*2,635*
*475*
*81MB*

*English*
*Pages 523*
*Year 23 July 2014*

- Author / Uploaded
- Krishnan Sathia

*Table of contents : Title page......Page 2Copyright......Page 3Table of Contents......Page 4Foreword......Page 15Note from the Author......Page 17CHAPTER 1 Loading......Page 21CHAPTER 2 Load Generation......Page 158CHAPTER 3 Combining Load Cases......Page 282CHAPTER 4 Dynamic Properties of Structures......Page 325CHAPTER 5 Dynamic Loads......Page 383Index......Page 493*

Principles of Structural Analysis—Static and Dynamic Loads Connecting Theory to Practice with STAAD.Pro® KRISHNAN SATHIA

STATIC AND DYNAMIC LOADS First Edition Copyright © 2014 by Bentley Institute Press Bentley Systems, Incorporated 685 Stockton Drive Exton, Pennsylvania 19341 www.bentley.com/books Printed in the United States of America All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. STAAD.Pro is a registered trademarks of Bentley Systems, Incorporated All other trademarks, brands, company or product names not owned by Bentley Systems or its subsidiaries are the property of their respective owners, who may or may not be affiliated with, connected to, or sponsored by Bentley Systems, Incorporated or its subsidiaries. Library of Congress Control Number: 2014937175 ISBN: 978-1-934493-37-3

Contents Foreword Note from the Author

CHAPTER 1

Loading

1.0 Loading 1.0.1 Introduction 1.0.1.1 Static Loads 1.0.1.2 Dynamic Loads 1.0.1.3 Combining Loads 1.0.2 The LOAD LIST command 1.1 Loading—Primary Load Types 1.1.1 Introduction 1.1.2 Description 1.1.2.1 What Comes under the Load Heading? 1.1.2.2 Loading Type 1.1.3 Load Item Categories 1.1.3.1 Selfweight 1.1.3.2 Loads on Frame Members 1.1.3.3 Direction of Loading 1.1.3.3.1 Local 1.1.3.3.2 Global 1.1.3.3.3 Projected 1.1.3.3.4 Concentrated Load along Projected Axis Directions 1.1.3.4 Applying Loads at an Offset from the Shear Center 1.1.3.5 Members with Singly Symmetric and Unsymmetric Cross-Sections 1.1.3.6 Axial Loads Applied away from the CG 1.1.3.7 Applying a Concentrated Force/Moment at the Start and/or End of a Member 1.1.3.7.1 Member Offsets 1.1.3.7.2 Member Orientation 1.1.4 Alternate Span Loading 1.1.5 Pre-tension Loads 1.1.6 Loads on Tension-Only and/or Compression-Only Members 1.1.7 Curved Members 1.1.8 Displaying the Loads in the STAAD.Pro GUI 1.1.9 Generation of Trapezoidally Varying Loads on Members 1.1.10 Generation of Concentrated and Distributed Loads on the Members and

Elements of Offshore and Floating Structures 1.1.11 Fixed End Loads 1.1.12 Empty Load Cases 1.1.13 Center of Action of the Applied Loads 1.1.14 The Maximum Number of Load Cases that Can Be Specified in a Model 1.1.15 The SET NL Command 1.1.16 Finding the Total Quantity of Loads in a Load Case 1.1.17 Finding the Loads on a Specific Member of a Model 1.2 Panel Loads—Floor Loads, Oneway Loads, Area Loads 1.2.1 Introduction 1.2.2 Floor Load 1.2.2.1 Load Distribution Principle 1.2.2.2 Assigning Floor Loads Using the GUI 1.2.2.3 What Are XRANGE, YRANGE, and ZRANGE? 1.2.2.4 Member Offsets and X/Y/Z Ranges 1.2.2.5 Direction of Action of the Loads 1.2.2.6 Limitations of the Floor Load Algorithm and Modeling Errors That Prevent Successful Load Generation 1.2.2.7 Floor Groups 1.2.2.8 Excluding the Slab from the Model 1.2.2.9 Crisscrossing Members and Panel Identification 1.2.2.10 Openings on Floors 1.2.2.11 Floor Load and Oneway Load on Inclined Planes 1.2.2.12 Comparing a “Beam+Floor-Load” Model with a “Beam+Plate+ElementLoad” Model 1.2.3 Oneway Load 1.2.3.1 The TOWARDS Option 1.2.4 Curved Members 1.2.5 Area Load 1.2.6 Oneway Loads and Floor Loads as Seismic Weights for ELFP-Based Seismic Analysis 1.2.7 Oneway Loads and Floor Loads as Seismic Weights for Dynamic Analysis 1.2.8 Using the FLOAD and ONEWAY Load Facilities to Apply Pressures along Horizontal Directions on a Structure 1.3 Support Displacement Loads 1.3.1 Introduction 1.3.2 Discussion 1.3.3 Specifying Support Displacement Loads Using the STAAD.Pro GUI 1.3.4 Forcibly Inducing a Displacement at a Point Which Is Not a Support 1.3.5 Estimating the Load that Will Cause a Known Displacement 1.3.6 Forces and Moments Caused by Rigid Body Movements at Lifting Points 1.3.7 Support Displacement Loads and Cables 1.4 Prestressing Loads

1.4.1 Introduction 1.4.2 Discussion 1.4.3 Results of the Analysis 1.4.4 What Command Should I Use—MEMBER PRESTRESS or MEMBER POSTSTRESS 1.4.5 Cable Profile 1.4.6 Syntax of the Commands in the STAAD.Pro Input File 1.4.7 Cable Arrangement that Produces a Pure Axial Compression 1.4.8 Effects of Creep and Shrinkage 1.4.9 Initial Stress in a Member 1.4.10 Prestress Load in Plates and Solids 1.5 Loads on Plates and Solids 1.5.1 Introduction 1.5.2 Discussion 1.5.3 Load Options for Plate Elements 1.5.3.1 Uniform Pressure Loads on Plate Elements 1.5.3.2 Trapezoidally Varying Pressure Loads on Plate Elements 1.5.3.3 Plate Meshing—How It Affects the Processing of Loads on Plates 1.5.3.3.1 Pressure Loads and Mesh Density 1.5.3.4 Pressure Loading on a Partial Area of Elements 1.5.3.5 Friction Loads on Plate Elements 1.5.3.6 Concentrated Loads on Plate Elements 1.5.3.7 Line Loads on Plate Elements 1.5.3.8 Loads along the Edge of Plate Elements 1.5.3.9 Fixed End Actions 1.5.3.9.1 Element Nodes Declared as Supports 1.5.3.10 Hydrostatic Loads 1.5.3.11 Wind Load Generation on Structural Components Modeled Using Plate Elements 1.5.3.12 Prestress Load on Plates 1.5.4 Applying Pressure Loads on Surfaces 1.5.5 Loads on Solid Elements 1.5.5.1 Pressure Loads on Solids 1.5.5.2 Applying a Moment on a Solid 1.6 Temperature and Strain Loads 1.6.1 Introduction 1.6.2 Temperature Loading—Discussion 1.6.2.1 Types of Temperature Loads 1.6.2.1.1 Uniform Increase or Decrease in Temperature 1.6.2.1.2 Temperature Gradient across the Depth or Width 1.6.2.2 Data Needed to Calculate Input Terms for Specifying Temperature Loads 1.6.2.3 Temperature Loads on Members—How to Specify 1.6.2.4 Temperature Loads on Plates—How to Specify 1.6.2.5 Temperature Loads on Solids—How to Specify

1.6.2.6 Example for Uniform Increase or Decrease in Temperature in Beams, Plates, or Solids 1.6.2.7 Analysis Procedure for a Uniform Rise or Fall in Temperature in a Frame Member 1.6.2.8 Example for Temperature Gradient across the Depth or Width for Frame Members 1.6.2.9 Analysis Procedure for Temperature Gradient across the Depth or Width of a Frame Member 1.6.2.9.1 Member Depth and Width 1.6.2.10 Conversion of Units of Temperature 1.6.2.11 Temperature Loads and Buckling 1.6.2.12 Heat Transfer Analysis 1.6.2.13 Relationship between Material Properties and Temperature 1.6.3 Strain Load—Discussion

CHAPTER 2

Load Generation

2.0 Load Generation 2.0.1 Introduction 2.1 Wind Load Generation 2.1.1 Introduction 2.1.2 Data Required for Wind Load Generation 2.1.3 Types of Structures for Wind Load Generation 2.1.3.1 Closed Structures 2.1.3.1.1 Windward and Leeward Faces 2.1.3.1.2 Factor Term in the Wind Load Generation Input 2.1.3.1.3 The TYPE Command 2.1.3.1.4 Wind Intensity 2.1.3.1.5 Exposure Factor 2.1.3.1.6 Pressure versus Height Table 2.1.3.1.7 Specifying a Set of Members on Which to Generate the Load 2.1.3.1.8 Procedure Used by STAAD.Pro for Calculating the Joint Load from the Wind Pressure 2.1.3.2 Open Structures 2.1.3.2.1 Wind Load Generation and Ice Formation on Members of Open-Lattice Structures 2.1.4 Types of Load Generated 2.1.5 Obtaining a Report of the Joint and Member Loads Created by the Wind Load Generator 2.1.6 Converting the Wind Pressures to Concentrated and Distributed Loads on the Structure—Is It Based on the Rules of Any Code? 2.1.7 Modeling Aspects Which Hinder the Performance of the Wind Load Generation Facility for Closed Structures 2.1.7.1 Multiple Structures 2.1.7.2 Duplicate Members

2.1.7.3 Overlapping Members 2.1.7.4 Intersecting Members 2.1.7.5 Round-off Errors in Joint Coordinates 2.1.7.6 Structures Declared as the PLANE Type 2.1.7.7 Incomplete Panels 2.1.8 Excluding Members from Receiving Loads 2.1.9 Out-of-Plane Nodes 2.1.10 Directions along Which the Wind Load Generation Can Be Performed 2.1.10.1 Wind Blowing along Non-global Directions 2.1.11 Time Taken to Display Wind Loads in the GUI 2.1.12 Wind Load Generation for Structures Composed Entirely of Plate Elements 2.1.13 Fireproofing and Wind Loads 2.1.14 Wind Load Magnification Due to the Presence of External Equipment 2.1.15 Wind Pressure Profile Calculation per Building Codes 2.1.16 Wind Load Generation on Plane Frames 2.1.17 Wind Load Generation for Structures with Complex External Facades 2.1.18 Applying Wind Load on Surface Entities 2.2 Snow Loads 2.2.1 Introduction 2.2.2 Discussion 2.2.2.1 The Data Associated with Step 1 2.2.2.2 The Data Associated with Step 2 2.2.3 Excluded Portions of the ASCE 7-02 Code 2.2.4 Output Produced by STAAD.Pro for Snow Load Generation 2.2.5 Two-way Distribution versus One-way Distribution 2.2.6 Generation of Snow Load on Individual Members of an Open-Lattice Structure 2.3 Moving Loads 2.3.1 Introduction 2.3.2 Discussion 2.3.3 Data required by STAAD.Pro 2.3.4 Definition of the Vehicle 2.3.4.1 Description of the Vehicle 2.3.4.1.1 The WIDTH Parameter 2.3.4.1.2 Standard Vehicular Loading from Specifications Documents 2.3.5 Placement of the Vehicle on the Deck and Generation of the Load Cases 2.3.6 Vehicles Moving in Negative Global Directions 2.3.7 Syntax of the Commands in the STAAD.Pro Input File for Stage 2 Input 2.3.8 Method for Breaking up a Trailer into Two or More Vehicles 2.3.9 Transferring the Wheel Loads to the Members of the Structure 2.3.10 Sign of the Wheel Loads—Positive versus Negative 2.3.11 Moving Loads on Structures Whose Type Is STAAD PLANE 2.3.12 Loads Consisting of Just a Single Axle 2.3.13 Defining the Moving Load Description through an External File

2.3.14 Viewing the Values (Magnitude) of the Generated Loads 2.3.15 Displaying (Viewing) the Generated Loads in the GUI 2.3.16 Lane Loads 2.3.17 Member Specifications 2.3.18 Moving a Vehicle on a Sloping Roadway or Ramp 2.3.19 Moving a Vehicle in a Skewed Direction 2.3.20 Multiple Lanes of Vehicles 2.3.21 Moving a Vehicle along a Curved Roadway 2.3.22 Generating Moving Loads on Plate and Solid Elements 2.3.23 Automatically Generating Combination Cases that Include the Generated Moving Load Cases 2.3.24 Including More than One Load Case Using ADD LOAD 2.3.25 Displaying the Deflection Diagram and Generated Loads Simultaneously 2.3.26 Generating Loads Acting along the Horizontal Direction Due to a Moving Vehicle 2.3.27 RM Bridge and LEAP Software—Alternatives to STAAD.Pro's Moving Load Generator 2.4 Seismic Load Generation 2.4.1 Introduction: Dynamic Analysis—The Basics 2.4.2 Discussion 2.4.3 Procedure 2.4.3.1 Part 1: Input for Step 1 2.4.3.2 Part 2: Input for Step 2 2.4.4 Weight of Fireproofing 2.4.5 Specifying Seismic Weights through Reference Load Cases 2.4.6 Periods PX and PZ 2.4.7 Accidental Torsion 2.4.7.1 Multiplying Factor for Accidental Torsion 2.4.7.2 Accidental Torsion and Instability in Frames 2.4.8 Center of Rigidity 2.4.9 Distribution of Base Shear 2.4.10 Structures with Supports at Different Elevations 2.4.11 Distribution of Lateral Force between the Nodes on a Floor 2.4.12 Buried Structures 2.4.13 Order of Load Cases in the STAAD.Pro Input File 2.4.14 Understanding the Results 2.4.14.1 Additional Information for PRINT STATICS CHECK 2.4.14.2 Obtaining a Report of the Lateral Loads and Accidental Torsion Moments 2.4.15 Viewing the Generated Loads in the GUI 2.4.16 Structures with Weights and Stiffness Below their Support Elevation 2.5 Notional Loads 2.5.1 Introduction 2.5.2 Description 2.5.2.1 Under the Hood

2.5.3 Assigning Notional Loads Using the STAAD.Pro GUI 2.5.4 Syntax of the Notional Loads Specification in the STAAD.Pro Editor 2.5.5 Using the GUI to Automatically Create Combination Cases Involving Notional Loads 2.5.6 Obtaining a Report of the Lateral Loads Created by Notional Loads 2.5.7 Viewing the Generated Lateral Loads in the STAAD.Pro GUI

CHAPTER 3

Combining Load Cases

3.0 Combining Load Cases 3.0.1 Introduction 3.0.2 Discussion 3.1 Repeat Loads and Load Combinations 3.1.1 Introduction 3.1.2 Discussion 3.1.2.1 The REPEAT LOAD Method 3.1.2.1.1 How Does the Program Calculate the Displacements for a REPEAT LOAD Case? 3.1.2.1.2 Other Ways to Use the REPEAT LOAD Command 3.1.2.2 The LOAD COMBINATION Method 3.1.2.3 Why Should the Difference in the Way STAAD.Pro Treats a REPEAT LOAD Case versus a COMBINATION LOAD Case Matter? 3.1.2.4 Why Not Use Repeat Loads (or Reference Loads) All the Time? 3.1.2.5 Load Combination of Other Combination Cases 3.1.2.6 Dynamic Load Cases as Component Cases of REPEAT LOAD 3.1.2.7 Creating Load Combination Cases—Manual versus Automatic 3.1.2.8 Automatic Generation of Combination Load Cases 3.1.2.9 Editing the Tables Containing Factors for Automatic Load Combination Generation 3.1.2.10 Combining the Results of Primary Load Cases Using the SRSS Method 3.1.2.11 Combining the Results of Primary Load Cases Using the ABSOLUTE Method 3.1.3 Summary 3.2 Reference Loads 3.2.1 Introduction 3.2.2 Discussion 3.2.3 Load Selection Drop-down List Box in the GUI 3.2.4 Editing the Individual Reference Cases Using the GUI 3.2.5 LOAD COMBINATION Syntax versus the REFERENCE LOAD Syntax 3.2.6 Load Generation and Reference Load Cases 3.2.7 Using Reference Load Cases for Load-Dependent Structural Conditions 3.2.8 Using Data from Static Load Cases to Generate Seismic Weights for IBC, IS 1893, UBC, and Other Static Equivalent Methods 3.2.9 Mass Reference Load Cases—Specifying the Weight Data Just Once for Seismic and Dynamic Analyses

3.2.10 Reference Load Cases and Large Models

CHAPTER 4

Dynamic Properties of Structures

4.0 Dynamic Properties of Structures 4.0.1 Introduction 4.1 Frequencies and Modes 4.1.1 Introduction 4.1.2 Discussion 4.1.3 Methods Available in STAAD.Pro for Calculating Frequencies 4.1.3.1 Rayleigh Method 4.1.3.1.1 Using the Rayleigh Method to Calculate the Frequency of a Simple Beam 4.1.3.2 Modal Extraction Method 4.1.3.2.1 Crucial Items of Input 4.1.4 Dynamic Weight 4.1.5 Obtaining a Report of the Masses Lumped at Each Node of the Model 4.1.6 Missing Mass 4.1.7 Output Produced by STAAD.Pro for Eigenvalue Analysis 4.1.7.1 Mode Number and Corresponding Frequencies and Periods 4.1.7.2 Generalized Weight 4.1.7.2.1 Normalizing Mode Shapes 4.1.7.3 Modal Participation Factor 4.1.7.4 Modal Weight and Modal Mass 4.1.7.5 Mass Participation Factor 4.1.8 Viewing the Mode Shapes 4.1.9 Viewing the Mode Shapes in Animation 4.1.10 Saving the Animation of the Mode Shapes in a File 4.1.11 Instabilities and their Effect on Eigenvalue Extraction 4.1.12 Computing Multiple Sets of Frequencies for the Same Model 4.1.13 Damping and Frequencies 4.1.14 Taking into Account Axial Forces (P-Delta Effect) When Performing Modal Analysis 4.1.15 Member Tension/Member Compression Attributes and Eigensolution 4.1.16 Spring Tension/Spring Compression Attributes and Eigensolution 4.1.17 Structures with Multilinear Spring Supports 4.1.18 Structures with Cables 4.1.19 Comparing Rayleigh Frequencies with Eigenvalue Frequencies 4.1.20 Rigid Body Modes 4.1.21 Structural Response for a Frequency Analysis 4.1.22 Closely Spaced Modes 4.1.23 Structures that Have Identical Attributes along Two Global Directions 4.1.24 Shear Stiffness 4.1.25 Frequencies of Parts of the Model

4.1.26 Torsional Mode of Vibration of Individual Members 4.1.27 Adding a Concentrated Weight to Represent a Machine 4.1.28 Summary 4.2 Damping 4.2.1 Introduction 4.2.2 Discussion 4.2.2.1 DAMP 4.2.2.2 CDAMP (Composite Damping) 4.2.2.2.1 Input for Composite Damping 4.2.2.2.2 Method Used in the Calculation of CDAMP 4.2.2.2.3 Information in the Output File When CDAMP Is Used 4.2.2.3 MDAMP (Damping Ratio for Individual Modes) 4.2.2.3.1 Output for MDAMP-EVALUATE 4.2.2.3.2 Output for MDAMP-CALCULATE 4.2.3 Damping in Frequency Calculation 4.2.4 Incorporating the Damping Characteristics of Soil for a Response Spectrum Analysis 4.2.5 Incorporating the Damping Characteristics of Soil for a Time History Analysis 4.2.6 Modeling a Shock Absorber Which Is a Viscous Damper

CHAPTER 5

Dynamic Loads

5.0 Dynamic Loads 5.0.1 Introduction 5.1 Response Spectrum Analysis 5.1.1 Introduction 5.1.2 Discussion 5.1.3 Input Required by STAAD.Pro for RSA 5.1.3.1 Weights for Frequency Calculation (Mass Modeling) 5.1.3.1.1 Multiple Spectrum Cases and Weight Data 5.1.3.2 Spectrum Pairs Input—A Lookup Table for Spectral Data 5.1.3.2.1 Spectrum Type—Acceleration Spectra or Displacement Spectra? 5.1.3.2.2 Where Can We Get the Spectral Data From? 5.1.3.3 Spectrum Parameters 5.1.3.3.1 Scale Factor 5.1.3.3.2 Direction Factor 5.1.3.3.3 Interpolation Type—Linear Versus Logarithmic 5.1.3.3.4 Modal Combination Methods 5.1.3.3.5 Missing Mass Correction 5.1.3.3.6 ZPA 5.1.3.3.7 Damping 5.1.3.3.8 How Many Modes? 5.1.3.3.9 Viewing the Graph of the Spectrum Input 5.1.3.3.10 Multiple Response Spectrum Load Cases

5.1.4 Steps Followed by STAAD.Pro in Performing a Response Spectrum Analysis 5.1.5 Results from STAAD.Pro for a Spectrum Analysis 5.1.5.1 Mass Participation Factor 5.1.5.2 Table of Accelerations Evaluated from the Input Spectral Data Using LOG/LIN Interpolation 5.1.5.3 Base Shear 5.1.5.4 Dynamic Weight, Missing Weight, Modal Weight 5.1.5.5 Damping Ratio Used in the Individual Modes 5.1.5.6 Modal Base Action 5.1.6 P-Delta Effects on Spectrum Load Cases 5.1.7 Combining Response Spectrum Cases with Static Cases 5.1.8 ELFP Versus Response Spectrum Analysis—What Codes Require 5.1.9 Missing Mass 5.1.10 Structural Response—Absolute Values 5.1.11 Reactions in Directions Other Than the Direction of the Spectrum 5.1.12 Spectrum Analysis of Structures with Cable Members, Tension-Only and Compression-Only Members, Tension-Only and Compression-Only Supports, and so on 5.1.13 Spectrum Analysis and Multilinear Springs 5.1.14 Obtaining the Maximum Nodal Acceleration for Response Spectra Runs 5.1.15 Symmetrical Structures and Double Root Modes 5.1.16 Calculating the Response from Just a Few Specific Modes—The MODE SELECT Command 5.1.17 Recent Improvements 5.1.18 Summary 5.2 Time History Loading and Analysis 5.2.1 Introduction 5.2.2 Discussion 5.2.3 Performing Time History Analysis—Workflow 5.2.4 Types of Dynamic Loads Available in STAAD.Pro 5.2.4.1 Ground Motion (Seismic Base Excitation) 5.2.4.2 Random Excitation—Arbitrarily Varying Force or Moment with Time 5.2.4.3 Machine Vibration 5.2.5 Input Required by STAAD.Pro for THA 5.2.5.1 Plotting a Graph of the Time-Force and Time-Acceleration Pairs 5.2.6 Calculation of Frequencies and Modes 5.2.6.1 Weights for Frequency Calculation (Mass Modeling) 5.2.6.2 How Many Modes 5.2.7 Analysis Procedure 5.2.7.1 Solving the Equations 5.2.7.2 Duration for Which Dynamic Loading Acts and Response Is Calculated 5.2.7.3 The CUT OFF TIME Command 5.2.7.4 Arrival Times 5.2.7.5 Starting Time for the Time-Force Data

5.2.8 Description of the Input 5.2.8.1 Damping 5.2.8.2 The DT Option 5.2.8.3 The SAVE Option 5.2.8.4 Harmonic Loading—Stage 1 Input 5.2.8.4.1 Duration of Load for Harmonic Loads 5.2.8.4.2 CYCLES—How Many to Apply 5.2.8.4.3 STEP and SUBDIV Options 5.2.8.4.4 Difference between DT and STEP 5.2.8.5 Harmonic Loading—Stage 2 Input 5.2.8.6 Ground Motion Loading—Stage 2 Data 5.2.8.7 Random Excitation—Stage 2 Data 5.2.8.8 Explosion/Blast Loading—Stage 1 Data 5.2.8.9 Explosion/Blast Loading—Stage 2 Data 5.2.8.9.1 Explosion/Blast Loads in the Form of a Pressure Wave 5.2.8.9.2 Multiple Explosions 5.2.9 Other Dynamic Load Types 5.2.9.1 Impact Loads 5.2.9.2 Wind Loading as a Dynamic Force on a Structure 5.2.10 Output Produced by STAAD.Pro 5.2.10.1 Response History—How to Obtain 5.2.10.1.1 Joint Displacements 5.2.10.1.2 Support Reactions and Member End Forces 5.2.10.1.3 Maximum Base Shear 5.2.10.2 Displacements, Velocities, and Accelerations of Joints—Absolute or Relative 5.2.10.3 Viewing the Variation of Displacements over Time at Individual Nodes 5.2.10.4 Transient Phase Versus Steady-State Phase 5.2.10.5 Number of Cycles Needed to Attain Steady State 5.2.10.6 Selecting Modes from the Post-processing screens 5.2.10.7 Analysis Results for Blast Loading 5.2.10.8 Obtaining Results in the Frequency Domain 5.2.11 Multiple Load Cases for Time History 5.2.12 Load Combinations for Time History Loading 5.2.13 Resonance 5.2.14 MODE SELECT—Calculating the Response from Just a Few Specific Modes 5.2.15 Missing Mass 5.2.16 Modal Participation Factor for a Time History Analysis 5.2.17 Member Tension/Compression and Spring Compression/Tension 5.2.18 Cables and Multi-linear Springs 5.2.19 Floor Spectrum Index

Foreword As we enter the age of “form factor” computing where the pervasiveness of tablets, smartphones, and the cloud is beginning to reshape the rigid workflows engineers have followed for years, I begin to marvel at how far the boundaries of our imagination are being pushed to create some of the most impressive pieces of infrastructure around the world—buildings that are approaching a mile in height, suspension bridges over a mile in length, and floating production storage and offloading vessels drilling for oil that weigh over 300,000 tons. The engineering behind these truly amazing structures is nothing short of mindboggling. However, none of these structures could ever have come to fruition if it wasn’t for the advancement in simulation software. When building structures to withstand natural disasters like tsunamis, magnitude 9.0 earthquakes, and category 5 hurricanes, it would be unfathomable to think we could build such assets in an economical manner without the use of software. We now live in a competitively global environment where some of the largest engineering, procurement, and construction firms come from countries that use their currency and pricing power as their biggest weapon in securing bids. This means a firm from the United States may be designing an liquefied natural gas plant in Australia using engineers from China or India. Design software like STAAD.Pro has adapted over the years to encompass international design codes from all over the world, including custom seismic, wind, and gravity loadings particular to a certain region. However, as projects become increasingly complex, engineers have to be exponentially more cognizant of the models they produce and interpretation of the resulting output. As the old adage goes…. garbage in, garbage out. One problem, which has always existed but in recent years has been magnified, is the mapping of the physical world with its analytical counterpart. Accurately emulating how a structure would respond to certain external forces is directly proportional to the accuracy of the model. An engineer can model the behavior of a structural system using software like STAAD.Pro in a myriad of ways, but to capture the intended purpose of the system means having to understand concepts like partial moment releases, when to use spring supports, and when to use plate elements versus solid elements. This brings me to the purpose of this book. I have known the author of this book, Kris Sathia, for over 25 years. He is undoubtedly one of the most knowledgeable and professional engineers I know. He has been supporting thousands of structural engineers from around the world on countless different topics ranging from simple 2D analysis to geometric nonlinear analysis. For years, Kris wanted to write a book that would explain why certain modeling techniques would produce better results than others. Kris covers concepts like stability, different loading techniques, and the various types of dynamic analyses. However, what this book covers that very few others do is how to appropriately simulate a real-world structure in a design software. Using just four basic building blocks (nodes, beams, plates, and solids), Kris explains how engineers need to formulate a proper sequence of load transfer from one part of the structural system to the next. The concepts of instability are well documented in various scenarios, including when to release certain degrees of freedom to produce the desired effects or how to prevent uplifting in your foundations due to lateral instabilities. Another major problem in using structural software today is understanding when to use certain element types. For example, an engineer wants to model a mat foundation for a nuclear plant. Should he/she be using plate elements or solid elements? Or if the engineer is modeling a tilt-up

panel with openings, should he/she use a mesh with triangular elements, quad elements, or both? Visually, models created in various ways will look exactly the same. However, the results will differ vastly, with spurious discontinuities arising in some models and instabilities in others. Kris walks you through the various pitfalls he has encountered his fellow engineers fall into over the years. Another unique and interesting vision Kris has managed to include in this book is how to model various loading conditions experienced in the physical world. Whether it is modeling traffic across a bridge, ice accumulation on a guyed tower, winds on open-faced structures, or vibrations due to machinery in a plant, this book covers how to model static and dynamic loading conditions using more empirical methods like the International Building Codes or mathematical methods like a time history analysis. The proper way to make load combinations is also addressed so that the engineer can create various scenarios to see which loading pattern would be the governing forcing function. The author also cleverly discusses the concept of “incongruous results” where everything at first seems copasetic, but a deeper dive into the post-processing reveals improper modeling techniques that may not have been intended. The book utilizes the powerful input file from STAAD.Pro as a tool to help pinpoint these issues from the start. A section of the book is also dedicated to relating the theory behind some structural mechanics to a computer model. For example, we are all taught about the concepts of a stiffness matrix or unbraced length of a physical member. However, assigning an infinite stiffness to a member to make it a rigid body or deciding what is the unbraced length of a steel girder that is being framed into by several secondary stringers in multiple planes is not an easy task. And no matter what numbers the engineer provides, any software would happily churn out results in a matter of seconds. This book is a great reference to preemptively address these issues. My father, Amrit Das, started Research Engineers International in 1981, writing one of the first structural analysis and design software for the PC. STAAD (an acronym for STructural Analysis And Design) had its roots from the mainframe world but was the first software to take advantage of iterative design, conducive to the workflow on a PC. Through the years, software like STAAD has been used on projects all over the world on every continent to design the most impressive structures. Engineers are continuing to design structures that test the limits of our imagination, but in doing so, they must always keep in mind a few basic tenets—quality, safety, and practicality. This book does an exceptional job in guiding engineers to be successful while at the same time adhering to those three tenets. I hope you enjoy the book as much as I have. Santanu Das Senior Vice President – Design and Simulation, Bentley Systems, Incorporated

Note from the Author The complex nature of the demands that need to be met during the analysis and design of structures makes the use of software indispensable for such projects. Consider some of those demands: Degree of complexity in the types of structures - buildings, bridges, offshore and marine structures, industrial, power generation, large span roofs with cables, etc. to name a few - and their uniqueness in terms of the loads that act on them and their response to those loads. The types of structural analysis that needs to be performed - linear elastic, finite element, nonlinear, PDelta and buckling, seismic, response spectrum, machine vibration, and time history. Codes and specifications used for designing those structures in steel, concrete, aluminum, timber, etc., depends on the country where the structure is constructed. Perform component designs such as steel connection and base plate design, foundation design, etc. The task of analysis and design encompassing all of the above demands is daunting for even the engineer who has considerable knowledge of these topics. Consequently, comprehensive software tools equipped with these facilities have become indispensable in the design office. Naturally, in order to do this task well, it is imperative that he/she have a good understanding of the way the software works. One among the widely used software tools (judging by the size of the user base) for such projects is STAAD.Pro. This book, which is part 2 of a 3-part set, attempts to demonstrate the manner in which widely accepted principles of structural analysis and design as taught in universities and well documented in many text books are implemented in STAAD.Pro.

The Subject Matter of this Book Set The goal has been to create a manuscript that addresses the various theoretical issues involving the afore-mentioned tasks faced by structural engineers who use software like STAAD.Pro. Some of the topics discussed are: What input data to provide What is the source of that data How to provide that data to the software How to determine if there is a mistake in that data, including understanding the warnings and errors reported by the program as it processes that data How to determine if the program has used the data correctly Understanding the results of the analysis and design that are based on the data Methods for verifying the correctness of the results Troubleshooting errors and so on. A significant amount of this material presented has been based on answers that the engineers at Bentley's structural software groups have sent over the years to questions asked by STAAD users from around the world. Wherever possible, a Q & A form of presentation has been adopted.

Organization of the Subject Matter To organize the vast amount of subject matter, the book is written in 3 parts: Part 1: Generating the model - Geometry, properties, supports, member and element specifications Part 2: Static and Dynamic Loads (this book) Part 3: Analysis, viewing and validating results, steel and concrete design At the time of publishing part 2, parts 1 and 3 are in the advanced stages of being readied for publishing. This book is topic-centric, meaning, the author has strived to provide the reader with the maximum amount of information about any given feature in a single place. Note that this 3-part series is not intended to be a reference material on the principles of structural analysis or design which can be found in plenty of other books dedicated towards those topics. The material will be most useful to someone who has at least a basic familiarity with STAAD.Pro. First time users ought to go through the tutorials described in the program's Getting Started manual and Application Examples manual to become familiar with the program environment (GUI and editor) and to learn the methods for creating and analyzing at least simple models.

Acknowledgments This book represents the collective effort of a lot of people. Here are a few: My employer, Bentley Systems, for giving me the opportunity and latitude to work on this. My colleague at Bentley - Ray Curtis. The success of STAAD.Pro is due in no small measure to his considerable knowledge of structural mechanics (even though he is a mechanical engineer by education). The answers that he sent to questions from users and members of the STAAD team

form the source of a lot of the information in the book. My colleagues in the STAAD.Pro technical support and software development teams who did the painstaking work of implementing the features and investigating and answering hundreds of questions asked by users. My wife and son who provided a great amount of help in creating the manuscript and artwork, as well as proof-reading it. My colleague, Jeff Kelly, at Bentley Systems, and the staff at PreMediaGlobal for enabling the rubber to meet the road.

Dedication This book is dedicated to the users of STAAD.Pro, my parents, family, and colleagues at Bentley.

Always-on Learning from Bentley Institute Bentley Institute’s broad array of structural analysis and design learning opportunities enable you to master the capabilities of your STAAD.Pro software and apply best practices to improve design skills, increase productivity, and enhance infrastructure quality. From practical, hands-on virtual classrooms and personalized learning paths to a robust library of content-rich reference books to global infrastructure communities, our resources empower you to deliver better projects with greater efficiency. Structural Analysis and Design Software Training via the LEARNserver Available whenever and wherever you need it, the LEARNserver offers thousands of self-paced lectures and courses filled with skills refreshers, tips and tricks, and practical examples. Visit learn.bentley.com to view, personalize, and save learning paths and register for live and ondemand training courses. Infrastructure Design Reference Books Bentley Institute Press publishes cutting-edge university textbooks and professional reference works that deliver insight, background, and theory to global infrastructure communities. Browse our full lineup of reference books at www.bentley.com/books. Be Communities – Forums, Blogs, and More Connect, communicate, share, and learn from other structural analysis and design professionals through forums, wikis, blogs, and resource libraries. Visit communities.bentley.com to get information and answers to questions relating to your Bentley products and product technologies. For a full list of training resources, visit www.bentley.com/SathiaTraining.

CHAPTER 1

Loading 1.0 Loading 1.0.1 Introduction We know that there are various types of forces, moments, pressures, internal strains, and other stress-inducing agents that act on a structure. In structural engineering parlance, they are called loads. Loads can be broadly classified into: Static loads Dynamic loads

1.0.1.1 Static Loads A static load by definition is one whose magnitude and direction does not vary with time. In STAAD.Pro, with reference to applying loads on a model, two methods are involved: A. Apply the data as a “load item.” Load items come in many categories, such as a distributed load

on a member, a concentrated load at a joint, a pressure load on a plate or solid element, and temperature changes to members and elements. These are described in Sections 1.1 through 1.5. Needless to say, the load has to be known to the user in the format or syntax that STAAD.Pro “understands” for load items. B. Instruct the program to calculate the load item from a set of data that forms the source of that load item. After calculating it, the program will also apply the load item on the associated entities of the model. This is necessary when the load is in an abstract form, and not in the format that STAAD.Pro understands for load items. Examples of Method A: A distributed load on a beam A concentrated force at a joint A pressure load on a plate element Examples of Method B: A vehicle travelling on a bridge. The weight transmitted by the vehicle has to be reduced to a set of distributed and concentrated loads on the beams, plates, and joints. Wind pressure on a building. The pressure has to be converted into a set of concentrated forces at the nodes or distributed forces on the beams and columns. The various options available under Method A are discussed in this chapter. Method B is known in STAAD.Pro as LOAD GENERATION. It is required when the manual calculation of the load items from the load source is laborious. The load generation facilities available in STAAD.Pro are discussed in Chapter 2. The end product of both these methods are called Primary Load cases which are the packages containing the data that are used by the program for creating the load vector during stiffness analysis.

1.0.1.2 Dynamic Loads If the magnitude of a load or its direction changes with time, it is known as a dynamic load. Examples of dynamic loads are (a) the forces induced in a building due to seismic activity, (b) the forces induced in a structure due to vibrating machinery such as a turbine, and (c) a load that varies arbitrarily over time such as a blast load. The method used for analyzing a structure for these loads is discussed in Chapter 4.

1.0.1.3 Combining Loads Finally, the response of a structure has to be measured when load items from various load sources (gravity, wind, snow, vehicular, etc.) act simultaneously. This is necessary for ensuring that the structure is safe from the standpoint of structural adequacy of the beams, columns and slabs, and serviceability conditions. It brings us to the topic of combining loads, and is discussed in Chapter 3.

1.0.2 The LOAD LIST command A model may contain dozens or even hundreds of load cases (primary + combination). From those, specific sets may need to be short-listed for specific reasons. For example, capacity checks during

steel or concrete design will have to be done for factored combination cases, whereas serviceability checks will have to be done for service load cases (unfactored combination cases). Or we may want the support reactions or joint displacements to be reported in the output file for just a few primary load cases. The command that makes this possible is LOAD LIST n1 to n2

Example 1 LOAD LIST 1 TO 8 PRINT SUPPORT REACTIONS LIST 6 16 26 36

Example 2 LOAD LIST 31 TO 49 PARAMETER CODE BS5950 PY 150 MEMB 52 76 127 TO 165 LVV 0.5 MEMB 142 152 162 TRACK 2 ALL CHECK CODE ALL

Example 3 LOAD LIST 32 TO 40 START CONCRETE DESIGN CODE IS13920 CLEAR 0.05 ALL FC 25000 ALL FYMAIN 500000 ALL FYSEC 500000 ALL DESIGN BEAM 175 TO 197 201 TO 231

Keep in mind that the LOAD LIST command is for operations done by the analysis and design engine, not by post-processing. In the post-processing mode, there is a facility for selecting specific load cases for viewing specific results. It is called Select Load Case and is discussed in chapters 3 to 6 of Part III. To restore the full set of load cases for any subsequent operations, use the following command before that operation. LOAD LIST ALL

1.1 Loading—Primary Load Types 1.1.1 Introduction

As discussed in Section 1.0, a load item is a means of applying a load when it is known in a format that enables it to be applied directly on specific entities of a model such as nodes, members, and elements. In this section, we will look into the mechanisms available to apply them to the joints and members of the STAAD.Pro model. Required reading 1. Technical Reference manual—Section 1.16 Loads and Section 5.32 Loading Specifications 2. Application Examples manual—Examples 1–29 and many more in the Examples folder of the installation 3. Graphical Interface Help manual—Section 1.4 Fundamentals—Load Types in STAAD.Pro

FIGURE 1.1.1 Section 1.4 of the STAAD.Pro Graphical Interface Help manual

1.1.2 Description A load item is specified under a heading called a PRIMARY LOAD CASE that looks like this. LOADING n (LOADTYPE a1) (REDUCIBLE) (TITLE any_load_title)

The items shown in parentheses are optional items, meaning, it is not essential to specify them. Thus, the title can be as simple as LOAD n

or LOADING n TITLE any_load_title

or LOADING n any_load_title

n, generally known as the load case number, is a unique positive integer (including and between 1

and 99999) to identify the load case. The term “unique” is meant to indicate that no two LOAD CASES can have the same number. The individual load cases in the model are identified by the number. Load case numbers do not have to be in a sequential order. The first load case in the model can be numbered 12, the second case can be 3, the third case can be 1, the fourth case can be 8, and so on. In other words, any order is allowed. a1 in the aforementioned expression is one of the following loading types, as described in Section 5.32 of the STAAD.Pro Technical Reference manual. Dead Live

Rain Water/Ice Ponding

Wind on Ice Crane Hook

Roof Live

Dust

Mass

Wind

Traffic

Gravity

Seismic

Temperature

Push

Snow

Accidental

None

Fluids

Flood

Soil

Ice

These are described in more detail later in this section. REDUCIBLE, which refers to live load reduction per the UBC (Uniform Building Code) and IBC (International Building Code), is described in Section 5.32 of the STAAD.Pro Technical Reference manual. any_load_title is a user-specified character string (title) to help us understand the data contained in that load case. Some examples are equipment load, braking force, and 40 degree rise in temperature. This is only for the purpose of identification. It has no significance from the calculations standpoint.

1.1.2.1 What Comes under the Load Heading? Under the load case heading, we specify the various load items. Each load item has a distinct category. Some category names are: Selfweight Joint Load Member Load Element Load Prestress Load Temperature Load Fixed End Load A complete list of these categories is described in Section 5.32 of the STAAD.Pro Technical Reference manual. The following are some examples of primary load cases. Example 4

LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1 SELFWEIGHT Y -1.0 JOINT LOAD 4 5 FY -15. ; 11 FY -35.

Example 5 LOADING 4 WIND FROM WEST MEMBER LOAD 1 2 UNI GX 0.6 ; 8 TO 10 UNI Y -1.

Example 6 LOAD 17 LOADTYPE Roof Live TITLE Water Tank on Roof ELEMENT LOAD 48 TO 73 PR GY -0.9

FIGURE 1.1.2 Description of the contents of a primary load case

In the STAAD.Pro Graphical User Interface (GUI), primary load cases are created from the General-Load page as shown in Fig 1.1.3.

FIGURE 1.1.3 Dialog box in the STAAD.Pro GUI for creating a primary load case

1.1.2.2 Loading Type In Examples 4 and 6 of primary load cases, we used the term LOADTYPE. This is a tag through which the load case being created is identified in the event that the user chooses to run the program’s Automatic Load Combination generator. As described in Section 3.1, that feature requires the program to associate the primary load cases in the model with types such as DEAD, LIVE, and WIND, mentioned in building codes. If one does not set the type here, this load case will be disregarded during combination generation.

FIGURE 1.1.4 Dialog box in the STAAD.Pro GUI for specifying the loading type to a primary load case

If a primary load case has not been assigned a type, or has been assigned the wrong type, it can be set/modified at any time from the same place shown in Fig 1.1.4. Primary load cases created with the type tag will look like the following in the STAAD.Pro input file. LOAD 1 LOADTYPE Dead TITLE GRAVITY SELFWEIGHT Y -1 LIST 1 TO 3 LOAD 2 LOADTYPE Live TITLE EQUIPMENT MEMBER LOAD 2 UNI GY -2.3 LOAD 3 LOADTYPE Wind TITLE WIND FROM WEST JOINT LOAD 2 FX 14

1.1.3 Load Item Categories As discussed previously, there are several categories of load items that can be specified through a primary load type. Some of them are described in this chapter.

1.1.3.1 Selfweight Selfweight, as the name indicates, is the weight of the various entities of the model, and is one of the standard load items that can be assigned in STAAD.Pro. The command syntax is very simple. LOAD 1 GRAVITY LOAD SELF Y -1.0

FIGURE 1.1.5 Dialog box in the STAAD.Pro GUI for assigning selfweight

Starting with STAAD.Pro 2007 Build 03, the selfweight command has been enhanced in that it can be assigned to a specific list of members, plates, and solids. Entities not in this list will not have their weight considered. In previous versions, a list could not be associated with selfweight, and hence, the weight of all the entities in the model was automatically considered. Example 7 LOAD 1 GRAVITY LOAD SELFWEIGHT Y -1.1 LIST 1 TO 5 7 TO 18 20 TO 62 66 344 TO 349 – 351 353 TO 356 358 361 365 522 524 526 528 530 532 534 536 – 538 540 542 544 546 549 551 567

FIGURE 1.1.6 Assign the selfweight to individual entities using the Assign button

This can be useful to those who wish to exclude entities from weight calculation for situations such as stage construction modeling. However, there is a potential danger when assigning this selfweight item from the GUI. After this load item is added to the load case, it is now absolutely necessary to assign this to the entities in the structure. Failing to do so will result in the selfweight item being omitted from the model and you may not realize its absence unless you specifically look for it in the editor or in Tree View in the load page. So, merely adding the load item is not enough. It must be assigned too. There is one other aspect that needs to be paid attention to. Suppose that there are 543 members in the model when the selfweight is assigned. Subsequently, let us say that we add some members and plate or solid elements and/or surfaces. The program by itself will not automatically add their numbers to the list (that accompanies the selfweight load item), and thus, their weight will not be considered. Hence, it is important to inspect the load case that contains the selfweight item, and assign it to all the newly added entities. If the selfweight command is specified through the editor as shown in the first example, meaning, without any list, then the weight of all entities is automatically considered. In other words, the

command SELFWEIGHT Y -1

implies that the weight of all entities in the model is automatically considered. The analysis engine attempts to predict the weight of the full structure. If the calculated weight happens to be less than the predicted value, a warning message to that effect will appear in the output file. *WARNING- APPLIED SELFWEIGHT IS LESS THAN TOTAL WEIGHT OF ALL STRUCTURAL ELEMENTS IN LOAD CASE 1 ALONG Y. THIS COULD BE DUE TO SELFWEIGHT APPLIED TO SPECIFIC LIST OF MEMBERS/PLATES/SOLIDS/SURFACES. TOTAL UNFACTORED WEIGHT OF THE STRUCTURE = 8.842 KIP TOTAL UNFACTORED WEIGHT OF THE STRUCTURE APPLIED = 8.201 KIP

FIGURE 1.1.7 Warning in the STAAD.Pro output file if selfweight is less than the estimated value

However, if the weight is assigned with a factor that is different from 1, there is the possibility that this check may not be as accurate as intended. Hence, it is advisable for the engineer to treat this as one of the important items to check while verifying the accuracy of the results. Keep in mind that selfweight can be calculated only if the DENSITY is specified under the MATERIAL data for the members and elements. If a custom material—something other than one of the standard materials (STEEL, CONCRETE, etc.) supplied with the program—is assigned, ensure that DENSITY is specified along with Young’s modulus, Poisson’s ratio, and so on. Else, the following message will appear in the output file. “DENSITY NOT PROVIDED. SELFWEIGHT IGNORED”.

This can also happen if a MATERIAL has not been assigned to some members or elements. Related Question: How do I find the weight of the structure? Answer: A simple way is to create a load case containing just selfweight as the load item acting along global Y. Ensure that it is assigned to the full structure, as explained earlier. Then, run the analysis and go to the post-processing mode. In the Node-Reactions page, the table on the lower-right corner is called Statics Check Results. The value displayed under “Fy” for that load case will hence be the

weight of the structure.

FIGURE 1.1.8 Finding the weight of the structure from the Statics Check Results table

The same information can also be obtained by specifying the PRINT STATICS CHECK option with the ANALYSIS command. The total applied load from each primary load will be displayed in the output file, and the load for the selfweight load case ought to be the weight of the structure.

FIGURE 1.1.9 Command for obtaining the static equilibrium report in the output file

Yet another way to obtain the weight of the structure is using the command PRINT CG

FIGURE 1.1.10 Command for obtaining the center of gravity of the structure

The output will be as shown in Fig 1.1.11.

FIGURE 1.1.11 Weight of structure reported along with CG of structure

Related Question: If fireproofing is assigned to a member, does STAAD.Pro automatically consider the weight of fireproofing during selfweight calculations for the member? Answer: Yes, it does. This is based on the profile of the fireproofing material, as shown in Section 5.20.9 of the STAAD.Pro Technical Reference manual.

1.1.3.2 Loads on Frame Members For frame members (line entities), there are a number of options for specifying load items, such as: Uniform force/moment on full span or part of the span Concentrated force/moment at an intermediate section location on the member Linearly varying load on the full span Trapezoidally varying load on full span or part of the span

FIGURE 1.1.12 Options in the STAAD.Pro GUI for creating member load items

The Application Examples and Technical Reference manuals are good sources for information on these options. Related Question: I want to apply a parabolically varying load on a member. I do not see an option for this in the program. Answer:

It is true that this type of load is not currently available in STAAD.Pro. One solution is to write a macro in Excel that converts the load into a series of concentrated loads at discrete points along the member span and apply them on the member using the MEMBER LOAD option. The macro could be written in such a way that the data are saved into a text file. The contents of that file can then be copied and pasted into the STAAD.Pro input file. If one is familiar with the feature called OpenSTAAD, its load creation functions may also be used in conjunction with the macro to directly input those concentrated loads into the STAAD.Pro input file. Related Question: What does the following warning mean? WARNING: IN UNIFORM MEMBER LOAD. ITEM “f3” NOT PROVIDED FOR MEMBER 1596 CASE 3 “f3” ASSUMED TO BE MEMBER LENGTH = 6.35

FIGURE 1.1.13 Warning messages in the STAAD.Pro output file when the end point of the load is not specified

Answer: The warnings indicate that there are some uniform member loads for which start points have been defined but not the end points. The term “f3” that appears in the warning message is represented in Figs 1.1.14 and 1.1.15 as “d2.”

FIGURE 1.1.14 Start and end points for uniformly distributed load on members

FIGURE 1.1.15 Distance from start of member to end of load

For example, the following load instruction for member 768 specifies that the load of 0.3544 kN/m begins at a location 0.952 m from the start of the member but does not specify where it ends.

FIGURE 1.1.16 Example of an incomplete member load specification

By default, the software would apply it till the end of the member, which is what the warning message is conveying. So, if the rest of the member span is to be loaded with the same intensity, we may ignore the message. Alternatively, we may specify the end location as shown next, where 1.27 is the member length. 768 UNI GY -0.3544 0.952 1.27

1.1.3.3 Direction of Loading For some load types such as uniformly distributed load on members, there are three sets of directions to choose from – Local, Global and Projected.

FIGURE 1.1.17 Directions options for member loads

The difference between these sets of directions is illustrated in Figs 1.1.18 and 1.1.19. 1.1.3.3.1 Local This means that the load acts along the corresponding local axis for the member. A positive value of the load means that the load acts along the positive direction of the axis; a negative value indicates that the load acts along the negative direction of that axis. The total load acting on the member is equal to the length (along the member’s local X axis) over which the load acts multiplied by the load intensity. If the member’s local X axis is inclined to one of the global directions, the load too will be acting in an inclined direction.

FIGURE 1.1.18 Uniform distributed load along a member’s local axis

1.1.3.3.2 Global In this case, the load acts along the corresponding global axis. As in the case of local, a positive value of the load means that the load acts along the positive direction of that global axis; a negative value indicates that the load acts along the negative direction of that axis. The total load acting on the member is equal to the length (along the member’s local X axis) over which the load acts multiplied by the load intensity. Regardless of the direction of the member’s local X axis, the load will be along a global direction.

FIGURE 1.1.19 Uniform distributed load along a global axis

1.1.3.3.3 Projected

In this case, the line representing the member is projected on to the plane normal to the axis that the load is applied along. For example, if the load is applied along PY, the two ends of the member are projected on to the global X-Z plane and those points are then joined to obtain the length over which the load acts. If the two ends of the member are at (x1,y1,z1) and (x2,y2,z2) and the load is along PY, the projected length is the distance between the points (x1,0,z1) and (x2,0,z2). The total load becomes this projected length multiplied by the load intensity. Projected length is less than full length for inclined members. 1.1.3.3.4 Concentrated Load along Projected Axis Directions Projected axes are meaningful only for loads that have a width over which they act, such as a uniform distributed load. They are not meaningful for concentrated forces or moments. Hence, for concentrated loads, projected axis directions yield the same result as global axis directions.

FIGURE 1.1.20 Uniform distributed load along a projected direction

Related Question: What is the meaning of the following error message? **WARNING** LOAD BEYOND ITS LENGTH. FULL LENGTH ASSUMED. MEMB 91

FIGURE 1.1.21 Warning in the STAAD.Pro output file when loads are applied beyond the member length

Answer: This warning is usually associated with member loads. A member load by definition is one that is applied within the span of the member instead of at the start or end node. If it is a concentrated force or moment, its point of action has to be specified in terms of the distance to that point, measured from the start of the member. If it is a distributed load, such as a uniform distributed load or a trapezoidally varying load, there are two points involved—the point where the load starts and the point where the load ends. So, there are two distances to be specified. Therefore, for any of the distances described in these cases, if the value specified is greater than the length of the associated member, it will trigger this warning.

FIGURE 1.1.22 Uniform load whose end point is beyond the end of the member

In the case of a trapezoidal load, STAAD.Pro will print the following warning message. **WARNING** TRAP LOAD BEYOND ITS LENGTH. FULL LENGTH ASSUMED. MEMB nnn CASE pp

FIGURE 1.1.23 Warning message associated with trapezoidal load applied beyond member end

In the following example, a concentrated load of –9.78 kN is applied to member numbers 89 and 91 at a distance of 8.47 m from the start joint of the beam. MEMBER LOAD 89 91 CON Y -9.78 8.47

However, if member number 91 is only 4.50 m long, it will trigger that message. The STAAD.Pro engine automatically changes the load location for that member to be 4.50 m. If we do not want this load at 4.5 m on member 91, we will have to change the input command line. Sometimes, this may be triggered by an incorrect length unit. For example, if the value were intended to be in INCHES but the most recent unit statement in the model prior to the load data indicates FEET, it could be resolved by adding the correct length unit ahead of that load case. Another possibility is that the load may have been generated through the FLOOR LOAD or ONEWAY LOAD command or the MOVING LOAD generator. A precision error is causing the load to be placed at a minute distance longer than the member length. It may be OK to ignore that warning in such cases. To obtain the details of exactly which line in the STAAD.Pro input file is responsible for the message, add the words PRINT LOAD DATA

with the PERFORM ANALYSIS or PDELTA ANALYSIS command. For example, PERFORM ANALYSIS PRINT LOAD DATA

Then, run the analysis and view the output file. The warning will appear immediately after the line containing the erroneous value of the distance.

1.1.3.4 Applying Loads at an Offset from the Shear Center From time to time, we may need to apply a load to a member not at the center of gravity (CG) of the section, but at some distance away from it. In other words, the load is offset from the CG, such as at one of the flanges instead of the middle of the web of a doubly symmetric I-shape. In Section 5.32.2 of the STAAD.Pro Technical Reference manual, for the load types defined

using UNI, UMOM, and CON options, there is a term called “f4.” This term helps us define the distance from the shear center (which is the same as CG for doubly symmetric sections) where a transverse load acts. For example, if we want to specify that, for member 43 (which is 12 ft long), a 1.5 kip/ft load acts at 0.4 ft away from the shear center, the commands would be LOAD 1 MEMBER LOAD 43 UNI GY -1.5 0 12 0.4

In the STAAD.Pro GUI, the offset is denoted using the term “d3.”

FIGURE 1.1.24 Term in the STAAD.Pro GUI for specifying a transverse load at an offset from the shear center

FIGURE 1.1.25 Transverse load acting away from the shear center along local Y

FIGURE 1.1.26 Transverse load acting away from the shear center along local Z

For a load along local Y, the offset is along local Z. For a load along local Z, the offset is along local Y. If the local axes are aligned with the global axes, the term “global” can be substituted for “local.” A positive value for “d3” represents an offset along the positive direction of that local axis. In other words, the load acts on the positive side of the shear center. Similarly, a negative value indicates that the load is on the negative side. In Figs 1.1.25 and 1.1.26, a positive value is indicated. Related Question: How do I apply a horizontal load at the bottom flange of an I-beam, and not at the center of the beam? Answer: This is explained in Section 1.1.3.4. The load will be along local Z, and the value for “d3” will be a negative number equal to half the depth of the beam.

1.1.3.5 Members with Singly Symmetric and Unsymmetric Cross-Sections Related Question: On a channel, I want to specify a uniform distributed load along the local Y axis. Does STAAD.Pro apply the load through its CG or its shear center?

FIGURE 1.1.27 Location of shear center and CG for a channel

Answer: In Section 1.1.1 of Part I, under the heading “Modeling a Member as a Line—Shear Center versus Center of Gravity,” we saw one of the dilemmas that an engineer faces when specifying a line to represent a beam with a singly symmetric or unsymmetric cross-section such as a channel, angle, and Z section. For an axial load applied using the MEMBER LOAD option, the load is assumed to act through the CG. Hence, by default, the axial load will not produce any bending on that member. For a transverse load (a concentrated load or a distributed load that is applied along the local Y or local Z axis), the load is assumed to act through the shear center by default. Hence, by default, that load does not cause torsion on that member. So, when we represent a member as a line in the model, for axial load purposes, that line passes through the CG, but for bending purposes, it passes through the shear center. For doubly symmetric sections, this does not pose a problem because both have the same location. But for singly symmetric and unsymmetric sections for which they are separate points on the cross-section, we have to decide whether to apply any additional bending (in the case of an axial load) or torsion

(in the case of a flexural load). This is discussed next.

1.1.3.6 Axial Loads Applied away from the CG Related Question: How would a STAAD.Pro user account for the effects generated due to the eccentricity of axial loads in single angles used as truss members? Answer: If the axial load is in the form of a concentrated force acting at one of the ends of the angle member, the user may calculate the resulting moment at the end and apply that moment at that end as a joint moment in addition to the axial load. If the axial load is in the form of a distributed force acting throughout the length of the angle member, the user may calculate the resulting distributed moment and apply that moment as a distributed moment along the full length of the member in addition to the distributed axial load.

1.1.3.7 Applying a Concentrated Force/Moment at the Start and/or End of a Member There are two methods for applying this load: (a) using the NODAL LOAD method and (b) using the MEMBER LOAD method by providing the distance as zero or the member length depending upon where it acts. The NODAL LOAD is the preferable method. It is assumed to be acting at the exact joint location. For the MEMBER LOAD method, it is treated as acting not at the joint, but at an infinitesimal distance away from the corresponding joint within the member span. When the member end forces are computed for that location, the effect of this load will not be seen (and hence treated as zero at the member end) because it is at a miniscule distance away from that location. In the following example, a 10 kN force is applied at the start of the member, as a MEMBER LOAD in load case 1, and as a JOINT LOAD in load case 2. LOAD 1 MEMBER LOAD 1 CON GY -10 0 LOAD 2 JOINT LOAD 1 FY -10

Notice the difference in shear force at the start of the member as shown in the beam force output.

FIGURE 1.1.28 Beam forces table in post-processing mode

The corresponding results diagram (shear force diagram for concentrated forces and moment diagram for concentrated moments) will show a sudden jump in value between that end and the next 1/12th point along the span. The reason is that results diagrams are drawn by joining straight lines between values at a total of 13 points along the span—start, end, and 11 intermediate points. This will trigger warning messages such as the following. *** WARNING : A CONCENTRATED LOAD AT ONE OF THE END POINTS OF MEMBER # 2(LOAD # 6) SHOULD BE APPLIED AS A “JOINT LOAD” AND NOT AS A “MEMBER LOAD”. FOR MORE INFORMATION, USE THE COMMAND “PRINT LOAD DATA”. *** NOTE : THE CONCENTRATED MEMBER LOAD APPLIED AT ONE OF THE NODE POINTS OF MEMBER # 2 (LOAD # 6) WILL BE TREATED AS A LOAD ACTING, NOT AT THE JOINT, BUT AT AN INFINITESIMAL DISTANCE AWAY FROM THE JOINT WITHIN THE MEMBER SPAN. TO AVOID THIS, YOU MAY APPLY THE LOAD AS A JOINT LOAD INSTEAD.

FIGURE 1.1.29 Warning in the STAAD.Pro output when a CONCENTRATED load is applied at member ends as a MEMBER LOAD

If it is applied as a JOINT LOAD, the member end forces will correctly reflect the effect of the concentrated load. Other results such as nodal displacements or support reactions will not be affected by this difference. Other aspects that determine how the load should be applied are discussed next. 1.1.3.7.1 Member Offsets The manner in which this load is applied can also be dictated by whether or not member offsets are present at that end. If the face of the member associated with that node is shifted using the MEMBER OFFSET option, the node stays at its original place, and the face of the member moves. So, when the load is applied using the JOINT LOAD method, the point of application of the load is where the node is, not where the face is. But when the load is applied using the latter method, the point of application of the load is the member’s face, which is now at some distance from the node for that member. Therefore, the method by which the load is applied should be determined by the true point of action of the load. 1.1.3.7.2 Member Orientation A JOINT LOAD can be applied only in the global axis system. But the concentrated MEMBER LOAD can be applied in two axes systems—local and global. So, if the direction is not global, then either it will have to be resolved into global axis directions and applied as a JOINT LOAD, or if it is along one of the local axes of the member, the easier method is to apply it as a MEMBER LOAD.

1.1.4 Alternate Span Loading STAAD.Pro does not have a way to automatically generate a loading pattern where every alternate span is loaded. The user would have to do that on his/her own.

1.1.5 Pre-tension Loads Consider a rod that is pre-tensioned using torque nuts at its two ends. So, it develops an axial force and tries to pull its two ends toward each other. There are two ways to apply this type of load. If the member is of the truss type, it can be modeled as a linearized cable member and an initial TENSION can be specified. Section 5.4 of Part I has more details. In Section 1.6, a load type called STRAINRATE is described. This allows a load to be specified as an initial elongation or compression in length units. This load type can be used also in cases where the member resists bending and shear. The Member Prestress and Poststress type loads described in Section 1.4 may be a third option for specifying this type of load.

1.1.6 Loads on Tension-Only and/or Compression-Only Members Those members that are declared as MEMBER TENSION or MEMBER COMPRESSION are

treated as truss type and, hence, can carry only axial forces. For such members, a load applied within their span, such as a distributed load or a concentrated force applied using the MEMBER LOAD option, will be converted to two concentrated forces at their end nodes. They are considered to be unable to resist bending and shear and do not have any transverse deflection.

1.1.7 Curved Members For members that have been assigned the MEMBER CURVE specification, the only load types STAAD.Pro can presently handle are selfweight and a uniformly distributed load over the full span of the curved beam. Other types of loads, such as concentrated forces and moments at intermediate span locations, or a trapezoidal load cannot be applied on curved members. If a concentrated force or moment has to be applied at an intermediate section point on a curved member, a joint has to be created at that location and the load has to be applied using the JOINT LOAD feature. This requires the curved member to be split up into segments that meet at those nodes.

1.1.8 Displaying the Loads in the STAAD.Pro GUI Let us say that we are opening a STAAD.Pro model in which loads have already been specified. We want to see those loads. The steps are shown in Figs 1.1.30 and 1.1.31.

FIGURE 1.1.30 Displaying load arrows in the STAAD.Pro GUI

FIGURE 1.1.31 Displaying load values in the STAAD.Pro GUI

If the load arrows are too small to be visible, use the Scales option of Structure Diagrams dialog box to make them visible.

FIGURE 1.1.32 Changing the size of the load arrows

1.1.9 Generation of Trapezoidally Varying Loads on Members In Section 1.5.3.8, the procedure for generating trapezoidally varying pressures on plate elements is explained. A similar facility is available in STAAD.Pro for frame members too. It is shown in Fig 1.1.33. Instead of pressures, it generates distributed loads that vary trapezoidally. Imagine that we have a column modeled using many segments. If the column resists a linearly varying load over its full height, manually calculating the load intensity for each segment individually is a tedious task. In such cases, the hydrostatic load simplifies the task.

FIGURE 1.1.33 Generating trapezoidal loads on members due to hydrostatic pressure

The generated loads will look like that shown in the following example.

FIGURE 1.1.34 Input data created by trapezoidal load generation on a series of members

Trapezoidal loads are internally solved by STAAD.Pro using 24 equivalent concentrated forces at equal distances apart. As a result, the section forces and section displacements for the member will

be marginally different from the exact value.

1.1.10 Generation of Concentrated and Distributed Loads on the Members and Elements of Offshore and Floating Structures Related Question: I have a model representing an offshore structure. It is subjected to wave loading. However, calculating the loads is a complex task and I want to know if STAAD.Pro has any feature for generating the wave loading per the appropriate equations and codes. Answer: There is a companion (add-on) program called STAAD.Offshore that calculates loads due to waves acting on structures and applies them at the joints of the structure. Detailed information on STAAD.Offshore is available at http://www.bentley.com/enUS/Products/STAAD.Offshore/Product-Overview.htm. STAAD.Offshore reads the structure data from the STAAD.Pro model, calculates the loads, and writes the load data back into the STAAD.Pro model.

1.1.11 Fixed End Loads A FIXED END LOAD is a facility for specifying the forces and moments at the ends of the member by assuming that both ends of the member are fixed (no translation or rotation). Assume a type of load for which there is no mechanism in STAAD.Pro to specify that load (e.g., a parabolically or cubically varying load). If we were to place fixed supports at both ends of the beam, and apply that load, we will obtain a set of reactions at each end. Those values with their signs reversed are the fixed end actions. However, there is a drawback to using this facility. While the joint displacements, support reactions, and member end forces for all the entities of the structure will be calculated accurately, the intermediate section forces will not be accurate for that specific member. That is because, the program does not know the loads acting on the span. It has only been provided with an equivalent set of end actions for that load. So, the section forces and displacements cannot be calculated correctly for those members on which such loads have been applied. Instead of this, a better option would be to replace the load with an equivalent set of closely spaced concentrated forces.

1.1.12 Empty Load Cases An empty load case is one that has only a heading, and does not contain any load items. In the following example, load 12 is an empty load case. LOAD 11 WIND CASE ELEMENT LOAD 9031 TO 9043 9067 TO 9080 PR GX 0.9 LOAD 12 CRANE LOAD LOAD 14 SNOW

MEMBER LOAD 3423 TO 3431 3735 TO 3746 4053 TO 4064 UNI GY -0.4

When we launch the analysis run, STAAD.Pro displays a window containing a message that the file contains empty load cases.

FIGURE 1.1.35 Message regarding the presence of empty load cases in the model

There is nothing fundamentally wrong in having empty load cases. The reason the program reports this message is the following. At the end of the analysis, STAAD.Pro generates results such as joint displacements, member end forces, plate element stresses, and solid element stresses for every load case and stores them in files for post-processing. For empty load cases, all the entities in the model receive a zero value. Thus, the files will be filled with zeros for all the result terms for empty load cases. For large models with thousands of joints, members, and elements, empty load cases could result in an enormous quantity of unnecessary data that will be read and displayed in post-processing. It leads to wastage of computer resources. Worse could be that on very large models, the program may reach the limits of the operating system for the volume of data that can be handled using memory mapped files, and may not be able to display the results for even genuine load cases. If you do not wish to remove the load case from the model, you can ignore the message. If you do not want to have the aforementioned window displayed, add a load of a very small magnitude, say a 1 N load at a joint to convert that load case to a non-empty one.

