and I3.4, respectively, which also include the effects of local buckling for noncomposite and slender sections (classified according to Section I1.4). The section below describes three different approaches to design composite beamcolumns that are applicable to both concrete-encased steel shapes and to compact concrete-filled HSS sections. The first two approaches are based on variations in the plastic stress distribution method while the third method references AISC Design Guide 6, Load and Resistance Factor Design of W-shapes Encased in Concrete (Griffis, 1992), which is based on an earlier version of the Specification. The strain compatibility method is similar to that used in the design of concrete compression members as specified in ACI 318 Chapter 10. The design of noncompact and slender concrete-filled sections is limited to the use of method 1 described below (Varma and Zhang, 2009). Method 1—Interaction Equations of Section H1. The first approach applies to doubly symmetric composite beam-columns, the most common geometry found in building construction. For this case, the interaction equations of Section H1 provide a conservative assessment of the available strength of the member for combined axial compression and flexure (see Figure C-I5.1). These provisions may also be used for

Fig. C-I5.1. Interaction diagram for composite beam-column design—Method 1. Specification for Structural Steel Buildings, June 22, 2010

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combined axial tension and flexure. The degree of conservatism generally depends on the extent of concrete contribution to the overall strength relative to the steel contribution. The larger the load carrying contribution coming from the steel section the less conservative the strength prediction of the interaction equations from Section H1. Thus, for example, the equations are generally more conservative for members with high concrete compressive strength as compared to members with low concrete compressive strength. The advantages to this method include the following: (1) The same interaction equations used for steel beam-columns are applicable; and (2) Only two anchor points are needed to define the interaction curves—one for pure flexure (point B) and one for pure axial load (point A). Point A is determined using Equations I2-2 or I2-3, as applicable. Point B is determined as the flexural strength of the section according to the provisions of Section I3. Note that slenderness must also be considered using the provisions of Section I2. For many common concrete filled HSS sections, available axial strengths are provided in tables in the manual. The design of noncompact and slender concrete-filled sections is limited to this method of interaction equation solution. The other two methods described below may not be used for their design, due to lack of research to validate those approaches for cross sections that are not compact. The nominal strengths predicted using the equations of Section H1 compare conservatively with a wide range of experimental data for noncompact/slender rectangular and round filled sections (Varma and Zhang, 2009). Method 2—Interaction Curves from the Plastic Stress Distribution Method. The second approach applies to doubly symmetric composite beam-columns and is based on developing interaction surfaces for combined axial compression and flexure at the nominal strength level using the plastic stress distribution method. This approach results in interaction surfaces similar to those shown in Figure C-I5.2. The four points identified in Figure C-I5.2 are defined by the plastic stress distribution used

Fig. C-I5.2 Interaction diagram for composite beam-columns—Method 2. Specification for Structural Steel Buildings, June 22, 2010

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in their determination. The strength equations for concrete encased W-shapes and concrete filled HSS shapes used to define each point A through D are provided in the AISC Design Examples available at www.aisc.org (Geschwindner, 2010b). Point A is the pure axial strength determined according to Section I2. Point B is determined as the flexural strength of the section according to the provisions of Section I3. Point C corresponds to a plastic neutral axis location that results in the same flexural strength as Point B, but including axial compression. Point D corresponds to an axial compressive strength of one half of that determined for Point C. An additional Point E (see Figure C-I1.1) is included (between points A and C) for encased W-shapes bent about their weak axis. Point E is an arbitrary point, generally corresponding to a plastic neutral axis location at the flange tips of the encased W-shape, necessary to better reflect bending strength for weak-axis bending of encased shapes. Linear interpolation between these anchor points may be used. However, with this approach, care should be taken in reducing Point D by a resistance factor or to account for member slenderness, as this may lead to an unsafe situation whereby additional flexural strength is permitted at a lower axial compressive strength than predicted by the cross section strength of the member. This potential problem may be avoided through a simplification to this method whereby point D is removed from the interaction surface. Figure C-I5.3 demonstrates this simplification with the vertical dashed line that connects point C′′ to point B′′. Once the nominal strength interaction surface is determined, length effects according to Equations I2-2 and I2-3 must be applied. Note that the same slenderness reduction factor (λ = A′/A in Figure C-I5.2, equal to Pn /Pno, where Pn and Pno are calculated from Section I2) applies to points A, C, D and E. The available strength is then determined by applying the compression and bending resistance factors or safety factors.

Fig. C-I5.3 Interaction diagram for composite beam-columns—Method 2 simplified. Specification for Structural Steel Buildings, June 22, 2010

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Using linear interpolation between points A′′, C′′ and B′′ in Figure C-I5.3, the following interaction equations may be derived for composite beam-columns subjected to combined axial compression plus biaxial flexure: (a) If Pr < PC Mry Mrx + ≤1 MCx MCy

(C-I5-1a)

Mry Pr − PC M + rx + ≤1 PA − PC MCx MCy

(C-I5-1b)

(b) If Pr ≥ PC

where Pr = required compressive strength, kips (N) PA = available axial compressive strength at Point A′′, kips (N) PC = available axial compressive strength at Point C′′, kips (N) Mr = required flexural strength, kip-in. (N-mm) MC = available flexural strength at Point C′′, kip-in. (N-mm) x = subscript relating symbol to strong axis bending y = subscript relating symbol to weak axis bending For design according to Section B3.3 (LRFD): Pr = Pu = required compressive strength using LRFD load combinations, kips (N) PA = design axial compressive strength at Point A′′ in Figure C-I5.3, determined in accordance with Section I2, kips (N) PC = design axial compressive strength at Point C′′, kips (N) Mr = required flexural strength using LRFD load combinations, kip-in. (N-mm) MC = design flexural strength at Point C′′, determined in accordance with Section I3, kip-in. (N-mm) For design according to Section B3.4 (ASD): Pr = Pa = required compressive strength using ASD load combinations, kips (N) PA = allowable compressive strength at Point A′′ in Figure C-I5.3, determined in accordance with Section I2, kips (N) PC = allowable axial compressive strength at Point C′′, kips (N) Mr = required flexural strength using ASD load combinations, kip-in. (N-mm) MC = allowable flexural strength at Point C′′, determined in accordance with Section I3, kip-in. (N-mm) For biaxial bending, the value of the axial compressive strength at Point C may be different when computed for the major and minor axis. The smaller of the two values should be used in Equation C-I5-1b and for the limits in Equations C-I5-1a and b. Method 3—Design Guide 6. The approach presented in AISC Design Guide 6, Load and Resistance Factor Design of W-Shapes Encased in Concrete (Griffis, 1992) may Specification for Structural Steel Buildings, June 22, 2010

