Design Guide for Economical Reinforced Concrete Structures 9781943961207

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Design Guide for Economical Reinforced Concrete Structures

A guide to assist design professionals in achieving overall economy in the design and detailing of reinforced concrete structures. First Edition

Concrete Reinforcing Steel Institute

2016

Founded in 1924, the Concrete Reinforcing Steel Institute (CRSI) is a technical institute and an ANSI-accredited Standards Developing Organization (SDO) that stands as the authoritative resource for information related to steel reinforced concrete construction. Serving the needs of engineers, architects and construction professionals, CRSI offers many industry-trusted technical publications, standards documents, design aids, reference materials and educational opportunities. CRSI Industry members include manufacturers, fabricators, material suppliers and placers of steel reinforcing bars and related products. Our Professional members are involved in the research, design, and construction of steel reinforced concrete. CRSI also has a broad Region Manager network that supports both members and industry professionals and creates awareness among the design/construction community through outreach activities. Together, they form a complete network of industry information and support.

Design Guide for Economical Reinforced Concrete Structures

Publicaton No: 10-DG-STRUCTURES ISBN: 978-1-943961-20-7 Copyright © 2016 By Concrete Reinforcing Steel Institute First Edition Printed 2016

All rights reserved. This guide or any part thereof may not be reproduced in any form without the written permission of the Concrete Reinforcing Steel Institue.

Printed in the U.S.A

This publication is intended for the use of professionals competent to evaluate the significance and limitations of its contents and who will accept responsibility for the application of the material it contains. The Concrete Reinforcing Steel Institute reports the foregoing material as a matter of information and, therefore, disclaims any and all responsibility for application of the stated principles or for the accuracy of the sources other than material developed by the Institute.

Concrete Reinforcing Steel Institute

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Design Guide for Economical Reinforced Concrete Structures

Author David A. Fanella, Ph.D., S.E., P.E., F.ASCE, F.ACI is the Senior Director of Engineering at the Concrete Reinforcing Steel Institute. He has over 25 years of experience in the design of a wide variety of low-, mid-, and high-rise buildings and other structures. Fanella has authored numerous technical publications and recently authored a textbook on reinforced concrete design for McGraw Hill. He is a member of ACI Committees 314, Simplified Design of Concrete Buildings; 374, Performance-Based Seismic Design of Concrete Buildings; 375, PerformanceBased Design of Concrete Buildings for Wind Loads; and SA04, Design Award. Fanella is a Fellow of the American Concrete Institute (ACI) and the American Society of Civil Engineers (ASCE). He also serves as an Associate Member of ASCE Committee 7, Minimum Design Loads for Buildings and Other Structures. He received his BS, MS, and PhD in structural engineering from the University of Illinois at Chicago, Chicago, IL. He is a licensed structural and professional engineer in Illinois and is a licensed professional engineer in many other states.

The following figures and tables courtesy of Reinforced Concrete Structures: Analysis and Design, Second Edition by David Fanella. ©2015, McGraw-Hill Education: Figures 3.2, 4.1, 4.2, 4.3, 4.4, 4.5, 4.8, 4.9, 4.11, 4.12, 5.6, 5.24, 5.25, 5.26, 5.27, 5.28, 5.29, 5.30, 5.31, 5.32, 6.1, 6.2, 6.3, 6.11, 6.12, 6.13, 6.14, 6.15, 6.16, 7.22, 7.23, 7.24, 8.1, 8.2, 9.1, 9.2, 9.15, 9.16, 9.17, and 9.18 Tables 6.1 and 6.2

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Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures

Contents Author

ii

Chapter 1 Introduction

1-1

1.1 Overview

1-1

2.2 Scope

1-1

Chapter 2 Economical Reinforced Concrete Floor Systems

2-1

Chapter 4 Two-way Slabs 4.1 Overview

4-1

4.3 Detailing Requirements and Guidelines for Flexural Reinforcement

4-2

4.3.1 Overview

4-2

4.3.2 Concrete Cover

4-2

4.3.3 Minimum and Maximum Bar Spacing

4-2

4.3.4 Corner Reinforcement

4-2 4-3

4-3

2.1 Overview

2-1

2.2 General Guidelines for Economical Reinforced Concrete Floor Systems

2-1

2.2.1 Overview

2-1

4.3.6 Guidelines for Detailing the Flexural Reinforcement

2.2.2 Formwork

2-1

2.2.4 Concrete 2.3 Selecting an Economical Reinforced Concrete Floor System

2-2 2-4 2-5

2.3.1 Overview

2-5

2.3.2 One-way Joist System

2-5

2.3.3 Flat Plate System

2-8

2.3.4 Flat Slab System 2.3.5 Two-way Joist System

Chapter 3 One-way Slabs

2-9 2-11

3-1

3.1 Overview

3-1

3.2 Determining the Slab Thickness

3-1

3.3 Detailing Requirements and Guidelines for Flexural Reinforcement

3-1

4-1

4.2 Determining the Slab Thickness

4.3.5 Development of Longitudinal Reinforcement, Flexural Cutoff Points, and Splices

2.2.3 Reinforcement

4-1

4.3.7 Openings in Slab Systems 4.4 Detailing Requirements and Guidelines for Shear Reinforcement 4.4.1 Overview

4-4 4-4 4-4

4.4.2 Single- or Multiple-leg Stirrups

4-5

4.4.3 Headed Shear Studs

4-5

4.5 Detailing Requirements and Guidelines for SDC C

Chapter 5 Beams

4-6

5-1

5.1 Overview

5-1

5.2 Sizing the Cross-section

5-1

5.2.1 Beam Depth

5-1

5.2.2 Beam Width

5-1

5.3 Detailing Requirements and Guidelines for Flexural Reinforcement

5-2

5.3.1 Overview

5-2

5.3.2 Concrete Cover

5-2

3-2

5.3.3 Distribution of Flexural Reinforcement for Crack Control

5-2

3.3.4 Minimum Spacing of Flexural Reinforcement

3-2

5.3.4 Minimum Spacing of Flexural Reinforcement

5-3

3.3.5 Development of Longitudinal Reinforcement, Flexural Cutoff Points, and Splices

3-2

5.3.5 Development of Longitudinal Reinforcement, Flexural Cutoff Points, and Splices

5-4

3.3.1 Overview

3-1

3.3.2 Concrete Cover

3-1

3.3.3 Distribution of Flexural Reinforcement for Crack Control

Concrete Reinforcing Steel Institute

5.4 Detailing Requirements and Guidelines for Shear Reinforcement

5-5

5.4.1 Overview

5-5

5.4.2 Stirrup Configurations

5-5

5.4.3 Development of Shear Reinforcement

5-7

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Design Guide for Economical Reinforced Concrete Structures

Contents 5.5 Detailing Requirements and Guidelines for Torsional Reinforcement

5-8

5.5.2 Detailing Requirements and Guidelines for the Transverse Reinforcement

5-9

5.5.3 Detailing Requirements and Guidelines for the Longitudinal Reinforcement

5-9

5.5.4 Detailing Requirements and Guidelines for Combined Effects

5-9

5.6 Steps in Beams

5-10

5.6.1 Overview

5-10

5.6.2 Top Steps

5-10

5.6.3 Bottom Steps

5-11

5.6.4 Deep Steps

5-11 5-11

5.7.1 Overview

5-11

5.7.2 Design for Flexure

5-11

5.7.3 Design for Shear 5.8 Detailing Requirements and Guidelines for SDC D, E, or F 5.8.1 Overview

5-12 5-13 5-13

5.8.2 Dimensional Limits

5-13

5.8.3 Design for Flexure

5-13

5.8.4 Design for Shear

5-13

5.9 Beams Not Designated as Part of the SFRS

Chapter 6 Columns

6.6.1 Overview

6-8

6.6.2 Longitudinal Reinforcement Requirements 6-8

5.5.1 Overview

5.7 Detailing Requirements and Guidelines for SDC C

5-14

6.6.3 Transverse Reinforcement Requirements 6.7 Detailing Requirements and Guidelines for SDC D, E, or F

6-1 6-1

6.2 Preliminary Column Sizing

6-1

6.3 Detailing Requirements and Guidelines for Longitudinal Reinforcement

6-2

6.3.1 Overview

6-2

6.3.2 Minimum Number of Longitudinal Bars

6-2

6.3.3 Spacing of Longitudinal Bars

6-2

6.3.4 Splices

6-3

6-8 6-9

6.7.1 Overview

6-9

6.7.2 Dimensional Limits

6-9

6.7.3 Longitudinal Reinforcement Requirements 6-9 6.7.4 Transverse Reinforcement Requirements 6.8 Columns Not Designated as Part of the SFRS

Chapter 7 Walls

6-9 6-11

7-1

7.1 Overview

7-1

7.2 Determination of Wall Thickness

7-1

7.3 Minimum Reinforcement

7-1

7.4 Detailing Requirements and Guidelines for Reinforcement

7-2

7.4.1 Overview

7-2

7.4.2 Concrete Cover

7-2

7.4.3 Spacing Requirements

7-2

7.4.4 Lateral Support of Longitudinal Reinforcement

7-2

7.4.5 Wall Openings

7-3

7.4.6 Wall Corners and Intersections

7-4

7.5 Detailing Requirements and Guidelines for SDC D, E, or F

6.1 Overview

7-7

7.5.1 Overview

7-7

7.5.2 Web Reinforcement Requirements

7-7

7.5.3 Boundary Elements

7-8

Chapter 8 Diaphragms

8-1

8.1 Overview

8-1

8.2 Determing the Diaphragm Thickness

8-1 8-1

6-3

8.3 Detailing Requirements and Guidelines for Reinforcement

6-3

8.4 Detailing Requirements and Guidelines for SDC D, E, or F

8-2

6.4.1 Overview 6.4.2 Spiral Reinforcement

6-3

8.4.1 Overview

8-2

6.4 Detailing Requirements and Guidelines for Transverse Reinforcement

6.4.3 Tie Reinforcement

iv

5-8

6-4

8.4.2 Minimum Thickness

8-2

6.5 Detailing Requirements and Guidelines for Dowels

6-7

8.4.3 Minimum Reinforcement

8-2

6.6 Detailing Requirements and Guidelines for SDC C

6-8

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures

Chapter 9 Foundations

9-1

9.1 Overview

9-1

9.2 Spread Footings

9-1

9.2.1 Material Selection

9-1

9.2.2 Determining the Base Dimensions and Thickness

9-1

9.2.3 Detailing Requirements and Guidelines for Reinforcement

9-1

9.3 Mat Foundations

9-3

9.3.1 Overview

9-3

9.3.2 Determining the Mat Thickness

9-3

9.3.3 Detailing Requirements and Guidelines for Reinforcement

9-3

9.4 Drilled Piers

9-4

9.4.1 Overview

9-4

9.4.2 Determining the Shaft Diameter

9-5

9.4.3 Determining the Bell Diameter

9-5

9.4.4 Detailing Requirements and Guidelines for Reinforcement

9-5

9.5 Grade Beams

9-7

9.6 Detailing Requirements and Guidelines for SDC D, E, or F

9-9

9.6.1 Overview

9-9

9.6.2 Footings and Foundation Mats

9-9

9.6.3 Grade Beams

9-10

9.6.4 Piles, Piers, and Caissons

9-10

Chapter 10 References

10-1

Notations

N-1

Concrete Reinforcing Steel Institute

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Design Guide for Economical Reinforced Concrete Structures

CHA PTER 1 Introduction 1.1 Overview One of the main advantages of reinforced concrete is the ability to mold it into essentially any shape or form. There are no inherent restrictions that limit imagination and creativity when it comes to the aesthetic design of a reinforced concrete structure. Along with the freedom of shape and form comes the reality of cost. A finite budget is the norm on the vast majority of projects that are undertaken and the cost of a structure can be needlessly larger than it has to be if there is not a basic understanding of what it takes to achieve overall economy in a reinforced concrete structure.

Chapters 3 through 9 present requirements and guidelines for sizing, designing, and detailing the following structural members: • One-way slabs • Two-way slabs • Beams • Columns • Walls • Diaphragms • Foundations

The purpose of this Guide is twofold: • To present information on how to select an economical reinforced concrete floor system. • To present requirements and guidelines on how to size, design, and detail reinforced concrete structural members that, where implemented, will result in an economical reinforced concrete structure. The emphasis here is on building structures, but some of the information that is presented can be used in the design of bridges and other nonbuilding structures. It is assumed that the reader has a basic understanding of the design and detailing of reinforced concrete structural members for combinations of gravity and lateral loads in accordance with the requirements of ACI 318, Building Code Requirements for Structural Concrete. This Guide is not a comprehensive design guide on the fundamentals of reinforced concrete design. Rather, the information that is presented here is to be used by a design professional that will help in achieving overall economy in a reinforced concrete structure.

Included in the discussion for each member type are the specific design and detailing requirements that are applicable to structures in areas of high seismic risk, that is, structures assigned to seismic design category (SDC) D, E, or F. Emphasis is placed on constructability, which has a direct link to economy. The references that are cited in this Guide can be found in Chapter 10. Throughout the chapters, reference is made to the provisions of the 2014 edition of ACI 318, Building Code Requirements for Structural Concrete (Reference 1). For example, reference to Section 8.3 in ACI 318-14 is denoted here as ACI 8.3. A similar designation is provided for tables and figures from that document.

1.2 Scope Chapter 2 of this Guide contains general guidelines and information on how to select an economical reinforced concrete floor system. In particular, wide-module joist, flat plate, flat slab, and two-way joist systems are covered. Tables are provided that give relative cost indices of floor systems for various span and load conditions. This information can help in determining the most economical system for a given set of constraints.

Concrete Reinforcing Steel Institute

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Design Guide for Economical Reinforced Concrete Structures

CHA PTER 2 Economical Reinforced Concrete Floor Systems 2.1 Overview

for the crew when erecting the forms, resulting in reduced labor costs. In cases where multiple framing systems are specified, a separate forming system is needed for each system, which translates to additional costs associated with material and its mobilization. There are obvious exceptions to this guideline, particularly in areas of a building that have different usages. For example, it would be practical to have one framing system for the parking levels in a building and another for the typical residential or office floors.

General information is provided in this chapter on how to choose an economical reinforced concrete floor system and once chosen, how to achieve cost-savings when designing and detailing the structural members in the system. Tables are presented that can be utilized in selecting an economical system for a given set of constraints.

2.2 General Guidelines for Economical Reinforced Concrete Floor Systems 2.2.1 Overview

2.

Through careful planning and detailing, the overall cost of the structure of a building utilizing reinforced concrete can be reduced considering the overall costs related to the main components of any reinforced concrete building, which are formwork, reinforcement, and concrete. The costs associated with formwork are generally 40 to 60 percent of the completed structure. Material costs for the concrete and reinforcement range from 10 to 30 percent of the overall cost. The labor cost for placing the concrete and reinforcement is the remainder. This section covers general guidelines that will result in more economical reinforced concrete structures. Specific cost-saving guidelines and techniques are given in the next section and the following chapters of this Guide for particular reinforced concrete floor systems and reinforced concrete members.

Column capitals and drop panels are usually expensive to form. Consider using shear reinforcement to augment two-way shear capacity of a slab. 3.

Use modular formwork whenever practical. Traditionally, modular forms have been used for floors and walls where the forms can be moved in large sections and reused often (usually between 10 and 20 times). Such proprietary forming systems have become more common and are being used to form smaller members. This type of formwork can also be used in customized applications such as slip-formed shafts for elevators and stairways and curved exterior walls. The cost of using such specialized forms can usually be justified if they can be reused multiple times in a project.

4.

Use floor framing systems of minimum depth with a constant elevation for the bottom surface of the system. For most residential and office applications, the depth of the floor system is governed by serviceability (deflection) considerations. Providing the minimum depth based on these requirements will result in minimum floor-to-floor heights and, thus, an overall reduction in the building height. Overall height reduction translates to a reduction in the costs associated with essentially all of the vertical runs in the building (façade; elevators; stairs; interior partition walls; and plumbing, electrical, and mechanical conduit and ductwork).

2.2.2 Formwork By definition, formwork is the total system of support for freshly placed concrete, which includes the mold or sheathing that is in contact with the concrete and all of the supporting members, hardware, and bracing. Project specifications can have a major impact on formwork design and speed of construction. Examples include stripping time, tolerances, concrete finish requirements, strength of concrete at time of form removal, and reinforcing steel and accessory requirements. It is important that these items, as well as any other pertinent ones, be discussed with the concrete contractor as early as possible. Because formwork and the labor associated with it are typically the largest cost in a reinforced concrete structure, it is important to follow some basic guidelines, which when implemented, can result in overall cost savings. The following guidelines, which are not meant to be comprehensive, should be considered at the onset of any project. 1.

Select one framing system and use it throughout the structure wherever possible. Using the same framing system as often as practical throughout the structure has been shown to result in significant cost savings. Forms are reused many times and it is easier Concrete Reinforcing Steel Institute

Use standard shaped forms. Rectilinear members are the most cost effective to form. Whenever possible, avoid shapes that have to be either fabricated by the form supplier or customized by carpenters in the field. Large field fabrication costs can be incurred, for example, when the forms have to be modified for tapered members or for haunches.

The underside of a reinforced concrete floor or roof should be kept level for maximum economy. Sloping of floor or roof surfaces should be accomplished by varying the structural slab thickness or by using concrete fill. Depressions for floor coverings should be made by varying the top surface of the slab rather than by adjusting formwork beneath the slab.

2-1

Design Guide for Economical Reinforced Concrete Structures 5.

Orient one-way structural members to span in the same direction throughout the entire structure. Experience has shown that structures that have one-way members oriented in the same direction throughout the entire structure tend to be constructed more efficiently than those where multiple framing directions are used. This is attributed to less confusion and fewer mistakes made in the field because of the overall regularity of the structure.

6.

Arrange columns in a regular pattern. If possible, the columns should be arranged in a regular pattern throughout each floor of the structure. This helps in achieving consistency in the formwork and reinforcement layout of all the structural members. Installing the formwork in such cases is repetitive and efficient and the formwork can be reused easily. This repetitiveness and efficiency carries over to all aspects related to the reinforcing bars.

7.

Use a consistent column size. Experience has shown that it is more efficient to limit the number of changes in the column sizes throughout the height of a structure. In low-rise buildings, the same column size should be used throughout the entire height as should the same compressive strength of the concrete; the number of reinforcing bars can change over the height as needed. In taller buildings, the same column size should be used over a number of floors and then changed accordingly over the height depending on the total number of stories in the building. The concrete compression strength and the number of reinforcing bars vary over the height as well.

8.

Specify the time when forms may be stripped for selfsupporting members and the strength when forms may be stripped for other members. Forms for columns and walls can be stripped based on time after the concrete has been placed (e.g., 12 hours). For beams and slabs, forms can be stripped after a specific percentage of concrete compressive strength has been attained (e.g., 75% of the specified 28-day compressive strength). It is important to note that beams and slabs must be reshored until the compressive strength has been attained to minimize deflections. Appropriate stripping specifications will minimize the required amount of formwork and will result in lower formwork costs.

9.

Use high early strength concrete. The use of high early strength concrete enables the formwork to be stripped sooner than conventional concrete. Faster cycle times may allow for a faster overall construction time, which translates to significant overall cost savings.

10. Use predetermined construction joints. The location for construction joints should be the contractor’s prerogative with input from the engineer of record where required. Properly located construction joints will allow the contractor to sequence concrete placement efficiently. The use of dowel bar mechanical splices at construction joints should be considered (see Fig. 2.1). This splice type contains a flange that is nailed to the forms. After the forms are stripped, the adjoining reinforcement can be screwed into the coupler. This eliminates bar or dowel penetration through the forms.

2-2

Fig. 2.1 Dowel Bar Mechanical Splice.

2.2.3 Reinforcement 1.

Use Grade 60 reinforcing bars. ASTM A615 Grade 60 bars are the most widely used and inventoried reinforcing bars. Specifying Grade 40 bars may require 50% more steel than using Grade 60 bars. ASTM A615 Grade 75 or 80 bars are readily available, but are not normally inventoried by fabricators. It is important to note that these bars are usually available on mill orders ranging from 25 to 75 tons per bar size. However, smaller quantities may be obtained from warehouses, if available. In taller structures, the use of Grade 75 or 80 longitudinal bars in columns may decrease congestion at the joints and may reduce the number of crossties because a smaller number of longitudinal bars would generally be required.

2.

Use the largest bar size possible. Placing and fabrication costs are minimized by using the largest practical bar sizes that satisfy both strength and serviceability requirements. It is important to keep in mind that a greater quantity of smaller bars may be required for crack control or for other serviceability issues.

3.

Use straight bars wherever possible. Fabricating and placing straight bars is faster and easier than bent bars.

4.

Use ACI standard bar bend types. Specify standard bar shapes and bends provided in Reference 2. Nonstandard bends disrupt shop routine and are more costly to fabricate.

5.

Use bars in one plane. Wherever possible, reinforcing bars should have bends located in one geometric plane. Bars with bends in two or three planes are difficult and expensive to fabricate. Additionally, it is difficult to maintain proper field tolerances because adjustment of the bar in one direction impacts the tolerance in one or more of the other directions.

6.

Use repetitive bar sizes and lengths. The standard length for reinforcing bars is 60 ft, although some fabricators stock shorter lengths. In general, the longest available (and possible) bar lengths should be used to reduce fabrication and placing costs. Also, the number of bar sizes specified in a particular project should be minimized. This reduces the number of sizes that must be handled in the shop and placed in the field.