1.1.13 Center of Action of the Applied Loads The analyst may want to know the point of action of the sum of the loads that are acting on a structure for a certain load case such as gravity. An example of a situation where this information is required is a structure being lifted and transported. If the option PRINT STATICS CHECK is specified along with the analysis command, and the analysis is performed, this information is reported in the output file. PERFORM ANALYSIS PRINT STATICS CHECK

FIGURE 1.1.36 Specifying the STATICS CHECK option using the STAAD.Pro GUI

The output would look like Fig 1.1.37.

FIGURE 1.1.37 Center of action of the applied loads in a load case

Within a load case, the load items can act in more than one global direction. For each direction, the resultant of all the loads acting along that direction has a center of action. Hence, for each load case, the output contains three centers of action—one set for each global direction.

FIGURE 1.1.38 Report in the output file of center of action of applied loads for each global direction

This information is reported for: Primary load cases Combination cases created using the REPEAT LOAD syntax

Combination cases created using the REFERENCE LOAD syntax It is not reported for combination cases created using the LOAD COMBINATION syntax. Because this is based solely on the applied loads, the stiffness of the structure plays no role in this calculation. Related Question: How can I obtain the coordinates of the CG of the structure for two conditions: (a) for selfweight alone and (b) for selfweight plus some additional loads? Answer: Two load cases are needed—one for case (a) and the second for case (b). The first will have only the selfweight acting along global Y as the load item. The second load case will have the selfweight plus all the other loads for which the center of action is sought. LOAD 1 WEIGHT OF STRUCTURE ALONE SELFWEIGHT Y -1

LOAD 2 DEAD LOAD (SELF WEIGHT, PIPING, EQUIPMENT) SELFWEIGHT Y -1 MEMBER LOAD 13 UNI GY -0.273 51 CON GY -4.2

1.1.14 The Maximum Number of Load Cases that Can Be Specified in a Model In the case of large models, one of the parameters that controls the ability of the program to successfully complete the analysis and display the results in post-processing is the number of load cases in the model—the sum of the primary and combination cases. There is no single value that one can put on the maximum number of load cases that are permitted, because there are many other factors too that determine the ability of the program to analyze large models. There is a detailed discussion on this in Section 1 of Part 1 under the topic titled “Factors That Affect Performance.”

1.1.15 The SET NL Command There are certain features in STAAD.Pro where the ANALYSIS instruction has to be specified for each load case or for sets of load cases at a time. Some examples of this are: Seismic analysis using ELFP (IBC, NRC, IS1893, etc.) Non-linear analysis Non-linear cable analysis Change of support conditions Example 8: Multiple analysis due to change of support conditions SUPPORTS

1 FIXED BUT KFY 13 4 TO 8 PINNED LOAD 1 .. LOAD 2 .. PERFORM ANALYSIS CHANGE SUPPORTS 1 FIXED BUT KFY 17.5 4 TO 8 PINNED LOAD 3 .. LOAD 4 .. PERFORM ANALYSIS CHANGE

Example 9: Multiple analysis due to seismic loads per IBC SUPPORTS .. LOAD 1 IBC X 1.0 PERFORM ANALYSIS CHANGE LOAD 2 IBC Z 1.0 PERFORM ANALYSIS CHANGE LOAD 3 .. LOAD 4 .. LOAD COMBINATION 21 .. LOAD COMBINATION 22 .. PERFORM ANALYSIS CHANGE LOAD LIST 21 TO 35

There is a unique requirement in STAAD.Pro that, in such situations, the total number of primary load cases in the model, meaning, those explicitly defined or generated (the load cases that do not use the LOAD COMBINATION syntax) must be mentioned at the beginning of the

STAAD.Pro input file (before any joint, member, or load data). Note that this is simply a requirement specific to STAAD.Pro only and not based on any engineering principle. The mechanism to convey this information is a command called SET NL. It is specified as shown in the next example.

FIGURE 1.1.39 Example for specification of the SET NL command

The number that follows the term “SET NL” is the maximum (upper bound) of the number of load cases that the program can expect. In the case of the aforementioned example, if the model has more than 75 load cases, the program will report an error message in the output file along the following lines, and the analysis run will be terminated. **ERROR - Number of Primary Cases Exceeds Value Entered in SET NL Command of 75

FIGURE 1.1.40 Error message in the .ANL file when the number of load cases exceeds the SET NL value

The value doesn’t have to be precisely equal to the number of primary load cases in the file. It can be larger, albeit slightly. Specifying a very large value, such as say, SET NL 800, when there are only 64 primary cases, isn’t advisable because it may cause a termination of the run with a message that there isn’t enough system resources. SET NL has a default value, which is 30 in recent versions of STAAD.Pro. Thus, if the number of primary cases (not counting combination cases) is 30 or less, SET NL is not required. If SET NL is not specified, and the number of primary cases exceeds the default, it will trigger a message like this. *** ERROR *** ABOVE LINE CONTAINS ERRONEOUS DATA. DATA-CHECK MODE IS ENTERED. PRIMARY LOAD CASE CAN ONLY BE ADDED IF SET NL COMMAND IS USED.

FIGURE 1.1.41 Error message in the .ANL file if SET NL is not specified

1.1.16 Finding the Total Quantity of Loads in a Load Case We often want to know the total amount of forces and moments applied through a load case for each global direction. At various places in this section, we have seen the use of the PRINT STATICS CHECK command with the ANALYSIS instruction.

PERFORM ANALYSIS PRINT STATICS CHECK

We should also by now be familiar with the Statics Results Table displayed in the Node-Reactions page of the post-processing mode. Both of them provide a summary of the total loads and moments applied for each primary load case.

FIGURE 1.1.42 Report in the .ANL file of the summation of loads applied through a load case

1.1.17 Finding the Loads on a Specific Member of a Model There may be times when we want to find the loads on a specific member for all the load cases in a model. For a large model with a large number of members, elements, and load cases, searching for this data in the STAAD.Pro input file can be quite cumbersome. There is an easier method as explained here. The Member Query facility of the STAAD.Pro GUI is a quick way to find the loads on individual members. Fig 1.1.43 is the window that comes up when we double-click on a member. In that dialog box, there is a tab called Loading. It allows us to select the primary load cases in the model one at a time. If there is a load on the member for a certain load case, it will appear in the box as shown in Fig 1.1.43.

FIGURE 1.1.43 Finding the loads on a member using Member Query

For load cases for which there is no load on the member, there will be no data under the load case title (see Fig 1.1.44).

FIGURE 1.1.44 Member Query screen indicating the absence of any load on the selected member

Related Question: Is there a way to find out the overturning moment on a tower due to a given set of loads? Answer: The solution is one that we have already discussed—the static equilibrium report. Three of the terms in that report are the moments about the global X, Y, and Z axes. These are reported for each primary load case. So, to find the overturning moment for a set of loads, the first step is to create a load case containing those loads and run the analysis. There is one other issue that needs to be addressed—about what point do we want the moments to be reported. In the static equilibrium report, the moments due to the applied loads as well as those due to the reactions from the supports are calculated on the basis of a lever arm measured from the origin of the coordinate system (0,0,0). So, if one is desirous of obtaining the values about say, the center of the base of the tower, we may want to create the model in such a way that the origin of the coordinate system is located at the center of the legs.

FIGURE 1.1.45 Two different locations for the legs of a tower with respect to the origin of the axis system

If the model has been created with the origin at some distance away from the center of the base, there is a facility under the Geometry menu called Move-Origin that can be used to reposition the origin to the desired location.

1.2 Panel Loads—Floor Loads, Oneway Loads, Area Loads 1.2.1 Introduction Consider a building consisting of columns and beams. For the floor slab, there may be two possibilities: (a) it is a non-structural entity that, though capable of carrying the loads acting on itself, is not meant to be an integral part of the framing system, and merely transmits the load to the beam-column grid, and (b) it might be an integral part of the structure, as in the case of a reinforced-concrete floor slab in a building, but may have been left out of the model for simplification purposes. There are uniform pressure loads on regions of the floor (think of the load as wooden pallets supporting boxes of paper). Because the slab is not part of the structural model, there needs to be a way to instruct the program to transmit the load to the beams without manually calculating the beam loads. In STAAD.Pro, there are three ways by which such loads can be applied on the model. They are, floor loads, oneway loads, and area loads, depending on the nature of the slab, and the type of connectivity between the slab and the beams. All these are load generation facilities in the sense that they take pressure as the input and generate uniform, trapezoidal, or triangular distributed loads on members.

Required reading 4. Technical Reference manual—Section 5.32.4 5. Application Examples manual—Example 14 6. Graphical Interface Help manual—Section 2.3.7.8 Loading

1.2.2 Floor Load This is a facility where we specify the load as a pressure, and the program converts the pressure to individual beam loads. Thus, the input required from the user is very simple—load intensity in the form of pressure, and the region of the structure in terms of X, Y, and Z coordinates in space, of the area over which the pressure acts. The total load acting on that region is equal to the area of that region multiplied by the pressure. In the process of converting the pressure to member loads, STAAD.Pro will consider the empty space between crisscrossing beams to be panels, similar to the squares of a chess board. The load received by each member that forms the boundary of the panel is dependent upon the proportion of the panel area under the influence of that member. This is calculated using a triangular or trapezoidal load distribution method. This yields trapezoidal, uniform, or triangular member loads depending on the shape of the panel. In Fig 1.2.1, the member loads generated from a FLOOR LOAD are shown for a rectangular panel.

FIGURE 1.2.1 Member loads derived from a FLOOR LOAD

A typical floor load command looks like this. UNIT METER KNS LOAD 2 FLOOR LOAD YRANGE 7.29 7.31 FLOAD -5 XRANGE 5.41 9.601 ZRANGE -19.013-11.697 GY

The program is instructed to look for panels in the X-Z plane contained inside an imaginary box

whose bounds are Y = (7.29 m, 7.31 m), X = (5.41 m, 9.601 m), and Z = (–19.013 m, –11.697 m). Then, on those panels, a pressure of 5.0 kN/m2 is applied in the global Y direction downward. All the closed panels contained within this zone will be identified, and the pressure will be converted to trapezoidal and triangular loads on the constituent members.

FIGURE 1.2.2 Floor load distribution on a grid of floor beams

The triangular and trapezoidal tributary areas that are identified for each member of the panels can be displayed by switching on the Display Floor Load Distribution label as shown in Fig 1.2.3.

FIGURE 1.2.3 Dialog box in the STAAD.Pro GUI to display the Floor load distribution

1.2.2.1 Load Distribution Principle In Fig 1.2.3, the panel between members is subdivided into regions distinguished by specific colors and shading. These colored regions illustrate the manner in which the floor load is apportioned to the individual beams. This is also shown in Fig 1.2.4.

FIGURE 1.2.4 Load distribution pattern for a rectangular panel subjected to Floor Load

For rectangular panels as in Fig 1.2.4, the panel is divided into triangular and trapezoidal regions. The load on the trapezoidal region is applied on the beams in the longer direction (SR and PQ in Fig 1.2.4) as a trapezoidal load. The load on the triangular region is applied on the shorter direction beams (PS and QR in Fig 1.2.4) as a triangular load. This feature works best when all the points on the floor lie on a single plane. If there is a small difference in coordinates of the points, such as one node being at Y = 32.75 ft, while another is at Y = 32.83 ft, the load generation algorithm may fail. Adjusting the coordinate values so that all points form a single plane should remedy that.

1.2.2.2 Assigning Floor Loads Using the GUI Fig 1.2.5 shows the page in the STAAD.Pro GUI’s modeling mode from where the floor load items are assigned.

FIGURE 1.2.5 Adding a floor load using the STAAD.Pro GUI

1.2.2.3 What Are XRANGE, YRANGE, and ZRANGE? XRANGE, YRANGE, and ZRANGE are merely a way by which one tells the program the portion of the structure where the FLOOR LOAD is being applied. A structure can have many floors, and on each floor, there can be loads of various intensities on different parts of the floor. So, if we want to instruct the program to apply a load of certain intensity on a specific strip of area, there has to be a way to identify the location of that strip. XRANGE, YRANGE, and ZRANGE

are one of the means to identify that region. Another method is the FLOOR GROUP, which is described later in this section. For horizontal planes, YRANGE is meant for defining the elevation (Y coordinate) of that plane. Each of these terms has two values—a lower bound and an upper bound. Imagine a floor at an elevation of 8.25 m, as shown in Fig 1.2.6.

FIGURE 1.2.6 Coordinates of the various corners of a grid of floor beams

Assuming that the entire floor is to be defined through a single set of XRANGE, YRANGE, and ZRANGE values (not always advisable if re-entrant corners are present, as we will see later), here is how we would define those ranges. XRANGE and ZRANGE Because the floor spans the distance from X = 0 to X = 17, we could set the values of XRANGE to –1 and 18, –0.5 and 17.5, or –0.1 and 17.1. In other words, the lower bound is a value smaller than the X coordinate of the left edge and, the upper bound has a X coordinate larger than that of the right edge. Similarly, the ZRANGE could be any of the following: 1.0 and 10.0, 1.1 and 9.9, or 1.14 and 9.87. YRANGE All points of the floor are at the same elevation of Y = 8.25. So, any of the following are acceptable bounds: 8.0 and 9.0, 8.1 and 8.4, or 8.15 and 8.3. Notice that in all these examples we have diligently avoided using a set of numbers exactly equal to the coordinates of the edges. In other words, it is best to avoid using XRANGE = 0 and 17 YRANGE = 8.25 and 8.25 ZRANGE = 1.15 and 9.855 Although there is nothing wrong with these numbers, it is advisable to provide a small margin at either end because it reduces the probability of a failure in identifying panels. Occasionally, precision errors occur when the structure geometry is imported from a CAD (computer-aided design) drawing, or when mixed units are used in the STAAD.Pro project (e.g., creating the model in metric units when the base unit settings are imperial). So, while the coordinate may appear as

zero, the data might be recorded in the JOINT COORDINATES section of the STAAD.Pro input file as –0.0001, or as 8.2501 instead of 8.25, thus falling outside the range if no margin of tolerance is provided. The default value of each of these ranges is negative infinity to positive infinity. So, if a particular range is left out (not specified), the full extents of the structure along that direction are automatically included for panel identification. For example, if XRANGE is omitted, the full length of the structure along the direction of the X axis is considered.

FIGURE 1.2.7 A floor load command specified with restrictive levels for ranges

For the model shown in Fig 1.2.7, if the FLOOR LOAD command is specified as YRANGE 12.0 12.0 FLOAD -0.45 XRANGE -2 21.0 ZRANGE 3 24

it leaves no room for precision errors such as Y = 12.001 ft in the joint coordinate values. Similarly, the X and Z ranges too are very restrictive in this example. Instead, a better option would be to specify YRANGE 11.9 12.1 FLOAD -0.45 XRANGE -2.1 21.1 ZRANGE 2.9 24.1

1.2.2.4 Member Offsets and X/Y/Z Ranges STAAD.Pro does not consider the offset position of a member when evaluating whether or not a member lies within a range.

1.2.2.5 Direction of Action of the Loads The floor load can be used not only on a system of beams in the X-Z plane, but on vertical planes too. The user can choose the direction as shown in Fig 1.2.8. It becomes the first word of the FLOOR LOAD command. If the command begins with YRANGE, the load acts normal to the area projected on an X-Z plane. Similarly, for commands beginning with XRANGE, the load acts parallel to the global X and perpendicular to the area projected on a Y-Z plane. For commands

beginning with ZRANGE, the load acts parallel to the global Z and is based on the area projected on an X-Y plane. Loads acting along X and Z directions can be used for simulating a blast loading, or wind pressure loading.

FIGURE 1.2.8 Specifying the direction of the floor load

1.2.2.6 Limitations of the Floor Load Algorithm and Modeling Errors That Prevent Successful Load Generation 1. The floor load generation algorithm, similar to algorithms used for wind load generation or spring support generation for mat foundations, works best on regions that do not have re-entrant corners, also known as a concave hull. There is a detailed description of this geometric formation in Section 8.5 of Part I where it is explained in the context of spring support generation for mat foundations and in Section 5.32.4.3 of the Technical Reference manual. The floor plan of a typical multistory building is shown in Fig 1.2.9. The lines represent the crisscrossing beams. The floor contains numerous re-entrant corners, each of which is highlighted with a red circle. In such cases, panels adjacent to these corners may fail to receive any load, or may receive more than the appropriate quantity of load.

FIGURE 1.2.9 Re-entrant corners on a floor of a typical building

Fig 1.2.10 shows the influence area distribution among the various members of the aforementioned floor. If a closed panel is displayed without a color, it indicates that the program isn’t able to determine the contribution from that panel for the members surrounding that panel.

FIGURE 1.2.10 Load distribution pattern on an irregular floor

Re-entrant corners can be avoided by using FLOOR GROUPs, which are explained later in this section. For the model shown in Fig 1.2.11, create one group with members 101 through 113. Create a second group consisting of members 112 through 118. Apply the load separately on each group. For details, see Section 1.2.2.7.

FIGURE 1.2.11 Re-entrant corners on a floor grid

Fig 1.2.12 is another example of a floor with re-entrant corners.

FIGURE 1.2.12 Floor with re-entrant corners

Instead of specifying YRANGE 15.5 16.5 FLOAD -1.56 XRANGE -1 55 ZRANGE -1 35 GY

the prospects for accurate load generation are much better with the following three lines. YRANGE 15.5 16.5 FLOAD -1.56 XRANGE -1.0 17.4 ZRANGE -1 16.3 GY YRANGE 15.5 16.5 FLOAD -1.56 XRANGE 16.8 37.2 ZRANGE -1 35.0 GY YRANGE 15.5 16.5 FLOAD -1.56 XRANGE 36.6 55.0 ZRANGE -1 16.3 GY

Fig 1.2.13 shows the identification of the tributary areas.

FIGURE 1.2.13 Example for floor load distribution on a panel with re-entrant corners

Fig 1.2.14 illustrates another manifestation of the failure of panel identification. The blue lines that mark the boundaries congregate at a single point. Possible reasons for this could be the following: Presence of duplicate nodes on the floor Presence of duplicate members on the floor Collinear members that overlap Physically unconnected (disjointed) structures

FIGURE 1.2.14 Failure of floor load generation due to incorrect panel identification

Some of these causes are described in Section 5.32.4 of the STAAD.Pro Technical Reference manual. Several notes, sketches, and suggestions are provided on the ways to overcome this limitation. Instead of specifying the entire floor through a single FLOOR LOAD command, one alternative is to specify multiple commands each describing a smaller portion of the floor, as shown earlier. This would be the simplest way to avoid re-entrant corners. 2. The floor load generation also requires that the panels form closed quadrilaterals. Loads are not generated on open panels.

FIGURE 1.2.15 Open panels on a floor

FIGURE 1.2.16 Open panels at the edge of cantilever beams

FIGURE 1.2.17 Members that do not form closed panels

While members 2-3-4-5-6 form a closed region, member 7 does not. No load will be generated for member 7. In Fig 1.2.18, the shaded portion represents the region over which the load is applied. But since there are no boundary beams forming a closed polygon on the periphery of that region, no load will be generated.

FIGURE 1.2.18 Pressure on part of a floor

Related Question: The FLOOR LOAD generated by STAAD.Pro does not match my hand calculations. My building has four floors, which are at Y = 3.9 m, 4.8 m, 8.1 m, and 11.4 m, respectively. I have specified them under a single instruction like this. YRANGE 2 12 FLOAD -4.5 XRANGE -0.97 15.82 ZRANGE 0 12.06

Answer: The YRANGE of “2 12” instructs the program to apply the load at all floors between 2 m and 12 m. If two floors are not similar in their geometry, a single instruction for all floors can lead to errors. Apply the floor load on each floor separately. To do that, replace this command with four separate commands. YRANGE 3.8 4.0 FLOAD -4.5 XRANGE -0.97 15.82 ZRANGE 0 12.06 YRANGE 4.7 4.9 FLOAD -4.5 XRANGE -0.97 15.82 ZRANGE 0 12.06 YRANGE 8.0 8.2 FLOAD -4.5 XRANGE -0.97 15.82 ZRANGE 0 12.06 YRANGE 11.3 11.5 FLOAD -4.5 XRANGE -0.97 15.82 ZRANGE 0 12.06

For verification purposes, place each command in its own load case. For example, call them cases 4001 through 4004. This will enable us to see the total load from each command using the Statics

Check table in the Node-Reactions page of the post-processing mode. LOAD 4001 FLOOR LOAD YRANGE 3.8 4.0 FLOAD -4.5 XRANGE -0.97 15.82 ZRANGE 0 12.06

LOAD 4002 FLOOR LOAD YRANGE 4.7 4.9 FLOAD -4.5 XRANGE -0.97 15.82 ZRANGE 0 12.06

LOAD 4003 FLOOR LOAD YRANGE 8.0 8.2 FLOAD -4.5 XRANGE -0.97 15.82 ZRANGE 0 12.06

LOAD 4004 FLOOR LOAD YRANGE 11.3 11.5 FLOAD -4.5 XRANGE -0.97 15.82 ZRANGE 0 12.06

Next, examine each floor for re-entrant corners. If you find any, each of these commands must be replaced with two or more sub-commands. For example, here is a breakdown of the command for the floor at Y = 11.4 m. YRANGE 11.3 11.5 FLOAD -4.5 XRANGE -0.10 2.27 ZRANGE -0.10 5.0 YRANGE 11.3 11.5 FLOAD -4.5 XRANGE -0.98 2.27 ZRANGE 4.8 7.14 YRANGE 11.3 11.5 FLOAD -4.5 XRANGE 2.25 15.83 ZRANGE -0.10 12.07

After making these changes, run the analysis and go to the Statics Check table. Check to make sure that the total generated load matches your expectation for the floor load applied on each floor. If you still find discrepancies, examine the problem commands and discretize them further. NOTE If FLOOR GROUPs, which are described next, are used instead of XRANGE and ZRANGE, the program may be able to generate the load correctly even on panels with re-entrant corners. However, the safest option is to create as many groups as is necessary to avoid re-entrant corners.

1.2.2.7 Floor Groups Floor groups are containers for storing the list of just those members that are candidates for receiving a load. Members that should not receive the load due to the manner in which they are assembled in the structure should not be included in the group. Floor groups are created just like Node groups or Member groups using the Create New Group option of the Tools menu, as described in Section 2.2 of Part I.

FIGURE 1.2.19 Creating a floor group in the STAAD.Pro GUI

The members that constitute the floor group must form a closed panel as shown in Fig 1.2.20. This is necessary for the program to be able to find the total area confined within the outermost boundary formed by those members and determine the portion of the total that affects the individual members. FLOOR GROUPs are also helpful in avoiding another problem. Ordinarily, after the load is specified, if we decide to change the geometry of the structure (X, Y, or Z coordinates of the nodes of the regions over which the floor load is applied), we have to go back to the load case and modify its data too, such as the XRANGE, YRANGE, and ZRANGE values. By applying the load on the floor group, the FLOOR LOAD instruction does not have to be modified if the members that constitute the group do not change, even if the coordinates of their ends change.

FIGURE 1.2.20 Open and closed panels

Example 10 START GROUP DEFINITION FLOOR _PNL5A 21 22 23 28 END GROUP DEFINITION LOAD 2 FLOOR LOAD on intermediate panel @ Y = 10 ft FLOOR LOAD _PNL5A FLOAD -0.45 GY

Related Questions: 1. I have a platform with main beams running along global X and Z and bracing members that are connected to the main beams. Although their centerlines are at the same Y coordinate, the top of steel of the bracings is at a slightly lower elevation than the top of steel of the longitudinal and transverse beams because the main beams have deeper sections.

FIGURE 1.2.21 Brace whose top is not flush with the floor level

I have applied a floor load on the platform. I want the load to be generated on just the main members. But, STAAD.Pro still applies the floor load to my bracing members. How can I avoid this? 2. How can I apply the floor load command to a bay of steel framing that contains a horizontal diagonal brace in the plane of the framed bay? When I apply the floor load, the program applies the load to the horizontal diagonal brace in addition to the four perimeter beams. I want the floor load to be applied only to the four perimeter beams in the bay and exclude the brace. The purpose of the brace is to resist lateral loads only, not vertical gravity loads. Answer: The solution to these problems is to cluster the longitudinal and transverse beams into a FLOOR GROUP. While creating that group, exclude the bracing members. Next, when you go to the FLOOR LOAD assignment dialog box, the floor group name will be available for selection from a list of such groups. The load can thus be assigned to a group instead of a floor defined using XRANGE, YRANGE, and ZRANGE, as shown in Fig 1.2.22. In Section 5.32.4 of the Technical Reference manual, under the topic titled “Applying Floor Load on Members Grouped under a Floor Group Name,” an example has been provided to illustrate this method.

FIGURE 1.2.22 Dialog boxes in the STAAD.Pro GUI for assigning Floor Load to a Floor Group

Fig 1.2.23 shows the load distribution pattern for a load assigned in this manner.

FIGURE 1.2.23 Load distribution pattern for a Floor Load applied to a Floor Group

Separate (distinct) floor groups can also be created in place of X, Y, and ZRANGEs when the load is on non-contiguous areas in the structure as shown in Fig 1.2.24.

FIGURE 1.2.24 Floor groups to define non-contiguous zones in a structure

Related Question: When we do the analysis for a model containing the floor load instruction, there is a warning in the output file after the first instance of the floor load: **WARNING** ABOUT FLOOR/ONEWAY LOADS/WEIGHTS. Please note that depending on the shape of the floor you may have to break up the FLOOR/ONEWAY LOAD into multiple commands. For details please refer to Technical Reference Manual Section 5.32.4 Note 6.

FIGURE 1.2.25 Warning in STAAD.Pro output file regarding FLOOR LOAD

What is the significance of this warning? When the same model is run on older versions such as STAAD.Pro 2005, there is no such warning. Answer: This warning has been included merely as a reminder to the user that he/she should be careful when using the Floor or Oneway load function and to consider breaking up the floor into smaller regions for complex shapes. The warning does not necessarily mean that anything is wrong with the floor loads or oneway loads, but just that the user should be aware that in some instances it is necessary to break up the floor loads and oneway loads into smaller regions. Section 5.32.4 of the Technical Reference manual gives a detailed explanation of these situations. If you are confident that the regions on which you are applying this load do not have any characteristics that would adversely affect the

load generation, you can ignore the message. Older versions of the program such as 2005 did not display this warning. It was introduced only subsequent to that release. Related Question: I observed that the following warning message appears in the .ANL file. 630. _SURF2 FLOAD -3 GY *WARNING- NO MEMBERS LOADED FOR A FLOOR LOAD GENERATION.

Can you explain why this occurs? Answer: Here are the possible reasons. 1. You are defining the panel using a group name called _SURF2. Have you ensured that it is a FLOOR group? STAAD.Pro does not generate loads from MEMBER groups. Incorrect

Correct

START GROUP DEFINITION MEMBER _SURF2 101 TO 106 201 202 END GROUP DEFINITION

START GROUP DEFINITION FLOOR _SURF2 101 TO 106 201 202 END GROUP DEFINITION

2. Do the members that constitute this group form a fully closed panel with no part of it left open or incomplete? If ranges are used instead, make sure that the region confined within the XRANGE, YRANGE, and ZRANGE commands forms a closed polygon, and shouldn’t be too restrictive as explained earlier. 3. On a general basis, modeling errors such as duplicate nodes and duplicate beams too can cause the floor load generation to fail. In the STAAD.Pro GUI, go to Tools -> Check Duplicate -> Nodes and Tools -> Check Duplicate -> Members to rectify these errors and then check again if there is any problem with the load generation.

1.2.2.8 Excluding the Slab from the Model Related Questions: 1. When does one use FLOOR LOAD and when does one use ELEMENT LOAD? Which one is better? 2. Is it necessary to have plate elements for the generation of floor load? Answer: When modeling a grid system made up of horizontal beams and slabs that span between the beams, there are two approaches that engineers take: 1. They model only the beams, and do not include the slabs in the model. However, they take into account the large in-plane stiffness of the slab by using the master–slave relationship to tie together the nodes of the deck so that a rigid diaphragm effect is simulated for the horizontal plane at the slab level.

2. They model the slabs along with the beams. The slabs are modeled using plate elements. So, how does one account for the distributed loading (load per area of floor), which is present on top of the slab? If the structure is modeled using Method 1, the load can be assumed to be transferred directly on to the beams. The pressure that acts on the slab in the real-world structure is assumed to be passed on entirely to the beams using a triangular or trapezoidal load distribution method. You can do this in STAAD.Pro by defining the load intensity in the FLOOR LOAD command. In other words, the pressure loads on the slabs (which are not included in the model) are converted to individual beam loads by utilizing the FLOOR LOAD facility. The FLOOR LOAD command is intended to apply load to beams, not to plates. Its purpose is to enable us to avoid modeling plates in the first place. In Method 2, the fact that the slab is part of the model makes it very easy to handle the load. The load can be applied on individual elements using the ELEMENT LOAD facility. The connectivity between beams and elements ensures that the load will flow from the plates to the beams through the columns to the supports. However, applying them as element loads will work well only if the slab–beam interface has been meshed well. The element pressure load is converted to fixed end actions at the nodes of the individual elements. Because the continuity of connection between the slab and beams affects the way the load flows from the slab into the supports, it is essential that the slab be meshed well for a continuously connected system. Some additional facts on this topic are discussed in Section 1.2.2.12.

1.2.2.9 Crisscrossing Members and Panel Identification One of the causes of failure of the panel identification process is the presence of members that cross each other but do not have an intersection point at the location where their longitudinal axes cross each other. Hence, in the mathematical model, they are treated as unconnected at that location. In such cases, it is necessary to break them up at that point. It can be done using the Geometry-Intersect Selected Members facility (see Fig 1.2.26).

FIGURE 1.2.26 Modeling beams crossing at various angles

FIGURE 1.2.27 Panels formed by columns, beams, and diagonal braces

1.2.2.10 Openings on Floors By using appropriate values for the X, Y, and Z ranges, or with the help of a floor group name, the presence of openings on a floor or region can be communicated to the FLOOR and ONEWAY load facilities. For example, consider the arrangement shown in Fig 1.2.28.

FIGURE 1.2.28 Opening on a floor

The horizontal and vertical lines represent a system of beams on a floor. The shaded region indicates an opening in the middle. A floor load needs to be applied to this system. Because the opening is surrounded by beams on all four sides, the data must be specified in such a way that no load is generated for the opening. This can be achieved using either ranges or floor groups, as identified in Fig 1.2.29.

FIGURE 1.2.29 Candidates for various floor groups for modeling an opening on a floor

FIGURE 1.2.30 Floor groups for excluding the region with openings

Example 11 START GROUP DEFINITION FLOOR _PART1 1 2 5 6 8 9 11 TO 14 _PART2 3 4 7 10 15 TO 17 19 21 23 _PART3 2 3 18 22 _PART4 13 15 20 24 END GROUP DEFINITION

LOAD 1 LOADTYPE None TITLE LOAD CASE 1 FLOOR LOAD _PART1 FLOAD -0.3 GY _PART2 FLOAD -0.3 GY _PART3 FLOAD -0.3 GY _PART4 FLOAD -0.3 GY

Example 12 LOAD 2 LOADTYPE None TITLE LOAD CASE 2 FLOOR LOAD YRANGE -1 1 FLOAD -0.3 XRANGE -1 4 ZRANGE -1 11 GY YRANGE -1 1 FLOAD -0.3 XRANGE 6 11 ZRANGE -1 11 GY YRANGE -1 1 FLOAD -0.3 XRANGE 2 8 ZRANGE -1 4 GY YRANGE -1 1 FLOAD -0.3 XRANGE 2 8 ZRANGE 6 11 GY

FIGURE 1.2.31 Floor Load on a floor with openings

1.2.2.11 Floor Load and Oneway Load on Inclined Planes The floor load generation by default produces only loads that are normal to the global axis. Often, there are cases where the loads have to be generated on members that form inclined planes. One such model is a warehouse structure with sloping roofs.

FIGURE 1.2.32 Sloping faces of a roof

STAAD.Pro’s floor load and oneway load can be applied on inclined planes too. Two conditions need to be satisfied to enable this. The members on which this load is applied must be part of a floor group. The option called INCLINED must be activated either through the GUI or in the input file in the FLOOR LOAD command. The following is an example of the commands that appear in the STAAD.Pro input file. LOAD 7 FLOOR LOAD _ROOF FLOAD -1 GY INCLINED LOAD 13 ONEWAY LOAD _PANEL2 ONE -1 GY INCLINED TOWARDS 3

FIGURE 1.2.33 Dialog box in the STAAD.Pro GUI for applying an inclined floor load

For the INCLINED FLOOR LOAD to work correctly, the members of each floor group must all be in a single plane. If there is more than one inclined plane, specify the floor load on each of them using separate commands. In Fig 1.2.34, nodes A, B, and D are in one plane, while node C is 1 ft below that plane. So, even if these members are chosen for a floor group, the lack of planarity in the region formed by those members makes it impossible for the floor load generation to work. By adding a fictitious member (small section properties and a soft material) between nodes B and D or A and C, the quadrilateral region can be replaced with two floor groups each representing a triangular region and the floor load applied on each using separate commands.

FIGURE 1.2.34 A general inclined floor panel

In the STAAD.Pro editor, if you have a command encompassing two separate inclined planes such

as the one that follows, _INCLINED_FLRS 1 TO 31 34 TO 37

replace it with the following two lines: _PQR 1 3 5 7 TO 16 21 TO 25 31 34 35 _XYZ 2 4 6 TO 8 13 TO 20 26 TO 31 36 37

Then, locate the following line. _INCLINED_FLRS FLOAD -0.35 GY INCLINED

Replace it with the following two lines: _PQR FLOAD -0.35 GY INCLINED _XYZ FLOAD -0.35 GY INCLINED

Then, save the file and come out of the editor. Switch on the load display in the GUI to see if the loads are working correctly.

FIGURE 1.2.35 STAAD.Pro editor screen showing inclined floor load commands

FIGURE 1.2.36 Floor load distribution on multiple inclined panels

Alternatively, add plate elements to the inclined roof and apply the load as pressure load on the elements. Each panel made up of four members could be circumscribed by one element. You could assign the plates a very small thickness, zero density, and modulus of elasticity (E, which is 1/100th that of concrete) to ensure that neither the weight nor the stiffness of the plates would have any meaningful contribution to the structure. So, the plates act as nothing but a medium for applying a load.

1.2.2.12 Comparing a “Beam+Floor-Load” Model with a “Beam+Plate+Element-Load” Model In Section 7.2 of Part I, we saw that in building-type structures, the user has the option of specifying the master–slave command to simulate the large in-plane stiffness of a floor slab and thus avoid including the slab in the form of plate elements in the model. The bending stiffness of the slab is ignored. The pressure loads on the slabs are applied using the FLOOR LOAD option, which will cause those loads to act directly on the beams. The beams will then transfer the pressure loads to the columns and supports. How does this model (Model A) compare with the one in which the slab is included as plate elements and the vertically acting loads on the slab are applied using the ELEMENT

PRESSURE load option (Model B)? While the total applied load is the same in the two models, some results such as mid-span deflection of the beams and moments in the columns may not be the same between the two models due to the following reasons. 1. In Model A, the in-plane stiffness of the floor slab is considered infinite (due to the master– slave option). Plate elements have a certain amount of in-plane stiffness, but it is not infinite. Hence, in Model B, the in-plane stiffness of the floor will be less than infinite, with the actual value being decided by the thickness and E of the elements. 2. In Model A, the bending stiffness of the slab is not considered at all, whereas in Model B, it is considered. The bending and shear stiffness depends on the thickness, and can be considerable for a thick slab. So, along the boundary of the beam and slab, the load will be carried by bending and shear action by both entities in Model B, but by just the beam in Model A. At the corners, the bending+shear is shared between the column, beam, and slab in Model B, whereas it is just the beam+column that share the burden in Model A. So, the overall stiffness of the two models is not the same. 3. In Model A, the floor load goes entirely into the beams based on the influence area of the nodes that form the corners of the panel. For a rectangular-shaped panel, it is reduced to a triangular load on two sides and a trapezoidal load on the other two sides, as shown in Fig 1.2.1. What makes this possible is the assumption of a monolithic connection (they are continuously connected for the length of their common boundary) between the beams and the slab (which was omitted from the model). 4. On Model B, the density of the mesh determines how well the monolithic connection is reflected in the model. The beam and slab both need to be subdivided into a number of small pieces along their common edge (a dense mesh), and there should be no instance of improper beam–plate connectivity. A coarse mesh will poorly reflect the monolithicity. 5. Depending on the degree of meshing, the pressure will be discretized into a set of concentrated forces and moments at the joints of the mesh, as shown in Figs 1.2.37 and 1.2.38. It is apparent that in the coarsely meshed model, there will be a smaller set of loads, but of a larger magnitude than in the densely meshed model. Thus, although the two models are analyzed for the same overall quantity of load, the pattern of loading isn’t the same.

FIGURE 1.2.37 Equivalent concentrated forces and moments from an element pressure load on a coarsely meshed model with equal-sized rectangular elements

FIGURE 1.2.38 Equivalent concentrated forces and moments from an element pressure load on a finely meshed model with equalsized rectangular elements

6. The bending moments in the beams of Model A need to be compared with the summation of bending moments in the beams of Model B and the plates of Model B at their common nodes. 7. Yet another aspect to consider is the Poisson’s effect of the slab of Model B (deformation along one direction induces a deformation in the orthogonal direction). This effect is not considered in Model A. All these combine to produce a different response from the two models.

1.2.3 Oneway Load

In the FLOOR LOAD facility, the load is distributed on all the beams that circumscribe the individual panels. Often, the slab or the entity that covers the panel area may be supported in such a way that the load is transferred to only some of the members on its boundary. Other members on the panel may not be directly supporting the slab. FLOOR LOAD applied using a FLOOR GROUP may not be appropriate in such cases because the groups formed by the exclusion of nonload-bearing members may not constitute a closed panel. Related Question: I have an arrangement where all the load from the upper level goes directly into the cross beams. The longitudinals and diagonals do not take any load from the floor slab directly. The cross beams will then transfer the load to the longitudinals. Answer: The oneway load too is a mechanism to convert pressures on closed panels into loads on the members that border those panels. However, where it differs from the FLOOR LOAD is in the manner of distribution. While FLOOR LOAD is for load generation on all the surrounding members, in ONEWAY LOAD, the loads are assumed to flow in only one direction. Hence, it works best when the quadrilateral is shaped as close as possible to a rectangle. Square panels where both directions are equal are unsuitable for this load type. Panels that have the shape of other polygons such as three-sided, five-sided, or more are unsuitable for ONEWAY loading.

FIGURE 1.2.39 Dialog box in the STAAD.Pro GUI for specifying a Oneway Load

1.2.3.1 The TOWARDS Option In oneway load distribution, the flow of load is assumed to be along the shorter direction of the four-sided panel by default. In other words, if the panel is rectangular and the length of the longer

side is a and shorter side b, load flow along the shorter direction means all the load will go into the members of length a.

FIGURE 1.2.40 Typical panel for Oneway Load distribution

In Fig 1.2.40, the imaginary line PQ divides the rectangle into two halves. The load on the region A-B-Q-P goes into member AB and that on the region P-Q-C-D goes into the member CD. However, if the members are connected/supported in such a manner that the slab/roof rests directly on members AD and BC, the load needs to be applied on the shorter members and not the longer members. This information can be conveyed to STAAD.Pro through the TOWARDS option that is available in the ONEWAY load assignment dialog box as shown in Fig 1.2.41. The input for the TOWARDS option is a beam number of our choice. This is an instruction to STAAD.Pro that the load flows toward those beams that are parallel to that specific beam. The default, which is without the TOWARDS keyword, instructs the program that the load flows along the shorter direction.

FIGURE 1.2.41 The TOWARDS option in the Oneway Load dialog box

Example 13: Using floor groups LOAD 1 LOADTYPE Dead TITLE DEAD LOADS UNIT METER KN ONEWAY LOAD _P1 ONE -3.6 GY TOWARDS 45 _P2 ONE -3.82 GY TOWARDS 192 _P3 ONE -3.82 GY 157 _P8 ONE -4.3 GY

Example 14: Using ranges LOAD 1 LOADTYPE None TITLE LOAD CASE 1 ONEWAY LOAD YRANGE 4.5 5.5 ONE -2.7 GY TOWARDS 5

FIGURE 1.2.42 Oneway load distribution when the TOWARDS option is specified

1.2.4 Curved Members By curved members, we are referring to the line entities to which the MEMBER CURVE attribute has been assigned. MEMBER CURVE 51 TO 57 RADIUS 20 GAMMA 90 PRESSURE 0

One of the limitations of the curved member is that it can handle only a uniformly distributed load currently. FLOOR LOAD requires the member to be loaded with a triangular or trapezoidally varying loads, neither of which can be processed by STAAD.Pro for curved members. So, even if the program is able to consider the curved members for identifying the panels, no load gets applied on them.

FIGURE 1.2.43 A floor modeled with straight and curved beams

As a workaround, model the curved beams using a series of linear segments as shown in Fig 1.2.44. One may specify the command JOINT COORDINATES CYLINDRICAL REVERSE to obtain a circular configuration in the X-Z plane. STAAD SPACE INPUT WIDTH 79 UNIT METER JOINT COORDINATES CYLINDRICAL REVERSE 101 0 5 0 102 20 5 270 108 20 5 360 JOINT COORDINATES 4 4 5 19.5959; 5 8 5 18.2757; 6 12 5 16; 7 16 5 12; 8 4 5 0; 9 8 5 0; 10 12 5 0; 11 16 5 0; 12 0 5 4; 13 0 5 8; 14 0 5 12; 15 0 5 16; 16 19.5959 5 4; 17 18.2757 5 8; 18 16 5 4; 19 12 5 4; 20 8 5 4; 21 4 5 4; 22 16 5 8; 23 12 5 8; 24 8 5 8; 25 4 5 8; 26 12 5 12; 27 8 5 12; 28 4 5 12; 29 8 5 16; 30 4 5 16; MEMBER INCIDENCES 1 101 8; 2 101 12; 4 8 9; 5 9 10; 6 10 11; 7 11 108; 8 12 13; 9 13 14; 10 14 15; 11 15 102; 12 12 21; 13 13 25; 14 14 28; 15 15 30; 16 8 21; 17 9 20; 18 10 19; 19 11 18; 20 18 16; 21 19 18; 22 20 19; 23 21 20; 24 22 17; 25 23 22; 26 24 23; 27 25 24; 28 26 7; 29 27 26; 30 28 27; 31 29 6; 32 30 29; 33 30 4; 34 28 30; 35 25 28; 36 21 25; 37 29 5; 38 27 29; 39 24 27; 40 20 24; 41 26

6; 42 23 26; 43 19 23; 44 22 7; 45 18 22; 51 102 4 ; 52 4 103 ; 53 103 5 ; 54 5 104 ; 55 104 6 ; 56 6 105 ; 57 105 7 ; 58 7 106 59 106 17 ; 60 17 107 ; 61 107 16 ; 62 16 108 FINISH

FIGURE 1.2.44 Curved member modeled with piecewise linear segments

1.2.5 Area Load In addition to the two load types we have seen earlier in this section (FLOOR and ONEWAY), there is one more load type in STAAD.Pro for specifying loads on panels. It is called the AREA load. It was introduced in STAAD.Pro well before the FLOOR and ONEWAY load types were introduced. However, this feature has some limitations, such as, the lack of a method to communicate the presence of openings on the floor. It was with the intent of overcoming these limitations that the other two load types were introduced.

Over the past few years, the AREA LOAD feature has been de-emphasized in favor of the other two. It is recommended that the FLOOR LOAD or ONEWAY LOAD options be used in lieu of the AREA LOAD option. Going forward, this feature will probably be discontinued. Hence, it is not being discussed further.

1.2.6 Oneway Loads and Floor Loads as Seismic Weights for ELFP-Based Seismic Analysis In Section 2.4, an approach known as the equivalent lateral force procedure (ELFP) for performing seismic analysis is discussed. This method requires the various seismic weights in the structure to be specified. In that context, in Section 5.31.2.2 of the STAAD.Pro Technical Reference manual, terms such as JOINT WEIGHT, MEMBER WEIGHT and ELEMENT WEIGHT are mentioned. They are the means by which joint loads, distributed and concentrated loads on members and plate element loads can be specified for the purpose of computing the effective seismic weight for base shear calculation. Such a facility is available for floor loads and oneway loads too. They are termed FLOOR WEIGHT and ONEWAY WEIGHT, respectively. Example 15: For floor weight DEFINE NRC 2005 LOAD SA1 0.312 SA2 0.168 SA3 0.073 SA4 0.023 IE 1 SCLASS 4 MVX 1.04 - MVZ 1.04 JX 0.81 JZ 0.81 RDX 1.3 RDZ 1.3 ROX 1.5 ROZ 1.5 SELFWEIGHT JOINT WEIGHT 17 TO 48 WEIGHT 1.8 49 TO 64 WEIGHT 1.6 FLOOR WEIGHT YRANGE 2.9 3.1 FLOAD 1.3 YRANGE 5.9 6.1 FLOAD 1.3 YRANGE 8.9 9.1 FLOAD 0.7

Example 16: For oneway weight DEFINE 1893 LOAD ZONE 0.24 RF 3 I 1 SS 2 ST 1 DM 0.05 SELFWEIGHT 1 MEMBER WEIGHT 158 159 161 162 164 165 167 TO 170 UNI 1.65 ONEWAY WEIGHT YRANGE 4.69 4.71 ONELOAD 6.01 XRANGE 0 22.72 ZRANGE 0 13.24 YRANGE 7.89 7.91 ONELOAD 6.01 XRANGE 22.7 25.92 ZRANGE 18.3 23.4 YRANGE 11.0 11.2 ONELOAD 6.01 XRANGE 25.9 48.7 ZRANGE 18.3 31.6

1.2.7 Oneway Loads and Floor Loads as Seismic Weights for Dynamic Analysis To obtain the frequencies and modes of a structure, we need to specify the weights that will participate in the vibration of the structure, which is discussed in Chapters 4 and 5. FLOOR LOADs and ONEWAY LOADs are also load types that contribute to the vibrating masses in the structure. The instruction that is used for specifying a floor load in a static load case can be used with a minor change for a dynamic load case as shown in Fig 1.2.45 for the Floor load. A similar approach can be used for the Oneway load too.

FIGURE 1.2.45 Syntax for using floor loads for mass modeling

This will result in the following commands: LOAD 8 FREQUENCIES AND MODE SHAPES YRANGE 3.85 3.95 FLOAD 4.6 XRANGE 1.07 2.14 ZRANGE -0.2 28.2 GX YRANGE 3.85 3.95 FLOAD 4.6 XRANGE 1.07 2.14 ZRANGE -0.2 28.2 GY YRANGE 3.85 3.95 FLOAD 4.6 XRANGE 1.07 2.14 ZRANGE -0.2 28.2 GZ

Example 17 LOAD 5 LOADTYPE Seismic TITLE RESPONSE SPECTRUM ALONG X SELFWEIGHT X 1.0 SELFWEIGHT Y 1.0 SELFWEIGHT Z 1.0 FLOOR LOAD YRANGE 4 6 FLOAD 3.95 GX YRANGE 7 9 FLOAD 3.95 GX YRANGE 10 12 FLOAD 3.95 GX YRANGE 13 15 FLOAD 4.8 GX

YRANGE 4 6 FLOAD 3.95 GY YRANGE 7 9 FLOAD 3.95 GY YRANGE 10 12 FLOAD 3.95 GY YRANGE 13 15 FLOAD 4.8 GY YRANGE 4 6 FLOAD 3.95 GZ YRANGE 7 9 FLOAD 3.95 GZ YRANGE 10 12 FLOAD 3.95 GZ YRANGE 13 15 FLOAD 4.8 GZ SPECTRUM CQC X 1 ACC SCALE 9.806 DAMP 0.06 LOG SAVE 0.2 0.125; 0.4 0.165; 0.6 0.185; 0.8 0.251; 1.0 0.3; 2.0 0.079; 5 0.079; 10 0.079 LOAD 6 LOADTYPE Seismic TITLE RESPONSE SPECTRUM ALONG Z SPECTRUM CQC Z 1 ACC SCALE 9.806 DAMP 0.06 LOG SAVE 0.2 0.125; 0.4 0.165; 0.6 0.185; 0.8 0.251; 1.0 0.3; 2.0 0.079; 5 0.079; 10 0.079 PERFORM ANALYSIS

1.2.8 Using the FLOAD and ONEWAY Load Facilities to Apply Pressures along Horizontal Directions on a Structure Thus far, for static loading, the floor and oneway loads were applied on floors in the horizontal plane and the direction of the load was along global Y downward. Both these load types can also be used for generating loads along the horizontal directions on vertical or inclined planes due to agents such as wind. Wind load generation is conceptually similar to floor and oneway load generation as explained in Section 2.1. Both methods consider the area of the region circumscribed by members and multiply it by a pressure to obtain the total load acting on the panel. Where they differ is, wind load generation produces concentrated forces at the nodes. To generate loads in the horizontal direction, the panels must be in the vertical or sloped planes. So, Floor groups must be created as explained before, and, the direction of the load must be specified as GX or GZ. or If ranges are used, the instruction must start with the words XRANGE or ZRANGE, depending on whether the load is along global X or global Z. Example 18: Using ranges on a vertical plane (YZ), load acts along global X UNIT POUND FEET LOAD 7 WIND ALONG GLOBAL X FLOOR LOAD XRANGE -0.1 0.1 FLOAD 40 YRANGE -1 16 ZRANGE -1 31 GX XRANGE 59.9 60.1 FLOAD 40 YRANGE -1 16 ZRANGE -1 31 GX

FIGURE 1.2.46 Floor Load along GX to simulate wind

Example 19: Using ranges on a vertical plane (XY), load acts along global Z LOAD 8 WIND ALONG GLOBAL Z FLOOR LOAD ZRANGE -0.1 0.1 FLOAD 40 YRANGE -1 16 XRANGE -1 61 GZ ZRANGE 29.9 30.1 FLOAD 20 YRANGE -1 16 XRANGE -1 61 GZ

FIGURE 1.2.47 Floor Load along GZ to simulate wind

Example 20: Using floor groups, load acts along global Z LOAD 12 WIND ALONG GLOBAL Z FLOOR LOAD _WESTFACE FLOAD 20 GZ

1.3 Support Displacement Loads 1.3.1 Introduction Support displacements, also known as sinking supports or support settlements, are specified as loads in STAAD.Pro. Required reading 7. Technical Reference manual—Sections 1.16.7 and 5.32.8 8. Application Examples manual—Example 5 9. Graphical Interface Help manual—Section 2.3.7.12.6

1.3.2 Discussion The basic parameters involved when solving support displacement problems are: The degree of freedom (d.o.f.) along which the support settlement is being specified must have a support providing a restraint. This is because, if there is no restraint, the structure would be free to displace by any amount. So, either a restraint is required through a PINNED or FIXED command or a spring using the KF? term, or an ENFORCED-type support is needed. The support settlement itself is specified through a loading type called SUPPORT DISPLACEMENT LOAD. If the restraint at a d.o.f. is specified using the FIXED, PINNED, or FIXED BUT types, a support displacement load can be applied along that d.o.f. if and only if the entities in the model are members (beams, columns, braces). If the structure contains plate elements and/or solid elements, and a support displacement load is being applied along a d.o.f., the restraint at that d.o.f. has to be the ENFORCED type. In Section 5.32.8 of the STAAD.Pro Technical Reference manual, two modes of usage are described for the support displacement loads—a load mode and a displacement mode. The load mode describes the condition where the supports are defined using the FIXED syntax, while the displacement mode describes the condition where the supports are defined using the ENFORCED syntax. The load mode method cannot be used with any nonlinear solution such as PERFORM CABLE analysis, Multilinear springs, NONLINEAR analysis, Member Tension/Compression, and Spring Tension/Compression. Example 21: For “load mode” SUPPORT 43 FIXED BUT FX FZ MX MY MZ .. .. LOAD 1 GRAVITY SELF Y -1

.. LOAD 2 LIVE LOAD MEMBER LOAD .. UNIT INCHES LOAD 3 SUPPORT SETTLEMENT SUPPORT DISPLACEMENT LOAD 43 FY -1.0 LOAD 4 WIND LOAD WIND LOAD X 1 TYPE 1

Example 22: For “displacement mode” The following example is for a 10-degree rotation imposed at Joint 2. SUPPORTS 1 FIXED 3 ENFORCED BUT FX FZ MX MY MZ 2 ENFORCED BUT FX MY MZ LOAD 1 WEIGHT OF STRUCTURE SELFWEIGHT Y -1 UNIT INCHES KIP LOAD 2 INDUCED 10 degree TWIST AT JOINT 2 SUPPORT DISPLACEMENT LOAD 2 MX 10 PERFORM ANALYSIS PRINT LOAD DATA

There is a set of restrictions associated with each of these two modes. One of those restrictions is that under the load mode, a maximum of only four load cases are permitted for support displacement loads. Refer to the Technical Reference manual for the full list. Note that the real advantage of using the ENFORCED-type support is that it enables STAAD.Pro to accept support displacement loads at a d.o.f. at which a plate or solid element is attached. Support displacement loads are not permitted for plates and solids if the FIXED type is used along those d.o.f. at those support nodes.

1.3.3 Specifying Support Displacement Loads Using the STAAD.Pro GUI In the STAAD.Pro GUI, support displacement loads are specified from the Nodal Load option of the General-Load & Definition page, as shown in Fig 1.3.1.

FIGURE 1.3.1 Dialog box in the STAAD.Pro GUI for specifying support displacement loads

Note that a support displacement load cannot be specified along a direction at a joint if there is no restraint along that direction at that joint. Related Question: I encounter the following warning when I analyze a model with a support displacement load. **WARNING - SUPPORT DISPLACEMENT IN RELEASED DIRECTION IGNORED. JOINT 4 DIR. 1 CASE NO. 1

FIGURE 1.3.2 Warning in the output file for support displacement load

Answer: The message appears if the d.o.f. along which the support displacement load is applied does not have a restraint. Along that direction, the joint needs to be FIXED, should have a spring, or should have the ENFORCED-type support. DIR. 1 stands for FX. CASE NO. 1 stands for load case 1. For example, by providing the following SUPPORT instruction, the error message could be avoided.

SUPPORTS 4 FIXED BUT FY FZ MX MY MZ

1.3.4 Forcibly Inducing a Displacement at a Point Which Is Not a Support Related Question: I want to know how to model a column with an existing horizontal deflection of 3/4th of an inch at mid-span. Answer: This feature can also be used to force any point on the structure to displace by a known value along a certain direction. The first step is to create a node at that location. Then, because there is no support at that node, we have to create a fictitious one by releasing all d.o.f. except the one along which we want the point to displace. Let us assume that we have inserted a node (Node 3) at the mid-span of the column mentioned in this question. In the next example, we define a support at Node 3 with all d.o.f. free to displace except the translation along global X. SUPPORT 3 ENFORCED BUT FY FZ MX MY MZ

This will now allow us to apply a support displacement load of 3/4th of an inch along FX as shown in Load 3. UNIT INCH LOAD 3 SUPPORT DISPLACEMENT LOAD 3 FX 0.75

1.3.5 Estimating the Load that Will Cause a Known Displacement Normally, the structural problem that we try to solve is determining the displacements caused by a known set of loads. However, there may be situations where we may want to know the amount of load that will cause the structure to displace by a known amount. Related Question: Is it possible to specify a displacement and then have STAAD.Pro analyze a frame to determine the corresponding load (the load that would have been required to produce the said displacement)? Answer: If the goal is solely to determine the force that has to be applied at a specific joint to induce a displacement along a certain direction at that joint, without regard to what displacements are induced at the remaining nodes of the structure, then the simplest method is to define a support at that joint and fix that d.o.f. as shown in Section 1.3.4. Then, apply a support displacement of the known magnitude at that joint along that d.o.f. The reaction at that support along that d.o.f. will

be equal and opposite to the force or moment that needs to be applied there. If adding a support is not desirable, then another method may be employed. However, you first need to know the pattern or arrangement of the loading that will eventually cause the displacement you want to achieve. This is because there can be hundreds of loading arrangements which cause that amount of displacement at that node, so one needs to know in advance which of those patterns one wants. By pattern, we are referring to details such as—is the load going to consist of concentrated forces at nodes, distributed and trapezoidal loads on members, or pressures on plates. For example, any of these loads will cause a certain amount of displacement at a node along a certain direction. Let us say that by applying a member load of 750 pounds/ft, we get 0.4 in. of displacement along global X at Node 43. So, if the final desired displacement at Node 43 along X is say, 1.2 in., the applied load should simply be (1.2/0.4) × 750 = 2250 pounds/ft. Thus, knowledge of the loading pattern is necessary to determine the magnitude of the load needed to cause a known value of deflection.

1.3.6 Forces and Moments Caused by Rigid Body Movements at Lifting Points Related Question: I want to analyze the structure for the static forces caused by a 15-degree tilt about the global Z axis passing through a point where the structure is being lifted. So, this is not merely a 15-degree rotation at one support, but the whole structure pivots about a point as in a rigid body rotation. As the gravity loads will still be acting vertically, I want to know what kind of stresses would be induced. Should I be using the support displacement load? Answer: Support displacement loads are not the way to analyze this condition. Instead, first, make a copy of the model. Then, select the entire geometry of the structure and using the Rotate option in the Geometry menu, rotate it by 15 degrees about global Z. Ensure that you choose the right points through which the axis of rotation passes. This will cause the X and Y coordinates of the various joints of the model to change. If any other changes are needed in the model, such as modification or removal of some of the load cases, that needs to be done too. Note that rotation of the structure will cause the local axes to change directions for some members. So, if the original model had loads applied along local axes, the direction of those loads too would have changed. Once you are satisfied with the changes, save the file and run the analysis. View the results such as displacements, forces, and stresses as explained in Sections 3, 4, 5, and 6 of Part III.

1.3.7 Support Displacement Loads and Cables Cables are nonlinear entities. The cable analysis algorithm in STAAD.Pro is not designed to handle support displacement loads.

1.4 Prestressing Loads 1.4.1 Introduction Prestressing is the process by which steel cables that are draped either inside a member (inside a sheath embedded in the member) or along its sides are stretched using hydraulic jacks. At one end,

the cables are anchored to the beams before the start of stretching. The other end is anchored after the desired amount of stretch has been achieved. This induces an axial compression in the member. If the profile of the cable is such that the tendons are located eccentrically with respect to the CG of the cross-section, bending moments too will be induced. In STAAD.Pro, prestress forces can be specified through load cases, and are hence called prestress loads. Required reading 10. Technical Reference manual—Sections 1.16.5 and 5.32.5 11. Application Examples manual—Example 6 12. Graphical Interface Help manual—Section 2.3.7.8 Loading

1.4.2 Discussion There are two commands in STAAD.Pro for applying a prestressing force: MEMBER PRESTRESS MEMBER POSTSTRESS The difference between these two commands has to do with which part of the structure will experience the force. The primary issue involving prestress forces is the sequence of construction. As is well known, two possibilities exist: 1. The (concrete) member is pre-cast in a factory, or is cast separately from the rest of the structure. The cable is stressed before the member is attached to the structure. Due to this, prestressing effects such as axial shortening are experienced by that member before it is mounted on the structure. Thus, the effects are not transmitted by that member to the remainder of the structure. This type of a prestressing is specified in STAAD.Pro using the MEMBER POSTSTRESS command. 2. The cable is stressed after the member is attached to the structure. Due to the connectivity between the member and other columns, beams, and plates in the structure, as the member deforms under prestressing, the remaining structure too will deform with it and hence the other members and elements too will experience stresses and deformation. This type of a prestressing is specified in STAAD.Pro using the MEMBER PRESTRESS command. To summarize: POSTSTRESS means: Stress the member first. Then attach it to the structure. None of the other entities in the structure will experience the effects. PRESTRESS means: Attach the member to the structure. Then stress it. Due to the movement of the ends of the beam, other members in the structure experience the prestressing force indirectly. It is important to note that the terms PRESTRESS and POSTSTRESS as defined in STAAD.Pro are perhaps opposite to how they are defined by the industry. The industry defines PRE to mean that the member is stressed before it is placed on the structure, while it defines POST to indicate that the force is applied after the member behaves monolithically with the rest of the structure.

1.4.3 Results of the Analysis

We have used the term “effects” of prestressing in the aforementioned description. By “effects,” we mean the forces and moments in members, joint displacements, section displacements in beams, stresses in plates and solids, and so on. If MEMBER POSTSTRESS on one or more members is the only load in a load case, we will find that the member forces for every other member in the model is zero for that case. The joint displacements will be zero for all joints. The support reactions too will all be zero. The members to whom the load is applied will be the only members with non-zero forces and moments.

1.4.4 What Command Should I Use—MEMBER PRESTRESS or MEMBER POSTSTRESS It is a question of whether the member is connected to other members of the frame at the instance of time that the prestressing force is being applied. If the member is connected, then due to the movement of the ends of the beam, other members in the structure get to experience the force indirectly. So, this is what you have to find out. After the concrete sets for the beam in question, and before the prestressing cables are pulled, has this beam become monolithic with any other beam or any other entity such as a slab in your model, or connected to such entities? If the answer is no, then use the MEMBER POSTSTRESS command. With this command, the effects of prestressing are experienced only by the beam to which the force is applied. If the beam is capable of transmitting the end deformations caused by prestressing to other members, use the MEMBER PRESTRESS command.

1.4.5 Cable Profile The prestress cables can have a straight profile through the length of the member, or a parabolic profile. In Section 5.32.5 of the STAAD.Pro Technical Reference manual, figures illustrating various profile possibilities are shown. In some cases, it may be necessary to break the member into two or more segments to properly represent the profile.

1.4.6 Syntax of the Commands in the STAAD.Pro Input File In addition to the member number and magnitude of the prestress force, there are three terms that are part of the input. They are: ES: Eccentricity of the cable at the start of the member. This refers to the distance along the local Y axis of the CG of the cable group from the CG of the cross-section. EM: Eccentricity of the cable at the mid-span point of the member. EE: Eccentricity of the cable at the end of the member.

FIGURE 1.4.1 Longitudinal section showing typical layout of the prestressing cable

In Figs 1.4.2 and 1.4.3, views of the cable arrangement above and below the CG of the crosssection are shown.

FIGURE 1.4.2 Cross-section showing cables located below the neutral axis

FIGURE 1.4.3 Cross-section showing cables located above the neutral axis

In Figs 1.4.2 and 1.4.3, the distances between the CG of the cable group and CG of the crosssection represent the terms ES, EM, and EE. If the cables are located above the CG, the value is specified with a positive number. Cables located below the CG are specified with a negative number.

1.4.7 Cable Arrangement that Produces a Pure Axial Compression If the cable has no eccentricity at any of the three sections on the beam, it will produce only an axial compression without any bending moments. If ES, EM, and EE are not specified, it will have the same effect as providing an eccentricity equal to zero. Note that in STAAD.Pro, the cable can be eccentric only with respect to the local Z axis, meaning, ES, EM, and EE are measured along the local Y axis. Hence, the only moment that prestressing can produce is about the local Z axis (MZ).

FIGURE 1.4.4 Dialog box in the STAAD.Pro GUI for assigning prestressing and poststressing loads

Example 23: For PRESTRESS load LOAD 1 MEMBER PRESTRESS LOAD 1 FORCE 1800 ES 100 EM -350 EE 100

Example 24: For POSTSTRESS load LOADING 2 MEMBER POSTSTRESS 1 FORCE 1620. ES 0. EM -145 EE 0

1.4.8 Effects of Creep and Shrinkage STAAD.Pro does not have any provision for computing losses due to creep, shrinkage, or friction. So, the force in the cable is assumed to be uniform throughout the cable length.

1.4.9 Initial Stress in a Member In Section 1.6, an initial STRAIN LOAD is described as a way to specify conditions such as initial lack of fit (the member is slightly shorter than the distance between the points on the structure that it is attached to). The MEMBER PRESTRESS command too can be used to provide such loads. The amount of the prestress force, or the amount of the initial STRAIN, has to be based on the initial stress you want the member to have.

1.4.10 Prestress Load in Plates and Solids

In STAAD.Pro, prestress can currently be applied only on frame members. To apply prestress forces in plate or solid element-based entities such as slabs, the following workaround can be used. Add a beam that has properties of the prestress cable, and connect it between the same nodes as the elements. So, the meshing must take into account the layout of the cable. Ensure that the beams are segmented to as many pieces as the elements of the slabs and ensure proper connectivity between them. Then, apply the prestress load to the cable and set ES, EE, and EM to 0.0.

FIGURE 1.4.5 Modeling prestress cables in a finite element model of a slab

Example 25 STAAD PLANE FRAME WITH PRESTRESSING LOAD UNIT KNS METER JOINT COORD 1 0. 0. ; 2 7.3 0 0 MEMBER INCIDENCE 1 1 2 SUPPORT 1 2 PINNED UNIT MMS MEMB PROP 1 PRI YD 750 ZD 500 CONSTANT E CONC ALL DENS CONC ALL LOAD 1 SELF Y -1

LOADING 2 PRESTRESSING LOAD MEMBER POSTSTRESS 1 FORCE 1620. ES 0. EM -145 EE 0 LOAD 3 REPEAT LOAD 1 1 2 1 PERFORM ANALYSIS PRINT MEMBER FORCE PRINT SUPP REAC load list 3 SECTION 0.5 ALL PRINT SECTION FORCES UNIT NEWTON MMS PRINT MEMBER STRESSES FINISH

1.5 Loads on Plates and Solids 1.5.1 Introduction In this section, we look at the various methods available in STAAD.Pro for applying load items on plate and solid elements. Required reading 13. Technical Reference manual—Section 5.32.3 14. Application Examples manual—Examples 9, 10, 22, 24, 27

1.5.2 Discussion We have seen options such as SELFWEIGHT, JOINT LOAD, SUPPORT DISPLACEMENT LOADS, and TEMPERATURE LOAD (see Section 1.6), which are applied to frame members and their joints. Those loading options are available for plates and solids too. The load items that are specific to plates and solids are pressure loads of various types, and are discussed here.

1.5.3 Load Options for Plate Elements STAAD.Pro currently has the following options for applying loads on plate elements.

FIGURE 1.5.1 Dialog box in the STAAD.Pro GUI for applying pressure loads on plate elements

1.5.3.1 Uniform Pressure Loads on Plate Elements Pressure on the full area of the element in one of the three global directions. Pressure on a part of the area of the element in one of the three global directions. Pressure on the full area of the element perpendicular to the plane of the element (along the element Z axis). Pressure on a part of the area of the element perpendicular to the plane of the element (along the element Z axis). Pressure on the full area of the element parallel to the local X or local Y axes of the element (parallel to the element’s surface). Thus, this is a friction type of load.