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also be used to determine the beam-column strength of concrete encased W-shapes. Although this method is based on an earlier version of the Specification, axial load and moment strengths can conservatively be determined directly from the tables in this design guide. The difference in resistance factors from the earlier Specification may safely be ignored.

I6.

LOAD TRANSFER

1.

General Requirements External forces are typically applied to composite members through direct connection to the steel member, bearing on the concrete, or a combination thereof. Design of the connection for force application shall follow the applicable limit states within Chapters J and K of the Specification as well as the provisions of Section I6. Note that for concrete bearing checks on filled composite members, confinement can affect the bearing strength for external force application as discussed in Commentary Section I6.2. Once a load path has been provided for the introduction of external force to the member, the interface between the concrete and steel must be designed to transfer the longitudinal shear required to obtain force equilibrium within the composite section. Section I6.2 contains provisions for determining the magnitude of longitudinal shear to be transferred between the steel and concrete depending upon the external force application condition. Section I6.3 contains provisions addressing mechanisms for the transfer of longitudinal shear. The load transfer provisions of the Specification are primarily intended for the transfer of longitudinal shear due to applied axial forces. Load transfer of longitudinal shear due to applied bending moments is beyond the scope of the Specification; however, tests (Lu and Kennedy, 1994; Prion and Boehme, 1994; Wheeler and Bridge, 2006) indicate that filled composite members can develop their full plastic moment capacity based on bond alone without the use of additional anchorage.

2.

Force Allocation The Specification addresses conditions in which the entire external force is applied to the steel or concrete as well as conditions in which the external force is applied to both materials concurrently. The provisions are based upon the assumption that in order to achieve equilibrium across the cross section, transfer of longitudinal shears along the interface between the concrete and steel shall occur such that the resulting force levels within the two materials may be proportioned according to a plastic stress distribution model. Load allocation based on the plastic stress distribution model is represented by Equations I6-1 and I6-2. Equation I6-1 represents the magnitude of force that is present within the concrete encasement or concrete fill at equilibrium. The longitudinal shear generated by loads applied directly to the steel section is determined based on the amount of force to be distributed to the concrete according to Equation I6-1. Conversely, when load is applied to the concrete section only, the longitudinal shear required for cross-sectional equilibrium is based upon the amount of force to be distributed to the steel according to Equation I6-2. Where loads Specification for Structural Steel Buildings, June 22, 2010

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are applied concurrently to the two materials, the longitudinal shear force to be transferred to achieve cross-sectional equilibrium can be taken as either the difference in magnitudes between the portion of external force applied directly to the concrete and that required by Equation I6-1 or the portion of external force applied directly to the steel section and that required by Equation I6-2. When external forces are applied to the concrete of a filled composite member via bearing, it is acceptable to assume that adequate confinement is provided by the steel encasement to allow the maximum available bearing strength permitted by Equation J8-2 to be used. This strength is obtained by setting the term A2 / A1 = 2. This discussion is in reference to the introduction of external load to the compression member. The transfer of longitudinal shear within the compression member via bearing mechanisms such as internal steel plates is addressed directly in Section I6.3a.

3.

Force Transfer Mechanisms Transfer of longitudinal shear by direct bearing via internal bearing mechanisms (such as internal bearing plates) or shear connection via steel anchors is permitted for both filled and encased composite members. Transfer of longitudinal shear via direct bond interaction is permitted solely for filled composite members. Although it is recognized that force transfer also occurs by direct bond interaction between the steel and concrete for encased composite columns, this mechanism is typically ignored and shear transfer is generally carried out solely with steel anchors (Griffis, 1992). The use of the force transfer mechanism providing the largest resistance is permissible. Superposition of force transfer mechanisms is not permitted as the experimental data indicate that direct bearing or shear connection often does not initiate until after direct bond interaction has been breached, and little experimental data is available regarding the interaction of direct bearing and shear connection via steel anchors.

3a.

Direct Bearing For the general condition of assessing load applied directly to concrete in bearing, and considering a supporting concrete area that is wider on all sides than the loaded area, the nominal bearing strength for concrete may be taken as Rn = 0.85 fc′A1 A2 / A1

(C-I6-1)

where A1 = loaded area of concrete, in.2 (mm2) A2 = maximum area of the portion of the supporting surface that is geometrically similar to and concentric with the loaded area, in.2 (mm2) fc′ = specified compressive concrete strength, ksi (MPa) The value of

A2 / A1 must be less than or equal to 2 (ACI, 2008).

For the specific condition of transferring longitudinal shear by direct bearing via internal bearing mechanisms, the Specification uses the maximum nominal bearing Specification for Structural Steel Buildings, June 22, 2010

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strength allowed by Equation C-I6-1 of 1.7fc′A1 as indicated in Equation I6-3. The resistance factor for bearing, φB, is 0.65 (and the associated safety factor, ΩB, is 2.31) in accordance with ACI 318.

3b.

Shear Connection Steel anchors for shear connection shall be designed as composite components according to Section I8.3.

3c.