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures tains a list of overall bar diameters. Hook dimensions and bend radii for standard hooks and stirrup/tie hooks are given in Chapter 6 of Reference 3. Lap Varies, •0LQLPXP

Table 2.1 Overall Reinforcing Bar Diameter SECT. A 7RS%DUV/HQJWK³$´ %RWWRP%DUV/HQJWK³&´

Nominal Diameter

7RS%DUV/HQJWK³%´ %RWWRP%DUV/HQJWK³&´

Fig. 2.2 Using Stock Length Bars Cut and Spliced in the Field.

8.

9.

Use stock length bars. In the case of irregularlyshaped walls and slabs, it is usually more cost effective to use stock length bars that are cut and spliced in the field in lieu of using individual bars that have been sheared to a required length (see Fig. 2.2). The added cost associated with the extra material used due to variable lap lengths is usually minor and is more than offset by the savings due to reduced labor that would otherwise be required to cut and sort the individual bars. Use the appropriate splice in the appropriate situation. Wherever possible, bars should be lap spliced. A consistent lap splice length should be specified for a given bar size. For columns utilizing #14 and #18 bars, and for #11 and smaller bars where congestion is an issue, use mechanical splices. A compression mechanical splice should be specified for bars that will always be in compression because these types of splices are considered to be the fastest to install in the field. Provide a 4- to 6-in. gap to place concrete where bars are closely spaced. In heavily reinforced members, such as transfer girders, where the spacing between bars is relatively close, provide a gap of 4 to 6 in. between bars, if possible. Based on experience, a 4-in. slump concrete with 3/4-in. aggregate will not flow easily though a 2-in. space between bars. Also, vibrator heads, which are usually 2 to 3 in. in width, may not fit between the bars or can become entangled in the bars if the space between bars is too small.

10. Draw details to scale to ensure that the reinforcing bars will fit within the section. Scaled drawings that show all of the reinforcement are essential, especially in the following cases: • Narrow beams

A

A Overall Diameter

Approximate Diameter Outside Deformations, in.

Bar Size #3

7/

16

#4

9/

16

#5

11/

#6

7/

#7

1

#8

11/8

#9

11/4

#10

17/16

#11

15/8

#14

17/8

#18

21/2

16 8

Figure 2.3 illustrates how a scaled detail drawing can help identify problems. The conceptual beam detail with the reinforcement depicted as lines and dots is given in the figure as is the detail where the reinforcement has been drawn to scale. It can be seen in the scaled drawing that the stirrup hooks will likely interfere with the top bars and the minimum clearance between the bars may not be met. #3 closed stirrups

3-#6 T&B

• Slabs with multiple openings, especially near supports and edges • Slab-column and beam-column joints • Columns with more than 2% longitudinal reinforcement It is important to include the overall dimensions of the reinforcing bars, as well as hook dimensions and bend radii when drawing the scaled details. Table 2.1 con-

Concrete Reinforcing Steel Institute

Interference between stirrups & top bars

7 1/2"

7.

6" Beam Detail (Conceptual)

Insufficent clear distance between bars Beam Detail (Scaled)

Fig. 2.3 Beam Detail, Conceptual and Scaled.

2-3

Design Guide for Economical Reinforced Concrete Structures forced sections and complex formwork while ensuring good construction quality which may lead to increased productivity, reduces the labor requirement and cost, or both;

2.2.4 Concrete 1. Use moderate-strength concrete. 4,000 to 5,000 psi compressive strength concrete is usually sufficient. Exceptions are for columns in high-rises and floor systems in which there are shear capacity issues. Columns, shear walls, and joints may require higher strength concrete to enhance their axial and flexural capacity.

• Improved flexibility in spreading placing points during casting. This can reduce the need for frequent movement of transit trucks and the need to move the pump lines to place concrete (possible reduction in the number of pumps, pump operators, and so on). This greater flexibility in scheduling construction activities and procuring the required resources results in both time and resource savings.

2. Use high-performance concrete where placement and consolidation is expected to be difficult. Highperformance concrete is defined within ACI 116 as concrete meeting special combinations of performance and uniformity requirements that cannot always be achieved routinely using conventional constituents and normal mixing, placing, and curing practices. These requirements could potentially include the following enhancements:

SCC may be evaluated in the field using a standard slump test; however, the slump cone is often inverted. Instead of measuring the distance between the top of the cone and the top of the sample, the puddle of concrete is measured in 2 orthogonal directions to determine the spread diameter. Standard slump measurements of highly flowable concrete is practically irrelevant, as it has no measureable slump (>> 12 in.). Other mixture evaluation tests include the J-ring test, used to evaluate the flow and segregation characteristics of high-performance concrete.

• Ease of placement and consolidation without affecting strength; • Long-term mechanical properties; • Durability in severe environments; • High early strength; • Toughness; • Volume stability. These properties are usually achieved with special admixtures, which alter the plastic properties and workability of the concrete during placement, making it less viscous (more fluid) than conventional concrete. Long-term strength properties are usually unaffected. Self-consolidating concrete (SCC) is a special type of highperformance concrete. It is defined by the National ReadyMix Concrete Association (NRMCA) as a highly flowable, non-segregating concrete that can flow into place, fill the formwork, and encapsulate the reinforcement without any mechanical consolidation. In general, SCC is concrete made with conventional concrete materials and, in most cases, with a viscosity-modifying admixture (VMA). SCC is also useful in applications where high quality surface finishes are desired without bugholes or honeycombing. Increased form pressures may be generated when SCC is used, necessitating possible changes in formwork design.

3.

Use high-strength concrete in columns. Highstrength concrete can be justified in columns if the use of higher strength concrete reduces the amount of longitudinal reinforcement. Similarly, column sizes can be reduced or just use one column size on a project. Specify the same strength concrete in all columns of a story, to minimize mistakes.

4.

Specify few mix designs. On most projects only two strengths of concrete are necessary, a normal mix (4,000 to 5,000 psi) and a high-strength mix (8,000 psi or greater). Some projects may necessitate three. Consistent with the construction shown in Figure 2.4, it is most economical to use the high-strength column concrete in the slab puddling zone. In an effort to optimize concrete mixes on a project, some engineers have specified a separate puddling mix, because ACI 318 only allows a design concrete strength of 10,000 psi in shear. Some high-strength column concretes may have compressive strengths ranging from 12,000 psi to 15,000 psi.

ACI Committee Report 237R (Reference 24) indicates that SCC provides the following features, which are equally applicable to general high-performance concrete:

To make placement easier and avoid potential placement mistakes on the project, it is usually more economical to use the column concrete in the puddling zone, and design for a maximum concrete strength of 10,000 psi; a separate puddling mix is thus not recommended.

• It is good at replicating architectural form features; • Free fall into the formwork can be greater than the conventional limit of 5 ft.; • Less screeding operations are required to ensure flat surfaces (self-leveling characteristic); • It facilitates accelerated construction, through higher rate of casting or placing and shorter construction duration; • It facilitates and expedites the filling of highly rein-

2-4

5.

Limit coarse aggregate size to ¾ inch. As a matter of practice limit the coarse aggregate to ¾ inch since the minimum clear bar spacing is normally 1 inch and ACI 318 Code requires a clear distance of four-thirds the aggregate size.

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures

Column concrete placed in the nearby slab section.

Fig. 2.4 Concrete “Puddling” around Columns. Photo courtesy of Skidmore, Owings and Merrill LLP.

2.3 Selecting an Economical Reinforced Concrete Floor System 2.3.1 Overview Numerous types of cast-in-place, reinforced concrete floor systems are available to satisfy virtually any span and loading condition that is required. Because the cost of the floor system is often the major part of the structural cost of a building, selecting the most effective system for a given set of constraints is vital in achieving overall economy. This is especially important for low- and mid-rise buildings and for buildings subjected to relatively low wind and seismic forces because the cost of the lateral force-resisting systems in such cases is minimal compared to the typical floor systems. Provided in this chapter are preliminary estimates of material quantities for various cast-in-place reinforced concrete floor systems with a variety of span and loading conditions. In particular, the following conventionally reinforced concrete systems are covered: • One-way joist • Flat plate • Flat slab • Two-way joist (waffle) Voided slabs are reinforced concrete slabs similar to flat plates that contain regularly-spaced voids. The voids are usually created using hollow recycled plastic void formers and are positioned in wire cages to create modules, which are placed between the top and bottom layers of flexural reinforcement in the slab. Both squat and spherical void formers are available in different sizes. The main purpose of the voids is to eliminate concrete in areas where it is not needed, thereby reducing the overall weight of the floor system. Voided slabs are not addressed in this Guide; more information can be found in Reference 4 and in manufacturers’ literature. The structural members of the floor systems that are covered in this chapter were designed and detailed for the effects of gravity load in accordance with ACI 318-14 (Reference 1). CRSI’s Reinforced Concrete Concept, which is a preliminary design tool that provides material and cost estimates for a

Concrete Reinforcing Steel Institute

variety of conventionally reinforced concrete floor systems, was used to generate the information provided in the following tables (http://concept.crsi.org/index.cfm). It is assumed that the members in the various floor systems are not part of the lateral force-resisting system. Span and loading conditions that are typical for residential and office buildings are included in the analysis. In all cases, normal-weight concrete with a density of 150 pcf and a specified compressive strength of 4,000 psi is utilized. Also, Grade 60 reinforcing bars are used. The live load varies from 40 psf to 100 psf, and the superimposed dead load is taken as 10 psf in all cases. Concrete, reinforcing steel, and formwork quantities are given in the tables for various span and loading conditions. In general, unlimited design solutions are possible for a given set of constraints. The member sizes in the tables for a particular bay size and superimposed loading satisfy all applicable ACI 318 requirements and were chosen based on the guidelines presented in this Guide, practicality, experience, and formwork economy. This does not imply, however, the following: (1) the provided sizes result in the most economical solution because no mathematical attempt was made to optimize the overall cost of the floor system for a given set of constraints and (2) members sizes not contained in the tables are uneconomical and/or impractical and that they should not be considered for the case at hand. Cost indices of the various floor systems are also provided in the tables. Unit in-place costs for concrete, reinforcement, and formwork used in this analysis were obtained from Reference 5. These unit costs, which include both materials and installation, represent national average costs for major cities in the U.S. The cost index is the ratio of the total cost—in-place costs of concrete, reinforcement, and formwork for that particular case—to the average total cost of all cases in all systems considered in this Guide. These cost indices can be used to compare relative costs between different systems as a function of span and loading. The size and geographic location of the project, the availability of skilled labor, and local building code requirements are a few of the many factors that significantly affect costs. Thus, it is important to use the data in the tables as a preliminary guide in selecting an economical floor system.

2.3.2 One-way Joist System Overview A one-way joist floor system, which is commonly referred to as a wide-module joist system or a “skip” joist system when the clear spacing between the joist ribs exceeds 30 inches, consists of regularly spaced concrete joists (ribs) spanning in one direction, a reinforced concrete slab cast integrally with the joists, and beams (or, girders) that span between the columns, perpendicular to the joists (see Fig. 2.5). The joists are formed by using pan forms that are either 53 or 66 in. wide. Systems formed by the 66-in.-wide pans that range in depth between 14 and 24 in. are considered in this Guide.

2-5

Design Guide for Economical Reinforced Concrete Structures Table 2.2 Maximum Span Lengths for One-way Joist Systems with 66-in.-wide Pans

Fig. 2.5 One-way Joist System.

The main advantages of a one-way joist system are: (1) they are economical for long spans with heavy loads, (2) the pan voids reduce the dead load, and (3) electrical and mechanical equipment can be placed between joists, which means the overall floor depth need not be increased to accommodate this equipment. The longer spans and inherent vibration resistance make this an attractive floor system for office buildings, hospitals, and schools. It is important to note that wide-module joist construction does not satisfy the limitations of ACI 9.8.1 of standard joist systems; therefore, the members of the floor system are to be designed as one-way slabs and beams.

Member Sizes The thickness of the slab spanning between the joists (beams) can be controlled by either structural or fire resistance requirements. Specifying a lightweight aggregate may be advantageous in certain situations because a 2-hour fireresistance rating can be achieved with a relatively thin slab. This would also result in a reduction of dead load. A normalweight concrete slab with a 4.5-in. thickness is used in all cases considered in this Guide. One layer of reinforcement is usually provided in the slab at mid-depth perpendicular to the joists. The minimum amount of reinforcement required for temperature and shrinkage, as prescribed in ACI 7.6, usually governs. The dimensions of the joists depend on deflection and strength requirements. The minimum thickness of nonprestressed beams that are not supporting or attached to partitions and other construction likely to be damaged by deflections is given in ACI Table 9.3.1.1. According to this table, the slab thickness plus pan depth should be greater than or equal to C18.5 (exterior span) or C21 (interior span) in the case of normal-weight concrete and Grade 60 reinforcement, where C is the span length defined in ACI Chapter 2. Table 2.2 contains the maximum span lengths for one-way joist systems, assuming a 4.5-in. thick slab.

2-6

Pan Depth (in.)

Exterior Span, Maximum Span Length, C (ft)

Interior Span, Maximum Span Length, C(ft)

14

28.5

32.4

16

31.6

35.9

20

37.8

42.9

24

43.9

49.9

The overall depths of the systems contained in the tables in the Summary section satisfy the requirements of ACI Table 9.3.1.1. A thickness less than that prescribed in this table is allowed if it can be demonstrated that computed deflections are less than or equal to the limits prescribed in ACI Table 24.2.2. Once a thickness has been established, a joist width is chosen. The width of the joists can be tailored to satisfy virtually any requirement. In most cases, the thinnest practical joist width, for a given rib spacing, will be adequate for structural requirements. Bay sizes and floor layouts may also have an influence on the width of the joists. In certain cases, specific joist widths may be necessary in order to provide economical and practical formwork. The thickness of the supporting beams (or, girders) is dictated by the thickness of the joists. To achieve overall formwork economy, the depth of supporting members should be the same as the overall depth of the joists. If additional capacity is required, beams should be made wider, not deeper. Also, beams should be wider than the columns into which they frame, if possible. In addition to assuring formwork economy, this also alleviates some of the reinforcement congestion that can occur at the joints. In the tables in the Summary section below, the second to last column contains the pan area percentage, which is the percentage of the floor area that requires pan formwork.

Joist Orientation Depending on span lengths and superimposed loads, it is usually more cost effective to span the joists in the long direction. This also helps in assuring that a level floor soffit is achieved because the beams are spanning in the short direction. For bays with aspect ratios less than 1.5, the cost differential between joists framing in the short direction and long direction is typically very small.

Live Load Effects Material quantities are, to a large extent, controlled by deflection requirements. An increase in live loads does not have a proportional impact on cost. A live load of 100 psf results in an increase of less than 5% over the cost of a system designed for a live load of 40 psf.

Panel Aspect Ratio Effects The aspect ratio of the slab panels has a minimal effect on material quantities for ratios less than 1.5. As noted above, spanning the joists in the long direction usually results in the most economical solution.

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures Summary One-way joist systems are economically viable for medium to long spans with moderate to heavy loads. Systems formed with 66-in. pans are feasible for span lengths ranging from 35 to 50 ft and beyond. Large, column-free spaces can be achieved without vibration problems for typical residential and office occupancies.

Tables 2.3, 2.4, and 2.5 contain material quantities and cost indices for one-way joist systems with live loads of 40, 65, and 100 psf, respectively.

Table 2.3 Material Quantities and Cost Indices for One-way Joist Floor Systems, LL = 40 psf

Bay Size (ft)

Pan Depth (in.)

Beam Width (in.)

Square Column Size (in.)

Concrete (ft3/ft2)

Reinforcement (psf)

Pan Area (%)

Cost Index

25 w 25

14

26

22

0.62

2.09

89

0.80

30 w 30

16

32

28

0.65

2.43

89

0.83

30 w 35

20

34

30

0.71

2.36

90

0.85

30 w 40

24

36

32

0.77

2.53

90

0.88

35 w 35

20

34

30

0.71

2.65

90

0.86

35 w 40

24

36

32

0.77

2.76

90

0.89

40 w 40

24

36

32

0.77

3.05

90

0.91

Table 2.4 Material Quantities and Cost Indices for One-way Joist Floor Systems, LL = 65 psf Bay Size (ft)

Pan Depth (in.)

Beam Width (in.)

Square Column Size (in.)

Concrete (ft3/ft2)

Reinforcement (psf)

Pan Area (%)

Cost Index

25 w 25

14

28

24

0.62

2.49

88

0.82

30 w 30

16

34

30

0.65

2.73

88

0.84

30 w 35

20

36

32

0.71

2.75

89

0.87

30 w 40

24

38

34

0.77

2.70

90

0.89

35 w 35

20

36

32

0.71

3.16

89

0.89

35 w 40

24

38

34

0.77

3.00

90

0.90

40 w 40

24

38

34

0.77

3.36

90

0.92

Table 2.5 Material Quantities and Cost Indices for One-way Joist Floor Systems, LL = 100 psf Bay Size (ft)

Pan Depth (in.)

Beam Width (in.)

Square Column Size (in.)

Concrete (ft3/ft2)

Reinforcement (psf)

Pan Area (%)

Cost Index

25 w 25

14

30

26

0.63

2.82

87

0.84

30 w 30

16

36

32

0.66

3.41

87

0.88

30 w 35

20

38

34

0.72

3.18

89

0.89

30 w 40

24

40

36

0.78

3.29

89

0.92

35 w 35

20

38

34

0.72

3.67

89

0.92

35 w 40

24

40

36

0.78

3.70

89

0.94

40 w 40

24

40

36

0.78

4.10

89

0.96

Concrete Reinforcing Steel Institute

2-7

Design Guide for Economical Reinforced Concrete Structures compressive strength. Specifying a compressive strength greater than 4,000 psi will increase the cost of the concrete without any allowable reduction in slab thickness. Therefore, for live loads of 40 psf or less, the most economical flat plate floor system is one where a minimum thickness computed by ACI Table 8.3.1.1 and a concrete compressive strength of 4,000 psi are specified.

Fig. 2.6 Flat Plate.

2.3.3 Flat Plate System Overview A flat plate floor system is a two-way concrete slab supported directly on columns with reinforcement in two orthogonal directions (see Fig. 2.6). Primarily used in hotels, multi-family residential buildings, and office buildings, this system has the advantages of simple construction and formwork and a flat ceiling, the latter of which reduces ceiling finishing costs because the architectural finish can be applied directly to the underside of the slab. Even more significant are the cost savings associated with the low story heights made possible by the shallow floor system. Smaller vertical runs of cladding, partition walls, mechanical systems, plumbing, and other primarily vertical items of construction translate to large cost savings, especially for medium- and high-rise buildings. Moreover, where the total height of a building is restricted, using a flat plate can result in more stories accommodated within the set height.

Minimum Slab Thickness Minimum slab thickness requirements for flat plates are given in ACI Table 8.3.1.1. The minimum thickness of exterior and interior panels of flat plates without edge beams and containing reinforcement with a yield strength of 60,000 psi is equal to Cn 30 and Cn 33, respectively, where Cn is the length of the clear span in the long direction. The panel that yields the largest thickness is used throughout the entire floor plate. In no case should the thickness be less than 5 in.

Live Load Effects For live loads of 40 psf or less, the thickness of the slab will usually be controlled by deflection requirements. Also, the flexural reinforcement at the critical sections in the column and middle strips will be about the minimum amount prescribed in ACI Table 8.6.1.1. Thus, using a slab thickness greater than the minimum allowable thickness is not economical because a thicker slab will increase the concrete quantity and not reduce the reinforcement quantity. Note that minimum thickness requirements are independent of the concrete

2-8

For live loads of 100 psf or more, the thickness of the slab will more than likely be controlled by the two-way shear stresses at the critical section around the columns and the bending moments in the slab, and not by the deflection criteria described above. Thicker slabs are generally provided to resist the larger shear stresses due to larger live loads. Although a thicker slab may result in a decrease in the required amount of flexural reinforcement, the reduction in the cost of reinforcement will not offset the increase in the cost of concrete. Also, using a higher strength concrete is not the most effective way of increasing the nominal moment strength and, more importantly, the nominal two-way shear strength provided by the concrete at the critical section around the columns. Cost analyses show that the cost of a flat plate system with a concrete strength greater than 4,000 psi is greater than the cost of one with a compressive strength of 4,000 psi, even when reductions in thickness and/or reinforcement are taken into consideration for the systems with the higher strength concrete. Therefore, for live loads of 100 psf and greater, the most cost-effective solution is to use a slab thickness equal to the minimum required for strength and a concrete compressive strength equal to 4,000 psi. The use of shear studs to counteract the effects of two-way shear stresses is discussed in Chapter 4 of this Guide.

Panel Aspect Ratio Effects The aspect ratio of a slab panel is defined as the larger dimension of the panel divided by the smaller dimension of the panel, measured center-to-center of supports. Where the aspect ratio exceeds 2, the slab acts primarily as a one-way slab spanning in the short direction. As discussed above, the minimum slab thickness is dependent on the clear span length. The slab thickness requirement is the same in both directions for square bays. For an aspect ratio other than 1, the longer span will dictate the slab thickness, resulting in a loss of economy. A floor system that contains rectangular bays with an aspect ratio of 2 costs approximately 30% more than one with an aspect ratio of 1, for the same overall floor area. Unless column layout is dictated by architectural or other functional requirements, square bays should be used because they provide the most economical layout.

Summary Flat plate systems are economically viable for short to medium spans and for moderate live loads. The deflection criteria usually govern up to live loads of about 40 psf, and the economical span length range is 15 to 30 ft. For live loads of 100 psf or more, two-way shear stresses at the columns and

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures Tables 2.6, 2.7, and 2.8 contain material quantities and cost indices for flat plate systems with live loads of 40, 65, and 100 psf, respectively.

bending moments in the slab control the design. For these cases, the flat plate is economical for spans between 15 and 25 ft.