1.5.3.2 Trapezoidally Varying Pressure Loads on Plate Elements Pressure on the full area of the element acting along one of the three global directions. Pressure on the full area of the element acting perpendicular to the plane of the element (along the element Z axis). Pressure on the full area of the element acting parallel to the local X or local Y axes of the element (parallel to the element’s surface). Thus, this is a friction type of load. Load over the full area of the element where one happens to know the intensity at the joints of the element. If the axis is chosen as local Z instead of one of the global axes, the sign of the load needs particular attention. A positive value of the pressure indicates that the load is acting along the positive direction of the local Z axis. In a circular tank for example, if the local Z axis of the walls of the tank is pointing radially inward, to specify a pressure due to liquid in the tank that pushes the walls outward (making the tank expand), the pressure must be applied with a negative sign.

FIGURE 1.5.2 Local axes of elements of a cylindrical tank

To view the direction of the local Z axis, go to the View menu and choose Structure Diagrams. Select the tab called Labels. Switch on the option called Plate Orientation. LOAD 1 LOADTYPE None TITLE WEIGHT ELEMENT LOAD 1096 TO 1512 PR GY -2.5

Related Question: I am designing a water tank modeled using finite elements. For the bottom slab, the program reports bottom steel at supports and maximum top steel at center. What am I doing wrong? Answer: This is often the result of an incorrect sign assigned to the load acting along the direction of the local Z axis. Thus, on a slab in the horizontal plane, if local Z is pointing downward, and the pressure is specified as a negative number, the load will be interpreted by the program as acting upward producing moments opposite in sense to the true value. Wrong moments lead to wrong reinforcement calculations. Changing the sign of these loads acting along local Z, or changing the direction of the load from local Z to global Z, may be all that is required to rectify the problem.

1.5.3.3 Plate Meshing—How It Affects the Processing of Loads on Plates The manner in which loads on plate and solid elements are processed during a stiffness analysis underscores the importance of adequate meshing of entities such as slabs and walls. Any load that is applied within the body of an element—element pressure loads, hydrostatic pressure loads, concentrated forces at a point on the element, and so on—has to be transformed into equivalent end actions. End actions are concentrated forces and moments at the nodes of the elements. The assembling of the end actions into a matrix is reported under the process called Processing and setting up Load Vector in the Analysis window as shown in Fig 1.5.3.

At joints where supports are defined, the end actions that are acting directly along a restrained d.o.f. will be converted to a load transmitted into that support, and the element will hence not undergo deformation due to that specific end action. Only those end actions that are not directly on a restrained d.o.f. will be assembled into the load vector. Thus, the denser the mesh that is generated from the slab or wall, the larger the number of nodes on which to transform the pressure to discrete concentrated forces and moments, and the less the approximation that results from that transformation. A finer mesh will better reflect the deflection of the slab under uniform pressure than a coarse mesh. Additional information can be found in Section 1.2.2.12. Consider a slab or wall that is modeled using just a single element, with supports specified at the corners. According to the explanation given in the previous paragraph, all pressure loading will be directly transmitted to the supports. Thus, there are no translational d.o.f. available in the model. The joint displacements and element stresses will hence be zero.

FIGURE 1.5.3 Processes displayed in the STAAD.Pro Analysis window

1.5.3.3.1 Pressure Loads and Mesh Density Let us see an example of how the aforementioned facts affect the analysis results. Assume a slab modeled (a) in one case using 2500 elements (50 × 50 mesh) with 2601 nodes and (b) in another case using 625 elements (25 × 25 mesh) with 676 nodes. A uniform pressure is applied on all the elements of both models.

In Model a, the pressure is converted to 2601 concentrated loads. In Model b, the same pressure is converted to only 676 concentrated loads. The latter are higher in magnitude, but sparser in the distribution across the plate surface. Because of this, the 2500-element model is a more-uniformly loaded model than the 625-element model. Moreover, if there are supports along the edges of the slab, the number of points at which the slab is supported would be different between the two. An edge that is continuously supported is better modeled in Model a than in Model b. Thus, it is easy to see how Model a is a better representation of reality than Model b.

1.5.3.4 Pressure Loading on a Partial Area of Elements To apply a pressure load on a partial region of an element, the coordinates of the corners of the region measured from the origin of the axis system of the element must be established. Further, this measurement must be along the local X and Y axes. The origin of this local axis system is the center of the element as described in Section 4.5 of Part I. For quadrilateral elements that are not rectangular shaped, as well as for triangular elements, this can be a tedious task.

FIGURE 1.5.4 Load on a patch of a triangular element

A simpler solution may be the following: Subdivide those elements into smaller elements, and apply the load on the full area of one or more of those smaller elements. Convert the partial area load into an equivalent set of concentrated forces at the corner nodes of those elements. Then, apply those concentrated forces using the JOINT LOAD option. Related Question: Is there a way to apply a load on the projected area of an inclined element? Answer:

No. If a load is applied along a global direction on an element that is inclined to a global plane, the load on the element is calculated as the magnitude of the pressure multiplied by the full area of the element. A way around this limitation is to multiply the load by a fraction equal to the projected area divided by the full area. Then, apply the reduced load along the global direction.

1.5.3.5 Friction Loads on Plate Elements A friction load, such as between a tunnel wall and the surrounding soil, is a pressure that acts along the surface of the plate element. For such loads, the direction of loading can be specified using the terms LX and LY. More information is available in Section 5.32.3.1 of the Technical Reference manual. If the local X-Y plane of the element is aligned with a global axis, the pressure can also be applied as a global direction load (GX, GY, or GZ as applicable).

FIGURE 1.5.5 Dialog box in the STAAD.Pro GUI for applying a load parallel to the element surface

1.5.3.6 Concentrated Loads on Plate Elements A concentrated load can be applied within the bounds of an element in one of the global directions along the local Z axis of the element

FIGURE 1.5.6 Dialog box in the STAAD.Pro GUI for applying concentrated forces within the bounds of plates

1.5.3.7 Line Loads on Plate Elements Even though there is no direct facility to apply line loads on plates, there are some indirect ways in which this can be achieved. Apply it as a uniform pressure on a partial region shaped like a rectangle whose length is equal to the length of the line load, and of very small width. Add a dummy member spanning the distance between the two points at the extremities of the line load. The plate mesh should have at least a few nodes along that line. Ensure that the dummy member is segmented at those nodes. Thus, there will be a few points of connectivity between the member and the slab along that line. Apply the load as a uniformly distributed load on the dummy member segments. The segments of the dummy beam should be assigned a very small elasticity modulus and density, so their contribution to the stiffness and weight of the structure is negligible.

FIGURE 1.5.7 Line loads on plate elements

1.5.3.8 Loads along the Edge of Plate Elements Related Question: What we want to do is apply a uniform lateral load along the edge of the building. Is there a way to do this because the floors are modeled as plates? Answer: As described in the second method under the topic “Line Loads on Plate Elements,” create fictitious beams running along the edge. Then, apply the load on them as a uniform distributed load. By setting their properties and modulus of elasticity (E) value to be very small, and their density to be zero, their stiffness contribution will be negligible. At the same time, we’d have found a way to apply the load.

FIGURE 1.5.8 Line load along the edge of a slab

Alternatively, one could apply the load as a series of joint loads on the nodes along that edge. However, this would require some amount of manual calculation to determine the magnitude of those joint loads as they would be based on the spacing between the nodes, and hence is a more laborious method.

1.5.3.9 Fixed End Actions Loads applied on elements are converted to an equivalent set of concentrated forces and moments at the nodes of the element. The word “equivalent” comes from the assumption that they would be equal in magnitude but opposite in sign to the reactions that would develop at the corners of that element if that element were to be fixed supported at those nodes and subjected to those loads. So, these concentrated forces and moments are also known as fixed end actions. 1.5.3.9.1 Element Nodes Declared as Supports The fixed end action terms, which are along a d.o.f. that is supported, will go directly into the ground (supports). If all the nodes of an element are pinned, for example, the fixed end action terms FX, FY, and FZ at all nodes will disappear into the supports. Thus, there will be no displacements, corner forces, or stresses in those elements, regardless of loads applied to the element. That is why it is important to mesh the plate appropriately. If a single element has all of its nodes restrained, it typically indicates that, that element needs further meshing.

1.5.3.10 Hydrostatic Loads Related Questions: 1. I am modeling a tank. The walls are subjected to hydrostatic pressure of zero at the top and about 1250 psf at the bottom. Because the walls have been modeled using a mesh of plate elements, manually calculating the trapezoidal pressure load to be applied on each element is a

very tedious job. Is it possible to have STAAD.Pro automatically do that?

FIGURE 1.5.9 Cylindrical tank modeled using a plate element mesh

2. For a wall shown in Fig 1.5.10, how do I apply a trapezoidal load to all the plate elements simultaneously rather than each plate individually?

FIGURE 1.5.10 Wall subjected to hydrostatic pressure

Answer: As shown in Fig 1.5.11, in the Plate Loads page in the STAAD.Pro GUI, there is a facility called Hydrostatic loads using which the program will generate pressure loads on each element for the type of structures described in the aforementioned questions.

FIGURE 1.5.11 Facility for generating trapezoidal loads on plate elements

Needless to say, the wall should be represented using an element mesh. Select the elements on which the pressure needs to be calculated. We are required to specify the pressure at the top edge (or at the water line), and the bottom edge of the wall. These two locations are denoted by Max Global Axis and Min Global Axis in Fig 1.5.11. For Interpolate along, the value usually is global Y (i.e., pressure varies along this axis). Specify the load to act along the local Z of the elements if the wall is not aligned with a global plane. The program will use the linear interpolation method to find the intensity at each node that is between the top and bottom edges, and then create the individual element TRAPEZOIDAL loads. Once the load on the individual elements is generated using this facility, the resulting data in the STAAD.Pro input file will look like this.

FIGURE 1.5.12 Load commands generated using the Plate hydrostatic load facility in the GUI

The load diagram on the STAAD.Pro model will look like Fig 1.5.13.

FIGURE 1.5.13 Trapezoidally varying pressure loads generated on a wall made of plate elements

This facility can be used for generating linearly varying pressures not only due to liquids, but any material that produces such pressures, such as soil on a culvert wall and other underground structures, grain inside a silo, etc.

1.5.3.11 Wind Load Generation on Structural Components Modeled Using Plate Elements In Section 2.1, the procedure for generating loads on structures due to wind blowing against the structure is described. This facility is available only for panels bound by frame members. If the region exposed to the wind is a wall, it is not amenable for generating load using this facility. In such cases, the wall must be meshed and the wind pressure must be applied on it along the global direction (or local Z) using the element pressure load facility. A problem that users are faced with is—if the wall is curved, as in the case of a circular tank or a dome, does the program automatically reduce the load intensity or make any other adjustment due to the curved nature of the region. STAAD.Pro does not make a reduction in the pressure for the curved shape. However, in a curved structure, because the individual elements are at an inclination to the global planes, a pressure applied along global X or global Z will automatically result in the load having two components on each element—one normal to its plane and another parallel to its plane.

1.5.3.12 Prestress Load on Plates

There is no direct facility in STAAD.Pro to apply prestress load on plates. The closest we can get is to include dummy beam members between the plate nodes and apply the MEMBER PRESTRESS load to these members. We would have to assign zero density and negligible stiffness to these dummy beam entities to ensure that they do not change the loading or stiffness aspects of the structure.

1.5.4 Applying Pressure Loads on Surfaces By surfaces, we refer to the entity used in STAAD.Pro to represent a physical object such as a wall or slab. Pressure loads can be applied on the surface entity as described in Section 5.32.3.4 of the STAAD.Pro Technical Reference manual.

FIGURE 1.5.14 Page from the STAAD.Pro Technical Reference manual for loads on surfaces

Because the surface entity is internally converted by STAAD.Pro into a collection of plate elements, a pressure applied on a surface will be translated internally by STAAD.Pro into a pressure load acting on those individual plate elements.

1.5.5 Loads on Solid Elements Three types of loads can currently be applied on solids—its selfweight, uniform as well as a volumetric type pressure, and temperature load.

1.5.5.1 Pressure Loads on Solids Before we can apply a pressure load on a solid, we need to know which face of the solid the pressure is to be applied on. A solid can have anywhere from four to eight faces, as shown in Section 1.2.1 of Part I. A diagram showing the node configuration for each face is also present in that section. Example 26: Pressure load on Face 4 of some solid elements ELEMENT LOAD SOLIDS 3 6 9 12 FACE 4 PRE GY -500.0

FIGURE 1.5.15 Uniform pressure on one face of some solid elements

Example 27: Trapezoidally varying load on Face 6 of Element 5 ELEMENT LOAD SOLID 5 FACE 6 PRESSURE GZ 100 100 40 40

FIGURE 1.5.16 Trapezoidal load on the face of a solid element

1.5.5.2 Applying a Moment on a Solid The basic nature of solid elements is that they do not have any rotational stiffness at their nodes. Consequently, we cannot apply a moment at the node of a solid element unless there is a beam or a plate attached to that node. So, one solution is to create a fictitious two-segment beam whose one segment protrudes out of that joint by a small distance and its other segment is from that node to the next interior node of the solid element. Then apply the load at the free end of the member. Alternatively, apply two equal and opposite concentrated loads at two adjacent nodes in the vicinity of the point of action of the moment.

1.6 Temperature and Strain Loads

1.6.1 Introduction In this section, we look at ways in which we can specify changes in temperature and initial deformation (elongation and shrinkage). Required reading 15. Technical Reference manual—Sections 1.16.6, 5.26.2, and 5.32.6 16. Application Examples manual—Verification Example 11 17. Getting Started and Tutorials—Tutorial 3 18. Graphical Interface Help manual—Section 2.3.7.8

1.6.2 Temperature Loading—Discussion STAAD.Pro can compute the displacements, forces, stresses, reactions, and so on due to a change in temperature (not the absolute temperature). The coefficient of thermal expansion (Alpha) is needed to analyze the structure for temperature loads. If Alpha is missing from the material constants, and a temperature increase or decrease is specified, an error message will be reported and the analysis terminated.

FIGURE 1.6.1 Warning when Alpha is not specified

STAAD.Pro does not use any explicit unit system for temperature. One just needs to make sure that the temperature change is specified in the same units as that of ALPHA. If Alpha for steel is specified as 6.5E-6, then enter the temperature changes and differences in degree Fahrenheit. If we use 11.7E-6 as Alpha for steel, then we should enter the temperature changes and differences in degree Celsius. The default ALPHA value is in centigrade if the general unit system in the model is Metric. It is in Fahrenheit if the units in the model are in the English (FPS) system. This is also true of the ALPHA that gets assigned automatically along with the MATERIAL. If the base unit system for the model is metric, the data for the material called STEEL will look like this in the STAAD.Pro input file. DEFINE MATERIAL START ISOTROPIC STEEL E 2.05e+008 POISSON 0.3 DENSITY 76.8195

ALPHA 1.2e-005 DAMP 0.03 END DEFINE MATERIAL

If the base unit system for the model is English, the data for the Material called STEEL will look like this in the STAAD.Pro input file. DEFINE MATERIAL START ISOTROPIC STEEL E 29000 POISSON 0.3 DENSITY 0.000283 ALPHA 6.5e-006 DAMP 0.03 END DEFINE MATERIAL

The base unit system is explained in Section 2 of Part I.

FIGURE 1.6.2 Alpha value in the STAAD.Pro input file

In Fig 1.6.2, Alpha is listed as 1.2E-005, which is in centigrade units. The default values are listed in Section 5.26.2 of the STAAD.Pro Technical Reference manual.

FIGURE 1.6.3 Typical values of Alpha for various materials

In metric units, a 30-degree change in Celsius/Kelvin (e.g., from 0.0 to 30.0) is the equivalent amount of temperature change as a 54-degree change in Fahrenheit/Rankine in imperial units. Alpha can also be found in a few places in the GUI such as the Materials button in the GeneralProperty page as shown in Fig 1.6.4. It is also listed in the General-Materials page.

FIGURE 1.6.4 Alpha as reported in the General-Property page

FIGURE 1.6.5 Dialog box displaying the coefficient of thermal expansion

To ensure that there is no error in the input of the values associated with temperature loading, here are the steps. Examine the Alpha value in the input file or in the GUI as described earlier. If Alpha is in Fahrenheit, make sure that under your LOAD commands (explained later), the temperature change you provide is also in Fahrenheit. If it is in centigrade, the temperature changes specified in the LOAD cases too must be in centigrade units.

1.6.2.1 Types of Temperature Loads The net change or variation in temperature experienced by a beam or slab is defined through a combination of the following two types of temperature changes. 1.6.2.1.1 Uniform Increase or Decrease in Temperature This corresponds to the condition where all the points of the cross-section are uniformly heated or cooled. 1.6.2.1.2 Temperature Gradient across the Depth or Width This is the type of temperature change for which the extreme top fiber is at a different temperature than the extreme bottom fiber. So, temperature changes linearly from one edge or face to the other edge with the neutral axis experiencing a zero change.

1.6.2.2 Data Needed to Calculate Input Terms for Specifying Temperature Loads

To apply a temperature load, one has to know the following: The stress-free temperature which is the temperature that the member was at when it was constructed or installed. Call it A. Some people use the term “ambient temperature” in place of stress-free temperature. The temperature of the top fiber (the fiber that is farthest along the positive direction of the local Y axis). Call it B. The temperature of the bottom fiber (the fiber that is farthest along the negative direction of the local Y axis). Call it C. Similarly, if there is a change in temperature along the local Z axis, there will be a set of B and C values for the local Z axis too.

1.6.2.3 Temperature Loads on Members—How to Specify The data required for members are: The change in temperature (f1) associated with uniform expansion or contraction The difference in temperature in the local Y direction (f2) The temperature difference in the local Z direction (f3) Any values not entered will default to zero. The command for specifying the temperature load for members is member-list TEMPERATURE f1 f2

where f1 = (B + C)/2 – A f2 = B – C where A, B, and C are as described earlier. Also, depending on the conditions, f1 can be zero while f2 is non-zero, or vice-versa.

FIGURE 1.6.6 Dialog box for specifying temperature load

The third term in Fig 1.6.6—“Temperature Differential from Side to Side (Local Z)” —is applicable only for members (line entities used to represent beams, columns, etc.). It is not relevant for plates or solids. The Alpha that must be entered is the average thermal expansion constant value for the temperature range involved and for the degree units you are using. Related Question: How does STAAD.Pro know what the ambient temperature is? Does it assume a value, and if so, on what basis? Answer: No, STAAD.Pro does not know or assume the ambient temperature. Instead, it assumes that whatever temperatures we specify are the increase or the decrease from the ambient. In other words, it does not need to know the ambient. It only needs to know the change from the ambient. That change is represented using the terms f1, f2, and f3 that was mentioned earlier.

1.6.2.4 Temperature Loads on Plates—How to Specify A temperature change can be applied on a mesh of plate elements representing a wall or slab. The term f3 that we saw for members is not applicable for plates. So, the two values are: f1 = temperature change associated with uniform increase or decrease in temperature across the full plate f2 = temperature change between the top and bottom of the elements

FIGURE 1.6.7 Dialog box for temperature load input

For specifying f2, the terms “top” and “bottom” are defined with respect to the local axis system of the individual elements. See Section 4.5 of Part I for details.

FIGURE 1.6.8 Top and bottom sides for plate elements

If the wall or slab is in a single plane, f1 should produce membrane stresses SX, SY, and SXY. f2 should produce values for MX, MY, MXY, SQX, and SQY. These terms are described in Sections 6.1 and 6.2 of Part III. On large models with plates, to observe the effect of the two temperature changes separately, one could analyze for a load case in which f1 is non-zero while f2 is zero, and another load case in

which f1 is zero while f2 is non-zero.

1.6.2.5 Temperature Loads on Solids—How to Specify For solids, the only temperature change that STAAD.Pro can handle currently is a uniform increase or decrease (f1). So, temperature variations where one edge of one solid element is at a different temperature than other edges cannot be modeled (f2 or f3 will be disallowed).

FIGURE 1.6.9 Dialog box for specifying temperature load for solids

1.6.2.6 Example for Uniform Increase or Decrease in Temperature in Beams, Plates, or Solids LOAD 9 TEMPERATURE RISE TEMPERATURE LOAD 47 TO 54 TEMP 50

This means, in Load Case 9, for members 47–54, all points on the cross-section are experiencing the same 50-degree constant temperature rise throughout the length of those members. It is important to note that temperature loads can produce large stresses in members and elements. So, one has to pay careful attention to the input. For example, if a member appears more than once in a temperature load case, both instances of the temperature change will be considered. Consider the data in Load Case 6 in the next example. As you can see, there are two lists. Many members that are on the second list are part of the first list too (e.g., 18–27). For such members, STAAD.Pro accumulates the temperatures, so, a

member that is entered twice will have the two temperatures added up. So, in this example, they are loaded to 360 degrees instead of 180. LOAD 6 LOADTYPE Live TITLE THERMAL LOAD TEMPERATURE LOAD 5 TO 10 13 14 17 TO 32 34 TO 56 59 TO 62 67 69 TO 94 96 TO 103 106 107 110 111 TO 120 125 TO 134 139 TO 148 153 TO 163 166 TO 172 175 176 178 TO 205 208 TO 221 223 226 228 TO 239 241 TO 254 256 TO 258 261 TO 267 270 TEMP 180 18 TO 27 29 31 33 47 TO 56 59 TO 62 64 65 81 83 85 87 89 91 93 95 178 181 208 211 212 215 217 219 221 224 226 239 243 245 247 249 251 253 255 263 275 276 TO 560 TEMP 180

If the intention is to apply the temperature change of 180 degrees only once, change the second list to 33 64 65 95 224 255 275 TO 560 TEMP 180

So, Load Case 6 should look like this. LOAD 6 LOADTYPE Live TITLE THERMAL LOAD TEMPERATURE LOAD 5 TO 10 13 14 17 TO 32 34 TO 56 59 TO 62 67 69 TO 94 96 TO 103 106 107 110 111 TO 120 125 TO 134 139 TO 148 153 TO 163 166 TO 172 175 176 178 TO 205 208 TO 221 223 226 228 TO 239 241 TO 254 256 TO 258 261 TO 267 270 TEMP 180 33 64 65 95 224 255 275 TO 560 TEMP 180

1.6.2.7 Analysis Procedure for a Uniform Rise or Fall in Temperature in a Frame Member The procedure used to analyze a frame member for temperature change is as follows: When the temperature change is a uniform increase or uniform decrease, meaning, all the points of the cross-section are uniformly heated or cooled, 1. Fix the two ends of the member. The force induced in the member would now be A*E*Alpha*dT, where A = cross-section area of the bar E = Young’s modulus Alpha = coefficient of thermal expansion

dT = temperature change Call this force P1. 2. The fixities are removed and this force is now applied as a joint load at the two nodes in opposite directions. The structure is analyzed for the joint loads. Depending upon the stiffness of the various members and elements of the structure, the structure will deform. The axial force induced in the member due to the node displacements is then calculated. Call this force P2. Since the deformation of the member (force from Step 2) relieves the force from the locked condition (Step 1), P2 minus P1 will give us the final force in the member due to the temperature change.

1.6.2.8 Example for Temperature Gradient across the Depth or Width for Frame Members LOAD 11 TEMPERATURE GRADIENT RISE TEMPERATURE LOAD 31 TO 34 TEMP 30 16

This means, in Load Case 11, for members 31–34, there is a 30-degree uniform temperature rise and a 16-degree temperature difference between the top and bottom. Thus, the top of the section is at 38 degrees and the bottom of the section is at 22 degrees. The temperature varies linearly along local Y (over the cross-section depth) and hence bending occurs about local Z. LOAD 14 uniform minor axis bending due to temperature TEMPERATURE LOAD 1 TO 26 temp 0 0 10

In this example, there is a 10-degree difference in temperature across the section width (along local Z) and hence bending occurs about local Y. Because the first number is zero, there is no change in temperature at the neutral axis. So, the positive edge is hotter by 5 degrees and the negative edge is colder by 5 degrees, thus giving rise to a 10-degree differential. Related Question: How do we identify the top and bottom sides for specifying temperature change across the depth and width of a rectangular beam? Answer: One needs to know the local axis system of beams to understand this. It is explained in Section 4.1 of Part I.

FIGURE 1.6.10 Top and bottom sides of a beam along local Y axis

FIGURE 1.6.11 Top and bottom sides of a beam along local Z axis

1.6.2.9 Analysis Procedure for Temperature Gradient across the Depth or Width of a Frame Member 1. Fix the two ends of the member on which the temperature change is applied. The moment induced in the member would now be E*Alpha*MI*dT/Depth, where E = Young’s modulus Alpha = coefficient of thermal expansion MI and Depth = moment of inertia and dimension of the section corresponding to the axis about which the temperature change takes place. So, (Iz and D) or (Iy and B). dT = temperature change Call this moment P3. 2. The fixities are removed and this moment is now applied at the two joints in opposite directions. The structure is analyzed for the joint moments. The moment causes the structure

to deform. The moment induced in the member due to the node displacements are then calculated. Call this moment P4. P4 minus P3 will give us the final moment in the member due to the temperature change. 1.6.2.9.1 Member Depth and Width As explained in Section 1.6.2.9, when the temperature varies along the depth or width of the section, the values of depth and/or width are needed to calculate the moment induced in the member. So, it is important to pay attention to how the properties for the member are specified. For sections assigned from the built-in property tables, these dimensions are automatically retrieved by the program from the property databases. But when the properties are assigned using PRISMATIC, User Table, or other methods that do not involve built-in tables, it is essential that the dimensions of the cross-section be included along with other computed property terms. Otherwise, the program may assume a value for the dimensions when calculating the moments due to the temperature gradient. The value assumed is mentioned in Section 1 of the Technical Reference manual. So, in the following expression, MEMBER PROPERTIES 31 TO 34 PRIS AX 164.29 AY 85.35 AZ 100.55 IX 5532 IY 24841 - IZ 96964

the depth is absent, which means the program will have to assume the dimensions for processing a temperature that causes bending about the depth or width of members 31–34. Related Question: If I have a beam framing into a column at mid-height, it does not appear as though the thermal axial force in the beam causes additional bending in the column. Is this true? Answer: The amount of moment that the column receives will depend on the relative stiffness of the members in the structure. If the column is comparatively weak, it will deform without much resistance. A column with fixed supports at its base instead of pinned supports will have greater resistance to the temperature load in the beam. A stiffer column will probably see a larger moment than a weaker column. Related Question: If the highest temperature during the year of the place where my structure is located is 44 degrees Celsius, and, the lowest temperature is 18, should I specify 44 minus 18 as the temperature that causes axial elongation in the plate elements of a roof slab? Answer: No. We need to know the ambient temperature (stress-free temperature) too. Let us say that it is 30 degrees Celsius. Assume that the temperature change is purely of the “f1” type, meaning, we are not going to worry about a variation in temperature across the thickness of the roof slab. We will have to create two load cases. In one, f1 is equal to a temperature increase equal to 44 – 30 = 14 degrees Celsius. In the other, f1 will be a reduction equal to 18 – 30 = –12 degrees Celsius.

Related Question: I need to analyze a deck slab for a temperature change of ±60 degrees Fahrenheit. In addition, there is a temperature gradient of 25 degrees Fahrenheit between the top and bottom surfaces of the slab. How do I do this? The slab has been modeled using plate elements. Answer: If we assume that the temperature at the stress-free condition is A, then the structure must be analyzed for two conditions, each of which must have its own load case. Condition 1: (a) temperature at the top of concrete reaching (A + 60 + 12.5) (b) temperature at the bottom of concrete reaching (A + 60 – 12.5) Assuming that all the plate elements have the local Z axis pointing along the global Y direction, we specify this using the following syntax. element-list TEMPERATURE 60 25

The first number (60) is equal to the average temperature you want to design for minus the temperature corresponding to the stress-free condition. The second number is the temperature of the top surface (the fiber at the +Z surface) minus the temperature of the bottom surface (fiber at the –Z surface). Hence, it is important that the +Z surface corresponds to top of deck. For example, LOAD 10 TEMPERATURE INCREASE TEMPERATURE LOAD 501 TO 588 TEMP 60 25

Condition 2: (a) temperature at the top of concrete reaching (A – 60 – 12.5) (b) temperature at the bottom of concrete reaching (A – 60 + 12.5) The syntax for this is element-list TEMPERATURE -60 -25

For example, LOAD 11 TEMPERATURE DECREASE TEMPERATURE LOAD 501 TO 588 TEMP -60 -25

Related Question: I was trying to apply a temperature gradient between the top and bottom flange of a wide flange beam. I managed to get moments out of it as expected, but when I tried to change the size of that member without changing the temperature gradient, the stress results I obtain are exactly the same.

Does STAAD.Pro take into account the beam depth when doing temperature gradient calculations? Answer: STAAD.Pro uses E*a*I z*ΔT/Depth to compute the bending moment, where ΔT is the difference in temperature (T top – T bottom) from the bottom to top of the section. Most sections require that the depth be entered. If you enter a depth of zero or leave it out of prismatic, then STAAD.Pro will use a depth of 10 in. and write a message. If there are cover plates, the depth is increased by the cover plate thicknesses. Related Question: I have a question on the temperature load command. If I have the following: 1 TO 10 TEMP 50 25

would this mean that the top side of the plate is at 50 degrees and that the bottom side is at 75 degrees? If the command was changed to 1 TO 10 TEMP 50 -25

would the top side be at 50 degrees and the bottom side at 25 degrees? Answer: Assuming that the stress-free temperature is zero degrees, 1 TO 10 TEMP 50 25

means top is 62.5 degrees and the bottom is 37.5 degrees. The average is 50 degrees and the topbottom difference is 25 degrees. 1 TO 10 TEMP 50 -25

means top is 37.5 degrees and the bottom is 62.5 degrees. The average is 50 degrees and the topbottom difference is –25 degrees.

1.6.2.10 Conversion of Units of Temperature A common problem that users encounter is converting from centigrade to Fahrenheit when specifying the temperature load. The temperature load input that we provide to the program is the change in temperature, not the absolute temperature. So, a change amounting to 68 degrees Fahrenheit is equivalent to a change of 68/1.8 = 37.7778 centigrade. Instead, users erroneously specify the value as 20, based on the calculation (68 – 32)/1.8. This calculation is not valid because we are not trying to determine absolute temperatures, but only a change in temperature. Alpha in centigrade divided by 1.8 should give you Alpha in Fahrenheit. Basically, Alpha(F) *

T(F) must equal the Alpha(C) * T(C). Related Question: I am modeling a floor slab with a subgrade “k” value and the compression-only feature. I am applying a temperature gradient to the plate elements to simulate shrinkage of the concrete causing the edges and corners of the slab to curl up off of the subgrade. So, the geometry has changed because the slab is no longer supported at all nodes. Now I want to apply floor loads to this new geometry, which will push the floor back down and start to re-engage the subgrade, which changes the supported nodes again. Is there some way to model this using the change command or non-linear analysis? Answer: Superimposing the temperature gradient and the floor loads in one load case is an alternative. With the compression-only option you have chosen, STAAD.Pro will determine which points are in contact with the subgrade for the combined action of all the load items in that load case. So only those springs that are in contact for that load case are activated, which makes the solution nonlinear. Related Question: I am modeling an I-shape using plate elements—one layer of plates for each of the flanges, and two layers of plates for the web. A zoomed-in view of a portion of the model is shown. I want to analyze for a temperature increase of 1000 degrees for the top flange, 100 degrees for the bottom flange, and linearly varying across the depth of the web. Please tell me how to input this.

FIGURE 1.6.12 I-Beam modeled using plate elements

Answer: For the mathematical model shown in Fig 1.6.12, if the bottom flange elements experience an increase in temperature of 100 degrees, top flange elements are hotter by 1000, and if the neutral

axis is hotter by (100+1000)/2 = 550, then the increase in temperature for the lower layer of web elements is (100+550)/2 = 325, and for the upper layer is (550+1000)/2 = 775. For the sake of this example, if 1–20 are the elements of the bottom flange, first (lower) layer of the elements for the web are 21–30, second layer for the web are 31–40, and top flange is 41–60, here is one way to describe that set of temperature changes. LOAD 1 TEMP INCREASE TEMPERATURE LOAD 1 TO 20 TEMP 100 0 21 TO 30 TEMP 325 0 31 TO 40 TEMP 775 0 41 TO 60 TEMP 1000 0

These data assume that each flange is at a uniform temperature, and each layer of web elements is at a uniform temperature. More elements for the web will give better results. If you are trying to match theoretical results, then the supports would be at the center line of the web. Related Question: Is there a way to apply a temperature load in such a way that the plate expands or contracts along one direction and not the other? For example, for a slab in the horizontal plane XZ, I want it to expand only in X and not in Z. Answer: No. Uniform increase or decrease in temperature occurs along both the local axes (X and Y). Fig 1.6.13 shows the displaced shape (in plan view) of a doubly symmetric plate subjected to a uniform temperature increase. The dark lines form the original configuration of the mesh, and the faint lines indicate the displaced shape. Notice the doubly symmetric displaced shape.

FIGURE 1.6.13 Uniform expansion of a slab along two directions

However, the support conditions of the structure can be specified in such a way that it will allow expansion/contraction of the overall slab or wall along one direction only. For the above plate, if it is to be constrained from displacing in the Z direction, specify FIXED BUT FX supports at the nodes of the top and bottom edges. That will prevent translation along Z.

1.6.2.11 Temperature Loads and Buckling The buckling load caused by temperature change can be calculated by performing a buckling analysis. STAAD.Pro uses a linear finite element analysis buckling theory (3D Euler buckling) where the geometric stiffness matrix used in buckling is based on the original member length and the static linear axial force calculated for the members. For more information, see Section 1.6 of Part III.

1.6.2.12 Heat Transfer Analysis Heat transfer analysis is not available in STAAD.Pro.

1.6.2.13 Relationship between Material Properties and Temperature STAAD. Pro assumes that the material properties are not a function of temperature.

1.6.3 Strain Load—Discussion Axial elongation or axial shrinkage of a member can be input through a Strain Load facility. This

facility is available only for members, meaning, it is not available for plate elements or solid elements. There are two ways to specify a strain load. 1. Magnitude of elongation or shrinkage. Elongation is specified as a positive number and shrinkage as a negative number. It has units of length. It is specified using the keyword STRAIN. UNIT CMS LOAD 7 TEMPERATURE LOAD 7 TO 10 STRAIN 1.0

FIGURE 1.6.14 Dialog box in the STAAD.Pro GUI for specifying STRAIN load

2. Elongation or shrinkage as a fraction of the unstressed length of the member. This means that the elongation or shrinkage in length units is divided by the member length. The resulting value is a unit-less quantity. As before, a positive value is to be specified for elongation, and a negative value for shrinkage. It is specified using the keyword STRAINRATE. This type of strain can currently be specified only by typing the appropriate command in the STAAD.Pro input file. There is no facility in the STAAD. Pro GUI to specify this. UNIT CMS LOAD 7 TEMPERATURE LOAD 7 TO 10 STRAINRATE 0.00333

So, if there is a 100-in.-long member that was stretched for 1 in., we could enter it as UNIT INCHES

LOAD 18 TEMPERATURE LOAD 79 STRAIN 1.0

or UNIT INCHES LOAD 18 TEMPERATURE LOAD 79 STRAINRATE 0.01

Thus, the input that accompanies the keyword STRAIN is delta_L, while that for STRAINRATE is (delta_L)/L, where delta_L is the change in length L is the length of the member. The strain rate can be useful when several unequal length members have the same strain rates but different strains.

CHAPTER 2

Load Generation 2.0 Load Generation 2.0.1 Introduction The concept of load generation was introduced in Section 1.0.1.1. It is the process of taking a load source quantity such as wind pressure or a moving vehicle, and converting it to individual load items on the entities of the structure, in a format that enables the creation of the load vector for a stiffness analysis.

The following load generation facilities available in STAAD.Pro are discussed in this chapter: Wind loads Snow loads Moving loads Seismic loads (of the static equivalent type) Notional loads

2.1 Wind Load Generation 2.1.1 Introduction Wind load generation is a process that involves conversion of the wind pressure acting on structures into joint and member loads in the mathematical model. When wind acts on a panel bound by beams and columns, and the panel is an entity such as glass or a non-load-bearing wall, which is not defined as part of the structural model, then the load caused by wind needs to be computed and applied on the frame in the form of member loads and joint loads. This is the intent of the wind load generation facility. The input for this task consists of: 1. Structure geometry 2. Wind pressure profile, which is the table of pressure values versus the height ranges over which those pressures act Item 1 is known from the node coordinates and member incidences. The input for Item 2 is described in Section 2.1.15.STAAD.Pro is equipped with the facilities to calculate the wind pressure profile for only a few codes as mentioned in that section. For codes not on that list, the user must obtain the profile manually or using external tools. Also, the program generates loads only on frame members (line entities connected between two nodes). If the structure does not contain members, such as models consisting only of plates and/or solids, loads will not be generated. Required reading 1. Technical Reference manual—Sections 1.17.3, 5.31.3, and 5.32.12 2. Application Examples manual—Example 15 3. Graphical Interface Help manual—Section 2.3.7.12.1.3

2.1.2 Data Required for Wind Load Generation The input that is specific to wind load generation consists of the following steps: 1. A definition block in which the wind pressure (intensity) and exposure factor are provided. Example 1 UNIT FEET DEFINE WIND LOAD TYPE 1 INTENSITY 0.1 0.15 HEIGHT 12 24 EXPOSURE 0.90 YRANGE 11 13

FIGURE 2.1.1 Wind load definition block in the STAAD.Pro GUI

2. A command to generate the loads due to wind blowing in a certain direction. Example 2 LOAD 3 WIND LOAD IN X DIRECTION WIND LOAD X 0.3 TYPE 1

FIGURE 2.1.2 Creating a wind load case using the STAAD.Pro GUI

These steps are described in detail in the sections that follow.

2.1.3 Types of Structures for Wind Load Generation There are two types of structures for which this feature can be used: (a) closed structures and (b) open structures. We will look at the various aspects involved in load generation, first in the context of closed structures and later for open structures.

2.1.3.1 Closed Structures The term “closed” is used to describe structures such as office buildings that do not let the wind to blow through the structure. Instead, their walls and facades—which could be made of glass or wood or any other material—block the wind, which gives rise to the forces that the structural frame has to be designed to resist. The exterior portion or face of the structure that blocks the wind—on the windward side or the leeward side—is called the exposed face. The members of the structure on the exposed face will be used to form panels and determine the magnitude of the wind force on that face. In Fig 2.1.3, the exposed faces of a commercial/residential multistory building are shown. Interior members—those shielded from the wind because they are located behind the members on the exposed faces—will not be considered. On the exposed faces, the zones on which the wind pressure bears against are called panels. The panels represent materials such as the glass facade or walls made of wood or other material that was not considered for inclusion in the structural model. The panels on the upper storeys—floors above the ground floor—will be circumscribed, for example, by columns along the vertical direction, and beams in the horizontal direction. Or they could be triangular in shape if one were to consider the region between a beam, a column, and an inclined brace. On the ground floor, the panels will be circumscribed by the ground at the bottom level, and members (columns and beams) on all other sides. The bottom line is that the panels have to form a closed shape.

FIGURE 2.1.3 Exposed faces of closed structures

It is essential that the entities that form the boundary of the panel be all frame members. Or, there

could be a support on one side and frame members on all other sides. Using plate or solid elements to span one or more edges of the panels is not sufficient. Adding dummy members—members with a very small E and/or section properties due to which their stiffness and weight is negligible —so that the panels could have a closed shape could be a simple way to resolve this problem. The basis of this generation is as follows. Step 1. Identify the panels. One side of the panel can be the ground. This is identified by the elevation where the supports are located. Hence, it is imperative that all supports be at the same level in order for the program to be able to successfully identify the ground edge (see Figure 2.1.4).

FIGURE 2.1.4 Panel identification for closed structures

Step 2. The area contained within the panel is multiplied by the wind pressure to calculate the wind force within that panel. That force is then distributed between the joints on the boundary of that panel in the form of joint loads. The magnitude of each joint load depends on the influence area that the joint commands within the panel. Fig 2.1.5 shows a structure with incomplete panels along the top. Panels 1 and 2 are considered closed because there are members on three sides and the ground forms the fourth side at the support level. As they have members on all sides, Panels 3 and 4 are considered closed by definition. Panels 5 and 6, which consist of three members and a plate element for each, are open along the top, and could be made closed by adding dummy members along the top edge.

FIGURE 2.1.5 Closed and open panels

Similar to the floor load generation and mat foundation support generation facilities, the WIND LOAD commands too use the convex hull algorithm to determine what areas are bounded by members. Then, the tributary area for each member circumscribing the area is determined. In the STAAD.Pro Graphical User Interface (GUI), under the Labels menu, there is an option called Display Wind Load Contributory Area to view these areas (see Figure 2.1.6). The cross-hatched colored areas indicate the tributary areas loaded by the wind.

FIGURE 2.1.6 Graphical representation of the exposed face

Certain modeling methods that can hinder the wind load generation process are described in Section 2.1.7. When that happens, the colored hatched areas may overlap, resulting in an incorrect amount of load being applied on the associated members. In such cases, instead of instructing the program to determine the exposed face on its own, the engineer can assist by defining that region with the help of (a) X, Y and Z RANGES, or (b) group names. The WIND LOAD command will have to be replaced with multiple such commands each with its set of XRANGE/YRANGE/ZRANGE, individually encompassing a smaller exposed zone so that in none of these sub-regions, the requirements of the algorithm are violated. An example of this is provided in Section 2.1.11. Also, one must check the Statics Check table in the post-processing mode (see Section 4.1 in Part III) to ensure that the total loads generated from that wind load case are of the expected magnitude. 2.1.3.1.1 Windward and Leeward Faces If the user does not specify the region on the structure on which the wind is acting, STAAD.Pro needs to identify the exposed faces on its own. The basis for this identification is described in this section. For wind blowing in any given direction (from negative X or Z to positive X or Z, or vice versa), there is a near face and a far face for the building. For easy identification, the dialog box in the STAAD.Pro GUI refers to the near face as the windward face and the far face as the leeward face.

FIGURE 2.1.7 Dialog box in the GUI for specifying the faces

FIGURE 2.1.8 Sign convention for exposed faces and wind load factors

2.1.3.1.2 Factor Term in the Wind Load Generation Input The factor, indicated as +f and –f in Fig 2.1.8, can take positive or negative values as described earlier.

FIGURE 2.1.9 Factor term in the wind load generation input

FIGURE 2.1.10 Exposed faces and direction of wind

The following table shows examples of how the WIND LOAD command looks like in the STAAD.Pro input file. Its magnitude (absolute value), which can be any real number (not just 1.0), is the quantity by which the wind pressure is multiplied and is thus a tool to scale up or scale down the wind force. For example, if one wants to specify the full intensity on the near face, and 20% of the full intensity on the far face, the commands will look like this in a single load case. LOAD 7 WIND LOAD IN +X WIND LOAD X 1.0 TYPE 1 LIST _WESTFACE WIND LOAD X 0.2 TYPE 1 LIST _EASTFACE

where _WESTFACE and _EASTFACE are member groups containing the members of the exposed faces of the structure at the left and right extremities, respectively. Assigning the wind to specific members is discussed in Section 2.1.3.1.7. Direction of Wind West to East (positive global X) West to East (positive global X) East to West (negative global X) East to West (negative global X) North to South (positive global Z)

Exposed Face AB DC AB DC AD

Command in STAAD.Pro File WIND LOAD X 1.0 WIND LOAD -X 1.0 WIND LOAD -X -1.0 WIND LOAD X -1.0 WIND LOAD Z 1.0

North to South (positive global Z) South to North (negative global Z) South to North (negative global Z)

BC AD BC

WIND LOAD -Z 1.0 WIND LOAD -Z -1.0 WIND LOAD Z -1.0

FIGURE 2.1.11 Choosing the faces and directions

2.1.3.1.3 The TYPE Command Related Question: Is the TYPE command in the wind load definition referring to a term in any building code? Answer: STAAD.Pro permits the definition of several different wind loads, each with certain characteristics. To distinguish the wind load having a set of characteristics from another that has a different set of characteristics, each wind load is identified using a TYPE command followed by an identification number. In other words, the TYPE command and the number are entirely a creation of the user. They are not terminologies that the user will find in any code or handbook that provides guidelines on loading for structures. The advantage of this feature is that it enables the user to communicate to the program information such as the wind pressure at different heights,

and openings in the structure at various heights. 2.1.3.1.4 Wind Intensity Wind intensity as required for input in STAAD.Pro is merely the wind pressure in units of force per unit area. 2.1.3.1.5 Exposure Factor The exposure factor is just a number by which the wind force at a joint is multiplied. So, if the force at one or more joints needs to be increased by, for example, 15%, provide a value of 1.15 to that term. If it is not specified, the program assumes it to be 1.0 by default. If at a joint, there is no increase or decrease in the amount of force due to wind, the exposure factor need not be specified. If it is specified as zero for some joints, the applied force at those joints will become zero. Openings within the panels may be modeled with the help of exposure factors. The exposure factor is useful in catering to external attachments such as an advertising sign and appurtenances, including dish antenna or discs, which may be mounted on structures as communication devices. Such devices act as additional barriers to the wind and thus attract additional wind load on the building. By providing an exposure factor greater than 1 for the joints in the vicinity, the additional wind force can be approximately accounted for. 2.1.3.1.6 Pressure versus Height Table The pressure versus height values are interpreted by STAAD.Pro as follows: Pressure p1 is assumed to act from negative infinity to height “h1.” Pressure p2 acts from height “h1” to height “h2.” Pressure p3 acts from height “h2” to height “h3.” Pressure p4 acts from height “h3” to height “h4.” … Pressure pn acts from height “hn-1” to height “hn.” Finally, pressure pn is also assumed to act from height “hn” to height “positive infinity.” Note that the heights specified are the actual Y coordinates and not measured relative to the base of the structure.

FIGURE 2.1.12 Graphical representation of values of wind pressure versus height

Multiple Sets of Values of Wind Intensity versus Height Each set of values of intensity (wind pressure) versus height must be associated with a TYPE number. So, if multiple sets of values need to be specified, each set has to be preceded by a TYPE number, as shown in the following example. DEFINE WIND LOAD TYPE 1 INT 2.24 HEIG 20 TYPE 2 INT 1.4 HEIG 20 TYPE 3 INT 0.63 0.76 0.80 HEIG 5 10 15 LOAD 12 WIND LOAD IN +X WIND LOAD X 1.0 TYPE 1 LIST _WESTFACE LOAD 13 WIND LOAD IN –X WIND LOAD X -1.0 TYPE 2 LIST _EASTFACE LOAD 14 WIND LOAD IN +Z WIND LOAD Z -1.0 TYPE 3 LIST _SOUTHFACE LOAD 15 WIND LOAD IN –Z WIND LOAD –Z -1.0 TYPE 3 LIST _NORTHFACE

2.1.3.1.7 Specifying a Set of Members on Which to Generate the Load In complex structure geometries, the process of figuring out the panels of the exposed faces can be time consuming. To reduce the amount of searching that the program needs to do, the analyst can instruct the program to search only specific parts of the structure. Only those members will then be used as candidates for the panel identification task. Some examples of this approach are provided next. Related Question: I notice that the WIND LOAD command comes in a few variations: 1. 2. 3. 4.

WIND LOAD X 1 TYPE 1 WIND LOAD X TYPE 1 XRANGE -1 30 YRANGE 19 31 ZRANGE -1 1 WIND LOAD X 1.2 TYPE 1 LIST _EASTFACE WIND LOAD X 1 TYPE 1 LIST 2 5 TO 16 79 TO 84

Why are there so many variations? Answer: While all of them are ways to apply a wind pressure along global X, their differences lie in the manner in which information regarding the exposed face and panels is conveyed to the program. In the first method, there are no instructions following the expression TYPE 1, which is interpreted as an absence of a member set. So, STAAD.Pro scans the whole structure to determine the interior and exterior faces and then finds the panels on the near exterior face. In the second example, the exposed face is confined between an X coordinate range of (−1, 30), a Y coordinate range of (19, 31), and a Z coordinate range of (−1, 1). The purpose of these ranges is to communicate to the program the zone within which the members that constitute the face of the structure on which the wind acts are present. So, the program confines its search of panels to the

members lying in a fictitious box contained within these ranges. This figure is an example of a structure where the program needs to be informed of the location of the exposed face. Notice the beams cantilevering out from the main frame. So, the closed panels of the exposed face are not located at the extreme outer edge of the model, but a little on the inside. In the third example, the exposed face is defined through members that are in a group named _EASTFACE. So, the program confines its search of panels to these members only. In the fourth example, the exposed face is defined through the list of members 2, 5 to 16, and 79 to 84. The panels are formed from these members only. Thus, the commands in Examples 2, 3, and 4 are ways to assist the program in determining the exposed face from a localized region of the structure.

FIGURE 2.1.13 Isolating the exposed face

Potential Errors in Specifying the Member Set An incorrect pair of values for the X, Y, and Z ranges can cause the wind load generation to either fail or produce an erroneous set of loads. Two instances are when:

1. The structure lies outside the bounds of the ranges. For example, if the extreme left face of the building has an X coordinate of 2 m, the following command will fail to generate any load. LOAD 3 LOADTYPE Wind TITLE WEST TO EAST WIND LOAD X 1 TYPE 1 XR -1 1 YR 0 10 ZR -1 10

Notice in this example that the XRANGE is provided as −1 to +1. The entire building falls to the right of that range. 2. The range is so large that it encompasses a large portion of the structure and not just the face on which wind directly bears upon. For example, consider 0–70 for XRANGE. If the structure spans from X = 10 to X = 50, as shown in Fig 2.1.14, the XRANGE covers the full span along X, thus defeating the purpose behind providing a range.

FIGURE 2.1.14 Range limits that exceed the structure bounds

2.1.3.1.8 Procedure Used by STAAD.Pro for Calculating the Joint Load from the Wind Pressure The procedure used in this calculation is illustrated in Fig 2.1.15.

FIGURE 2.1.15 Influence areas for members on a panel

Step 1. Form closed panels. A closed panel is a region whose boundary consists entirely of members or of members and the ground surface. Step 2. Find the center of gravity of each of the panels. Step 3. For each panel, draw straight lines from the center of gravity (CG) to the midpoint of the members that form the panel boundary. So, the panel region will now contain several quadrilaterals whose two sides are made of portions of the respective members (or the ground) and the other two sides are lines going from the CG to the midpoint of the corresponding members. Step 4. The area contained in any quadrilateral is allocated as the influence area for the node located at the meeting point of two members. Step 5. Multiply the influence area by the average wind pressure contained inside the influence area and by the exposure factor for the node. This will yield the concentrated horizontal force for the joint. In Fig 2.1.15, the members form the periphery of the panel, and the nodes are its vertices. The location of the CG of the panel is circled. Each node is associated with a four-sided quadrilateral which provides the influence area for that node.

2.1.3.2 Open Structures In open lattice structures such as electrical transmission structures or communication towers, there is no exposed face or panels to block the wind or prevent it from flowing through the structure. Such structures are considered “open,” allowing the wind to blow through. The force exerted by the wind is from the wind pressure directly impacting the width of all the members in the model. In other words, in this type of loading, the load intensity is based on the individual dimensions of the members rather than on the panel dimensions.

Accordingly, the program first determines the width of the individual members of the model. Then, that width is multiplied by the wind pressure to arrive at a uniform distributed member load (force per length). It is assumed that all members of the structure are subjected to the pressure, and hence, they all will receive the load. However, members whose local X axis is parallel to the direction of wind will not receive the load. The concept of members on the windward side shielding the members in the interior regions of the structure does not exist for open structures. However, if the user wishes to apply the load on just specific members, the facilities described earlier such as X/Y/Z ranges and member lists may be used for open structures too. To achieve this type of load generation, in the dialog box for assigning wind loads, check the option Open Structure (see Fig 2.1.17).

FIGURE 2.1.16 An Open lattice structure

FIGURE 2.1.17 Dialog box in the STAAD.Pro GUI for wind load generation

If you prefer typing the commands in the editor, add the keyword OPEN at the end of the WIND LOAD command in the actual load case, as shown in the next example. For open structures, exposure factors (Section 2.1.3.1.5) are not applicable. Also, the factor term (Section 2.1.3.1.2) is used solely as a multiplying factor to increase or decrease the load intensity on all members and not as a means to identify an exposed face. The wind intensity versus height data is specified just like it is done for closed structures. Example 3 UNIT FEET DEFINE WIND LOAD TYPE 1 INTENSITY 0.1 HEIGHT 24 LOAD 1 WIND LOAD IN Z-DIRECTION WIND LOAD Z -1.2 TYPE 1 OPEN

In the X:\SProV8i\STAAD\Examp folder, there are a number of subfolders named AUS, CAN, EUR, UK, US, and so on. Most of these folders contain a STAAD.Pro model named “wind_on_open_structure.std,” which as the name suggests provides an example for wind load generation on open lattice structures in load cases 5 through 8. If the keyword OPEN is omitted, the load is generated on the basis for closed structures. Since this type of load generation requires the exposed width of the members to be known, the properties of all members have to be known for the load generation to work. So, before assigning the load, it is advisable to ensure that section property has been assigned to all members. Members to which it has not been assigned can be detected by going to Select -> By Missing Attributes -> Missing Property.

FIGURE 2.1.18 Identifying members for which property has not been assigned

2.1.3.2.1 Wind Load Generation and Ice Formation on Members of Open-Lattice Structures STAAD.Pro currently does not consider the thickness of ice formed on members of open lattice structures during the computation of the open structure type of wind load. Only the basic dimensions of the members are taken into consideration.

2.1.4 Types of Load Generated For closed structures Concentrated forces at joints, also known as joint loads in STAAD.Pro For open structures

Distributed loads on members, also known as member loads in STAAD.Pro

2.1.5 Obtaining a Report of the Joint and Member Loads Created by the Wind Load Generator By specifying the keywords PRINT LOAD DATA with the ANALYSIS command, one can instruct the program to produce a report consisting of all the generated loads in the output file. A sample is shown in Fig 2.1.9 for the open-type structure.

FIGURE 2.1.19 Load generation report in the. ANL file

2.1.6 Converting the Wind Pressures to Concentrated and Distributed Loads on the Structure—Is It Based on the Rules of Any Code? A generic method is used in STAAD.Pro for converting the wind pressure to concentrated loads at nodes and distributed loads on members. It is not necessarily based on the rules of any building code. It performs a simple calculation involving the multiplication of the pressure by the contributory area for a node in the case of closed structures and pressure times the width of the section in the case of open structures. However, STAAD.Pro can generate the pressure profile (the table of pressure versus height) as per the codes described in Section 2.1.15. Related Question: Can STAAD.Pro be instructed to calculate the wind loads if the exposed face of the structure is an inclined plane, that is, not perpendicular to the X or Z axes? Answer: In such a situation, it is advisable to compute the loads as joint and member loads manually or by other methods instead of using the wind load generator.

2.1.7 Modeling Aspects Which Hinder the Performance of the Wind Load Generation Facility for Closed Structures Related Question: There is a warning in the output file stating, *WARNING - NO MEMBERS LOADED FOR A WIND LOAD GENERATION

FIGURE 2.1.20 Warning when load generation fails

Answer: A problem that users come across is, why does the program fail to generate loads on some parts of the structure for the wind load case? Many of the same problems that are detrimental to the proper functioning of other load generation facilities such as FLOOR LOAD adversely affect the wind load generation algorithm too. Some of them are described in Sections 2.1.7.1 through 2.1.7.7.

2.1.7.1 Multiple Structures The concept of multiple or disjointed structures has been discussed in Sections 2.8 and 6.2 of Part I. In common terms, there are two types of multiple structures—the good and the bad. The good type is the one in which each of the physically separate units is properly grounded and has its own proper mechanism for transferring the loads to the ground. The bad type is caused by oversight, as, for example, floating members that are the result of duplicate nodes or members that haven’t been segmented at the point where their lines theoretically intersect. For the good type, wind load generation should typically take place without any complications. For the bad type, however, panel identification may fail because it depends on the program being able to establish the member as a valid side of a panel and that process depends on the member being connected between two nodes, which are also part of the remainder of the structure. It is necessary to rectify the modeling error in such cases.

2.1.7.2 Duplicate Members The wind load generator may fail to identify panels correctly if there are duplicate members. As described earlier, these are two or more members connected between the same two nodes. They can be detected and removed using Tools -> Check Duplicate -> Members.

2.1.7.3 Overlapping Members Use Tools -> Check Overlapping Collinear Members to identify and replace overlapping members with individual segments between nodes.

2.1.7.4 Intersecting Members In situations such as bracing where members cross each other, a node has to be defined at the

point where they cross. In Fig 2.1.21, by traversing the path along the member X axis, the program finds overlap of various panels. Loads are not generated in the right manner when panels overlap.

FIGURE 2.1.21 Crisscrossing members not joined at their intersection point

Fig 2.1.22 illustrates a case where the panel identification process fails because intersecting members are not segmented at the points where they cross each other. A long and pointed colored wedge will appear in place of the wind load contributory area.

FIGURE 2.1.22 Failure to identify panels correctly

Alternatively, some panels may not receive any load, as shown in Fig 2.1.23. To avoid this problem, there are two options: 1. Split the bracing members at their point of intersection. In the case presented in Fig 2.1.21, this will result in four distinct panels with no overlap. 2. Provide a list of members in the WIND LOAD command and exclude the bracing members from the list. For the structure in Fig 2.1.21, the list would comprise of just members 2, 3, 4, and 5. WIND LOAD Z 1 TYPE 1 LIST 2 3 4 5

For the first method, in the STAAD.Pro GUI, a node can be created where the members cross each other by: a. Selecting those members b. Going to the Geometry menu

c. Choosing Intersect selected members—Intersect.

FIGURE 2.1.23 Load generation failed due to improper panel identification

2.1.7.5 Round-off Errors in Joint Coordinates Round-off errors in the X/Y/Z coordinates of joints cause some of them to fall outside the plane formed by the rest of the portions of the panels. For example, in the following joint coordinates list, the X coordinate of several joints is entered as a very small number (e.g., 1.83691e-015) instead of 0. This may cause the external facade to be treated as nonplanar. 18 -1.83691e-015 0 15; 19 0 10 0; 20 -1.83691e-015 10 15; 21 0 19 0; 22 -1.83691e-015 19 15; 23 0 22 0; 24 -1.83691e-015 22 15; 25 -9.18455e-016 22 7.5; 26 -9.18455e-016 19 7.5; 27 10.5 19 0; 28 10.5 19 15; 229 42.5 28 15; 230 -7.34764e-016 28 6; 231 10.5 28 6; 232 18.5 28 6; 248 146.5 28 6; 249 -1.10215e-015 28 9; 250 10.5 28 9; 251 18.5 28 9;

This can be resolved by changing them to zero. 18 0.0 0 15; 19 0 10 0; 20 0.0 10 15; 21 0 19 0; 22 0.0 19 15; 23 0 22 0; 24 0.0 22 15; 25 0.0 22 7.5; 26 0.0 19 7.5; 27 10.5 19 0; 28 10.5 19 15; 229 42.5 28 15; 230 0.0 28 6; 231 10.5 28 6; 232 18.5 28 6; 248 146.5 28 6; 249 0.0 28 9; 250 10.5 28 9; 251 18.5 28 9;

2.1.7.6 Structures Declared as the PLANE Type When a structure is declared using the type STAAD PLANE (see Section 2.2 of Part I), and a load is applied along the global X direction, the exposed faces of the structures are lines in the global X-Y plane, not panels with closed boundaries. As a result, generating a load in the context of closed-type structures is not possible, and leads to a warning that loads cannot be generated. PLANE models are suitable only for open-type structure wind load generation.

FIGURE 2.1.24 Wind pressure along global X on a PLANE type of frame

Additional information on generating wind loads on plane frames is discussed further in Section 2.1.16.

2.1.7.7 Incomplete Panels These are panels that do not have a closed boundary, similar to that shown in Fig 2.1.25. For example, the user may have wanted to terminate the beam at the face of the column instead of at the column node. He/she may then have used the master–slave facility to link the beam end to the column node. An alternative to this method is connecting the beam end to the column node and specifying an offset for the beam end. This will ensure that no gap is formed, and the panel will be

identified as closed by the wind load generation facility.

FIGURE 2.1.25 A panel that is not a closed boundary

Related Question: What does the following warning indicate? **WARNING-fx fy fz wind forces: 0.0000E+00 0.0000E+00 -1.6585E-01 at coordinates: 7.4975E+00 8.6465E+00 0.0000E+00 ignored.

Answer: This is another manifestation of the problem discussed earlier. If the WIND LOAD GENERATION command is specified without a set of members or ranges and thus requires the program to scan through the entire structure to find an exposed face, it may run into what it perceives as intersecting members without a common node at the intersection point. In such instances, these messages are displayed. The warning messages indicate the approximate location of the points where such members cross each other. If the members are properly intersected and connected at such points, a load would have been generated and applied there. But since that has not been done, a warning stating that, a concentrated load that would have been generated and

applied at that point has been lost, is reported. To get rid of the warning, as in the aforementioned cases, provide the list of members, the member group name, or the coordinates of the exposed area through XRANGE, YRANGE, and ZRANGE in the wind load case. It is also a good practice to check whether there are multiple structures (Tools-Check Multiple Structures) or intersecting members that need to be connected (Geometry-Intersect Selected Members) and remedy those problems if any.

2.1.8 Excluding Members from Receiving Loads Related Question: How can I tell STAAD.Pro to exclude the bracing members when generating loads? Answer: The answer for this has been discussed in Section 2.1.7.4. For Closed-Type Structures. If a member is identified as part of a panel located on the exposed face, it will receive a load by default. If one wants to exclude it from receiving a load, the WIND LOAD command must be accompanied by a list, group name, or X/Y/ZRANGES in which this member has been omitted. To summarize, the steps are as follows: 1. Create a group containing all the members on the face of your structure except the cross-bracing members. START GROUP DEFINITION MEMBER _PANEL1 1873 TO 1896 _PANEL2 1976 TO 2009 _PANEL3 2128 TO 2171 END GROUP DEFINITION

For the procedure for creating a group, see Section 2.2 of Part I. 2. Go into the STAAD.Pro editor and locate the existing WIND LOAD command. It would look something like this: LOAD 16 LOADTYPE Wind TITLE E-W WIND LOAD (W E-W) WIND LOAD Z 1 TYPE 1

3. Modify the WIND LOAD command by adding the word MEMB followed by the group name: LOAD 16 LOADTYPE Wind TITLE E-W WIND LOAD (W E-W) WIND LOAD Z 1 TYPE 1 MEMB _GROUP NAME

Now, the wind load generator will load only the members in the group. For Open-Type Structures. There is no such provision. All members of the structures are loaded for the open type.

2.1.9 Out-of-Plane Nodes

The load generation algorithm requires all the nodes of the exposed face to form a single plane. Note that all the aforementioned conditions adversely affect the load generation for the closed type only. These conditions do not matter for the load generation for open structures.

2.1.10 Directions along Which the Wind Load Generation Can Be Performed In STAAD.Pro, wind load generation can be performed along the global horizontal directions only, that is X and Z axes, assuming Y is the vertical axis. STAAD.Pro doesn’t support wind load generation in the vertical (Y) direction.

2.1.10.1 Wind Blowing along Non-global Directions Related Question: I need to specify wind loads from various directions, which are at angles to the global X and Z directions. Can the wind load generator do that? Answer: The wind load generator is not designed to generate loads along any directions other than the global horizontal. So, if the wind pressure is acting at an angle, it has to be resolved along the global X and Z directions. If there is a component of that pressure along the global vertical (Y) direction, it has to be manually converted into concentrated loads at joints or distributed loads on members or pressure on plates and applied using the appropriate load type.

FIGURE 2.1.26 Plan view of wind acting at a skew to the horizontal plane

2.1.11 Time Taken to Display Wind Loads in the GUI Related Question: In the STAAD.Pro GUI, I want to see the loads generated for the wind load case. When I switch on the load display icon, the program takes a long time to display the loads. Answer: As stated earlier in this chapter, STAAD.Pro attempts to identify panels on the exposed faces of the structure. Unless the exposed region is defined through a member list or using XRANGES and ZRANGES, the software has to go through each and every location of the model sorting through the node and beam arrangement to determine the ones that are on the exterior and those in

the interior. On large models or those with complex geometries, this process may take a long time and it may appear that the software is not responding.

FIGURE 2.1.27 A closed-type large model

An efficient way of using the wind load generator is to narrow down this search process by specifying the X, Y, and ZRANGES. The search will then be limited to the members within that range only, thus making a significant difference to the time required for load generation. This approach can also be used on any part of the structure where the generation fails to produce satisfactory loads. An example of the change required is shown next. Replace the command WIND LOAD X 1 TYPE 1

with two or more subcommands, as shown next. A single wind load case can have multiple such subcommands. WIND LOAD X TYPE 1 XRANGE -1 30 YRANGE 19 31 ZRANGE -1 1 WIND LOAD X TYPE 1 XRANGE 29 59 ZRANGE -1 1

Alternatively, form a group consisting of only those members that should receive the load. That is,

these are the members that are part of the exposed face. START GROUP DEFINITION MEMBER _X_AT_WEST 1 TO 12 26 27 32 33 38 39 44 45 122 125 134 158 418 421 457 511 514 551 TO 553 590 TO 593 718 787 TO 789 _X_AT_EAST 13 TO 24 29 30 35 36 41 42 46 47 51 72 75 83 123 126 132 146 149 156 183 184 192 197 277 278 303 310 313 333 382 TO 384 400 419 422 462 512 515 569 TO 571 619 626 638 END GROUP DEFINITON LOAD 5 LOADTYPE WIND TITLE WL -X DIR WIND LOAD -X -1 TYPE 2 LIST _X_AT_WEST WIND LOAD X -1 TYPE 4 LIST _X_AT_EAST

2.1.12 Wind Load Generation for Structures Composed Entirely of Plate Elements Related Question: Can wind load be applied on a circular tank modeled using plate elements? Also, will STAAD.Pro make any reduction for the curved shape of the structure? Answer: When the structure is represented entirely with plate elements, the method of generating loads by converting the pressure into joint or member loads is no longer necessary. The wind pressure can directly be applied on the plate elements in the form of pressure loads. Section 1.5 has information on applying pressure loads on plates.

2.1.13 Fireproofing and Wind Loads Members of an open lattice structure may have fireproofing applied to their surfaces (exterior boundaries). However, the wind load generator currently does not consider the additional width that the fireproofing material contributes. Loads are generated based only on the dimensions of the steel, concrete, or timber sections.

2.1.14 Wind Load Magnification Due to the Presence of External Equipment Related Question: I am analyzing a communication tower structure on which there are appurtenances that obstruct the passage of wind. Is there a way to have the program calculate the additional load due to wind acting on those components? Answer: There is no direct way to consider the additional obstruction that occurs due to the presence of appurtenances. However, an approximate way is to specify an exposure factor greater than 1.0 for those nodes located in the vicinity of the appurtenances. Alternatively, the user would have to calculate it manually and apply it as a joint load.