Direct Bond Interaction Force transfer by direct bond is commonly used in filled composite members as long as the connections are detailed to limit local deformations (API, 1993; Roeder et al., 1999). However, there is large scatter in the experimental data on the bond strength and associated force transfer length of filled composite compression members, particularly when comparing tests in which the concrete core is pushed through the steel tube (push-out tests) to tests in which a beam is connected just to the steel tube and beam shear is transferred to the filled composite compression member. The added eccentricities of the connection tests typically raise the bond strength of the filled composite compression members. A reasonable lower bound value of the bond strength of filled composite compression members that meet the provisions of Section I2 is 60 psi (0.4 MPa). While push-out tests often show bond strengths below this value, eccentricity introduced into the connection is likely to increase the bond strength to this value or higher. Experiments also indicate that a reasonable assumption for the distance along the length of the filled composite compression member required to transfer the force from the steel HSS to the concrete core is approximately equal to twice the width of a rectangular HSS or the diameter of a round HSS, to either side of the point of load transfer. The equations for direct bond interaction for filled composite compression members assume that one face of a rectangular filled composite compression member or onequarter of the perimeter of a round filled composite compression member is engaged in the transfer of stress by direct bond interaction for the connection elements framing into the compression member from each side. If connecting elements frame in from multiple sides, the direct bond interaction strengths may be increased accordingly. The scatter in the data leads to the recommended low value of the resistance factor, φ, and the corresponding high value of the safety factor, Ω.

4.

Detailing Requirements To avoid overstressing the structural steel section or the concrete at connections in encased or filled composite members, transfer of longitudinal shear is required to occur within the load introduction length. The load introduction length is taken as two times the minimum transverse dimension of the composite member both above and below the load transfer region. The load transfer region is generally taken as the depth of the connecting element as indicated in Figure C-I6.1. In cases where the

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applied forces are of such a magnitude that the required longitudinal shear transfer cannot take place within the prescribed load introduction length, the designer should treat the compression member as noncomposite along the additional length required for shear transfer. For encased composite members, steel anchors are required throughout the compression member length in order to maintain composite action of the member under incidental moments (including flexure induced by incipient buckling). These anchors are typically placed at the maximum permitted spacing according to Section I8.3e. Additional anchors required for longitudinal shear transfer shall be located within the load introduction length as described previously. Unlike concrete encased members, steel anchors in filled members are required only when used for longitudinal shear transfer and are not required along the length of the member outside of the introduction region. This discrepancy is due to the adequate confinement provided by the steel encasement which prevents the loss of composite action under incidental moments.

Fig. C-I6.1. Load transfer region/load introduction length.

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COMPOSITE DIAPHRAGMS AND COLLECTOR BEAMS

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COMPOSITE DIAPHRAGMS AND COLLECTOR BEAMS In composite construction, floor or roof slabs consisting of composite metal deck and concrete fill are typically connected to the structural framing to form composite diaphragms. Diaphragms are horizontally spanning members, analogous to deep beams, which distribute seismic and/or wind loads from their origin to the lateralforce-resisting-system either directly or in combination with load transfer elements known as collectors or collector beams (also known as diaphragm struts and drag struts). Diaphragms serve the important structural function of interconnecting the components of a structure to behave as a unit. Diaphragms are commonly analyzed as simple-span or continuously spanning deep beams, and hence are subject to shear, moment and axial forces as well as the associated deformations. Further information on diaphragm classifications and behavior can be found in AISC (2006a) and SDI (2001). Composite Diaphragm Strength Diaphragms should be designed to resist all forces associated with the collection and distribution of seismic and/or wind forces to the lateral force resisting system. In some cases, loads from other floors should also be included, such as at a level where a horizontal offset in the lateral force resisting system exists. Several methods exist for determining the in-place shear strength of composite diaphragms. Three such methods are as follows: (1) As determined for the combined strength of composite deck and concrete fill including the considerations of composite deck configuration as well as type and layout of deck attachments. One publication which is considered to provide such guidance is the SDI Diaphragm Design Manual (SDI, 2004). This publication covers many aspects of diaphragm design including strength and stiffness calculations. Calculation procedures are also provided for alternative deck to framing connection methods such as puddle welding and mechanical fasteners in cases where anchors are not used. Where stud anchors are used, stud shear strength values shall be as determined in Section I8. (2) As the thickness of concrete over the steel deck is increased, the shear strength can approach that for a concrete slab of the same thickness. For example, in composite floor deck diaphragms having cover depths between 2 in. (50 mm) and 6 in. (150 mm), measured shear stresses in the order of 0.11 fc′ (where fc′ is in units of ksi) have been reported. In such cases, the diaphragm strength of concrete metal deck slabs can conservatively be based on the principles of reinforced concrete design (ACI, 2008) using the concrete and reinforcement above the metal deck ribs and ignoring the beneficial effect of the concrete in the flutes. (3) Results from in-plane tests of concrete filled diaphragms. Collector Beams and Other Composite Elements Horizontal diaphragm forces are transferred to the steel lateral load resisting frame as axial forces in collector beams (also known as diaphragm struts or drag struts). The design of collector beams has not been addressed directly in this Chapter. The rigorous design of composite beam-columns (collector beams) is complex and few Specification for Structural Steel Buildings, June 22, 2010