Table 2.6 Material Quantities and Cost Indices for Flat Plate Floor Systems, LL = 40 psf Bay Size (ft)

Slab Thickness (in.)

Square Column Size (in.)

Concrete (ft3/ft2)

Reinforcement (psf)

Formwork (ft2/ft2)

Cost Index

15 w 15

6.0

12

0.50

1.62

1.00

0.78

15 w 20

7.5

14

0.63

1.89

1.00

0.83

20 w 20

7.5

16

0.63

1.92

1.00

0.83

20 w 25

9.5

18

0.79

2.35

1.00

0.91

25 w 25

9.5

22

0.79

2.45

1.00

0.91

Table 2.7 Material Quantities and Cost Indices for Flat Plate Floor Systems, LL = 65 psf Bay Size (ft)

Slab Thickness (in.)

Square Column Size (in.)

Concrete (ft3/ft2)

Reinforcement (psf)

Formwork (ft2/ft2)

Cost Index

15 w 15

6.0

14

0.50

1.71

1.00

0.78

15 w 20

7.5

16

0.63

1.99

1.00

0.84

20 w 20

7.5

20

0.63

2.07

1.00

0.84

20 w 25

9.5

22

0.79

2.50

1.00

0.92

25 w 25

9.5

26

0.79

2.61

1.00

0.92

Table 2.8 Material Quantities and Cost Indices for Flat Plate Floor Systems, LL = 100 psf Bay Size (ft)

Slab Thickness (in.)

Square Column Size (in.)

Concrete (ft3/ft2)

Reinforcement (psf)

Formwork (ft2/ft2)

Cost Index

15 w 15

6.0

16

0.50

1.88

1.00

0.79

15 w 20

7.5

18

0.63

2.17

1.00

0.85

20 w 20

7.5

24

0.63

2.31

1.00

0.85

20 w 25

9.5

26

0.79

2.75

1.00

0.93

25 w 25

9.5

30

0.79

2.94

1.00

0.94

2.3.4 Flat Slab System Overview A flat slab floor system is similar to a flat plate floor system, with the exception that the flat slab has thickened portions around the columns called drop panels (see Fig. 2.7). The primary purpose of the drop panels is to increase the nominal two-way shear strength of the concrete at the critical section around the columns. The flat slab system has the advantages of relatively simple construction and formwork, low floorto-floor heights, and a relatively flat ceiling, which allows an architectural finish to be applied directly to the underside of the slab. This system is primarily used in buildings with moderate to heavy loads, such as office buildings, hospitals, and warehouses. Fig. 2.7 Flat Slab.

Concrete Reinforcing Steel Institute

2-9

Design Guide for Economical Reinforced Concrete Structures To achieve formwork economy, standard lumber dimensions should be used to form the drop panels. Table 2.9 contains drop panel heights based on actual lumber dimensions and 3/ -in.-thick formwork sheathing. Using other depths will un4 necessarily increase formwork costs.

Fig. 2.8 Minimum Drop Panel Dimensions.

Minimum Slab Thickness and Drop Panel Dimensions Minimum slab thickness requirements for flat slabs are given in ACI Table 8.3.1.1. The minimum thickness of exterior and interior panels of slabs with drop panels defined in ACI 8.2.4, without edge beams, and containing reinforcement with a yield strength of 60,000 psi is equal to Cn 33 and Cn 36, respectively, where Cn is the length of the clear span in the long direction. It is evident that the minimum thickness of flat slabs is 10% less than that required for flat plates; this is primarily due to the decrease in deflection from the addition of the drop panels around the columns. In no case should the slab thickness be less than 4 in. Minimum dimensions for drop panels are given in ACI 8.2.4. The drop panel should extend in each direction from the centerline of the support a distance not less than one-sixth of the span length measured from center-to-center of supports in that direction (see Fig. 2.8). Also, the projection of the drop panel below the slab should be at least one-quarter of the slab thickness. The minimum slab thickness must be increased by 10% if drop panel dimensions are provided that do not conform to these provisions. Table 2.9 Drop Panel Height for Formwork Economy

In the preliminary design stage, a slab thickness is chosen based on the minimum thickness requirements of ACI Table 8.3.1.1. The plan dimensions of the drop panel are then determined based on the minimum lengths specified in ACI 8.2.4. Two-way shear stresses at the critical section around the column should be checked for a minimum drop depth of 2.25 in. If this proves to be inadequate, the next larger drop depth (4.25 in.) should be used until the shear strength requirements are satisfied. According to ACI 22.6.4, shear stresses must be checked at the critical sections around the columns and the drop panels.

Live Load Effects The material quantities for a flat slab are typically controlled by deflections. Therefore, an increase in live loads will not cause a proportional increase in costs. Flat slab systems subjected to live loads of 100 psf are usually 3 to 7% more expensive than those with live loads of 40 psf.

Panel Aspect Ratio Effects Square bay sizes with an aspect ratio equal to 1 represent the most economical floor layout because the required minimum slab thickness is the same in both directions. A rectangular bay with an aspect ratio of 1.2 is about 17% more expensive than a square bay with the same floor area.

Summary Flat slab systems are economically viable for medium spans and for moderate to heavy live loads. For a live load of 65 psf or less, flat slabs are cost-effective for span lengths between 30 ft and 35 ft. The economical range is 25 ft to 35 ft for a live load of 100 psf. Although the drop panels result in somewhat higher formwork costs, a relatively shallow slab system is achieved in situations where two-way shear stresses would otherwise preclude the use of a flat plate. Tables 2.10, 2.11, and 2.12 contain material quantities and cost indices for flat slab systems with live loads of 40, 65, and 100 psf, respectively.

Standard Lumber Dimensions and Drop Panel Height Lumber Size Nominal

Actual

Drop Panel Height, h1*

2x

11/2"

21/4"

4x

31/

2"

41/4"

6x

51/2"

61/4"

8x

71/4"

8"

* 3/4"-inch form sheathing

2-10

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures Table 2.10 Material Quantities and Cost Indices for Flat Slab Floor Systems, LL = 40 psf Drop Size

Bay Size (ft)

Slab Thickness (in.)

L w W (ft)

20 w 20

7.0

7w7

8.5

81/

20 w 25 25 w 25

8.5

7w 81/

2

81/

2

w

81/

2

Concrete (ft3/ft2)

Reinforcement (psf)

Formwork (ft2/ft2)

Cost Index

2.25

14

0.61

2.01

1.01

0.84

2.25

16

0.73

2.23

1.01

0.89

2.25

18

0.73

2.36

1.01

0.90

4.25

20

0.92

2.82

1.02

0.99

25 w 30

10.5

30 w 30

10.5

10 w 10

4.25

24

0.92

2.99

1.02

0.99

30 w 35

12.0

10 w 12

4.25

26

1.04

3.44

1.02

1.06

35 w 35

12.0

12 w 12

4.25

30

1.05

3.69

1.01

1.07

2

w 10

h1 (in.)

Square Column Size (in.)

Table 2.11 Material Quantities and Cost Indices for Flat Slab Floor Systems, LL = 65 psf Bay Size (ft)

Slab Thickness (in.)

20 w 20 20 w 25 25 w 25 25 w 30

Drop Size L w W (ft)

h1 (in.)

Square Column Size (in.)

Concrete (ft3/ft2)

Reinforcement (psf)

Formwork (ft2/ft2)

Cost Index

7.0

7w7

2.25

16

0.61

2.15

1.01

0.85

8.5

81/

2.25

18

0.73

2.47

1.01

0.91

2.25

22

0.73

2.66

1.01

0.91

4.25

24

0.92

3.09

1.02

1.00

8.5 10.5

7w 81/

2

81/

w

2

2

81/

2

w 10

30 w 30

10.5

10 w 10

4.25

26

0.92

3.37

1.02

1.02

30 w 35

12.0

10 w 12

4.25

30

1.05

3.76

1.02

1.08

35 w 35

12.0

12 w 12

4.25

34

1.05

4.09

1.01

1.09

Table 2.12 Material Quantities and Cost Indices for Flat Slab Floor Systems, LL = 100 psf Drop Size

Slab Thickness (in.)

L w W (ft)

h1 (in.)

Square Column Size (in.)

Concrete (ft3/ft2)

Reinforcement (psf)

Formwork (ft2/ft2)

Cost Index

20 w 20

7.0

7w7

2.25

20

0.61

2.44

1.01

0.87

20 w 25

8.5

81/

2.25

22

0.73

2.79

1.01

0.92

25 w 25

8.5

81/2 w 81/2

2.25

26

0.73

3.08

1.01

0.94

25 w 30

10.5

81/2 w 10

4.25

28

0.92

3.47

1.02

1.02

30 w 30

10.5

10 w 10

4.25

32

0.92

3.85

1.02

1.04

30 w 35

12.0

10 w 12

4.25

34

1.06

4.22

1.02

1.10

35 w 35

12.0

12 w 12

6.25

40

1.07

4.68

1.02

1.14

Bay Size (ft)

7w

2

2.3.5 Two-way Joist System Overview A two-way joist system, which is also commonly referred to as a waffle slab, consists of evenly spaced concrete joists spanning in both directions and a reinforced concrete slab cast integrally with the joists (see Fig. 2.9). The floor system is formed with domes that are 30, 41, and 52 in. wide, resulting in 3-, 4-, and 5-ft modules, respectively. Systems with a 3-ft module are considered in this Guide. A solid slab section around the columns is usually provided for two-way shear resistance. Fig. 2.9 Two-way Joist (Waffle Slab). Concrete Reinforcing Steel Institute

2-11

Design Guide for Economical Reinforced Concrete Structures The main advantages of this type of system are that they are economical for long spans with heavy loads, the dome voids reduce the dead load, and electrical fixtures or other items can be placed in the voids. It is common for these systems to be exposed so architectural finishes are usually not required, which results in cost savings. Two-way joist systems are commonly used in office buildings, warehouses, libraries, civic buildings, and industrial plants.

Member Sizes The thickness of the slab is controlled by either structural or fire resistance requirements. In most cases, the thickness is governed by the latter. Specifying a lightweight aggregate may be advantageous in certain situations. A normal-weight slab with a 4.5-in. thickness is used in all cases considered in this Guide. The standard joist width is 6 in. for a 3-ft module. Because slab thickness is controlled by fire resistance requirements and joist width is set by industry standards, the only geometric variable to be determined is joist depth. Standard dome depths for the 3-ft module are 8, 10, 12, 14, 16, 20 and 24 in. For design purposes, waffle slabs are considered as flat slabs with the solid heads acting as drop panels. Thus, the minimum thickness of exterior and interior panels of two-way slabs with drop panels defined in ACI 8.2.4, without edge beams, and containing reinforcement with a yield strength of 60,000 psi is equal to Cn33 and Cn36, respectively, where Cn is the length of the clear span in the long direction. In no case should the slab thickness be less than 4 in. To determine the deflection requirements, the cross-section of the actual floor system is transformed into an equivalent section of uniform thickness. This is accomplished by determining a slab thickness that provides the same moment of inertia as the two-way joist section. Table 2.13 contains the equivalent slab thickness for the standard domes depths of a 3-ft module waffle slab.

In the tables in the Summary section below, the second to last column contains the dome area percentage, which is the percentage of the floor area that requires dome formwork.

Live Load Effects Because material quantities are typically controlled by deflection constraints, an increase in live load does not have a proportionate impact on costs. Waffle slabs with live loads of 100 psf are typically only 3 to 7% more expensive than those with live loads of 40 psf.

Panel Aspect Ratio Effects Square bay sizes are the most cost-effective because the deflection requirements are the same in both directions. A rectangular bay with an aspect ratio of 2 is about 15% more expensive than a square bay with the same floor area.

Summary Two-way joist systems are economically viable for long spans and heavy loads. Systems with 3-ft modules are usually economical for spans ranging from 40 to 50 ft and beyond. Tables 2.14, 2.15, and 2.16 contain material quantities and cost indices for two-way joist systems with live loads of 40, 65, and 100 psf, respectively.

Table 2.13 Equivalent Slab Thickness for Two-way Joists with a 3-ft Module Dome Depth (in.)

Rib Width (in.)

Equivalent Slab Thickness (in.)

8

6

8.8

2-12

10

6

10.3

12

6

11.7

14

6

13.1

16

6

14.6

20

6

17.4

24

6

20.2

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures Table 2.14 Material Quantities and Cost Indices for Two-way Joist Floor Systems, LL = 40 psf Bay Dome Size (ft) Depth (in.)

Solid Head

Square Column Size (in.)

Concrete (ft3/ft2)

Reinforcement (psf)

Dome Area (%)

Cost Index

30 w 30

10

12'-6" w 12'-6"

24

0.81

1.97

84

1.11

36 w 36

14

14'-6" w 14'-6"

28

0.98

2.37

86

1.19

36 w 42

16

14'-6" w 16'-6"

30

1.09

2.75

86

1.24

42 w 42

16

16'-6" w 16'-6"

30

1.10

2.91

86

1.26

48 w 48

20

18'-6" w 18'-6"

32

1.30

3.85

85

1.37

51 w 51

20

20'-6" w 20'-6"

38

1.27

4.07

86

1.37

Table 2.15 Material Quantities and Cost Indices for Two-way Joist Floor Systems, LL = 65 psf Bay Dome Size (ft) Depth (in.)

Solid Head

Square Column Size (in.)

Concrete (ft3/ft2)

Reinforcement (psf)

Dome Area (%)

Cost Index

30 w 30

10

12'-6" w 12'-6"

24

0.81

2.12

84

1.12

36 w 36

14

14'-6" w 14'-6"

28

0.98

2.83

86

1.21

36 w 42

16

14'-6" w 16'-6"

30

1.09

2.94

86

1.25

42 w 42

16

16'-6" w 16'-6"

32

1.10

3.11

86

1.27

48 w 48

20

18'-6" w 18'-6"

38

1.31

4.04

85

1.38

51 w 51

20

20'-6" w 20'-6"

44

1.28

4.24

86

1.38

Table 2.16 Material Quantities and Cost Indices for Two-way Joist Floor Systems, LL = 100 psf Bay Dome Size (ft) Depth (in.)

Solid Head

Square Column Size (in.)

Concrete (ft3/ft2)

Reinforcement (psf)

Dome Area (%)

Cost Index

30 w 30

10

12'-6" w 12'-6"

26

0.81

2.85

84

1.16

36 w 36

14

14'-6" w 14'-6"

30

0.98

3.05

86

1.22

36 w 42

16

14'-6" w 16'-6"

34

1.09

3.13

86

1.26

42 w 42

16

16'-6" w 16'-6"

38

1.10

3.96

86

1.31

48 w 48

20

18'-6" w 18'-6"

44

1.31

4.28

85

1.40

51 w 51

20

20'-6" w 20'-6"

50

1.28

5.30

86

1.44

Concrete Reinforcing Steel Institute

2-13

Design Guide for Economical Reinforced Concrete Structures

CHA PTER 3 One-way Slabs 3.1 Overview Guidelines and recommendations on the economical design and detailing of one-way slabs are contained in this chapter. Information is provided on determining the thickness of the slab and detailing the flexural reinforcement. Shear reinforcement is typically not provided in one-way slabs. The design shear strength can be increased by providing a thicker slab and/or by increasing the compressive strength of the concrete, with the former being the most efficient solution in cases where more than a relatively small amount of additional shear strength needs to be provided. Because one-way slab systems are usually not part of the seismic force-resisting system (SFRS), the following requirements and guidelines are essentially applicable for one-way slabs in buildings assigned to any SDC.

3.2 Determining the Slab Thickness The thickness of a one-way slab is usually determined initially based on the minimum thickness requirements in ACI 7.3.1. ACI Table 7.3.1.1 contains the minimum thickness h that must be provided as a function of the support conditions and the span length of the slab for normal-weight concrete and Grade 60 reinforcement in situations where the slab is not supporting or attached to partitions or other construction likely to be damaged by large deflections. For the usual case of continuous construction, the depth of the slab must be the same for all spans and it should be determined on the basis of the span that yields the largest minimum depth. Specifying more than one slab depth results in formwork that is not economical. It is also important to consider fire resistance requirements when specifying a slab thickness, especially for one-way slabs that are supported by joists, which are spaced relatively closely together. It is possible in certain cases that the required slab thickness based on fire resistance requirements needs to be greater than the minimum slab thickness determined by ACI Table 7.3.1.1 for serviceability.

to limit the size the flexural crack widths. Finally, a minimum amount of concrete cover is needed to protect the bars from the effects of fire, weather, and corrosive environments, to name a few. The flexural reinforcement must be properly developed or anchored on both sides of a critical section. This ensures that the one-way slab system will perform as intended in accordance with the strength design method. Temperature and shrinkage reinforcement in accordance with ACI 24.4.3 must be provided perpendicular to the main flexural reinforcement. ACI Table 24.4.3.2 contains minimum reinforcement ratios to counteract temperature and shrinkage stresses and ACI 24.4.3.3 stipulates the maximum spacing of such reinforcement.

3.3.2 Concrete Cover Reinforcing bars are placed in a concrete member with a minimum concrete cover to protect it from weather, fire, and other effects. Minimum cover requirements for nonprestressed, cast-in-place concrete members are given in ACI Table 20.6.1.3.1. For one-way slabs, concrete cover is measured from the surface of the concrete to the outer edge of the longitudinal reinforcement. Drip grooves or drip edges along the edge of a slab soffit can cause issues related to the required cover to the longitudinal reinforcement. These grooves are usually formed using a form chamfer strip or a one-inch piece of dimension lumber nailed to the formwork deck near the slab edge. There are essentially two ways to maintain the required concrete cover in such cases (Reference 6): (1) offset the bars crossing the groove (see Fig. 3.1a) and (2) relocate the transverse and longitudinal layers of reinforcing bars so that the affected reinforced bar (shown as an open circle in Fig. 3.1b) can be moved away from the groove, thereby maintaining the required minimum cover.

3.3 Detailing Requirements and Guidelines for Flexural Reinforcement 3.3.1 Overview Once the required area of flexural reinforcement has been determined for the factored bending moments along the span length using the strength design method, the size of reinforcing bars must be chosen to provide an area of steel that is greater than or equal to the amount that is required. Additionally, minimum spacing between the flexural bars must be provided so that concrete can adequately flow in the voids between the bars. A maximum spacing between the flexural bars is required

Concrete Reinforcing Steel Institute

Fig. 3.1 Slab with Drip Groove at Edge of Soffit (a) Cover is Maintained at Drip Groove by Offsetting the Bottom Longitudinal Bars (b) Cover is Maintained at Drip Groove by Relocating Longitudinal Bars.

3-1

Design Guide for Economical Reinforced Concrete Structures Layering of the top steel in the slab over intersecting beams that are supporting the slab can create constructability issues for the detailer and placer. More information on this topic can be found in Section 5.3.2 of this Guide.

3.3.3 Distribution of Flexural Reinforcement for Crack Control Requirements for the distribution of flexural reinforcement in one-way slabs (which are also applicable to beams) are given in ACI 24.3. The intent of these requirements is to control flexural cracking: a larger number of fine cracks are preferable to a few wide cracks mainly for reasons of durability and appearance. A simple approach to address crack control in flexural members is given in ACI 24.3.2. The maximum center-to-center bar spacing s determined by the equations in ACI Table 24.3.2 for deformed bars is specifically meant to control cracking:

 40,000 
40,000  s = 15  
2.5cc
12    fs   fs  In this equation, fs is the calculated stress in the flexural reinforcement closest to the tension face of the section caused by the service loads. Note that it is permitted to take fs equal to 2fy /3. The term cc is related to the clear cover of the reinforcement and is defined as the least distance from the surface of the reinforcement to the tension face of the member. For Grade 60 bars with cc " 0.75 in. (minimum specified cover in ACI Table 20.6.1.3.1 for concrete that is not exposed to weather or in contact with the ground), the longitudinal reinforcing bars must be spaced no greater than 12 in. on center in order to satisfy crack control requirements. This value is generally less than the maximum spacing prescribed in ACI 7.7.2.3. Note that s is independent of the size of the flexural bars.

are contained in ACI 7.7.3. Provided in these sections are required development lengths and termination locations for the flexural bars. Development of flexural reinforcement must occur at the following critical sections in a one-way slab: (1) points of maximum stress, that is, sections of maximum bending moment and (2) locations where adjacent reinforcement is terminated. Development length or anchorage of reinforcement is required on both sides of a critical section. In continuous one-way slabs subjected to uniform loads, the maximum positive and negative bending moments typically occur near the midspan and at the faces of the supports, respectively. Positive and negative flexural reinforcing bars must be developed or anchored on both sides of these critical sections. For cost savings, it is common for some of the reinforcing bars to be terminated (or cut off) at locations away from the critical sections. For example, reinforcing bars are no longer required past a point of inflection on the bending moment diagram. Also, a portion of the bars can be theoretically cut off prior to the point of inflection at a location where the continuing bars are adequate to supply the required design strength. Because a critical section occurs at a cutoff point, the bars must be properly developed at that location as well. Recommended flexural reinforcement details for one-way slabs are given in Fig. 3.2, which is adapted from Reference 7. The bar lengths in the figures are based on one-way slabs subjected to uniformly distributed gravity loads. Adequate bar lengths must be determined by calculation for members subjected to the effects from other types of gravity loads. The bar lengths in these figures can also be used for one-way slabs that have been designed using the approximate bending moment coefficients given in ACI Table 6.5.2.