2.1.15 Wind Pressure Profile Calculation per Building Codes Related Question: When I go to the Wind Load Definition page, I can see only the Russian code. How can I select any other code such as the IS-875 (Indian) code? Answer: As mentioned in Section 2.1.1, one of the items of input is the wind pressure profile. It is a table of data consisting of the wind pressure versus height. The field titled INTENSITY brings up a box in which these pairs can be entered as shown in Fig 2.1.28.

FIGURE 2.1.28 Pressure profile table—generation using the tools of the GUI

The program also has a facility for generation of this data as per the following codes. ASCE-7. At the bottom of Fig 2.1.28, there is a button titled “Calculate as per ASCE-7.” This allows for generation of this data as per two codes—ASCE 7-95 and ASCE 7-02. A sample screen containing the input for these codes is shown in Fig 2.1.29.

FIGURE 2.1.29 Wind pressure profile calculation per ASCE 7

Russian. For calculation of the pressures per the Russian code, click inside the box titled “Select Type” as shown in Fig 2.1.30.

FIGURE 2.1.30 Wind pressure profile calculation per Russian code

The description of the parameters for both these types is available in Section 2.3.7.12.1.3 of the STAAD.Pro Graphical Environment manual. If the code that the user wants is something other than the two mentioned previously, he/she will have to manually calculate the pressure at various heights and enter them in the Intensity versus Height box shown in Fig 2.1.31.

FIGURE 2.1.31 Code-based pressure profile calculation

2.1.16 Wind Load Generation on Plane Frames In the STAAD.Pro terminology, a structure declared using the type PLANE (see Section 2.2 of Part I) is assumed as spanning in the global X-Y plane and deforms entirely in that plane only. There is no scope for out-of-plane deformation (along the global Z). Consequently, a load cannot have any component along global Z. Thus, wind load generation on a PLANE frame can be along global X only (STAAD.Pro does not have wind load generation along global Y). Further, because the structure is planar, there is no panel spanning the global Y-Z plane to block the wind. This rules out load generation applicable to closed structures. Hence, the only type of wind load generation that can be performed on plane structures is the OPEN structure, with wind blowing along positive or negative global X resulting in a uniform load along the length of all members of the model perpendicular to or at an inclination to the global X axis (see Fig 2.1.32).

FIGURE 2.1.32 Wind load generation on a plane frame

2.1.17 Wind Load Generation for Structures with Complex External Facades To conclude, the STAAD.Pro algorithm for automatic computation of loads due to wind works best for regular structures that conform as close as possible to the straight-edged rectangularshaped ones in plan and elevation. If an inspection of the generated joint and member loads reveals that the load values are not satisfactory, the alternatives are (a) compute the loads yourself and apply them as joint and member loads and (b) add dummy plate elements on those regions of the model, and apply the load on them using the plate element pressure facility. Dummy plate elements are those with a very small value for thickness, E (modulus of elasticity), and density. That way, their contribution to the stiffness and weight of the structure will be minimal.

2.1.18 Applying Wind Load on Surface Entities Since a surface is treated by STAAD.Pro as an object representing a collection of plate elements, wind bearing upon a surface can be represented using the surface pressure load. The concept of generating loads based on panels circumscribing members as described in this chapter is not applicable to surfaces. The magnitude and direction of the pressure needs to be first determined by the user and applied directly using the Surface Pressure Load option described in Section 1.5.

2.2 Snow Loads 2.2.1 Introduction Snow load generation is a process that involves conversion of the weight of snow on flat or sloping roofs into member loads in the mathematical model. Currently, the principles for calculating the snow load intensity are implemented in STAAD.Pro in accordance with Section 7.0 of ASCE 702. Loads on the individual members are calculated using the same methods as in FLOOR LOAD

generation (see Section 1.2). Hence, the roofs must comprise closed panels that are bounded by members on all sides. Required reading 4. Technical Reference manual—Sections 1.17.4, 5.31.5, and 5.32.13 5. Graphical Interface Help manual—Section 2.3.7.8

2.2.2 Discussion The input for snow load generation is specified in two steps: Step 1. A definition block in which we provide the code-related parameters that enable the calculation of the flat roof snow load intensity. Step 2. Create a load case containing Snow Load as a load item. Certain additional parameters too are specified in this step. These serve as the instruction to the program to take the data provided in these two steps, and calculate the sloped roof snow load intensity. This intensity is then used to derive the individual member loads using the principles of floor loading.

2.2.2.1 The Data Associated with Step 1 Here, we specify the data that STAAD.Pro uses to calculate p f, which is the snow load on a roof with a slope equal to or less than 5 degrees. This calculation is as per Equation 7-1 in Section 7.3 of ASCE 7-02, which is reproduced next. Pf = 0.7 • Ce • Ct • I •Pg where p f – snow load intensity for a flat surface (units of pressure). p g – ground snow load. Values of p g can be obtained from Figure 7-1 and Table 7-1 of ASCE 7-02. It has units of pressure (lb/ft2 or kN/m2). C e – exposure factor that accounts for the exposure condition of the roof. A roof that is guarded or sheltered is likely to receive more snow load than a completely exposed roof. The factor is obtained from Table 7-2 of ASCE 7-02. C t – thermal factor that accounts for the thermal condition of the roof. Heated roofs have lower values of thermal factor than unheated roofs that can freeze. Appropriate value for thermal factors can be obtained from Table 7-3 of ASCE 7-02. I – importance factor that can be obtained from Table 7-4 of ASCE 7-02. In the STAAD.Pro GUI, these data can be input from General -> Load & Definition -> Definitions -> Snow Definition as shown in Fig 2.2.1.

FIGURE 2.2.1 Dialog box in the STAAD.Pro GUI for creating the Snow Load definition

Since there can be more than one type of snow load defined in the model, each type is identified using a Type number. Once these data are specified, the commands in the STAAD.Pro input file would look like this. Example 4 DEFINE SNOW LOAD TYPE 1 PG 15 CE 1.0 CT 1.2 I 1.1 TYPE 2 PG 40 CE 0.9 CT 1.1 I 1.2

2.2.2.2 The Data Associated with Step 2 In this step, a load case is created with Snow Load as a load item. Certain parameters have to be specified at this stage too, and they are explained later in this section. Using these parameters, and the data from Step 1, the program calculates the sloped roof snow load intensity ps. It is at this stage that the program needs to know on which members the load should be applied. This information is conveyed to the program through a floor group. This term is same as the one mentioned in Section 1.2 for applying a floor load. The roof members that should receive the load should be part of a FLOOR GROUP. After p s is calculated, the loads on the individual members of the floor group are calculated. In the STAAD.Pro GUI, these data are provided through a new load case as shown in Fig 2.2.2.

FIGURE 2.2.2 Dialog box in the STAAD.Pro GUI for creating a Snow Load item

Certain other parameters too are specified in the dialog box shown in Fig 2.2.2, which is highlighted in Fig 2.2.3.

FIGURE 2.2.3 Terms in the dialog box for creating a load case containing the snow load item

Before a load case containing Snow Load as a load item is created, the FLOOR GROUP has to be created. The name of that group will then appear in the dialog box as shown in Fig 2.2.3. The parameters that are specified in Step 1 are associated with a Type number. Because more than one type can be created for one model, the appropriate one has to be chosen from the list that drops down when we click Defined Snow Type.

There are two possible conditions for snow loads—balanced and unbalanced. Depending on the Roof Type (mono, hip, or gable—as explained in Figures 6-3 and 6-6 of ASCE 7-02), ASCE provides guidelines to calculate the balanced and unbalanced loading. Details on these are available in Section 7.6 of ASCE 7-02. The default value for Roof Type is MONO, as explained in Section 5.32.13 of the STAAD.Pro Technical Reference manual. Roof Obstruction is a term that can take one of two values—obstructed and unobstructed. It is one of the terms that the value of C s is dependent on, as explained in Section 7.4 of ASCE 7-02. Its default value is unobstructed. The Roof Slope Factor C s is defined in Section 7.4 (Figures 7-2a, 7-2b, and 7-2c) of ASCE 702. In Fig 2.2.3, it is an optional item, meaning, it does not have to be specified. If it is not specified, or if it is assigned a value of 0.0, STAAD.Pro calculates it and reports its value in the output file. The sloped roof snow load intensity p s is calculated by the program using Equation 7-2 of ASCE 7-02. ps = Cs • pf Once the aforementioned data are specified, the commands in the STAAD.Pro input file would look like this. Example 5 LOAD 8 LOADTYPE Snow TITLE SNOW LOAD SNOW LOAD _WESTSIDE BALANCED TYPE 1 CS 1 _EASTSIDE BALANCED TYPE 1 CS 1

Example 6 LOAD 3 LOADTYPE Snow TITLE SNOW SNOW LOAD _ROOF BALANCED TYPE 1 GABLE UNOBSTRUCTED CS 0.8

Example 7 LOAD 8 SNOW LOAD SNOW LOAD _RIGHTSLOPE UNBALANCED TYPE 1 HIPPED UNOBSTRUCTED CS 1

FIGURE 2.2.4 Structure with a multi-sloped (hipped) roof

2.2.3 Excluded Portions of the ASCE 7-02 Code Some of the requirements of Section 7 of ASCE 7-02 in connection with snow loading are currently not implemented in the program’s snow load generation facility. They are: Sliding snow—Section 7.9 of ASCE 7-02 Rain-on-snow surcharge load—Section 7.10 of ASCE 7-02 Drift—Section 7.7 of ASCE 7-02 Some of them such as Rain-on-snow surcharge load can be considered by applying additional floor loads or one way loads on the floor groups. Example 8 UNIT POUND FEET LOAD 5 LOADTYPE Snow TITLE SNOW SNOW LOAD _ROOF_1 BALANCED TYPE 1 HIPPED CS 1 * RAIN ON SNOW FLOOR LOAD _ROOF_1 FLOAD -25 GY INCLINED

2.2.4 Output Produced by STAAD.Pro for Snow Load Generation In the STAAD.Pro output file, information similar to that shown in Fig 2.2.5 will be displayed.

FIGURE 2.2.5 Information reported in the STAAD.Pro output file for snow load generation

2.2.5 Two-way Distribution versus One-way Distribution Snow load is generated as a two-way-type loading. The one-way-type distribution is not available at present. If you would like to have this generated as a one-way-type loading, you will have to manually calculate the term p s (equal to C s * p f) described earlier and apply it using the Oneway Load option on the roof panels. Related Question: I noticed the following message in the output file. *WARNING- NO MEMBERS LOADED FOR A SNOW LOAD GENERATION.

FIGURE 2.2.6 Warning reported in the STAAD.Pro output file when snow load generation fails

Answer: It means that snow load generation has failed for the model. The causes are generally similar to those for floor load generation. This is because the procedure for generating the individual member loads from a pressure acting on the panels is the same for both methods. So, the roof has to have panels. Single bay frames such as a football goal post or a gable frame modeled as STAAD PLANE are not the right candidates for this feature. If the loaded area has panels, try applying a floor load on the same region and see if that works. If the roof is inclined, the test should be based on an INCLINED floor load. On such roofs, the

nodes defining the panels should form a single plane. For structures where the roof has two slopes, use multiple floor groups. Section 1.2 has detailed information on these aspects.

FIGURE 2.2.7 Frame with two sloping roof panels

If floor load can be made to work for those panels, chances are the snow loads will work as well.

2.2.6 Generation of Snow Load on Individual Members of an Open-Lattice Structure Open-lattice structures are those with open frames such as electrical transmission towers. Due to the nature of their geometry and location, all their parts are exposed to the sun, wind, and ice. For such structures, accumulation of ice takes place on the basis of the individual widths of their component members and not on the basis of covered panels found in roofs of buildings. As mentioned in Section 1.17.4 of the STAAD.Pro Technical Reference manual, STAAD.Pro’s snow load generation facility cannot be used for such structures at present. A way around this limitation may be to use the fireproofing feature described in Section 5.6 of Part I. Related Question: The roof system consists of a slab that is supported on beams spanning between columns. The slab is modeled using plate elements. Can I use the snow load generator to apply the load? Answer: As we have seen in earlier discussions, snow load generation is based on the same principles as floor load generation and that requires closed panels bounded by beams. If your roof system satisfies this condition, it is OK to use snow load generation for your model.

However, since the slab is included in the model as plate elements, it makes more sense to apply the snow load as a pressure load on the plate elements. This is a more logical approach because the entities in the model that directly receive the snow load are the elements. If you decide to do this, you will have to manually calculate the term p s (equal to C s * p f) described earlier and apply that as the pressure load on the elements.

2.3 Moving Loads 2.3.1 Introduction In this section, the procedure for generating loads on members due to a vehicle or a crane moving on structures is discussed. This feature is termed as the moving load generator. Some of the common applications of the moving load generator are: Vehicle(s) on a bridge deck Crane load(s) on a girder in a factory building

FIGURE 2.3.1 STAAD.Pro model of a truss bridge

FIGURE 2.3.2 A gantry girder (Aswathanarayana & Eswara, Chennai, India)

In this facility, a vehicle (represented by a train of concentrated loads) is moved along a structure. The movement is controlled using three parameters:

1. It is along a user-specified direction. 2. The distance of each such movement, called the increment, is specified by the user. 3. The number of times the vehicle has to be moved by that increment is also user specified. Hence, with each increment of movement (Item 2), the vehicle arrives at a different position on the structure. For that position, the concentrated wheel loads are transferred to the structure as concentrated member loads, and those loads form a load case. So, if the number of times the movement occurs (Item 3) is n, n + 1 load cases are generated, where the first of these cases represents the loads brought on by the starting position of the vehicle. Required reading 6. Technical Reference manual—Sections 1.17.1, 5.31.1, and 5.32.12.1 7. Application Examples manual—Example 12 8. Graphical Interface Help manual—Sections 2.3.7.12.1.1 and 2.3.7.12.3

2.3.2 Discussion Moving load generation is the process of setting the vehicle at a number of positions on the bridge along the direction of movement of the vehicle. When STAAD.Pro sets the vehicle at any specific position, it scans to the left and right of the load to see whether the axis of any existing member crosses the line of the load. In other words, if an imaginary beam, perpendicular to the direction of movement, is laid beneath a wheel, does that imaginary beam cross the axis of members on either side of the wheel? If the answer is yes, the load goes on to those members through simply supported action. This facility can generate loads on frame members only. Loads are not generated on plate or solid elements. So, if the paths along which the wheels move have plates only and no members, as in the case of a deck slab with no beams, then modeling some fictitious members (line entities) along the path is required, and this procedure is described in Section 2.3.22. In STAAD.Pro, a moving load can be made to travel only along a straight line. That line can be parallel to the global X or Z axis and also at a skew to those directions. The vehicle cannot be made to follow a curved path.

2.3.3 Data required by STAAD.Pro To analyze a structure for a moving load, the required data consist of two parts: (a) definition of vehicle and (b) placement of the vehicle on the deck and generation of the load cases.

2.3.4 Definition of the Vehicle The data for vehicle definition consist of: The load transmitted through each wheel of an axle. An axle can have either one wheel or two wheels, and this depends upon the “width” term described later. The spacing between the axles. The number of spacings will be one less than the number of axles. The width of an axle, that is, the distance between the two wheels of an axle. If there is only one wheel, the width is either not specified or specified as zero. These data must be provided before any load case is specified. In the STAAD.Pro editor, the data are initiated with the following command:

DEFINE MOVING LOAD

2.3.4.1 Description of the Vehicle The command syntax for describing the vehicle in the STAAD.Pro input file is explained in Section 5.31.1 of the Technical Reference manual. In Fig 2.3.3, the position of the wheels is indicated by the black dots at the intersection of the lines. Each axle is idealized as either (a) a one-wheeled axle similar to that of a crane moving on a girder in a factory or (b) a two-wheeled axle—one on either side (driver or passenger) of the truck. In the case of heavy-duty trucks, which have a set of two or more wheels on the driver side, and another set on the passenger side, each set is idealized to one wheel. The distinction between these is achieved through the WIDTH parameter explained later. The program can handle at the most two wheels per this idealized axle. One wheel per axle is denoted using the terms f1, f2, f3, and f4 in Fig 2.3.3, and this terminology is also used in Section 5.31.1 of the Technical Reference manual. For one-wheeled axles, these terms indicate the only wheel of the axles.

FIGURE 2.3.3 Representation of a 5-axle vehicle

Note that the wheel weights for the vehicle are specified from back to front. Hence, a truck similar to the one shown in Fig 2.3.4 will be described as follows:

FIGURE 2.3.4 Vehicle configuration and axle loads

FIGURE 2.3.5 Vehicle configuration—isometric view UNIT KIPS FEET DEFINE MOVING LOAD TYPE 1 LOAD 4.25 3.75 3.25 2.75 2.25 1.75 1.25 DIST 4.5 3.0 2.5 2.0 4.0 3.5 WIDTH 5.0

The numbers following the DIST keyword are the spacing between the axles. They are not the distance of each axle from the rear axle or the front axle. 2.3.4.1.1 The WIDTH Parameter Related Question:

For specifying the loads associated with a truck, does STAAD.Pro require the axle weights or the individual wheel weights? I provided the axle weights to the user interface and I got results that were twice the amount they should be. Does this mean that STAAD.Pro asks for the weights of each wheel or point load? Answer: The information to be specified in the STAAD.Pro input is the load going through each wheel of an axle. If the axle has only one wheel, the wheel load and axle load are the same. If an axle has two wheels, the axle load is considered to be twice the wheel load. How does the program understand that an axle has only one wheel instead of two wheels? It is through the value assigned to the WIDTH parameter. If WIDTH is zero, or not specified, it means the axle has only one wheel. If WIDTH is greater than zero, the axle has two wheels separated by that WIDTH. Thus, if WIDTH is nonzero, all axles automatically become equipped with two wheels.

FIGURE 2.3.6 WIDTH between the tires of an axle

FIGURE 2.3.7 A typical vehicle

FIGURE 2.3.8 Dialog box in the GUI for describing the vehicle

2.3.4.1.2 Standard Vehicular Loading from Specifications Documents Currently, four standard vehicular loadings found in the AASHTO code — H15, H20, HS15, and HS20 — are available in (a feature that is incorporated) STAAD.Pro. Note that it is only the vehicle configuration (spacing between axles, width between the tires of an axle, and axle loads) that is supplied with the program. The code requirements for the spacing between the vehicles, the number of lanes that must be loaded simultaneously, the uniformly distributed loads that must accompany these vehicles, and so on, are not implemented, and hence, the burden of adhering to these rules rests upon the analyst. Some of those, but not all, can be done to some extent by providing appropriate values for (a) the number of types of vehicles to be considered in a load generation case, (b) the increment of movement, and (c) the starting position. The only difference between these vehicles and the ones we have seen earlier is that, in this case, the analyst simply chooses one of the four vehicle names mentioned earlier. The program automatically fetches the vehicle configuration from its database (see Fig 2.3.9).

FIGURE 2.3.9 Page from the STAAD.Pro Technical Reference manual for AASHTO loads DEFINE MOVING LOAD TYPE 1 LOAD 21 21 17 17 DIST 6 12 6 WID 8 TYPE 2 LOAD 32 32 24 DIST 7 10 WID 9 TYPE 3 HS15 1 1

In this example, Types 1 and 2 are user defined, while Type 3 is the AASHTO HS15 truck. Fig 2.3.10 shows the means for assigning the load using the STAAD.Pro Graphical User Interface (GUI).

FIGURE 2.3.10 Dialog bog in the STAAD.Pro GUI for defining the vehicle

2.3.5 Placement of the Vehicle on the Deck and Generation of the Load Cases This is the second stage of data requirement for the moving load generation. The information needed here is: The type number of the vehicle to be moved. This comes from the load definition. In the aforementioned examples, one type has been declared in the first example, and two types in the second. The coordinates of the starting position of the reference wheel of the vehicle. The reference wheel is preset as one of the wheels on the rear axle of the vehicle. The figure shown in Section 5.31.1 of the Technical Reference manual where the reference wheel is annotated is shown in Fig 2.3.11.

FIGURE 2.3.11 Location of reference wheel for vehicles moving in positive direction of global axes

The direction in which the load is moving and the distance traversed by a single movement (called INCREMENT). The number of load cases to be generated to traverse the length of the deck on which the load is moving. Any other load case that is to be added with each of the generated moving load cases. Thus, to ensure that all possible load positions ranging from the front axle entering the bridge to the rear axle leaving the bridge are taken into consideration, it is important to provide the appropriate values for all these terms.

FIGURE 2.3.12 Vehicle positions to consider

2.3.6 Vehicles Moving in Negative Global Directions A negative value of the X and Z increments instructs STAAD.Pro to move the vehicles along the negative directions of the corresponding global axis. As stated previously, the starting position of the reference wheel is crucial to the successful generation of loads. In Fig 2.3.13, the reference wheel is identified.

FIGURE 2.3.13 Location of reference wheel for vehicles moving in negative direction of global axes

2.3.7 Syntax of the Commands in the STAAD.Pro Input File for Stage 2 Input Example 9 LOAD GENERATION 15 TYPE 1 7.5 0. 0. ZI 10.

FIGURE 2.3.14 Description of the second stage of input for moving load generation

The first line in this example means that 15 load cases are to be generated. The second line means that the Type 1 load is to be moved in the Z direction (ZI stands for Z increment) by 10 units of length at a time. The vehicle starts from an initial position of X = 7.5, Y = 0, and Z = 0. These coordinates refer to the starting position of the reference wheel of the vehicle. The INCREMENT may need to be small to capture the position that provides the maximum value of any specific result such as shear or moment in the span. However, a smaller increment can

also mean that the number of cases generated needs to be larger, leading to an increase in the size of the model. Figures 2.3.15 and 2.3.16 show the procedure for assigning the data using the STAAD.Pro GUI for the second stage of the input.

FIGURE 2.3.15 Dialog boxes in the GUI for generating loads due to a moving vehicle

FIGURE 2.3.16 Dialog box for specifying parameters of movement of vehicle

After the aforementioned information is provided, the starting position, vehicle configuration, and direction of movement are represented using red dots and lines in the GUI. In Fig 2.3.17, the reference load is the wheel at the northwest corner of the wheel layout.

FIGURE 2.3.17 Graphical representation of the starting position of a vehicle

2.3.8 Method for Breaking up a Trailer into Two or More Vehicles Sometimes, conditions may require that a chain of axles be broken down into two or more vehicles (TYPEs in the STAAD.Pro moving load terminology) instead of modeling it as one type. Let us consider the vehicle shown in Figures 2.3.4 and 2.3.5. Suppose that the WIDTH between the wheels of axles 1, 2 and 3 is 7 ft, but for axles 4-7, it is 5 ft. This is what we could do: UNIT KIPS FEET DEFINE MOVING LOAD TYPE 1 LOAD 4.25 3.75 3.25 DIST 4.5 3.0 WIDTH 7.0 TYPE 2 LOAD 2.75 2.25 1.75 1.25 DIST 2.0 4.0 3.5 WIDTH 5.0

2.3.9 Transferring the Wheel Loads to the Members of the Structure Related Question: How does STAAD.Pro distribute a wheel load onto beams if the wheel is not directly standing on a beam? Answer: If a wheel falls inside a panel composed of beams on either side of the wheel running parallel to the direction of the movement of the vehicle, the load is distributed on the two beams as simply supported reactions. In Fig 2.3.18, assume that the wheel is at the point P. If the load going through that wheel is W, it will be distributed between points Q and R in the following proportion: Load at Q = Wb/(a + b) Load at R = Wa/(a + b)

FIGURE 2.3.18 Distribution of wheel loads on the adjacent members

Hence, if the wheel load is 10 kips, and if the distance from the wheel to the beam on the left is 7 ft, and the distance to the beam on the right is 3 ft, the beam on the left gets a 3-kip load, and the beam on the right gets a 7-kip load.

2.3.10 Sign of the Wheel Loads—Positive versus Negative Positive values of the wheel loads indicate that the weight from the wheel acts in the negative global Y direction (downward). Negative values can be specified if the load is intended to act upward. This feature (the facility for specifying upward acting wheel loads) was not available in older versions.

2.3.11 Moving Loads on Structures Whose Type Is STAAD PLANE Structures that are in a single plane, such as a simple or continuous beam, are often created using the type STAAD PLANE. The general principles for generating loads on PLANE structures are the same as those for SPACE frames. Note that if the WIDTH parameter is specified for a PLANE structure, only one of the wheels of each axle is positioned to be on the beam, and the other wheel will automatically be outside the structure and hence ignored.

2.3.12 Loads Consisting of Just a Single Axle In current and recent versions of STAAD.Pro, a vehicle with a single axle can be specified by providing the value for DIST as zero. Type 2 in the following example illustrates this. DEFINE MOVING LOAD TYPE 1 LOAD 8 32 32 DIST 14 14 TYPE 2 LOAD 18 DIST 0

Older versions of STAAD.Pro require a minimum of two axles per vehicle. In such cases, create a second axle whose magnitude is very small, say, 1 lb (0.001 kip), placed at a small distance, for example, 6.0 in away from the first axle.

UNIT KIPS INCHES DEFINE MOVING LOAD TYPE 1 LOAD 18 0.001 DIS 6

The following is an example of a single-axle single-wheel load moving on a 30-m-span beam. STAAD PLANE UNIT METER KN JOINT COORDINATES 1 0 0 0; 2 30 0 0; MEMBER INCIDENCES 1 1 2; DEFINE MATERIAL START ISOTROPIC STEEL E 2.05e+008 POISSON 0.3 DENSITY 76.8195 ALPHA 1.2e-005 DAMP 0.03 TYPE STEEL STRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2 END DEFINE MATERIAL MEMBER PROPERTY AMERICAN 1 TABLE ST B451610 CONSTANTS MATERIAL STEEL ALL SUPPORTS 1 PINNED 2 FIXED BUT MY MZ DEFINE MOVING LOAD TYPE 1 LOAD 30 DIST 0 LOAD 1 SELF Y -1 LOAD GENERATION 31 TYPE 1 0 0 0 XINC 1 PERF ANALY PRINT LOAD DATA FINISH

2.3.13 Defining the Moving Load Description through an External File If the vehicle definition is a standard one that will be reused over several models, it may be convenient to (a) specify the data in an external file and (b) refer to that file (by specifying its name) instead of providing the vehicle definition within the STAAD.Pro input file. The syntax for the definition is provided in Section 5.31.1 of the STAAD.Pro Technical Reference manual. The following is an example of three vehicles described within an external file named “Liveload.txt.” 70RW 4 6 6 8.5 8.5 8.5 8.5 3.96 1.52 2.13 1.37 3.05 1.37

1.93 70RT 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 0.457 0.457 0.457 0.457 0.457 0.457 0.457 0.457 0.457 2.06 CLA 1.35 1.35 5.7 5.7 3.4 3.4 3.4 3.4 1.1 3.2 1.2 4.3 3 3 3 1.8

Within the STAAD.Pro input file, the command will look like this. DEFINE MOVING LOAD FILE LIVELOAD.TXT TYPE 1 70RT 1.15 LOAD GENERATION 20 TYPE 1 0.9 0 0 ZINC 1.0

2.3.14 Viewing the Values (Magnitude) of the Generated Loads To see the generated moving load in the output file, we need to specify the words PRINT LOAD DATA with the PERFORM ANALYSIS command. During the analysis, the generated loads will be written in the output file.

FIGURE 2.3.19 Report of the generated loads in the STAAD.Pro output file

2.3.15 Displaying (Viewing) the Generated Loads in the GUI Related Question:

Can I see the loads moving along the bridge? Answer: Although an animated view of the loads actually moving along the bridge is difficult to obtain, it is possible to see the progression of the vehicle by viewing the loads in succession. Before we can display the generated loads in the GUI, the analysis has to be successfully completed. If we attempt to view the loads before the analysis, the following message will appear (see Fig 2.3.20).

FIGURE 2.3.20 Displaying the generated loads before the analysis

Once the analysis is completed, we have to switch on the load display icon (see Fig 2.3.21).

FIGURE 2.3.21 Load display icon in the GUI

FIGURE 2.3.22 Selecting the generated moving loads in the GUI

Then, select the desired generated case from the Select Load drop-down box. For example, if the sequence of load data is LOAD 1 .. LOAD 2 .. LOAD 3 .. LOAD GENERATION 30

then, after the analysis, the load selection box will list them as LOAD 1 LOAD 2 LOAD 3 LOAD GENERATION, LOAD # 4 LOAD GENERATION, LOAD # 5 LOAD GENERATION, LOAD # 6 …

To see the loads “marching down” the bridge, keep the mouse cursor inside the load selection box and select the load cases one at a time in sequence.

FIGURE 2.3.23 Viewing the generated loads moving along the structure

2.3.16 Lane Loads Codes such as AASHTO ASD and AASHTO LRFD have a distributed load component to the vehicular loading definitions. This is called lane loading. However, STAAD.Pro does not have any provision to handle lane loading. Hence, it is only the individual wheel loads that can be moved along the span. Lane loads have to be specified through a separate load case, and that load case has to be combined with the appropriate generated moving load cases. LOAD 3 LANE LOAD 1 TO 45 UNI GY -3.0 LOAD GENERATION 30 TYPE 1 7.5 0. 0. ZI 10. LOAD COMBINATION 34 3 1.0 4 1.0

LOAD COMBINATION 35 3 1.0 5 1.0 LOAD COMBINATION 36 3 1.0 6 1.0

If the same lane load is to be combined with all the generated cases, it can be done using the ADD LOAD command that is explained later in this chapter in Section 2.3.23.

2.3.17 Member Specifications Since moving loads are generated at the intermediate span points of members, members on which the loads will be generated should have bending and shear capacity to carry those loads. So, the MEMBER TRUSS specification, which by definition deprives a member of its bending capacity, should not be used for such members. However, it is OK to use MEMBER RELEASES. If the releases become a cause of instability, use a high percentage partial moment release instead.

2.3.18 Moving a Vehicle on a Sloping Roadway or Ramp Related Question: Is it possible to use the moving load generator if the surface is not level? The elevation ( Y coordinate) at the start of the bridge is different from the elevation at the end of the bridge. Can I generate a load for a vehicle moving on this sloping bridge? Answer: Moving load can be generated on a sloping roadway or inclined planes (ramps) by specifying the YRANGE option. This option tells the program to look for members whose ends lie between the Y coordinates (A, A+YRANGE) where A is the Y coordinate of the wheel.

FIGURE 2.3.24 Page from the STAAD.Pro Technical Reference manual for loads on a sloping bridge

Example 10

UNIT METER LOAD GENERATION 30 TYPE 1 914 0 XINC 0.5 YRANGE 3.5

In Example 10, the bridge is assumed to have a rise of 3.5 m between start and end.

2.3.19 Moving a Vehicle in a Skewed Direction Related Question: Can I move the load in two directions at the same time? Answer: Moving the load in two directions would be sensible only if the objective is to move the vehicle at a skew to one of the global directions as shown in Fig 2.3.25. It is possible to do that, and the procedure requires the increments in both the horizontal directions to be specified simultaneously in a single load generation instruction. LOAD GENERATION 25 TYPE 1 18.2 0.4.5 XINC 1.7321 ZINC 1.0.

The initial position of the reference wheel of the vehicle is (18.2, 0, 4.5). Twenty-five load cases are generated, each obtained by moving the vehicle by an X increment of 1.7321 ft and a Z increment of 1.0 ft at a time.

FIGURE 2.3.25 A skewed bridge

2.3.20 Multiple Lanes of Vehicles

Related Question: Is it possible to generate loads due to two vehicles moving on the structure simultaneously? Answer: Yes, it is possible to define more than one moving load on the structure. These could be defined in any order. In the next example, Two types of vehicles are defined They are simultaneously run along the bridge side by side UNIT METER KNS DEFINE MOVING LOAD TYPE 1 LOAD 20 20 10 DIST 7 4 WID 4 TYPE 2 LOAD 18 18 DIST 7 WID 3 LOAD GENERATION 27 TYPE 1 0.5 0. -11 ZI 3.0 TYPE 2 6.5 0. -7 ZI 3.0 PERFORM ANALYSIS PRINT LOAD DATA

FIGURE 2.3.26 Two vehicles simultaneously moving on a bridge

2.3.21 Moving a Vehicle along a Curved Roadway The moving load generator that is available within STAAD.Pro can only handle a vehicle or chain of axles that moves along a straight line, usually one which is parallel to the global X or global Z directions. Using parameters such as XINC, YINC, and ZINC, it is possible to move the loads along a line inclined to one of the three global directions also. But, simulating the motion along the profile of a curved roadway is very tedious.

Bentley offers a portfolio of software specifically for bridge analysis and design that overcomes many of the limitations of STAAD.Pro’s moving load generator. These are discussed in Section 2.3.27.

2.3.22 Generating Moving Loads on Plate and Solid Elements Related Question: My model is a single-cell reinforced concrete box culvert modeled using plate elements. How can I generate the AASHTO HS20-44 wheel loads on this structure?

FIGURE 2.3.27 Vehicular traffic on a roadway over a box culvert

Answer: The moving load generator implemented within the STAAD.Pro engine can generate moving loads on frame members only. Loads are not generated on plate elements or solid elements; instead, the program searches only for beam members in the vicinity of wheel locations. The load is then transferred to those members as simply supported end reactions, and these reactions then become the member loads that the structure is analyzed for. In other words, the weight from the wheels is not converted into a pressure load or a concentrated load on plates or solids. If the path traversed by the vehicle is modeled with plate elements and/or solid elements and does not have any beam members in the vicinity of line of movement of the vehicles, here is a way to trick the program into generating loads. Add a number of fictitious members in the model along the direction of movement of the vehicle. Without creating any new nodes, simply add the members to the existing nodes that belong to the plate or solid elements. Remember that for proper connectivity, you need to ensure that the beam members must run along the plate and solid element boundaries and be attached

to the same nodes that those plate/solid elements are connected to. These members must be located as close as possible to the line of movement of the wheels. Assign them a small property, very small E (say 1/1000th that of steel) and zero density so that they do not contribute to any structural stiffness or gravity load. The moving loads may then be applied in the same manner as they are applied on beam member models. STAAD.Pro will convert the vehicle wheel weights to concentrated loads on those members, and the members would then pass them on to the plate or solid element nodes to which those beams are connected. Thus, by ensuring that these fictitious weak members are connected to elements, the load will be entirely borne by the elements. The members will merely act as mechanisms for transferring the load on to the plates.

FIGURE 2.3.28 Fictitious members provided along traffic lanes on a finite element model of a deck slab

Also, recall that there are two ways to model a structure using plate elements— (a) using a plate element mesh and (b) using surface entities. The box culvert model mentioned in the question must be modeled using plate elements, not surface entities. This is to allow for proper connectivity between the fictitious beams and the top of the culvert. Related Question: There are several warnings of the following kind in the output file. **WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES OF THE STRUCTURE HAS BEEN IGNORED. CASE= 2 WHEEL 1 OF 6

FIGURE 2.3.29 Warnings in the STAAD.Pro output file for wheels lying outside the structure

Answer: The general meaning of this warning is that some of the axles of the vehicle lie outside the bounds of the structure. During moving load generation, for each wheel, STAAD.Pro attempts to determine whether the wheel is located directly on a member, or whether it is located within the bounds of a panel formed by members on all sides. If neither of these conditions is satisfied, it indicates that the wheel is outside the bridge. A warning message is generated specific to that wheel. Some of the reasons why one or more wheels may fall outside the bounds of the model are the following: 1. In the LOAD GENERATION command, if the reference wheel position is defined in such a manner that the first wheel is before the bridge or just entering the bridge, the rear wheels will be located on the approach to the bridge, which means outside its span. 2. If the number of load cases being generated and the increment of movement of the vehicle are such that the first or subsequent wheels have crossed the bridge and have proceeded beyond it, those wheels are now outside its span. In other words, if N cases are generated, the total distance covered by all the axles for those N cases may have exceeded the bridge length. 3. In the direction transverse to the vehicle movement also, the relative position of the vehicle and the members of the bridge must be checked to ensure that the wheels are not just “hanging” in space. We will look at the cause using Example problem 12 (examp12.std) located in the folder D:\SProV8i\STAAD\Examp\UK. To help us understand it better, we first have to make a minor change to the data. Open the STAAD.Pro model. Go into the editor. Locate the following lines: LOAD GENERATION 10 TYPE 1 2.25 0. 0. ZI 3.0

Change 10 to 17 and (2.25, 0, 0) to (2.25, 0, −4.5) as shown next. LOAD GENERATION 17 TYPE 1 2.25 0. -4.5 ZI 3.0

Next, exit the editor and go to the General-Load page, expand that load case and click on the line TYPE 1 2.25 0. -4.5 ZI 3.0

as shown in Fig 2.3.30.

FIGURE 2.3.30 Wheels outside the structure

In Fig 2.3.30, the starting position of the vehicle with respect to the entrance to the bridge is shown. This is also depicted in Fig 2.3.31.

FIGURE 2.3.31 Vehicle entering a bridge—axles outside the bridge

We provided the coordinates of the reference point of the vehicle as (2.25, 0, −4.5). Due to this, as shown in Figures 2.3.30 and 2.3.31, the rear and middle axles are both outside the bridge. This is one of the reasons why the warning message appears in the output file.

The other reason is as follows. The length of the truck from rear axle to front axle, based on the spacing between their axles is 3.0 + 1.5 = 4.5 m. The term ZINC(rement) indicates that the vehicle should move along the global Z direction. The length of the bridge along global Z is 45 m. Based on a ZINC of 3 m, and as the first load case to be generated is one where the vehicle is positioned in the manner shown in Figures 2.3.30 and 2.3.31, the number of increments required for the front axle to reach the other end of the bridge = 1 + (45/3) = 16. The first generated case is associated with the starting position of the vehicle. The 16th generated case will be the result of applying 15 increments. Because load case 1 is the dead load case, the 16th generated case will be sequentially called load case 17. This is the last case for which all the axles are still on the bridge.

FIGURE 2.3.32 Load representation in the GUI for a vehicle reaching the end of the bridge

So, in the 17th generated load case (associated with the 16th increment), the front wheel of the vehicle is at 48 m from the start of the bridge, whereas the bridge is only 45 m long. Hence, two of the axles (the front and the middle axles) have crossed the bridge. Due to this, warnings referred to in the question will be reported for the 17th generated case. This is evident if we run the analysis and look at the load display diagram.

FIGURE 2.3.33 Loads corresponding to a vehicle just leaving the bridge

In Fig 2.3.33, the loads for the 17th generated load case (named load case 18) are displayed. These four concentrated loads represent the two wheels of the rear axle. The first and second axles have left the bridge, thus triggering the warning. Therefore, the warnings indicate that the following axles are outside the bridge: First generated case (Load Case 2)

Rear and middle axles

Second generated case (Load Case 3)

Rear axle

17th generated case (Load Case 18)

The front and middle axles

With the right set of values for the starting position, increment of movement and number of load cases generated, one could generate all the positions from the vehicle entering the bridge (shown earlier) to the vehicle leaving the bridge (Fig 2.3.34).

FIGURE 2.3.34 Vehicle leaving the bridge — axles outside the bridge

These warnings do not necessarily mean that there is a problem in the model. It is inevitable that some of the wheels will lie outside the bridge if we want all the axles of the vehicle to travel the full length of the deck. So, in many cases, these warnings may be harmless. Another related, but a more serious situation is when there is an error in the starting position (coordinates of the reference wheel) of the vehicle due to which the vehicle never actually gets placed on the deck. Such a condition is shown in Fig 2.3.35.

FIGURE 2.3.35 Error in the Y coordinate of wheel location

The deck level is at the top of the columns whereas the vehicle is positioned at the elevation of the bottom of the columns. Needless to say, no load can be generated. If no member gets loaded for a generated load case, the following warning will appear in the

output file.

FIGURE 2.3.36 Error in coordinates of starting position

**WARNING-NO MEMBERS IN SPECIFIED VERTICAL RANGE.

In the case of the above structure, as no member will receive a load for any of the generated cases, one warning will appear for each case that is to be generated.

FIGURE 2.3.37 Warnings associated with loads outside the vertical extents of the structure

Related Question: Can we generate an eccentric moving load using the moving load generator? The wheel is moving 8 in. away from the centroid of the section assigned to the girder, which is represented using a line. So, the girder is loaded on one side only. For instance, I want to apply a 20-kip point load suspended 8 in. from the centerline of the member. This load shall be moved in 3-ft intervals.

Answer: Any torsion resulting from the eccentric position of the wheel with respect to the centerline of the member has to be manually calculated and applied. There is no automated way to have the program generate the moments at this time.

2.3.23 Automatically Generating Combination Cases that Include the Generated Moving Load Cases Related Question: How do I get STAAD.Pro to automatically combine static load cases such as the Dead and Live Load cases with load cases generated using the MOVING LOAD generation facility? Answer: The LOAD GENERATION command has an option called ADD LOAD and is described in Section 5.32.12 of the Technical Reference manual. Using this, other load cases that are specified before the moving load generator can be combined with the load cases generated by the moving load generator (see the following example). DEFINE MOVING LOAD TYPE 1 LOAD 20. 20. 10. DISTANCE 10. 5. WIDTH 10. LOAD 1 DEAD LOAD SELF Y -1.0 LOAD 2 LIVE LOAD MEMBER LOAD 31 TO 37 UNI GY -3.2 * GENERATE MOVING LOADS AND ADD THE SELFWEIGHT LOAD TO EACH * GENERATED LOAD CASE LOAD GENERATION 10 ADD LOAD 1 TYPE 1 7.5 0. 0. ZI 10. PERFORM ANALYSIS PRINT LOAD DATA

In the above example, the dead load is declared in Load 1. The live load case is Load 2. The generated moving load cases are 3 through 12 (10 cases generated). In each of these, Case 1 is included by virtue of the ADD LOAD command. Fig 2.3.38 illustrates the dialog box in the GUI where this facility is available.

FIGURE 2.3.38 Predefined load to be included using ADD LOAD

2.3.24 Including More than One Load Case Using ADD LOAD In the method explained previously, only one load case can be added to each of the generated load cases. If multiple load cases need to be added, then these cases must first be combined into one case using the REPEAT LOAD option. Let’s say we want to add dead load (Load Case 1) and live load (Load Case 2) to the generated moving load cases. First, create a REPEAT LOAD (Load Case 11), which combines Cases 1 and 2. LOAD 1 DEAD LOAD SELFWEIGHT Y -1 LOAD 2 LIVE LOAD MEMBER LOAD 1 TO 6 12 TO 17 23 TO 28 34 TO 39 45 TO 50 UNI GY -1.5 LOAD 11 DEAD + LIVE REPEAT LOAD 1 1.0 2 1.0

Next, Load 11 has to be added to each case generated from the moving load. So, in the GUI, the “Predefined Load to be Added” would be Case 11. Or, in the editor, add the words, ADD LOAD 11 to the LOAD GENERATION command. LOAD GENERATION 17 ADD LOAD 11 TYPE 1 7.5 0 0 ZINC 10

FIGURE 2.3.39 Dialog box in the STAAD.Pro GUI for ADD LOAD

The result is that each generated load case will be a combination of the moving load and the static loads.

FIGURE 2.3.40 Load diagram for a defined load case plus a generated case

To verify that STAAD.Pro is handling it correctly, specify the command:

PERFORM ANALYSIS PRINT LOAD DATA

Run the analysis and view the output file (.ANL file). The details of each of the generated cases will be written into the output file. Each of those will include the contents of Load Case 11 also.

2.3.25 Displaying the Deflection Diagram and Generated Loads Simultaneously Earlier, we saw the procedure for displaying the generated loads on the structure. By having the load display icon switched on, and by scrolling through the load list from the load selection box, it is possible to get an impression that the loads are traveling along the bridge. The same procedure may also be used to view the deflection diagram along with the loads. For this, we have to be in the Node-Displacement page of the post-processing mode. Adjust the scale of the deflection diagram so that its shape is noticeable in a magnified manner. Then, switch on the load display icon, and use the drop-down list of the load selection box to go through the cases sequentially.

FIGURE 2.3.41 Deflection diagram for moving load cases

Related Question: Can the moving load be applied on a curved member? By that, I mean, a member with the MEMBER CURVE specification? Answer:

The answer is no. As the moving load generation works only for vehicles moving along a straight line, it will not work for members with the MEMBER CURVE specification.

2.3.26 Generating Loads Acting along the Horizontal Direction Due to a Moving Vehicle Related Question: I have a model containing a crane girder. Due to the moving crane, loads acting vertically downward need to be generated. In addition, due to acceleration and braking of the crane, as well as swinging of the suspended load, horizontal forces will act on the girder along the longitudinal and transverse directions. In addition to the vertical loads, is there a way to simultaneously generate the loads in the horizontal directions, such as those due to centrifugal forces? Answer: As part of the moving load generator facility, STAAD.Pro can calculate only the vertical loads. It does not have an automatic facility for generating any horizontal loads from the motion of the vehicle or a crane on a gantry girder. However, the feature called notional loads can be used to instruct the program to apply a certain percentage of the vertical load as a horizontal force. Notional loads are described in Section 2.5. In the next example, along with the vertical loads, a horizontal load equal to 2% of the vertical load is generated along the global X direction. However, as the vertical and horizontal loads are in separate load cases, load combination cases must be created to combine them. Example 11 LOAD GENERATION 10 TYPE 1 7.5 0. 0. ZI 10. LOAD 21 NOTIONAL LOAD 2 X 0.02 PERFORM ANALYSIS PRINT LOAD DATA

2.3.27 RM Bridge and LEAP Software—Alternatives to STAAD.Pro’s Moving Load Generator As we have seen, there are some limitations in the moving load generator built into STAAD.Pro. Bentley has a portfolio of software called Bentley Bridge exclusively meant for analysis and design of bridges of various types. Two of the well-known programs in this portfolio are RM Bridge and Leap Bridge Enterprise. Besides having advanced capabilities in this domain, data exchange between STAAD.Pro and those programs is also facilitated. More information on these is available at the Bentley Web site http://www.bentley.com/enUS/Products/Bridge+Design+and+Engineering/.

2.4 Seismic Load Generation 2.4.1 Introduction: Dynamic Analysis—The Basics In the loading types discussed so far, all the loads act statically, that is, there is no variation in the

magnitude or direction of load over time. Structures, however, are frequently subjected to loads that change in both magnitude and direction. Such loads are called dynamic loads. Examples of such loads are earthquakes—also known as seismic loads, machine vibration such as vibrations induced by turbine generators, random excitation as in explosions or blasts, and so on. The topic of discussion for this section is Seismic loads, primarily in the context of the procedure recommended by the ASCE 7-05 and the 2006 International Building Code (IBC). However, some of the other seismic codes implemented in STAAD.Pro are also referred to wherever applicable. Required reading 9. Technical Reference manual—Section 1.17.2 Seismic Load Generator 10. Technical Reference manual—Section 5.31.2 Definitions for Static Force Procedures for Seismic Analysis 11. Technical Reference manual—Section 5.32.12.2 Generation of Seismic Loads 12. Application Examples manual—Example 14 In the STAAD.Pro GUI manual, several sections are devoted to the discussion of this topic. A screenshot of the manual listing these topics is shown in Fig 2.4.1.

FIGURE 2.4.1 Page from the STAAD.Pro GUI manual listing the topics related to seismic loading

2.4.2 Discussion When a building is subjected to an earthquake, it undergoes vibrations. The weights of the structure, when accelerated along the direction of the earthquake, induce forces in the building. Normally, an elaborate dynamic analysis called time history analysis is required to solve displacements, forces, and reactions resulting from the seismic activity. The methods specified in many codes for seismic analysis contain provisions for an equivalent

lateral force procedure (ELFP) (see Section 12.8 of ASCE 7-05). Some codes also call it the equivalent static analysis procedure. That is to say, even if seismic forces are dynamic in nature, they can be solved using a static approach. In this procedure, static lateral forces are generated and applied on the structure, and they produce maximum effects similar to what an elaborate dynamic analysis procedure would yield.

2.4.3 Procedure This consists of three steps. Step 1. Calculate the aggregate lateral force on the building, which codes refer to as the seismic base shear. For most codes that recommend the ELFP, the expression for the seismic base shear is similar to the following equation V = Cs * W where V = Seismic base shear. It is the net horizontal force that the structure experiences due to the seismic disturbance. W = Sum of all the weights in the structure that are subjected to the seismic forces. Section 12.7.2 of IBC 2006 calls it the effective seismic weight. C s = A term known as the seismic response coefficient. For IBC 2006, this can be found in Section 12.8.1. Various codes have their own terminology for referring to C s. Step 2. The V calculated from Step 1 has to be distributed among the various floors of the building as a set of point loads. Section 12.8.3 of IBC 2006 describes this process as “vertical distribution of seismic forces.” In STAAD.Pro, as there is no clear concept of a floor because any type of structure can be modeled, set(s) of nodes that have a common Y coordinate constitute a floor. Once the total horizontal force that is to be applied on a given floor is calculated, that amount of force is distributed between the various joints of that floor in the same proportion as the seismic weight lumped at the node to the total lumped seismic weight for that floor. Step 3. The model is then analyzed for the horizontal forces generated in Step 2. The input required in STAAD.Pro consists of two parts.

2.4.3.1 Part 1: Input for Step 1 In STAAD.Pro, the input of data used to determine V has to be initiated under commands such as DEFINE IBC 2006 LOAD, DEFINE AIJ LOAD, and DEFINE 1893 LOAD. In the Graphical User Interface (GUI), they appear in the General-Load page as shown in Fig 2.4.2.

FIGURE 2.4.2 Seismic codes available in STAAD.Pro

Terms such as Occupancy Importance factor, Response Modification factors, and Soil Type factors (details of which can be found in the respective seismic code documents) enable the computation of C s. Depending on the code that is selected, these terms vary, because each code has its own set of rules for calculating C s. The following is an example for IBC 2006. SS 0.284 S1 0.068 I 1.5 RX 3 RZ 3 SCLASS 4 TL 6

The remainder of the input consists of weights, which are used for the computation of the term W. W is calculated by aggregating the contribution from various weights such as selfweight, weight of items on slab panels, and weights from distributed loads on members. The means by which these various types can be specified in the STAAD.Pro model are: SELFWEIGHT (for considering the weight of all the components defined in the model) JOINT WEIGHT (weight of items lumped at nodes) MEMBER WEIGHT (distributed and concentrated weights specified on members). An example of member weight would be the weight per unit length of partition walls resting on beams. FLOOR WEIGHT (weights defined through pressures applied over panels) ELEMENT WEIGHT (weights defined through pressures applied on plate elements) As with loads, users are free to use just the ones they want. It is not mandatory to include all these weight types. For example, if there are no plate elements in the model, there is no need for the ELEMENT WEIGHT. If plate elements span the region between members, one may use ELEMENT WEIGHT instead of FLOOR WEIGHT.

FIGURE 2.4.3 Seismic weights definition dialog box in the STAAD.Pro GUI

Some instances of the full set of input for IBC 2006 are shown in the following examples titled Methods 1, 2 and 3. For other seismic codes, you may refer to the STAAD.Pro Technical Reference manual. Method 1—Input based on Ss and S1 DEFINE IBC 2006 SS 0.5 S1 0.15 I 1.25 RX 3 RZ 3 SCLASS 3 TL 12 FA 1.2 FV 1.65 SELFWEIGHT JOINT WEIGHT 23 WEIGHT 1.747 24 51 WEIGHT 1.949 25 52 WEIGHT 1.076 MEMBER WEIGHT *Exterior and Interior Beams 3008 TO 3010 3029 3037 3038 3058 TO 3060 UNI 0.9 FLOOR WEIGHT *DL ROOF OFFICE YRANGE 35 37 FLOAD 0.02 XRANGE 0 506 ZRANGE 0 92 ELEMENT WEIGHT 191 TO 245 PRESSURE 0.6

For this method, if any of the terms that are essential for the calculation of C s are omitted, an error message will be displayed in the output file. ***ERROR*** THE ESSENTIAL PARAMETERS FOR IBC 2006 CODE HAVE NOT BEEN SPECIFIED.

FIGURE 2.4.4 Warnings due to incorrect seismic parameters

A similar message is displayed for the other codes if the key terms are found missing. Method 2—Input based on zip code DEFINE IBC 2006 ZIP 37743 I 1.25 RX 3.25 RZ 3.25 SCLASS 3 CT 0.02 TL 12 FA 1.2 FV 1.69 K 0.75 SELFWEIGHT JOINT WEIGHT 51 56 93 100 WEIGHT 650 MEMBER WEIGHT 151 TO 156 158 159 222 TO 225 324 TO 331 UNI 45

NOTE Zip codes are available only for sites in the United States.

When we specify the ZIP code, we do not need to specify LAT, LONG, SS, and S1. These are automatically determined by the software based on the zip code. The program reports the following message in the output file indicating the values it has chosen for terms such as Ss, S1, Fa, Fv, SDS, and SD1.

FIGURE 2.4.5 Seismic parameters report in the output file for input based on zip code

Method 3—Input based on latitude and longitude

DEFINE IBC 2006 LAT 33.8845 LONG -117.9274 I 1.25 RX 2.5 RZ 2.5 SCLASS 4 TL 12 FA 1 FV 1.5 SELFWEIGHT JOINT WEIGHT 51 56 93 100 WEIGHT 650 MEMBER WEIGHT 151 TO 156 158 159 222 TO 225 324 TO 331 UNI 45

NOTE This method of input involving latitudes and longitudes is available only for sites in the United States.

In this case too, information regarding the values chosen for SS, S1, and so on is displayed in the output file.

FIGURE 2.4.6 Seismic parameters report in the output file for input based on LAT and LONG

For other seismic codes too, there are similar input requirements. The dialog box in the STAAD.Pro GUI where one can specify the input for the IS 1893 code is shown in Fig 2.4.7.

FIGURE 2.4.7 Screens in the GUI for input for IS 1893 (Part 1)-2002

2.4.3.2 Part 2: Input for Step 2

The instructions for this part appear within a load case. They instruct the program to generate the lateral forces and then analyze the structure for those forces. Example 12: For IBC LOAD 1 (SEISMIC LOAD IN X DIRECTION) IBC LOAD X 0.75 LOAD 2 (SEISMIC LOAD IN Z DIRECTION) IBC LOAD Z 0.75

Example 13: For IS 1893 LOAD LOAD 1 EQX 1893 LOAD X 1 LOAD 2 EQZ 1893 LOAD Z 1

Example 14: For Canadian NBCC NRC LOAD 1 SEISMIC LOADING ALONG X NRC LOAD X 1 ACC 1 LOAD 2 SEISMIC LOADING ALONG Z NRC LOAD Z 1 ACC 1 LOAD 3 SEISMIC LOADING ALONG -X NRC LOAD X -1 ACC 1 LOAD 4 SEISMIC LOADING ALONG -Z NRC LOAD Z -1 ACC 1

Related Question: I need to do seismic analysis per IBC 2006 for a structure being built outside the United States. The zip code method of applying the seismic parameters cannot be used. What can I do? Answer: For analysis using the IBC 2006, the zip codes are specific to the United States and so are the values of latitude and longitude. So, if the site is outside the United States, you need to know the value of Ss (mapped MCE, 5% damped, spectral response acceleration parameter at short periods as defined in Section 11.4.1 of ASCE 7-05) and S1 (mapped MCE, 5% damped, spectral response acceleration parameter at a period of 1 s as defined in Section 11.4.1 of ASCE 7-05) and specify them as shown in Method 1 earlier. The seismic definition should look similar to that mentioned in the next example: DEFINE IBC 2006 SS 1.34 S1 0.52 I 1 RX 3 RZ 4 SCLASS 4 TL 12

Related Questions: While specifying the seismic definition for IBC 2006, NBCC NRC-2005, IS 1893–2002, and

so on, I have applied selfweight, member weight, and floor weight. Is it necessary to provide joint weight also? What is the difference between joint weight and joint load? Answers: A joint weight is one of the means through which the weights that go into the making of the total weight term W are specified for all the aforementioned codes. The remaining weights mentioned in the question (plus ELEMENT WEIGHT) are the other means. It is not mandatory to add joint weights in a seismic definition. If a convenient way to consider the weight of fixtures on the structure is through a concentrated weight applied at a joint, the JOINT WEIGHT is the appropriate means to do so. It can also be used in cases such as modeling the weight associated with bolts, rivets, gusset plates, and so on, which are not usually considered part of the structural geometry. In other words, it is the amount of lumped weight at the joint and will contribute toward the total base shear for the structure. Since the weights specific for seismic definition are used only for the lateral load analysis, it becomes necessary to re-specify all or most of these weights once again in load cases for the gravity analysis. So, the MEMBER WEIGHT data is re-specified through MEMBER LOADS, JOINT WEIGHTS are specified as JOINT LOADs, and so on. In other words, all the WEIGHTS in the seismic definition have to be provided once again as LOADS for the gravity analysis through the means of DEAD, LIVE, and other such load cases. Related Question: What is the difference between specifying a floor load as a load item in a load case versus specifying a floor weight in a seismic definition? Answer: A floor load applied as a load item in a load case is for the purpose of applying a load to the structure, such as Dead Load, or Live Load. It is associated with the analysis for gravity loads. Specifying a floor weight in a seismic definition is for the purpose of adding the weight (induced by the underlying load-producing agent, such as an equipment) that will be considered for the calculation of the seismic base shear. This is part of the lateral load analysis. Related Question: What would happen if a load that is present on a member or a plate element is not included under seismic weights? Answer: The total seismic weight calculation W would not include the contribution of the weight derived from that load item. If its contribution ought to be considered, you should include it.

2.4.4 Weight of Fireproofing In the seismic definition, the weight of fireproofing, if assigned to members, is automatically considered by the program in the selfweight calculation. The engineer needs to just ensure that SELFWEIGHT is specified as one of the weights.

2.4.5 Specifying Seismic Weights through Reference Load Cases Related Question: I define weights under the DEFINE IBC command. Then I have to re-specify them in the actual load cases. This is an unnecessary exercise. Why can’t STAAD.Pro re-use the data I specified under the DEFINE IBC for the actual load cases also? Answer: The load information contained in Reference load types can be used as the feeder data with which to assemble the seismic weights. For a description of Reference load types, see Section 3.2. To illustrate this method, let us assume that there are four Reference load types defined in the following manner. DEFINE REFERENCE LOADS LOAD R1 LOADTYPE None TITLE DL1 SELFWEIGHT Y -1 LIST 1 TO 1101 LOAD R2 LOADTYPE None TITLE DL2 - EQUIPMENT MEMBER LOAD 42 60 78 92 CON GY -6 3.0 1 TO 31 41 TO 73 UNI GY -0.025 273 282 324 336 349 410 426 548 UNI GY -0.028 JOINT LOAD 44 56 78 90 FY -12 LOAD R3 LOADTYPE None TITLE LL1 - LIVE LOAD ONEWAY LOAD YRANGE 4.69 4.71 ONE -2.5 XRANGE -1 13 ZRANGE -1 11 GY YRANGE 4.69 4.71 ONE -3.5 XRANGE 12.9 23.1 ZRANGE -1 11 GY JOINT LOAD 69 78 81 84 95 FX 3.5 LOAD R4 LOADTYPE None TITLE LL2 - UPSET OPERATING LIVE LOAD ELEMENT LOAD 1029 TO 1277 PR GY -2.1 JOINT LOAD 69 78 81 84 95 FZ 3.5 END DEFINE REFERENCE LOADS

The various loads described under these Reference loads can then be used to provide the seismic weights for the seismic definition in the following manner. DEFINE 1893 LOAD ZONE 0.36 RF 3 I 1 SS 1 ST 1 DM 0.05 REFERENCE LOAD Y R1 1.0 R2 1.0 R3 0.25 R4 0.25

The term Y in the expression REFERENCE LOAD Y instructs the program that among the

various load items that are contained in the Reference load cases, only those load items acting along the Y direction should be used for creating the seismic weights. Terms specified along X and Z (such as those present in Reference load cases 3 and 4) should not be used.

FIGURE 2.4.8 Direction term for seismic weights assigned using Reference Loads

So, the seismic load case in the model will look like this: LOAD 1 EQ IN X 1893 LOAD X 1.0

and, the gravity load case will look like this: * COMBINATION LOAD CASE FOR CONCRETE DESIGN LOAD 7 REFERENCE LOAD R1 1.2 R2 1.2 R3 1.5 R4 1.5

Thus, the load data have to be specified only once in the model and can be used for lateral as well as gravity analysis. Related Question: What does the following error message mean? *** STAAD.Pro ERROR MESSAGE *** NO LOADING DEFINED FOR UBC LOAD. RUN TERMINATED.

FIGURE 2.4.9 Error message due to absence of seismic weights

Answer: As described earlier, to compute V, the program expects input for the two terms C s and W. The aforementioned error message states that the weights necessary to calculate W is missing from the input. In other words, no weights have been specified through the SELFWEIGHT, JOINT WEIGHT, MEMBER WEIGHT, FLOOR WEIGHT, or ELEMENT WEIGHT commands, due to which W is equal to zero. You could verify it by adding just SELFWEIGHT as one of the weights to start with, and check if the message disappears. DEFINE IBC 2006 SS 0.284 S1 0.068 I 1.5 RX 3 RZ 3 SCLASS 4 TL 6 SELFWEIGHT

Add the joint weights, member weights, and any other weights as relevant. Although the message specifically says UBC LOAD, it is a generic message that is applicable for all seismic codes—IBC, NBCC, IS 1893, AIJ, UBC 1997, and so on. Related Question: If I specify selfweight, member weight, and floor weight for a seismic analysis per IBC 2006, will the program also use that information to analyze the structure for those loads acting vertically? If I specify them separately under a load case, would that constitute twice the load for gravity effects? Answer: The data specified through the selfweight, joint weight, member weight, element weight, and floor weight are used just to compute the V. Once the H is derived from the V, the V is discarded. If one wants the structure to be analyzed for the vertical loads, these have to be explicitly specified with load cases. This is demonstrated through the next example in which the seismic load cases per the Canadian code (NBCC NRC 2005) are specified as Cases 1 and 2. Even though the dead weight, equipment weight, weight from a partial live load, and all other such loads are specified as the

seismic weight, they are specified again through load cases 3, 4, 5, 6, and so on. The seismic weights are not automatically used as the feeder data for dead, live, and such load cases for gravity analysis. LOAD 1 EARTHQUAKE LOAD X NRC LOAD X 1.0 PERFORM ANALYSIS CHANGE LOAD 2 EARTHQUAKE LOAD Z NRC LOAD Z 1.0 PERFORM ANALYSIS CHANGE LOAD 3 DEAD LOAD SELF Y -1.0 LOAD 4 LIVE LOAD JOINT LOAD 3135 FY 30.7 1224 FX 20 FY -31.5 .. ..

LOAD 5 CONDENSER WEIGHT ON SLAB ELEMENT LOAD 1099 3124 PR GY -15.2 1115 3140 PR GY -17.4 LOAD 6 MEMBER LOAD

So, there is no double counting. Related Question: Can we include the member weight/joint weight (mass equivalent) due to applied moment for IBC loads? Answer: No. STAAD.Pro only allows translational weight terms and horizontal translational accelerations in the IBC analyses. Moment terms cannot be input as seismic weight terms. Related Question: In the command 1893 LOAD X 1.1

what is the purpose of 1.1? Answer: It is a factor through which the user can increase or decrease the amount of lateral forces actually applied on the structure. The seismic base shear calculated is multiplied by this factor to arrive at the total force, which is distributed among the floors of the building. Let us assume that the base shear computed per the 1893 equation is 1893 FACTOR V = 0.0611 X 285.53 = 17.446 kNS

Due to the factor of 1.1, the total horizontal force applied on the structure amounts to 17.446 *1.1 = 19.191 kNS

Related Question: How do we apply a seismic load along the negative horizontal directions? Answer: This can be done in two ways. Method 1: This requires using a negative factor after the direction term. LOAD 2 IBC LOAD X -1.0 PERFORM ANALYSIS CHANGE .. LOAD 4 IBC LOAD Z -1.0 PERFORM ANALYSIS CHANGE

Method 2: If load cases 1 and 3 are for the seismic load (IBC load in this example) applied along the positive X and Z directions, respectively, then, create a combination load case, using either the REPEAT LOAD command or the LOAD COMBINATION command, where a negative factor is applied. For example, LOAD 11 REPEAT LOAD 1 -1.0 LOAD 12 REPEAT LOAD 3 -1.0

So, load cases 11 and 12 will correspond to the seismic load being applied along negative X and Z directions, respectively.

2.4.6 Periods PX and PZ

Related Question: I want to perform a seismic analysis per the 1997 Uniform Building Code (UBC). However, instead of using the code specifications for calculating the periods of the structure, I want to specify my own. Answer: In the various seismic codes implemented in STAAD.Pro, the period calculation by the Rayleigh method is a standard part of the calculations. However, some users prefer to specify their own values instead. PX and PZ are terms that a user can provide in case he/she wishes to override the periods that STAAD.Pro calculates using the Rayleigh method. If you do not wish to override those STAAD.Pro calculated values, there is no need to specify PX and/or PZ. Related Question: I am doing a seismic analysis per the ASCE 7-05/IBC 2006. I see that the STAAD.Pro interface has the option for providing the periods PX and PZ. Can you explain when and how these are used by STAAD.Pro?

FIGURE 2.4.10 User-specified periods for base shear calculation

Answer: According to ASCE 7-05, the period has to be calculated using two methods. a. As per Section 12.8.2.1 of ASCE 7-05. This is reported in the STAAD.Pro output file as Ta. b. If PX and/or PZ are not specified, STAAD.Pro calculates the period as per the Rayleigh method. This appears in the STAAD.Pro output file as the term T. This is done to satisfy the following requirement stated in Section 12.8.2 of ASCE 7-05: The fundamental period of the structure, T, in the direction under consideration shall be established using the structural properties and deformational characteristics of the resisting elements in a properly substantiated analysis.

If you specify PX and/or PZ (depending on the direction of the IBC load), that value is used in lieu of the calculation mentioned in Item b.