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detailed guidelines exist on such members. Until additional research becomes available, a reasonable simplified design approach is provided as follows: Force Application. Collector beams can be designed for the combined effects of axial load due to diaphragm forces as well as flexure due to gravity and/or lateral loads. The effect of the vertical offset (eccentricity) between the plane of the diaphragm and the centerline of the collector element should be investigated for design. Axial Strength. The available axial strength of collector beams can be determined according to the noncomposite provisions of Chapter D and Chapter E. For compressive loading, collector beams are generally considered unbraced for buckling between braced points about their major axis, and fully braced by the composite diaphragm for buckling about the minor axis. Flexural Strength. The available flexural strength of collector beams can be determined using either the composite provisions of Chapter I or the noncomposite provisions of Chapter F. It is recommended that all collector beams, even those designed as noncomposite members, contain enough anchors to ensure that a minimum of 25% composite action is achieved. This recommendation is intended to prevent designers from utilizing a small amount of anchors solely to transfer diaphragm forces on a beam designed as a noncomposite member. Anchors designed only to transfer horizontal shear due to lateral forces will still be subjected to horizontal shear due to flexure from gravity loads superimposed on the composite section and could become overloaded under gravity loading conditions. Overloading the anchors could result in loss of stud strength which could inhibit the ability of the collector beam to function as required for the transfer of diaphragm forces due to lateral loads. Interaction. Combined axial force and flexure can be assessed using the interaction equations provided in Chapter H. As a reasonable simplification for design purposes, it is acceptable to use the noncomposite axial strength and the composite flexural strength in combination for determining interaction. Shear Connection. It is not required to superimpose the horizontal shear due to lateral forces with the horizontal shear due to flexure for the determination of steel anchor requirements. The reasoning behind this methodology is twofold. First, the load combinations as presented in ASCE/SEI 7 (ASCE, 2010) provide reduced live load levels for load combinations containing lateral loads. This reduction decreases the demand on the steel anchors and provides additional capacity for diaphragm force transfer. Secondly, horizontal shear due to flexure flows in two directions. For a uniformly loaded beam, the shear flow emanates outwards from the center of the beam as illustrated in Figure C-I7.1(a). Lateral loads on collector beams induce shear in one direction. As these shears are superimposed, the horizontal shears on one portion of the beam are increased, and the horizontal shears on the opposite portion of the beam are decreased as illustrated in Figure C-I7.1(b). In lieu of additional research, it is considered acceptable for the localized additional loading of the steel anchors in the additive beam segment to be considered offset by the concurrent unloading of the steel anchors in the subtractive beam segment up to a force level corresponding to the summation of the nominal strengths of all studs placed on the beam. Specification for Structural Steel Buildings, June 22, 2010

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I8.

STEEL ANCHORS

1.

General

[Comm. I8.

This section covers the strength, placement and limitations on the use of steel anchors in composite construction. A new definition is provided for “steel anchor” which replaces the old term “shear connector” in the 2005 and earlier Specifications. This change was made to recognize the more generic term “anchor” as used in ACI 318, PCI and throughout the industry. This term includes the traditional “shear connector,” now defined as a “steel headed stud anchor” and a “steel channel anchor” both of which have been part of previous Specifications. Both steel headed stud anchors and hot-rolled steel channel anchors are addressed in the Specification. The design provisions for steel anchors are given for composite beams with solid slabs or with formed steel deck and for composite components. A new glossary term is provided for “composite component” as a member, connecting element or assemblage in which steel and concrete elements work as a unit in the distribution of internal forces. This term excludes composite beams with solid slabs or formed steel deck. The provisions for composite components include the use of a resistance factor or safety factor applied to the nominal strength of the steel anchor, while for composite beams the resistance factor and safety factor are part of the composite beam resistance and safety factor. Studs not located directly over the web of a beam tend to tear out of a thin flange before attaining full shear-resisting strength. To guard against this contingency,

(a) Shear flow due to gravity loads only

(b) Shear flow due to gravity and lateral loads in combination Fig. C-I7.1. Shear flow at collector beams. Specification for Structural Steel Buildings, June 22, 2010

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the size of a stud not located over the beam web is limited to 21/2 times the flange thickness (Goble, 1968). The practical application of this limitation is to select only beams with flanges thicker than the stud diameter divided by 2.5. Section I8.2 requires a minimum ratio value of four for the overall headed stud anchor height to the shank diameter when calculating the nominal shear strength of a steel headed stud anchor in a composite beam. This requirement has been used in previous Specifications and has had a record of successful performance. For calculating the nominal shear strength of a steel headed stud anchor in other composite components, Section I8.3 increases this minimum ratio value to five for normal weight concrete and seven for lightweight concrete. Additional increases in the minimum value of this ratio are required for computing the nominal tensile strength or the nominal strength for interaction of shear and tension in Section I8.3. The provisions of Section I8.3 also establish minimum edge distances and center-to-center spacings for steel headed stud anchors if the nominal strength equations in that section are to be used. These limits are established in recognition of the fact that only steel failure modes are checked in the calculation of the nominal anchor strengths in Equations I8-3, I8-4 and I8-5. Concrete failure modes are not checked explicitly in these equations (Pallarés and Hajjar, 2010a, 2010b), whereas concrete failure is checked in Equation I8-1. This is discussed further in Commentary Section I8.3.

2.

Steel Anchors in Composite Beams

2a.

Strength of Steel Headed Stud Anchors The present strength equations for composite beams and steel stud anchors are based on the considerable research that has been published in recent years (Jayas and Hosain, 1988a, 1988b; Mottram and Johnson, 1990; Easterling et al., 1993; Roddenberry et al., 2002a). Equation I8-1 contains Rg and Rp factors to bring these composite beam strength requirements comparable to other codes around the world. Other codes use a stud strength expression similar to the AISC Specification but the stud strength is reduced by a φ factor of 0.8 in the Canadian code (CSA, 2009) and by an even lower partial safety factor (φ = 0.60) for the corresponding stud strength equations in Eurocode 4 (CEN, 2003). The AISC Specification includes the stud anchor resistance factor as part of the overall composite beam resistance factor. The majority of composite steel floor decks used today have a stiffening rib in the middle of each deck flute. Because of the stiffener, studs must be welded off-center in the deck rib. Studies have shown that steel studs behave differently depending upon their location within the deck rib (Lawson, 1992; Easterling et al., 1993; Van der Sanden, 1995; Yuan, 1996; Johnson and Yuan, 1998; Roddenberry et al., 2002a, 2002b). The so-called “weak” (unfavorable) and “strong” (favorable) positions are illustrated in Figure C-I8.1. Furthermore, the maximum value shown in these studies for studs welded through steel deck is on the order of 0.7 to 0.75Fu Asc. Studs placed in the weak position have strengths as low as 0.5Fu Asc. The strength of stud anchors installed in the ribs of concrete slabs on formed steel deck with the ribs oriented perpendicular to the steel beam is reasonably estimated by the strength of stud anchors computed from Equation I8-1, which sets the default Specification for Structural Steel Buildings, June 22, 2010

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value for steel stud strength equal to that for the weak stud position. Both AISC (1997a) and the Steel Deck Institute (SDI, 2001) recommend that studs be detailed in the strong position, but ensuring that studs are placed in the strong position is not necessarily an easy task because it is not always easy for the installer to determine where along the beam the particular rib is located relative to the end, midspan, or point of zero shear. Therefore, the installer may not be clear on which location is the strong, and which is the weak position. In most composite floors designed today, the ultimate strength of the composite section is governed by the stud strength, as full composite action is typically not the most economical solution to resist the required strength. The degree of composite action, as represented by the ratio ΣQn /Fy As (the total shear connection strength divided by the yield strength of the steel cross section), influences the flexural strength as shown in Figure C-I8.2.