3.3.4 Minimum Spacing of Flexural Reinforcement Spacing limits for nonprestressed reinforcing bars in a horizontal layer are given in ACI 25.2.1. In particular, the clear spacing between the bars must be at least the greatest of the following: 1 in., the diameter of the reinforcing bar, and (4/3) times the diameter of the largest aggregate in the concrete mix. These limits have been established primarily so that concrete can flow readily into the spaces between adjoining reinforcing bars and between reinforcing bars and formwork. Concrete must fully surround the reinforcing bars without honeycombing so that a good bond is established between the concrete and the steel.

3.3.5 Development of Longitudinal Reinforcement, Flexural Cutoff Points, and Splices Development of Flexural Reinforcement and Cutoff Points Flexural reinforcement must be properly developed or anchored in a one-way slab in order for it to perform as intended in accordance with the strength design method. General requirements for development of reinforcement are given in ACI 25.4 and provisions for positive and negative flexural reinforcement in one-way slabs

3-2

Fig. 3.2 Recommended Flexural Reinforcement Details for One-way Slabs.

Splices ACI 25.5 contains the requirements for lap splices, which, as noted in Section 1.3.3, are typically the most economical type of splice. Tension lap splices must be provided for flexural reinforcement, and a consistent lap splice length should be specified for a given bar size. Lap splice length is determined based on the concrete strength, the grade of the reinforcement, and the reinforcing bar size, location, and spacing. Lap splice requirements for one-way slabs are essentially the same as those for beams (see Section 5.3.5 of this Guide for more information).

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures

Fig. 4.1 Minimum Slab Thickness for Two-way Slabs without Interior Beams with Grade 60 Reinforcement.

CHA PTER 4 Two-way Slabs 4.1 Overview Guidelines and recommendations on the economical design and detailing of two-way slabs are contained in this chapter. Information is provided on determining the thickness of the slab and detailing the reinforcement for the effects of flexure and shear. Specific requirements for two-way slab systems without beams that are part of the SFRS in structures assigned to SDC C are given in Section 4.5.

4.2 Determining the Slab Thickness The first step in the design of a two-way slab system is to determine a preliminary slab thickness. A minimum slab thickness must be provided to control deflections and to provide adequate shear strength, where applicable. Serviceability requirements for two-way slab systems with nonprestressed reinforcement are given in ACI 8.3.1. ACI Table 8.3.1.1 contains minimum thicknesses for two-way slabs without interior beams in systems without drop panels (flat plates) and with drop panels (two-way slabs). Also given in this table are minimum thicknesses for these systems where exterior panels have an edge beam present and where they do not. Where beams are present on all sides of a panel, the minimum thickness is given in ACI Table 8.3.1.2. Figure 4.1 provides a summary of the minimum slab thickness requirements for two-way slabs without interior beams. For two-way slab systems without beams, the minimum slab thickness that is required is often controlled by the two-way shear stresses that occur in the slab around the perimeter of the columns. Edge columns can be subjected to the largest shear stresses in the entire two-way system. Because two-way shear requirements are related to flexural requirements (the assumed distribution of shear stress around the critical section of a column includes the effects of unbalanced moments at a support), a slab thickness that satisfies both sets of requirements cannot be Concrete Reinforcing Steel Institute

Fig. 4.2 Preliminary Slab Thickness for Flat Plates. obtained unless some simplifying assumptions are made. Figure 4.2, which is adapted from Reference 7, can be used to obtain a preliminary slab thickness for flat plates. The information in the figure is based on the following assumptions: • Square edge column of size bending perpendicular to the slab edge with a three-sided critical section • Column supporting a tributary area A • Square bays • Gravity load moment transferred between the slab and the edge column in accordance with the Direct Design Method requirement of ACI 8.10 • 4,000 psi normal-weight concrete

4-1

Design Guide for Economical Reinforced Concrete Structures The term qu is the total factored load, which must include an estimate of the slab weight; this weight can be estimated based on a slab thickness determined from the serviceability requirements. The ratio d/c1 is determined from Fig. 4.2 as a function of qu and the area ratio A/c12. A preliminary slab thickness h can be obtained by adding 1.25 in. to d acquired from the figure. The purpose of this design aid is to help decrease the number of iterations that are needed to establish a viable slab thickness based on shear strength requirements; it is not meant to replace shear strength calculations. It is common that the slab thickness determined based on strength and serviceability requirements will satisfy fire resistance requirements for typical residential and office occupancies. There is usually no need to increase the slab thickness to achieve a required fire rating in such cases.

how to provide the required cover is given in Section 3.3.2 for one-way slabs, which is also applicable to two-way slabs.

4.3.3 Minimum and Maximum Bar Spacing The minimum and maximum spacing of the flexural reinforcement in two-way slabs is given in ACI 8.7. As in the case of one-way slabs and beams, the minimum clear spacing is the greatest of 1 in., the diameter of the flexural bar, and (4/3) times the maximum aggregate size (ACI 25.2.1). For nonprestressed solid slabs, the maximum center-to-center spacing of the flexural reinforcement is the lesser of 2 times the overall slab thickness and 18 in. This limitation helps control cracking and provides for the possibility of loads concentrated on small areas of the slab.

The depth of the slab must be the same for all spans and it should be determined on the basis of the span that yields the largest minimum depth based on serviceability and shear strength requirements. Specifying more than one slab depth results in formwork that is not economical.

When selecting the size of the reinforcing bars, the largest bar size that will satisfy strength and serviceability requirements will usually provide overall economy. The spacing of the top bars should be limited to account for construction traffic. It is recommended that not less than #4 bars spaced at 12 in. on center be used to avoid displacement of the top bars.

4.3 Detailing Requirements and Guidelines for Flexural Reinforcement

4.3.4 Corner Reinforcement

4.3.1 Overview Once the required area of flexural reinforcement has been determined in the column strips and middle strips for the factored bending moments along the span length using the strength design method, the size of reinforcing bars must be chosen to provide an area of steel that is greater than or equal to the amount that is required. Additionally, minimum spacing between the flexural bars must be provided so that concrete can adequately flow in the voids between the bars. A maximum spacing between the flexural bars is required to limit the size the flexural crack widths. Finally, a minimum amount of concrete cover is needed to protect the bars from the effects of fire, weather, and corrosive environments, to name a few.

ACI 8.7.3 addresses exterior corners of slabs that are supported by stiff elements such as walls and edge beams. The presence of stiff elements restrains the lifting and causes additional bending moments at the exterior corners. Corner reinforcement must be provided at both the top and the bottom of the slab, and the reinforcement in each layer in each direction must be designed for a bending moment equal to the largest positive bending moment per unit width in the slab panel. The top and bottom reinforcement must be placed parallel and perpendicular to the diagonal, respectively, as shown in Fig. 4.3 for a distance of at least one-fifth of the longer of the two span lengths in the corner panel. Reinforcement parallel to the edges is permitted to be used instead of the diagonal bars (see Fig. 4.4). This layout is preferred because of ease in constructability compared to the other layout.

The flexural reinforcement must be properly developed or anchored on both sides of a critical section. This ensures that the two-way slab will perform as intended in accordance with the strength design method.

4.3.2 Concrete Cover Reinforcing bars are placed in a concrete member with a minimum concrete cover to protect it from weather, fire, and other effects. Minimum cover requirements for nonprestressed, castin-place concrete members are given in ACI Table 20.6.1.3.1. Like in the case of one-way slabs, concrete cover is measured from the surface of the concrete to the outer edge of the longitudinal reinforcement for two-way slabs without stirrups. Drip grooves or drip edges along the edge of a slab soffit can cause issues related to providing the required cover to the longitudinal reinforcement in two-way slabs. A discussion on

4-2

Fig. 4.3 Reinforcement Required at Corners of Slabs Supported by Stiff Edge Members.

Fig. 4.4 Alternative Reinforcement Layout at Corners of Slabs Supported by Stiff Edge Members. Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures 4.3.5 Development of Longitudinal Reinforcement, Flexural Cutoff Points, and Splices Development of Flexural Reinforcement and Cutoff Points Flexural reinforcement must be properly developed or anchored in a two-way slab in order for it to perform as intended in accordance with the strength design method. General requirements for development of reinforcement are given in ACI 25.4 and provisions for positive and negative flexural reinforcement in column and middle strips of two-way slabs are contained in ACI 8.7.4. Provisions for required development lengths and termination locations for the flexural bars are given in that section. Development of flexural reinforcement must occur at the following critical sections in a two-way slab in both the column and middle strips: (1) points of maximum stress, that is, sections of maximum bending moment and (2) locations where adjacent reinforcement is terminated. Development length or anchorage of reinforcement is required on both sides of a critical section. In continuous two-way slabs subjected to uniform loads, the maximum positive and negative bending moments in the column and middle strips typically occur near the midspan and at the faces of the supports, respectively. Positive and negative flexural reinforcing bars must be developed or anchored on both sides of these critical sections. For cost savings, it is common for some of the reinforcing bars to be terminated (or cut off) at locations away from the critical sections. For example, reinforcing bars are no longer required past a point of inflection on the bending moment diagram. Also, a portion of the bars can be theoretically cut off prior to the point of inflection at a location where the continuing bars are adequate to supply the required design strength. Because a critical section occurs at a cutoff point, the bars must be properly developed at that location as well. ACI Fig. 8.7.4.1.3a contains the minimum bar extensions in the column and middle strips in two-way slab systems without beams. These minimum lengths and extensions were developed for uniformly distributed gravity loads only; adequate bar lengths must be determined by calculation for members subjected to the effects from other types of gravity loads and/ or lateral loads from wind or earthquakes. The purpose of the structural integrity requirements of ACI 8.7.4.2 is to enable a two-way slab to span to adjacent supports should a single intermediate support be damaged or destroyed. Two continuous column strip bottom bars through a support are provided to give the slab some residual strength after two-way shear failure at a single support. Recommended flexural reinforcement details for two-way slabs subjected to uniform gravity loads are given in Fig. 4.5, which is adapted from Reference 7. Details for two-way slab systems without beams that are part of the SFRS are given in Section 4.5 of this Guide.

Concrete Reinforcing Steel Institute

Fig. 4.5 Recommended Flexural Reinforcement Details for Two-way Slabs.

Lap Splices ACI 25.5 contains the requirements for lap splices, which, as noted in Section 1.3.3, are typically the most economical type of splice. Tension lap splices must be provided for flexural reinforcement, and a consistent lap splice length should be specified for a given bar size. Lap splice length is determined based on the concrete strength, the grade of the reinforcement, and the reinforcing bar size, location, and spacing. Lap splices requirements for two-way slabs are essentially the same as those for beams (see Section 5.3.5 of this Guide for more information).

4.3.6 Guidelines for Detailing the Flexural Reinforcement The following guidelines are recommended when detailing the flexural reinforcement (Reference 8): 1.

Layering. It is important to identify which reinforcing bars are to be placed in the outer layers and which are to be placed in the inner layers. It is common for the reinforcement in the direction of the larger design moments be placed in the outer layers. A note or a section on the structural drawings can be provided to identify the inner and outer layers of flexural reinforcement.

2.

Spacing. Reinforcing bars that are required in addition to the main, uniformly-spaced reinforcing bars in the column and middle strips should have a spacing that is a multiple of that provided for the main bars. These bars need to be clearly identified on the structural drawings.

4-3

Design Guide for Economical Reinforced Concrete Structures

Fig. 4.7 Placement of Slab Reinforcement at Column-line Beams. Fig. 4.6 Placement of Reinforcement at Offset Columns.

3.

Offset columns. Where columns are offset in plan, the top and bottom reinforcing bars should be placed orthogonally, if possible (see Fig. 4.6). This minimizes constructability issues compared to skewed bars. If skewed bars are required, they should be provided only in a separate, bottom layer; the top bars should be placed orthogonally. Top bars in the middle strip should be centered on a line connecting the column center lines.

4.

Negative reinforcement at columns. In two-way slab systems without beams, the amount of negative reinforcement at the columns may need to be increased above that required for pure flexure to satisfy the requirements in ACI 8.4.2 pertaining to the portion of the unbalanced moment transferred by flexure at the slabcolumn joint. This additional reinforcement needs to be clearly documented on the structural drawings. Where required, the additional bars are usually provided in the columns strip directly over the column while maintaining the typical bar spacing for the columns strip bars.

5.

Beams. The location of the slab top reinforcement must be clearly indicated on the structural drawings where column-line beams are present. Because the minimum cover to the slab bars is smaller than that of the beam bars, the slab bars are typically placed above the top bars in the beam in the same plane as the beam stirrups (see Fig. 4.7).

The total area of reinforcement in a panel without an opening must be preserved in both directions of a panel with an opening. In other words, any reinforcement that is interrupted by an opening must be replaced on each side of the opening.

4.4 Detailing Requirements and Guidelines for Shear Reinforcement 4.4.1 Overview According to ACI 8.4.3 and 8.4.4, both one-way and two-way shear strength requirements must be satisfied for any two-way slab system supported directly on columns. One-way shear rarely governs; in most cases, two-way shear is more critical.

4.3.7 Openings in Slab Systems ACI 8.5.4.1 permits openings of any size in two-way slab systems provided that an analysis of the system with the openings is performed that shows that all applicable strength and serviceability requirements of the Code are satisfied. For slabs without beams, such an analysis is waived when the provisions of ACI 8.5.4.2 are met. These provisions are illustrated in Fig. 4.8, which is adapted from Reference 7.

4-4

Fig. 4.8 Openings in Slab Systems Without Beams (ACI 8.5.4).

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures In cases where the two-way shear strength of the slab is not adequate and where other means to increase shear strength are not practical or feasible (for example, specifying a thicker slab or a larger column, introducing column-line beams, or providing drop panels or shear caps), it is permitted to supplement shear strength by providing one of the following types of reinforcement (see ACI Fig. R8.7.6(a)-(c)): 1.

Single- or multiple-leg stirrups

2.

Shearheads

3.

Headed shear studs

Requirements for stirrups and headed shear studs are given in the following sections. Although once popular, shearheads and column capitals are rarely used anymore because they are not cost effective.

4.4.2 Single- or Multiple-leg Stirrups Research has shown that the two-way shear strength of slabs can be increased by shear reinforcement consisting of properly anchored single- or multiple-leg stirrups fabricated from bars or wires. The use of such reinforcement is permitted provided that the effective depth of the slab d is greater than 6 in. but not less than 16 times the bar diameter of the shear reinforcement (ACI 22.6.7.1).

Fig. 4.10 Shear Studs at an Exterior Column used to Increase Punching Shear Capacity. Anchorage provisions for stirrups are given in ACI 25.7.1.3 for deformed reinforcing bars. For Grade 60 #5 stirrups and smaller and for Grade 40 #6 through #8 stirrups, anchorage is to be provided using a standard hook around the longitudinal reinforcement. For Grade 60 #6 through #8 stirrups the additional embedment length noted in that section must be provided in addition to the standard hooks. Table 5.4 in Section 5.4.3 of this Guide gives the minimum depth that is needed to develop Grade 60 #6 through #8 stirrups according to the provisions of ACI 25.7.1.3; it is evident from the table that these stirrups cannot be used in slabs of typical thickness that are found in buildings with typical occupancies. Illustrated in Fig. 4.9, which is adapted from Reference 7, are required details for closed stirrup shear reinforcement in twoway slabs.

4.4.3 Headed Shear Studs Tests have shown that shear reinforcement consisting of large headed studs welded to flat steel rails are effective in resisting two-way shear in slabs (see Fig. 4.10). Headed shear stud reinforcement can take the place of or can be used in conjunction with other means (drop panels, shear caps, etc.) to increase design shear strength. The base rail, which is set on chairs, is nailed to the formwork around the column. The size and spacing of the studs and the length of the base rail depends on the shear requirements. Sufficient concrete cover must be provided to protect the base rail and head from weather, fire, and other effects. ACI 20.6.1.3.5 contains the minimum cover requirements for headed shear stud reinforcement. In particular, the concrete cover for the base rail and heads must not be less than that required for the reinforcement in the slab. ACI Fig. R20.6.1.3.5 illustrates these concrete cover requirements for headed shear stud reinforcement in slabs with both top and bottom bars

Fig. 4.9 Details for Closed Stirrup Shear Reinforcement in Two-way Slabs.

Concrete Reinforcing Steel Institute

Illustrated in Fig. 4.11, which is adapted from Reference 7, are required details for headed shear stud reinforcement in twoway slabs.

4-5

Design Guide for Economical Reinforced Concrete Structures

Fig. 4.11 Details for Headed Shear Stud Reinforcement in Two-way Slabs.

Fig. 4.12 Flexural Reinforcement Details for Two-way Slabs Without Beams in Structures Assigned to SDC C.

4.5 Detailing Requirements and Guidelines for SDC C Two-way slabs without beams are permitted to part of an intermediate moment frame, which is the required SFRS for structures assigned to SDC C; they are not permitted to be part of the SFRS in SDC D, E, or F. All of the requirements and guidelines presented above are also applicable when such systems are part of the SFRS. In addition, the requirements in ACI 18.4.5 must be satisfied. Flexural reinforcement details based on these requirements are given in Fig. 4.12, which is adapted from Reference 7.

4-6

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures

CHA PTER 5 Beams 5.1 Overview Guidelines and recommendations on the economical design and detailing of beams are contained in this chapter. Information is provided on sizing the cross-section and detailing the reinforcement for the effects due to flexure, shear, and torsion and combinations thereof. Specific requirements for beams in intermediate moment frames (SDC C) and special moment frames (SDC D, E, and F) are given in Sects. 5.7 and 5.8 of this Guide, respectively.

5.2 Sizing the Cross-section 5.2.1 Beam Depth

Assuming f c’ " 4,000 psi, fy " 60,000 psi, and a reinforcement ratio W of approximately 50% of that corresponding to the reinforcement strain limit in ACI 9.3.3, the above equation for bw reduces to the following:

bw "

20M u d2

where Mu is in foot-kips and bw and d are in inches. Providing a beam width that is equal to or greater than the value from this equation will result in cross-sectional dimensions that satisfy both strength and serviceability requirements of ACI 318.

Establishing the dimensions of the cross-section is typically the initial step in the design of a reinforced concrete beam. The depth is usually determined first on the basis of deflection requirements (see ACI Table 9.3.1.1 and Section 2.2.2 of this Guide). This depth sometimes needs to be modified for constructability, economy, or architectural reasons, to name a few.

Because beams are part of a continuous floor and/or roof system, the largest factored bending moment Mu along the spans should be used in this equation. The beam width determined from the maximum Mu must be used for all spans; this will help in achieving economical formwork. Varying the amount of flexural reinforcement along the span lengths for different factored bending moments is by far more economical than varying the beam width (or depth).

It is important to consider economical formwork when choosing the depth of a beam. It is evident from ACI Table 9.3.1.1 that the minimum depth depends on the support conditions. For the usual case of continuous construction, the depth of the beam must be the same for all spans and it should be determined on the basis of the span that yields the largest minimum depth. More than one beam depth along the same line of beams results in formwork that is not economical. The same beam depth should be used not only throughout an entire floor/roof level but the entire structure as often as possible. In wide-module joist systems, the depth of the joists (beams) and the supporting beams (girders) must be the same for overall economy.

When selecting a beam width, it is also important to consider the width of the columns at the ends of the beam. Consider Cases A and B in Fig. 5.1. Greatest economy is achieved when the beam is as wide as or wider than the column: the formwork is much simpler compared to Case C where the beam is narrower than the column. Even though the formwork is simple where the width of the beam is the same as the column, it is good practice to have a wider beam to avoid interference between the longitudinal corner bars of the beam and the column corner bars. It is recommended to have a beam width that is at least 4 in. wider than the column it frames into. Beamside Form

5.2.2 Beam Width Once the overall depth of the beam has been established based on serviceability requirements and economy, the width of a beam can be determined by setting the design flexural strength KMn equal to the required flexural strength Mu for an assumed reinforcement ratio W. Using the basic principles of the strength design method, the required width bw can be calculated by the following equation:

Mu bw "
Rn d 2

Beam Bottom Plyform

A

B

C

Plan View

In this equation, K"0.9 for tension-controlled sections, d " distance from the extreme compression fiber to the centroid of the reinforcing steel, and Rn " nominal strength coefficient of resistance, which can be determined by the following equation:


0.59
f y   Rn "
f y 1
f c'  

Concrete Reinforcing Steel Institute

Isometric

Fig. 5.1 Selecting a Beam Width for Formwork Economy.

5-1

Design Guide for Economical Reinforced Concrete Structures 5.3 Detailing Requirements and Guidelines for Flexural Reinforcement

sures the beam will perform as intended in accordance with the strength design method.

5.3.1 Overview

5.3.2 Concrete Cover

Once the required area of flexural reinforcement has been determined for the factored bending moments along the span length using the strength design method, the number of reinforcing bars must be chosen to provide an area of steel that is equal to or greater than the amount that is required. It is important to ensure that the reinforcing bars will adequately fit within the cross-section of the beam.

Concrete protection for reinforcement plays an important role in the formulation of the requirements of bar spacing and bar development. Reinforcing bars are placed in a concrete member with a minimum concrete cover to protect it from weather, fire, and other effects. Minimum cover requirements for nonprestressed, cast-in-place concrete construction are given in ACI Table 20.6.1.3.1. For beams that have transverse reinforcement in the form of stirrups that enclose the main flexural reinforcing bars, concrete cover is measured from the surface of the concrete to the outer edge of the stirrups.