FIGURE 2.4.11 IBC 2006 report in the STAAD.Pro output file

Before it can be used in the base shear calculation, the value obtained using the two methods discussed previously is subjected to the following condition stated in Section 12.8.2 of ASCE 705: The fundamental period, T, shall not exceed the product of the coefficient for upper limit on calculated period (Cu ) from Table 12.8-1 and the approximate fundamental period, Ta, determined from Eq. 12.8-7. So, the answer to the question is this: If you agree with the Rayleigh period that STAAD.Pro calculates as per Item b, there is no need to specify PX or PZ. They should be specified only if you want to override what STAAD.Pro calculates as periods for the structure in X and Z directions. This general principle is applicable not just to IBC, but all seismic codes where the code requires the period to be calculated per the Rayleigh method in addition to another method. Related Question: I wish to know how the Rayleigh period is calculated for an ELFP-based seismic analysis. Answer: The seismic weights entered under the heading DEFINE IBC LOAD or DEFINE NRC 2005 LOAD (or similar such commands for any of the other seismic codes) are first transformed into lumped weights at the nodes of the structure. They are then subjected to a 1g acceleration in the direction specified. Following this, a static analysis is performed to compute the displacements of the nodes of the structure. Using the displacements as the assumed mode shape and the weights/g as the mass, a single Rayleigh iteration is performed to compute the frequency. This method is used not just for IBC, but for all the seismic codes in STAAD.Pro. Related Question:

For IS 1893-2002, how is the time period calculated if the user does not input the value for the ST option? Answer: STAAD.Pro first checks whether the user has specified values for the PX and/or PZ terms in the 1893 seismic definition. If they have not been specified, it then checks whether the parameter ST (type of structure) is specified. If it is, the periods are calculated according to Clause 7.6.1 of IS 1893-2002. If none are provided, the program calculates the approximate time period of the structure using the Rayleigh method.

2.4.7 Accidental Torsion Many codes require an accidental torsion to be computed alongside the lateral forces. In ASCE 705, this requirement can be found in Section 12.8.4.2. This calculation is triggered when the program encounters the ACCIDENTAL keyword in the DEFINE command. DEFINE IBC 2006 ACCIDENTAL LOAD ZIP 92887 I 1 RX 3 RZ 4 SCLASS 4 TL 12 SELFWEIGHT

In the GUI, it can be found in the Seismic Definition dialog box.

FIGURE 2.4.12 Accidental torsion facility in the seismic definition dialog box

If that keyword is omitted, as in the next example, DEFINE IBC 2006 LOAD

ZIP 92887 I 1 RX 3 RZ 4 SCLASS 4 TL 12 SELFWEIGHT

the torsion is not calculated. This feature is available only with some of the seismic codes in STAAD.Pro. The option is not available for codes in which there are no clear guidelines on the procedure for calculating the accidental torsion. The torsion is calculated as the lateral force computed for the node multiplied by a lever arm. The steps for computing the lever arm for most of those codes are as follows. In ASCE 7-05 (which forms the basis for IBC 2006), for example, this provision can be found in Section 12.8.4.2. The program calculates the largest floor dimension perpendicular to the direction in which the seismic load is acting. So, for UBC LOAD X, for the floor where the accidental torsion component is being calculated, it calculates the largest Z dimension. If we specify UBC LOAD Z, it calculates the largest X dimension for the floor under consideration. This quantity is multiplied by 0.05 to obtain the lever arm by which the force at that node is multiplied. All nodes on the structure experience the moment in the same sense (either all positive or all negative). As explained later in this section, the magnitude of the generated torsional moment can be viewed in the .ANL file as well as in the GUI.

2.4.7.1 Multiplying Factor for Accidental Torsion By default, the program multiplies the force (whatever its sign) by a positive value of a lever arm to arrive at the moment. Thus, the default is that the moment will have the same sign as the force. In recent versions of STAAD.Pro, there is a facility by which the generated torsion can be factored by a user-defined value. In the GUI, it is called “multiplying factor for accidental torsion moment.”

FIGURE 2.4.13 Multiplying factor for accidental torsion in the seismic definition dialog box

In the STAAD.Pro input file, it is specified following the word ACC as shown in the following example. The product of the sign of that factor and the sign of the force will determine the direction of the moment. LOAD 1 IBC LOAD X 1.0 ACC -1.0

The factor of −1.0 in this example will force the generated torsion to take on a sign opposite to the default. Also, all nodes at a floor experience the moment in the same sense (either all positive or all negative). If the factor were +0.75, it implies that the full torsion is first calculated and then reduced by 25%. This factor is not a criteria used to decide whether accidental torsion should be considered or not. That is controlled by the ACCIDENTAL keyword as mentioned earlier. This is a multiplication factor which indicates that “if and only if accidental torsion moments are generated, then, those moments should be multiplied by this factor.” Using this factor, eight seismic load conditions can be checked: 1. 2. 3. 4. 5. 6. 7.

Positive Z with CLOCKWISE Accidental Torsion Positive Z with COUNTER-CLOCKWISE Accidental Torsion Negative Z with CLOCKWISE Accidental Torsion Negative Z with COUNTER-CLOCKWISE Accidental Torsion Positive X with CLOCKWISE Accidental Torsion Positive X with COUNTER-CLOCKWISE Accidental Torsion Negative X with CLOCKWISE Accidental Torsion

8. Negative X with COUNTER-CLOCKWISE Accidental Torsion

2.4.7.2 Accidental Torsion and Instability in Frames In steel frames, it is customary to release MY and MZ at most, if not all, of the joints where beams meet columns. This is done to represent a pinned connection between those components. If the beam happens to be a continuous beam resting on the column as sometimes happens at the roof level, MY and MZ are released at the column tops to indicate that no moment is transferred from the beam into the column. In addition, braces that frame into columns are declared trusses. One such structure is shown in Fig 2.4.14. In Section 2.2 of Part III, the potential for an excessive number of releases to engender instability in structures is documented in detail. The accidental torsion moment that is generated during seismic load generation by ELFP amplifies this problem. As we saw earlier, ACCIDENTAL torsion causes torsional moments to be generated along MY at all joints where a lumped weight is present. Due to the MY release in beams (or MZ if a BETA 90 is specified), and, TRUSS specification for the braces, those moments will not enter the beams or braces. So, the columns by themselves have to transmit the moment, which is now a torsion on the columns, to the supports. If the supports at the column bases are PINNED, it will definitely spawn an instability warning message, because the torsion has no path to reach the supports. The program will add a weak rotational spring to prevent the stiffness matrix from becoming singular, but it will still lead to very large rotations along global Y, which will make the results worthless from a practical standpoint. The instability can be averted if the MY degree of freedom is restrained at the support at the column base. However, we may still end up with excessive displacements. If the height from the base to roof is large (say 10 m or more), and the columns are assigned open sections that aren’t torsionally strong (I-shape, channels, etc.), those torsional moments along the column at each floor level will twist the column and cause large rotations at the top. One way to avoid this is to change the manner of the connection between the column and other members at each floor, so there is a better arrangement for resisting torsion.

FIGURE 2.4.14 Instability resulting from accidental torsion and MY release

The reason why we said that accidental torsion amplifies the problem is that the torsional moment acts along an unstable degree of freedom. As mentioned in Section 2.2 of Part III, an instability condition by itself does not lead to unacceptable results unless there is a load acting along that unstable degree of freedom.

2.4.8 Center of Rigidity For most seismic codes, STAAD.Pro does not calculate the center of rigidity. One exception is the IS 1893-2002 code for which it is computed for soft story checking. For the purpose of computation of lateral stiffness of the structure at a floor level, columns and shear walls without openings are considered as vertical components. However, shear walls with openings and bracings are excluded.

2.4.9 Distribution of Base Shear For IBC 2006 (ASCE 7-05), the base shear is distributed according to the rules of Section 12.8.3 of ASCE 7-05. According to Equation 12.8-12 in this section, the vertical distribution of seismic forces depends on the term h i, which the code terms height from base to Level i. So, two questions that need to be answered are: a. How does STAAD.Pro calculate h i? b. What happens if the model contains portions below the supports such as a sub-basement? STAAD.Pro uses the elevation of the lowest support node(s) (those with the lowest Y coordinate) as the datum from where h i is measured. As STAAD.Pro is a general-purpose software meant for any type of structure, building-related concepts such as floors or stories are not integral to the program. So, every node with a distinct Y elevation becomes a candidate to receive the seismic force provided it has a lumped weight.

It appears that Section 12.8.3 of ASCE 7-05 was meant for those structures whose supports are all at the same elevation, since Equation 12.8-12 deals with distributing the seismic forces only on regions above the foundation. If there are lumped weights suspended below the lowest supports, there is some ambiguity in the manner in which these must be accounted for. There is a possibility that loads generated for the sub-basement regions may not be correct.

2.4.10 Structures with Supports at Different Elevations As mentioned in Section 2.4.9, the rules of the code are meant to be used on structures where all the supports are at the same elevation. However, the burden of ensuring this is upon the user. STAAD.Pro does not check whether the supports are at the same Y coordinate or not.

2.4.11 Distribution of Lateral Force between the Nodes on a Floor For any node on a floor, the ratio of the seismic weight at that node to the seismic weight on that floor is calculated. This fraction of the generated lateral force for that floor is then applied at that node. For example, let us say that the lateral force for the floor at Y = 9.5 m is 45 kN. Let us also assume that the total weight on that floor is 500 kN, and the weight acting through Node 29 is 8 kN. So, the lateral force at Node 29 is obtained as 45 * (8/500) = 0.72 kN. So, the summation of the forces at all the nodes of a floor must equal the lateral force generated for that floor. Later in this section, the method for obtaining a report of the generated lateral forces at each node is shown.

2.4.12 Buried Structures As discussed in Section 2.4.9, the question that arises is: Is it OK to analyze structures fully embedded in soil like culverts or buried pipes per ELFP-based methods?

FIGURE 2.4.15 Buried structures such as culverts

If the pipe is defined as line members attached to several collinear nodes, all of which are at the

same elevation, the base shear distribution rules become impossible to apply. Besides, conceptually, the ELFP isn’t applicable to such models. Models representing single beams and continuous beams fall in this category. For other buried structures such as mat foundations, even if the superstructure is excluded from the model, the ELFP is not recommended. However, the seismic base shear calculated for the superstructure must be considered during the design of the foundation. A more elaborate dynamic analysis such as time history analysis would be appropriate for such structures.

2.4.13 Order of Load Cases in the STAAD.Pro Input File STAAD.Pro has a peculiar requirement that the ELFP cases be the first set of load cases in the model. They can be called by any number—5 or 6 or 1201, and so on—but they must appear before the dead, live, and other primary cases. Consequently, the order of load cases must look like this: LOAD 5 LOADTYPE Seismic TITLE SEISMIC X IBC LOAD X 0.75 PERFORM ANALYSIS CHANGE LOAD 6 LOADTYPE Seismic TITLE SEISMIC Z IBC LOAD Z 0.75 PERFORM ANALYSIS CHANGE LOAD 1 LOADTYPE Dead TITLE SELF WEIGHT SELFWEIGHT Y -1 LOAD 2 LOADTYPE Dead TITLE DEAD LOAD MEMBER LOAD 3 TO 10 13 16 TO 18 29 TO 40 UNI GY -0.02 LOAD 3 LOADTYPE Live TITLE LIVE LOAD MEMBER LOAD 3 TO 10 13 16 TO 18 29 TO 40 UNI GY -0.125 LOAD COMB 4 1.2SW+1.2DL+1.6LL 1 1.2 2 1.2 3 1.6 PERFORM ANALYSIS CHANGE

If the sequence is violated, that is, if a load case containing non-seismic load content is sequentially specified before the seismic cases, a warning as shown in Fig 2.4.16 will be displayed in the output file. ** ERROR: IBC LOAD CASES MUST BE DEFINED BEFORE ANY OTHER LOAD CASE. **

Note that this is only due to a limitation of the program and is not based on any engineering requirements for seismic analysis.

FIGURE 2.4.16 Warning in output file regarding sequence of seismic load cases

Related Question: The following warning appears in the output file when I run the analysis for a model with IBC 2003 load cases. **WARNING: IF THIS UBC/IBC ANALYSIS HAS TENSION/COMPRESSION OR REPEAT LOAD OR RE-ANALYSIS OR SELECT OPTIMIZE, THEN EACH UBC/IBC CASE SHOULD BE FOLLOWED BY PERFORM ANALYSIS & CHANGE.

FIGURE 2.4.17 Warning in output file regarding analysis for seismic load cases

Answer: In the example shown earlier, the PERFORM ANALYSIS and CHANGE commands are

specified after both the ELFP cases. Instead, if a single analysis command is specified at the end of all the load cases, the aforementioned warning message appears in the .ANL file. This warning too is due to a limitation of the program and is not based on any engineering requirements for seismic analysis. The intent of this warning is the following. In STAAD.Pro, when you analyze a model containing IBC, NRC, AIJ, IS 1893, and various other seismic loads, the program has to first generate lateral loads per the rules of that code. If subsequently, there are other load cases which refer to the aforementioned cases through the means of a REPEAT LOAD command, as in Cases 21 and 22 in the following example, LOAD 1 IBC LOAD X 1.0 LOAD 2 IBC LOAD Z 1.0 LOAD 3 GRAVITY SELF Y -1.0 LOAD 4 LIVE MEMBER LOAD .. .. LOAD 21 DEAD + SEISMIC IN X REPEAT LOAD 1 1.0 3 1.0 LOAD 22 DEAD + SEISMIC IN Z REPEAT LOAD 2 1.0 3 1.0

then, load cases 21 and 22 must have access to the lateral load values generated in Cases 1 and 2, respectively. This means that STAAD.Pro must be instructed to retain those generated load values. If not, it will simply “forget” those load values once it has finished processing Cases 1 and 2. Consequently, Cases 21 and 22 will not reflect any effects of the seismic loads. Another instance where STAAD.Pro needs to remember those generated lateral loads due to seismic cases is when a re-analysis has to be done following a member selection in steel design, as in LOAD 1 IBC LOAD X 1.0 LOAD 2 IBC LOAD Z 1.0 LOAD 3 GRAVITY SELF Y -1.0 LOAD 4 LIVE MEMBER LOAD .. PERFORM ANALYSIS PARAMETER CODE AISC ..

SELECT ALL PERFORM ANALYSIS

The analysis instruction that follows the SELECT ALL command is called re-analysis. During re-analysis, all previously defined load cases are re-analyzed using the member properties which resulted from the member selection. The warning message we saw earlier is merely intended to remind us of these facts. The means by which we can tell STAAD.Pro that it has to “remember” the generated load values is to specify a PERFORM ANALYSIS and CHANGE commands following those individual seismic cases, as shown in the following example. LOAD 1 IBC LOAD X 1.0 PERFORM ANALYSIS CHANGE LOAD 2 IBC LOAD Z 1.0 PERFORM ANALYSIS CHANGE LOAD 3 GRAVITY SELF Y -1.0 LOAD 4 LIVE MEMBER LOAD .. LOAD 5 .. LOAD 21 DEAD + SEISMIC IN X REPEAT LOAD 1 1.0 3 1.0 LOAD 22 DEAD + SEISMIC IN Z REPEAT LOAD 2 1.0 3 1.0 PERFORM ANALYSIS CHANGE

This will ensure that the warning message does not appear.

2.4.14 Understanding the Results Related Question: Where can I find the base shear calculated by the program for the seismic load cases? Answer: The base shear and some of the associated key values for seismic analysis are reported in the STAAD.Pro output file. A few examples for some of the widely used codes are shown.

FIGURE 2.4.18 Key output for seismic load based on IBC 2006

FIGURE 2.4.19 Report in the output file for seismic load based on NBCC NRC 2005

FIGURE 2.4.20 Report in the output file for seismic load based on IS 1893 (Part 1)-2002

2.4.14.1 Additional Information for PRINT STATICS CHECK If the keywords PRINT STATICS CHECK are used with the PERFORM ANALYSIS command, as in, PERFORM ANALYSIS PRINT STATICS CHECK

some additional information is reported in the output file. It contains the net lateral forces generated as a result of the seismic load along that direction and the moment about the origin as a result of those forces (see Fig 2.4.21).

FIGURE 2.4.21 Additional information provided with STATICS CHECK output

2.4.14.2 Obtaining a Report of the Lateral Loads and Accidental Torsion Moments Related Question: I am able to view the load icons and values for all load cases except the seismic load case. Please tell me how I can get the loads for the seismic cases to appear on the screen. Answer: Seismic load cases based on the ELFP are different from other load cases in that the loads are generated by the program at the end of one cycle of analysis. This is because, to calculate the lateral forces, the period of the structure by the Rayleigh method is required, which in turn requires joint displacements of the displaced structure. Thus, seismic analysis is a two-part analysis. In the first part, the structure is analyzed for a static force generated from a 1g base acceleration along global X or global Z as the case may be. Using the displacements computed for those forces, the Rayleigh frequency is calculated, following which the lateral forces and accidental torsions are generated. The structure is then analyzed for those lateral forces and moments. Hence, viewing of the generated loads either in the output file or in the GUI is possible only after the analysis. Specify the words PRINT LOAD DATA with the ANALYSIS command, as in the following example. PERFORM ANALYSIS PRINT LOAD DATA

FIGURE 2.4.22 Keywords required for obtaining the lateral load report

A report that consists of the force and torsional moment at each of those nodes where the lateral load is generated is created in the output file. The total of those lateral loads and torsion at each level will also be reported. A sample output is shown in Figures 2.4.23 and 2.4.24. The output file can be viewed by going to File -> View -> Output File -> STAAD Output from the GUI.

FIGURE 2.4.23 Generated lateral loads report in the .ANL file

FIGURE 2.4.24 Aggregate of forces and moments from the generated lateral loads

2.4.15 Viewing the Generated Loads in the GUI To view the generated forces and moments in the GUI, the steps are: After running the analysis, go to the View menu, choose Structure Diagrams. Click the Loads and Results tab. Select the load case corresponding to the IBC load command. Switch on the checkbox for Loads, click OK. Or Choose the seismic load case as your active load case from the drop-down list. If you do not see the load arrows, press the load icon in the toolbar. Press “SHIFT+V” on the keyboard and you will have the magnitudes displayed for the generated forces.

FIGURE 2.4.25 Viewing the generated loads in the GUI

If the generated loads are too small in magnitude, they may not be visible on the screen. In that case, use the Scales tab to modify the scale in which the load arrows are drawn.

FIGURE 2.4.26 Adjusting the scale of the load icons displayed in the GUI

Related Question: We are required to analyze our model for loads generated according to a seismic code that is currently not implemented in STAAD.Pro. However, many of the rules of that code are similar to IBC, but some differences are there in the rules for computing accidental torsion. So, we plan to generate the lateral forces using STAAD.Pro’s IBC load generator and then

calculate the torsional moments using formulas we have typed into an Excel sheet. So, we need to be able to: 1. Extract the STAAD.Pro-generated seismic lateral loads and bring it into our Excel sheet. 2. 2.Put back the torsion into the STAAD.Pro model. Can you suggest a way? Answer: Here is a simple way to extract the STAAD.Pro-generated lateral forces for the IBC load case. As we saw in the previous question, specify the command PRINT LOAD DATA along with the PERFORM ANALYSIS command. Run the analysis. Go into the output file and scroll down to the pages where the generated lateral forces and torsional moments (if any) are listed. Copy and paste that data from the output file to your Excel sheet. As the data may not be in the format you want, you may need to insert them first in an intermediate text file or Excel sheet, edit it so the forces are arranged in the format you want, and then transfer it to your Excel sheet containing the equations for calculating the accidental torsion. After you calculate the torsion, that data needs to be transferred back to the STAAD.Pro model. Make a copy of your STAAD.Pro input file (call it File B for easy reference), so your original file is left unchanged. In File B, delete the IBC load commands. Then, from the Excel calculation sheet, copy the lateral forces and torsional moments and paste them into File B. In other words, you have replaced the commands for generating the seismic forces and moments with the actual lateral forces and torsion moments that the structure will be analyzed for. Related Question: Can the IBC LOAD be applied along the Y (vertical) direction? Answer: No. The Vertical Seismic Load Effect described in Section 12.4.2.2 of ASCE 7-05 is not implemented in STAAD.Pro. However, if you examine Equation 12.4-4, which is E v = 0.2 * Sds * D where D is the Dead load, and Sds is the design spectral response acceleration parameter at short periods obtained from Section 11.4.4 of ASCE 7-05, it is apparent that this can be easily achieved using a simple static load case defined using the following command LOAD 11 REPEAT LOAD n1 f1

where n1 is the load case number corresponding to the dead load case defined as a primary load with factor of 1.0, and f1 is equal to 0.2 * Sds. In the following example, load case 11 corresponds to E h, and load case 12 corresponds to E v. For E v, load case 12 is based on the equation shown in Section 12.4.2.2 of ASCE 7-05. For E h, load case 11 is based on Sections 12.8.3 and 12.8.4 of ASCE 7-05. DEFINE IBC LOAD ZONE ………

SELFWEIGHT JOINT WEIGHT 624 WEIGHT 200 LOAD 11 Seismic Lateral Effect IBC LOAD X 1 LOAD 12 Seismic Downward Effect SELFWEIGHT Y -0.2 624 WEIGHT -40

2.4.16 Structures with Weights and Stiffness Below their Support Elevation Related Question: I encounter the following error message when analyzing a model per UBC 1997. **ERROR- STRUCTURE HAS NO WEIGHT ABOVE THE BASE FOR UBC ANALYSIS. NUMBER OF LEVELS IN STRUCTURE = 1

FIGURE 2.4.27 Warning in the output file for structures in a single horizontal level

The structure looks like that shown in Fig 2.4.28.

FIGURE 2.4.28 Single-level structures

Answer: Although the error message has been reported in the context of analysis per UBC 1997, it is a generic message that pertains to all codes that are based on the ELFP method. Let us look at the reason, and we will use IBC 2006/ASCE 7-05 as the reference. In Section 12.8.3 of ASCE 7-05, we will find that it contains equations that describe how the shear at the base of the structure has to be distributed among the various levels of the structure. Those equations contain the term h, which is the height of any given level above the base. This implies that the ELFP described in IBC 2006 (which in turn refers to Section 12.8 of ASCE 7-05) is to be applied only on those structures whose geometry consists of various levels and floors. The supports of the structure must all be at the lowest level; h for any level would then be measured above the supports. Your model has only one level which is just the foundation mat alone. So, all the entities—plates and nodes—are at just a single elevation; h is hence zero, and the lateral forces cannot be computed using Equations 12.8-11 and 12.8-12 of ASCE 7-05. Unless you include the columns and beams of at least one or more floors and make the model resemble a frame having distinct Y coordinates, seismic analysis per the IBC 2006 or UBC 1997 cannot be performed.

FIGURE 2.4.29 Unsuitability of single-level structures for seismic analysis

The message in the STAAD.Pro output file indicates this fact.

2.5 Notional Loads 2.5.1 Introduction The expression Notional Loads owes its origin to design codes that use the term to signify a lateral force (horizontal force) that the building should be analyzed for. AISC 360-05, for example, defines it as a Virtual load applied in a structural analysis to account for destabilizing effects that are not otherwise accounted for in the design provisions. Appendix 7 of AISC 360-05 requires structures to be analyzed for notional loads when the Direct Analysis method is used. In Appendix Y, Section 7.2 of the code, the following is mentioned: Notional loads shall be applied to the lateral framing system to account for the effects of geometric imperfections, inelasticity, or both. Notional loads are lateral loads that are applied at each framing level and specified in terms of the gravity loads applied at that level. In the British code BS5950-2000, in Section 1.5.1, it is mentioned that the structure must be analyzed for a notional horizontal force equal to 0.5% of the vertical force to account for possibilities such as potentially misaligned members. In STAAD.Pro too, notional loads are a mechanism by which a lateral load can be applied on the structure. They are a form of load generation in that the program creates these loads in the horizontal directions (X and Z) from pre-assigned loads acting along the vertical (global Y) direction, by multiplying the vertical loads by a user-specified fraction. The value of the fraction in building codes tend to be in the range of 0.1 to 0.5%. Required reading 13. Technical Reference manual—Sections 1.18.2.1.4, 5.31.7, and 5.32.14 14. Graphical Interface Help manual—Section 2.3.7.8

2.5.2 Description

Notional loads were introduced in STAAD.Pro primarily to cater to the requirements of Direct Analysis as described in Appendix 7 of AISC 360-05. The manner in which it is specified for that analysis is described in Section 1.5 of Part III.

2.5.2.1 Under the Hood When there is an instruction to create a notional load, the lateral loads are created in the following manner. 1. The program determines the lumped weight at the various nodes of the structure from the vertical loads that the notional loads are a function of. For example, when we declare the notional load as 7 X 0.002, the program first generates the vertical weights (in the global Y direction) at all the nodes of the structure from the loading data we specified in case 7. 2. The nodal weights obtained in Step 1 are then multiplied by the notional load factor. The resulting value is applied along the direction that we want the notional load to act in. In this example, the vertical weights lumped at the nodes are multiplied by 0.002, and the results are then applied at the same respective locations along the global X direction. Thus, at every joint in the model where a lumped weight is created from the underlying vertical loads, a lateral force will also be created. In the model, if all the entities meeting at a node are truss members in a single plane, and the lateral loads are orthogonal to that plane, they will be a source of instability and “lost loads.” Almost always, selfweight happens to be one of the load items of the underlying vertical loads. For entities with a support at one of their nodes, such as columns or braces originating from the support level, as half their weight is lumped at the bottom node, a notional load will be created at the support node too.

2.5.3 Assigning Notional Loads Using the STAAD.Pro GUI To assign Notional Loads, we first need to go to the General - Load and Definitions page. Under the New Load Items dialog box, it is one of the sub-items under Repeat Load, as shown in Fig 2.5.1.

FIGURE 2.5.1 Dialog box in the STAAD.Pro GUI for adding notional loads to a load case

2.5.4 Syntax of the Notional Loads Specification in the STAAD.Pro Editor The following are some examples showing the command language used for specifying notional loads in the STAAD.Pro input file. Example 15: Notional loads in an independent load case LOAD 1 FACTORED DL SELF Y -1.4 LOAD 2 FACTORED LL MEMB LOAD 11 TO 16 UNI GY -2.8 11 TO 16 UNI GY -5.1 LOAD 3 NOTIONAL LOAD (+NLX) NOTIONAL LOAD 1 X 0.005 2 X 0.005

Example 16: Notional loads in conjunction with REPEAT LOADS LOAD 1 FACTORED DL SELF Y -1.4 LOAD 2 FACTORED LL MEMB LOAD 11 TO 16 UNI GY -2.8 11 TO 16 UNI GY -5.1 LOAD 100 REPEAT LOAD 1 1.0 2 1.0 NOTIONAL LOAD

1 X 0.005 2 X 0.005

Example 17: Notional loads in conjunction with REFERENCE LOADS LOAD 12 REFERENCE LOAD R1 1.2 R2 1.0 R4 -1.6 NOTIONAL LOAD R1 Z -0.0024 R2 Z -0.002

Example 18: Combining notional load cases with other primary load cases LOAD 1 FACTORED DL SELF Y -1.4 LOAD 2 FACTORED LL MEMB LOAD 11 TO 16 UNI GY -2.8 LOAD 3 NOTIONAL LOAD (+NLX) NOTIONAL LOAD 1 X 0.005 2 X 0.005 LOAD 100 REPEAT LOAD 1 1.4 2 1.4 3 1.4

Example 19: Load combinations of gravity loads and notional loads LOAD 1 SELFWEIGHT Y -1.0 FLOOR LOAD YRANGE 8.9 9.1 FLOAD -0.5 LOAD 7 NOTIONAL LOAD 1 0.002 LOAD COMB 109 DL + NOTIONAL LOAD (X) 1 1.0 7 1.0

2.5.5 Using the GUI to Automatically Create Combination Cases Involving Notional Loads Creating the numerous combination cases required by the building codes is a laborious task if it has to be done manually, one at a time, either using the GUI or with the editor. The STAAD.Pro GUI contains a facility that automates this task (with a few clicks of the mouse) and this is explained in Section 3.1. Notional loads too can be included in these combination cases using this feature. The dialog box in the STAAD.Pro GUI that enables this is shown in Fig 2.5.2 and the sequence of mouse clicks is marked.

FIGURE 2.5.2 Dialog box in the STAAD.Pro GUI for creating combination cases containing notional loads

Related Question: Can we assign the notional load in X and Z directions in a single load case? Answer: Yes. See the following example. LOAD 12 REFERENCE LOAD R1 1.2 R2 1.0 R4 -1.6 NOTIONAL LOAD R1 Z -0.0024 R2 Z -0.002 NOTIONAL LOAD R1 X -0.0024 R2 X -0.002

Note that as the principle behind notional loads involves creating a lateral load that is a function of a vertical load, it does not make sense to specify notional loads which are based on non-vertical loads such as wind, seismic, braking or friction forces, and temperature loads.

2.5.6 Obtaining a Report of the Lateral Loads Created by Notional Loads The lateral loads that the program generates can be seen in the output file. Specify the PRINT LOAD DATA command with the analysis command. For example, PERFORM DIRECT ANALYSIS PRINT LOAD DATA

The values will be reported in the output file as shown in Fig 2.5.3.

FIGURE 2.5.3 Keywords required for obtaining the lateral load report

2.5.7 Viewing the Generated Lateral Loads in the STAAD.Pro GUI The lateral loads that are generated can be viewed after the analysis is performed, not before. This is because, they are created from the load vector (matrix) of the constituent vertical loads, which is not assembled until the stiffness analysis takes place. To view the loads, click on the load icon as shown in Fig 2.5.4.

FIGURE 2.5.4 Displaying the lateral loads generated from the notional load case

Since the magnitude of each concentrated force is very small, the scale of the Point Loads item in View-Structure Diagrams-Scales, as shown in Fig 2.5.4, may need to be adjusted. Also, if the load values are to be displayed on the screen, it may be necessary to use a smaller unit such as pounds or Newtons, else the value may be displayed as 0. Related Question: When I try to create a notional load using the following commands, LOAD 1 LOADTYPE None TITLE LOAD CASE 1 SELFWEIGHT Y -1 ELEMENT LOAD 49 TO 60 PR GY -1.2 NOTIONAL LOAD 1 Z .003

I get an error message in the STAAD.Pro output file. **ERROR- CASE BEING FACTORED DOES NOT EXIST OR IS THE CURRENT CASE. CASE= 1

Answer: The notional load cannot refer to the very load case within which it is contained. In the example shown in the aforementioned question, the notional load is based on the vertical load of Case 1, but is also contained in Load Case 1, and that is not permitted. So, there are two ways to rectify this. Method 1 LOAD 1 LOADTYPE None TITLE LOAD CASE 1 SELFWEIGHT Y -1 ELEMENT LOAD 49 TO 60 PR GY -1.2 LOAD 2 LOADTYPE None TITLE LOAD CASE 2 REPEAT LOAD 1 1.0 NOTIONAL LOAD 1 Z 0.003

Method 2 DEFINE REFERENCE LOADS LOAD R1 LOADTYPE None TITLE LOAD CASE 1 SELFWEIGHT Y -1 ELEMENT LOAD 49 TO 60 PR GY -1.2 END DEFINE REFERENCE LOADS LOAD 1 REFERENCE LOAD R1 1.0 NOTIONAL LOAD R1 Z 0.003

In both these alternatives, the notional load resides in one case, but the weights that it is based on are in another case.

CHAPTER 3

Combining Load Cases 3.0 Combining Load Cases 3.0.1 Introduction In Chapter 1, it was mentioned that primary load cases can be created in two ways: (a) the load items are explicitly specified by the user and (b) the load items are generated using the program’s load generation capabilities. In this chapter, we look at the different ways in which these primary load cases can be combined to create combination cases.

3.0.2 Discussion For the purpose of this discussion, consider the following primary load cases. UNIT KNS METER LOAD 1 GRAVITY SELFWEIGHT Y -1.0 LOAD 2 IMPOSED LOAD MEMBER LOAD 2 TO 8 UNI GY -2.5 JOINT LOAD 35 TO 45 FY -12 LOAD 3 LIVE LOAD FLOOR LOAD YRANGE 2.9 3.1 FLOAD -4.0 XRANGE -1 12 ZRANGE -1 26

Let us suppose that we are interested in knowing the effect of load cases 1, 2, and 3 acting simultaneously. Let us also assume that appropriate load factors need to be applied as required by the building code. There are two methods in STAAD.Pro for doing this. 1. LOAD COMBINATION method 2. REPEAT LOAD method These methods are explained in detail in Section 3.1. We also look at a third type of combination case known as the REFERENCE LOAD type. This is described in Section 3.2.

3.1 Repeat Loads and Load Combinations 3.1.1 Introduction In this chapter, we look at the methods for combining load cases using the REPEAT LOAD and LOAD COMBINATION commands. Required reading 1. Technical Reference manual—Section 5.32.11 Repeat Load Specification and Section 5.35 Load Combination Specification 2. Application Examples manual—Examples 1, 4, 8, 9, 11, 21, 24, 25, and 29 3. Graphical Interface Help manual: Section 1.4 Fundamentals—Load Types in STAAD.Pro Section 2.3.7.12.4 Commands -> Loading -> Load Combination … Section 2.3.7.12.5 Commands -> Loading -> Automatic Load Combination …

FIGURE 3.1.1 Section 1.4 of the STAAD.Pro GUI manual

3.1.2 Discussion For the purposes of this discussion, the example shown in Section 3.0 is used here. UNIT KNS METER LOAD 1 GRAVITY SELFWEIGHT Y -1.0 LOAD 2 IMPOSED LOAD MEMBER LOAD 2 TO 8 UNI GY -2.5 JOINT LOAD 35 TO 45 FY -12 LOAD 3 LIVE LOAD FLOOR LOAD YRANGE 2.9 3.1 FLOAD -4.0 XRANGE -1 12 ZRANGE -1 26

Recall that we are interested in knowing the effect of load cases 1, 2, and 3 acting simultaneously after the appropriate load factors are applied as required by the building code.

3.1.2.1 The REPEAT LOAD Method Repeat loads are a means by which a new load case can be created and populated with load items (Joint Loads, Member Loads, Element Loads, etc.) using data contained in previously specified primary load cases. So, in a sense, the program internally uses a copy–paste mechanism for fetching load items from prior load cases to build a new one, with the advantage that it allows factoring of that data. Factoring means these load items can be increased or decreased by a user-defined magnitude. The advantage of this feature is that if the loading data are organized in the STAAD.Pro model into load types, such as Dead Load, Live Load, and Wind Load, then the engineer can combine them later without having to laboriously re-enter all those load items into a combination load case. Let us say that we are combining load cases 1, 2, and 3 described in the aforementioned example

to create load case 11. The command syntax that has to be used in the STAAD.Pro input file is LOAD 11 Combining Load cases 1, 2 and 3 REPEAT LOAD 1 1.2 2 1.4 3 1.3

In this example, we are instructing the program to assemble a new load case called 11. If we imagine load case 11 to be a bucket, the REPEAT LOAD method involves filling this bucket with the following ingredients: Take the contents of load case 1, multiply them by 1.2, deposit them into the bucket Take the contents of load case 2, multiply them by 1.4, add them into the bucket Take the contents of load case 3, multiply them by 1.3, add them into the bucket Note that this operation is equivalent to specifying load case 11 in the following manner: UNIT KNS METER LOAD 11 (1.2*GRAVITY + 1.4*IMPOSED + 1.3*LIVE) SELFWEIGHT Y -1.2 MEMBER LOAD 2 TO 8 UNI GY -3.5 JOINT LOAD 35 TO 45 FY -16.8 FLOOR LOAD YRANGE 2.9 3.1 FLOAD -5.2 XRANGE -1 12 ZRANGE -1 26

By using the REPEAT LOAD command, we are instructing STAAD.Pro to do a load gatheringfactoring-assembling operation. It saves us the trouble of needless amount of typing, or manually copying and pasting, of load data, which has already been specified in prior load cases. Yet another definition of a primary load case is that a load vector (or a matrix {P} as we call it) is created internally by STAAD.Pro. In that sense, a combination case based on the REPEAT LOAD syntax is also a primary load case. The procedure for creating a load case containing repeat loads using the STAAD.Pro GUI is shown in Fig 3.1.2.

FIGURE 3.1.2 Dialog box in the STAAD.Pro GUI for creating REPEAT LOAD cases

3.1.2.1.1 How Does the Program Calculate the Displacements for a REPEAT LOAD Case? If we use the example of load case 11, the program creates a load vector (matrix with one column) called, for example, {P11}. The displacements for that case are computed by solving the matrix equation [Kinv]{P11} where [Kinv] is the inverted stiffness matrix. Limitation The REPEAT LOAD command cannot be used with certain types of load cases such as response spectrum, time history, and others associated with dynamic analysis. 3.1.2.1.2 Other Ways to Use the REPEAT LOAD Command The REPEAT LOAD command is useful in other ways too. Look at the following example: LOAD 1 DEAD SELF Y -1.4 MEMB LOAD 11 TO 16 UNI GY -2.8 LOAD 2 .75(DEAD + WIND) REPEAT LOAD 1 0.75 JOINT LOAD 15 16 FZ 8.5 11 FZ 20.0 12 FZ 16.0 10 FZ 8.5

In load case 2, we are performing two tasks:

1. Explicitly define some load items in the form of joint loads along global Z. 2. Instruct the program to fetch the vertical loads from load case 1. The second task is done through the REPEAT LOAD command with a factor of 0.75 on load case 1. Related Question: Can a REPEAT LOAD case have another REPEAT LOAD case as a component? For example, can load case 41 be a REPEAT LOAD case in the following example? LOAD 101 REPEAT LOAD 1 1.0 41 1.0

Answer: Yes it can. For example, LOADING 1 SELFWEIGHT Y -1.0

load 2 repeat load 1 1.0 JOINT LOAD 4 5 FY -15. ; 11 FY -35.

load 3 repeat load 2 1.0 MEMB LOAD 8 TO 13 UNI Y -0.9 ; 6 UNI GY -1.2

So, load 3 is equivalent to load 4 SELFWEIGHT Y -1.0 JOINT LOAD 4 5 FY -15. ; 11 FY -35. MEMB LOAD 8 TO 13 UNI Y -0.9 ; 6 UNI GY -1.2

3.1.2.2 The LOAD COMBINATION Method For models in which there is no nonlinearity in the system being solved, the combination exercise can be performed on the results of the primary load cases. In other words, instead of combining factored loads, we just combine the factored results of those individual loads. By results, we refer to joint displacements, support reactions, member end forces, element stresses, and so on. To do this, use the syntax LOAD COMBINATION nn as shown in the following example:

LOAD COMBINATION 11 Combining Load cases 1, 2 and 3 1 1.2 2 1.4 3 1.3

Using the aforementioned bucket analogy, the following happens in this case: Take the results of load case 1, multiply them by 1.2, deposit them into the bucket Take the results of load case 2, multiply them by 1.4, add them into the bucket Take the results of load case 3, multiply them by 1.3, add them into the bucket Hence, the program has no need to know the load items that constitute this load case. It just needs to know the results of the constituent cases being combined. Thus, the structure is not actually analyzed for a combination load case (where the term “analysis” means the [Kinv]{P} operation). It may be apparent to the user that the phrase LOAD COMBINATION is a misnomer. A more appropriate phrase would have been RESULT COMBINATION. Unfortunately, this inexact phrase has been in STAAD.Pro for a long time, and for backward compatibility reasons, that name continues to exist. The procedure for creating a load case containing the LOAD COMBINATION syntax using the STAAD.Pro GUI is shown in Fig 3.1.3.

FIGURE 3.1.3 Dialog box in the STAAD.Pro GUI for creating load combination cases

3.1.2.3 Why Should the Difference in the Way STAAD.Pro Treats a REPEAT LOAD Case versus a COMBINATION LOAD Case Matter? Related Question: In Section 5.35 of the STAAD.Pro Technical Reference manual, Item (b) under Notes mentions that the LOAD COMBINATION command is inappropriate for a P-DELTA analysis. Why? Answer:

Normally, if we are doing a linear static analysis, and when nonlinear conditions do not exist, it should make no difference which of the two combination types we use. But in nonlinear situations, and for load-dependent structural geometries, because the principle of superposition (see Section 5.2 of Part I for details) is not valid, combination cases based on the LOAD COMBINATION nn syntax should not be used. The expression that defines the invalidity of this principle is (Results of Load A) + (Results of Load B) is not equal to (Results of Load (A + B)). So, nodal displacements have to be evaluated for the combination case using matrix multiplication [Kinv]{P}, and hence that case has to be based on the REPEAT LOAD syntax. These displacements should then form the basis for calculating member forces, support reactions, plate and solid stresses, and so on. The P-DELTA effect (referred to in the previous question) results from the interaction of the vertical load and the lateral load. This requires both load items to act on the structure simultaneously. And the only way to make them act simultaneously is to get the program to compute the displacement with both loads being present in a single load case. A REPEAT LOAD case achieves that. A COMBINATION load case does not. An example of the difference between linear and nonlinear situations brought about by a loaddependent structure geometry is described in Section 5.2 of Part I in connection with the MEMBER TENSION attribute.

FIGURE 3.1.4 Command syntax for combination load cases for load-dependent structural configuration

Examples of nonlinear conditions are: 1. 2. 3. 4. 5. 6. 7. 8. 9.

Member tension and member compression Spring tension and spring compression Plate Mat with compression-only springs Elastic Mat with compression-only springs P-DELTA analysis Direct analysis per the AISC 360-05 and AISC 360-10 codes Multilinear spring support Nonlinear analysis Nonlinear cable analysis

To summarize, In the REPEAT LOAD method, the entities being combined are previously defined primary load cases. In the LOAD COMBINATION method, the entities being combined are the results of the

primary load cases that were solved. If nonlinear conditions exist, LOAD COMBINATION is not the appropriate combination method; REPEAT LOAD is. REPEAT LOAD command can also be used in linear situations. In such situations, REPEAT LOAD command will produce the same results as an equivalent LOAD COMBINATION command. Example 1 Let us say that there are two load cases 1 and 2 for which the displacement at joint 252 along X is 21 mm and 18 mm, respectively. Now, let us consider the following two combination cases. LOAD 31 REPEAT LOAD 1 1.4 2 1.6

LOAD COMBINATION 32 1 1.4 2 1.6

In both cases, the same two load cases are being combined using the same factors. For combination case 32, the result is predictable. It will be 21 * 1.4 + 18 * 1.6 = 29.4 + 28.8 = 58.2 mm. For a linear analysis, and when no nonlinear conditions such as MEMBER TENSION or SPRING COMPRESSION cases are present, load case 31 will also produce 58.2 mm at Node 252. However, for a nonlinear type of analysis, such as the P-DELTA analysis, or when nonlinear conditions such as those mentioned previously are present with a linear analysis, the displacement for load case 31 is very likely to be different from 58.2 mm, and so is the case with member forces, support reactions, and plate stresses.

3.1.2.4 Why Not Use Repeat Loads (or Reference Loads) All the Time? There are certain types of load cases such as dynamic cases—response spectrum, time history, and so on—that do not work with the REPEAT LOAD syntax. Another downside is that repeat loads require some additional analysis efforts compared with LOAD COMB, so run-times may be somewhat longer. But except for large models, this may be a negligible effect. So, whenever possible, use repeat loads. It is important to note that there are instances where LOAD COMB is a perfectly legitimate method of obtaining combined results. If the model does not have any nonlinearities, if a linear elastic analysis is being performed, and if superposition is valid, then LOAD COMB provides an analytically efficient way to obtain results without performing any unnecessary analysis. LOAD COMB also comes with some added features such as the SRSS (square root of sum of squares) and ABS (absolute) types of combination, which are not available with the REPEAT LOAD syntax. Related Question: How do I create the following combination?

1.2(0.9D-EQX) where D is dead load and EQX is seismic along X. Answer: 1.2(0.9D-EQX)

reduces to 1.08 * Load case 1 – 1.2 * Load case 7

If we assume that the Dead Load case is load case 1, and the earthquake load case is load case 7, then the commands for the two methods will be as shown in the following table.

FIGURE 3.1.5 Comparison of command syntax for the two combination methods

Related Question: I had created a number of combination cases using the LOAD COMBINATION syntax but realized that because I will be doing a P-DELTA analysis, I need to change them all to the REPEAT LOAD syntax. Is there a way without deleting them all and starting all over? There are more than 45 cases to convert. Answer: A simple way to convert a LOAD COMBINATION to REPEAT LOAD would be to do it using the STAAD.Pro editor, which can be accessed by going to the Edit menu and choosing the Edit Input Command File. You can also use any other editor such as Notepad or WordPad. Make the changes as suggested next. For example, the commands LOAD COMBINATION 101 1 1.4 4 1.7

should be changed to LOAD 101 REPEAT LOAD 1 1.4 4 1.7

3.1.2.5 Load Combination of Other Combination Cases

Recently, there has been an enhancement to the LOAD COMBINATION syntax. The load cases that are being combined can now be other combination cases (specified previously) with the LOAD COMBINATION syntax. Example 2 LOAD COMB 31 1 1.0 2 1.0 LOAD COMB 32 3 0.75 4 0.75 LOAD COMB 34 31 1.0 32 1.0

Hence, LOAD COMBINATION 34 is the same as LOAD COMB 35 1 1.0 2 1.0 3 0.75 4 0.75

3.1.2.6 Dynamic Load Cases as Component Cases of REPEAT LOAD The load cases that are being combined through a REPEAT LOAD command must only be static load cases, not dynamic load cases such as response spectrum or time history. STAAD.Pro is not capable of handling response spectrum and time history load cases that are referred through a REPEAT LOAD command.

3.1.2.7 Creating Load Combination Cases—Manual versus Automatic The method described so far is the manual way of creating combination cases one at a time. By this, we mean that the responsibility of deciding which primary load cases and the load factors to use in the combination cases rests entirely upon the user. If a large number of combination cases have to be created, the manual way can be laborious. There is a simpler method for creating them, which is described next.

3.1.2.8 Automatic Generation of Combination Load Cases The STAAD.Pro GUI provides a facility for automatic generation of load combination cases. The load types and load factors described in well-known American (ACI, AISC, UBC, and IBC or ASCE 7), British, Canadian, and other building codes for combining standard load types, such as DEAD, LIVE, WIND, and SEISMIC, are built into the program. In order for this feature to work, it is essential that the primary load case be assigned a load type, which we discussed in Section 1.1.2.

FIGURE 3.1.6 Assigning the loading type for generating load combination cases

If a type is not assigned, it will default to None, which will result in that load case being disregarded during the load combination generation phase. The steps involved in generating the load combinations are described in the STAAD.Pro documentation under the topic titled “Create Auto Load Combination Dialog” in the STAAD.Pro Graphical Environment section.

FIGURE 3.1.7 Pages of the STAAD.Pro GUI manual describing the automatic load combination generator

Related Question: What are the building codes for which the automatic load combination generator is available? Answer: This can be seen from the drop-down list box as shown in Fig 3.1.8. In STAAD.Pro V8i SELECT series 2 (Build 20.07.07.32), the load factors for the following codes are supplied with

the program: ACI 318-05 AISC 9th edition UBC 1997 IBC 2006 British NBCC 1995 & 2005 (Canadian) IS 875 (Indian) SNiP (Russian)

FIGURE 3.1.8 List of codes available in the STAAD.Pro GUI for load combination factors

By default, these combinations are created using the LOAD COMBINATION nn syntax. But in recent versions of STAAD.Pro, they can also be created using the REPEAT LOAD syntax. A checkbox is now available for this purpose as shown in Fig 3.1.9.

FIGURE 3.1.9 Using the automatic combination load cases generator to create REPEAT LOAD cases

A typical set of combination cases generated in this manner is shown in Fig 3.1.10.

FIGURE 3.1.10 LOAD COMBINATIONs generated using the Automatic generation facility

3.1.2.9 Editing the Tables Containing Factors for Automatic Load Combination Generation The built-in tables of load factors can now be altered by the user if he/she so chooses. Also, new codes containing their own definitions and factors can be created.

FIGURE 3.1.11 Menu in the STAAD.Pro GUI for editing the rules for automatic load combination generation

The details of this feature are explained in Section 2.3.7 Commands Menu -> Loading -> Definitions -> Edit Auto Load Rules -> Edit Load Rules for Auto Load Combination Generator Dialog of the STAAD.Pro GUI manual.

FIGURE 3.1.12 Page from the STAAD.Pro GUI manual for automatic combination generator

3.1.2.10 Combining the Results of Primary Load Cases Using the SRSS Method The examples we have seen so far for the LOAD COMBINATION syntax involve algebraic summation. LOAD COMBINATION SRSS means that the results of the individual load cases are combined using the SRSS method.

FIGURE 3.1.13 Dialog box in the STAAD.Pro GUI for creating the SRSS-type combination cases

There are two options available with this command. A. Where the SRSS procedure is applied on all the primary cases being combined. B. Where the SRSS procedure is applied on some of the primary cases and that result is then added to some other primary cases algebraically.

Hence, we could write it as Term A + Term B, where Term A = SRSS (Li, fi) for i = 1, m Term B = Algebraic (Lj, fj) for j = 1, n Example 3 LOAD COMBINATION SRSS 35 -7 0.75 8 1.3 13 2.42 0.67

The combination formula will be as follows:

FIGURE 3.1.14 Equation representing the SRSS type of load combination

where v is the combined value, and L7, L8, and L13 are the values from load cases 7, 8, and 13, respectively. In Section 5.35 of the STAAD.Pro Technical Reference manual, there are a number of examples that demonstrate this feature. Although the results of the individual component cases being combined will have proper signs (positive/negative), after the application of the SRSS procedure, the quantities that are associated with the square root term become positive and thus lose their sign. The results referred to are: Displacements at nodes Member end forces and member section forces Plate element stresses and moments Solid element stresses and moments One of the consequences of this method is that it destroys the static equilibrium that is inherent in the results of the individual cases which are being combined. The sign of the result is vital for checking static equilibrium at nodes and supports. For example, at a support node at the base of a column, the forces in the column member and the support reactions both need to have proper signs for them to be in equilibrium with each other. For example, let us assume that load cases 6, 7, and 8 are combined by the SRSS method. Let us say that the FY reaction from those cases are 13.5, −4.3, and 12.8 kip, respectively. If they are combined algebraically, we get 13.5 − 4.3 + 12.8 = 22 kip. If they are combined using the SRSS method, we get sqrt(13.2 * 13.2 + (−4.3) * (−4.3) + 12.8 * 12.8) = 18.8 kip. In the algebraic method, the summation of all the FY reactions at all supports for that combination case will match the applied load for that combination case. For the SRSS type of combination, it won’t. Also, the reaction at the support may not be in equilibrium with the forces at the end of members meeting at that support. The SRSS combination method also adversely affects the plots of member results such as shear force and bending moments. Due to these anomalies, they may appear to be erroneous but that is due to the nature of the SRSS method.

3.1.2.11 Combining the Results of Primary Load Cases Using the ABSOLUTE Method

This is a combination method where the results of the constituent cases are first factored and, then, their absolute values are combined.

FIGURE 3.1.15 Dialog box in the STAAD.Pro GUI for creating the ABSOLUTE-type combination cases

The word ABS needs to be included at the end of the phrase LOAD COMBINATION. For example, the following command means LOAD COMBINATION ABS 7 DL+LL+WL 1 0.85 2 0.65 3 2.12

A = 0.85 * Results of load case 1 B = 0.65 * Results of load case 2 C = 2.12 * Results of load case 3 Final result = ABS(A) + ABS(B) + ABS(C) Similar to the SRSS type of combination, the ABS (absolute) type of load combination also does not satisfy the principles of static equilibrium at nodes and supports. Consider, for example, the joint at the top of a portal frame with the shape of a football goal post. Let us examine a load case that contains a uniform distributed load applied on the top beam. At the top of the column, a compressive force will develop due to this load. As explained in Section 5.1 of Part III, a compressive force at the end of a member has a negative sign in the local coordinate system. At the start node of the beam, a shear acting along positive global Y will develop. Because it acts along positive local Y of the beam, it has a positive sign.

FIGURE 3.1.16 Portal frame with a uniform load on the beam

If an algebraic summation were to be performed at the top-left node, the negative column force will be equal in magnitude and hence cancel the positive shear on the beam. The net force at that joint will hence be zero thus satisfying static equilibrium. However, this requires a summation of the algebraic values. In an ABSOLUTE combination, when a summation of forces is performed at that node, the negative column force will be transformed into a positive number, which will be added to the shear force on the beam, which is also a positive number. The net result will be a positive value that, by virtue of not being zero, does not satisfy static equilibrium. A similar anomaly will be found at the support nodes when an equilibrium test is performed by comparing the absolute sum of the member end forces of all members meeting at that support with the support reactions over there. Another example that shows the lack of equilibrium between the applied loads and support reactions is shown next. In Fig 3.1.17, the reactions at the supports for two loading conditions are shown.

FIGURE 3.1.17 Portal frame under two loading conditions

In Fig 3.1.18, the values resulting from combining the reactions of the two cases are shown—for the ALGEBRAIC and the ABSOLUTE combination methods.

FIGURE 3.1.18 Support reactions for the two combination methods

Note that, in the latter, there is no equilibrium between the loads and reactions.

3.1.3 Summary A REPEAT LOAD case is a combination scheme in which the following steps are employed by the program internally to create a new primary load case: Fetch the load items from each of the constituent load cases Factor them with their respective load factors

Combine them. Loads created by the REPEAT LOAD syntax are treated as primary load cases and hence solved by STAAD.Pro by pre-multiplication with the inverted stiffness matrix. Cases created using the LOAD COMBINATION command are not solved in this elaborate way. Instead, results (displacements, forces, reactions, plate stresses, etc.) of their constituent cases are fetched, factored, and summed up using the algebraic, SRSS, or ABS methods as specified.

3.2 Reference Loads 3.2.1 Introduction As we have seen in Chapters 1 and 2, we can include several types of primary load cases in our model, such as Dead, Live, Wind, or Seismic. We then have combination load cases, which combine the individual primary cases using one of the two combination methods we have seen— REPEAT LOAD and LOAD COMBINATION. STAAD.Pro generates results for all load cases—primary as well as the combination types. There may be situations where we want the program to solve only some of them and not others. For example, from the standpoint of steel, concrete, or aluminum design, the only cases that will be of interest to us are the combination load cases. Hence, we want the results to be generated for only those cases. How can we instruct STAAD.Pro not to analyze the Dead, Live, and Wind cases? In this chapter, we examine the method to do that. That does not mean that solving primary cases is completely unnecessary. There may be situations where solving them is required for troubleshooting abnormal or erroneous results stemming from instability conditions or modeling errors. In linear elastic cases where the principle of superposition is applicable, it also helps us understand what portion of the structural response is associated with the individual component cases of the combination load case. Required reading 4. Technical Reference manual—Sections 5.31.6 and 5.33 5. Graphical Interface Help manual—Section 2.3.7.8 Loading

3.2.2 Discussion Before we examine what reference loads are, let us take a look at some primary load cases. Let us assume that there are three primary load cases as shown here. SUPPORTS 45 46 228 FIXED 448 FIXED 451 892 923 FIXED UNIT KIP FEET LOAD 1 D.L.- SELF WEIGHT SELFWEIGHT Y -1 LOAD 2 L.L. MEMBER LOAD

193 654 886 1096 1769 TO 1772 1829 1831 – 1838 1843 2346 2347 UNI GY -0.4 JOINT LOAD 605 FY -1.62 606 FY -1.9 LOAD 3 WIND W to E MEMBER LOAD 508 599 793 796 797 986 – 1098 TO 1100 1466 UNI GZ 0.37

In a typical STAAD.Pro model, these will be followed by other primary load cases and then by the combination cases (using the REPEAT LOAD syntax when non-linear conditions are involved). For this example, let us assume that there is only one combination case. LOAD 11 DL + LL + WL REPEAT LOAD 1 1.0 2 1.0 3 1.0

Following the combination case(s) will be the ANALYSIS command: PDELTA 30 ANALYSIS SMALLDELTA

In this example, load case 1 is a pure dead load case, load 2 is a pure live load case, and load case 3 is a pure wind load case. Such “pure” cases can be referred to as “component” load cases. In the real world, component load cases never act alone. Instead, several types of component cases act in tandem. For example, wind loads, or live loads, or seismic loads act in conjunction with gravity loads. That is why building codes require us to solve for combination loading cases. This brings up these questions—if a component case doesn’t act alone, why solve such a case? Isn’t that simply a waste of time and computing resources? Why not solve just the combination cases? Isn’t this particularly true in non-linear situations such as SPRING COMPRESSION where solving a component case such as WIND or SEISMIC can lead to a failure to converge? To solve this problem, a new feature was introduced in STAAD.Pro 2007 Build 01. It is called the REFERENCE LOAD. When a component load is defined under the heading “REFERENCE LOAD,” it is not solved. Instead, it serves as a building block for cases that are actually solved. A new type of combination case has also been introduced to facilitate this. There is an analogy between STAAD.Pro’s wind, moving, and seismic load generation, and the REFERENCE LOAD. In these generation cases, there is a definition block of data (DEFINE WIND LOAD, DEFINE MOVING LOAD, DEFINE SEISMIC LOAD etc. ) followed by the load cases where that information is actually referred to and applied on the model (e.g., WIND LOAD X 1.2, LOAD GENERATION 20, IBC X 1.0). REFERENCE LOAD too has a similar format. There is a definition block of data (DEFINE REFERENCE LOADs), followed by the actual usage of that data in a real combination case.

FIGURE 3.2.1 Dialog box in the STAAD.Pro GUI for creating reference load cases

If the data we saw earlier were to be specified using the REFERENCE LOAD syntax, it would be similar to that in the following example in two parts. Part 1 is the definition block where the information serves as the feeder data. Part 2 represents the combination load case, which uses the data from Part 1 to assemble a load case. Part 1 UNIT FEET KIP SUPPORTS 45 46 228 FIXED 448 FIXED 451 892 923 FIXED DEFINE REFERENCE LOADS LOAD R1 D.L.- SELF WEIGHT SELFWEIGHT Y -1 LOAD R2 L.L. MEMBER LOAD 193 548 589 654 886 1096 1734 1759 1760 1769 TO 1772 - 1829 1831 1838 1843 2346 2347 UNI GY -0.4 JOINT LOAD 605 FY -1.62 606 FY -1.9

LOAD R3 WIND W to E MEMBER LOAD 508 599 793 796 797 986 1098 TO 1100 1466 UNI GZ 0.37 END DEFINE REFERENCE LOADS

Part 2 LOAD 11 REFERENCE LOAD R1 1.0 R2 1.0 R3 1.0 PDELTA 30 ANALYSIS SMALLDELTA

Without REFERENCE LOADs, the three component cases will be solved individually, and then combination case 11 will be solved. In the approach that uses reference loads, only load case 11 will be solved. A reference load case is solved only when it is called in an actual load case as shown in load 11 in Part 2 of the aforementioned example. This way, we instruct the program to solve only a limited number of “real” load cases, which are the combination cases based on the REFERENCE LOAD syntax (Dead + Live, Dead + Live + Wind, etc.) as shown in Part 2. Hence, the time spent on solving the pure component-only load cases can now be avoided. Depending on the size of the model and the number of component-only cases, the savings in time could be substantial, not to mention avoiding creation of large amounts of unnecessary data for post-processing. This is ideal for P-DELTA ANALYSIS and many other situations where an element of nonlinearity is present, because of which we want only load case 11 to be solved. Here is the comparison table for the two methods, with the differences highlighted in boldface. REPEAT LOAD method UNIT KNS METER

REFERENCE LOAD method UNIT KNS METER

LOAD 1 GRAVITY LOAD

DEFINE REFERENCE LOAD

SELFWEIGHT Y -1.0

LOAD R1 GRAVITY LOAD SELFWEIGHT Y -1.0

LOAD 2 EQUIPMENT LOAD

LOAD R2 EQUIPMENT LOAD

MEMBER LOAD

MEMBER LOAD

23 TO 45 UNI GY -1.45

23 TO 45 UNI GY -1.45

JOINT LOAD

JOINT LOAD

121 TO 124 FY -15

121 TO 124 FY -15

LOAD 3 LIVE LOAD

LOAD R3 LIVE LOAD

FLOOR LOAD

FLOOR LOAD

YRANGE 2.9 3.1 FLOAD -2.7 XRA -1.0

YRANGE 2.9 3.1 FLOAD -2.7 XRA -1.0

25 ZRA -0.5 36

25 ZRA -0.5 36

LOAD 11 – 1.2 L1 + 1.3 L2 + 1.4 L3

LOAD 11 – 1.2 L1 + 1.3 L2 + 1.4 L3

REPEAT LOAD

REFERENCE LOAD

1 1.2 2 1.3 3 1.4

R1 1.2 R2 1.3 R3 1.4

PDELTA 20 ANALYSIS SMALLDELTA

PDELTA 20 ANALYSIS SMALLDELTA

LOAD LIST 11

LOAD LIST 11

PARAMETER

PARAMETER

CODE EC3

CODE EC3

…

…

Note: All the four cases—1, 2, 3, and 11—are solved.

Note: Only load case 11 is solved.

Observe that one of the differences is in the number that the load case is denoted with. Load cases that we saw earlier are numbered using positive integers—1, 2, 31, 101, and so on. Reference load definitions have the prefix “R” in front of those numbers. Hence, they are denoted R1, R2, R31, R101, and so on. To include the reference load sets in a load case using the STAAD.Pro GUI, we first need to go to the General-Load page. Under the New Load Items dialog box, it is one of the sub-items under Repeat Load (Fig 3.2.2).

FIGURE 3.2.2 Dialog box for adding reference load sets to a load case

Example 4: Combination of dead load and temperature load using reference load cases DEFINE REFERENCE LOADS LOAD R1 LOADTYPE Dead TITLE DEAD LOAD MEMBER LOAD 1 TO 6 UNI GY -10.72 1 TO 6 UNI GY -1.43

LOAD R2 LOADTYPE Temperature TITLE TEMPERATURE LOAD TEMPERATURE LOAD 1 TO 6 101 TO 134 201 TO 212 TEMP -15 END DEFINE REFERENCE LOADS LOAD 18 LOADTYPE None TITLE DEAD + TEMPERATURE REFERENCE LOAD R1 1.0 R2 1.0

3.2.3 Load Selection Drop-down List Box in the GUI The individual reference load cases described previously as constituting Part 1 of the input (R1, R2, R3, etc.) will not be displayed in the drop-down box that shows the available load cases in the model. Instead, only the combined cases described in Part 2 will be displayed (Fig 3.2.3).

FIGURE 3.2.3 Load selection box showing the combination cases

3.2.4 Editing the Individual Reference Cases Using the GUI If we want to modify the data of cases R1, R2, R3, and so on, using the GUI, it would have to be done from the General-Load page.

FIGURE 3.2.4 Editing the data in the individual reference cases

3.2.5 LOAD COMBINATION Syntax versus the REFERENCE LOAD Syntax The following example illustrates the manner in which the LOAD COMBINATION syntax can be replaced with the REFERENCE LOAD syntax. LOAD COMBINATION syntax LOAD COMB 101 0.9DL+1.5HL 1 0.9 2 0.9 6 0.9 10 0.9 11 0.9 16 0.9 17 0.9 19 0.9 20 0.9 - 22 1.5 23 1.5 24 1.5 25 1.5

REFERENCE LOAD syntax LOAD 101 0.9DL+1.5HL REFERENCE LOAD R1 0.9 R2 0.9 R6 0.9 R10 0.9 R11 0.9 R16 0.9 R17 0.9 R19 0.9 - R20 0.9 R22 1.5 R23 1.5 R24 1.5 R25 1.5

3.2.6 Load Generation and Reference Load Cases In Chapter 2, we saw various types of load generation facilities—wind, moving, seismic, and so on. These cannot be applied using reference load cases.

3.2.7 Using Reference Load Cases for Load-Dependent Structural Conditions Load-dependent conditions are those where the configuration of the structure varies from load case to load case. We have seen some instances of these—MEMBER TENSION/COMPRESSION, SPRING TENSION/COMPRESSION, and MAT FOUNDATION. In all these instances, the members or supports that are active/inactive may not be the same between any two load cases. Load-dependent structures are ideal situations for using reference load cases. For such models, the results of the individual component-only load cases have limited value and often do not tell us how the structure would behave under the combined loads. Also, it is for the component load cases that the iterations usually fail to converge. Example 5: Format of input for structure with tension-only members and reference load cases MEMBER TENSION 16 TO 27 DEFINE REFERENCE LOADS LOAD R1 GRAVITY SELFWEIGHT Y -1 .. LOAD R2 DEAD MEMBER LOAD ..

LOAD R3 LIVE JOINT LOAD .. LOAD R4 WIND JOINT LOAD ... END DEFINE REFERENCE LOADS LOAD 1 GRAVITY + DEAD REFERENCE LOAD R1 1.0 R2 1.0 LOAD 2 GRAVITY + DEAD + LIVE REFERENCE LOAD R1 1.0 R2 1.0 R3 1.0 LOAD 3 GRAVITY + DEAD + WIND REFERENCE LOAD R1 1.0 R2 1.0 R4 1.0 .. .. PERFORM ANALYSIS

Thus, the MEMBER TENSION, SPRING COMPRESSION, and ANALYSIS commands don’t have to be specified repeatedly. Example 6: Mat foundation with compression-only springs SUPPORTS 37 TO 356 PLATE MAT DIRECT Y SUBGRADE 12 PRINT COMPRESSION DEFINE REFERENCE LOADS LOAD R1 DEAD LOAD SELFWEIGHT Y -1 MEMBER LOAD 5 15 24 31 CON GY -2 ELEMENT LOAD 27 TO 30 33 TO 36 39 TO 42 45 TO 48 51 TO 54 57 TO 60 63 64 TO 66 69 TO 72 PR GY -0.9 LOAD R2 LIVE LOAD MEMBER LOAD 2 7 13 16 22 25 30 32 UNI GY -0.3 LOAD R3 JOINT LOAD 2 5 9 TO 11 FX 1.2

END DEFINE REFERENCE LOADS LOAD 101 REFERENCE LOAD R1 1.0 R2 1.0 LOAD 102 REFERENCE LOAD R1 1.0 R2 0.75 R3 0.75 PERFORM ANALYSIS PRINT STATICS CHECK

Importantly, similar to the REPEAT LOAD syntax, the REFERENCE LOAD syntax too can be used in all those situations where the LOAD COMBINATION syntax is not appropriate, such as P-DELTA, BUCKLING, NONLINEAR, NONLINEAR CABLE, and DIRECT ANALYSIS.

3.2.8 Using Data from Static Load Cases to Generate Seismic Weights for IBC, IS 1893, UBC, and Other Static Equivalent Methods One of the input terms for seismic analysis as described in Section 2.4 is “seismic weights.” They are made up of the weight of the structure, other permanent gravity load items, and a portion of the live loads. In the STAAD.Pro model, they are specified as weights in the form of SELFWEIGHT, JOINT WEIGHT, MEMBER WEIGHT, ELEMENT WEIGHT, and FLOOR WEIGHT under the seismic definition block of input. However, for the gravity analysis for these load items, these terms are specified again through the dead and live load cases. Thus, there is a duplication of the data. A typical instance of this duplication is illustrated in the following example.

FIGURE 3.2.5 Example of duplication of weights data in the input file

In the items termed (a) and (b), notice that the same data are specified twice—once as weights for the seismic definition and again as load items for the static cases. Using reference load cases, this duplication can be avoided. The procedure is as follows: 1. Create reference load cases, either through the STAAD.Pro GUI or using the editor. For this example, they will look like the following.