Fig. C-I8.1. Weak and strong stud positions [Roddenberry et al. (2002b)].

Fig. C-I8.2. Normalized flexural strength versus shear connection strength ratio (W16×31, Fy = 50 ksi, Y2 = 4.5 in.) (Easterling et al., 1993). Specification for Structural Steel Buildings, June 22, 2010

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It can be seen from Figure C-I8.2 that a relatively large change in shear connection strength results in a much smaller change in flexural strength. Thus, formulating the influence of steel deck on shear anchor strength by conducting beam tests and backcalculating through the flexural model, as was done in the past, leads to an inaccurate assessment of stud strength when installed in metal deck. The changes in stud anchor requirements that occurred in the 2005 Specification were not a result of either structural failures or performance problems. Designers concerned about the strength of existing structures based on earlier Specification requirements need to note that the slope of the curve shown in Figure C-I8.2 is rather flat as the degree of composite action approaches one. Thus, even a large change in steel stud strength does not result in a proportional decrease of the flexural strength. In addition, as noted above, the current expression does not account for all the possible shear force transfer mechanisms, primarily because many of them are difficult or impossible to quantify. However, as noted in Commentary Section I3.1, as the degree of composite action decreases, the deformation demands on steel studs increase. This effect is reflected by the increasing slope of the relationship shown in Figure C-I8.2 as the degree of composite action decreases. Thus designers should specify 50% composite action or more. The reduction factor, Rp, for headed stud anchors used in composite beams with no decking has been reduced from 1.0 to 0.75 in the 2010 Specification. The methodology used for headed stud anchors that incorporates Rg and Rp was implemented in the 2005 Specification. The research (Roddenberry et al., 2002a) in which the factors (Rg and Rp) were developed focused almost exclusively on cases involving the use of headed stud anchors welded through steel deck. The research pointed to the likelihood that the solid slab case should use Rp = 0.75, however, the body of test data had not been established to support the change. More recent research has shown that the 0.75 factor is appropriate (Pallarés and Hajjar, 2010a).

2b.

Strength of Steel Channel Anchors Equation I8-2 is a modified form of the formula for the strength of channel anchors presented in Slutter and Driscoll (1965), which was based on the results of pushout tests and a few simply supported beam tests with solid slabs by Viest et al. (1952). The modification has extended its use to lightweight concrete. Eccentricities need not be considered in the weld design for cases where the welds at the toe and heel of the channel are greater than 3/16 in. (5 mm) and the anchor meets the following requirements: 1.0 ≤

tf ≤ 5.5 tw

H ≥ 8.0 tw Lc ≥ 6.0 tf 0.5 ≤

R ≤ 1.6 tw

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where tf = flange thickness of channel anchor, in. (mm) tw = thickness of channel anchor web, in. (mm) H = height of anchor, in. (mm) Lc = length of anchor, in. (mm) R = radius of the fillet between the flange and the web of the anchor, in. (mm)

2d.

Detailing Requirements Uniform spacing of shear anchors is permitted, except in the presence of heavy concentrated loads. The minimum spacing of anchors along the length of the beam, in both flat soffit concrete slabs and in formed steel deck with ribs parallel to the beam, is six diameters; this spacing reflects development of shear planes in the concrete slab (Ollgaard et al., 1971). Because most test data are based on the minimum transverse spacing of four diameters, this transverse spacing was set as the minimum permitted. If the steel beam flange is narrow, this spacing requirement may be achieved by staggering the studs with a minimum transverse spacing of three diameters between the staggered row of studs. When deck ribs are parallel to the beam and the design requires more studs than can be placed in the rib, the deck may be split so that adequate spacing is available for stud installation. Figure C-I8.3 shows possible anchor arrangements.

3.

Steel Anchors in Composite Components This section applies to steel headed stud anchors used primarily in the load transfer (connection) region of composite compression members and beam-columns, concrete-encased and filled composite beams, composite coupling beams, and composite walls (see Figure C-I8.4), where the steel and concrete are working compositely within a member. In such cases, it is possible that the steel anchor will be subjected to shear, tension, or interaction of shear and tension. As the strength of the connectors in the load transfer region must be assessed directly (rather than implicitly within the strength assessment of a composite member), a resistance or safety factor should be applied, comparable to the design of bolted connections in Chapter J.

Fig. C-I8.3. Steel anchor arrangements. Specification for Structural Steel Buildings, June 22, 2010

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These provisions are not intended for hybrid construction where the steel and concrete are not working compositely, such as with embed plates. Section I8.2 specifies the strength of steel anchors embedded in a solid concrete slab or in a concrete slab with formed steel deck in a composite beam. Data from a wide range of experiments indicate that the failure of steel headed stud anchors subjected to shear occurs in the steel shank or weld in a large percentage of cases if the ratio of the overall height to the shank diameter of the steel headed stud anchor is greater than five for normal weight concrete. In the case of lightweight concrete, the necessary minimum ratio between the overall height of the stud and the diameter increases up to seven (Pallarés and Hajjar, 2010a). A similarly large percentage of failures occur in the steel shank or weld of steel headed stud anchors subjected to tension or interaction of shear and tension if the ratio of the overall height to shank diameter of the steel headed stud anchor is greater than eight for normal weight concrete. In the case of lightweight concrete, the necessary minimum ratio between the overall height of the stud and the diameter increases up to ten for steel headed stud anchors subjected to tension (Pallarés and Hajjar, 2010b). For steel headed stud anchors subjected to interaction of shear and tension in lightweight concrete, there are so few experiments available that it is not possible to discern sufficiently when the steel material will control the failure mode. For the strength of steel headed stud anchors in lightweight concrete subjected to interaction of shear and tension, it is recommended that the provisions of ACI 318 (ACI, 2008) Appendix D be used.