In general, the minimum and maximum number of reinforcing bars in a single layer is a function of the cover and spacing requirements given in ACI 318-14. Minimum spacing between the longitudinal bars needs to be provided so that concrete can adequately flow in the voids between the bars. A maximum spacing between the longitudinal bars is required to limit the size the flexural crack widths. Also, a minimum amount of concrete cover is needed to protect the bars from the effects of fire, weather, and corrosive environments, to name a few. The longitudinal reinforcement must also be properly developed or anchored on both sides of a critical section. This en-

A drip groove or edge in a beam soffit often times presents a problem in maintaining the required cover to the bars (see Reference 6 and Fig. 5.2a). It is not feasible to increase the concrete cover after the reinforcing bars in the beam have been detailed. Raising the stirrups from the bottom to achieve the required cover decreases the cover at the top (see Fig. 5.2b). The only practical solution is to measure the concrete cover from the drip groove and detail the stirrups accordingly, as shown in Fig. 5.2c. This will usually impact the overall depth of the beam and should be accounted for in design. Maintaining the proper concrete cover can also be challenging at beam intersections. In particular, layering of the top steel in the slab at such intersections can create constructability issues. The sequencing and layering of beam and slab top reinforcement can also create serious congestions issues (see Fig. 5.3). The following bar placing sequence is one way of avoiding the problems associated with this situation (see Reference 9):

Fig. 5.2 Beam Sections Showing Drip Groove at Bottom Soffit: (a) Inadequate Cover at Drip; (b) Shifting Reinforcing Cage to Maintain Adequate Cover at Drip Will Cause top Cover Problems; and (c) to Maintain Adequate Cover at all Locations, Stirrup Sizes may Need to be Changed. The Designer Must Consider the Effects of Shifting or Changing the Stirrups on Beam Capacity.

1.

Erect the reinforcement for the primary beams (bottom bars, stirrups, and top bars) as stand-alone cages and set in place.

2.

Place the stirrups (bottom pieces of two-piece stirrups) and the bottom bars for the secondary beams.

3.

Place the bottom bars for the slab (not depicted in Fig. 5.3 for clarity).

4.

Place the top bars and the top pieces of the two-piece stirrups for the secondary beams.

5.

Place the top bars for the slab.

5.3.3 Distribution of Flexural Reinforcement for Crack Control Requirements for the distribution of flexural reinforcement in beams (which are also applicable to one-way slabs; see Section 3.3.3 of this Guide) are given in ACI 24.3. As discussed in Section 3.3.3, the maximum center-to-center bar spacing s determined by the equations in ACI Table 24.3.2 for deformed bars is as follows (see Fig. 5.4): Fig. 5.3 Layering of Beam and Slab Reinforcing Bars can Create Sequencing Issues. Structural Drawings Should Designate Layer Locations and Concrete Covers.

5-2

 40,000 
40,000  s = 15  
2.5cc
12    fs   fs  Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures Table 5.1 Minimum Number of Reinforcing Bars Required in a Single Layer Bar Size

Beam Width (in.) 12 14 16 18 20 22 24 26 28 30 36 42 48

Fig. 5.4 – Maximum Spacing Requirements of Flexural Reinforcement.

In this equation, fs is the calculated stress in the flexural reinforcement closest to the tension face of the section caused by the service loads. Note that it is permitted to take fs equal to 2fy /3. The term cc is related to the clear cover of the reinforcement and is defined as the least distance from the surface of the reinforcement to the tension face of the member. For Grade 60 bars with cc " 2 in. (1.5 in. cover to a #4 stirrup), the longitudinal reinforcing bars must be spaced no greater than 10 in. on center in order to satisfy crack control requirements. Note that s is independent of the size of the flexural bars. On the basis of the information given in Fig. 5.4 and the discussion above, the following equation provides the minimum number of bars nmin required in a single layer to control cracking:

nmin =

#4

2

2

3

3

3

3

3

4

4

4

5

5

6

#5

2

2

3

3

3

3

3

4

4

4

5

5

6

#6

2

2

3

3

3

3

3

4

4

4

5

5

6

#7

2

2

3

3

3

3

3

4

4

4

5

5

6

#8

2

2

3

3

3

3

3

4

4

4

5

5

6

#9

2

2

3

3

3

3

3

4

4

4

5

5

6

#10

2

2

3

3

3

3

3

4

4

4

5

5

6

#11

2

2

3

3

3

3

3

4

4

4

5

5

6

5.3.4 Minimum Spacing of Flexural Reinforcement As noted in Section 3.3.4, spacing limits for reinforcing bars in a horizontal layer are given in ACI 25.2.1. The spacing requirements are summarized in Fig. 5.5 for beams where dagg is the nominal maximum aggregate size in the concrete mixture. The following equation provides the maximum number of bars nmax that can fit in a single layer on the basis of the spacing requirements of ACI 25.2.1:

nmax =

bw
2 (c s + d s + r ) +1 (clear space )+db

bw
2 (cc + 0.5db ) +1 s

The values of nmin determined by this equation should be rounded up to the next whole number. Note that a minimum of two bars are required to anchor the stirrups in beams. The minimum number of bars can be tabulated for various beam widths, as shown in Table 5.1. The information in this table is based on the following: • Grade 60 reinforcement • Overall reinforcing bar diameter given in Table 2.1 • Least distance from the surface of the reinforcement to the tension face of the member cc " 2 in. • Calculated stress in the flexural reinforcement closest to the tension face of the section, caused by the service loads fs " 40 ksi Providing at least the number of flexural reinforcing bars in Table 5.1 for a given beam width automatically satisfies the crack control requirements of ACI 24.3.2.

Concrete Reinforcing Steel Institute

Fig. 5.5 Spacing Limits of Flexural Reinforcement.

Values of nmax determined by this equation should be rounded down to the next whole number.

5-3

Design Guide for Economical Reinforced Concrete Structures Table 5.2 contains the maximum number of bars that can fit in a single layer for various beam widths. The information in this table is based on the following: • Grade 60 reinforcement. • Clear cover to the stirrups cs " 1.5 in. • Maximum aggregate size dagg " 3/4 in. • #3 stirrups are used for #4 to #6 longitudinal bars, and #4 stirrups are used for #7 and larger longitudinal bars Table 5.2 Maximum Number of Reinforcing Bars Permitted in a Single Layer Bar Size

Beam Width (in.) 12 14 16 18 20 22 24 26 28 30 36 42 48

#4

5

6

7

8

10 11 12 14 15 16 20 24 28

#5

4

5

7

8

9

10 11 13 14 15 19 22 26

#6

4

5

6

7

8

9

10 11 12 14 17 20 23

#7

3

4

5

6

7

8

9

10 11 12 15 18 21

#8

3

4

5

6

7

7

8

9

10 11 14 16 19

#9

3

4

4

5

6

7

8

8

9

10 12 15 17

#10

2

3

4

5

5

6

7

7

8

9

11 13 15

#11

2

3

3

4

5

5

6

7

7

8

10 11 13

Selecting the number of bars within the limits of Tables 5.1 and 5.2 provides automatic conformity with the ACI 318 requirements for cover and spacing given the assumptions noted above. As discussed in Section 1.3.3, using the largest practical bar sizes that satisfy both strength and serviceability requirements results in overall cost savings.

5.3.5 Development of Longitudinal Reinforcement, Flexural Cutoff Points, and Splices Development of Flexural Reinforcement and Cutoff Points Flexural reinforcement must be properly developed or anchored in a concrete beam in order for the member to perform as intended in accordance with the strength design method. General requirements for development of reinforcement are given in ACI 25.4 and provisions for positive and negative flexural reinforcement in nonprestressed beams are contained in ACI 9.7.3. Provided in these sections are required development lengths and termination locations for the flexural bars. Development of flexural reinforcement must occur at the following critical sections in a reinforced concrete beam: (1) points of maximum stress, that is, sections of maximum bending moment and (2) locations where adjacent reinforcement is terminated. Development length or anchorage of reinforcement is required on both sides of a critical section. In continuous beams subjected to uniform loads, the maximum positive and negative bending moments typically occur near the midspan and at the faces of the supports, respectively. Positive and negative flexural reinforcing bars must be

5-4

Fig. 5.6 Recommended Flexural Reinforcement Details for Beams. developed or anchored on both sides of these critical sections. For cost savings, it is common for some of the reinforcing bars to be terminated (or cut off) at locations away from the critical sections. For example, reinforcing bars are no longer required past a point of inflection on the bending moment diagram. Also, a portion of the bars can be theoretically cut off prior to the point of inflection at a location where the continuing bars are adequate to supply the required design strength. Because a critical section occurs at a cutoff point, the bars must be properly developed at that location as well. Recommended flexural reinforcement details for reinforced concrete beams are given in Fig. 5.6, which is adapted from Reference 7. Included are the structural integrity requirements of ACI 9.7. The bar lengths in the figures are based on members subjected to uniformly distributed gravity loads. Adequate bar lengths must be determined by calculation for members subjected to the effects from other types of gravity loads and lateral loads. The bar lengths in these figures can also be used for members that have been designed using the approximate bending moment coefficients given in ACI Table 6.5.2.

Lap Splices Splices of reinforcing bars are unavoidable in any reinforced concrete structure mostly because of transportation limitations. As noted in Section 2.2.3, lap splices are typically the most economical type of splice. ACI 25.5 contains the requirements for lap

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures splices. Tension lap splices must be provided for flexural reinforcement, and a consistent lap splice length should be specified for a given bar size. In a tension lap splice, the force in the reinforcing bars is transferred to the concrete by bond, which, in turn, transfers the force back to the adjacent reinforcing bars resulting in an essentially continuous line of reinforcement. As a result of this interaction, lap splice length is determined based on the concrete strength, the grade of the reinforcement, and the reinforcing bar size, location, and spacing. There are two types of tension lap splices: contact lap splices and noncontact lap splices. The reinforcing bars in a contact lap splice touch and are wired together (see Fig. 5.7a). This type of splice is preferred because the bars are secured together and less likely to displace during construction compared to a noncontact lap splice where the bars do not touch (see Fig. 5.7b). There is a limit on how far the bars can be separated in a noncontact lap splice: the transverse center-to-center spacing of noncontact spliced bars must not exceed the lesser of one-fifth the required lap splice length and 6 in. (ACI 25.5.1.3). Lap splice lengths of deformed bars in tension are given in ACI Table 25.5.2.1, and are a function of the tension development length of the bar Cd that is calculated in accordance with ACI 25.4.2.1(a). Class B tension splices are usually provided for beams. Tension splices should be confined with transverse reinforcement, and if possible, located in zones of low tensile stresses (for example, near inflection points). This is intended to help prevent splice failure at the end of the splice due to splitting tensile stresses in the concrete. The location of a lap splice is different for top and bottom bars. For continuous top bars, lap splices generally occur away from the supports, which are typically the sections of maximum negative moment. Such splices are usually located within the middle third of the span length. Similarly, for bottom bars, the splices should occur near the supports. Lapping of continuous bottom bars at supports often presents congestion and installation problems. Table 5.3, which is adapted from Reference 10, contains four splice arrangements for the bottom flexural bars along with their advantages and disadvantages based on constructability. In Arrangement No. 1, all of the bottom bars are spliced over the columns away from the section of maximum

Fig. 5.7 Contact and Noncontact Tension Lap Splices. Concrete Reinforcing Steel Institute

positive moment, which is common. This arrangement can result in the most congestion in the beam-column joint. Arrangement No. 2 consists of half of the bottom bars spliced on one side of the joint and the other half on the other side of the joint, while Arrangement No. 3 has all of the splices located on one side of the joint. Finally, Arrangement No. 4 shows splice bars that pass through the joint, which are spliced to the bottom bars on both sides of the joint. Even though this arrangement increases the amount of steel that is required, the cost of the additional steel may be more than offset by the savings in labor and other costs, so it may be the most costeffective arrangement in certain situations. In addition to constructability, the appropriate splice arrangement must be chosen based on structural requirements for a particular situation.

5.4 Detailing Requirements and Guidelines for Shear Reinforcement 5.4.1 Overview Shear reinforcement is provided in reinforced concrete beams to supplement the shear strength provided by the concrete. ACI 22.5.10 permits the following types of shear reinforcement: 1.

Stirrups, ties, or hoops perpendicular to the longitudinal axis of the member

2.

Welded wire reinforcement with wires located perpendicular to the longitudinal axis of the member

3.

Spiral reinforcement

4.

Inclined stirrups making an angle of at least 45 degrees with the longitudinal axis of the member and crossing the plane of the potential shear crack

5.

Longitudinal reinforcement that is bent an angle of 30 degrees or more with respect to the longitudinal axis of the member

The most commonly used type of shear reinforcement in beams is stirrups that are oriented perpendicular to the axis of the member and are anchored to the longitudinal flexural reinforcement. The following discussion focuses on this type of shear reinforcement.

5.4.2 Stirrup Configurations Illustrated in Fig. 5.8 is a two-legged U-stirrup, which is commonly utilized in reinforced concrete beams. Minimum inside bend diameters and standard hook geometry for stirrups are given in ACI Table 25.3.2.

Fig. 5.8 Two-legged U-stirrup.

5-5

Design Guide for Economical Reinforced Concrete Structures Table 5.3 Splice Arrangement for Bottom Bars in a Reinforced Concrete Beam Arrangement

Advantages

• Simplest to detail 1

LAP

• Suitable arrangement where beams are wider than columns

LAP

BEAM

• No additional reinforcing steel is required

Only continuous bottom bars are shown COLUMN

Disadvantages • Can cause significant congestion, especially where the beam and column have the same width and/or where a large amount of continuous reinforcement is required • Installation of single-bay preassembled beam cages is difficult • Installation of multiple-bay preassembled cages is virtually impossible • Detailing and preassembled cages are slightly more complex

• Congestion is eased with no splices over the columns 2

LAP

LAP

BEAM

LAP

LAP

• No additional reinforcing steel is required

Only continuous bottom bars are shown COLUMN

• Preassembled beam cages are longer and more difficult to install • Installation of multiple-bay preassembled cages is very difficult

• Detailing and preassembled cages are relatively simple

3

LAP

BEAM

• Preassembled cages pass through only one joint, which make them easier to install than Arrangement No. 1 even though both arrangements have the same length

LAP

Only continuous bottom bars are shown COLUMN

• It is important to ensure that the cages are oriented correctly if installation begins at the center of the beam and progresses both ways

• No additional steel is required • No congestion at columns because the splice bars that pass through the column are added later • Preassembled cages are the shortest of all the arrangements 4

LAP

LAP

BEAM

LAP

Only continuous bottom bars are shown COLUMN

LAP

• The preassembled cages are very easy to install because no bottom bars pass through the column during installation

• Additional steel is required

• Best arrangement for installation of multiple-bay preassembled cages

5-6

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures In general, the size and spacing of the stirrups depends on the magnitude of the factored shear force at the section under consideration. It is common for the maximum shear force to occur at the supports and to decrease in magnitude to zero near midspan. An intricate stirrup layout closely following the variation in the shear diagram is not a cost-effective solution. Small stirrup sizes at a close spacing require disproportionately high costs in labor for fabrication and placement. To achieve overall economy, larger stirrups at wider spacing (preferably the maximum spacing prescribed in ACI 318) should be provided, and the number of changes in the stirrup spacing along the span length should be kept to a minimum wherever practical.

Fig. 5.9 Beam Stirrup Configuration with Three Closed Stirrups Distributed Across the Beam Width.

As discussed in Section 5.2.2, beams should be wider than the columns that they frame in to. As floor systems become shallower, beams generally need to become wider. Proper stirrup detailing in wide beams is essential to ensure that the longitudinal flexural reinforcement and the stirrups are fully effective. Research has shown that locating stirrups solely around the perimeter of a wide beam is not efficient where the beams are subjected to a relatively high shear demand (Reference 11). Stirrup legs are required in the interior of a wide beam. Illustrated in Fig. 5.9 is a common stirrup configuration for a wide beam where three closed stirrups are provided. This configuration presents the following problems: 1.

2.

None of the stirrups traverse the full net width of the beam (the net width is defined as the gross width of the beam minus the required concrete cover on each side). Because of this, the overall width of the stirrup arrangement needs to be measured and verified in the field prior to installation. During installation, it is possible for the net width to change when the preassembled cage is hoisted into position by crane, which increases the risk that the provided cover will be less than that which is required. If the stirrups are built in place instead of preassembled, the closed, one-piece stirrups make it difficult to place all of the required longitudinal reinforcement in the beam. It is especially difficult to place large, long longitudinal bars through the stirrups when stirrup top bars are present.

Two alternate stirrup configurations are illustrated in Figs. 5.10 and 5.11. In both configurations, a single, open stirrup is provided that extends the full net width of the beam. A stirrup cap consisting of a horizontal bar with a 135-degree hook at one end and a 90-degree hook at the other end is provided at the top of the configuration, which also extends the full net width of the beam. Providing a full-width stirrup helps in maintaining the correct concrete cover and facilitates installation of the beam reinforcement: the longitudinal bars can easily be placed within the beam from the top prior to installation of the stirrup cap.

Concrete Reinforcing Steel Institute

Fig. 5.10 Alternate #1 Beam Stirrup Configuration.

Fig. 5.11 Alternate #2 Beam Stirrup Configuration.

The difference between the configurations in Figs. 5.10 and 5.11 occurs within the interior portion of the beam. In Fig. 5.10, two sets of identical U-stirrups with 135-degree hooks are shown symmetrically placed within the interior of the beam. Figure 5.11 shows one narrower U-stirrup nested inside a wider U-stirrup in the interior of the beam. Both of these configurations provide a cost-effective way of providing shear reinforcement for wide beams.

5.4.3 Development of Shear Reinforcement Like in the case of flexural reinforcement, it is essential to properly develop and anchor shear reinforcement in order for it to be fully effective, that is, for it to develop its full yield strength. Requirements for the development of stirrups are given in ACI 25.7.1 and are illustrated in Fig. 5.12. Note that stirrups are to be provided as close to the tension and compression faces of the member as cover requirements and other reinforcement in the section permits.

5-7

Design Guide for Economical Reinforced Concrete Structures Table 5.5 Minimum Beam Widths for Stirrup Development

Standard hook per ACI 25.3.2

Stirrup Size

h/2

h/2

• #5 stirrup bars and smaller • #6, #7 and #8 stirrup bars with fyt f 40,000 psi

• #6, #7 and #8 stirrup bars with fyt f 40,000 psi

Fig. 5.12 Anchorage Details for U-stirrups.

Each bend in the continuous portion of the U-stirrup must enclose a longitudinal bar and the ends of the stirrups must be anchored around the longitudinal bars using a standard hook defined in ACI 25.3.2 for #5 bar and smaller bars and #6 through #8 bars with fyt less than or equal to 40,000 psi. In addition to a standard hook, a minimum embedment length

(

equal to 0.014dbfyt /


f c'

)

must be provided between the

outside edge of the hook and the mid-height of the member where #6, #7, or #8 stirrups with fyt greater than 40,000 psi are utilized. This additional anchorage requirement takes into consideration that (1) it is not possible to bend a #6, #7, or #8 stirrup tightly around a longitudinal bar, and (2) a large force can exist in the larger stirrup bars with fyt # 40,000 psi. The beam height that must be provided to satisfy the development requirements of ACI 25.7.2.3 is controlled by the size of the stirrup bar that is used. Minimum beam heights that satisfy these requirements are given in Table 5.4 for #6, #7, and #8 stirrup bars. The information that is provided in the table is based on the following: • Normal-weight concrete • Grade 60 reinforcement • 1.5-in. cover to the stirrup hook In short, #6, #7, and #8 stirrups are not permitted to be used in beams with heights less than those listed in the table.

Beam Width bw (in.)

#3

10

#4

12

#5

14

#6

18

#7

20

#8

22

Provisions for closed stirrups formed from two U-stirrups are given in ACI 25.7.1.7. The legs of the stirrups must be lap spliced with a splice length of at least 1.3Cd but not less than 12 in. where the tension development length Cd is determined in accordance with ACI 25.4.2 (see Fig. 5.13). In cases where the required lap length cannot fit within a member that has a height of at least 18 in., these stirrups can still be used, provided that the force in each leg is equal to or less than 9,000 lb. Thus, for Grade 60 reinforcement, only a #3 stirrup satisfies this requirement (force in stirrup leg " 0.11 w 60,000 " 6,600 lb).

5.5 Detailing Requirements and Guidelines for Torsional Reinforcement 5.5.1 Overview Once a beam has cracked due to effects from a torsional moment, its torsional resistance is provided primarily by closed stirrups and longitudinal bars. In beams subjected to torsion, shear, and bending moments, the amounts of transverse reinforcement and longitudinal reinforcement required to resist all actions are determined using superposition (ACI 9.5.4.3). In other words, the required amounts of shear and torsion transverse reinforcement are added together as are the required amounts of flexural and torsional longitudinal reinforcement. It is important to note that only the two legs of the stirrups that are adjacent to the sides of the beam are effective for torsion; stirrup legs within the interior of the beam can resist the effects from shear but not from torsion. This is consistent with the thin-walled tube methodology that forms the basis of the torsional provisions in ACI 318.

Table 5.4 Minimum Beam Height to Accommodate #6, #7, and #8 Stirrups of Grade 60 Reinforcement Stirrup Size

Beam Height h (in.) Concrete Compressive Strength f 'c (psi) 3,000

4,000

5,000

6,000

#6

26

23

21

20

#7

30

27

24

22

#8

34

30

27

25

Similarly, to allow for bend radii at corners of U stirrups, the minimum beam widths given in Table 5.5 must be provided.

5-8

Fig. 5.13 Pair of U-Stirrups Forming a Closed Stirrup.