FIGURE 3.2.6 A Reference Load definition in the input file

2. Next, create the seismic definition. If this is done using the GUI, at the time of specifying the seismic weights, choose the option called Reference Load (Figures 3.2.7 and 3.2.8).

FIGURE 3.2.7 Selecting Reference Load cases as the source for weights in a seismic definition

FIGURE 3.2.8 Choosing the direction of the weights for the seismic definition

If we then save the file and go into the editor, we will find the following commands.

FIGURE 3.2.9 Seismic load definition in input file with weights drawn from Reference load cases

Thus, the seismic load definition block now comprises of the following lines. DEFINE IBC 2003

SDS 1.69 SD1 1.49 S1 1.49 IE 1 RX 3 RZ 3 SCLASS 4 REFERENCE LOAD Y R1 1.0 R2 1.0

By assembling the seismic weights from predefined REFERENCE LOADS, all the seismic weight information is condensed to just two lines. We can then provide the seismic load cases as well as the combination cases in the following manner:

FIGURE 3.2.10 Example of Reference load types used with seismic and other load cases

Load cases 12 and 13 can be worded in the following alternative manner too.

FIGURE 3.2.11 Example of REFERENCE LOAD used in conjunction with REPEAT LOAD

In Fig 3.2.8, there is a term called “Along” and its value is set to “Y.” Its effect is to create a command like this. REFERENCE LOAD Y

Its purpose is the following. The load items in any reference load case can potentially be in many possible directions. In reality, only those that act vertically downward are the direct result of gravity acting on masses. Therefore, only such items should be used for generating seismic weights. By setting the Along term to Y, we

are instructing the program to take only those items that are acting along global Y downward.

3.2.9 Mass Reference Load Cases—Specifying the Weight Data Just Once for Seismic and Dynamic Analyses The duplication of efforts for specifying the loads/weights occurs in another context also—when, in a single model, two types of analyses are performed: 1. A seismic analysis using ELFP (Section 2.4) 2. A dynamic analysis such as frequency extraction, response spectrum analysis, or time history analysis (Chapters 4 and 5) In situation 1, the loads that contribute to the seismic weight have to be specified using terms such as selfweight, member weight, and joint weight. In situation 2, the masses for the mass matrix for calculating the frequencies have to be specified in the form of loads in all the global directions. Reference load cases offer a way to avoid this. The solution is known as a mass reference case. If the LOADTYPE is specified as Mass as encircled in the next example (as opposed to Dead, Live, Wind, Flood, None, etc.), that case is identified as the source for the weights for seismic weight and the mass matrix. A single reference case can serve as the source of weights for IBC, UBC, IS 1893, NRC 2005, and masses for frequency analysis, response spectrum, time history, and any other process that requires weights or masses.

FIGURE 3.2.12 Syntax of a MASS Reference Load case

FIGURE 3.2.13 Dialog box in the STAAD.Pro GUI for creating mass reference load cases

FIGURE 3.2.14 Pages from the STAAD.Pro GUI manual explaining mass reference loads

FIGURE 3.2.15 A mass reference load case as seen in the STAAD.Pro editor NOTE Note that even though the type of case is titled “Mass,” the data being specified is weights, not masses. Where masses are required, the program will divide the weights by “g,” the acceleration due to gravity.

Once the mass reference case is added, the IBC or dynamic analysis cases do not need to contain any additional weight data information. An example is shown here. Example 7: Mass reference loads for IBC and response spectrum

FIGURE 3.2.16 Mass reference loads used in IBC and response spectrum load cases

In this example, the mass reference case R1 contains the weights acting along the global X, Y, and Z directions. Of these, the Y direction weights will be used for the lateral analysis based on ELFP

per IBC 2006 for load cases 1 and 2. The weights in all three directions will be used to populate the mass matrix and find the frequencies and modes for the response spectrum load cases 3 and 4. NOTE Note that the DEFINE REFERENCE LOADS—END DEFINE REFERENCE LOADS block of data must be specified before the IBC/UBC/IS 1893/NRC definition, the time history definition, and the response spectrum and time history load cases.

Example 8: Mass reference loads for weights for modal calculation

FIGURE 3.2.17 Mass Reference loads as weights for Modal Calculation

Example 9: Mass reference loads for time history analysis

FIGURE 3.2.18 Mass Reference loads as weights for a Time History load case

3.2.10 Reference Load Cases and Large Models

Since reference load cases can be used as the method for instructing the program to solve only the combination cases, it can provide considerable savings in analysis run-time. Additionally, because the results data can be avoided for the component load cases, it means less data to be memorymapped for post-processing. The benefit can be seen in large models where large volumes of result data can slow down or even hinder the program from displaying them in post-processing.

CHAPTER 4

Dynamic Properties of Structures 4.0 Dynamic Properties of Structures 4.0.1 Introduction The load types we have discussed so far are static loads. The magnitude and direction of these loads are constant over time. A structure is not subjected to any significant vibration because of these loads. A dynamic load is one whose magnitude or direction or both vary with time, and induces vibrations in the structure. An example would be the vibrations caused by people walking on floors or doing aerobics. A “regular” dynamic load is the vibration caused by a turbine generator. The vibrations and forces induced in a structure by an earthquake are known as seismic loads. Various methods are available for calculating the response of the structure to such loading. Nearly all these methods require the knowledge of the dynamic properties of the structure, and the key properties are: Frequencies Mode shapes

Damping characteristics The procedure for using STAAD.Pro to calculate the frequencies and mode shapes is discussed in Section 4.1, which includes the input required, the theoretical basis wherever applicable, the output produced by the program, and the methods for viewing and verifying the results. In Section 4.2, the methods for specifying or calculating the damping properties are examined.

4.1 Frequencies and Modes 4.1.1 Introduction Two of the important characteristics of a structure when it undergoes vibrations are: The mode of vibration, denoted using the term mode shape The frequency of the structure for the individual modes of vibration The procedure for calculating the mode shapes and frequencies is known as modal analysis. It is also known as frequency and modal extraction analysis. Modal analysis is a free-vibration analysis, which indicates the computation of the aforementioned attributes of a structure vibrating freely without any dynamic loading. For example, when the branch of a tree or a clothesline is pulled down slowly and then released, the ensuing vibrations are free vibrations. Mode shapes and frequencies are required to determine the behavior of a structure under various types of dynamic loads. Therefore, modal analysis helps us obtain the parameters that can later be used in finding the response of the structure to a real dynamic loading such as a machine vibration or seismic movements at the supports.

4.1.2 Discussion Users often assume that a structure has only one frequency, which they associate with the fundamental frequency. This misunderstanding perhaps stems from the interpretation of code clauses, such as 9.5.5.3 of ASCE 7-02, which provide the guidelines for the fundamental period to be used in the equivalent lateral force procedure (ELFP) for seismic analysis. Structures have many frequencies, each of which has an associated mode of vibration. A dominant mode is usually considered as one with a high modal participation factor or force participation factor. If there is a mode whose participation is high, for example, 80% or more, only then is it probably OK to assume that it is the primary or fundamental mode for the structure for that direction. Different directions usually have different fundamental frequencies. Required Reading 1. Technical Reference manual—Sections 1.18.3.2, 5.30, and 5.34 2. Application Examples manual—Example 28 3. Graphical Interface Help manual—Sections 2.3.7.8, 2.3.7.12, and 3.2.7

4.1.3 Methods Available in STAAD.Pro for Calculating Frequencies In STAAD.Pro, there are two methods for obtaining the frequencies of a structure. The Rayleigh method, which is an approximate method The modal extraction method, which involves extracting eigenvalues from a matrix based on the structure stiffness and lumped masses in the model. This is considered to be a more accurate method provided the model is generated correctly.

FIGURE 4.1.1 Dialog box in the STAAD.Pro GUI for specifying frequency calculation instructions

4.1.3.1 Rayleigh Method The Rayleigh method in STAAD.Pro is a one-iteration approximate method from which a single frequency is obtained. It uses the displaced shape of the model to obtain the frequency. There is a misconception that the Rayleigh frequency method always successfully fetches the fundamental (lowest) frequency. However, as explained next, users have to be careful in the choice of loading for this method to yield satisfactory results. The accuracy of the frequency computed by the Rayleigh method depends on the deflected shape it is based on. The closer that this shape resembles an actual mode shape, the more similarity there will be between the Rayleigh frequency and the one from the modal extraction method. This deflected shape depends on the choice of loading. If one is interested in the fundamental mode, the loading on the model should cause it to displace in a manner that resembles the fundamental mode. For example, the fundamental mode of vibration of a tall building would be a cantilever type, where the building sways from side to side with the base remaining stationary. The type of loading that creates a displaced shape which resembles this mode is a lateral force such as a wind force. Hence, if one were to use the Rayleigh method for such a structure, the loads that should be applied are lateral loads, not vertical loads. Due to the difficulty in estimating the mode shape for higher modes, producing deflected shapes that resemble higher modes isn’t easy. Therefore, the Rayleigh method is best used to estimate the frequency of the lowest modes. For most of the seismic codes built into STAAD.Pro that advocate ELFP, a period calculation based on the Rayleigh method is an integral part. The seismic weights that are input for the base shear calculation are subjected to a 1g acceleration in the direction along which the seismic response is sought, and the resulting deflected shape is used for the Rayleigh frequency calculation.

Example 1: Rayleigh frequency along X LOAD 1 DEAD LOAD ALONG X FOR RAYLEIGH SELFWEIGHT X -1 MEMBER LOAD 17 20 23 26 92 TO 139 151 153 UNI GX -0.3 16 18 19 21 22 24 25 27 UNI GX -0.15 CALCULATE RAYLEIGH FREQUENCY

Example 2: Rayleigh frequency along Z LOAD 3 DEAD LOAD ALONG Z FOR RAYLEIGH SELFWEIGHT Z -1 MEMBER LOAD 17 20 23 26 92 TO 139 151 153 UNI GZ -0.3 16 18 19 21 22 24 25 27 UNI GZ -0.15 CALCULATE RAYLEIGH FREQUENCY

For each of the two load cases shown in these examples, the STAAD.Pro output file will contain one frequency and will look similar to the report in Fig 4.1.2.

FIGURE 4.1.2 Report in the STAAD.Pro output file for Rayleigh frequency calculation

Related Question: What is the significance of the expression MAX DEFLECTION in the Rayleigh frequency output? Answer: As part of the output, the highest displacement along that direction is reported alongside the term MAX DEFLECTION. The deflected shape of the structure is an important criterion in calculating the frequency using the Rayleigh method. The maximum deflection is one of the measures of that displaced shape. Besides that, it doesn’t have any particular significance. NOTE Using the Raxyleigh method, 1. We obtain one frequency 2. We do not get a mode shape

4.1.3.1.1 Using the Rayleigh Method to Calculate the Frequency of a Simple Beam Because of the dependency of the Rayleigh method on the deflections of the structure, a model such as a single beam supported at both ends must be represented using a number of segments. If the beam is modeled as a single member between supports, the ends do not displace. The reported frequency will also be erroneous, or at least, will not correspond to the fundamental mode of vibration.

FIGURE 4.1.3 Beam segmented into 12 parts for calculating the Rayleigh frequency

4.1.3.2 Modal Extraction Method The process of calculating the MODES and FREQUENCIES using the stiffness and mass matrices of the structure is known as modal extraction and is performed by solving the equation: ω2 [m] {q} − [K] {q} = 0 where [m] = the mass matrix (assumed to be diagonal, i.e., no mass coupling) ω = the natural frequencies (eigenvalues) {q} = the (un-normalized) mode shapes (eigenvectors) Frequency (Hz or cycles per sec [cps]) = ω/2π The solution method used in STAAD.Pro is the subspace iteration method. Various terms are used to refer to the quantities produced by a modal analysis, some of which are eigenvalues (i.e., frequencies), natural frequency, modal frequency, eigenvectors (i.e., mode shapes), modal vector, normal modes, and normalized mode shape. As mentioned in Section 4.1.2, theoretically, a structure has as many modes and frequencies as the number of degrees of freedom for which its stiffness matrix is assembled. From that total, some modes will primarily be along X, some will be along Y, some will be along Z, some will be a mix of two or all three of those directions, some will be torsional modes, some will simply be localized flutter (just a few weak members or elements vibrating while the rest of the structure is unaffected), and so on. Out of this total, the eigenvalue method calculates a certain number of modes and frequencies. This number is determined by certain parameters that are discussed in Section 4.1.3.2.1, and a cutoff point established by the mathematical limitations of the algorithm used in STAAD.Pro. The various results that STAAD.Pro reports after a modal extraction analysis are described in Sections 4.1.4 thru 4.1.7. The mathematical procedure in the subspace iteration method involves using trial vectors for the mode shapes. If the structure has very low frequencies (close to 0), the process may fail. In such cases, through a command called SET SSVECT, the program can be instructed to start the eigensolution process with an alternative set of trial vectors. This is explained in Section 4.1.11. 4.1.3.2.1 Crucial Items of Input Mass Modeling—Selfweight and Other Weights

One of the critical components of a frequency analysis is the amount of mass undergoing vibration. For a structure, this mass comes from the selfweight and from permanent/imposed loads on the building. Since the selfweight calculation depends on the cross-sectional area of all the members, thickness of plate elements, density of all the materials in the structure, and so on, all the relevant terms that go into the correct computation of selfweight are required. STAAD.Pro uses the lumped mass method. That is, if distributed weights are present, as in the case of selfweight or a distributed applied load, they will be lumped into concentrated values and applied at either ends of a beam or the nodes of a plate or solid and divided by g to convert them to masses. If a concentrated force is acting at an intermediate span point on a member, it too will be lumped into two components and STAAD.Pro will consider them to be acting at the ends of the beam. Due to the adoption of the lumped mass method, structures such as a single beam supported at both ends must be modeled using a number of segments (see Fig 4.1.3). Else, the entire weight gets lumped at the ends and absorbed into the supports. There is no mass that is unrestrained and able to vibrate, thereby making it impossible to perform the eigensolution. The more the number of divisions, the better the chances of obtaining higher modes. Number of Modes—The CUT OFF MODE SHAPE Command Theoretically, a structure has as many modes of vibration as the number of degrees of freedom in the model. However, the limitations of the mathematical process used in extracting modes may limit the number of modes that can actually be extracted. In a large structure, the extraction process can also be very time consuming. Further, not all modes are of equal importance. (A measure of the importance of modes is the participation factor of that mode.) In many cases, the first few modes may be sufficient to obtain a significant portion of the total dynamic response. Because of these reasons, in the absence of any explicit instruction, STAAD.Pro calculates only the first six modes. This is similar to saying that the command CUT OFF MODE SHAPE 6 has been specified. (Versions of STAAD.Pro before STAAD/Pro 2000 calculated only three modes by default.) If an inspection of the first six modes reveals that the overall vibration pattern of the structure has not been obtained, one may ask STAAD.Pro to compute a larger (or smaller) number of modes with the help of this command. The number that follows this command is the number of modes being requested. In the next example, 30 modes are requested through the command CUT OFF MODE SHAPE 30. SUPPORTS 23 47 85 FIXED BUT FX MX MY MZ 241 268 324 PINNED CUT OFF MODE SHAPE 30

Upper Limit of Frequency—The CUT OFF FREQUENCY Command Related Question: I added CUT OFF MODE SHAPE 15, but I get only 10 modes. Answer: The number of modes that STAAD.Pro calculates is also restricted by another factor—a built-in

cutoff point for the frequency. This threshold is 108 cps. STAAD.Pro can be instructed to use a higher threshold, through the CUT OFF FREQUENCY command. In the absence of that instruction, even if CUT OFF MODE SHAPE is specified, STAAD.Pro will calculate only those modes whose frequency is less than or equal to 108 cps. Both the CUT OFF commands must be specified before the first load case. SUPPORTS 193 TO 202 208 TO 217 221 TO 224 249 250 FIXED CUT OFF MODE SHAPE 15 CUT OFF FREQUENCY 500 LOAD 1 DEAD WEIGHT SELF Y -1 LOAD 2 ..

The MODAL CALCULATION REQUESTED Command To calculate modes and frequencies, the MODAL CALCULATION REQUESTED command is used. It is specified inside a load case. In other words, this command accompanies the loads that are to be used in generating the mass matrix. Frequencies and modes also have to be calculated when dynamic analyses such as response spectrum, time history, or steady state are carried out. But in such analyses, the MODAL CALCULATION REQUESTED command is not explicitly required. When STAAD.Pro encounters the commands for these types of analyses, it automatically will carry out a frequency extraction using the weights in that load case. The MASSES that Are to Be Used in Assembling the MASS MATRIX The mathematical method that STAAD.Pro uses is called the subspace iteration eigen extraction method. Information on this method is available in Section 1.18.3 of the STAAD.Pro Technical Reference manual. The method involves two matrices—the stiffness matrix and the mass matrix. The stiffness matrix, usually called the [K] matrix, is assembled using data such as member and element lengths, member and element properties, modulus of elasticity, Poisson’s ratio, member and element releases, member offsets, and support information. For assembling the mass matrix, called the [M] matrix, STAAD.Pro uses the load data specified in the load case in which the MODAL CALCULATION REQUESTED command is specified. Thus, the load data should consist of weights that will move along with the structure, such as selfweight, weight of permanent fixtures, weight of equipment, and also live loads that have a high likelihood of being present when the structure is subjected to a dynamic force such as an earthquake. In the case of the response spectrum or time history load case, the load data that form the basis for the masses is specified within those load cases. Thus, some of the important aspects to bear in mind are: In STAAD.Pro, the terms of the mass matrix are assembled from the loading data in the load case containing the instruction for eigenvalue extraction or the dynamic analysis commands. The input we specify are weights, not masses. Internally, STAAD.Pro will convert weights to masses by dividing the input by g, the acceleration due to gravity.

Direction in Which the Weights Need to be Applied If the structure is declared as a PLANE frame, the lumped weights have two possible directions of vibration—global X and global Y. If the structure is declared as a SPACE frame, they have three possible directions—global X, global Y, and global Z. However, this does not guarantee that STAAD.Pro will automatically consider the masses for vibration in all the available directions. We have control over and are responsible for specifying the directions in which the masses ought to vibrate. If a weight is not specified along a certain direction, the corresponding degrees of freedom (e.g., global Z at node 34) will not receive a contribution in the mass matrix. The mass matrix is assembled using only the masses from the weights and directions specified by the user. In the next example, notice that we are specifying the selfweight along global X, Y, and Z directions. Similarly, the element pressure load is also specified along all three directions. We have chosen not to restrict any direction for this problem. If one wishes to restrict a certain weight to certain directions only, all that he/she has to do is to not provide the directions in which those weights cannot vibrate in. As much as possible, provide absolute values for the weights. STAAD.Pro is programmed to algebraically add the weights at nodes. Hence, if some weights are specified as positive numbers, and others as negative, the total weight at a given node is the algebraic summation of all the weights in the global directions at that node. STAAD SPACE UNIT FEET KIP JOINT COORDINATES .. MEMBER INCIDENCES .. ELEMENT INCIDENCES SHELL .... MEMBER PROPERTY .. ELEMENT PROPERTY .. CONSTANTS E CONCRETE ALL DENSITY CONCRETE ALL POISSON CONCRETE ALL CUT OFF MODE SHAPE 10 CUT OFF FREQUENCY 500 SUPPORTS .. UNIT POUND FEET *WEIGHTS DATA AND INSTRUCTION FOR COMPUTING FREQUENCIES AND MODES LOAD 1 SELFWEIGHT X 1.0 SELFWEIGHT Y 1.0

SELFWEIGHT Z 1.0 ELEMENT LOAD 41 TO 88 PR GX 300.0 41 TO 88 PR GY 300.0 41 TO 88 PR GZ 300.0 MODAL CALCULATION REQUESTED PERFORM ANALYSIS FINISH

Related Question: I find the following message in the .ANL file. *ERROR* NO UNSUPPORTED MASSES ENTERED - CHECK DENSITIES

*** ERRORS IN SOLVER ***

FIGURE 4.1.4 Warning message in the event of zero masses in the model

Answer: This usually happens when there are no nonzero masses in the mass matrix. One such example is LOAD 10 MODAL CALCULATION REQUESTED PERFORM ANALYSIS

Notice that there are no weights preceding the MODAL CALC REQ command. At the least, selfweight must be applied in at least one direction (preferably in all three) in that load case. Another cause of this is when DENSITY is not provided in the MATERIAL data. However, in that case, a warning indicating that fact will appear in the .ANL file. *** STAAD.Pro ERROR MESSAGE ***

DENSITY NOT PROVIDED. SELFWEIGHT COMMAND IGNORED Related Question: How do we consider the weight of the equipment for frequency calculation? Answer:

Weight of entities that are not part of the structural model, such as equipment and brick walls, can be specified with the help of commands such as JOINT LOAD, MEMBER LOAD, and ELEMENT LOAD. Or if they are of a distributed nature on a panel between floor beams, one could also use the FLOOR LOAD option. The important aspects in all these are that (a) these weights must be specified as positive numbers and (b) all possible directions of vibration must be included. LOAD 21 SELF X 1.0 SELF Y 1.0 SELF Z 1.0 ELEMENT LOAD 1103 TO 1145 PR GX 3.8 1103 TO 1145 PR GY 3.8 1103 TO 1145 PR GZ 3.8 JOINT LOAD 457 458 461 464 469 612 613 616 619 FX 35 457 458 461 464 469 612 613 616 619 FY 35 457 458 461 464 469 612 613 616 619 FZ 35 MODAL CALCULATION REQUESTED PERFORM ANALYSIS

Using the FLOOR LOAD and ONEWAY LOAD Items to Generate Masses from Pressure Load on Panels This is described in Section 1.2.7. The example shown there is for response spectrum. Use the MODAL CALCULATION COMMAND instead of the SPECTRUM command for a frequency and mode extraction analysis. Example 3 LOAD 5 LOADTYPE Seismic TITLE FREQUENCY CALCULATION SELFWEIGHT X 1.0 SELFWEIGHT Y 1.0 SELFWEIGHT Z 1.0 FLOOR LOAD YRANGE 4 6 FLOAD 3.95 GX YRANGE 4 6 FLOAD 3.95 GY YRANGE 4 6 FLOAD 3.95 GZ MODAL CALCULATION REQUESTED PERFORM ANALYSIS

Related Question: What is the difference between specifying weights in all directions in a single load case versus three separate load cases each with one global direction? In the following data, instead of case 11, can’t I specify cases 12, 13, and 14? LOAD 11

SELFWEIGHT X 1.0 SELFWEIGHT Y 1.0 SELFWEIGHT Z 1.0 MODAL CALCULATION REQUESTED LOAD 12 SELFWEIGHT X 1.0 MODAL CALCULATION REQUESTED LOAD 13 SELFWEIGHT Y 1.0 MODAL CALCULATION REQUESTED LOAD 14 SELFWEIGHT Z 1.0 MODAL CALCULATION REQUESTED

Answer: Recall that the reason for including all the possible weights in all three global directions is due to the fact that STAAD.Pro treats those weights as the input from which to obtain the magnitude of vibrating masses and the directions they will vibrate in. Therefore, every weight, whether permanent or temporary, which we think will be present on the structure at the time that the dynamic loading acts, ought to be specified. Additionally, STAAD.Pro can generate the mass matrix only once per file, and thus, compute only one set of frequencies for a model. It expects all possible weights and all associated directions to be included in the first of those modal extraction cases. Subsequent modal calculation cases containing weights are disregarded. Thus, if weights are specified along one direction only, the frequencies extracted will be for vibration along that direction only. We will get neither the modes nor the frequencies for vibration along the other directions.

4.1.4 Dynamic Weight Dynamic weight is a term that represents the total weight that is identified as vibrating along each of the three global directions. For this, we need to understand how the mass matrix is assembled. The mass matrix for the structure is generated based on the load data provided in the loading case that contains the command for modal calculation requisition, response spectrum analysis, or time history analysis. The following are the steps in obtaining the mass matrix. 1. For each member, the span loads on the member are first converted to the equivalent concentrated loads at the two end joints of the member. 2. At each joint, all the various equivalent concentrated loads coming from all the members meeting at the joint are algebraically added up for each of the three global directions: X, Y, and Z. 3. The absolute value of the quantity obtained after this algebraic combination is the effective mass at the node for the corresponding direction. Here are some points to consider in STAAD.Pro when specifying the loading for obtaining the mass matrix: The sign of the loading on each member does matter. The following loading

MEMBER LOAD 7 8 UNI GY -3.2 7 8 UNI GY 2.4

will result in a total load of −0.8 units for members 7 and 8. The amount of −0.8 load units will then be converted to the equivalent concentrated loads at the two ends of the members 7 and 8. The direction of the loading on each member does matter. The following loading MEMBER LOAD 7 8 UNI GY 4.8 7 8 UNI Y 1.9

will result in a total load of 6.7 units for members 7 and 8 if the local Y and global Y axes are the same for members 7 and 8. If the local Y and global Y axes are opposite to each other, this example will result in a load of 2.9 units for members 7 and 8 in the global Y direction. Once the resultant loads are determined for each of the three global directions for each member, equivalent nodal masses are calculated for the two ends of each member. These masses are evaluated as absolute values. Hence, when the total mass at a joint is evaluated, the absolute value of the contributions from all the members meeting at that joint is totaled up. This process is repeated for every joint, and the end result of this will be the mass matrix. Dynamic weight in any given direction is the total of all the masses in that direction multiplied by g.

4.1.5 Obtaining a Report of the Masses Lumped at Each Node of the Model The mass at each joint in each direction and the total mass in each direction are reported in the file called inputfilename_MASS.TXT. For example, if our input consists of a 500 kg/m distributed weight on a member whose span is 10 m, the total load is 5000 kg, which represents 2500 kg at each node of the member. These are in units of weight. Divide this by g (9.8 m/sec2), and we get 255.102 kg-mass. This is the value we will find in the _MASS.TXT file, except that it is converted and reported in pounds instead of kilograms.

FIGURE 4.1.5 Contents of inputfilename_MASS.TXT

Related Question: Is the suggestion regarding applying all positive values for weights for generating the mass matrix applicable for the Rayleigh method too? Answer: No. For the Rayleigh method, the important step is to generate a deflected shape that resembles a mode shape. It may be necessary to apply the loads along the positive direction on some parts of the structure and the negative direction on other parts to achieve this. Related Question: I have applied the same amount of weight in all three directions. But in the _MASS.TXT file, the total mass reported for one direction (Y) is different from the other two.

FIGURE 4.1.6 Report of total applied masses along the global directions

Answer: This difference occurs if the structure has springs in some directions but is restrained using FIXED BUT supports for the others. SUPPORTS 845 TO 867 FIXED BUT MX MZ KFY 1.3e+003

In this example, 845 TO 867 are restrained against translation along X and Z and have a spring along Y. It also occurs if the supports have been generated using an ELASTIC MAT or PLATE MAT. For these types, usually each support node gets an FX and FZ restraint and a KFY spring. 1 TO 496 PLATE MAT DIRECT Y SUBGRADE 180

Selfweight and other distributed weights applied on columns and elements will be converted to lumped weights and distributed among the various nodes of those entities. The base nodes of the columns of the lowest floor, and nodes of elements of mat foundations will usually be supports. Those weights that end up at support nodes along the restrained directions will not be used for populating the mass matrix because those directions are not active degrees of freedom. Hence, in the _MASS.TXT file, the value reported as the total mass in a given direction is equal to the total mass applied along that direction minus the mass that goes directly into the support nodes due to restraints provided along that direction. If the structure contains only members, and selfweight is the only weight applied along all three directions, the difference will typically be equal to half the mass of the columns of the lowest floor. Related Question: What is the best way to ensure that I will not inadvertently omit any weight when the mass matrix is generated? Answer: When STAAD.Pro forms the mass matrix, it will algebraically add the weight terms at each node, and the mass at the node is then extracted from the resultant weight. Because of the positive and negative nature of weights, there will be some cancellation involved if the signs are not all the same. So, apply all the loads in the global directions only. And use positive signs for all the load values.

That way, the full contribution of all the applied weights will receive proper consideration in the mass matrix. You can verify the mass at each joint by going through inputfilename_MASS.TXT.

4.1.6 Missing Mass For response spectrum or time history analysis, STAAD.Pro uses only as many modes as defined by the CUT OFF MODE SHAPE command, or a lesser number in case it cannot calculate as many as specified through that command. STAAD.Pro by default calculates only a maximum of six, unless a higher value is requested through this command. In theory, a structure has as many modes of vibration as there are degrees of freedom, typically represented through a variable n. If you consider the sum total of masses that go into the mass matrix, to obtain the full effect of that mass while calculating the displacements, forces, reactions, and so on, all those n modes have to be considered. However, the limitations of the mathematical procedures used in calculating modes and frequencies means that all those n modes cannot be calculated in many cases. Thus, only a lesser number of modes (call it p) is actually extracted. Usually, p is equal to or less than the number specified through the CUT OFF MODE SHAPE command. Consequently, the displacements and forces calculated in these cases are not the true numbers, but ones derived through a less than full participation of vibrating masses. For response spectrum analysis, or for a time history analysis for ground motion, the extent of the participation of the masses can be seen from the MASS PARTICIPATION factor table, which is described in Section 4.1.7.5.

FIGURE 4.1.7 Report of the mass participation factors in the output file

The cumulative number in the SUMM-X, SUMM-Y, and SUMM-Z columns tells you what the total participation is in the X, Y, and Z directions, respectively. For example, if you are looking at these values corresponding to the seventh mode, the SUMM-X, SUMM-Y, and SUMM-Z would represent the summation of mass participation up to and including the seventh mode. Most design codes require that number to be 90% or more for acceptable results in a response spectrum analysis and for a time history analysis for ground motion. One potential way to achieve that 90% is to ask for more modes through the CUT OFF MODE

SHAPE command (and the CUT OFF FREQUENCY command that may also be needed sometimes). However, there are times when you can ask for a very high number of modes, but the program is unable to calculate any more than a certain number of modes, and consequently, not able to achieve the 90% participation level. The difference between this SUMM value and 100% is called MISSING MASS for that direction. In Chapter 5, we’ll see how a feature called MISSING MASS correction can be used to compensate for the amount of mass participation that is not captured by the calculated modes. Related Question: Which of the following am I supposed to ensure? Mass participation in X + mass participation in Y + mass participation in Z = 100% or Mass participation in X = 100%, mass participation in Y = 100%, mass participation in Z = 100%. Answer: Mass participation should be 100% (or at least 90%) for each direction. This means, Mass participation in X = 100%, mass participation in Y = 100% percent, mass participation in Z = 100%. While 100% may be difficult to achieve, participation of more than 90% is considered acceptable. Related Question: If the mass participation factor for a certain direction is reported as zero even after 100 modes, what could be the cause? Answer: It could mean that you haven’t specified weights along that direction. Open inputfilename_MASS.TXT and find the total mass for that direction. If it is shown as zero, it is clear that there are no vibrating masses for that direction.

4.1.7 Output Produced by STAAD.Pro for Eigenvalue Analysis As in the case of static analysis, there are two places in STAAD.Pro where the results of the frequency calculation can be viewed: (a) the output file and (b) the post-processor. The output file can be viewed from File -> View -> Output File -> STAAD output. The output produced by the command MODAL CALCULATION REQUESTED consists of mode shapes, frequencies, participation factors, and other items. These are generally considered to be attributes of the structure. They are not a structural response.

4.1.7.1 Mode Number and Corresponding Frequencies and Periods Depending on the number of modes calculated, we obtain a report that is as follows, under the heading CALCULATED FREQUENCIES FOR LOAD CASE nnn.

FIGURE 4.1.8 Report of frequencies in the output file

Related Question: There is a message in the output file that reads as The following Frequencies are estimates that were information only and will not be used. Remaining cut off mode/freq values or are of low accuracy. rerun with a higher cutoff mode (or mode + freq)

After this message, two more frequencies are shown.

calculated. These are for values are either above the To use these frequencies, value.

FIGURE 4.1.9 Additional frequencies reported in the output file

Answer: The nature of the method used in eigensolution enables STAAD.Pro to calculate a few more modes than that specified in the CUT OFF MODES command. These additional modes are printed for the user’s information. There may be frequencies among this additional set, which may be close to the excitation frequency of equipment to be mounted on the structure. It will help the user decide if these additional modes are needed in the response spectrum or time history analysis, and in that event, the model will have to be re-run with a higher value for the CUT OFF MODES command. Related Question: What are the numbers shown in the column titled “Accuracy”?

FIGURE 4.1.10 Frequency table in the output file along with the “accuracy” term

Answer: In the subspace iteration method, during each iteration, for each mode, the frequency computed during that iteration (i), namely, wi, is compared against the frequency computed during the previous iteration (i − 1), namely, wi − 1, using the following equation ABS [w2i − w2i − 1]/ w2i When this value falls below a built-in tolerance for each one of the computed frequencies, the iterations are stopped. The value for the last iteration is reported in the output file under the heading “Accuracy.”

4.1.7.2 Generalized Weight The eigenvector {ϕn} for each mode n has an associated generalized mass defined by Generalized mass (GM) = {ϕn}T [M] {ϕn} where [M] is the diagonal mass matrix (off-diagonal terms are zero). Generalized weight (GW) = GM * g In these calculations, {ϕn} is normalized in such a way that the largest value in any given mode is 1.0.

FIGURE 4.1.11 Report showing generalized weights in the STAAD.Pro output

4.1.7.2.1 Normalizing Mode Shapes Many textbooks discuss normalizing modes in such a way that the generalized mass for the mode becomes 1. Some call it mass normalization. STAAD.Pro normalizes modes in such a way that the highest value is set to 1.0 for each mode, and values at all other joints being scaled with respect to that value.

FIGURE 4.1.12 Post-processing tables showing the normalization method for modes

4.1.7.3 Modal Participation Factor A participation factor (Q i) is computed for each eigenvector for each of the three global (X, Y, and Z) translational directions. For direction i and mode k, it is equal to

where Matrix {A} = The transpose of an (N × 1) size matrix {ϕ} whose terms consist of the mode shape (eigenvector) value corresponding to direction i for mode k. Matrix {B} = An (N × 1) size matrix {w} whose terms consist of the weight value (mass multiplied by g) corresponding to direction i. Its terms can be obtained by multiplying the relevant values in the inputfilename_MASS.TXT by g. N is the number of joints in the model. GW is the generalized weight described earlier. For both matrices and for each of the three directions, only the translational terms are considered. Rotational terms are not. The modal participation factors are not reported by STAAD.Pro unless they are explicitly asked for. They can be obtained in the STAAD.Pro output file by adding the following command in the STAAD.Pro input. SET PART FACT

FIGURE 4.1.13 Command for obtaining the modal participation factors

The output will be as shown in Fig 4.1.14.

FIGURE 4.1.14 Table of modal participation factors in the STAAD.Pro output

Related Question: Instead of computing a participation factor based on a 1g ground acceleration, can STAAD.Pro calculate a similar factor that is based on a pulse-type load acting on the structure at some height above the base? In other words, can this factor be calculated for the load type known as a time function load or an arbitrarily varying force/moment? Answer: The term you are asking about is sometimes called the force participation factor. For force/moment dynamic loading, that factor is the dot product of the mode shape vector and the force vector divided by the generalized weight. STAAD.Pro calculates them, but does not report them.

4.1.7.4 Modal Weight and Modal Mass The modal weight for each mode is (GW)(Q i²), where GW is the generalized weight and Q i the modal participation factor described earlier. Modal mass = Modal weight/g The summation of modal weights for all modes in a given direction is equal to the base shear, which would result from a 1g base acceleration. The sum of the modal weights for the computed modes may be compared with the total weight applied along that direction minus the weight that gets lumped at supports. The total weight can be read from the bottom of the inputfile_MASS.TXT file, which gets created each time a frequency analysis is performed. The difference is the amount of weight missing from a dynamic,

base excitation, modal response analysis. If too much is missing, then re-run the eigensolution asking for a greater number of modes, or use the MISSING MASS feature in a response spectrum analysis.

FIGURE 4.1.15 Table of modal weights in the STAAD.Pro output file

The summation of modal weights for each of the three directions is reported if a response spectrum analysis is performed. In the output file, look for the terms listed under the heading “Dynamic Weight, Missing Weight, Modal Weight.” See Section 5.1 for detailed information. If all possible modes are used, the sum of the modal weights for the individual directions will equal the weight of the structure (i.e., of weights that are free to move, relative to the base) along those directions. The masses lumped at each node, and the total mass along each of the three global directions, are listed in the inputfilename_MASS.TXT file. These values if multiplied by g give us the total weight applied along the three directions.

4.1.7.5 Mass Participation Factor The modal mass of a mode as a percentage of the total mass vibrating in that direction is listed under the headings X, Y, and Z. A running sum (cumulative value) for all modes is given under the headings SUMM-X, SUMM-Y, and SUMM-Z, so that the last line indicates the percent of the total weight that all the modes extracted would represent in a 1g base excitation. This tells us what percentage of the total base shear would come from that mode if it were excited by a 1g acceleration at all the supports. In building design for earthquake loading, MASS PARTICIPATION FACTORS IN PERCENT is very important. Codes require us to consider enough modes to represent at least 90% participation. For a given mode and direction, the MASS PARTICIPATION FACTORS IN PERCENT multiplied by the total mass times g would be the modal weight. It should be noted that a sinusoidal displacement pattern on a column-like structure would have very little participation in base shear but still may have significant member forces and storey drift.

FIGURE 4.1.16 Table of mass participation factors in the STAAD.Pro output file

FIGURE 4.1.17 Table of mass participation factors in the post-processing mode

In Section 4.1.3.2.1, under the heading “Number of Modes—The CUT OFF MODE SHAPE Command,” we discussed that one measure of the importance of a mode is the participation factor of that mode. As observed from Fig 4.1.16, for vibration along the X direction, the first mode has 91.73% participation. It is also apparent that the fourth mode is primarily a Y direction mode due to its 50.97% participation along Y and 0 in X and Z. The SUMM-X, SUMM-Y, and SUMM-Z columns show the cumulative value of the participation of all the modes up to and including a given mode. One can infer from these terms that for 95% participation along X, the first five modes are sufficient. In the aforementioned example, the cumulative participation factor along the global Z direction with 10 modes is only 0.54%. This happens when the structure is very stiff along that direction.

Consider a model that has a shear wall that spans in the Y-Z plane. It makes the structure extremely stiff in that plane. It would take a lot of energy to make the structure vibrate along the Z direction. Modes are extracted in the ascending order of energy. The higher modes are high-energy modes, compared with the lower modes. It is likely that, unless we raise the number of modes extracted from 10 to a much larger number—30 or more—using the CUT OFF MODE SHAPE command (CUT OFF FREQ too may be needed sometimes), we may not be able to obtain substantial participation along the Z direction. Another unique aspect of this result is modes where all three directions have zero or near zero participation. This happens when the mode shape has positive and negative terms due to which masses are moving in opposite directions, resulting in partial or full cancellation of each other’s effect. Torsional modes too exhibit this behavior. See Section 4.1.8 for the method for viewing the shape of vibration. Localized modes, where small pockets in the structure undergo flutter due to their relative weak stiffness compared with the rest of the model, also result in small participation factors. The mass participation factor has relevance for time history analysis for seismic acceleration and for response spectrum analysis. It may not be of much value for time history analysis for an arbitrary forcing function, sinusoidal loading, blast loading, and so on; that is, for time-varying forces that are applied directly at the nodes. Related Question: If I am not able to get 90% participation in the three directions, what can I do? Answer: Here are some methods to resolve this. 1. Use the CUT OFF MODE SHAPE with a value greater than 6. If the highest mode thus calculated has a frequency close to 108 cps, you’ll also have to add CUT OFF FREQUENCY 1000. 2. Make sure you are specifying weights along all directions. If the weight along a given direction is zero, the participation factor too will be zero for that direction. 3. If the slabs and/or walls are not meshed, or are coarsely meshed, replace them with a denser mesh. 4. If these three methods don’t help, try this. Since the eigensolution is based on the lumped mass method, consider dividing the columns and beams into two or more segments to obtain a better distribution of mass. 5. For response spectrum analysis, use the missing mass option (described in Chapter 5). Related Question: When running a modal analysis for a structure that is somewhat unusual in that it has got supports at several points across its length, width, and height, and not just at its base, I find that the mass participation for all six modes is zero. Can you help me understand why this is the case? Answer: If a structure is supported in the manner you describe, only a small local area deforms in any one mode shape. Hence, it will take many modes to describe a uniform motion of the whole structure, which is what the participation factor is trying to measure. You could try calculating the frequency using the Rayleigh method. Apply the selfweight along X, Y, and Z in three separate load cases, and calculate the Rayleigh frequency for each case.

LOAD 1 SELF X 1.0 CALC RAYL FREQ LOAD 2 SELF Y 1.0 CALC RAYL FREQ LOAD 3 SELF Z 1.0 CALC RAYL FREQ PERF ANALY

Although this test is approximate, it makes it possible to displace a large part of the structure along those directions. It is possible that the Rayleigh frequencies associated with such displaced shapes will have high values. If so, it would indicate that it could take numerous modes (100 or more) before a significant participation is obtained. You could then add the line CUT OFF MODE SHAPE 100 and CUT OFF FREQUENCY 1000 and re-run the analysis. In most structures that are only supported at the base, only a few modes will have significant participation. However, structures that have a majority of their body supported will have hundreds of modes each with a very small participation that will add up to the 100%.

4.1.8 Viewing the Mode Shapes After the analysis is completed, select post-processing from the Mode menu. This screen contains facilities for graphically examining the shape of the mode in non-animated and animated views.

FIGURE 4.1.18 Viewing the mode shapes in the post-processing mode

The Dynamics page on the left side of the screen is available for viewing the shape of the mode in a non-animated manner. The mode number can be selected from a drop-down list (see Fig 4.1.19), as well as from the Loads and Results tab of the View-Structure Diagrams dialog box. The size to which the mode is drawn is controlled using the Scales tab of the Diagrams dialog box.

FIGURE 4.1.19 Selecting the mode for viewing in the post-processing mode

Two tables are displayed on the right side of the page. The upper table consists of frequencies and participation factors. The lower table contains the mode shape values at each node.

FIGURE 4.1.20 Tables for mode shapes and frequencies in the post-processing mode

We have to examine all the modes, and the participation factor values to see which ones are local modes, which ones are torsional modes, and which ones are significantly along X, Y, or Z. Mode shape values can be obtained in the output file with the help of the command PRINT

MODE SHAPES. On large models, this could produce voluminous output. Note that mode shapes are not to be confused with joint displacements. Mode shapes are a property of the structure, indicating the manner in which the structure vibrates. Displacement occurs only when the structure is subjected to a static or a dynamic load. NOTE Quality of the mode shape Is only as good as the quality of the model.

Related Question: Why are mode shapes looking so jagged? Shouldn’t they resemble a smooth sine curve?

FIGURE 4.1.21 Mode shape of a continuous span beam with insufficient segmentation

Answer: When subdividing a member into several segments, it is necessary to create nodes where the motion of the mass will be the maximum (at or near the mid-span usually), as well as at locations that will become the inflection points for higher modes (such as the quarter span point). The crude shape represented in Fig 4.1.21 is the result of absence of nodes to capture the motion of the mass at such critical points. Even though the beam is segmented, it is not segmented in the right manner.

4.1.9 Viewing the Mode Shapes in Animation The Animation option of the Results menu as well as the Animation page can be used for animating the mode. In Section 3.1 of Part II, a description for animating the deflection diagram of the structure for a load case has been provided. The steps for animating the mode shape are similar to that.

4.1.10 Saving the Animation of the Mode Shapes in a File The animated view of the mode shape can be recorded in a movie file. Other participants in the project can then view the animation using any one of several free viewer programs available such as Windows Media Player or Real Player. Currently, this facility is available in STAAD.Pro for node deflection, beam section displacement, mode shape, and plate stress contour diagrams. The analysis has to be successfully completed before this facility can be accessed.

FIGURE 4.1.22 Animated view of the mode shapes in the STAAD.Pro GUI

This facility is available under the Tools menu and is called Create AVI File. The file with the extension .AVI will be created in the same folder where the STAAD.Pro input file is present. Tutorial problem 3 in the STAAD.Pro Getting Started manual contains a detailed procedure for creating .AVI files.

4.1.11 Instabilities and their Effect on Eigenvalue Extraction A fundamental condition that needs to be met for frequencies and modes to be calculated is that the structure needs to be stable, that is, no singularities or instability warnings. In Section 2.2 of Part III, there is a detailed discussion on the causes of instabilities, as well as the remedies. Related Question: I am encountering a couple of error messages when I try to run a model. ERROR- ZERO ON DIAGONAL IN JACOBI ITERATION. A PROBLEM HAS BEEN ENCOUNTERED WHILE SOLVING FOR THE MODES

FIGURE 4.1.23 Error messages in the STAAD.Pro output file during eigensolution

Answer: The possible causes for this problem are: 1. One of the frequencies—probably the first frequency—is very nearly zero. The subspace iteration method used in STAAD.Pro cannot solve structures that are free with zero or near-zero frequencies. 2. There is “spurious mode” singularity, which occurs when the structure is a regular grid of flat plates lying in one plane with no edge-beams or out-of-plane members to suppress modes. Normally, the program automatically puts a weak spring in. Try fixing the moment degree of freedom normal to the plane of the plates to suppress this meaningless displacement mode. 3. If the structure has beams and plates, ensure that the beams aren’t too stiff compared to the plates. 4. When the slabs and walls are modeled using plate element meshes, care must be taken to ensure that the element mesh is properly connected to the beams and columns in the model. This requires that the members too are divided into segments wherever element nodes fall on their span. The resulting elements and the beam segments must be properly connected to each other without any instance of duplicate nodes. In the STAAD.Pro GUI, instances of improper connectivity can be identified using the following options in the Tools menu. • Check duplicate nodes • Check beam plate connectivity • Check improperly connected plates Without proper connectivity, the stiffness at nodes will not reflect the monolithic nature of the connection that exists there. These modeling errors have been discussed in detail in Section 2.5 of Part I. 5. Check if there are any instability messages during the triangular factorization phase of the analysis. STAAD.Pro cannot solve an unstable structure for frequencies. A static load case containing the very same loads used as weights for the modal calculation case and applied along the three directions will reveal the problem. Temporarily comment out the MODAL CALC REQ command, insert a PERFORM ANALYSIS command, followed by the FINISH command and then analyze. Do you see excessive displacements? One way to reduce this is to replace the MEMBER TRUSS and full MEMBER RELEASES with PARTIAL MOMENT RELEASES (see Section 2.2 of Part III for other remedies). 6. Try increasing the number of modes requested. The subspace iteration eigensolver uses more “trial shape vectors,” which can improve the probability of a successful modal extraction. Use the CUT OFF MODE SHAPE n command and CUT OFF FREQUENCY f to do this.

7. In the STAAD.Pro model, are there any members crossing each other but not connected at their intersection point? If their counterparts on the actual structure are connected, we should do the same on the STAAD.Pro model too. Else, each beam will vibrate independent of the other. In the GUI, go to Geometry -> Intersect Selected Members to split and connect such members. 8. In the GUI, go to Tools -> Check Multiple Structures, and check if there are two or more independent structures in the model that have no physical connection to each other. If so, each of these structures needs to have its own set of supports, which ensures that each one is individually stable in all directions. If they happen to be independent because of a lack of proper connectivity between each other, we need to examine those problem areas and correct them. “Floating” members and elements are a common cause of instability. 9. STAAD.Pro lumps the mass of a beam at the end joints for dynamics. Consider using more joints to improve the mass and stiffness distribution. 10.Is selfweight applied in just the vertical direction? Most structures vibrate in all three global directions. It is essential that the mass matrix has terms representing all those directions. Remember, in STAAD.Pro, the loads that we define in the dynamic load case go into the making of the mass matrix. Selfweight applied in all three directions is usually the most basic ingredient of a proper mass matrix. 11.Does the model have spring supports? If so, check the length and force units of the spring constants. A wrong unit could result in a very weak (soft) spring that could then cause the structure to move like a rigid body along one or more directions. Try increasing the stiffness of the springs by a factor of 100 or 1000, or replacing them with PINNED or FIXED supports and re-run the analysis. Does the problem still occur? 12.It is a good idea to check the units in which member properties and material constants are assigned. Incorrect units could make parts of the structure extremely flexible or extremely stiff compared to the remaining portions. 13.Even if there are no instability warnings, run a static analysis with just three load cases—one with selfweight along X, another for Y, and the third for Z. Are there any excessive deflections for those cases? If so, the cause of that needs to be determined and rectified. 14.The subspace iteration method uses a starting point technique to come up with preconditioning vectors for the modal analysis. Sometimes, choosing an alternate set of starting vectors in eigenanalysis may work. This can be done by adding the command SET SSVECT just before the JOINT COORDINATES command. It chooses an alternate set of starting vectors in eigenanalysis. The syntax in the STAAD.Pro input file is END JOB INFORMATION INPUT WIDTH 79 SET SSVECT UNIT METER KN JOINT COORDINATES

15.There is an alternative solver in STAAD.Pro known as the advanced solver. It uses a method for calculating modes and frequencies that is mathematically different from that of the standard solver. It is better at calculating low-frequency modes than the basic solver. Perform the analysis using this solver and examine the frequencies it reports. Related Question: Can you suggest a method for calculating frequencies when only stiffness and mass are known, but

no structural model is involved? Answer: Equate the stiffness value to EA/L, and specify a set of values for E, A, and L, which will yield that stiffness. Define the mass using the JOINT LOAD option in weight units, and apply it along the Y axis of a vertical member. To ensure that frequencies due to flexural and torsional deformation are not computed, specify very high values for IX, IY, and IZ. STAAD SPACE UNIT METER KN JOINT COORDINATES 1 0 0 0; 2 0 10 0; MEMBER INCIDENCES 1 1 2; UNIT CM KN MEMBER PROPERTY 1 PRIS AX 150 IX 1e+010 IY 1e+010 IZ 1e+010 CONSTANTS E CONCRETE ALL POISSON CONC ALL SUPPORTS 1 FIXED LOAD 1 LOADTYPE None TITLE LOAD CASE 1 JOINT LOAD 2 FY -5 MODAL CALCULATION REQUESTED PERFORM ANALYSIS FINISH

4.1.12 Computing Multiple Sets of Frequencies for the Same Model Related Question: I want to calculate the frequencies once without the weight of snow on the roof and then get a revised set of frequencies with snow included. Do I create two load cases—the first without the weight of snow and the second with it included, and provide the MODAL CALC REQ command in both cases, as shown in Fig 4.1.24?

FIGURE 4.1.24 Multiple load cases containing weights for frequency calculation

Answer: STAAD.Pro performs the eigensolution only once per analysis run. If more than one load case is specified with the MODAL CALC command, as shown in Fig 4.1.24, the following messages will appear in the output file. **ERROR** MORE THAN ONE MODAL-CALCULATION-REQUESTED COMMAND ENTERED IN THIS ANALYSIS

FIGURE 4.1.25 Error message in the output file in the event of multiple load cases for frequency calculation

So, you need to create two models, one with the snow weight, and the other without.

4.1.13 Damping and Frequencies Related Question: I am applying damping to the support springs either by using SET SDAMP or by specifying SPRING DAMPING commands. Is this damping considered during the frequency calculation?

Answer: No. STAAD.Pro calculates undamped frequencies only. Damping is not taken into consideration during frequency calculation.

4.1.14 Taking into Account Axial Forces (P-Delta Effect) When Performing Modal Analysis Related Question: The frequencies that STAAD.Pro calculates are based on the stiffness matrix of the unloaded structure. The effect of the axial load in the columns and other members is not reflected in the stiffness matrix. Will the influence of the axial load on the member stiffnesses be considered by STAAD.Pro during eigensolution? Answer: The significance of axial forces in vibration is easily understood by considering a simple rope. When that rope is held taut between its ends, it has a different frequency than when it is allowed to sag. In recent versions of STAAD.Pro, the axial effect (also called the P-Delta effect) has been incorporated into the modal analysis process. The global stiffness matrix and the global geometric stiffness matrix are combined to yield the [K + Kg] matrix, which is then used in the frequency calculation. So, stiffness changes due to the P-Delta effect are reflected in the frequencies. Section 1.18.2.1.3 of the STAAD.Pro Technical Reference manual has information on this feature.

FIGURE 4.1.26 Page from the STAAD.Pro Technical Reference manual for P-Delta and modal extraction

4.1.15 Member Tension/Member Compression Attributes and Eigensolution By definition, member tension or member compression stands for a condition where a member is active when the axial force is of one state, but inactive when the force is of the opposite state. An active state is accounted by including the member’s stiffness in the stiffness matrix, while the inactive state is handled by omitting it. In a structure that is oscillating, the forces in members change sign continuously. Since only a single stiffness matrix is used in the eigensolution, that matrix has to account for the ever-changing nature of these members. The procedure implemented in STAAD.Pro is not designed to handle this situation. Fig 4.1.27 shows the error and warning messages that appear in the .ANL file if this situation is encountered.

FIGURE 4.1.27 Warning message for member tension and eigensolution

Hence, member tension and member compression are not considered during eigensolution. These members are treated as active for frequency calculation purposes.

4.1.16 Spring Tension/Spring Compression Attributes and Eigensolution For the same reasons described in Section 4.1.15, spring tension and spring compression are not considered during eigensolution. If they are present in the model, warning and error messages similar to those shown in Fig 4.1.28 will be reported in the .ANL file.

FIGURE 4.1.28 Warning message for spring tension/compression and eigensolution

Frequency is calculated assuming that those springs are all active.

4.1.17 Structures with Multilinear Spring Supports STAAD.Pro can calculate frequencies only for linear conditions for which the solution can be determined using a single iteration. Multilinear springs come under the realm of nonlinear conditions and require multiple iterations. STAAD.Pro calculates the frequency for such models using the stiffness specified by the user for the first iteration.

4.1.18 Structures with Cables As cables are large displacement entities, a transverse load will induce an axial force in the cable. If the cable is pre-tensioned, that tension will increase or decrease depending on how the two ends of the cable displace under loading. If cables are present in the model, STAAD.Pro calculates their stiffness based on the initial

conditions only. The axial force that the stiffness is based on is the initial tension. The change in axial force as a result of the deformation of the cable under the selfweight and other loads on the cable is not taken into consideration in the stiffness matrix formation. The MEMBER TENSION command is disregarded, and, STAAD.Pro will include all cables in the stiffness matrix. The frequencies and modes of the structure are calculated on the basis of these conditions. The page from the STAAD.Pro Technical Reference manual relating to frequency calculation for cables is shown in Fig 4.1.29.

FIGURE 4.1.29 Page from the STAAD.Pro Technical Reference manual for the analysis of cables

4.1.19 Comparing Rayleigh Frequencies with Eigenvalue Frequencies Example 4 LOAD 1 DEAD LOAD ALONG X FOR RAYLEIGH SELFWEIGHT X -1 MEMBER LOAD 17 20 23 26 92 TO 139 151 153 UNI GX -0.3 16 18 19 21 22 24 25 27 UNI GX -0.15 CALCULATE NATURAL FREQUENCY LOAD 2 DEAD LOAD ALONG Y FOR RAYLEIGH SELFWEIGHT Y -1 MEMBER LOAD 17 20 23 26 92 TO 139 151 153 UNI GY -0.3 16 18 19 21 22 24 25 27 UNI GY -0.15 CALCULATE NATURAL FREQUENCY LOAD 3 DEAD LOAD ALONG Z FOR RAYLEIGH SELFWEIGHT Z -1 MEMBER LOAD 17 20 23 26 92 TO 139 151 153 UNI GZ -0.3 16 18 19 21 22 24 25 27 UNI GZ -0.15 CALCULATE NATURAL FREQUENCY LOAD 4 DEAD LOAD ALONG ALL 3 FOR EIGENSOLUTION SELFWEIGHT X -1 SELFWEIGHT Y -1 SELFWEIGHT Z -1 MEMBER LOAD 17 20 23 26 92 TO 139 151 153 UNI GX -0.3

16 18 19 21 22 24 25 27 UNI GX -0.15 MEMBER LOAD 17 20 23 26 92 TO 139 151 153 UNI GY -0.3 16 18 19 21 22 24 25 27 UNI GY -0.15 MEMBER LOAD 17 20 23 26 92 TO 139 151 153 UNI GZ -0.3 16 18 19 21 22 24 25 27 UNI GZ -0.15 MODAL CALCULATION REQUESTED

For load cases 1, 2, and 3, we will get one frequency each. For load case 4, we will get six frequencies. Each of the first three should have a very close resemblance to one among the latter six. If the deflected shape used for the Rayleigh method does not match the lowest mode shape, the Rayleigh frequency too won’t match the lowest frequency from the eigensolution. Instead, we have to find which among the various modes resembles the displaced shape generated by the loading applied in the Rayleigh method. When we do find a match, we will find that the frequencies too are comparable. Fig 4.1.30 shows a model for comparing the frequency from the two methods. The structure is a two-span beam with three pinned supports. The first mode is similar to a sine wave, with the first span displacing in the opposite direction to the second span.

FIGURE 4.1.30 First mode shape of a two-span beam

Remember that unless the displaced shape for the Rayleigh method matches the mode shape from the eigenvalue method, the frequencies from the two methods won’t match. Hence, the loading on the structure for the Rayleigh method must not be a uniform downward load on both spans or a uniform upward load on both spans. Instead, the load must be downward on one span and upward on the other span. This produces a displaced shape that resembles the first mode of the eigensolution. It underscores the significance of the right type of loading on the Rayleigh frequency.

FIGURE 4.1.31 Loading on a two-span beam for Rayleigh frequency calculation

Example 5: Two-span beam for Rayleigh frequency STAAD PLANE UNIT METER KN JOINT COORDINATES 1 0 0 0 25 10 0 0; MEMBER INCIDENCES 1 1 2 24 MEMBER PROPERTY AMERICAN 1 TO 24 TABLE ST W6X16 CONSTANTS E STEEL ALL POISS STEEL ALL SUPPORTS 1 13 25 PINNED LOAD 1 RAYLEIGH FREQUENCY MEMBER LOAD 1 TO 12 UNI GY -1.0 13 TO 24 UNI GY 1.0 CALCULATE RAYLEIGH FREQUENCY LOAD 2 EIGENVALUES MEMBER LOAD 1 TO 24 UNI GY -1.0 MODAL CALCULATION REQUESTED PERFORM ANALYSIS FINISH

FIGURE 4.1.32 Eigenvalue table in the STAAD.Pro output file

FIGURE 4.1.33 Rayleigh frequency report in the STAAD.Pro output file

Notice that the frequency values in Figures 4.1.32 and 4.1.33 are very similar—10.1 cps.

4.1.20 Rigid Body Modes A rigid body mode is one in which there is no motion of one node relative to another. A structure that is not restrained along a certain direction, and hence free to move physically in that direction, has a rigid body mode in that direction. STAAD.Pro cannot calculate rigid body modes.

4.1.21 Structural Response for a Frequency Analysis For this analysis also, we will obtain the structural response—the node displacements, support reactions, member end forces, plate and solid element stresses, and so on. However, it is important to understand that these results are not for any type of dynamic loading. Instead, these are the static results obtained by subjecting the structure to the various weights specified in that particular load case applied statically. This is because, the instruction MODAL CALCULATION REQUESTED by itself does not constitute a dynamic loading just as CALCULATE RAYLEIGH FREQUENCY does not constitute dynamic loading. It is simply a way to communicate to STAAD.Pro to derive the mode shapes and frequencies by using those weights as the source of the vibrating masses for a free-vibration analysis. A dynamic response can be obtained only when instead of a frequency and mode extraction analysis, a true dynamic analysis, such as response spectrum or time history analysis, is performed. Related Question: I am trying to determine whether the seismic forces would shake the tower so much that members will fail. I can see the mode shape in the post-processor. How do I use that information to gauge the ability of the structure to withstand the earthquake? Answer: Knowing the mode shapes and frequencies by itself is not sufficient to know how a structure will respond to a dynamic load. You will have to perform the analysis for a specific dynamic load, such as an earthquake. The load could be applied in the form of a response spectrum or a time history. Alternatively, you could use a psuedostatic approach such as the IBC 2006 method. Related Question: How can I get the amplitude of vibration? Answer:

Amplitude of vibration can be obtained if a time history analysis is performed. If only a mode shape and frequency extraction analysis is performed, it will be a free-vibration problem. There is no dynamic force on the structure, either external or induced by ground movement. If you do a time history analysis, you will be able to see a displacement—time graph for each node, which will help you identify the amplitude of vibration—peak as well as steady state.

4.1.22 Closely Spaced Modes If the frequencies of two or more consecutive modes of vibration differ from each other by a small magnitude, such as 10% or less, they are known as closely spaced modes. Such modes usually occur for structures that have similar properties in two directions such as X and Z. In response spectrum analysis, an appropriate modal combination method such as CQC (complete quadratic combination) or CSM (closely spaced modes) must be used when such modes are present. Widely used combination methods such as SRSS (square root of sum of squares) may not be suitable when such modes are present.

4.1.23 Structures that Have Identical Attributes along Two Global Directions Occasionally, we come across structures whose geometry, member and material properties, support conditions, and weights are identical along two global directions—usually X and Z. For such doubly symmetric structures, the sequential order of the mode shapes often contain double root modes, that is, two successive modes that have identical values of mode shape ordinates and frequencies but are in orthogonal directions. Double root modes are an example of closely spaced modes. Such modes can be either at 0 and 90 degrees to the global directions, or at +θ and −θ degrees where θ is any angle between 0 and 90, usually 45. That means, they could be in the X direction for one mode and the Z direction for the other mode (which would be desirable). Or, those modes could be at 45 degrees and 135 degrees, respectively, to global X. Alternatively, they could be at any other angle. If the double root modes are not aligned with the global axes, modifying the weights used in the modal calculation can help in aligning them. Basically, increase the weights marginally along one of those two directions (e.g., the X direction), decrease the weights marginally along the other (e.g., the Z direction), and leave the weights in the third direction unchanged.

FIGURE 4.1.34 Double root modes in the output file and post-processing mode

The CQC method must be used if a response spectrum analysis is done for structures with double root modes, not to mention the fact that both modes must be included in the solution (using CUT OFF MODE SHAPE if they happen to be greater than modes one through six).

4.1.24 Shear Stiffness Related Question: I am trying to validate the frequency of a cantilever beam with a lumped weight at the free end. The beam has a standard steel section. The STAAD.Pro result is slightly different from the theoretical value based on an equation I found in a text book. What might be the reason? Answer: The probable cause is the following. In STAAD.Pro, the stiffness of a beam consists of its flexural stiffness plus its shear stiffness. The shear stiffness is based on the shear area terms. On the other hand, the equation in the text book may not consider the shear stiffness term. If so, the difference in the total stiffness can cause the frequencies to be different. W can instruct STAAD.Pro to omit the shear stiffness term. The command for this is SET SHEAR, and should be provided somewhere near the beginning of the input file. STAAD SPACE START JOB INFORMATION ENGINEER DATE 07-Jul-11 END JOB INFORMATION INPUT WIDTH 79 SET SHEAR UNIT METER KN

JOINT COORDINATES …

4.1.25 Frequencies of Parts of the Model Related Question: Although I have created a complete model, I want to find out the frequency of just a portion of it. I am concerned with the walking-induced vibration of just one floor. Answer: Unfortunately, there is no easy way to do a frequency analysis of just a portion of a larger model. If that floor is joined to the rest of the structure through PINNED connections only, you could consider extracting that portion into a separate model with PINNED supports and do a frequency analysis for just that substructure. Alternatively, place a fixed support at every joint on the structure except at the ends of the entities whose frequencies you are interested in. Then do an eigensolution. The calculated frequencies will be for that portion alone.

4.1.26 Torsional Mode of Vibration of Individual Members Related Question: I want to find the torsional frequency of a solid rod that is fixed at one end and free at the other. Can you show me an example? Answer: In the following example, a rotational mass is provided at the free end of the pipe. Note that the rotational mass is entered in weight units. Although this value is entered in the same format as an applied moment, it is used as a weight moment of inertia. STAAD SPACE UNIT KIP INCH JOINT COORDINATES 1 0 0 0; 2 0 120 0; MEMBER INCID 1 1 2; MEMBER PROP * 6 INCH DIAMETER ROD 1 PRISMATIC YD 6. CONSTANT E STEEL POIS STEEL DENS STEEL SUPPORT 1 FIXED LOAD 1

JOINT LOAD * WEIGHT MOMENT OF INERTIA = .432 KIP-INCH^2 2 MY .432 MODAL CALC REQUESTED PERFORM ANALYSIS FINISH

4.1.27 Adding a Concentrated Weight to Represent a Machine Related Question: I want to add the weight of a machine to the model. But instead of adding the weight to a node or within the span of a beam, I want to specify it at the coordinates of the center of gravity (CG) of the machine. Answer: Create a node in the model at the location of the CG of the machine. Connect the node to the appropriate entities of the structure (nodes or members or elements) through dummy members. The member could be assigned a large E, for example, 10–100 times that of steel to simulate a rigid entity. For mass modeling, the weight of the machine could be included as concentrated weights along the three global directions at that node.

4.1.28 Summary There are two methods in STAAD.Pro for calculating the frequencies of a structure. 1. Rayleigh method, which is an approximate method 2. The modal calculation method For Method 1, specify the command CALCULATE RAYLEIGH FREQUENCY in the load case in which the load data which produce a mode-shape-type deflected shape are specified. With this method, only one frequency is calculated. The accuracy of the frequency depends on the closeness in resemblance between the deflected shape and a mode shape. For Method 2, specify the command MODAL CALCULATION REQUESTED in the load case in which the load data for the mass matrix are specified. Frequencies (eigenvalues), mode shapes, participation factors, and some other details will be listed in the output file and in the tables of the Dynamics page of the post-processing mode. Mode shapes (eigenvectors) can be viewed from that page, graphically and in tables. If the stiffness and mass data are specified correctly, Method 2 is more reliable than Method 1. Modes and frequencies can be computed only for stable structures. Ensure that there are no instability problems with the model.