Fig. C-I8.4. Typical reinforcement detailing in a composite wall for steel headed stud anchors subjected to tension. Specification for Structural Steel Buildings, June 22, 2010

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The use of edge distances in ACI 318 Appendix D to compute the strength of a steel anchor subjected to concrete crushing failure is complex. It is rare in composite construction that there is a nearby edge that is not uniformly supported in a way that prevents the possibility of concrete breakout failure due to a close edge. Thus, for brevity, the provisions in this Specification simplify the assessment of whether it is warranted to check for a concrete failure mode. Additionally, if an edge is supported uniformly, as would be common in composite construction, it is assumed that a concrete failure mode will not occur due to the edge condition. Thus, if these provisions are to be used, it is important that it be deemed by the engineer that a concrete breakout failure mode in shear is directly avoided through having the edges perpendicular to the line of force supported, and the edges parallel to the line of force sufficiently distant that concrete breakout through a side edge is not deemed viable. For loading in shear, the determination of whether breakout failure in the concrete is a viable failure mode for the stud anchor is left to the engineer. Alternatively, the provisions call for required anchor reinforcement with provisions comparable to those of ACI 318 Appendix D, Section D6.2.9 (which in turn refers to Chapter 12 of ACI 318) (ACI, 2008). In addition, the provisions of the applicable building code or ACI 318 Appendix D may be used directly to compute the strength of the steel headed stud anchor. The steel limit states and resistance factors (and corresponding safety factors) covered in this section match with the corresponding limit states of ACI 318 Appendix D, although they were assessed independently for these provisions. As only steel limit states are required to be checked if there are no edge conditions, experiments that satisfy the minimum height/diameter ratio but that included failure of the steel headed stud anchor either in the steel or in the concrete were included in the assessment of the resistance and safety factors (Pallarés and Hajjar, 2010a, 2010b). For steel headed stud anchors subjected to tension or combined shear and tension interaction, it is recommended that anchor reinforcement always be included around the stud to mitigate premature failure in the concrete. If the ratio of the diameter of the head of the stud to the shank diameter is too small, the provisions call for use of ACI 318 Appendix D to compute the strength of the steel headed stud anchor. If the distance to the edge of the concrete or the distance to the neighboring anchor is too small, the provisions call for required anchor reinforcement with provisions comparable to those of ACI 318 Appendix D, Section D5.2.9 (which in turn refers to Chapter 12 of ACI 318) (ACI, 2008). Alternatively, the provisions of the applicable building code or ACI 318 Appendix D may be also be used directly to compute the strength of the steel headed stud anchor.

I9.

SPECIAL CASES Tests are required for composite construction that falls outside the limits given in this Specification. Different types of steel anchors may require different spacing and other detailing than steel headed stud and channel anchors.

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CHAPTER J DESIGN OF CONNECTIONS

The provisions of Chapter J cover the design of connections not subject to cyclic loads. Wind and other environmental loads are generally not considered to be cyclic loads. The provisions generally apply to connections other than HSS and box members. See Chapter K for HSS and box member connections and Appendix 3 for fatigue provisions.

J1.

GENERAL PROVISIONS

1.

Design Basis In the absence of defined design loads, a minimum design load should be considered. Historically, a value of 10 kips (44 kN) for LRFD and 6 kips (27 kN) for ASD have been used as reasonable values. For smaller elements such as lacing, sag rods, girts or similar small members, a load more appropriate to the size and use of the part should be used. Both design requirements and construction loads should be considered when specifying minimum loads for connections.

2.

Simple Connections Simple connections are considered in Sections B3.6a and J1.2. In Section B3.6a, simple connections are defined (with further elaboration in Commentary Section B3.6) in an idealized manner for the purpose of analysis. The assumptions made in the analysis determine the outcome of the analysis that serves as the basis for design (for connections that means the force and deformation demands that the connection must resist). Section J1.2 focuses on the actual proportioning of the connection elements to achieve the required resistance. Thus, Section B3.6a establishes the modeling assumptions that determine the design forces and deformations for use in Section J1.2. Sections B3.6a and J1.2 are not mutually exclusive. If a “simple” connection is assumed for analysis, the actual connection, as finally designed, must perform consistent with that assumption. A simple connection must be able to meet the required rotation and must not introduce strength and stiffness that significantly alter the rotational response.

3.

Moment Connections Two types of moment connections are defined in Section B3.6b: fully restrained (FR) and partially restrained (PR). FR moment connections must have sufficient strength and stiffness to transfer moment and maintain the angle between connected members. PR moment connections are designed to transfer moments but also allow rotation between connected members as the loads are resisted. The response characteristics of a PR connection must be documented in the technical literature or established by analytical or experimental means. The component elements of a PR

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connection must have sufficient strength, stiffness and deformation capacity to satisfy the design assumptions.

4.

Compression Members with Bearing Joints The provisions for “compression members other than columns finished to bear” are intended to account for member out-of-straightness and also to provide a degree of robustness in the structure to resist unintended or accidental lateral loadings that may not have been considered explicitly in the design. A provision analogous to that in Section J1.4(2)(i), requiring that splice materials and connectors have an available strength of at least 50% of the required compressive strength, has been in the AISC Specifications since 1946. The current Specification clarifies this requirement by stating that the force for proportioning the splice materials and connectors is a tensile force. This avoids uncertainty as to how to handle situations where compression on the connection imposes no force on the connectors. Proportioning the splice materials and connectors for 50% of the required member strength is simple, but can be very conservative. In Section J1.4(2)(ii), the Specification offers an alternative that addresses directly the design intent of these provisions. The lateral load of 2% of the required compressive strength of the member simulates the effect of a kink at the splice, caused by an end finished slightly out-of-square or other construction condition. Proportioning the connection for the resulting moment and shear also provides a degree of robustness in the structure.