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures permitted in beams subjected to torsion because tests have shown that they are inadequate for resisting torsion due to a loss of bond when the concrete cover spalls. The spacing of the transverse reinforcement is limited to the smaller of ph /8 and 12 in. where ph is equal to the perimeter of the centerline of the closed stirrups (ACI 9.7.6.3.3).

5.5.3 Detailing Requirements and Guidelines for the Longitudinal Reinforcement Longitudinal torsional reinforcement must be developed at both ends for tension. Proper bar anchorage is especially important at the ends of a beam where high torsional moments commonly occur. Fig. 5.14 Transverse Reinforcement Detail for Torsion Where Spalling is Restrained.

5.5.2 Detailing Requirements and Guidelines for the Transverse Reinforcement Diagonal cracks can form around all faces of a beam when it is subjected to a torsional moment in excess of that which causes cracking. Consequently, closed stirrups conforming to ACI 25.7.1.6 perpendicular to the axis of the beam must be provided. It has been observed that the corners of beams subjected to torsion can spall off because of the inclined compressive stresses that occur at these locations. Thus, the transverse reinforcement must be properly anchored so that it performs as intended. Because spalling is essentially prevented in beams with a slab on one or both sides of the web, ACI 25.7.1.6(b) permits the transverse reinforcement to be anchored by standard 90-degree hooks like in the case for shear anchorage (see Fig. 5.14). The 90-degree hook for the beam shown in this figure is located on the side that is adjacent to the slab, which restrains spalling. ACI 25.7.1.6(a) requires that the transverse reinforcement be anchored by 135-degree hooks where spalling cannot be restrained (see Fig. 5.15). It has been observed that closed stirrups with 90-degree hooks fail when there is no restraint. Lapped U-stirrups, which are depicted in Fig. 5.13, are not

The following detailing requirements must be satisfied for longitudinal reinforcement for torsion (see Fig. 5.16 and ACI 9.7.5): 1.

Longitudinal reinforcement must be distributed around the perimeter of the closed stirrups at a maximum spacing of 12 in.

2.

At least one longitudinal bar is required in each corner of the stirrups.

3.

The diameter of the longitudinal bars must be greater than or equal to 0.042 times the transverse reinforcement spacing, but not less than 3/8 in.

Fig. 5.16 Detailing Requirements for Longitudinal Torsional Reinforcement.

Torsional reinforcement must be provided for a distance that is greater than or equal to bt  d beyond the point that it is theoretically required, where bt is the width of that part of the cross-section that contains the closed stirrups resisting torsion (ACI 9.7.5.3). This distance is larger than that used for shear reinforcement and flexural reinforcement because, as noted previously, torsional diagonal tension cracks develop in a helical form around a member.

5.5.4 Detailing Requirements and Guidelines for Combined Effects

Fig. 5.15 Transverse Reinforcement Detail for Torsion Where Spalling is Not Restrained.

Concrete Reinforcing Steel Institute

As was discussed in Section 5.5.1, for beams subjected to torsion, shear, and bending moments, the amounts of transverse reinforcement and longitudinal reinforcement required to resist all actions are determined using superposition. The

5-9

Design Guide for Economical Reinforced Concrete Structures more restrictive of the provisions associated with these combined effects must be satisfied.

Top Step In Beam

Raised Floor System

The following must be considered when detailing the reinforcement for combined effects: 1.

The most restrictive requirements for reinforcement spacing, cutoff points, and placement for torsion, shear, and flexure must be satisfied.

2.

Negative and positive flexural reinforcement may be cutoff using the provisions of ACI 9.7.3 (see Section 5.3.5). When determining the theoretical cutoff points, the area of longitudinal torsional reinforcement must be subtracted from the total area of longitudinal reinforcement provided at that face.

3.

Concrete Beam

Bottom Step In Beam

Fig. 5.17 Top and Bottom Steps in a Reinforced Concrete Beam.

The structural integrity requirements of ACI 9.7.7 must also be satisfied when detailing the reinforcement.

Provide Min. Cover Per Aci 318

5.6 Steps in Beams

≤ 3 in.

Additional Bars For Crack Control Increased Cover To Main Bars Optional Per Analysis

D1

Fig. 5.18 Reinforcement Details for a Reinforced Concrete Beam with a Top step Less Than or Equal to 3 in.

Ideal locations for steps would be at a column line or where support is provided by another beam. Obviously, it is not always possible to have the steps occur at these locations. The following sections provide detailing guidelines for steps of various depths.

Where the top step in a beam is 3 in. or less, the recommended detailing depends on when in the design and construction phases of the project the top step is introduced. In cases where the top step is known during the design phase, the beam can be designed for the smaller overall depth D1, which is illustrated in Fig. 5.18. The appropriate amounts of flexural and shear reinforcement are provided for this reduced depth. Additional longitudinal bars are provided in the deeper section for crack control. In cases where the step occurs after the design is complete, additional flexural and shear reinforcement may be required compared to the original design because of the reduced beam depth. Both flexural and shear strength need to be checked and the corresponding longitudinal bars and stirrups may have to be adjusted accordingly. A top step introduced late in the design phase or early in the construction phase can be accommodated using bent top reinforcement as illustrated in Fig. 5.19. ACI 10.7.4.1 limits the slope of the inclined portion of the offset bent longitudinal bars to 1 in 6 relative to the longitudinal axis of the beam. Additional stirrups need to be provided in the beam at this location to resist the upward component of the tensile force in the longitudinal bars. Two #4 bars are commonly provided at bent bar locations.

5-10

Provide Min. Cover Per Aci 318

Max. 1 To 6 Slope Bend Top Bars

*

D1

5.6.2 Top Steps

≤ 3 in.

D2

Steps in a reinforced concrete beam can occur for many reasons (Reference 12). For example, as shown in Fig. 5.17, the top of a beam would be needed to accommodate a raised flooring system. A bottom step in a beam would be required because of conflicts with mechanical equipment.

D2

5.6.1 Overview

* Alternately, Drape Top Bars

2 in.

Provide Additional Stirrups At Each Bent Bar To Resist Upward Component Of Bar Tension (2 # 4 Min.)

Fig. 5.19 Alternative Reinforcement Details for a Reinforced Concrete Beam with a Top Step Less Than or Equal to 3 in. In lieu of using the bent bar configuration illustrated in Fig. 5.19, either the top bars can be draped or the top reinforcement on either side of the step can be spliced using a noncontact lap splice provided the spacing limitations of ACI 25.5.1.3 can be satisfied. In cases where top steps exceed 3 in., the recommended detail depends on where along the length of the beam the step occurs. If the step occurs near midspan or at other sections where the force in the top reinforcement is relatively low, the top bars of the shallower beam can extend into the deeper beam a distance equal to the development length of these bars (see Fig. 5.20). The top bars of the deeper section can be hooked at the location of the step as illustrated in the figure. If the step occurs near a support or at other sections where the force in the top bars are relatively high, structural design

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures

> 3 in. Splice *

D1

D2 D1

D2

Top Bars Hooked Or Developed Into Beam

Cover Per ACI 318

Standard 90° Hook 90° Hook

Provide Additional Stirrups As Required Per Design * Development Length When Top Steel Is Not In Tension Class 'B' Splice When Top Steel Is In Tension

Fig. 5.20 Reinforcement Details for a Reinforced Concrete Beam with a Top Step Greater than 3 in.

Column

Fig. 5.21 Reinforcement Details for a Reinforced Concrete Beam with a Top Step at a Column.

Greater Of D1, D2, Or Ldh + Cover

Additional Stirrups As Required (Typ.)

Greater Of D1 Or D2 If Possible Extend The Beam And Bottom Reinforcement To Support

D1

D1

D2

Beam Step

D2

Class 'B' Splice (Min.)

Ldh Min. Diagonal Bars As Required Rigid Bent Shear Stirrups As Required Standard 90° Hook

Fig. 5.22 Reinforcement Details for a Reinforced Concrete Beam with a Bottom Step at a Column.

Fig. 5.23 Reinforcement Details for a Reinforced Concrete Beam with a Deep Step.

of the reinforcement is required using conventional or strutand-tie methods. It is good practice to extend the top bars of the shallower beam at least a Class B splice length into the deeper beam (Note: technically this is not a lap splice because the spacing requirements of ACI 25.5.1.3 are not satisfied).

5.6.4 Deep Steps

Additional stirrups may be required at the location of the step to resist the reaction of the shallower beam into the deeper beam. The amount and spacing depends on the shear demand at this section. As noted previously, the ideal location for a top step occurs where a beam frames into another beam or into a column. Illustrated in Fig. 5.21 are recommended details where the step occurs at a column. The top bars of the shallower beam can be either hooked or extended a development length into the deeper beam.

5.6.3 Bottom Steps The reinforcement details illustrated in Fig. 5.22 can be used where a bottom step in a beam is located near a column. The length of the intersecting beam segment should be at least equal to the depth of the deeper member to ensure that a 45-degree strut can form within this region.

Concrete Reinforcing Steel Institute

Illustrated in Fig. 5.23 are recommended details for beams with deep steps, that is, steps that exceed the depth of the beam. It is good practice to have the width of the bent greater than or equal to the depths of the adjacent beams.

5.7 Detailing Requirements and Guidelines for SDC C 5.7.1 Overview The requirements in ACI 18.4.2 must be satisfied for beams that are part of an intermediate moment frame, which is the required SFRS for structures assigned to SDC C. All of the requirements and guidelines presented above are also applicable.

5.7.2 Design for Flexure ACI 18.4.2.2 requires that the minimum positive moment strength at the faces of the supports be equal to at least 33% of the negative moment strength at that joint. This allows for the possibility that the positive moment caused by earthquake-induced lateral displacements exceeds the negative moment due to gravity loads. Similarly, the minimum negative and positive moment strength at any section along the span of the beam must be equal to at least 20% of the maximum moment strength at either joint.

5-11

Design Guide for Economical Reinforced Concrete Structures

Fig. 5.24 Flexural requirements for beams in intermediate moment frames.

A summary of the flexural requirements for beams in intermediate moment frames is given in Fig. 5.24, which is adapted from Reference 7. ACI 18.4.2.2 does not contain any restrictions on where lap splices of the flexural reinforcement can be located along the span. As noted in Section 5.3.5, top reinforcement is spliced near midspan and bottom reinforcement is spliced near the ends. However, because the potential exists for plastic hinges to form at the ends of the beam, it would be appropriate to locate the splices of the bottom bars somewhere between the ends of the beam and midspan.

Fig. 5.25 Examples of Hoops and Overlapping Hoops.

5.7.3 Design for Shear ACI 18.4.2.3 contains two methods on how to determine the maximum shear force on a beam in an intermediate moment frame. In the first method, the maximum factored shear force is obtained from the factored gravity loads acting on the beam plus the shear force associated with the application of the nominal moment strength Mn at each end of the beam. Both sidesway to the right and to left must be considered. In the second method, the maximum shear force is obtained from the design load combinations that include earthquake effects E, where E is assumed to be twice that prescribed by the building code. It is permitted to design for not less than the smaller of the two shear forces obtained from these methods. The required shear reinforcement is obtained from the maximum shear force described above. Because the shear reinforcement depends on Mn, it is important not to needlessly provide more flexural reinforcement than required because that can have a direct impact on the amount of shear reinforcement that has to be provided. Within a distance of at least 2h from the face of each support, hoops must be provided to resist the required shear force. A hoop is defined as a closed tie or continuously wound tie that is made up of one or several reinforcement elements, each having seismic hooks that conform to ACI 25.3.4 at both

5-12

Fig. 5.26 Transverse Reinforcement Requirements for Beams in Intermediate Moment Frames.

ends (ACI 2.3 and 25.7.4.1). The ends of the reinforcement elements in hoops must engage a longitudinal bar in the beam (ACI 25.7.4.2). Examples of hoops and overlapping hoops are illustrated in Fig. 5.25, which is adapted from Reference 7. As discussed in Section 5.4.2, hoops made from Details B and C make placement of the longitudinal bars in the beam much easier than those using Detail A. Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures

Fig. 5.28 Flexural Requirements for Beams in Special Moment Frames. Fig. 5.27 Dimensional Limits of Beams in Special Moment Frames. Once the required size and spacing of the hoops are determined, the spacing must be checked against the minimum spacing requirements of ACI 18.4.2.4. Outside of the regions where hoops are required, stirrups may be used; these stirrups must be provided over that entire region. Figure 5.26, which is adapted from Reference 7, illustrates the transverse reinforcement requirements for beams in intermediate moment frames.

5.8 Detailing Requirements and Guidelines for SDC D, E, or F 5.8.1 Overview The requirements in ACI 18.6 must be satisfied for beams that are part of a special moment frame, which is the required SFRS for buildings assigned to SDC D, E, or F. All of the requirements and guidelines presented above are also applicable.

loads. Similarly, the minimum negative and positive moment strength at any section along the span of the beam must be equal to at least 25% of the maximum moment strength at either joint. A summary of the flexural requirements for beams in special moment frames is given in Fig. 5.28, which is adapted from Reference 7. It is usually best to specify a smaller number of larger longitudinal bars to help reduce congestion at the beam-column joints. ACI 18.6.3.3 contains specific requirements for lap splice locations in beams of special moment frames. Lap splices are permitted as long as they are properly confined with hoop or spiral reinforcement over the entire lap length and that they are located away from potential hinge areas at the ends of the beam. Provisions for lap splices are illustrated in Fig. 5.29, which is adapted from Reference 7.

5.8.4 Design for Shear 5.8.2 Dimensional Limits Dimensional limits for beams in special moment frames are given in ACI 18.6.2.1. These limits have been guided by experimental evidence and observations of reinforced concrete frames that have performed well in the past during an earthquake. A summary of these limits is given in Fig. 5.27, which is adapted from Reference 7. It is important that these limits are satisfied once the beam dimensions have been initially established using the information in Section 5.2 of this Guide.

Shear design for beams in a special moment frame is related to the maximum flexural strength that can be developed in the

5.8.3 Design for Flexure ACI 18.6.3 requires that the minimum positive moment strength at the faces of the supports be equal to at least 50% of the negative moment strength at that joint. This allows for the possibility that the positive moment caused by earthquake-induced lateral displacements exceeds the negative moment due to gravity

Concrete Reinforcing Steel Institute

Fig. 5.29 Lap Splice Requirements for Beams in Special Moment Frames.

5-13

Design Guide for Economical Reinforced Concrete Structures beam, which is defined in ACI 18.6.5.1 as the probable flexural strength Mpr. The maximum factored shear force is obtained from the factored gravity loads acting on the beam plus the shear force associated with the application of the probable flexural strength Mpr at each end of the beam. Both sidesway to the right and to the left must be considered. The required shear reinforcement is obtained from the maximum shear force described above. Because the shear reinforcement depends on Mpr , which is a function of the amount of flexural reinforcement in the section, it is important not to needlessly provide more flexural reinforcement than required because that can have a direct impact on the amount of shear reinforcement that has to be provided. According to ACI 18.6.4.2, the spacing between longitudinal bars that are restrained by legs of crossties or hoops is limited to 14 in. This provision helps to ensure that proper lateral support is provided for such bars in case they are subjected to compressive forces under moment reversals. Within a distance of at least 2h from the face of each support, hoops must be provided to resist the required shear force. A hoop is defined as a closed tie or continuously wound tie that is made up of one or several reinforcement elements, each having seismic hooks that conform to ACI 25.3.4 at both ends (ACI 2.3 and 25.7.4.1). The ends of the reinforcement elements in hoops must engage a longitudinal bar in the beam (ACI 25.7.4.2). Examples of hoops and overlapping hoops are illustrated in Fig. 5.25, which is adapted from Reference 7. As discussed in Section 5.4.2, hoops made from Details B and C make placement of the longitudinal bars in the beam much easier than those from Detail A.

Fig. 5.30 Transverse Reinforcement Requirements for Beams in Special Moment Frames.

Once the required size and spacing of the hoops are determined, the spacing must be checked against the maximum spacing requirements of ACI 18.6.4.4. Outside of the regions where hoops are required, stirrups with seismic hooks may be used; these stirrups must be provided over that entire region. Figure 5.30, which is adapted from Reference 7, illustrates the transverse reinforcement requirements for beams in special moment frames.

5.9 Beams Not Designated as Part of the SFRS

Fig. 5.31 Requirements of ACI 18.14.3.2(a) for Beams.

Detailing requirements for beams that have not been assigned to the SFRS are given in ACI 18.14.3. In cases where the bending moments and shear forces in a beam due to the lateral displacements from a seismic event do not exceed the design moment and shear strength of the beam, the detailing requirements of ACI 18.14.3.2(a) must be satisfied. These requirements are illustrated in Fig. 5.31, which is adapted from Reference 7. Where the induced bending and shear exceed the design moment and shear strength of the beam, or where the induced moments and shear are not calculated, the detailing requirements of ACI 18.14.3.3 must be satisfied (see Fig. 5.32, which is adapted from Reference 7).

5-14

Fig. 5.32 Requirements of ACI 18.14.3.3 for Beams.

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures

CHA PTER 6 Columns 6.1 Overview Guidelines and recommendations on the economical design and detailing of columns are contained in this chapter. Information is provided on sizing the cross-section and detailing the longitudinal and transverse reinforcement. Specific requirements for columns in intermediate moment frames (SDC C) and special moment frames (SDC D, E, and F) are given in Sects. 6.6 and 6.7 of this Guide, respectively.

6.2 Preliminary Column Sizing The preliminary size of a typical column in a reinforced concrete building is needed for a variety of reasons, including frame analysis and initial cost estimation. It is common practice to obtain preliminary column sizes in the early stages of design utilizing axial gravity loads only. It is assumed that the effects from bending moments are relatively small and that slenderness (secondary) effects are negligible. The first of these assumptions is usually valid for columns that are not part of the lateral force-resisting system. For many columns, slenderness effects are not an issue. A preliminary column size can be obtained by setting the total factored axial load Pu equal to the design axial load strength KPn,max given in ACI Table 22.4.2.1 for columns with ties conforming to ACI 22.4.2.4 and with spirals conforming to ACI 22.4.2.5. The appropriate equation is solved for the gross area of the column Ag, assuming practical values for the total area of longitudinal reinforcement Ast , the compressive strength of the concrete f 'c , and the yield strength of the longitudinal reinforcement : Tied Column:

Ag " Pu /0.80[(0.85)f 'c  W)  fy W]

Spiral Column: Ag " Pu

/0.85[(0.85)f '  c

W)  fy W]

where W " Ast /Ag. The minimum and maximum areas of longitudinal reinforcement are prescribed in ACI 10.6.1.1. The following limits are applicable regardless of the type of transverse reinforcement that is used in the column: • Minimum Ast " 0.01Ag • Maximum Ast " 0.08Ag The 1% lower limit is meant to provide resistance to any bending moments that are not accounted for in the analysis because of, for example, construction tolerances or misalignments. This lower limit is also meant to help reduce creep and shrinkage in the concrete under sustained compressive stresses. In order for the concrete to be properly placed and consolidated, the size and number of longitudinal reinforcing bars must be chosen to minimize reinforcement congestion (see Section 6.3 of this Guide). The upper limit on the longitudinal reinforcement is meant to help achieve these goals. The maximum area of reinforcement must not exceed 4% of the gross column area at sections where lap splices are utilized.

Concrete Reinforcing Steel Institute

Fig. 6.1 Preliminary Sizing Chart for Nonslender Columns with Tie Reinforcement. A preliminary column size should be determined using a low percentage of longitudinal reinforcement. Columns that have longitudinal reinforcement ratios Ast /Ag in the range of 1 to 2% are usually the most economical because concrete carries axial compressive loads more cost-effectively than reinforcing steel. Generally, it is usually more economical to use larger column sizes with less longitudinal reinforcement. The information contained in Fig. 6.1, which is adapted from Reference 7, can be used to obtain a preliminary size of a nonslender, tied column with Grade 60 longitudinal reinforcement. The chart can be entered with a longitudinal reinforcement ratio and concrete compressive strength; the ratio of factored axial force Pu to gross area of the column Ag can be read from the vertical axis, which can be solved for Ag. Similar design charts can be generated for other column sizes and shapes and other material strengths. As noted in Section 2.2.2 of this Guide, the same column size should be used as often as possible throughout the entire building to achieve overall economy. The dimensions of a column can be influenced by architectural and functional requirements. One or both dimensions of a rectangular column may be limited, which could result in a column that is slender. A number of design aids are available that can be utilized in the design of columns subjected to axial load and bending moment. Reference 13 contains nondimensionalized nominal strength interaction diagrams for rectangular and circular sections with a variety of bar arrangements. Numerous tables for rectangular and circular columns are contained in Reference 14, which cover a wide range of cross-sectional dimensions,

6-1

Design Guide for Economical Reinforced Concrete Structures concrete compressive strength, longitudinal reinforcement ratios, and bar arrangements. These tables contain values corresponding to key points on the interaction diagram.

Table 6.1 Minimum Face Dimension (inches) of Rectangular Tied Columns with Normal Lap Splices.

6.3 Detailing Requirements and Guidelines for Longitudinal Reinforcement 6.3.1 Overview Longitudinal reinforcement for columns must satisfy the requirements in ACI 10.7. Limitations are provided on the size and spacing of the longitudinal bars. Number of Bar Per Face

The longitudinal bars must be spaced far enough apart so that concrete can flow easily between the bars. Minimum bar spacing is especially critical at splice locations. Generally, it is more economical to have a fewer number of larger longitudinal bars than a greater number of smaller bars.