4.2 Damping 4.2.1 Introduction The dynamic analysis facilities in STAAD.Pro—response spectrum and time history—use the modal superposition method. Damping is one of the dynamic properties of the structure that is used during such analyses. It is also required for STAAD.Pro’s steady-state analysis facility. Damping is not used in static or in quasi-dynamic analysis such as those in the UBC or IBC

codes. The damping property that is conveyed to STAAD.Pro is called the damping ratio. In this section, we look at the various options and methods available for specifying the damping ratio. In addition to the examples presented here, more examples on the application of damping are available in Section 5.1 for response spectrum and Section 5.2 for time history. Required Reading 4. Technical Reference manual—Sections 1.18.3.3, 5.26.4, and 5.26.5 5. Graphical Interface Help manual—Sections 2.3.7.2 and 2.3.7.7

4.2.2 Discussion The damping options available in STAAD.Pro are summarized in Table 4.1. TABLE 4.1 Damping Options Available in STAAD.Pro

Type No. 1

Identification Keyword

Definition

Input Data

Whether Calculated by the Program

DAMP

A single damping ratio for all modes

A number between No 0 and 1

2

MDAMP (modal damping)

Individual Depends on the damping ratios for options (see next individual modes column) specified through a DEFINE DAMPING table

Yes. Methods are EXPLICIT EVALUATE CALCULATE

3

CDAMP (composite damping)

Program calculates damping based on damping ratio of materials and springs

Yes

Individual damping ratios of each material and spring

The options listed in this table can be classified into two categories. Category A. The user provides the value that is directly used by the program for the individual modes. Examples of this category for response spectrum and time history are: 1. DAMP 2. MDAMP-EXPLICIT Category B. The user provides a set of data (feed data) using which the program calculates the damping ratios for the individual modes. Examples of this category for response spectrum and time history are: 1. MDAMP-EVALUATE 2. MDAMP-CALCULATE 3. CDAMP

4.2.2.1 DAMP DAMP is used in situations where a single damping ratio is applicable for all modes. In other words, all modes have the same modal damping ratio. All the dynamic analysis methods in STAAD.Pro have provisions for this type of damping (see Section 5.1.3.3.7 for response spectrum

analysis and Section 5.2 for time history analysis), and two examples are shown here. Example 6: DAMP in response spectrum analysis

Example 7: DAMP in time history analysis

NOTE The value for DAMP is a fraction between 0 and 1. A damping ratio of 5% is specified as DAMP 0.05. Values greater than 1 are erroneous. Even a value such as DAMP 0.3, which stands for 30% damping, isn’t normal for materials used in buildings, unless it represents a material such as fluid dampers, which have high damping properties.

4.2.2.2 CDAMP (Composite Damping) In dynamic analysis, it is customary to use a single damping ratio for all modes of the structure. But if a structure consists of more than one material, such as steel and concrete, some modes will strain the steel the most and the damping would be closer to that of steel. Other modes will strain the concrete the most with damping nearer to that of concrete. Further, if the support mechanism consists of springs, it makes its own contribution to damp the motions caused by dynamic loading. So, an effective damping ratio has to be calculated that accounts for these parameters. This is known as composite damping and is denoted using the term CDAMP. It is based on the relative

strain energy of each region of a structure to the total strain energy of the structure and that region’s damping ratio. This calculation is performed by the program during dynamic analysis. Thus, composite damping is a weighted average (hence, the term “composite”) damping ratio, which is based on the strain energy and damping ratio of: The various materials used in the structure The spring supports of the structure if spring damping is specified It is useful only if there are two or more materials with different damping values in the model. If there is only one material, and there is no spring damping, the composite damping ratio should be equal to the damping ratio of the material. For response spectrum, the CDAMP values will not be used except in CQC and ASCE4 combinations. 4.2.2.2.1 Input for Composite Damping The data required to calculate composite damping ratios come from two sources: 1. Damping Ratio of the Individual Materials of the Structure (Material Damping) The materials that are used in the structure for members (beams, columns, braces, etc.) and elements (walls, slabs, roofs, etc.) all have their own damping ratio called the material damping ratio. For standard materials such as steel and concrete, it is built into the program’s material library and gets automatically assigned if the properties are assigned through the STAAD.Pro GUI. If the data are assigned through the editor, users will have to ensure that they provide the damping ratio just like E, density, or alpha using one of the methods described in Section 3.8 of Part I.

FIGURE 4.2.1 Model containing two materials

FIGURE 4.2.2 Dialog box in the STAAD.Pro GUI for specifying the damping ratio through the material data

2. Spring Damping Ratios (If Springs Are Present) This is the damping property of the medium such as soil that represents the supports of the structure. There are two ways to specify spring damping. a. The SET SDAMP nnnn command: This is a blanket declaration that affects all the support springs of the model. In other words, no support spring is excluded through this method. STAAD SPACE START JOB INFORMATION .. .. END JOB INFORMATION SET SDAMP 0.15 UNIT FEET KIP JOINT COORDINATES 1 10 0 0 ; ….

FIGURE 4.2.3 Dialog box in the STAAD.Pro GUI to specify a fixed spring damping for all springs

Thus, when all springs get the same value, specify that using SET SDAMP nnnn. b. The SPRING DAMPING command: This is a way to specify damping for support springs by specific joint number and direction, and is thus joint-list based. Currently, it can be specified only through the editor (typing the commands into the STAAD.Pro input file) as there is no GUI interface for this. In the STAAD.Pro Technical Reference manual, this feature is described in Section 5.26.5. An example of the syntax in the STAAD.Pro input file is shown next. SPRING DAMPING 14 67 125 KFX 0.08 KFY 0.08 KFZ 0.08 25 TO 35 KFX 0.35 KFY 0.35 KFZ 0.35 58 74 83 92 KFX 0.3 KFY 0.3 KFZ 0.3 SUPPORTS 14 67 125 FIXED BUT MX MY MZ KFX 200 KFY 1200 KFZ 200 25 TO 35 FIXED BUT MX MY MZ KFX 18 KFY 12 KFZ 18 58 74 83 92 FIXED BUT MX MY MZ KFX 120 KFY 55 KFZ 120

Thus, the SPRING DAMPING table is used when different springs have different damping values. Keep in mind that spring damping can be assigned to only those degrees of freedom that are assigned a spring. 4.2.2.2.2 Method Used in the Calculation of CDAMP The equation used by STAAD.Pro in calculating the damping ratio of the individual modes is available in Section 1.18.3.3 of the program’s Technical Reference manual. Section 3.1.5 of the publication ASCE 4-98—Seismic Analysis of Safety-Related Nuclear Structures and Commentary is also a good source of information on composite damping. For each mode of the structure, the steps are as follows: 1. For each member/element/spring, calculate its damped strain energy by multiplying its strain energy by its damping constant.

2. Sum the damped strain energy from Step 1 over all the members/elements/springs. Call this Result A. 3. For each member/element/spring, calculate its strain energy. 4. Sum the value from Step 3 over all the members/elements/springs. This is the total strain energy of the structure. Call this Result B. 5. Divide A by B to get the effective damping ratio for that mode. Repeat these steps for all modes. Example 8: CDAMP in response spectrum analysis

Example 9: CDAMP in time history analysis

In Example 9, the damping ratio for steel is 3%, and that for the support spring is 8%. Also, in the time history definition, the program is instructed (through the term CDAMP) to use composite damping. If a mode is almost all motion of the steel structure, the damping ratio for the mode would be near 0.03. When a mode is nearly all motion of the support spring, its damping ratio would be near 0.08. 4.2.2.2.3 Information in the Output File When CDAMP Is Used A table of damping ratios for the various modes of the structure will appear in the output file if composite damping is specified.

FIGURE 4.2.4 Table of damping ratios output for CDAMP

Importantly, based on this discussion, it is clear that the damping ratio of the individual materials will be used if and only if CDAMP is specified as the damping method in the dynamic analysis. Related Question: Is it possible to enter the damping ratio for individual members without creating a material definition for each? Answer: Yes. That can be specified under the heading CONSTANTS as shown in the following example. CONSTANTS E STEEL ALL POIS STEEL ALL DAMP 0.07 MEMB 2 DAMP 0.05 MEMB 3 DAMP 0.02 MEMB 4 DAMP 0.03 MEMB 5

4.2.2.3 MDAMP (Damping Ratio for Individual Modes) The MDAMP method is used when the dynamic analysis must be performed using a known set of modal damping ratios (specific damping ratios for specific modes), or ones calculated by the program on the basis of damping ratios that are known for two specific modes. Modal damping is explained in Section 5.26.4 of the Technical Reference manual. The instruction is specified through a command block that begins with the line DEFINE DAMPING INFORMATION.

FIGURE 4.2.5 Dialog box in the STAAD.Pro GUI for specifying a table of damping values for individual modes

There are three options available with MDAMP. They are: Option 1. The individual damping ratio for each mode is known, and we want the program to use them. The method for assigning this to the program is through a term called EXPLICIT. Example 10 DEFINE DAMPING INFORMATION EXPLICIT 0.05 0.06 0.08 0.02 0.01 0.01 0.01 0.01 0.01 END

In this example, mode 1 has a damping ratio of 0.05, mode 2 has 0.06, mode 3 has 0.08, mode 4 has 0.02, and modes 5 through 9 have 0.01. Example 11 DEFINE DAMPING INFORMATION EXPLICIT 10*0.02 12*0.03 20*0.05 END

In this example, 10*0.02 means that the first 10 modes have a damping of 0.02. 12*0.03 means that modes 11 through 22 have a damping of 0.03. 20*0.05 means that modes 23 through 42 have a damping of 5%. If the number of terms entered in these tables is less than the number of modes that the program

calculates during eigensolution, the last damping entered will apply to those modes for which damping is not entered. Option 2. This method can be used when the damping ratio for the first two modes and the maximum permissible damping ratio (the value that cannot be exceeded for any mode) are known. Using these values, we want the program to evaluate the damping for modes 3 through N, where N is the number of modes calculated. The method for assigning this to the program is through a term called EVALUATE.

Example 12 DEFINE DAMPING INFORMATION EVALUATE 0.02 0.12 END

4.2.2.3.1 Output for MDAMP-EVALUATE Information similar to that shown in Fig 4.2.6 is reported in the output file for this option during the analysis.

FIGURE 4.2.6 Report of calculated damping ratios for MDAMP-EVALUATE

Notice that in Fig 4.2.6, the first two modes have the same damping ratio (same as the input). Also, modes 12 onward have the same value, which is the same as the specified upper limit. Option 3. This method instructs STAAD.Pro to calculate the damping ratio using the Rayleigh damping equation.

The method for assigning this to the program is through a term called CALCULATE. The input is a and b, and they are associated with the first and second modes. Additionally, the upper and lower limits for the damping ratios are optional items that can be entered (the range between which the calculated values must be restricted to). More information on this method is available in Section 5.26.4 of the Technical Reference manual. Example 13 DEFINE DAMPING INFORMATION CALC ALPHA 1.13097 BETA 0.0013926 MAX 0.15 MIN 0.01 END

4.2.2.3.2 Output for MDAMP-CALCULATE Information similar to that shown in Fig 4.2.7 is reported in the output file for this option during the analysis.

FIGURE 4.2.7 Report of calculated damping ratios for MDAMP-CALCULATE

Example 14: MDAMP in response spectrum analysis DEFINE DAMPING INFORMATION EVALUATE 0.02 0.1 END .. LOAD 31 SEISMIC - Y SELF X 1.0 .. SPECTRUM SRSS Y 0.3 ACC SCALE 7.2 MDAMP MIS 0.002 0.15; 0.05 0.18 ; 0.10 0.25; 0.15 0.28 ..

Example 15: MDAMP in time history analysis UNIT KIP FEET DEFINE DAMPING INFORMATION EXPLICIT 5*0.05 5*0.02 10*0.03 0.012 END DEFINE TIME HISTORY

TYPE 1 FORCE FUNCTION SINE AMPLITUDE 3.2 RPM 1500 CYCLES 100 ARRIVAL TIME 0 MDAMP

4.2.3 Damping in Frequency Calculation Damping ratios are not used in calculating modes or frequencies. STAAD.Pro calculates only undamped modes and frequencies. Related Question: My model contains steel and concrete members. In the material definition, the damping ratio for both materials is provided. This takes care of the input required for CDAMP. I have also defined the damping ratios for the individual modes through a DEFINE DAMPING table. This takes care of the input required for MDAMP. My question is, since the model has input for both types of damping, which type will STAAD.Pro actually use for the time history analysis? Answer: The type of damping actually used in the time history analysis depends on what command has been specified under the DEFINE TIME HISTORY block of data. We saw three examples earlier for time history—one with DAMP, another with CDAMP, and a third with MDAMP. That is the input that STAAD.Pro goes by to decide which damping type to use. In other words, it is not the input for material damping ratios or the damping table that determines which damping is actually used. To summarize, if the instruction entered at the end of the DEFINE TIME HISTORY block is DAMP nnnn, then that number will be used for all modes regardless of any other damping data entered. MDAMP, then the individual modal damping ratios generated from the data entered with DEFINE DAMPING INFO will be used regardless of any other damping data entered. CDAMP, then the individual modal damping ratios for each mode will be calculated using the strain energy terms as explained earlier, and these modal damping ratios will be used regardless of any other damping data entered.

4.2.4 Incorporating the Damping Characteristics of Soil for a Response Spectrum Analysis Steps: 1. 2. 3. 4.

Under the material data, enter the damping ratio for each material. Enter Spring Damping for each spring. Enter CDAMP on the SPECTRUM command. Use FILE FN option in the SPECTRUM data. Enter several acceleration versus period spectrum curves in the file. Each will be for a different damping ratio including those of the materials and springs. 5. During the analysis, STAAD.Pro will calculate the damping ratio for each mode. 6. Then, for those damping ratios, STAAD.Pro will interpolate between the spectrum curves on the file to get the spectral data for each mode. This will yield one spectrum curve per mode.

Then, using the period of the mode, it will find the spectral acceleration or spectral displacement for that mode from that curve.

4.2.5 Incorporating the Damping Characteristics of Soil for a Time History Analysis Steps: 1. 2. 3. 4.

Under the material data, enter the damping ratio for each material. Enter Spring Damping for each spring. Use CDAMP as the damping type under DEFINE TIME HISTORY. During the analysis, the response of each mode will be based on the calculated damping ratio for the mode.

Related Question: I want to consider the damping effect of laminated rubber bearings, which are placed beneath the girders in my model. What would be the best way to consider that? Answer: If the bearings are modeled using spring supports, the damping characteristic can be specified using the SPRING DAMPING command. Alternatively, one could model the laminated rubber bearings as layers of solid elements beneath the girder. For solid elements, damping should be entered with the material constants. In both cases, remember to use CDAMP with the dynamic analysis instruction.

4.2.6 Modeling a Shock Absorber Which Is a Viscous Damper STAAD.Pro does not have a point-to-point damper element (discrete dampers at nodes). One way around is: Model the damper as a truss member The weight can be modeled using the JOINT LOAD option Assign the member a material with a damping ratio equal to the damper value Use CDAMP in the response spectrum or time history analysis command

CHAPTER 5

Dynamic Loads 5.0 Dynamic Loads 5.0.1 Introduction Dynamic loads are those loads whose magnitude and/or direction varies with time. Generally, for the analysis of a structure for dynamic loads, a rigorous procedure known as dynamic analysis is necessary. It is also termed “vibration analysis.” Certain types of dynamic loads can be analyzed using quasi-static methods. In Table 12.6-1 of the

American standard ASCE/SEI 7-05 titled “Minimum Design Loads for Buildings and Other Structures,” a method known as Equivalent Lateral Force Analysis is permitted for structures (subjected to earthquake ground motions) that satisfy the characteristics described in that table. Building codes of other nations too permit a similar procedure. A detailed discussion on this method is available in Section 2.4. In Chapter 4, we learnt the methods for calculating a structure’s dynamic properties such as mode shapes and frequencies. These properties are used in dynamic analysis. The types of rigorous dynamic analysis methods available in STAAD.Pro for dynamic loading are: 1. 2. 3. 4.

Response spectrum Time history - machine vibration Time history - ground motion Time history - for a force that varies arbitrarily over time

Item 1 is discussed in Section 5.1 and Items 2–4 are discussed in Section 5.2. It is not the intent of this chapter to be a treatise on the principles of response spectrum or time history analyses. There are many good textbooks on dynamic analysis that address those subjects. Instead, the objective here is to illustrate the many aspects of these topics in the context of their application in structural analysis and design using software, specifically, STAAD.Pro.

5.1 Response Spectrum Analysis 5.1.1 Introduction A response spectrum analysis (RSA) is one of the methods of dynamic analysis for determining the peak response of the entities of a structure—displacements of nodes, forces and moments in beams, stresses in plates—to a base excitation. Base excitation is the motion of the supports of the structure. Some examples of base excitation are: An earthquake that causes a structure to vibrate The excitation of the supports of a machinery mounted on a structure because that structure itself is under vibration The focus in this section is on the first type. The ground movement due to an earthquake is measured in terms of ground acceleration versus time. There are three ways in which a structure can be analyzed for this ground acceleration. These methods are also listed in Table 12.6-1 of ASCE 7-05. 1. The equivalent lateral force procedure. This method is discussed in detail in Section 2.4. Although it requires the calculation of certain dynamic properties, it is not a dynamic analysis method in the true sense of the term. A better term is perhaps “pseudo-dynamic” or “pseudostatic.” 2. Time history analysis. The structure’s response is directly computed for the ground acceleration. The method for doing this type of analysis in STAAD.Pro is discussed in detail in Section 5.2. 3. RSA. Instead of using the ground acceleration as the load for which to measure the structure’s response, the peak response of a single degree of freedom (SDOF) system to that earthquake is used as the input. That input consists of a range of periods of the SDOF system versus its peak response (displacement or acceleration) to that ground motion. Hence, it is a table of values of

period versus displacement or period versus acceleration. So, the “input spectral data” table is the primary data for an RSA. If a load case contains input spectral data and other parameters used in RSA, it is called a response spectrum load case (RS load case). The analysis that is done on that load case is called response spectrum analysis or RSA. Readers are urged to go through Section 4.1 before reading this chapter. A knowledge of the terms described in that section, especially relating to output, is required to understand the material presented in this chapter. In the following pages, we will see the various calculations that are performed for RSA, the data needed to perform them, and the output produced by STAAD.Pro. Required Reading 1. Technical Reference manual—Sections 1.18.3.4 and 5.32.10.1 2. Application Examples manual—Example 11

5.1.2 Discussion The instruction that enables STAAD.Pro to understand that an RSA is to be performed is a load case containing a command line that starts with the word SPECTRUM. A typical spectrum load case is shown next.

FIGURE 5.1.1 Syntax in the input file of a typical response spectrum load case

The terms annotated in that load case constitute the input required for STAAD.Pro to perform an RSA. Their details are discussed in this chapter. We will then examine the output produced by STAAD.Pro for an RSA. The engineering principles that form the basis of the input and output are also mentioned whenever possible.

5.1.3 Input Required by STAAD.Pro for RSA The following is a summary of the input that is needed for STAAD.Pro to perform an RSA. Weights for calculating frequencies and modes (mass modeling) Spectrum command along with the parameters Period-acceleration or period-displacement pairs, also known as spectral data or Commands to generate the spectral data

5.1.3.1 Weights for Frequency Calculation (Mass Modeling) The RSA procedure requires knowledge of the dynamic properties of the structure—mode shapes, frequencies, and damping characteristics. If STAAD.Pro detects an RS load case in the model, it automatically performs an eigensolution. The MODAL CALCULATION REQUESTED command that we saw in Chapter 4 does not have to be specified in an RS load case. There is no harm in providing it though. STAAD.Pro simply treats it as a superfluous input command. As discussed in Section 4.1, all the weights that are capable of vibrating, such as selfweight, permanent loads, and the weight of equipment, should be specified as loads (as positive values) acting in all possible directions of vibration (usually all three global directions). They are the source for the masses used to populate the mass matrix and should be included in the first RS load case. If no weights are entered, the following message will appear in the output file. *ERROR* NO UNSUPPORTED MASSES ENTERED - CHECK DENSITIES *** ERRORS IN SOLVER ***

FIGURE 5.1.2 Error message in the output file if no weights are entered for the spectrum case

A common misapprehension is that the weights that are specified for the extraction of the masses for the mass matrix are also going to be applied as forces acting statically in the respective directions. This is not correct. For example, if the data are provided as shown in the following example, LOAD 6 LOADTYPE Seismic TITLE SPECTRUM ANALYSIS SELFWEIGHT X 1 SELFWEIGHT Y 1 SELFWEIGHT Z 1 SPECTRUM CQC X 1.0 ACC SCALE 9.806 LOG MIS ………

the selfweight is used solely as the source for the mass matrix. The structure is not solved for the selfweight acting statically along the three directions. So, to solve the structure for the gravity load (dead load), a new load case must be created with SELFWEIGHT acting along Y with a negative factor. 5.1.3.1.1 Multiple Spectrum Cases and Weight Data

If the model is being solved for more than one RS load case, the weight data need to be entered for only the first of those cases. The frequencies and mode shapes are computed only once and are based on those weights only. No weight data are needed for the subsequent spectrum cases, and even if they are specified, they will not be used. When more than one spectrum case is present, the second through last spectrum cases will utilize the mode shapes and frequencies calculated using the weights specified in the first spectrum load case.

FIGURE 5.1.3 Multiple spectrum load cases containing the weight data

5.1.3.2 Spectrum Pairs Input—A Lookup Table for Spectral Data Spectral data mean several pairs of two numbers: Period versus acceleration or Period versus displacement The first number of each pair is the period of the SDOF system. The second number is the peak acceleration (known as spectral acceleration) or peak displacement (the spectral displacement) of that system to the underlying earthquake. In the following example, several pairs are shown separated by semi-colons. 0.001 0.46; 0.05 0.68; 0.1 0.88; 0.15 1.19; 0.2 2.23; 0.25 2.87

These pairs are a critical input item for a spectrum load case. They constitute a lookup table that the program goes to for finding the spectral acceleration (or displacement) corresponding to the period of a mode being considered in the RSA. This process is repeated for each of the modes

considered for the solution. Figs 5.1.4 and 5.1.5 illustrate the manner in which these data have to be specified. A linear or logarithmic interpolation technique is used to obtain the appropriate value from this lookup table (explained in Section 5.1.3.3.3).

FIGURE 5.1.4 Specifying the spectral data in the STAAD.Pro GUI

FIGURE 5.1.5 Specifying the spectral data in the STAAD.Pro input file

The spectrum pairs must be in the ascending order of the period. 5.1.3.2.1 Spectrum Type—Acceleration Spectra or Displacement Spectra? As discussed earlier, the second term of each spectrum pair is either acceleration or displacement.

This has to be communicated to STAAD.Pro in the manner shown in Fig 5.1.6.

FIGURE 5.1.6 Dialog box in the STAAD.Pro GUI for specifying the spectrum type

Example 1: The ACCeleration type of spectrum

Example 2: The DISPlacement type of spectrum

It is important to pay attention to the units. If the acceleration or displacement terms are unnormalized (having units of length and time), ensure that they are in the correct length units. 5.1.3.2.2 Where Can We Get the Spectral Data From? The spectral data are usually obtained from the building codes used for that project, such as, IBC, ASCE 7, Eurocode 8 (EC8), and AIJ. Other organizations such as the U.S. Geological Society also may have publications with such information. Section 11.4.5 of ASCE 7-05 suggests an equation using which the spectral data can be generated. STAAD.Pro can generate the spectral data for codes such as IBC 2006, EC8 (1996 and 2004), and IS 1893. Generation of Spectral Data for IBC 2006 This feature is available only for sites within the United States (zip code or latitude/longitude). The dialog box associated with this input is shown in Fig 5.1.7, and for the meaning of the terms in the dialog box, see Section 5.32.10.1.5 of the STAAD.Pro Technical Reference manual. The generation of the spectra is done as per Section 11.4.5 of the ASCE 7-05 code. Subsequently, the type of analysis done using this data is a generic RSA and not code specific. In Section 2.4.3.1, we saw three methods for specifying the input data for the equivalent lateral force procedure (ELFP) method for IBC 2006. The spectral data too are generated on the basis of these methods.

FIGURE 5.1.7 Generating the spectral data per the ASCE 7-05 code

If one wishes to specify the data through the input file instead of the graphical user interface (GUI), here are some examples. Method 1: Generation based on latitude and longitude LOAD 6 LOADTYPE Seismic TITLE SPECTRUM ANALYSIS SELFWEIGHT X 1 SELFWEIGHT Y 1 SELFWEIGHT Z 1 SPECTRUM CQC IBC 2006 X 1 ACC DAMP 0.03 LAT 40.725 LONG -112.169 SITE CLASS C FA 1.054 FV 1.588 TL 12.000

Method 2: Generation based on zip code LOAD 101 EQ ALONG GLOBAL Z SELFWEIGHT X 1 SELFWEIGHT Y 1 SELFWEIGHT Z 1 JOINT LOAD 21 TO 24 37 FX 26 FY 26 FZ 26 12 FX 7.5 FY 7.5 FZ 7.5 54 FX 12.2 FY 12.2 FZ 12.2 MEMBER LOAD 201 204 232 UNI GX 31.25

201 204 232 UNI GY 31.25 201 204 232 UNI GZ 31.25 SPECTRUM CQC IBC 2006 Z 1 ACC SCALE 1 DAMP 0.05 LOG ZIP 94804 SITE CLASS C FA 0.600 FV 1.400 TL 8.000

Method 3: Generation based on Ss and S1 LOAD 27 SELF X 1.0 SELF Y 1.0 SELF Z 1.0 ELEMENT LOAD .. SPECTRUM SRSS IBC 2006 X 0.286 ACC DAMP 0.05 LOG SS 1.539 S1 0.622 SITE CLASS D TL 8.000

The zip option works only for locations in the United States. It is used to determine the latitude and longitude, which in turn are used to determine the values of Ss and S1. For other locations (where zip or latitude/longitude are not available), one needs to know the values of Ss and S1. Generation of Spectral Data for EC8-2004 For EC8, the spectral data are not input as frequency-acceleration pairs. Instead, as explained in Section 5.32.10.1.4 of the STAAD.Pro Technical Reference manual, it is generated by the program based on a few parameters, some of which are: Type of spectra (elastic or design) Soil type Alpha Q The software generates the response spectrum pairs using the guidelines of Section 3.2.2.2, 3.2.2.3, or 3.2.2.5 of EC8-2004 as applicable.

FIGURE 5.1.8 Parameters for generating the spectral data for Eurocode 8-2004

Example 3 SPECTRUM SRSS EURO 2004 ELASTIC RS1 X 1 ACC DAMP 0.03 LOG SOIL TYPE A ALPHA 1 Q 1

Generation of Spectral Data for IS 1893 The following example instructs the program to fetch the Sa/g values from the 1893 code for the type of soil that we specify (when SOIL TYPE parameter is used). SPECTRUM SRSS 1893 X 0.024 ACC SCALE 1 DAMP 0.05 SOIL TYPE 2

The (Sa/g) values will be multiplied by the factor as specified in Table 3 of the code for different values of damping. DAMP 0.05 stands for 5% damping. Providing the Spectral Pairs in an External File If the damping methods are defined as CDAMP or MDAMP (described in Section 5.1.3.3.7), multiple sets of spectral data will have to specified because one set is needed for each damping ratio that the program will use during the RSA. The format of the data in that external file is explained in Section 5.32.10.1.1 of the Technical Reference manual. If one intends to specify just a single value of damping (using the keyword DAMPING), then only one set of spectral data is applicable, and the simplest method is to specify that in the same file as the rest of the model data.

5.1.3.3 Spectrum Parameters

There are a number of parameters that are part of the response spectrum input (see Fig 5.1.9).

FIGURE 5.1.9 Dialog box in the STAAD.Pro GUI for specifying the spectrum parameters

5.1.3.3.1 Scale Factor Scale factor is a term that the second number (acceleration or displacement) of each spectrum pair is multiplied by. In the specifications documents or building codes, the acceleration or displacement values in the spectral data may be listed in one of two forms: Normalized data Un-normalized data Normalization means that the acceleration or displacement values have been divided by a number (called normalization factor), which represents some reference value. One of the commonly used normalization factors is g, the acceleration due to gravity. If the spectrum data are a normalized set, the SCALE factor is the same as the NORMALIZATION FACTOR. If it is an un-normalized set of values, there is no need to provide a scale factor. Thus, for un-normalized spectrum values, the scale factor is 1, which happens to be the default value also. The user needs to ensure that the SCALE factor entered is in accordance with the current length in the input file. A frequent error is that if the scale factor is g, users provide 32.2 when the length unit is in inches. Example 4: Specifying the scale factor for a generic SPECTRUM data

STAAD.Pro multiplies the spectral acceleration or spectral displacement values by the scale factor. Hence, if we provide a normalized acceleration value of 0.5 and a scale factor of 386.4 in./sec2, it has the same effect as providing an un-normalized acceleration value of 193.2 in./sec2 and a scale factor of 1.0. There is a quick way to assess whether a scale factor is needed for an acceleration spectrum. Take a look at the acceleration data in the following example. 0 0.23; 0.05 0.37; 0.1 0.51; 0.15 0.58; 0.6 0.58; 0.65 0.55; 0.7 0.51; 0.8 0.45; 0.9 0.4; 1 0.36; 1.1 0.33; 1.2 0.3; 1.3 0.28; 1.4 0.26; 1.5 0.24; 1.6 0.23; 1.7 0.21; 1.8 0.2; 1.9 0.19; 2 0.18; 2.1 0.17; 2.2 0.16; 2.3 0.16; 2.4 0.15;

From a practical standpoint, one expects the structural response of an SDOF system to be approximately between 0.1 and 1.0 g. In units of meter and seconds, it comes to a range of 0.98– 9.806 m/sec2, and in inch and seconds, it would have to be in the range of 38.6–386 in./sec2. Notice that the acceleration values in the previous example fall in the range 0.15–0.58, and this is significantly below the range we expect them to be in. Hence, it indicates that some kind of normalization factor has been used, and thus a scale factor greater than 1.0 is almost a certainty. Related Question: Consider the following period-acceleration data. What should the scale factor be? UNIT METER LOAD 10 EQ X SPECTRUM CQC X 1.0 ACC SCALE ???? LOG 0 0.19; 0.109 0.475; 0.2 0.475; 0.547 0.475; 1.0 0.260; 1.2 0.216; 1.3 0.20;

Answer: In the first pair of numbers, 0 0.19, the 0 means that the period is 0 sec. The second number, 0.19, is the acceleration. If 0.19 is in m/sec/sec, then enter a SCALE of 1.0. If 0.19 is in g, enter a SCALE of 9.80665 (1 g = 9.80665 in m/sec/sec) If 0.19 is in ft/sec/sec, enter SCALE as 0.3048 (1 foot = 0.3048 m) If 0.19 is in in./sec/sec, enter SCALE as 0.0254 (1 in. = 0.0254 m) In other words, the spectral value in the curve is multiplied by SCALE to get m/sec/sec. Scale Factor for RSA Based on IS 1893 (Part 1):2002 If the spectral data are generated by the program as per Section 6.4.5 of the code on the basis of the specified soil type, then the program automatically multiplies the generated values by g because the generated data have the form (Sa/g). Therefore, the user does not need to specify a SCALE FACTOR (which is similar to saying that the SCALE FACTOR should be set to 1.0). Example 5: Scale factor for the IS1893 Spectrum data

However, if there are other valid reasons for specifying a SCALE FACTOR that is different from 1.0, one may specify that. Related Question: We are using site-specific response spectra where the input pairs have been given to us by our client. So, we will not be using the Sa/g data from Section 6.4.2 of the 1893 code. What scale factor should we be using? Answer: Are the data that you obtained from your client normalized with respect to any quantity? By normalization, we are referring to the process of the accelerations being divided by some term such as g, so that they will have the form Sa/g. If the answer is yes, that normalization factor is your scale factor. If the answer is no, set the scale factor to 1.0. 5.1.3.3.2 Direction Factor The direction factor indicates the direction along which the spectrum load is to be applied, and the fraction of the spectral value (spectral acceleration or displacement) that is effective for that direction. The spectrum can be applied in more than one direction at a time with each direction having a factor. If a certain direction is left out (not specified), the factor for that direction is Zero, and hence the spectral value in that direction becomes Zero. Example 6: Specifying the direction factor for a generic SPECTRUM data

After the spectral value is obtained from the lookup table, it is multiplied by the direction factor. In the next command, the factor is specified as 1 for the Z direction and not specified for X or Y. It implies that the seismic load is acting entirely along Z only. So, the value read in from the lookup table is applied with 100% intensity solely along the Z direction. SPECTRUM SRSS Z 1. ACC SCALE 9.807 MIS

More than one direction factor in a single command represents an earthquake acting at an angle to

the global X, Y, and Z directions. A command such as this SPECTRUM SRSS X 0.7 Y 0.5 Z 0.65 DISP DAMP 0.05

instructs STAAD.Pro to do the following: 1. For each mode, the period is determined. 2. Corresponding to the period, the spectral displacement for that mode is calculated by interpolation from the input spectral data. Call this “sd.” 3. Calculate the spectral displacement for each direction by multiplying “sd” by the associated direction factor. The X direction spectral displacement = sd * 0.7 The Y direction spectral displacement = sd * 0.5 The Z direction spectral displacement = sd * 0.65 These factored values are then used in the subsequent steps leading to the calculation of node displacements. Direction Factor for the IS 1893 Code For the 1893 code, a possible value of the direction factors in X and Z is the quantity (Z/2)*(I/R), where Z = zone coefficient, I = importance factor, and R = response reduction factor, as per the code. The design acceleration spectrum for the vertical direction should be two-thirds of the horizontal acceleration spectrum. This is according to Section 6.4.5 of IS 1893 (Part 1): 2002. Thus, in the Y direction, the direction factor would be 2/3 × Z/2 × I/R. SPECTRUM CQC 1893 Y 0.028 ACC SCALE 1 DAMP 0.04 SOIL TYPE 2

Sign of the Direction Factor The nature of the arithmetic used in the modal combination methods is such that the sign of the direction factor has no bearing on the final results, which are always positive. Direction Factor and Spectra in Multiple Directions When more than one direction is specified in a single command, SPECTRUM SRSS X 0.7 Y 0.5 Z 0.65 DISP DAMP 0.05 SCALE 32.2

it is equivalent to a spectrum that is acting in the vector sum of those three directions. It is not the same as applying a spectrum in each of those three directions in independent load cases and then obtaining the square root of a sum of the squares (SRSS) of the results. In the following example, the results of load 21 and load 32 will not be the same. LOAD 21 SPECTRUM AT 45 DEGREES TO GLOBAL X and Z DIRECTIONS SELF X 1.0 SELF Y 1.0 SELF Z 1.0

SPECTRUM CQC X 0.7 Z 0.7 ACC DAMP 0.05 SCALE 9.80665 LOG 2.754 0.021; 1.078 0.048; 0.793 0.064; 0.405 0.100; 0.37 0.100; 0.278 0.100; 0.238 0.100; 0.238 0.100; 0.233 0.100; 0.209 0.100;

is not the same as LOAD 30 SPECTRUM IN X DIRECTION SELF X 1.0 SELF Y 1.0 SELF Z 1.0 SPECTRUM CQC X 0.7 ACC DAMP 0.05 SCALE 9.80665 LOG 2.754 0.021; 1.078 0.048; 0.793 0.064; 0.405 0.100; 0.37 0.100; 0.278 0.100; 0.238 0.100; 0.238 0.100; 0.233 0.100; 0.209 0.100; LOAD 31 SPECTRUM IN Z DIRECTION SPECTRUM CQC Z 0.7 ACC DAMP 0.05 SCALE 9.80665 LOG 2.754 0.021; 1.078 0.048; 0.793 0.064; 0.405 0.100; 0.37 0.100; 0.278 0.100; 0.238 0.100; 0.238 0.100; 0.233 0.100; 0.209 0.100; LOAD COMBINATION SRSS 32 30 1.0 31 1.0

Related Question: My structure is a SPACE frame. I have applied the spectrum along the X direction. Is it necessary to apply a spectrum along Z also? Answer: Since the direction in which an earthquake will strike cannot be predicted, it is advisable to analyze the structure for (a) each of the two lateral directions individually, (b) a combination of those directions for the eventuality that the quake may be at an angle to the global axes, and (c) along the vertical direction because earthquakes usually have a vertical component. The following example shows the spectrum being applied in the two lateral directions in two separate cases. LOAD 4 EQ IN X SELF X 1.0 SELF Y 1.0 SELF Z 1.0 SPECTRUM CQC X 1.0 DISP DAMP 0.075 SCALE 32.2 0.03 1.03; 0.04 1.31; 0.05 1.615; 0.104 3.21; 0.124 3.798; 0.622 3.798; 0.667 3.543; 1.067 2.215; 2.1671 1.09; 2.567 0.921; 2.667 0.886; 3.0 0.77; LOAD 5 EQ IN Z SPECTRUM CQC Z 1.0 DISP DAMP 0.075 SCALE 32.2 0.03 1.03; 0.04 1.31; 0.05 1.615; 0.104 3.21; 0.124 3.798; 0.622 3.798; 0.667 3.543; 1.067 2.215; 2.1671 1.09; 2.567 0.921; 2.667 0.886; 3.0 0.77;

The following example is for the earthquake with a component in all three directions applied in a single load case. SPECTRUM CQC X 0.6 Y 0.3 Z 0.4 ACC DAMP 0.05 SCALE 32.2 0.03 1.00 ; 0.05 1.35 ; 0.1 1.95 ; 0.2 2.80 ; 0.5 2.80 ; 1.0 1.60

Because the quake is at an inclination to each of the three global directions, each direction is provided with a direction factor less than 1. A value of 1 is indicative of the seismic load acting entirely in one direction. Section 9.5.2.5.2 of ASCE 7-02 has recommendations on the directions in which seismic loads should be applied and the factors to be considered. Other codes such as the ASCE 4-98 too have similar guidelines. 5.1.3.3.3 Interpolation Type—Linear Versus Logarithmic The period of each mode is used to look up the corresponding acceleration from the input spectrum. These modal periods may not exactly match with the periods specified in the spectrum input in which case one would have to interpolate between values available from the spectra. The procedure used for this interpolation is either linear (LIN) or logarithmic (LOG), depending upon the input. Example 7: Specifying the method for interpolation of spectral data for the spectrum analysis

The acceleration value thus obtained for each mode is reported in the output file (Fig 5.1.10).

FIGURE 5.1.10 Spectral acceleration for each mode obtained using logarithmic interpolation

5.1.3.3.4 Modal Combination Methods Various modal combination methods such as SRSS, CQC (complete quadratic combination), ABSolute, and ASCE are available. Their details can be found in many textbooks on dynamic analysis. The SRSS method is not recommended if there are close frequencies. The TEN Percent method is published in the U.S. Nuclear Regulatory Guide 1.92, Feb. 1976. CSM stands for “closely spaced modes” (see Section 4.1.22). In this connection, it is worth mentioning that the following statement can be found in Section 12.9.3 of ASCE 7-05. The CQC method shall be used for each of the modal values or where closely spaced modes that have significant cross-correlation of translational and torsional response.

FIGURE 5.1.11 Dialog box in the STAAD.Pro GUI for selecting the modal combination method

The data would look like this in the STAAD.Pro input file. Example 8: Specifying the modal combination method for spectrum analysis

5.1.3.3.5 Missing Mass Correction Those modes that are left out of the dynamic solution can be accounted for using this facility. All the modes except the missing mass mode are combined using equation 3.2-20 of ASCE 4-98

“Seismic Analysis of Safety-Related Nuclear Structures and Commentary.” Then, that result is SRSSed together with the missing mass result. So, this option will add the static effect of the uncalculated modes as if that static effect was at 33 Hz or the ZPA (zero period acceleration) frequency.

FIGURE 5.1.12 Dialog box in the STAAD.Pro GUI for selecting the missing mass option

The data would look like this in the STAAD.Pro input file. Example 9: Instruction for considering missing mass for spectrum analysis

Alongside the Missing Mass term shown in Fig 5.1.12, there is a box in which the spectral acceleration (in the current units) can be specified for the missing mass mode. This will not be factored by SCALE. If the engineer does not specify a value for this term, then the spectral acceleration for missing mass will be fetched from the input spectra versus period data that he/she has input for that spectrum case. The frequency (or period) used in that fetching process is the ZPA frequency as described in the following example or a frequency of 33 Hz if ZPA is not specified.

Example 10 LOAD 1 STATIC CASE GRAVITY SELFWEIGHT Y -1.1 * LOAD 2 SEISMIC X-DIR SELFWEIGHT X 1.1 .. .. SPECTRUM CQC X 1 ACC DAMP 0.05 MIS ZPA 14 0 3.0183; 0.0769766 7.54575; 0.326977 7.54575; 0.384883 7.54575; .. .. 4.63488 0.626603; 4.88488 0.594534; LOAD 3 SEISMIC Z-DIR SPECTRUM CQC Z 1 ACC DAMP 0.05 MIS ZPA 14 0 3.0183; 0.0769766 7.54575; 0.326977 7.54575; 0.384883 7.54575; .. .. 4.63488 0.626603; 4.88488 0.594534;

Initially, the modal combination results are calculated without the missing mass mode, and then that result is combined via SSRS with the missing mass result. The effect that the missing mass mode has on the overall results depends on the amount of contribution that is left to be captured by that mode. If, for example, a large percentage (greater than 95%) is captured by the real modes and only a small amount is left for the missing mass mode (5%), the difference in results such as displacements and reactions with and without missing mass will not be very significant. On the other hand, if the real modes capture a much smaller percentage, and hence the missing mass mode has a larger contribution, the difference will be much more palpable. 5.1.3.3.6 ZPA This is applicable only if the MISSING MASS correction is used in the response. The ZPA value (default = 33 Hz) is currently used only to look up the spectral acceleration (of the missing mass mode) from the input curve (spectral displacement or acceleration vs. periods) if an acceleration was not entered with the MIS parameter as explained earlier. If nothing is specified for ZPA, STAAD.Pro uses a frequency of 33 Hz.

FIGURE 5.1.13 Table in the output file showing the participation factor of the missing mass mode

Example 11: ZPA term in missing mass consideration for spectrum analysis

The ZPA and the frequency associated with that value are reported in the output file.

FIGURE 5.1.14 Information in the STAAD.Pro output file for the ZPA parameter

Related Question: We have 75 modes and are getting only 62% mass participation in the vertical direction. For missing mass, should we be picking the acceleration at 33 Hz or at the frequency of the 75th mode?

Answer: You should use the acceleration at the frequency of the highest frequency mode that you are using in the analysis. 5.1.3.3.7 Damping There are three ways to specify damping for RSA. 1. The DAMP method 2. The CDAMP method 3. The MDAMP method The technical details of each of these options are explained in Section 4.2.

FIGURE 5.1.15 Dialog box for specifying the response spectrum input

Method 1: This method is best used when the damping ratio is the same for all modes. That value is provided alongside the term called DAMPING (see Fig 5.1.15). Most of the examples we have seen earlier use this method. It leads to a term called DAMP 0.nnn being written into the command. A value of 0.03 would result in 3% damping for calculating the additional response caused by modal interaction when modes are close to each other in frequency. Example 12: Specifying a single damping ratio with the spectrum command

Method 2: MDAMP is used when we want STAAD.Pro to use a different damping ratio for each mode. The damping versus the frequency of each mode ought to be entered into a DEFINE DAMPING table ahead of the SPECTRUM specification. Here is an example of the input for that table. DEFINE DAMPING RATIO EXPLICIT 0.050 0.045 .052 .043 .043 END

Then, at the time of specifying the SPECTRUM command, the term MDAMP should be used. STAAD.Pro will then use the data from that table. Example 13: Instruction for considering unique damping ratios for individual modes

The primary means for reflecting the effect of damping is in the spectral data itself (a set of spectral data is associated with a specific damping ratio). Hence, if MDAMP is used as the damping method, then the program needs to be provided with as many spectral data sets as there are modal damping ratios in the DEFINE DAMPING table. For example, let us say that the DEFINE DAMPING table contains six damping ratios—those for Modes 1 through 6. Then, we need to provide the program with six sets of spectral data. The method to do it is through an external file. The procedure for specifying the data in that file is explained in Section 5.32.10.1.1 of the STAAD.Pro Technical Reference manual. Method 3: CDAMP is used when we want STAAD.Pro to use weighted average damping ratios based on the strain energy and damping ratio of each material type and springs (if spring damping is entered) for each mode of the structure. Example 14: Instruction for considering damping ratios based on material damping properties

For this example, consider a structure with two materials—steel and concrete. Let us say the strain energy is 50% in each material. If the damping ratio is 3% for steel and 5% for concrete, the effective damping would be 4.0%. As in the case of MDAMP, CDAMP too results in a different damping ratio for each mode. The computed damping ratios are reported by the program in a table in the output file.

FIGURE 5.1.16 Damping ratios calculated and reported by STAAD.Pro for composite damping

Consequently, as with MDAMP, this requires that the spectral data associated with each damping ratio be specified in an external file. The format of this file is identical to that mentioned for MDAMP. Effect of Damping on Structural Response It should be noted that a set of period-versus-spectral acceleration (or period vs. spectral displacement) values (also known as the curve) entered is for a specific damping value. For all combination methods, this is where the primary effect of damping is reflected. For SRSS, CSM, ABS, and Ten Percent methods, the damping value specified in the SPECTRUM command has no effect on the results. However, for the CQC and ASCE 4 combination methods, a modal interaction matrix is

constructed to account for the increased response due to closely spaced frequencies. The calculation of this matrix uses the damping values. This is true for all methods explained earlier for entering the damping term. Related Question: Why is it that the displacements, forces, and reactions do not change when I change the damping ratio? Answer: In an SRSS type of combination, the effect of damping is implicit in the time-acceleration pairs. The values in those pairs are specific to a certain value of damping. In other words, if the damping ratio changes from 2% to 5%, the spectral acceleration input for that load case should also change accordingly. It is not enough to merely state that the damping ratio has changed. The acceleration input has to change too and that information can be obtained from those tripartite charts we obtain the input from. In the CQC combination, the effect of damping ratio is two pronged. First, the spectrum pairs themselves reflect the damped value, and second, the damping ratio appears in the modal interaction matrix used in combining the contribution from the various modes. Only the first of those effects is a factor in the SRSS method. Related Question: I have specified a spectrum for 5% damping. However, I want to run the model to see how it would behave for 7% damping. Will STAAD.Pro convert the given spectrum to one for 7% damping on its own? Answer: STAAD.Pro does not do the conversion on its own. You will have to provide the spectral values for 7% damping. Related Question: I am doing a spectrum analysis on a structure. I run it once with DAMPING 0.02, and a second time with DAMPING 0.04. I am using the CQC method. I notice that the base shear is higher with DAMPING 0.04. I expected it to be less. Can you explain why? Answer: The probable cause is that you are changing only the DAMPING value and keeping the spectral pairs input (period versus acceleration or period versus displacement) the same for the two cases. As we said earlier, the spectral pairs associated with 2% damping will not be the same as the spectrum pairs for 4% damping. The latter will have smaller accelerations and displacements than the former. So, it is essential that you provide the spectral input associated with that specific damping and not just change the damping ratio. Needless to say, the incorrect spectral input will yield an incorrect base shear. 5.1.3.3.8 How Many Modes? Related Question: How many modes does STAAD.Pro use by default in RSA?

Answer: STAAD.Pro uses as many modes as those calculated during the modal analysis step. The number of modes calculated by this step (six by default) is described in Section 4.1. As explained there, there are two instructions for controlling that value—CUT OFF MODE SHAPE and CUT OFF FREQUENCY. Related Question: Are there any guidelines on how many modes should be used in RSA of a structure? Answer: Section 12.9.1 of ASCE 7-05 offers guidance in this matter. The following statement is extracted from that section. The analysis shall include a sufficient number of modes to obtain a combined modal mass participation of at least 90 percent of the actual mass in each of the orthogonal horizontal directions of response considered by the model. Similar requirements can be found in other seismic codes, such as Clause 7.8.4.2 of IS 18932002. In Section 5.1.9, additional information is available on the methods that help in ensuring that sufficient modes (hence, masses) are included in the solution. 5.1.3.3.9 Viewing the Graph of the Spectrum Input The method by which the input spectrum pairs that we specify can be viewed in the form of a graph is shown in Fig 5.1.17.

FIGURE 5.1.17 Graph of the spectral data in the STAAD.Pro GUI

5.1.3.3.10 Multiple Response Spectrum Load Cases As discussed in Section 5.1.3.3.2, almost always, a space frame should be analyzed for earthquake

acting in both the lateral directions and often for a vertical direction spectrum too. This requires specifying the spectra input in multiple load cases. We have seen many examples of multiple spectrum cases. An example is shown here nevertheless. LOAD 7 WIND N-S WIND LOAD Z 1 TYPE 1 XR 33.9 77.1 YR -0.1 18.1 WIND LOAD Z 1 TYPE 1 LIST _FRONT_FACE * LOAD 8 SEISMIC IN X-DIR SELFWEIGHT X 1.0 SELFWEIGHT Y 1.0 SELFWEIGHT Z 1.0 ELEMENT LOAD 341 TO 498 634 TO 865 PR GX 0.025 341 TO 498 634 TO 865 PR GY 0.025 341 TO 498 634 TO 865 PR GZ 0.025 SPECTRUM CQC X 1 ACC DAMP 0.05 MIS ZPA 14 0 3.0183; 0.0769766 7.54575; 0.326977 7.54575; 0.384883 7.54575; ... ... 4.63488 0.626603; 4.88488 0.594534; LOAD 9 SEISMIC IN Z-DIR SPECTRUM CQC Z 1 ACC DAMP 0.05 MIS ZPA 14 0 3.0183; 0.0769766 7.54575; 0.326977 7.54575; 0.384883 7.54575; ... ... 3.63488 0.798989; 3.88488 0.747572; 4.13488 0.702373; 4.38488 0.662328; 4.63488 0.626603; 4.88488 0.594534;

For multiple spectrum cases, the weight data (which goes into the making of the mass matrix) should be specified with only the first of those cases. Even if they are specified in the second or subsequent spectrum cases, they will not be used. This is because STAAD.Pro can generate only one mass matrix during one analysis run. So, if the user intends to have varying sets of weights for different mass matrices, they will have to be specified through separate models.

5.1.4 Steps Followed by STAAD.Pro in Performing a Response Spectrum Analysis 1. Assemble the mass matrix and stiffness matrix. 2. Perform an eigensolution. Calculate the mode shapes and frequencies. There is no need to specify a MODAL CALCULATION command. When STAAD.Pro encounters a SPECTRUM command, it automatically computes frequencies and modes, and a modal participation factor for each mode. 3. Fetch the spectral acceleration or spectral displacement for each mode from the user’s spectral data input (lookup table). This is done by interpolation of the data in the input spectral curve. 4. For each mode, multiply the mode shapes by the spectral acceleration from Step 3 and participation factor in that excited direction of acceleration. The scaled modes are then combined using the modal combination method selected (SRSS, CQC). So, every result (joint

displacements, member forces, support reactions, element stresses, etc.) is calculated from the combination of all modes.

5.1.5 Results from STAAD.Pro for a Spectrum Analysis There are two categories of output produced by STAAD.Pro: A. Intermediate terms generated during the spectrum analysis B. Response of the structure to the loading—absolute maximum values of node displacements, support reactions, member forces, plate stresses, and so on. The terms that come under Item B are the same type of results obtained from a static analysis and are described in Part III. The terms that come under Item A are discussed in the following sections.

5.1.5.1 Mass Participation Factor This output quantity was explained in detail in Section 4.1. Recall that in an RSA, the participation factors are associated with an excitation force corresponding to a 1g base acceleration. So, the cumulative value signifies the percentage of the base shear that can be represented by the modes calculated. While it may not be difficult to obtain the required participation along the lateral directions (X and Z), getting 80% or more for the vertical direction (Y) may not be easy, especially for buildings, because they are the higher frequency modes. Generally, Y is a much stiffer direction because columns are very stiff axially. So, a large number of modes will be needed to get a high participation along Y. Although it will vary from model to model, a medium-sized model may require a CUT OFF MODE SHAPE of 50 or greater. We may also have to set CUT OFF FREQUENCY (default 108 Hz) to a high value such as 1000 due to the high frequency associated with Y modes. In the event that even a large number of modes do not fetch enough mass participation factor, one could use the MISSING MASS option to capture the response of the missing modes. Related Question: The participation factor for some modes is reported as zero. Does it indicate that those modes are not important?

FIGURE 5.1.18 Mass participation factor table in the STAAD.Pro GUI

Answer: If the mass in a certain direction times the mode shape ordinate along that direction sums to zero, then the participation of that mode with a base excitation in that direction will be zero. But we cannot ignore a mode simply because its participation for a certain direction is zero. As an analogy, when there are multiple supports, the sum of the reactions along a certain direction can be zero, but the individual supports won’t necessarily have a zero reaction. Related Question: I am attaching a screenshot (Fig 5.1.19) of the participation factor report in the output file. As you can see, the participation factor along the X direction is zero.

FIGURE 5.1.19 Output showing the mass participation factor for various modes

Answer: It shows that modes 1, 2, 4, and 6 are Z direction modes, and, modes 3 and 5 are local flutter or torsional modes or ones where masses move in opposite directions along Z. In other words, none of the six modes being used in the solution is a substantial X direction mode. Experiment with the CUT OFF MODE SHAPE command. Try progressively increasing the value to, for example, 10, 20, 30, and so on, until the desired cumulative participation is obtained.

FIGURE 5.1.20 Shape of a mode that will produce a low-participation factor for a beam

5.1.5.2 Table of Accelerations Evaluated from the Input Spectral Data Using LOG/LIN Interpolation It was mentioned earlier that the spectral data we provide serve as a lookup table. Each mode of vibration has an associated period. For each of these modes, the program goes to that table and finds the spectral acceleration or spectral displacement for that period by using logarithmic or linear interpolation techniques as specified in the input. The mode number, the spectral acceleration, and the damping used for that mode are reported in a tabular form as shown next.

FIGURE 5.1.21 Spectral accelerations evaluated for each mode

Related Question: What does the following warning message signify? **WARNING- ZERO SPECTRAL ACCELERATION ENTERED FOR MODE 1

This message appears inside a table as shown next.

FIGURE 5.1.22 Warning message indicating Zero Spectral Acceleration

Answer: In the lookup table that was referred to in the previous question, the spectral data cover only a

limited range. The lower and upper bounds of that range are the minimum and maximum periods for which the data are specified. If one or more of the structure periods falls outside that range, a warning message similar to the one you encountered will appear in the output file if the program is unable to calculate a realistic value of the spectral acceleration through extrapolation. Examining the table of frequencies of the structure and the spectral input (period vs. acceleration data) will reveal the reason. First, let us look at the table of frequencies that were calculated by the program.

FIGURE 5.1.23 Table of frequencies computed from the eigensolution operation

Notice that the first mode has a period of 2.70 sec. Next, let us look at the spectral data that we specified (the lookup table).

FIGURE 5.1.24 Period versus acceleration pairs in the response spectrum load case

The last spectrum pair (1 1.6) indicates that the spectrum is specified up to a period of 1.0 sec. Since the period of the first mode (2.70032 sec) exceeds the last period for which the spectral data are specified, the program is not able to find a spectral acceleration corresponding to 2.7 sec. So, it has to extrapolate from the last two period-acceleration pairs to obtain the acceleration corresponding to the first mode of this structure. This triggers the aforementioned warning

message. If we provide at least one more pair of period-spectral acceleration and ensure that its period is higher than 2.7 sec, the warning message should no longer appear. An example of such an input would be SPECTRUM CQC X 0.72 ACC DAMP 0.05 SCALE 32.2 MIS 32.3 0.03 1; 0.05 1.35; 0.1 1.95; 0.2 2.8; 0.5 2.8; 1 1.6 ; 3.0 1.6

The aforementioned warning should not be ignored. In the example shown in the previous question, even if the first mode has a high participation factor in X, the zero spectral value will mean that the base shear as well as node displacements and support reactions for that mode will be zero. With the remaining modes contributing very little, the structure will show insignificant response in that direction. Related Question: How many pairs of period versus spectral acceleration must I provide? Answer: As we have seen earlier, the spectrum pairs are just a lookup table. So, theoretically, one only needs twice as many pairs of period versus acceleration or period versus displacement data as the number of modes being used—for each mode, a set of values on either side of its period. So, for each mode being solved, the table needs to have one acceleration or displacement value corresponding to a period slightly less than the period of the mode being solved, and one value corresponding to a period slightly greater (the period of the mode lies in between these two). These then form the basis for linear or logarithmic interpolation to obtain the acceleration or displacement for the mode being solved (the resulting values are reported in the output file as described earlier). The next table shows a 15-mode structure with periods ranging from 8.49 to 0.007 sec. Mode 1

Frequency (Hz) 0.118

Period (sec) 8.493

2

2.59

0.386

3

6.408

0.156

4

8.214

0.122

5

10.294

0.097

6

16.731

0.06

7

21.226

0.047

8

36.727

0.027

9

46.766

0.021

10

56.439

0.018

11

80.029

0.012

12

90.054

0.011

13

106.867

0.009

14

129.407

0.008

15

135.768

0.007

So, there should be enough period-acceleration or period-displacement pairs in the lookup table for the program to find a spectral acceleration or displacement for each of the 15 periods of the structure—8.493 sec, 0.386 sec, 0.156 sec, 0.122 sec, and so on. A set of period-acceleration data that covers this range is shown next. SPECTRUM CQC Z 1 ACC DAMP 0.05 LOG MIS 0.005 1.635; 0.03 1.635; 0.046 2.514; 0.048 2.627; 0.055 3.023; 0.065 3.591; 0.095 5.311; 0.1 5.599; 0.12 5.599; 0.125 5.74; 0.15 5.74; 0.16 5.74; 0.38 5.119; 0.4 4.864; 8 0.042; 8.5 0.037;

For example, to find the acceleration corresponding to a period of 0.386 sec of Mode 2 in the previous table, the program goes to the table and reads 5.119 corresponding to the period of 0.38, 4.864 corresponding to the period of 0.4 sec, and logarithmically interpolates in between to obtain the acceleration for a period of 0.386 sec. The resulting value is reported in the output file in terms of g.

FIGURE 5.1.25 Acceleration values selected from spectral data for modal combination

However, providing more than the minimum required doesn’t hurt. So, one could provide a more elaborate set as shown in the next example. But, because the program still looks just for the values closest to the periods of the structure, many of the pairs aren’t going to be used.

SPECTRUM CQC Y 1 ACC DAMP 0.05 LOG MIS 0.01 1.635; 0.025 1.635; 0.0299999 1.635; 0.03 1.635; 0.030303 1.635; 0.042 2.289; 0.044 2.402; 0.046 2.514; 0.048 2.627; 0.05 2.74; 0.055 3.023; 0.06 3.307; 0.065 3.591; 0.07 3.876; 0.075 4.162; 0.08 4.449; 0.0833333 4.64; 0.085 4.736; 0.09 5.023; 0.095 5.311; 0.1 5.599; 0.11 5.599; 0.12 5.599; 0.125 5.74; 0.13 5.74; 0.14 5.74; 0.15 5.74; 0.16 5.74; 0.17 5.74; 0.17426 5.74; 0.176429 5.74; ... ... ... 1.5 1.202; 1.58316 1.079; 1.6 1.056; 1.60959 1.044; 1.7 0.936; 1.70707 0.928; 1.79533 0.839; 1.8 0.835; 1.9 0.749; 1.95586 0.707; 2 0.676; 2.17604 0.571; 2.2 0.559; 2.4 0.469; 2.6 0.4; 2.8 0.345; 3 0.3; 3.2 0.264; 3.4 0.234; 3.6 0.209; 3.8 0.187; 4 0.169; 4.2 0.153; 4.4 0.14; 4.6 0.128; 4.8 0.117; 5 0.108; 5.5 0.089; 6 0.075; 6.5 0.064; 7 0.055; 7.5 0.048; 8 0.042; 8.5 0.037; 9 0.033; 9.5 0.03; 10 0.027;

5.1.5.3 Base Shear When the weight of the building is accelerated in a certain direction, it produces a force in that direction. That force can be broken down into small parts, with each part coming from a specific mode. The sum of the values of these parts is called the base shear. STAAD.Pro reports the base shear in the output file in a tabular form alongside the mass participation factors.

FIGURE 5.1.26 Base shear report in the STAAD.Pro output file

The base shear, for a given mode for a given direction, reported in the RSA is obtained as A*B*C*D where A = Mass participation factor for that mode for that direction B = Total mass specified for that direction C = Spectral acceleration for that mode D = Direction factor for the associated direction for that spectrum load case A is calculated by the program from the mass matrix and mode shapes. In Fig 5.1.26, A is reported for each mode under the headings X, Y, and Z (55.10, 0.37, 3.92, 1.24, etc. in the above example). B is obtained from the masses specified in the RS load case. The total mass for each direction can be found in the file inputfilename_MASS.txt, which is located in the same folder as the input file.

FIGURE 5.1.27 Term B for the various directions as reported in the _MASS.TXT file

C is obtained by logarithmic or linear interpolation from the data in the lookup table (as described earlier) and multiplying the resulting value by the SCALE FACTOR. This too is reported in the output file.

FIGURE 5.1.28 Spectral acceleration values used for base shear calculation

D is input by the user. In the spectrum command in the next example, it is specified as 0.72 for the X direction. As no direction factor is specified for Y or Z, their default values are chosen, which is 0.

FIGURE 5.1.29 Direction factor used for base shear calculation

So, if the contribution to the base shear from a mode has to be non-zero, that mode needs to have a non-zero participation factor for that direction. Related Question: The response spectrum loading in my model is along global Z. But I do not get any base shear along Z. I am attaching the output.

FIGURE 5.1.30 Base shear report showing zero force

Answer: If the base shear is zero along a certain direction, here are some of the things to check. 1. Have you specified weights along that direction in the first spectrum load case? These

weights are necessary for the frequency calculation. If the weights are similar to that in the following example, LOAD 3 EQ IN Z DIRECTION SELFWEIGHT X 1 SELFWEIGHT Y 1 SPECTRUM CQC Z 1 ACC SCALE 32.2 DAMP 0.05 0 0.2; 0.1 0.24; 0.2 0.32; 0.25 0.36; 0.3 0.5; 0.94 0.5; 1 0.48; ... ... 10 0.06; 100 0.003

the total dynamic weight along Z is zero, and no frequencies can be computed for Z. This will lead to zero participation along that direction for all modes. 2. If weights have indeed been specified along that direction, check the CUT OFF MODE SHAPE value. If you haven’t specified it, do so, with a value greater than 6, for example, 15 or 30 or higher. The lower modes may be contributing to the other directions only, hence the need for higher modes.

5.1.5.4 Dynamic Weight, Missing Weight, Modal Weight These terms are displayed in the output file as shown in Fig 5.1.31.

FIGURE 5.1.31 Report of critical weight terms in the STAAD.Pro output file

The dynamic weight line contains the total potential weight for base shear calculations. In Section 4.1, we discussed a file with the name inputfilename_MASS.txt, which is located in the same folder as the input file. It contains details of all the masses lumped at the various nodes of the structure. At the bottom of that file, the total masses for the three directions are reported (Fig 5.1.32).

FIGURE 5.1.32 Cumulative mass information reported in the inputfilename_MASS.txt file

If those totals are multiplied by g (386.08858), the resulting values will be the dynamic weight for the respective directions in pound-force units. Modal weight is the total weight actually used in the modes. That means, with the number of modes considered in the solution, only a part of the dynamic weight is actually used in the solution. The part that doesn’t get considered for the solution is the missing weight. If we algebraically add dynamic and missing weights, we should get modal weight. The modal weight for the individual modes can be obtained by specifying the command SET PART FACT (see Section 4.1 for more details). Missing weight is reported as a negative number to signify that it is a quantity that is “absent” from the calculations based on the number of modes that the program has actually used in the calculations, that is, the amount of weight that the program deems “missing.” Either with the help of a higher CUT OFF MODE SHAPE number or with the help of the MIS option, the user would have to reduce this deficit (bring it close to zero). Related Question: I have applied the same amount of weight in all three directions. But the dynamic weight reported for one direction (Y) is different from the other two. Answer: The answer to this is the same as the one in Section 4.1.5 for a similar question related to the topic of the inputfilename_MASS.TXT file. At the supports, if two of the translational directions are restrained, and a translational spring is provided for the third, the total mass for the direction with the spring will be higher than for the other two directions. Accordingly, the dynamic weight for the direction with the spring will be different from the other two.

5.1.5.5 Damping Ratio Used in the Individual Modes If composite or modal damping is specified, damping ratio used in each mode will also be reported.

FIGURE 5.1.33 Calculated damping ratios for individual modes for composite damping

FIGURE 5.1.34 Interpolated spectral accelerations and associated damping ratios

5.1.5.6 Modal Base Action To understand what this means, we need to understand a term known as the FLOOR MODAL BASE ACTION. The FLOOR MODAL BASE ACTION is calculated in the following manner. Take any floor of the structure. A floor is identified by a set of joints that have a distinct Y coordinate. For any given joint on that floor, Calculate the global X, Y, and Z components of the force at the joint by multiplying the X, Y, and Z masses at that joint by their acceleration along X, Y, and Z. Due to these three forces, calculate the three moments (along the global axes directions) about the origin of the global coordinate system. Algebraically add these forces and moments for all the joints on that floor. Thus, for each floor, we will get three forces and three moments on a mode-by-mode basis. The results are all signed quantities because no modal combination method has been applied. If we sum up all of the individual FLOOR MODAL BASE ACTIONs from all the floors of the

structure, we get the MODAL BASE ACTION. The MODAL BASE ACTION is reported in the output file as shown in Fig 5.1.35.

FIGURE 5.1.35 Table of MODAL BASE ACTIONS reported in the STAAD.Pro output file

5.1.6 P-Delta Effects on Spectrum Load Cases Related Question: The Technical Reference manual states that the REPEAT LOAD command must not be used on RS load cases. How can I get P-Delta effects for the earthquake and gravity cases acting together because the LOAD COMBINATION syntax is not deemed suitable for obtaining P-Delta effects? Answer: A discussion on the topic of P-Delta analysis and combination load cases can be found in Section 1.2 of Part II. For the P-DELTA effect to be computed accurately, it is necessary to (a) know the sign (positive or negative) of the “DELTA” as well as the “P” (as it is important to determine whether the member or element is in tension or compression) and (b) ensure that “DELTA” at the various nodes of a member or element occurs at the same instant of time. Therefore, the conventional method of performing a P-Delta analysis isn’t feasible when the load case being solved is a spectrum load case. In Section 12.9.6 of the ASCE 7-05 code, there is a recommendation that the approach described in Section 12.8.7 of that document be followed. This method is currently not implemented in STAAD.Pro. ELFP-based methods such as those described in IBC 2006 do not have the limitation that the spectrum method has with reference to the sign of the forces and displacements or the synchronicity aspect of displacements. Hence, P-Delta analysis is well suited for earthquake analysis that is based on the ELFP method. Consequently, to combine the spectrum load case with another case such as DEAD or LIVE, the LOAD COMBINATION type is a better alternative to the REPEAT LOAD type (although it does not provide a solution to the problem of finding the P-Delta effect for the combined action of

the spectrum case and a static case). Generally, two combinations are created with each spectrum case—one that applies a positive factor to the spectrum case and the other that applies a negative factor to the spectrum case. If you go to Help S Contents S Application Examples S Example 11, you will see two load combination cases that illustrate this. A way for acccounting for the P-Delta effect during the frequency calculation is discussed in section 4.1.14.