5.

Splices in Heavy Sections Solidified but still hot weld metal contracts significantly as it cools to ambient temperature. Shrinkage of large groove welds between elements that are not free to move so as to accommodate the shrinkage causes strains in the material adjacent to the weld that can exceed the yield point strain. In thick material the weld shrinkage is restrained in the thickness direction, as well as in the width and length directions, causing triaxial stresses to develop that may inhibit the ability to deform in a ductile manner. Under these conditions, the possibility of brittle fracture increases. When splicing hot-rolled shapes with flange thickness exceeding 2 in. (50 mm) or heavy welded built-up members, these potentially harmful weld shrinkage strains can be avoided by using bolted splices, fillet-welded lap splices, or splices that combine a welded and bolted detail (see Figure C-J1.1). Details and techniques that perform well for materials of modest thickness usually must be changed or supplemented by more demanding requirements when welding thick material. The provisions of AWS D1.1/D1.1M (AWS, 2010) are minimum requirements that apply to most structural welding situations. However, when designing and fabricating welded splices of hot-rolled shapes with flange thicknesses exceeding 2 in. (50 mm) and similar built-up cross sections, special consideration must be given to all aspects of the welded splice detail: (1) Notch-toughness requirements are required to be specified for tension members; see Commentary Section A3. Specification for Structural Steel Buildings, June 22, 2010

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(2) Generously sized weld access holes (see Section J1.6) are required to provide increased relief from concentrated weld shrinkage strains, to avoid close juncture of welds in orthogonal directions, and to provide adequate clearance for the exercise of high quality workmanship in hole preparation, welding, and for ease of inspection. (3) Preheating for thermal cutting is required to minimize the formation of a hard surface layer. (See Section M2.2.) (4) Grinding of copes and weld access holes to bright metal to remove the hard surface layer is required, along with inspection using magnetic particle or dye-penetrant methods, to verify that transitions are free of notches and cracks. In addition to tension splices of truss chord members and tension flanges of flexural members, other joints fabricated from heavy sections subject to tension should be given special consideration during design and fabrication. Alternative details that do not generate shrinkage strains can be used. In connections where the forces transferred approach the member strength, direct welded groove joints may still be the most effective choice. Earlier editions of this Specification mandated that backing bars and weld tabs be removed from all splices of heavy sections. These requirements were deliberately removed, being judged unnecessary and, in some situations, potentially resulting in more harm than good. The Specification still permits the engineer of record to specify their removal when this is judged appropriate. The previous requirement for the removal of backing bars necessitated, in some situations, that such operations be performed out-of-position; that is, the welding required to restore the backgouged area had to be applied in the overhead position. This may necessitate difficult equipment for gaining access, different welding equipment, processes and/or procedures, and other practical constraints. When box sections made of plate are spliced, access to the interior side (necessary for backing removal) is typically impossible.

(a) Shear plate welded to web

(b) Shear plate welded to flange tips

(c) Bolted splice plates

Fig. C-J1.1. Alternative splices that minimize weld restraint tensile stresses.

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Weld tabs that are left in place on splices act as “short attachments” and attract little stress. Even though it is acknowledged that weld tabs might contain regions of inferior quality weld metal, the stress concentration effect is minimized since little stress is conducted through the attachment.

6.

Weld Access Holes Weld access holes are frequently required in the fabrication of structural components. The geometry of these structural details can affect the components’ performance. The size and shape of beam copes and weld access holes can have a significant effect on the ease of depositing sound weld metal, the ability to conduct nondestructive examinations, and the magnitude of the stresses at the geometric discontinuities produced by these details. Weld access holes used to facilitate welding operations are required to have a minimum length from the toe of the weld preparation (see Figure C-J1.2) equal to 1.5 times the thickness of the material in which the hole is made. This minimum length

Alternate 1

Alternate 2

Rolled shapes and built-up shapes assembled prior to cutting the weld access hole.

Alternate 3 Built-up shapes assembled after cutting the weld access hole.

Notes: These are typical details for joints welded from one side against steel backing. Alternative details are discussed in the commentary text. 1) Length: Greater of 1.5tw or 11/2 in. (38 mm) 2) Height: Greater of 1.0tw or 3/4 in. (19 mm) but need not exceed 2 in. (50 mm) 3) R: 3/8 in. min. (10 mm). Grind the thermally cut surfaces of weld access holes in heavy shapes as defined in Sections A3.1(c) and (d). 4) Slope ‘a’ forms a transition from the web to the flange. Slope ‘b’ may be horizontal. 5) The bottom of the top flange is to be contoured to permit the tight fit of backing bars where they are to be used. 6) The web-to-flange weld of built-up members is to be held back a distance of at least the weld size from the edge of the access hole.

Fig. C-J1.2. Weld access hole geometry. Specification for Structural Steel Buildings, June 22, 2010

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is expected to accommodate a significant amount of the weld shrinkage strains at the web-to-flange intersection. The height of the weld access hole must provide sufficient clearance for ease of welding and inspection and must be large enough to allow the welder to deposit sound weld metal through and beyond the web. A weld access hole height equal to 1.0 times the thickness of the material with the access hole but not less than 3/4 in. (19 mm) has been judged to satisfy these welding and inspection requirements. The height of the weld access hole need not exceed 2 in. (50 mm). The geometry of the reentrant corner between the web and the flange determines the level of stress concentration at that location. A 90° reentrant corner having a very small radius produces a very high stress concentration that may lead to rupture of the flange. Consequently, to minimize the stress concentration at this location, the edge of the web is sloped or curved from the surface of the flange to the reentrant surface of the weld access hole. Stress concentrations along the perimeter of weld access holes also can affect the performance of the joint. Consequently, weld access holes are required to be free of stress raisers such as notches and gouges. Stress concentrations at web-to-flange intersections of built-up shapes can be decreased by terminating the weld away from the access hole. Thus, for built-up shapes with fillet welds or partial-joint-penetration groove welds that join the web to the flange, the weld access hole may terminate perpendicular to the flange, provided that the weld is terminated a distance equal to or greater than one weld size away from the access hole.