Bar Size

2

3

#5

8

10 12 14 17 19 21 23 25 27 29 31 34

#6

9

11 13 15 18 20 22 24 27 29 31 33 36

#7

9

11 14 16 18 21 23 26 28 30 33 35 37

Splice requirements for longitudinal reinforcement in columns are given in ACI 10.7.5. The type of lap splice that must be provided is based on the stress in the reinforcing bars under factored loads.

#8

9

12 14 17 19 22 24 27 29 32 34 37 39

6.3.2 Minimum Number of Longitudinal Bars According to ACI 10.7.3.1, a minimum of four longitudinal bars are required in columns where rectangular or circular ties are used as transverse reinforcement. For columns where the longitudinal reinforcement is enclosed by spirals, a minimum of six longitudinal bars are required.

4

5

6

7

8

9

10 11 12 13 14

#9

10 13 16 18 21 24 26 30 33 35 38 41 44

#10

11 14 17 20 23 27 30 33 36 39 42 46 49

#11

11 15 18 22 25 29 32 36 40 43 47 50 54

Table 6.2 Maximum Number of Bars in Columns Having Longitudinal Bars Arranged in a Circle and Normal Lap Splices.

For other tie shapes, one bar should be provided at each apex or corner and proper transverse reinforcement provided. For example, a tied triangular column needs three longitudinal bars, with one at each apex of the triangular ties.

6.3.3 Spacing of Longitudinal Bars The longitudinal bars in reinforced concrete columns must be spaced at a sufficient distance so that concrete can flow easily between the bars and between the bars and the formwork. According to ACI 25.2.3 the minimum clear distance that is to be provided between longitudinal bars is equal to the largest of the following: • 1.5 times the diameter of the longitudinal bar

Bar Size

h (in.) 12

#5 8

#6 7

#7 6

#8

#9

#10

#11

6

4*

—

— 4*

• 1.5 in.

14

11

10

9

8

7

5*

• (4/3) times the diameter of the largest aggregate in the concrete mix

16

14

13

12

11

9

7

6

18

17

16

14

13

11

9

8

These minimum clear distance requirements are also applicable to the clear distance between a contact lap splice and any adjacent bars or splices.

20

20

19

17

16

13

11

10

22

23

21

20

18

16

13

12

24

26

24

22

21

18

15

13

Table 6.1, which is adapted from Reference 7, contains the minimum face dimension of rectangular tied columns with normal lap splices based on the requirements presented above. The column face dimensions have been rounded to the nearest inch and a 1.5-in. clear cover to #4 ties has been used.

26

29

27

25

23

20

17

15

28

32

30

28

26

22

19

17

30

35

33

30

28

25

21

19

32

38

35

33

31

27

23

21

34

41

38

36

33

29

25

22

36

44

41

38

36

31

27

24

The maximum number of bars in a circular or square column that has longitudinal bars arranged in a circle with normal lap

* Applicable to circular tied columns only

6-2

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures splices is contained in Table 6.2, which is also adapted from Reference 7. The information given in this figure satisfies the minimum clear distance requirements of ACI 25.2 and the reinforcement limits of ACI 10.6.1.1. The number of bars have been rounded to the nearest whole number and were determined using a 1.5-in clear cover to #4 spirals or ties.

6.3.4 Splices Provisions for lap splices, mechanical splices, butt-welded splices, and end-bearing splices are given in ACI 10.7.5. In general, column splices must satisfy the requirements for all load combinations. Where the longitudinal bar stress due to factored loads is compressive, all of the splice types listed above may be used. Lap splices and mechanical or butt-welded splices are permitted when the longitudinal bar stress is tensile; end-bearing splices are not permitted in such cases. Lap splices are the most popular and usually the most economical type of splices used in columns. The type of lap splice—compressive or tensile—that must be used depends on the stress in the longitudinal bars due to the factored load combinations. Lap splices in columns that are not part of special moment frames are permitted to occur immediately above the top of the slab, as shown in Fig. 6.2. This location facili-

tates the overall construction of the structure. The longitudinal bars from the column below extend above the slab a distance equal to or greater than the required lap splice length. It is common to have construction documents that show lap splices occurring at each floor level. Depending on a number of factors, the tension lap splice lengths may be relatively long, in some cases close to the entire story height. This results in doubling of the longitudinal bars, which may cause congestion in the column and make concrete placement more difficult. As a general rule, if the lap splice length is more than about one-third to one-half the story height, it may be more economical to splice the bars every other floor, if possible. Additional information on lap splice location and guidelines on constructability can be found in Reference 15. At lap splice locations or at locations where the column size changes, offset bends conforming to ACI 10.7.4 are required (see Fig. 6.4). It is standard construction practice for the longitudinal bars in the column below to be offset bent into the column above. From a construction perspective, it is easier to lower the larger column cage over the smaller offset cage that protrudes from the floor slab.

6.4 Detailing Requirements and Guidelines for Transverse Reinforcement 6.4.1 Overview Transverse reinforcement for columns must satisfy the requirements given in ACI 10.7. Limitations are provided on the size and spacing of both tie and spiral transverse reinforcement. The transverse bars must be spaced far enough apart so that concrete can flow easily between the bars without honeycombing. Additionally, these bars must be spaced close enough to provide adequate lateral support to the longitudinal reinforcement and to provide sufficient shear strength where needed.

6.4.2 Spiral Reinforcement Requirements for columns with spiral reinforcement are given in ACI 10.7.6 and 25.7.3. Standard spiral sizes are #3 to #5, and the clear spacing between spirals should not exceed 3 in. or be less than the greater of 1 in. or (4/3) times the diameter of the largest aggregate in the concrete mix. ACI Eq. (25.7.3.3) is to be used to determine the minimum amount of spiral reinforcement that must be provided:


Ag  f'
s = 0.45 
1 c  Ach  f yt

Fig. 6.2 Tie and Splice Details in a Reinforced Concrete Column. Concrete Reinforcing Steel Institute

The volumetric spiral reinforcement ratio is equal to the volume of the spiral reinforcement divided by the volume of the concrete core measured to the outside edges of the spiral reinforcement. The term Ach is the area of the column core enclosed by the spiral, which is equal to U Dch )2/4 where Dch is the diameter of the column core measured to the outside edges of the spiral reinforcement (see Fig. 6.3, which is adapted from Reference 7).

6-3

Design Guide for Economical Reinforced Concrete Structures Thus, for a given spiral bar with an area of Abs , the center-tocenter spacing of the spirals s (i.e., the pitch) must be less than or equal to the value obtained by the following equation:

s=

8.9Abs
Dch  Ag /Ach
1 f c' /fyt

(

)

(

)

Spiral reinforcement provides a higher degree of lateral confinement than that provided by ties; this has a direct impact on the design strength of a column. This is reflected in the larger strength reduction factor K that is permitted to be used in the design of a spiral column compared to that in a tied column. One drawback of spiral reinforcement occurs at beam-column joints: it may be difficult to thread the longitudinal bars of the beam through the joint, especially where the pitch is relatively small.

Fig. 6.3 Spiral Reinforcement.

6.4.3 Tie Reinforcement Requirements for columns with tie reinforcement are given in ACI 10.7.6 and 25.7.2. Standard hook dimensions for ties, which are the same as those for stirrups, are given in ACI 25.3.2. Maximum tie spacing and other requirements are illustrated in Fig. 6.4 (Reference 16). Illustrated in ACI Fig. R25.7.2.3(a) are the requirements of ACI 25.7.2.3 pertaining to tie arrangement and maximum clear spacing between laterally supported bars. The corner bars and every other longitudinal bar must have lateral support in cases where the center-to-center spacing of the longitudinal bars on a side is equal to or less than 6 in. plus the diameter of the longitudinal bar. Additional lateral support for the intermediate bars must also be provided if the spacing is greater than that. This is usually in the form of a crosstie (sometimes referred to as a candy cane because of its shape), which is a reinforcing bar that has a seismic hook on one end and a hook not less than 90 degrees with at least a six-diameter extension on the other. A seismic hook is defined as a hook with a bend that is not less than 135 degrees and an extension that is not less than 6 bar diameters or 3 in., whichever is greater. For circular hoops, the bend should not be less than 90 degrees. Standard arrangements of column ties are depicted in Figs. 6.4 and 6.5. The Notes: 1) Alternate position of hooks in placing successive sets of ties; 2) minimum lap shall be 12 in.; 3) “B” indicates bundled bars. one-piece tie arrangements in Fig. 6.4 are Bundles shall not exceed four bars; and 4) elimination of tie for center bar in groups of three limits clear spacing to be 6 in. maximum. sufficiently rigid to be lifted into place after Unless otherwise specified, bars should be so grouped. being preassembled on site. If possible, Fig. 6.4 Standard Column Ties Applicable for Either Preassembled Cages or Field Erection.

6-4

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures it is preferred to preassemble one-story column cages where all of the lap splices occur at or near the same elevation above the floor line. There are numerous ways to arrange ties in a column and some arrangements are preferred more than others. For example, consider the arrangements in Fig. 6.6a and 6.6b, which consist of an outer confinement tie with an inner tie and crossties, respectively. These arrangements are generally preferred over the arrangement in Fig. 6.6c, which consists of paired overlapping ties, because of the following (Reference 16): • The outer confinement tie acts as a template for the ironworker to place the longitudinal bars in the column. • It is easier to maintain the required concrete cover using side-form spacers. • It is more efficient at preventing displacement of the longitudinal bars while the column cage is being moved into place by crane. • The tasks that are needed to be completed by the ironworker are simplified, which translates to increased productivity. Notes: 1) Alternate position of hooks in placing successive sets of ties; 2) minimum lap shall be 12 in.; 3) elimination of tie for center bar in groups of three limits clear spacing to be 6 in. maximum. Unless otherwise specified, bars should be so grouped; and 7) bars shown as open circles may be accommodated provided clear spaces between bars do not exceed 6 in. (Figure does not include Notes 3-6.)

Fig. 6.5 Standard Column Ties Applicable for Either Preassembled Cages or Field Erection, Special-shaped Columns, and Columns with Bars in Two Faces Only.

One exception to using outer confinement ties is where a column is dimensionally large. In such cases, the arrangement in Fig. 6.6c is preferred so as to avoid difficulties associated with fabricating, shipping, and placing the ties. Generally, crossties (Fig. 6.6b) are preferred over closed ties (Fig. 6.6a) because the latter are difficult to place and align around the longitudinal bars. Crossties can easily be placed after the column cage has been constructed with the outer confinement ties.

(a)

(a)

(b)

The diamond ties depicted in Fig. 6.7 are difficult to fabricate and difficult to place and align around the longitudinal bars in the column. Crossties should be used instead, which facilitates bar placement and allows more accurate column cage fabrication.

(b) Fig. 6.7 Column Tie Configurations Using Multiple Bars: (a) Diamond Tie (avoid use); and (b) Single Closed Tie with Candy Cane Ties.

Illustrated in Fig. 6.8 are examples of tie arrangements where precise fabricating dimensions are difficult to maintain and where the fabricated pieces are costly to place (Reference 16). The alternate details are more efficient and economical for the reasons stated in the figure.

(c) Fig. 6.6 Column Tie Sets Comprising Multiple Ties: (a) With Outer Confinement Tie and Inner Closed Tie; (b) With Outer Confinement Tie and Candy Cane Ties; and (c) With Paired Overlapping Ties. Concrete Reinforcing Steel Institute

6-5

Design Guide for Economical Reinforced Concrete Structures

TIES FOR 12 BAR COLUMN

Initial Detail Problem: Any out of location placement of the 12 bars will affect the others

ALTERNATE HOOKS (TYP.)

Suggested Alternate Detail Advantage: Bars are less dependent on location of others

TIES FOR 10 BAR COLUMN

ALTERNATE HOOKS (TYP.)

Initial Detail Problem: Any out of location placement of the 10 bars will affect the others

Suggested Alternate Detail Advantage: Bars are less dependent on location of others

TIES FOR 8 BAR COLUMN

ALTERNATE HOOKS (TYP.)

Initial Detail Problem: Out of location placement of any bars will affect the others

Suggested Alternate Detail Advantage: Bars are less dependent on location of others

SMALL DIAMETER (12” OR LESS) CIRCULAR COLUMNS USING #3 OR #4 TIES

Initial Detail Problem: Small circle (Bend Type T3) is difficult to bend and keep in the same plane

Suggested Alternate Detail Advantage: More accurate and better alignment of bars

Fig. 6.8 Costly and Economical Column Tie Configurations.

6-6

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures The location of the dowels protruding from a footing can have an impact on the installation of the preassembled reinforcing cages of the columns (Reference 17). Dowels should be positioned so as not to interfere with the longitudinal bars or the tie hooks from the column.

Fig. 6.9 Column and Footing Detail: (a) as shown in construction documents; and (b) as detailed for constructibility, with dowels supported on the footing reinforcing bars and straight column bars (no offsets).

6.5 Detailing Requirements and Guidelines for Dowels The interface between a column and a concrete foundation must be designed to adequately transfer vertical and horizontal forces between the members (ACI 13.2.2). ACI 16.3 contains design requirements for force transfer from a column to a footing. Vertical compressive loads are transferred by bearing on the concrete or by a combination of bearing and reinforcement at the interface. Tensile loads must be resisted entirely by reinforcement, which may consist of extended longitudinal bars, dowels, anchor bolts, or mechanical connectors. Lateral loads are transferred using the shear friction provisions of ACI 22.9 or other appropriate methods.

Consider the arrangements of the column longitudinal bars and the dowel bars depicted in Fig. 6.10a. Except for the bars located adjacent to the center crosstie, the dowel bars are offset by 45 degrees from the column longitudinal bars relative to the long side of the column. It is evident that there is no interference between the dowel bars and the 135-degree tie hooks in this arrangement. At the center crosstie, the dowel bars are located 90 degrees inboard relative to the long side of the column so that no interference occurs between them and the hooks of the crosstie. Depicted in Fig. 6.10b is the same column, but in this case, all of the dowel bars occur adjacent to the tie on the long side of the column. This arrangement is not as preferable as that shown in Fig. 6.10a, however, it is manageable because the ends of the hooks are relatively flexible and can be maneuvered around the dowels. Finally, Fig. 6.10c shows some of the dowel bars located on the long face of the column and some on the short face. This is the least preferable arrangement because there is more potential for difficulties during installation; lowering the column cage over the dowels will be challenging because the ties will not allow the same degree of flexibility as will the hooks at the ends of ties.

(a)

The amount of reinforcement that is required between a reinforced concrete column and footing depends on the type of stress in the bars of the supported member under all applicable load combinations. Minimum embedment lengths into both members also depend on this stress. Dowels are commonly used as interface reinforcement between columns and footings. The dowel bars are set in the footing prior to casting the footing concrete and are subsequently spliced to the longitudinal bars in the column. Dowel bars should never be driven or pushed into position in wet concrete. Where columns are supported on footings, the minimum area of reinforcement across the interface is equal to 0.5% of the gross area of the column (ACI 16.3.4.1). To facilitate placement, a dowel should have a 90-degree hook on its end that rests on the bottom mat of the footing bars, as illustrated in Fig. 6.9b (Reference 16). If the dowel bars are detailed as shown in Fig. 6.9a, additional bars and bar supports are required to position the dowel bars higher in the depth of the footing, which is not cost effective.

Concrete Reinforcing Steel Institute

(b)

(c) Fig. 6.10 (a) Ideal Arrangement of Dowels (b) Dowels Arranged on Long Face of Column (c) Least Preferable Arrangement of Dowels.

6-7

Design Guide for Economical Reinforced Concrete Structures 6.6 Detailing Requirements and Guidelines for SDC C 6.6.1 Overview Requirements for columns that are part of an intermediate moment frame, which is the required SFRS for structures assigned to SDC C, are given in ACI 18.4.3. All of the requirements and guidelines presented above are also applicable.

6.6.2 Longitudinal Reinforcement Requirements Limits for longitudinal reinforcement are given in ACI 10.6.1.1; these are the same limits for columns in buildings assigned to SDC A or B (see Section 6.2 of this Guide). No restrictions are given on the location of splices of longitudinal reinforcement in columns in intermediate moment frames. However, as discussed in Section 6.6.3 of this Guide, the plastic hinge regions are anticipated to form at the ends of the column. Thus, it is good practice to locate lap splices outside of these regions.

6.6.3 Transverse Reinforcement Requirements Transverse reinforcement requirements for columns in intermediate moment frame are given in ACI 18.4.3. Like beams, plastic hinges are anticipated to form at the ends of the column where moments are usually maximum. As such, hoops or spirals are required at each end over the distance Co. This length is indicated in Fig. 6.11, which is adapted from Reference 7, for the case of transverse reinforcement consisting of hoops. The hoops provide confinement to ensure column ductility in the event of hinge formation during a seismic event. Outside of the anticipated hinge length Co, the spacing of the transverse reinforcement must conform to the lateral reinforcement provisions of ACI 25.7.2 for ties and ACI 25.7.3 for spirals, and to the provisions for spacing limits for shear reinforcement of ACI 10.7.6.5.2. The smallest spacing obtained from these requirements is to be used in the center region of a column outside of the plastic hinge zones. The transverse reinforcement requirements of ACI 18.4.3.6 must be satisfied for columns that support reactions from discontinuous stiff members, such as walls.

Fig. 6.11 Transverse Reinforcement Requirements for Columns in Intermediate Moment Frames.

6-8

Fig. 6.12 Dimensional Limits of Columns in Special Moment Frames. Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures 6.7 Detailing Requirements and Guidelines for SDC D, E, or F

in all of the other SDCs. The main reason for this is to control steel congestion and the development of high shear stresses.

6.7.1 Overview

Lap splices of the longitudinal reinforcement must occur within the center half of the member length and must be enclosed with transverse reinforcement that conforms to ACI 18.7.5.2 and 18.7.5.3. The main reason for the location of the lap splices is to keep them away from the regions where plastic hinges are likely to form during a seismic event.

Requirements for columns that are part of a special moment frame, which is the required SFRS for structures assigned to SDC D, E, or F, are given in ACI 18.7. All of the requirements and guidelines presented above are also applicable.

6.7.2 Dimensional Limits Dimensional limits for columns in special moment frames are given in ACI 18.7.2.1. These limits have been guided by previous practice. A summary of these limits is given in Fig. 6.12, which is adapted from Reference 7. It is important that these limits are satisfied once the column dimensions have been initially established using the information in Section 6.2 of this Guide.

6.7.3 Longitudinal Reinforcement Requirements Limits for longitudinal reinforcement are given in ACI 18.7.4.1. The lower limit is 0.01Ag and the upper limit is 0.06Ag , which is less than the upper limit for columns in buildings located

6.7.4 Transverse Reinforcement Requirements Closely spaced transverse reinforcement, in the form of hoops or spirals, is required over the length Co at each end of a column to confine the concrete because the largest bending moments are expected to occur at these locations, which could lead to flexural yielding. Transverse reinforcement requirements are illustrated in Fig. 6.13, which is adapted from Reference 7, for columns reinforced with rectilinear hoops where Pu f 0.3Ag f c' and f c' f10,000 psi. Figure 6.14 depicts the details where Pu > 0.3Ag f c' and/or f c' #10,000 psi.

Fig. 6.13 Transverse Reinforcement Requirements for Rectilinear Hoops in Columns of Special Moment Frames where Pu f 0.3Ag f c' and f c' f10,000 psi. Concrete Reinforcing Steel Institute

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Design Guide for Economical Reinforced Concrete Structures

Fig. 6.14 Transverse Reinforcement Requirements for Rectilinear Hoops in Columns of Special Moment Frames where Pu # 0.3Ag f c' and/or f c' #10,000 psi.

Fig. 6.15 Transverse Reinforcement Requirements for Spiral or Circular Hoops in Columns of Special Moment Frames.

6-10

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures As mentioned previously, the use of crossties instead of closed ties are preferred mostly for ease of construction. Requirements for columns reinforced with spiral and circular hoops are illustrated in Fig. 6.15, which is adapted from Reference 7. Spiral reinforcement is generally the most efficient form of confinement reinforcement; however, the extension of the spirals into the beam-column joint usually causes construction difficulties, especially when placing longitudinal reinforcement from the beam through the joint.

6.8 Columns Not Designated as Part of the SFRS

In cases where the bending moments and shear forces in a column due to the lateral displacements from a seismic event do not exceed the design moment and shear strength of the beam, the detailing are illustrated in Fig. 6.16, which is adapted from Reference 7 where Pu f 0.3Ag f c' and f c' f10,000 psi. Where the induced bending and shear exceed the design moment and shear strength of the beam, or where the induced moments and shear are not calculated, the detailing requirements of ACI 18.14.3.3(c) are essentially the same as those for columns in special moment frames (see Section 6.7 of this Guide).

Detailing requirements for columns that have not been assigned to the SFRS are given in ACI 18.14.3.

Fig. 6.16 Requirements of ACI 18.14.3.2(b) and (c) for Columns. Concrete Reinforcing Steel Institute

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Design Guide for Economical Reinforced Concrete Structures

CHA PTER 7 Walls 7.1 Overview Guidelines and recommendations on the economical design and detailing of walls are contained in this chapter. The focus is on walls found specifically in building structures; retaining walls, for example, are not covered. Information is provided on determining the wall thickness and detailing the longitudinal and transverse reinforcement. Specific requirements for special structural walls in structures assigned to SDC D, E, or F are given in Section 7.5 of this Guide.

7.2 Determination of Wall Thickness In typical building structures, reinforced concrete walls are usually located around stair and elevator openings. As such, the lengths of the walls are often dictated by the architectural requirements associated with these openings. In general, the thickness of a wall is determined based on strength requirements for axial load, flexure, and shear and sometimes on serviceability requirements (overall building deflection), especially for high-rise buildings. The thickness of a wall in a low-rise building can be governed by in-plane shear due to lateral forces, although a combination of axial load and out-of-plane bending due to lateral forces and/or eccentric gravity loads may control if the wall is relatively tall and slender. Where in-plane shear forces govern, the following equation can be used to determine a conservative estimate for the wall thickness h:

h=

0.8Vu

f c'
w

This equation can be solved for h (where Ag " h Cw ) for a given set of design criteria:

h=

2
k
2
P n c  +  '   32   1.1 f c l w 

Pn + 1.1  f c'
w

Relatively tall and/or slender walls are generally governed by a combination of axial load and in-plane bending moments. The strength design method must be used to design the wall in such cases. A wall thickness and the size and spacing of the longitudinal reinforcement are assumed so that an interaction diagram can be constructed. Applicable load combinations for combined axial load and bending can then be checked. Because there is no closed-form solution for multiple load cases, iterations must be performed until all strength design criteria are satisfied. In addition to satisfying all strength and serviceability requirements, wall thicknesses are sometimes provided that make the columns in the building part of a nonsway frame (that is, the frame is braced against sidesway). This can be advantageous especially in situations where the columns are slender; secondary effects increase dramatically with increasing sway. ACI 6.2.5 permits columns to be considered braced against sidesway when the bracing elements in the structure (typically, walls or a combination of walls and moment frames) have a total lateral stiffness in the direction of analysis of at least 12 times the gross lateral stiffness of all the columns within a given story. This criterion can be used to determine the thicknesses of the walls to produce a nonsway frame.

7.3 Minimum Reinforcement

In this equation, which is based on ACI Eq. (11.5.4.4), Vu is the maximum factored shear force determined from the load combinations in ACI Table 5.3.1 and Cw is the length of the wall. This equation will give a conservative value for h for walls of normalweight concrete because the contribution of the transverse reinforcement to the overall shear strength has not been included. For relatively short walls subjected to only vertical loads, the simplified method of ACI 11.5.3 can be used to determine a preliminary wall thickness. The limitations of this method are the following: (1) the wall has a solid, rectangular cross-section and (2) the resultant of all applicable factored loads falls within the middle third of the wall thickness. Where these limitations are satisfied, ACI Eq. (11.5.3.1) is permitted to be used:

Minimum longitudinal and transverse reinforcement depend on the magnitude of the in-plane factored shear force Vu. The minimum longitudinal (vertical) distributed reinforcement ratio WC and the minimum transverse (horizontal) distributed reinforcement ratio Wt are given in Table 7.1 where Vu f 0.5KVc for deformed bars in castin-place concrete. Table 7.1 is based on Table 11.6.1 of ACI 318. Table 7.1 Minimum Reinforcement Ratios where Vu f 0.5KVc Bar Size ≤#5

f y(psi)

Minimum WC

Minimum Wt

v60,000

0.0012

0.0020

!60,000

0.0015

0.0025

Any

0.0015

0.0025

>#5



k
2  Pn = 0.55 f c' Ag 1
 c     32h  

The limits in this table need not be satisfied if it can be demonstrated by structural analysis that the wall has adequate strength and stability.

In this equation, Cc is the height of the wall and k is defined as follows:

Where Vu # 0.5KVc , the following requirements must be satisfied:

• k " 0.8 when the wall is restrained against rotation at one or both ends • k " 1.0 when the wall is unrestrained against rotation at both ends Concrete Reinforcing Steel Institute

0.0025 + 0.5 2.5
h /
( w w ) (
t
0.0025)

• WC v greater of  • Wt v 0.0025

 0.0025                                                     

Note that WC need not exceed Wt .

7-1

Design Guide for Economical Reinforced Concrete Structures The maximum spacing is also the lesser of 3 times the wall thickness and 18 in. for spacing of the transverse bars. The spacing is limited to one-fifth of the length of the wall for shear reinforcement that is required for in-plane shear.

Fig. 7.1 Rustication Over Entire Length or Height of a Wall.

7.4 Detailing Requirements and Guidelines for Reinforcement 7.4.1 Overview As noted in the previous section, the size and spacing of the longitudinal and transverse reinforcement in a wall must be chosen to satisfy all applicable requirements for strength and serviceability. This section provides a summary of the requirements in ACI 318 and includes guidelines that can be used to obtain more economical walls.

7.4.2 Concrete Cover Concrete protection for reinforcement plays an important role in the formulation of the requirements of bar spacing and bar development. Reinforcing bars are placed in a concrete member with a minimum concrete cover to protect it from weather, fire, and other effects. Minimum cover requirements for nonprestressed, cast-in-place concrete construction are given in ACI Table 20.6.1.3.1. For walls, concrete cover is measured from the surface of the concrete to the outer edge of the layer of reinforcement closest to the wall surface. Where reveals or rustications run the entire length or height of a wall, the minimum required cover to the reinforcing bars is indicated in Fig. 7.1 (Reference 6). A constant concrete cover is maintained from the inside of the reveal to the surface of the wall. Potential problems with the minimum required concrete cover can occur where rustications are located at specific areas of a wall (see Fig. 7.2a). It is clear from the figure that the cover to the transverse reinforcement is smaller than that which is required. One solution is to offset the reinforcing bars in the localized area to maintain the required cover (see Fig. 7.2b). The detailing and placing of the reinforcement can become quite challenging if more than one area of rustication is required and/or if the rustication is located near an opening in a wall. A more viable solution is to treat the rustication area as an opening and provide an inner layer of reinforcement with the proper cover (see Fig. 7.2c). This reinforcement should be developed beyond the rustication area in all directions.

Walls that are greater than 10 in. in thickness are required to have two layers of reinforcement in both directions and distributed in accordance with the provisions in ACI 11.7.2.3. Flexural tension reinforcement is to be well distributed and placed as close as practical to the tension face of the wall. Like for beams and slabs, the longitudinal and transverse bars in reinforced concrete walls must be spaced at a sufficient distance so that concrete can flow easily between the bars and between the bars and the formwork. According to ACI 25.2.3, the minimum clear distance that is to be provided between bars is equal to the largest of the following: • 1.5 times the diameter of the longitudinal bar • 1.5 in. • (4/3) times the diameter of the largest aggregate in the concrete mix To simplify placement of the reinforcement in the field, bars should be placed at a consistent spacing or using multiples of a given spacing. Similarly, to avoid installation errors, the same bar size should be used in both the longitudinal and transverse directions.

7.4.4 Lateral Support of Longitudinal Reinforcement In cases where the longitudinal reinforcement in a wall is required for axial strength or where the area of the longitudinal reinforcement exceeds 1% of the gross area of the wall, transverse ties are required around the longitudinal reinforcement (ACI 11.7.4).

(a)

(b)

7.4.3 Spacing Requirements Spacing requirements for longitudinal and transverse reinforcement walls are given in ACI 11.7.2 and 11.7.3, respectively. The spacing of longitudinal bars in cast-in-place walls should not exceed the lesser of 3 times the wall thickness and 18 in. For shear reinforcement that is required for in-plane shear, the spacing is limited to one-third of the length of the wall.

7-2

(c) Fig. 7.2 Rustication Over a Portion of a Wall (a) Minimum Concrete Cover Not Provided (b) Offset Bars (c) Inner Layer of Bars. Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures

#

#

Fig. 7.3 Typical Reinforcement at Wall Openings. While it may be feasible to provide such ties in thicker walls, it is very difficult to do so in thinner walls, especially where the bars are spaced relatively close together. Development of the tie bars and interference of the adjoining hooks at the ends of the ties can pose major problems.

7.4.5 Wall Openings In a typical building, it is inevitable that openings of various sizes and shapes for doors, windows, conduit, piping, and ductwork will need to be made in the structural walls. Mechanical, plumbing, and electrical openings are usually located just below the slab, but, in general, could occur anywhere. Additional reinforcement must be provided around the perimeter of wall openings and it is commonly referred to as trim bars, opening bars, or corners bars (Reference 18). In essence, these bars are to replace the reinforcement interrupted by the opening. ACI 11.7.5 requires that for walls with one layer of reinforcement in both the longitudinal and transverse directions, at least one #5 bar must be provided around an opening. Similarly, at least two #5 bars are required around openings in walls that have two layers of reinforcement in both directions. These are the minimum amounts of reinforcement that is required; in walls subjected to relatively large lateral loads, for example, an analysis of the wall must be made and the required amounts of reinforcement in the wall and around the perimeter of the openings must be provided based on the analysis. Regardless of the size and amount of the required reinforcement, the trim bars must be fully anchored to develop the yield strength of the bars in tension at the corners of an opening. Unless required for structural purposes, longitudinal trim bars around the sides of an opening that run the full height of a wall and that get lap spliced with dowels protruding from the footing

Concrete Reinforcing Steel Institute

should be avoided (see Fig. 7.3). Detailing and placing full-height trim bars can be a problem because the exact locations of the wall openings may not be available at the time the concrete for the footing is placed; thus, the dowels may not be at the correct location. As noted above, longitudinal trim bars need to be developed only past the edge of the opening. Providing fullheight bars when they are not required is not recommended. In regards to the development length of the trim bars, the preferred reference point to measure the development length from is the corner of the opening, as shown in Fig. 7.4. This is an advantageous location for the detailer and placer because it is a fixed point. Measuring the embedment length from a longitudinal or transverse trim bar is frequently done, but the embedment length may wind up being too short if the perpendicular trim bars adjacent to the opening shift for whatever reason Fig. 7.4 Preferred Reference Point from their intended location for Development Length of Trim (see Fig. 7.5). Bars.

Fig. 7.5 Development Length of Trim Bars Measured from Perpendicular Trim Bars.

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Design Guide for Economical Reinforced Concrete Structures

Fig. 7.6 Reinforcement Details for Column-like Wall Segments. It is very important to indicate on the structural drawings the limitations for typical reinforcement around an opening. When openings become relatively wide or long, portions of the wall may behave more like beams or columns and they need to be detailed accordingly. For example, for relatively wide openings, the segment of the wall above and below the opening may require beam-type reinforcement (longitudinal bars and stirrups). Similarly, vertical wall segments adjacent to an opening may behave more like columns and should be detailed as such. Recommended details are illustrated in Fig. 7.6. The spacing of the trim bars need to be indicated on the structural drawings as well. In cases where a large number of bars are cut either because of the size of the opening or the amount of reinforcement that is required in the wall, a large amount of trim bars will be required on each side of the opening. Some of the bars may be too far from the opening to be considered fully effective if the same bar size is used for the trim bars as in the wall. This is illustrated in Fig. 7.7 where the cut wall bars are replaced one-for-one with trim bars.

Fig. 7.8 Cut Wall Bars Replaced with Larger Trim Bars. The main purpose of the diagonal bars at the corners of openings is to arrest cracks that can form at these reentrant corners. For openings that occur close to the top of a wall or where openings are stacked on top of each other, the typical straight diagonal bar detail may not be possible. In order to properly develop the diagonal bars, either a standard hook needs to be provided at one end or the bar can be bent, as illustrated in Fig. 7.9 for the case of stacked openings.

A possible solution to this is to use fewer bars that are larger. This is illustrated in Fig. 7.8 for the case depicted in Fig. 7.7.

Fig. 7.9 Diagonal Bar Development.

7.4.6 Wall Corners and Intersections

Fig. 7.7 Cut Wall Bars Replaced One-for-one with Trim Bars.

7-4

The reinforcement at wall corners and intersections need to be carefully detailed to avoid installation and other problems. Long transverse bars with hooks at one or both ends should be avoided because they are very difficult to install. Wall bars are often assembled in curtains or mats that are lifted into position. Hooks complicate preassembly, transportation, storage, and handling of the curtains. Constructability is enhanced by providing straight horizontal bars that are lapped spliced together by separate bars; by doing so, adjacent curtains can be installed without interference (Reference 19). Furthermore, the curtains can easily be adjusted to maintain proper con-

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Design Guide for Economical Reinforced Concrete Structures

Fig. 7.10 Wall Corner and Intersection Details that Should Be Avoided – Single Layers of Transverse Reinforcement.

Fig. 7.14 Wall Intersection Detail That Should Be Avoided – Double Layers of Transverse Reinforcement.

0 in. (typ.)

(a)

(b)

Fig. 7.11 Preferred Wall Corner and Intersection Details – Single Layers of Transverse Reinforcement.

Fig. 7.15 Preferred Wall Intersection Details – Double Layers of Transverse Reinforcement.

crete cover as the independent hooked bars used for the lap splices are tied in place. The costs associated with the extra reinforcing bars needed for the lap splices are far outweighed by the costs associated with the labor needed for increased handling and installation of the bars with hooks on the ends.

The detail illustrated in Fig. 7.14 should be avoided at wall intersections for the reasons stated previously. The preferable layouts are shown in Fig. 7.15. Once again, the layout in Fig. 7.15b is only possible in relatively thick walls.

Depicted in Fig. 7.10 are three examples of details at corners and intersections that should be avoided in walls with one layer of transverse reinforcement because of the reasons noted above. Illustrated in Fig. 7.11 are the preferred details, which show the separate hooked bars that are doweled to the straight bars in the wall.

The location of the longitudinal bars at wall corners and intersections must also be carefully investigated (Reference 20). Depicted in Fig. 7.16 is a common detail for bar arrangement at a corner of a wall. The location of the longitudinal bars at the corner appears to be reasonable, but problems become readily apparent once transverse bars are included (see Fig. 7.17).

The details shown in Fig. 7.12 at the corners of walls with two layers of transverse reinforcement with hooks on their ends should be avoided because they make it difficult to use preassembled curtains of bars. Of the three arrangements illustrated in Fig. 7.13, detail a is common, but detail b is preferred because the separate 90-degree hooked bars that are lap spliced with the two preassembled double-bar curtains of transverse reinforcement is easy to construct. Detail c is also easy to construct for preassembled curtains but it can only be used in walls that are thick enough to accommodate the width of the U bars (hairpins) at the ends that are lap spliced to the transverse reinforcement in the walls. Fig. 7.16 Common Reinforcement Detail at Wall Corners (sp is the centerto-center distance between bars).

(a)

(b)

Fig. 7.12 Wall Corner Details That Should Be Avoided – Double Layers of Transverse Reinforcement.

(a)

(b)

(c)

Fig. 7.17 Standard Details at Wall Corners (a) Longitudinal Bars Located Outside of the Transverse Bars (b) Longitudinal Bars Located Inside of the Transverse Bars.

Fig. 7.13 Preferred Wall Corner Details – Double Layers of Transverse Reinforcement. Concrete Reinforcing Steel Institute

7-5

Design Guide for Economical Reinforced Concrete Structures

(a)

(b)

Fig. 7.18 Preferred Details at Wall Corners (a) Longitudinal Bars Located Outside of the Transverse Bars (b) Longitudinal Bars Located outside of the Transverse Bars. Fabrication and placing tolerances for the transverse bars in the wall can result in an irregular layout at the corner. Because of this, placing a longitudinal bar at the intersection of the transverse bars is not possible. Instead, the longitudinal bar will need to be offset from this working point. As noted above, the transverse bars in the wall at the corner will be lap spliced together by a separate hooked bar. The fabrication tolerance for the bend radius of this bar and the angular deviation of the corner bars in the wall also make it difficult to locate and tie the longitudinal bar on the outside face. Furthermore, if the two outside face curtains of reinforcing steel were preassembled, it would be difficult to locate the corner longitudinal bar once the curtains have been erected and the transverse corner bars have been placed.

verse bars. It is evident that the longitudinal bar that is located on the inside face of the core is not needed and only adds to congestion at this location. Illustrated in Fig. 7.21 is the preferred detail for the longitudinal bars at a wall intersection.

(a)

The details illustrated in Fig. 7.18 are preferred because the single longitudinal bar shown in Fig. 7.17 has been replaced with two longitudinal bars (one on each wall located slightly away from the corner). These longitudinal bars can be easily placed, especially if the curtains are preassembled. A similar situation occurs at wall intersections. Depicted in Fig. 7.19 is a common detail for bar arrangement at a wall intersection. Figure 7.20 shows the same detail with the trans-

Fig. 7.19 Common Reinforcement Detail at Wall Intersections.

7-6

(b)

Fig. 7.20 Standard Details at Wall Intersections (a) Longitudinal Bars Located Outside of the Transverse Bars (b) Longitudinal Bars Located Inside of the transverse Bars.

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Design Guide for Economical Reinforced Concrete Structures

(b)

(a)

Fig. 7.21 Preferred Details at Wall Intersections (a) Longitudinal Bars Located Outside of the Transverse Bars (b) Longitudinal Bars Located Inside of the Transverse Bars.

7.5 Detailing Requirements and Guidelines for SDC D, E, or F

requirements for walls in structures assigned to SDC C; it is assumed that the provisions in ACI Chapter 11 provide the required level of ductility in such cases.

7.5.1 Overview Special structural walls are required in structures assigned to SDC D, E, or F that utilize bearing wall systems, building frame systems, and dual systems. Detailing requirements for such walls are given in ACI 18.10. All of the requirements and guidelines presented above are also applicable. The requirements in ACI Chapter 11 are applicable to walls in structures assigned to SDC A, B, and C. Unlike two-way slabs without beams, beams, and columns, there are no separate

7.5.2 Web Reinforcement Requirements The provisions of ACI 18.10.2.1 for required web reinforcement in special structural walls are summarized in Fig. 7.22, which is adapted from Reference 7. Reinforcement provided for shear strength must be continuous and uniformly distributed across the shear plane. This uniform distribution helps control the width of inclined cracks.

Fig. 7.22 Web Reinforcement Requirements for Grade 60 Bars in Special Structural Walls.

Concrete Reinforcing Steel Institute

7-7

Design Guide for Economical Reinforced Concrete Structures

Fig. 7.23 Design and Detailing Requirements for Special Boundary Elements.

7.5.3 Boundary Elements During a seismic event, the ends of a wall and the edges adjacent to openings can be subjected to large compressive forces as the wall undergoes cyclic deformations. Special transverse reinforcement may be required at these locations to confine the concrete and to restrain the longitudinal reinforcement in the wall so that buckling of the bars does not occur.

Regardless of the method, the detailing requirements of ACI 18.10.6.4 must be satisfied. A summary of these requirements is given in Fig. 7.23, which is adapted from Reference 7. Even though special boundary elements may not be required, additional transverse reinforcement at the ends of the wall may be required where the provisions of ACI 18.10.6.5 are met. The reinforcement details in this case are illustrated in Fig. 7.24, which is adapted from Reference 7.

Two methods to determine whether special elements are required or not are given in ACI 18.10.6.2 and 18.10.6.3.

Fig. 7.24 Reinforcement Details Where Special Boundary Elements are not Required and the Provisions of ACI 18.10.6.5 are Met.

7-8

Concrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures

CHA PTER 8 Diaphragms 8.1 Overview Guidelines and recommendations on the economical design and detailing of conventionally reinforced, cast-in-place diaphragms and collector elements are contained in this chapter. Information is provided on determining the thickness and detailing the longitudinal and transverse reinforcement. Specific requirements for diaphragms and collectors in structures assigned to SDC D, E, or F are given in Section 8.4 of this Guide.

8.2 Determining the Diaphragm Thickness In general, the thickness of a diaphragm must be sufficient to resist in-plane bending moments, shear forces, and axial forces due to the combinations of gravity and lateral loads. ACI Chapter 12 requires that floor and roof diaphragms in buildings assigned to SDCs A through C have a thickness not less than that required for floor and roof elements that are contained in other chapters of ACI 318. Thus, diaphragms can be initially checked for the applicable load combinations using the thickness determined by the information provided in Chapters 3 and 4 of this Guide. There are no minimum thickness requirements prescribed in ACI Chapter 12.

8.3 Detailing Requirements and Guidelines for Reinforcement The reinforcement that is required in the diaphragm is determined using the applicable load combinations for axial force, bending moment, and shear force.

According to ACI 12.5.2.3, nonprestressed chord reinforcement must be located within h/4 of the tension edge of the diaphragm where h is the depth of the diaphragm in the direction of analysis (see Fig. 8.1, which is adapted from Reference 7). This helps ensure that the shear flow through the depth of the diaphragm is uniform. Chord reinforcement is usually positioned near the edge of the diaphragm and is placed within the middle third of the slab or beam depth to minimize interference with the slab or beam longitudinal reinforcement. Furthermore, at this position, the chord reinforcement has a minimal effect on the flexural strength of the slab or beam. Required transverse reinforcement for shear is commonly incorporated into the bottom mat of the uniformly distributed reinforcement in the slab. It is important to call out the required lap splice lengths for these bars on the structural drawings because they may exceed the lengths that are required for the typical slab reinforcement. Collector reinforcement is typically located within the mid-depth of the slab, similar to chord reinforcement. The amount of collector reinforcement is determined based on the applicable load combinations for combined axial force and bending moment. In cases where the slab is not sufficient to act as a collector, beams must be provided. The requirements and guidelines given in Chapter 5 can be used in such cases.

Fig. 8.1 Location of Reinforcement Resisting Tension Due to Moment and Axial Force (ACI 12.5.2.3).

Concrete Reinforcing Steel Institute

8-1

Design Guide for Economical Reinforced Concrete Structures 8.4 Detailing Requirements and Guidelines for SDC D, E, or F 8.4.1 Overview Earthquake design forces for diaphragms are to be obtained from the general building code using the applicable provisions and load combinations. In the case of the IBC and ASCE 7, the load combinations amplify the code-prescribed earthquake forces by the overstrength factor