7.

Placement of Welds and Bolts Slight eccentricities between the gravity axis of single and double angle members and the center of gravity of connecting bolts or rivets have long been ignored as having negligible effect on the static strength of such members. Tests have shown

Fig. C-J1.3. Balanced welds Specification for Structural Steel Buildings, June 22, 2010

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that similar practice is warranted in the case of welded members in statically loaded structures (Gibson and Wake, 1942). However, the fatigue life of eccentrically loaded welded angles has been shown to be very short (Klöppel and Seeger, 1964). Notches at the roots of fillet welds are harmful when alternating tensile stresses are normal to the axis of the weld, as could occur due to bending when axial cyclic loading is applied to angles with end welds not balanced about the neutral axis. Accordingly, balanced welds are required when such members are subjected to cyclic loading (see Figure C-J1.3). 8.

Bolts in Combination with Welds As in previous editions, this Specification does not permit bolts to share the load with welds except for bolts in shear connections. The conditions for load sharing have, however, changed substantially based on recent research (Kulak and Grondin, 2003). For shear-resisting connections with longitudinally loaded fillet welds, load sharing between the longitudinal welds and bolts in standard holes or short-slotted holes transverse to the direction of the load is permitted, but the contribution of the bolts is limited to 50% of the available strength of the equivalent bearing-type connection. Both ASTM A307 and high-strength bolts are permitted. The heat of welding near bolts will not alter the mechanical properties of the bolts. In making alterations to existing structures, the use of welding to resist loads other than those produced by existing dead load present at the time of making the alteration is permitted for riveted connections and high-strength bolted connections if the bolts are pretensioned to the levels in Tables J3.1 or J3.1M prior to welding. The restrictions on bolts in combination with welds do not apply to typical bolted/ welded beam-to-girder and beam-to-column connections and other comparable connections (Kulak et al., 1987).

9.

High-Strength Bolts in Combination with Rivets When high-strength bolts are used in combination with rivets, the ductility of the rivets permits the direct addition of the strengths of the two fastener types.

10.

Limitations on Bolted and Welded Connections Pretensioned bolts, slip-critical bolted connections, or welds are required whenever connection slip can be detrimental to the performance of the structure or there is a possibility that nuts will back off. Snug-tightened high-strength bolts are recommended for all other connections.

J2.

WELDS Selection of weld type [complete-joint-penetration (CJP) groove weld versus fillet versus partial-joint-penetration (PJP) groove weld] depends on base connection geometry (butt versus T or corner), in addition to required strength, and other issues discussed below. Notch effects and the ability to evaluate with nondestructive testing may affect joint selection for cyclically loaded joints or joints expected to deform plastically. Specification for Structural Steel Buildings, June 22, 2010

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Tables J2.1 and J2.2 show that the effective throat of partial-joint-penetration and flare groove welds is dependent upon the weld process and the position of the weld. It is recommended that the design drawings should show either the required strength or the required effective throat size and allow the fabricator to select the process and determine the position required to meet the specified requirements. Effective throats larger than those in Table J2.2 can be qualified by tests. Weld reinforcement is not used in determining the effective throat of a groove weld but reinforcing fillets on T and corner joints are accounted for in the effective throat. See AWS D1.1/D1.1M Annex A (AWS, 2010).

1b.

Limitations Table J2.3 gives the minimum effective throat thickness of a PJP groove weld. Notice that for PJP groove welds Table J2.3 goes up to a plate thickness of over 6 in. (150 mm) and a minimum weld throat of 5/8 in. (16 mm), whereas for fillet welds Table J2.4 goes up to a plate thickness of over 3/4 in. (19 mm) and a minimum leg size of fillet weld of only 5/16 in. (8 mm). The additional thickness for PJP groove welds is intended to provide for reasonable proportionality between weld and material thickness. The use of single-sided PJP groove welds in joints subject to rotation about the toe of the weld is discouraged.

2.

Fillet Welds

2a.

Effective Area The effective throat of a fillet weld does not include the weld reinforcement, nor any penetration beyond the weld root. Some welding procedures produce a consistent penetration beyond the root of the weld. This penetration contributes to the strength of the weld. However, it is necessary to demonstrate that the weld procedure to be used produces this increased penetration. In practice, this can be done initially by cross-sectioning the runoff plates of the joint. Once this is done, no further testing is required, as long as the welding procedure is not changed.

2b.

Limitations Table J2.4 provides the minimum size of a fillet weld for a given thickness of the thinner part joined. The requirements are not based on strength considerations, but on the quench effect of thick material on small welds. Very rapid cooling of weld metal may result in a loss of ductility. Furthermore, the restraint to weld metal shrinkage provided by thick material may result in weld cracking. The use of the thinner part to determine the minimum size weld is based on the prevalence of the use of filler metal considered to be “low hydrogen.” Because a 5/16-in. (8 mm) fillet weld is the largest that can be deposited in a single pass by the SMAW process and still be considered prequalified under AWS D1.1/D1.1M, 5 /16 in. (8 mm) applies to all material greater than 3/4 in. (19 mm) in thickness, but Specification for Structural Steel Buildings, June 22, 2010

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minimum preheat and interpass temperatures are required by AWS D1.1/D1.1M. The design drawings should reflect these minimum sizes, and the production welds should be of these minimum sizes. For thicker members in lap joints, it is possible for the welder to melt away the upper corner, resulting in a weld that appears to be full size but actually lacks the required weld throat dimension. See Figure C-J2.1(a). On thinner members, the full weld throat is likely to be achieved, even if the edge is melted away. Accordingly, when the plate is 1/4 in. (6 mm) or thicker, the maximum fillet weld size is 1/16 in. (2 mm) less than the plate thickness, t, which is sufficient to e