5.1.7 Combining Response Spectrum Cases with Static Cases To combine the spectrum load case with another case such as DEAD or LIVE, the LOAD COMBINATION type should be used because the REPEAT LOAD is not compatible with RSA. Also, the RSA results are absolute values—that is, all positive numbers. Therefore, for results such as support reactions, it is not possible to determine whether the force is upward or downward. For an axial force in the member, there is no way to determine whether it is tensile or compressive. One way to deal with the problem is to create two load combination cases for each set of load cases you wish to combine—one that applies a positive factor to the spectrum case and the other that applies a negative factor. For example, if the dead load case is 1, and the spectrum load case is 5, we could create LOAD COMB 10 1 1.1 5 1.3 LOAD COMB 11 1 1.1 5 -1.3

and use the critical value from among these two load combination cases for design purposes. Through this process, we are considering a positive effect as well as the negative effect of the spectrum load case.

5.1.8 ELFP Versus Response Spectrum Analysis—What Codes Require Often users create two models of a structure—one for an RSA, and the other for a seismic analysis using the ELFP. And frequently, they find that the results such as the base shear are not similar. The seismic codes recognize the incongruities between the two methods. The ASCE 7-05 code, for example, in Section 12.9.4, states that “Where the combined response for the modal base shear (Vt) is less than 85 percent of the calculated base shear (V) using the equivalent lateral force procedure, the forces, but not the drifts, shall be multiplied by 0.85 V/Vt.” Section 7.8.2 of the IS 1893 code also has a similar requirement. Related Question: I am doing a spectrum analysis in accordance with the IS 1893 code. Can you tell me what the significance of the following message in the output file is? WARNING : SOME MODES ARE CLOSELY SPACED. CSM METHOD ADOPTED.

FIGURE 5.1.36 Warning regarding closely spaced modes in the STAAD.Pro output file

Answer: This message is reported because, although the modal combination method specified by the user through the SPECTRUM command is SRSS, as in the following command, 164 FZ 52.257 165 FZ 52.075 166 FZ 52.07 SPECTRUM SRSS 1893 X 0.01 ACC SCALE 1 DAMP 0.05

the program is disregarding that and adopting the CSM method instead. CSM is a grouping method for closely-spaced modes (considered to be within 10% of each other) where the peak response quantities for those modes are combined by the absolute method. This peak response quantity for closely spaced modes is then combined with those of widely spaced modes by the SRSS method.

5.1.9 Missing Mass For response spectrum or time history analysis, STAAD.Pro uses only as many modes as defined by the CUT OFF MODE SHAPE command, or a lesser number if it cannot calculate as many as specified through that command. STAAD.Pro by default calculates only a maximum of six, unless a higher value is requested through this command. In theory, a structure has as many modes of vibration as there are degrees of freedom, typically represented through a variable n. If you consider the sum total of masses that go into the mass matrix, in order to obtain the full effect of that mass while calculating the displacements, forces, and reactions, all those n modes have to be considered. However, the limitations of the mathematical procedures used in calculating modes and frequencies mean that, frequently, not all those n modes can be calculated. Thus, only a lesser number of modes (call it p) is actually extracted. Usually, p is equal to or less than the number specified through the CUT OFF MODE SHAPE command.

Consequently, the displacements and forces calculated in these cases is not the desired number but one derived through a less than full participation of vibrating masses. The extent of the participation of the masses can be seen from the MASS PARTICIPATION factor table that is reported in the STAAD.Pro OUTPUT file (Fig 5.1.37).

FIGURE 5.1.37 Mass participation factor table in the STAAD.Pro output file

The cumulative number in the SUMM-X, SUMM-Y, and SUMM-Z columns tells us what the total participation is. Most design codes require that number to be 90% or more. One potential way to achieve that 90% is to ask for more modes through the CUT OFF MODE SHAPE command. However, there are times when we can ask for a very high number of modes, but the program is unable to calculate more than a certain number, and consequently is not able to achieve the 90% participation level. The difference between this “SUMM” value and 100% is called MISSING MASS for that direction. In those cases, the contribution of the portion that is not participating can be calculated through an alternative procedure. In STAAD.Pro, we can request the program to consider the effect by using the MIS option as explained in Section 5.32.10.1 of the Technical Reference manual. The command is as follows: Example 15: Instruction to consider missing mass during spectrum analysis

5.1.10 Structural Response—Absolute Values

All results calculated from an RSA are the absolute maximas. Therefore, in the post-processing mode, the plots of these results are lines joining the maximum values at the various nodes. Some results such as plate stress contours or solid stress contours cannot be plotted as their maximas are known at just a few locations. Related Question: The results of the RS load case are always positive numbers. Why? How do I know that the positive value is always critical, especially from the design standpoint? Answer: In a spectrum analysis, the contribution of the individual modes is combined using methods such as SRSS or CQC to arrive at the overall response. The limitation of these methods is that the sign of the response cannot be determined after the method is applied. This is the reason why the output you get from STAAD.Pro (or any program) for an RSA is absolute values. As we saw earlier, one way to deal with the problem is to create two load combination cases for each set of load cases you wish to combine. Related Question: Can the direction factors be provided a negative value? If the spectrum is applied in the X direction, does it imply that it acts in the positive X direction as well as in the negative X direction? Answer: Since the equations for combining the structural response from the individual modes involve squares and square roots, it is immaterial what the sign of the direction factors are. The end result is always an absolute value. That is why it is necessary to create two load combinations—one that combines the static loads with the positive result of the spectrum load and the other that combines the static loads with the negative result of the spectrum load. Related Questions: 1. Why isn’t the static equilibrium between member end forces and support reactions satisfied in an RSA? 2. When the spectrum is applied along a horizontal direction (X or Z), I expect the supports to develop reactions that form a restoring couple, meaning, positive reactions at some supports and negative (uplift) at others. But I don’t see this happening. Instead, all reactions are positive. They do not add up to zero even though I have no downward acting load in my spectrum case. Answer: The sign of the forces and reactions is lost once the contribution from the individual modes is combined using the SRSS or the CQC method. Hence, all responses from a spectrum analysis, such as member forces and support reactions, are absolute positive numbers. It is also a reflection of the fact that the responses may not attain their peak at the same instant of time. It is best to think of each result (Fx, Fy, Fz, Mx, My, Mz) for a beam to be the absolute upper bound for that result value and that each value could be plus or minus. In addition, each result value is independent (max Fy probably occurs at a different time than max Mz). So, a shear/moment diagram cannot be constructed from the data calculated. Related Question:

The summary of reactions in the direction along which the spectrum is applied is 147 KN, and it does not match the base shear for that direction (97 KN). Answer: All results from an RSA are obtained through an SRSS of the desired output quantity from each mode. The CQC method too involves an SRSS operation. Within a single mode, the reactions may have equal but opposite values at the various supports such that the base shear for that mode is nearly zero. Therefore, the contribution of that mode to an SRSS of all the modal base shears will be nearly zero. However, in the same mode, a particular support may have a large reaction value. Therefore, when that value is SRSSed with that support’s reaction value from all the other modes, that same mode may be a major contributor to the final result for the reaction at that support. Thus, while that mode contributes little to the base shear, its contribution to the final reaction at that support is significant. The base shear will be less than the sum of the reactions for that direction. If all the support reactions in all the modes have the same sign, the aggregate reaction from all modes will be similar to the aggregate base shear from all modes. Let us say that there are two modes and four supports in the X direction. Then for the SRSS combination method, the results are computed as follows: Support no. 1

Mode 1 reaction 10

Mode 2 reaction −15

Sum of squares 325

SRSS 18

2

−5

19

386

19.6

3

17

43

2138

46.2

4

−3

−12

153

12.4

96.2

Sum of reactions

Base shear

19

35

1586

39.8

Note that the SRSS base shear (39.8) does not equal the sum of the SRSS reactions (18.0 + 19.6 + 46.2 + 12.4 = 96.2). In effect, the calculation in this table illustrates the maximum likely value of the reaction that would occur at each support. It also indicates the maximum likely base shear that would result from those reactions. Their seeming lack of congruence is due to the fact that the individual maximums may not occur at the same time and are not necessarily with the same sign. Therefore, the base shear magnitude is usually less than the sum of the reactions. Related Question: The vertical reactions I get from a spectrum analysis are all positive numbers. What downward reaction do I design the foundation for? Answer: One way to deal with the problem is to create two load combination cases for each set of load cases you wish to combine. For example, if the dead load case is 1, and the spectrum load case is 5, you

could create LOAD COMB 10 1 1.1 5 1.3 LOAD COMB 11 1 1.1 5 -1.3

and use the critical value from among these two load combination cases for design purposes. Through this process, you are considering the positive as well as the negative effects of the spectrum load case. Alternatively, use an ELFP-based method such as those recommended by the IS 1893 code or IBC. Since this is a static method, the support reactions will have signs.

5.1.11 Reactions in Directions Other Than the Direction of the Spectrum Often, we will notice that although the spectrum is applied entirely in one direction (direction factor is 1.0 for that direction and 0 for the other two), non-zero reactions are reported for the other two directions, and these do not add up to 0. It makes us wonder how it is that there can be a net reaction along a direction even though there is no force in that direction. Related Question: The spectrum is applied along the X direction. However, nearly all the supports have a positive Y reaction as well, and they do not add up to zero. I expected the net reaction in Y and Z to be either zero or a negligible value. Answer: This is once again caused by the arithmetic inherent in the modal combination method. At the individual mode level, each support can have a reaction in all three directions. However, along directions in which the spectrum is not applied, the net reaction calculated by algebraically adding the values from all the supports has to be zero for each mode. The final values we see in the Node-Reactions page is the total reaction at each support obtained after the contribution from the individual modes have been subjected to the SRSS or CQC method or whatever combination method has been applied. The next table illustrates this. The spectrum is applied along X. The table shows the reactions along Y at the five supports of a model.

Joint number 11

Fy Fy reaction Fy reaction Fy reaction reaction Fy reaction calculated through the from from from from SRSS method mode 1 mode 2 mode 3 mode 4 −136 −67 38 23 157.981

12

87

36

21

−11

97.09274

13

59

21

−19

−9

66.06058

14

19

15

−25

−2

34.85685

15

− 29

−5

−15

−1

33.04542

Algebraic total

0

0

0

0

389.0366

The second through the fifth columns of the table show the reactions at the five supports on a mode-by-mode basis. Note that in the last row, the algebraic total obtained by summing up over all the supports of the structure is 0 for each mode. However, we do not get to see these numbers because they are not printed (a recent enhancement in STAAD.Pro known as the individual modal response—IMR—makes it possible to see it in STAAD.Pro version V8i onward, which is not discussed in this book). What we see in the Node-Reactions page are the values shown in the last column. For example, 157.981 is obtained as SRSS of the numbers (−136, −67, 38, 23). In other words, it is the resultant reaction at joint 11 after the signed values from each mode are combined through the SRSS method. In a similar way, the resultant reactions at the remaining supports are also calculated and shown in the aforementioned table as 97.09274, 66.06058, 34.856, and 33.045 for nodes 12, 13, 14, and 15, respectively. These are also the numbers that we see in STAAD.Pro’s post-processing mode’s Node-Reactions page for the spectrum load case. When we add the numbers in the last column, we get 389.0366, which being a non-zero value leads us to think that the summation of reactions from all the supports is wrong because it ought to be zero. But that is just a fictitious number and doesn’t mean much.

5.1.12 Spectrum Analysis of Structures with Cable Members, Tension-Only and Compression-Only Members, Tension-Only and Compression-Only Supports, and so on As discussed earlier, the nature of the modal combination methods used in a spectrum analysis makes it impossible to determine whether the resulting quantity represents a positive value or a negative value. But without knowing the sign of the result, one cannot determine whether the member or support is in tension or compression. Hence, the solution for structures with cable members, tension-only and compression-only members, tension-only and compression-only supports, and so on is not possible in a spectrum analysis.

5.1.13 Spectrum Analysis and Multilinear Springs An iterative process is used by STAAD.Pro to determine the displacement of the support when the model has multilinear springs. Besides the fact that the response spectrum procedure is not compatible with iterative methods, the difficulties described in the case of other nonlinear conditions, such as MEMBER TENSION and COMPRESSION, SPRING COMPRESSION and TENSION, and cable members, are also applicable for multilinear springs, namely, without knowing the sign of displacements, the appropriate support stiffness cannot be considered. Hence, currently, multilinear springs cannot be used with spectrum analysis in STAAD.Pro. Related Question: In a response spectrum input, STAAD.Pro requires that I specify an input consisting of period versus acceleration. For time history also, STAAD.Pro requires that I specify an input consisting of time versus acceleration. Are they both the same set of data? Answer: No, they are not the same data.

The data we enter for a response spectrum is a table of values of period of a SDOF system versus the peak acceleration experienced by that SDOF system. In the period column, we are entering the reciprocal of the frequency of an SDOF system. Though it is in seconds, it is not to be mistaken for a time input. Similarly, in the acceleration column, we are entering the response of that SDOF system. Though it is in units of acceleration, it is not to be mistaken for an excitation input. It does not represent the excitation that is transmitted on to that system by the ground. It is the response of the system to the ground movement. It is a positive number because it is the absolute largest value of acceleration that the system will ever experience when subjected to an earthquake that the spectrum data are representative of. A response spectrum is thus the behavior of an SDOF structure to a specific earthquake. That earthquake is not what the input represents primarily. That is why the second column of a response spectrum input can be in the form of an acceleration or a displacement. In some programs, it can be specified as a velocity too. Also, in the first column, some programs allow us to enter the frequency of the SDOF system instead of its period. In time-history data input, we are specifying time versus the ground acceleration transmitted to the structure by an earthquake. The time stands for a relative value time with respect to the hour and minute hands of a clock. So, if the earthquake occurs at 12:00:13 am, and we set 12:00:00 as the datum point, then the first timepoint is set as 13 sec. The corresponding acceleration value is what is measured with a seismograph. The data have nothing to do with the building. It is entirely a property of the ground’s movement, not the structure’s response.

5.1.14 Obtaining the Maximum Nodal Acceleration for Response Spectra Runs The maximum acceleration experienced by each node of the structure for each of the 6 degrees of freedom at the node can be saved into a text file. To instruct STAAD.Pro to create this file, add the word SAVE at the end of the SPECTRUM command. In the GUI, switch on the box against the word SAVE shown in Fig 5.1.38. During the course of the analysis, a file with the name inputfilename.ACC containing the nodal accelerations will be created in the same folder where the STAAD.Pro input file is located.

FIGURE 5.1.38 Dialog box in the GUI for requesting the peak nodal accelerations to be saved

Example 16: SAVE command in the STAAD.Pro input file LOAD 10 LOADTYPE None TITLE LOAD CASE 7 SEISMIC Y SELFWEIGHT Y 1 SELFWEIGHT X 1 SELFWEIGHT Z 1 REPEAT LOAD 7 1.0 8 1.0 9 1.0 SPECTRUM SRSS Y 1 ACC SCALE 9.81 DAMP 0.05 LOG MIS SAVE 2.5 0.015; 1.667 0.03; 1 0.053; 0.5 0.105; 0.333 0.158; 0.25 0.211; 0.2 0.264; 0.185 0.284; 0.083 0.284; 0.067 0.231; 0.05 0.177; 0.04 0.144; 0.034 0.126; 0.029 0.106; 0.025 0.093;

There is no facility available for displaying the maximum nodal accelerations in the post-processing mode. However, since the .ACC file is simply a text file, it can be opened using a text editor such as Notepad, as well as in Excel where we can use the graph-generation facilities for plotting the accelerations.

An excerpt from the .ACC file is shown in Fig 5.1.39.

FIGURE 5.1.39 Peak nodal accelerations reported in the inputfilename.ACC file

X1, X2, and X3 are the accelerations for translation along global X, Y, and Z. X4, X5, and X6 are for rotation about global X, Y, and Z. The translational values are expressed in terms of g (i.e., the acceleration due to gravity) and the rotational values are in radians/sec2.

5.1.15 Symmetrical Structures and Double Root Modes In Section 4.1.23, we discussed the phenomena of double roots. Identical attributes means symmetry in geometry, properties, supports, seismic weights, and so on along two or more global directions. For such structures, the sequential order of the mode shapes may indicate double root modes, meaning, two successive modes having identical values of mode shape ordinates and frequencies but are in orthogonal directions. Such modes can be at 90 degrees to each other, that is, 0 and 90, or +45 and −45, or 20 and 110, and so on. So, successive modes will have the same frequency, such as 1 and 2, or 5 and 6, or 8 and 9, and so on. The SRSS combination method is not an efficient technique for combining double root modes if they are not aligned with global axes. Therefore, CQC must be used if there are duplicated or nearly duplicated frequencies. CQC combines double root values so that they form a vector sum in the direction of loading, whereas SRSS does not. Also, both roots of the double root must be included in the solution. Excluding one of those modes could result in erroneous output. For example, if modes 10 and 11 are double roots, and CUT OFF MODE SHAPE 10 is specified, it implies that mode 11 is not considered, which will lead to exclusion of the contribution of that mode, resulting in erroneous displacements, forces, and reactions. Thus, CUT OFF MODE SHAPE must be at least 11. Both modes of the modal pairs are required to get symmetric results using the CQC method.

5.1.16 Calculating the Response from Just a Few Specific Modes—The MODE SELECT Command As was mentioned earlier, the structural response obtained from a spectrum analysis is the one resulting from all the modes calculated by the program. Occasionally, one may wish to obtain the response by having the program consider just a few specific modes, such as modes 2, 3, and 7. This can be done with the help of an instruction called MODE SELECT.

FIGURE 5.1.40 Page from the STAAD.Pro Technical Reference manual for MODE SELECT

Example 17 CUT OFF MODE SHAPE 10 MODE SELECT 2 3 7 LOAD 1 SELF X 1.0 SELF Y 1.0 SELF Z 1.0 ..

In this example, all modes other than 2, 3, and 7 will have their participation factor set to zero. This feature is useful for evaluating the contribution of specific modes to the overall response. It is also a useful tool from a pedantic perspective. There is a notion that modes with low participation factors do not contribute much to the overall response. Using this feature, we could specify just such modes and calculate the response of the structure (call it A). Then compare that response with another run in which this command has not been used (call it B). If A is a significant percentage of B, it means those low participation modes are important.

5.1.17 Recent Improvements There have been some recent developments in STAAD.Pro in connection with the RSA facility, some of which are mentioned here, which will be described in detail in a future edition of this book.

1. Obtaining signed results from an RSA. The recent versions of STAAD.Pro offer methods by which a sign can be forced upon the results from an RSA. This can be quite useful from the standpoint of concrete or steel design where the sign of the force or moment is needed. 2. Individual modal response. The displacements and other results can be obtained on a modeby-mode basis. 3. Floor response spectrum. For a structure analyzed for a time history loading, STAAD.Pro can create a response spectrum for a floor of the structure. A floor is defined using a node group or a list of nodes that are present at that elevation. The spectrum is based on the average of the responses of those nodes to the earthquake.

5.1.18 Summary To summarize, the following are some of the aspects to be considered inorder to ensure that the RSA is done accurately. 1. For the SRSS method, damping has to be accounted for in the spectrum data input. The damping ratio on its own will have no effect on the final outcome. 2. Ensure that the weights are specified for all possible directions of vibration, which usually means all three global directions. Not specifying one or more directions means some vital frequencies and modes won’t be calculated. 3. Make sure that a sufficient number of modes are used to account for at least 90% participation in all directions. 4. The spectrum data must cover the entire range of periods of the structure. Else, the program will resort to linear extrapolation to determine the period corresponding to a mode for which no spectral input is available. 5. The CQC method ought to be used when two or more modes are closely spaced. Closely spaced modes are those whose frequencies are very similar. For closely spaced eigenvalues, the CQC method will amplify the response of those modes as compared with the SRSS method. 6. The modal combination methods used—SRSS, CQC, and so on—use square root of sum of squares, due to which all calculated results are positive. Displacements, forces, stresses, and so on can be computed only in terms of their magnitude, not their sign.

5.2 Time History Loading and Analysis 5.2.1 Introduction Time history analysis (THA) is perhaps the most elaborate form of linear dynamic analysis in the sense that it enables us to determine the complete response of a structure to a dynamic load. By complete response, we mean that the displacements, forces, stresses, reactions, and so on can be determined at each instance of time during the vibration of the structure to that loading, thereby providing us with a time history of each response quantity. This analysis is performed in STAAD.Pro using the mode superposition method. The duration of the response—the time taken from start of vibration till the end of vibration—is discretized into individual time points. The time separation between adjacent time points is called the time step (DT). Using numerical methods, the structure’s response is calculated at each of these time points in intervals of DT. Because the time steps are usually very small (of the order of thousandths of a second), a dynamic load lasting for even a short duration, for example, 10 sec, translates into thousands or tens of thousands of time points. For models with many degrees of freedom, this requires powerful

desktops or laptops and significant amounts of time (hours of analysis runtime) to solve. Displaying the results using the graphical tools also takes a lot of computer resources. Verification using the graphical tools is important to understand when the peak response is attained, when the displacements start to die out, when the transient phase ends and the steady-state phase begins, and so on. Building codes such as ASCE 7-05 recommend RSA and THA as two among various methods used to analyze a structure for ground acceleration (Table 12.6-1 of ASCE 7-05). The response spectrum method was discussed in Section 5.1. The difference between RSA and THA is that, for any response quantity: In RSA, only the maximum response is calculated for each mode. Then, those maximas are combined using the specified modal combination method, providing us a single number, which is the absolute maximum value for that quantity, albeit without a sign. In THA, its history (value at each time step) is calculated for each mode. The histories from the individual modes are then combined to give us a composite value of the history for that quantity. Because the history of response at each node is calculated during THA, it is important that the maximum values of displacement at nodes, forces in members, and stresses in elements be captured. This requires the solution to be calculated for a long-enough duration that the deformation should decay or reach steady state depending on the type of loading. Fig 5.2.1 shows evidence of such an analysis because it clearly shows both phases of a structure’s response to a periodically varying force.

FIGURE 5.2.1 History of displacements at a joint showing the transient and steady-state phases

Required Reading 1. Technical Reference manual—Sections 1.18.3.5, 5.31.4, and 5.32.10.2 2. Graphical Interface Help manual—Section 2.3.7.8 Loading S Define Time History dialog S Define (Time History) Parameters dialog S Create New Load Items S Time History 3. Application Examples manual—Examples 16, 22, and 29

FIGURE 5.2.2 A structure for mounting a turbine generator

5.2.2 Discussion The instruction that enables STAAD.Pro to understand that a THA is to be performed is a load case containing a command line that has the expression GROUND MOTION or TIME LOAD. A typical time history load case is shown in Fig 5.2.3.

FIGURE 5.2.3 Syntax in the input file of a typical time history load case

The terms annotated in this figure constitute the input required for STAAD.Pro to perform a THA, and these are discussed in Section 5.2.8. Then, the output produced by STAAD.Pro for a THA is examined in Section 5.2.10. The engineering principles that form the basis of the input and output are also mentioned wherever necessary.

5.2.3 Performing Time History Analysis—Workflow 1. Model the structure using line members for beams, columns and braces, quad and triangular elements for plates. If the model contains units such as a block foundation, model these using solid elements. 2. Assign the member properties and material constants just as it is done for any static analysis model. Other specifications such as trusses, member and element releases, and offsets may also be assigned as needed. Member tension and compression and nonlinear cables cannot be used for THA for reasons explained later. 3. Assign the supports—those that we have discussed in Section 8.1 of Part I, or if the foundation is a mat resting on an elastic medium, use the ELASTIC MAT or PLATE MAT type of supports (see Section 8.4 of Part I). Multi-linear springs, spring tension, and spring compression do not work for THA for reasons explained later. 4. The data specified in the first three steps are used to form the stiffness matrix—same as the one used for static analysis. 5. Provide the static load cases using the principles explained in Chapters 1 and 2. 6. Next, the time history load data should be specified. The various options for this are explained in the remainder of this section. This is followed by the load combinations. 7. Provide the analysis command. Currently, only the linear type of analysis is available for time history loading. 8. Run the analysis and view the results as explained in Section 5.2.10.

5.2.4 Types of Dynamic Loads Available in STAAD.Pro There are three types of dynamic loads available for a THA. 1. Seismic base excitation, which is an earthquake 2. Random excitation—an arbitrarily varying force or moment with time (explosion, impact load, etc.) 3. Vibrations induced by machines that are periodic in nature Of these, the first, which is also known as GROUND MOTION, is in the form of ground accelerations that vary with time. Because the accelerations are transmitted to the structure through the supports, all the joints of the structure are simultaneously subjected to that excitation. The second and third are specified in the form of a “forcing function,” also known as a TIME LOAD. These are applied in the form of a force or a moment only at specific nodes of the structure that are in the vicinity of the source of the load.

FIGURE 5.2.4 Dialog box in the STAAD.Pro GUI for defining the dynamic load for THA

The methods for applying these loads are discussed in Sections 5.2.5 and 5.2.8.

5.2.4.1 Ground Motion (Seismic Base Excitation) For GROUND MOTION, the basic data consist of a table of values representing the ground acceleration at various instances of time. The data as they appear in the STAAD.Pro input file are shown next and consist of several pairs of numbers of the form “ti ai” specified after a command TYPE nnnn, where: nnnn = an integer with which the data can be identified and fetched later ai = acceleration of the ground ti = time at which that ground acceleration occurs. The start of the earthquake is set to be at time zero. Example 1: Time-Acceleration pairs and other input for a Ground Motion loading

In the aforementioned example, TYPE 1 is the identifier through which this data can later be referred. The first point of time is set to 0.0, and the ground acceleration at that time is 0.0063 units. As described in Section 5.2.8.6, the acceleration values can be in units of length/(sec2) or a real number representing a normalized value (e.g., ground acceleration divided by g). The data can be specified within the STAAD.Pro input file along with the rest of the structure data or in an external file if one intends to reuse it in other projects.

FIGURE 5.2.5 Dialog box in the GUI for providing the excitation load data through an external file

Related Question: If an acceleration is applied as a ground motion, I assume it is being applied to the structure at the supports. If the supports are pinned and they don’t translate, then how is the ground motion exciting the structure? Answer: The supports represent the connection between the base of the columns or walls and the ground. An earthquake causes the ground to move, and those accelerations are transmitted to the structure above the support level. The weights distributed throughout the structure experience these accelerations and they in turn move. Due to the flexible nature of the columns and beams, the differential movements between various points on the structure will induce stresses in the structure.

5.2.4.2 Random Excitation—Arbitrarily Varying Force or Moment with Time When the variation of the force or moment with time does not follow a well-defined (periodic) pattern, it is called a random excitation or a force that varies arbitrarily with time. In STAAD.Pro terminology, this type is also called a forcing function load. The primary input describing this type of load consists of the variation of force (or moment) versus time specified in the following sequence: Type nnnn t 1 f1 t 2 f2 t 3 f3 t 4 f4 …. where TYPE nnnn is an identifier through which these data can later be referred. nnnn takes on integer values 1, 2, 3, and so on. t 1, t 2, t 3, t 4 … are the time values, and f1, f2, f3, f4 … are the force (or moment) values. If there is more than one set of time-force pairs, each is preceded by a TYPE nnnn. The data as they appear in the STAAD.Pro input file are shown in the following example.

Example 2: Time-Force pairs and other input for a Random Excitation

In the case of the ground motion and forcing function, the input pairs of ground acceleration versus time or force versus time can be specified either in the same file as the rest of the input data or in an external file. The program can be instructed to read the data from the external file.

5.2.4.3 Machine Vibration Machines such as turbines induce dynamic loads that are called mechanical vibrations. This type of load is referred to as harmonic loading or sinusoidal loading. The engineer has to know the peak amplitude, operating frequency of the equipment, number of cycles of loading, phase angle, and so on that constitute the input terms of the dynamic load. The variation of the force with time is represented through the following equation, which is shown in Section 1.18.3.5 of the STAAD.Pro Technical Reference manual. F t = F 0 + sin(wt + f) A frequently asked question is from where can one obtain the values of the input. The input constitutes the terms on the right side of the aforementioned equation. Typically, the equipment manufacturer provides these. There are many books in which this topic is discussed, one of them being Design of Structures and Foundations for Vibrating Machines by Suresh C. Arya, Michael W. O’Neil, and George Pincus. The input and other factors associated with this type of load are described in Section 5.2.8.4.The following is an example of harmonic loading. Example 3: Input representing the Harmonic Loading definition

As in the other two categories of dynamic loads, each harmonic force is described after a Type nnn for subsequent identification.

5.2.5 Input Required by STAAD.Pro for THA The following is a summary of the input that is needed for STAAD.Pro to perform a THA. 1. The parameters that describe the characteristics of the dynamic load and certain other terms 2. Weights for calculating frequencies and modes (mass modeling) 3. The application of the time history load on the structure through a load case as shown in the example in Section 5.2.2 These data are specified in two stages. Item 1 is specified in Stage 1 and Items 2 and 3 in Stage 2. Stage 1: This is called the time history DEFINITION block. It is also called the Stage 1 input.

FIGURE 5.2.6 Dialog box in the STAAD.Pro GUI showing Stage 1 input for time history loading

Examples 1, 2 and 3 discussed in Section 5.2.4 were for the Stage 1 input. Stage 2: This consists of the weights for assembling masses for eigensolution and the application of the time-varying load on the structure.

FIGURE 5.2.7 Dialog box in the STAAD.Pro GUI showing Stage 2 input for time history loading

Example 4: Contents of the time history load case for harmonic loading

The three examples cited under the Required Reading section are useful in understanding the time history input in its entirety. The first example (Example 16) is a bit unrealistic in that a ground motion and a forcing function load are applied on a structure simultaneously. It ought to be viewed purely as an example illustrating the feature and not to be considered a real-life situation with a high probability of occurrence.

5.2.5.1 Plotting a Graph of the Time-Force and Time-Acceleration Pairs If the excitation force or acceleration data are specified within the STAAD.Pro input file, a plot of that data is displayed in the STAAD.Pro GUI (Fig 5.2.8).

FIGURE 5.2.8 Plotting the input force or acceleration data

5.2.6 Calculation of Frequencies and Modes The THA procedure requires knowledge of the dynamic properties of the structure—mode shapes, frequencies, and damping characteristics. If the model contains instructions for a THA, STAAD.Pro automatically performs an eigensolution. The MODAL CALCULATION REQUESTED command in Section 4.1 need not be specified in a time history load case. There is no harm in providing it though. STAAD.Pro simply treats it as a superfluous input command.

5.2.6.1 Weights for Frequency Calculation (Mass Modeling) This is identical to the information presented in Section 5.1.3.1. It is also shown in many of the earlier examples in this section. As described in Section 4.1, all the weights that are capable of vibrating, such as selfweight, permanent loads, and the weight of the equipment that causes vibration, should be specified as loads (all positive values) acting in all possible directions of vibration in the time history load case. If no weights are entered, the following message will appear in the output file. *ERROR* NO UNSUPPORTED MASSES ENTERED - CHECK DENSITIES *** ERRORS IN SOLVER ***

FIGURE 5.2.9 Error message in the output file if no weights are entered for the time history case

Related Question: In a THA, when I specify the selfweight and joint loads as acting along X, Y, and Z, and if a forcing function or harmonic loading is applied, is the structure being analyzed for the selfweight and joint loads acting statically in addition to the forcing function loads? Answer: No. The weights in the Stage 2 input are used only for the creation of the mass matrix. These data are not used as static loads. Consequently, if the structure is to be analyzed for those weights acting statically in the form of dead loads or live loads, they have to be specified again separately as static load cases. Example 5: Weights data for mass matrix in a time history load case

5.2.6.2 How Many Modes STAAD.Pro uses as many modes as those calculated during the modal analysis step. As explained in Section 4.1, there are two instructions for controlling that value—CUT OFF MODE SHAPE nnn and CUT OFF FREQUENCY mmm. Their default values are 6 and 108 Hz, respectively.

5.2.7 Analysis Procedure The following is the basic equation that governs the response of a structure to a time-varying load and is given in Section 1.18.3.5 of the Technical Reference manual. The left side of the equation represents the response of the structure in terms of acceleration, velocity, and displacement. The

right side is a general term representing the dynamic load in all its forms described earlier.

The modal superposition method is used to uncouple the global system of equations into independent single degree of freedom equations in the modal coordinate system. The procedure can be found in textbooks on dynamic analysis. The structural response is evaluated at several time points as described in Section 5.2.1.

5.2.7.1 Solving the Equations The uncoupled equations are solved using the Wilson-Theta integration scheme to obtain the nodal displacements in the global coordinate system at each time point. STAAD.Pro then solves for the member end forces, support reactions, element center stresses, and so on at each of these time steps.

5.2.7.2 Duration for Which Dynamic Loading Acts and Response Is Calculated Because the response of the structure (displacements, forces, reactions, etc.) to the dynamic load varies with time, the program first decides on a total time duration for which the response will be calculated. That decision is based on certain criteria, which are explained later. Then, using a solution time step (which the user may override through a variable named DT), the total duration is digitized into a number of equally spaced time steps. The total duration, value of the time step, and number of these time steps are reported in the output file (.ANL file).

FIGURE 5.2.10 Information in the STAAD.Pro output file regarding the numerical solution for THA

DT and the number of time steps are significant in that they have a bearing on the time taken to perform the analysis. Even on a medium-sized model with, for example, 5000 joints or about 30,000 degrees of freedom and 20,000 time steps, the nodal displacements alone represent 30,000 × 20,000 = 600 million numbers. To calculate them and all the other results, a significant amount of memory and storage space are required. Related Question: How does STAAD.Pro decide how long or for what amount of time the response of the structure needs to be solved for the dynamic load? How is the total vibration time worked out? Answer: The default time is the latest ending time amongst all of the forcing functions. This could be the number of cycles multiplied by the cyclical frequency or the last time point in a time-amplitude input curve.

If there are non-zero arrival times, then the latest arrival time is added to this time span. This default duration can be overridden by a CUT OFF TIME input as described in Section 5.2.7.3.

5.2.7.3 The CUT OFF TIME Command We previously saw how the default duration for which the structural response has to be calculated is determined. This is equal to the time at which the dynamic load that ends last, stops, after including the longest of the arrival times specified. In reality, the structure will most likely continue to vibrate past that time. If we wish to override this default, or if we wish to obtain the response till any specific time, it can be done with the help of a command called CUT OFF TIME. In the STAAD.Pro Technical Reference manual, this is described in Section 5.30. In general, if the peak responses are likely to occur after the end of the dynamic load of the longest duration, the CUT OFF TIME command should be entered as shown in the next example. Example 6: Specifying the upper bound of duration of the response

where 15 is in seconds. For loads that last a significant amount of time, such as the harmonic loads produced by a turbine generator, the CUT OFF TIME command may not make any sense. As explained earlier, CUT OFF TIME is meant to evaluate the response of a structure past the time where the load stops. Therefore, for a load with a finite duration, such as the ground motion due to an earthquake, the

load will stop at say 30 sec, while the building will continue to vibrate past the 30-sec point till damping brings it to a halt. To evaluate the response till, for example, 40 sec from the start of vibration, we specify CUT OFF TIME as 40 sec. But take the case of a sine function of a frequency of 3000 cps. If the load is applied for, for example, 300 cycles, the duration of the load is 300/3000 = 0.1 sec. In this circumstance, it makes no sense to specify a CUT OFF TIME of, for example, 5 sec. That is because the load will be considered to be acting from 0 to 0.1 sec only (that is, when the 300 cycles of harmonic load ends). Beyond 0.1 sec till 5 sec, the structure is analyzed as if it is under free vibration, which doesn’t reflect reality. This is represented in the following figure. Instead, we ought to increase the number of cycles so that the load acts for the full 5-sec duration, which means, 15,000 cycles (obtained as 3000 cps multiplied by 5 sec).

FIGURE 5.2.11 Duration of loading versus duration of structure’s response

In practice, the structure may reach steady-state vibration in fewer than 15,000 cycles. Hence, CUT OFF TIME is appropriate for a dynamic load of finite duration such as seismic or explosion loads For a load of indefinite duration such as vibrating machinery, specify as many cycles of loading as needed to reach steady state

FIGURE 5.2.12 Specifying the number of cycles of harmonic loading

5.2.7.4 Arrival Times Consider the following: The dynamic load is induced by vibrating machines or other forms of forcing function loads such as blast loads There is more than one machine on the structure, or multiple forcing function loads These machines or blasts commence at different instances of time One may use the Arrival Time facility to convey the time separation between the commencement of the individual dynamic loads. The arrival time of the load that acts first is usually set to zero, and those of the others would be set with respect to that. For example, consider two pumps A and B. Pump A is started while Pump B is off. Sometime later, Pump B is started. From then on, Pump A and Pump B will be operating simultaneously. To model this, Pump A is defined through TYPE 1 and Pump B through TYPE 2 in the “DEFINE TIME HISTORY” block of input. In the ARRIVAL TIME block of input too, we specify two different arrival times. For Pump A, it is 0. For Pump B, it is the interval after which Pump B is started. We apply these using the TIME LOAD command at the appropriate joints. The input for this scenario is specified as shown in Example 7. Example 7: Specifying two dynamic loads at their respective arrival times

In this example, the force due to Pump A is conveyed through the line “215 FZ 1 1,”which means that the Type 1 load acts along FZ at node 215 starting at arrival time 1 (which has a value of 0.0); “416 FZ 2 2” means that the Type 2 load acts along FZ at node 416 starting at arrival time 2 (which has a value of 5.0).

Figs 5.2.13 and 5.2.14 show the screens from the GUI where the arrival time data are specified.

FIGURE 5.2.13 Dialog box in the STAAD.Pro GUI for defining the arrival times

FIGURE 5.2.14 Dialog box in the STAAD.Pro GUI for specifying arrival times with the dynamic loads

5.2.7.5 Starting Time for the Time-Force Data It is best to start the time-force data as close as possible to Time = 0.0. Otherwise, the program integrates from 0 up to the first starting time, during which time there is no load, thus producing a great deal of null results. Related Question:

If the time-force pairs are given by the equipment manufacturer in intervals of 0.5 sec, and if the arrival time is set to 2.0 sec, how exactly does STAAD.Pro read that data? Is it going to ignore all the forces from 0 to 2.0 sec? Answer: No. STAAD.Pro will shift only the time values in the time-force pairs by the duration of the arrival time. The force data are not affected. In your question, because the arrival time is specified as 2 sec, a time of 0.0 sec will change to 2.0 sec, 0.5 to 2.5 sec, 1.0 to 3.0 sec, 1.5 to 3.5 sec, and so on. So, if you apply a time history load with an arrival time of 2 sec, the load that was supposed to start acting at 0 sec (if its arrival time had been 0) will now start to act at 2 sec. The one that was associated with 0.5 sec will now be associated with 2.5 sec and so on, as shown in the following table. With arrival time = 0.0 sec Time Force

With arrival time = 2.0 sec Time Force 0.00 0.00 1.99

0.00

0.00

0.75

2.00

0.75

0.50

2.00

2.50

2.00

1.00

4.00

3.00

4.00

1.50

5.00

3.50

5.00

2.00

6.00

4.00

6.00

2.50

5.00

4.50

5.00

3.00

4.00

5.00

4.00

3.50

3.00

5.50

3.00

4.00

2.00

6.00

2.00

4.25

1.25

6.25

1.25

4.50

0.75

6.50

0.75

5.00

0.00

7.00

0.00

5.2.8 Description of the Input There are a number of items of input associated with THA.

5.2.8.1 Damping The three types of damping described in Section 4.2 are available for THA. Many of the examples in the previous pages contain the first type—the one that is defined using the keyword DAMPING. The following two examples are of the other two types. Example 8: Time history loading with CDAMP

Example 9: Time history loading with MDAMP

STAAD.Pro has modal damping that does not vary with time or with response. Also, STAAD.Pro handles only classical damping, so the damping matrix is diagonal. A damping ratio of 3–5% for steel and 5–8% for concrete is typical. If no damping is entered, or if a damping ratio of 0.0 (or a very small number) is entered, STAAD.Pro uses a damping ratio of 0.05.

5.2.8.2 The DT Option In the modal superposition method, the uncoupled equations in the modal coordinate system are solved using a step-by-step integration technique. DT stands for the solution time step used in the step-by-step integration. It has a default value of 0.0013888 sec.

FIGURE 5.2.15 Dialog box in the STAAD.Pro GUI for assigning the solution time step

The rule of thumb is that to capture the contribution of a mode, DT must be smaller than (1/10th) the period of that mode. With high-frequency modes, the period of the modes will be so small that the default DT may become larger than one cycle of that mode’s response. It is not possible to calculate the response for that mode accurately with that DT. Hence, STAAD.Pro rejects modes where DT is greater than three times the modal period. If a structure has higher modes that are prominent, one can specify a lower DT as shown in the following example. Example 10: Command in the STAAD.Pro input file for specifying the solution time step

DT does not have to equal the time increment of the time-force or time-acceleration input data. Because the specified load data constitutes a lookup table, the program uses linear interpolation to

obtain a force if there isn’t one available in that table for an integration time point.

5.2.8.3 The SAVE Option As explained earlier, during THA, the displacements are calculated at all nodes for each time step used in the solution process. By default, these data are not stored in files because they can take up enormous amounts of disk space. However, if one wishes to obtain these data, it can be done by switching on the Save option in the Time History load dialog box in the STAAD.Pro GUI as shown in Fig 5.2.16. The history of displacements at each node is saved in a file with the name inputfilename.TIM (see Section 5.31.4 of the STAAD.Pro Technical Reference manual). A file with the extension .FRC is also created. It contains the 12 forces at the ends of each member and six reactions at each support at each time step.

FIGURE 5.2.16 Dialog box in the STAAD.Pro GUI for specifying the SAVE parameter

After the analysis is completed, these files can be opened using a text editor such as Notepad or WordPad or using Microsoft Excel. These files may be very large in size depending on the duration of the dynamic load and the time step value. For example, consider a harmonic load of a frequency of 50 revolutions per minute (RPM) applied for 20 cycles. At 50 RPM, the period of 1 cycle is 1.2 sec; thus, for 20 cycles, the duration of loading is 24 sec. If the time step used in the analysis is 0.00139 sec, the number of time steps is 24/0.00139 = 17,266. Hence, displacements, member forces, support reactions, and so on have to be computed and written into the respective files for 17,267 time points (including the start point). It could lead to a large amount of data if there are thousands of nodes in the model.

FIGURE 5.2.17 Output in the .TIM and .FRC files

5.2.8.4 Harmonic Loading—Stage 1 Input As explained earlier, a harmonic load stands for a dynamic force that is periodic in nature and its variation with time can be described using a sine or cosine function. In Section 5.2.4.3, we saw the expression describing the variation of the force F t with time t. The various terms in that equation are described in the following figure.

The terms in this equation are similar to those in the dialog box in the STAAD.Pro GUI (Fig 5.2.18).

FIGURE 5.2.18 Dialog box in the STAAD.Pro GUI for specifying a harmonic load

The FREQUENCY of the applied load can be specified as cycles per second (Hz) or as RPM. AMPLITUDE has units of force or moment depending on the type. 5.2.8.4.1 Duration of Load for Harmonic Loads The duration of loading for any given harmonic load is calculated in the following manner. If frequency is specified, then F = frequency in cps If RPM is specified, then frequency in cycles (revolutions) per second = F = RPM/60 Time period of the load = 1/F (in other words, duration of one cycle of loading) Total duration of loading = number of cycles multiplied by time period of the load. The load is assumed to stop once its duration has been reached. If there are no other harmonic loads acting beyond that duration, the structure will be under free vibration beyond that point of time. For example, FUNCTION SINE AMPLITUDE 8 FREQUENCY 60 CYCLES 400

means that the duration of load = (1/60) * 400 = 6.667 sec FUNCTION COSINE AMPLITUDE 3.5 RPM 2500 CYCLES 300

means that the frequency in cps = 2500/60 = 41.667 cps, and duration of load = (1/41.667) * 300 = 7.2 sec. Ordinarily, the response of the structure is not calculated beyond the longest duration from among the various harmonic loads. This can be overridden using the CUT OFF TIME command described in Section 5.2.7.3.

Fig 5.2.19 reports the information contained in the output file for harmonic loads.

FIGURE 5.2.19 Key terms in the STAAD.Pro output file regarding THA for harmonic loads

5.2.8.4.2 CYCLES—How Many to Apply The number of cycles to be applied shouldn’t be too small or too large. A right number is one that causes the structure to reach steady state so that there is no more useful information to be obtained by applying the load for a longer duration. Too few cycles means that the load will not be applied long enough for the oscillations of the structure to attain steady state. If too many cycles are specified, the duration will be so large that the response is calculated well past the point of attainment of steady state. Hence, a large amount of data will be calculated unnecessarily. If as described earlier, the duration of load is say 15 sec, and the solution time step is 0.0013888 sec, the number of solution time steps will be 15/0.0013888 = 10,800. The analysis runtime can be pretty large if the model has thousands of joints, members, and elements. The right number can be obtained through a trial and error process. Apply a certain number of cycles, run the analysis, view the time displacement graphs at a few joints, and assess whether a steady-state pattern is attained. If a significant part of the graph indicates steady-state behavior, reduce the number of cycles. If steady state has not been attained, increase the number of cycles. The way to view the time-displacement graph to make these assessments is described in section 5.2.10 along with the factors that determine the right number of cycles. 5.2.8.4.3 STEP and SUBDIV Options The harmonic loading, which is defined using a SINE or a COSINE function, is a continuous function. STAAD.Pro digitizes it, meaning, converts it into discrete values of force at discrete points in time. The analysis is performed using these discrete pairs.

By default, 1/4th of a cycle is divided into 3 parts, as shown in the previous figure. That means, for a cycle that lasts 1.2 sec, adjacent time points are 0.1 sec apart. There are two ways by which we can instruct STAAD.Pro to change this interval—one using the SUBDIV parameter, the other using the STEP parameter (Fig 5.2.20). The SUBDIV parameter represents the integer number of divisions of a quarter cycle. The STEP parameter is for specifying the time interval between two adjacent points (in time) in that cycle. Its default value is 1/12th the duration of 1 cycle. That is equivalent to the duration that one obtains by using a default SUBDIV of 3.

FIGURE 5.2.20 Parameters for digitizing a harmonic function

The duration of 1 cycle is equal to the reciprocal of the cyclic frequency (frequency in cycles per second) of the harmonic load. This duration divided by STEP gives the value of the number of divisions of 1 cycle. Care must be taken to ensure that STEP isn’t wider than the duration of one quarter of one cycle of loading. For example, if the cyclic frequency is 500, duration of one cycle is 1/500=0.002 sec. Specifying a STEP such as 1 sec would be wrong, as it would be wider than the duration of an entire cycle, and hence wouldn’t digitize the function correctly.

FIGURE 5.2.21 Parameters of harmonic loading

FIGURE 5.2.22 Errors in the harmonic loading parameters

For most cases, it is not necessary to specify the STEP or the SUBDIV options. The default value is a reasonably good one. If it is necessary to provide them, SUBDIV is preferable to STEP, with preferable values being integer multiples of 3. 5.2.8.4.4 Difference between DT and STEP It is important to understand the distinction between STEP and DT. STEP is the time interval used to digitize the applied harmonic load into discrete values of force at discrete points in time. DT, on the other hand, is the time interval used in the integration of the differential equations (also called the solution time step), and hence, it is the time interval at which the response of the structure is computed.

5.2.8.5 Harmonic Loading—Stage 2 Input The type number, arrival time number, and multiplication factor, if any, have to be applied at one or more joints of the model following the TIME LOAD command. Example 11: Terms in the Stage 2 input for a harmonic load

In this example, the TYPE 1 force is applied at node 264 with the first arrival time, and the TYPE 2 force is applied at node 265 with the second arrival time. Both loads act along global Z. Types 1 and 2, and the arrival times ought to have been defined in the Stage 1 input.

5.2.8.6 Ground Motion Loading—Stage 2 Data The Stage 2 data set for specifying a ground motion load is shown in the next example. Example 12: Terms in the Stage 2 input for a ground motion load

The multiplying factor shown in this example is applied when the ground acceleration is normalized by some factor, such as 9.806 in this case. This multiplying factor is shown in the STAAD.Pro GUI using the term Force Amplitude Factor as shown in Fig 5.2.23.

FIGURE 5.2.23 Dialog box in the STAAD.Pro GUI for specifying the multiplying factor for the dynamic loads

For example, if the ground acceleration at time 5.6 sec is 2.3 m/sec2, the time-acceleration pair would be 5.6 2.3

However, if that acceleration is normalized by g, the normalized value (= 2.3 divided by 9.806 = 0.23455) would be input as 5.6 0.23455

and the multiplying factor (force amplitude factor) would be input as 9.806. Keep in mind that a factor such as 32.2 (ft/sec2), 9.806 (m/sec2), or 386.4 (in/sec2) is associated with accelerations, not forces. So, it usually does not make sense to specify those values for the force amplitude factor when the dynamic load is a harmonic force or a randomly varying force with time. Related Question: The description for the Time History Load definition in the STAAD.Pro Technical Reference manual refers to a term “SCALE f7.” What is its purpose?

FIGURE 5.2.24 Description in the STAAD.Pro Technical Reference manual for the SCALE factor for time history loading

Answer: The scale factor is a multiplying factor that all the forces in the time-force pairs or all accelerations in the time-acceleration pairs are multiplied by. It has the same purpose as the force amplitude factor mentioned earlier. If it is a sinusoidal loading, the AMPLITUDE is multiplied by the scale factor term. If a series of time-force pairs are specified, the force terms are multiplied by the scale factor term. If a series of time-acceleration pairs are specified for ground motion data, the acceleration terms are multiplied by the scale factor term. For example, if the accelerations are provided in terms of g (the acceleration due to gravity), one simply has to specify the scale factor as the value of g. DEFINE TIME HISTORY TYPE 1 ACCELERATION SCALE 32.2

The weights we specify for calculating masses are not multiplied by the scale factor. Remember to specify only one—that is, either the force amplitude factor or the scale factor. Applying both could mean that the applied load is factored twice, resulting in a much higher response than would actually occur.

5.2.8.7 Random Excitation—Stage 2 Data As discussed previously, the Stage 1 input for random excitation is specified as a series of time versus force values (in the ascending order of time) following the TYPE n keyword. Example 13: Terms in the Stage 2 input for a random excitation load

In the Stage 2 input, the type number, arrival time number, and multiplication factor, if any, have to be applied at one or more joints of the model following the TIME LOAD command. These are illustrated in the aforementioned example.

5.2.8.8 Explosion/Blast Loading—Stage 1 Data A blast load can be applied as a FORCING FUNCTION. It is specified as discrete time-force pairs, with the force changing from a very small value to a large value, and then back to a small value over a very small time interval. It is then applied at specific nodes using the TIME LOAD command discussed in earlier examples.

The structure’s response to blast load is usually a higher frequency response than to an earthquake; hence, more modes (CUT OFF MODE) and a higher frequency limit (CUT OFF FREQUNCY) may be required. So, it may be necessary to use a smaller integration step DT. Because the program uses linear interpolation to find the forces at the DT intervals, on a general basis, a blast load should be represented using a minimum of five time-force pairs. t1 p1 t2 p2 t3 p3 t4 p4 t5 p5

(t1, p1) is set to (0,0). (t2, p2) is for the instant before the blast commences, p2 is set to a very small force. So, (0.1, 1.0). (t3, p3) represents the condition when the blast attains its maximum value. So, (0.2, 250). (t4, p4) is for the instant after the blast is over, p4 is set to a very small force. So, (0.3, 1.0). (t5, p5) is to capture the free-vibration response of the structure for a few seconds after the blast is complete. So, (5.0, 0.0). This is because, the peak response could occur after the end of the load. Remember, the program stops calculating the response once the loading stops. Alternatively, one could also omit (t5, p5) and specify CUT OFF TIME t5 instead. A blast load cannot be specified as an acceleration. Example 14: Stage 1 input for blast loading

In this example, the load increases from 0 to 85 and back to zero over a duration of 0.07 sec. An intermediate value of 10 is specified at 0.015 sec and 0.055 sec to facilitate interpolation.

5.2.8.9 Explosion/Blast Loading—Stage 2 Data This is similar to the input for harmonic loading or random excitation. Example 15: Stage 2 input for blast loading

5.2.8.9.1 Explosion/Blast Loads in the Form of a Pressure Wave A blast load that is in the form of an element or panel pressure has to be converted to a force. Because a blast is a pressure wave, we need to make an assessment regarding the portion of the structure that will be directly subjected to the blast. Then, just as in the case of the wind load generator, find the influence area surrounding the nodes in that region and multiply the respective areas by the blast pressure. If that region is defined using plate elements, the pressure multiplied by approximately one-third (for three-noded) or one-fourth (for four-noded) the area of the individual plate elements, aggregated over all those elements, will give you the peak force acting at each of those nodes. 5.2.8.9.2 Multiple Explosions In the event of multiple blasts that are separated by time intervals, one may use the ARRIVAL TIME command to convey the time separation between the commencement of the loads. For each force, generate a unique TYPE in the Time History definition. Apply each type at its corresponding node as a forcing function.

5.2.9 Other Dynamic Load Types Structures are subjected to dynamic loads from other sources too. The method for modeling two such loads is described in Sections 5.2.9.1 and 5.2.9.2.

5.2.9.1 Impact Loads The method used to analyze a model for blast loading can be used for impact loads also. If the force that is transmitted to the model at the instant of the impact can be determined, we can apply it using the forcing function time history load type—namely, a load that goes from zero to the magnitude at the impact moment and down to the static value of the load over a very short time interval. Beyond that interval, the load will be the constant static value over a certain duration till steady-state displacements are attained. Yet another way is to solve the model for a static load whose value is equal to the weight of the falling object multiplied by an impact factor (a number greater than 1.0). In the AASHTO 1998 code, for example, Table 3.6.2.1-1 contains a “Dynamic Load Allowance” for considering the hammering effect caused by a truck wheel going over a pothole on the deck surface or an expansion joint. The dynamic response is usually about 15–25% more than the static response.

5.2.9.2 Wind Loading as a Dynamic Force on a Structure The following are the steps to analyze a structure for wind loads acting as a time-varying force.

Because the load acts above the ground, it would have to be specified using the “TIME LOAD” category. The variation with time of the force acting at a joint due to wind has to be entered using a TYPE definition under the DEFINE TIME HISTORY block of input. Because more than one joint will receive the load, it needs to be determined whether the variation of the force with time follows the same basic pattern at the various joints with the difference between the force at one joint and that at another being just a simple force amplitude factor. In other words, if all the joint forces fluctuate together in a constant relative ratio, then the data are simple. If every joint has its own fluctuation pattern, then each set of time-force data has to be specified under a TYPE. If the wind force is fluctuating as a sine wave, then the AMPLITUDE can be entered as the height of the sine wave, FREQUENCY as the frequency (cycles per second), and CYCLES as the number of cycles before the wind load stops.

5.2.10 Output Produced by STAAD.Pro In theory, each of the structure’s responses that we saw in static analysis—nodal displacements, support reactions, member forces, element stresses, and so on—are available for a THA also. The difference is, because the structure vibrates, each of these values changes with time. So, each response quantity has a value at each time step for the entire duration for which the responses are calculated. This is also known as the response history for that item. Usually, for each response item, such as the FY reaction at support node 18, or moment MZ at the start of member 65, engineers are interested in only the maximum value over that duration, not the full history of that item. With this in mind, the following results are available from STAAD.Pro for a THA: 1. Maximum displacement for each degree of freedom at each node in the output file and the postprocessing mode. 2. Maximum member end forces for each member in the output file and the post-processing mode. 3. Maximum plate stresses and unit-width moments in the output file and the post-processing mode. 4. History of displacements, velocities, and accelerations at each node for the three global directions. Can be plotted in a graph form on the screen, and the numbers can be saved in external files. 5. History of member end forces and support reactions can be saved in external files. The method for viewing these results is explained in the following sections. Output from THA gives us the dynamic effects only. If we look at the classical time history equation, the right side of the expression is a vector of loads that vary with time. It does not include the static loads. We have to manually combine (using load combination cases) the results from dynamic cases with the results from static load cases. The maximum for a response quantity is based on the one with the larger magnitude from among the highest positive and highest negative values for that quantity. In the post-processing mode, the node displacement diagram for a time history load case is plotted for specific instances of time. Because the displacements at intermediate sections of members are not calculated for a THA, the plots are simply straight lines joining the displacements at the nodes.

FIGURE 5.2.25 Displacement diagram at a specific instance of the duration of the dynamic load

5.2.10.1 Response History—How to Obtain 5.2.10.1.1 Joint Displacements The history of displacements for each of the six degrees of freedom at each node is available with the SAVE command described in Section 5.2.8.3, as well as in the post-processing mode. Section 3.1 of Part II has detailed information on the method by which the displacement history (as well as velocities and accelerations) can be viewed in the post-processing mode. 5.2.10.1.2 Support Reactions and Member End Forces The value of these terms for each degree of freedom at each node is written for each time point in the .FRC file as explained in the context of the SAVE command described in Section 5.2.8.3. For these result terms, only the maximas can be viewed in the post-processing mode, not the histories. 5.2.10.1.3 Maximum Base Shear After the support reactions are calculated for each time step, the sum of the reactions for each of the three global directions is also calculated for each time step. This sum represents the base shear at each time step. The maximum base shear for each of the three directions and the associated time is reported in the .ANL file (see Section 4.1 of Part III for additional information).

FIGURE 5.2.26 Report of maximum base shear for THA

The individual output items are described in Part III. By default, STAAD.Pro calculates the response only for the duration of the applied load. However, a structure will continue to vibrate past that point, until the motion comes to a halt due to structural damping. It is very important that the structural response (nodal displacements) be graphically inspected to ensure that it is calculated past the peak response point.

5.2.10.2 Displacements, Velocities, and Accelerations of Joints—Absolute or Relative By default, STAAD.Pro calculates the relative response in a THA. The relative acceleration, velocity, and displacement of the base is zero. The reported base shear and reactions are from the relative acceleration of the masses. However, in recent versions, ABSOLUTE values can be obtained as discussed in Section 3.1 of Part III. Related Question: I get the following warning when I perform a THA on a solid model. **WARNING: NUMBER OF TIME STEPS FOR TIME HISTORY RESULTS FOR SOLIDS IS TOO LARGE. ONLY EVERY 2TH STEP OF FIRST 4972 STEPS WILL BE CALCULATED.

Answer: At the center and at each joint of each solid element, STAAD.Pro calculates six stress values for each time step. On a large model with thousands of solid elements, this can easily be millions of eight-byte numbers. If the number of solid stress values to be calculated and examined exceeds a built-in limit, STAAD.Pro examines every second, third, or fourth step to determine each of the nine maximum solid stress values for each solid over the time span rather than every step. This does not affect beam, plate, or nodal results.

5.2.10.3 Viewing the Variation of Displacements over Time at Individual Nodes Use the post-processing mode’s Dynamics-Node Displacement page to observe the displacement history of any node, which is discussed in detail in Section 3.1 of Part III.

FIGURE 5.2.27 Plots of displacement, velocity, and accelerations versus time in the STAAD.Pro GUI

Related Questions: 1. Can we find the acceleration of the roof of the building in a THA? 2. Is it possible to obtain the average acceleration, velocity, or displacement of a set of nodes such as the nodes of a floor? Answer: Yes. Refer to the topic titled “Results for a Group of Nodes” in Section 3.1 of Part III.

5.2.10.4 Transient Phase Versus Steady-State Phase If the applied loading is harmonic (sinusoidal), the question arises as to whether the displacements calculated by the program represent just the transient phase of vibration of the structure, or the steady-state phase, or both. In STAAD.Pro’s THA, the results (joint displacements, member forces, support reactions, etc.) are calculated from the time when the load starts to act till the time dictated by either the CUT OFF TIME command or the time for which the load is applied on the structure. Thus, the history of results includes the transient phase of the response followed by the steady-state phase of the response (if steady state is attained within the total duration for which results are calculated). The maximum values reported are obtained by considering both phases. The displacement, velocity, and acceleration graphs for joints can help us determine whether the motion has attained steady state or not. In Fig 5.2.1, one can visually observe when the transient response ends and when the steady-state response begins. However, this is a manual approach. There is no message to be obtained from the program in case steady state has not been attained. NOTE There is another type of analysis available in STAAD.Pro called Steady-State analysis. It is different in the sense that it is an exclusive module for obtaining solely the steady-state response of systems without going through the THA procedure described here. This feature is available with the program’s Advanced analysis

engine (see Section 1 of Part I ).

Related Question: For any node in the structure, when does peak displacement occur? During the transient phase or the steady-state phase? Answer: The maximums almost always occur during the start-up transient period, not during the later steady-state response period.

5.2.10.5 Number of Cycles Needed to Attain Steady State Related Question: What is a reasonable value for the number of cycles that the harmonic load should be applied? Answer: The number of cycles to achieve steady state is dependent on the damping. With light damping, it takes longer to reach steady state. Generally, in structures with 5% or more damping, it shouldn’t take more than a few hundred cycles to attain steady state. In Section 3.1 of Part III, we discuss how the tools of the GUI can be used to assess whether the response is in the transient phase or the steady-state phase. Also, there is no need to specify more cycles of loading than what is needed to go past the transient phase into a few cycles of the steady-state phase. For example, if steady state can be reached in 1200 cycles, it is pointless to apply the load for 2000 or 3000 cycles. The response beyond 1200 cycles is going to be no different than what it is in the vicinity of 1200 cycles.

FIGURE 5.2.28 Opening screen of STAAD.Pro where available licenses are displayed

FIGURE 5.2.29 Plots in the STAAD.Pro GUI that show the history of displacement at nodes

Related Question: If I do not have the license for the advanced analysis engine, how do I find out the results during

the steady-state phase? Answer: Because steady state occurs after the transient state, it is important that the structural response be computed for a duration that is long enough to capture the transient state plus the steady state. For nodal displacements, view the Time-Disp history plots shown in Fig 5.2.29 (also see Section 3.1 of Part III) to obtain the peak values during the steady-state phase. For reactions and member end forces, the .FRC file needs to be created (see the SAVE command described in Section 5.2.8.3). Open that file using Notepad or Wordpad and visually scan for the maximas in the steady-state phase of the results. This is a tedious but reliable method. Alternatively, import it into Excel, plot the values, and check if there is a way to get the maximas from the graphs, or use the sorting facilities of Excel to obtain the maximas for any duration of the response. Related Question: Without doing a steady-state analysis, how is it possible to know whether a structure subjected to a harmonic load has been solved for sufficiently long time in terms of duration of vibration? Answer: The Time-Disp graphs shown in Fig 5.2.30 can provide a clue. Note that within the duration for which the response has been calculated, the peak displacements occur closer to the end of that range. This indicates the likelihood that even larger displacements may be possible beyond that range. We would have to analyze it for a longer duration (more cycles) to find that out.

FIGURE 5.2.30 Viewing the joint motion plots to determine whether peak response has been attained

Fig 5.2.31 shows the displacement graphs for the same node after the analysis has been done for twice as many cycles.

FIGURE 5.2.31 Viewing the joint motion plots to determine whether steady state has been attained

The displacement history of another node is shown in Fig.5.2.32 with the response calculated from the application of sufficient cycles to capture the transient and attenuation phase. Thus, Figs 5.2.30 to 5.2.32 illustrate the importance of solving the model for sufficient number of cycles to cover the full duration of the transient response and beyond. Related Question: I want to analyze a structure for a harmonic load with a range of frequencies—from 10 to 60 Hz in steps of 5 Hz. Is there a way to instruct STAAD.Pro to automatically check for all these frequencies? Answer: Because of the range of frequencies, we are looking at analyzing the model for 11 harmonic functions—one function with a frequency of 10 Hz, another with 15 Hz, a third one with 20 Hz, and so on up to 60 Hz.

FIGURE 5.2.32 Viewing the joint motion plots to examine the vibration pattern at a node

Since there can currently be only one time history load case in a single STAAD.Pro model, you’ll have to create separate models for each of those harmonic functions. If you are interested only in the steady-state response, you can use the steady-state analysis feature available with the advanced solver. It can analyze a single model for a range of harmonic frequencies you want. Section 5.37.6 of the STAAD.Pro Technical Reference manual has the details.

5.2.10.6 Selecting Modes from the Post-processing screens In the STAAD.Pro GUI, there is a list box from which the individual modes can be selected (Fig 5.2.33).

FIGURE 5.2.33 Selecting specific modes for viewing

This facility is solely for viewing the mode shape. It is not a means by which to ask the program to show a result quantity for just that mode. Related Questions: 1. Why doesn’t the deflection diagram change when I select a different mode? 2. How can I find out which mode is responsible for the results I am getting for displacements and reactions? Answer: The answer to the first question is, it is not supposed to, for the same reasons provided in the answer to the second question. The responses being plotted (displacements, velocities, acceleration, etc.) are based on the contribution of all the modes for which the THA was performed. (If the MODE SELECT command has been specified, then all the modes listed in that command are considered.) They are not just for specific modes. Therefore, if nine modes were used in the THA, the THA results are the cumulative effect based on all nine modes. It is not possible to take them apart on a mode-bymode basis after the analysis is completed. Hence, selecting the individual modes from the dropdown list won’t have any effect.

5.2.10.7 Analysis Results for Blast Loading The results STAAD.Pro produces for this kind of loading are the same as that for any other type of time-force loading or a ground motion loading. These include the history of displacements, forces and reactions, and the maximas from that history.

5.2.10.8 Obtaining Results in the Frequency Domain As we have seen in the discussions so far, the nature of the results for a THA is that they are a function of time. This is because, the structural response is measured in terms of displacements, reactions, forces, and stresses at specific points in time over the course of the duration of the response. This is also known as determining the results in the time domain. It is also possible to obtain the results in the frequency domain. In this domain, the acceleration, velocity, and displacements of the nodes are plotted against the frequencies of the structure.

FIGURE 5.2.34 Obtaining frequency domain plots at nodes

The procedure for obtaining the results in the frequency domain is explained in Section 3.1 of Part III. The responses being plotted (displacements, velocities, accelerations, etc.) are based on the contribution of all the modes for which the THA was performed. It is a graphical representation of how much of the response is occurring at a given frequency. This graph can be used to determine which frequencies are critical for the structure. So, for example, suppose there is a machinery that vibrates at a certain frequency. You could consult the response plot in the frequency domain for the structure, view the peaks in the curve, and note the frequency at these peaks. If the machine’s frequency falls within the range of the frequency at these peaks, then it raises the possibility of resonance.

5.2.11 Multiple Load Cases for Time History Currently, in one model (input file), STAAD.Pro can process only one load case with time history loading. In other words, one input file cannot have multiple load cases containing time history loads. If one wishes to solve a model for more than one time history load case, it would have to be done using separate input files containing that same structure with one time history load case per file.

FIGURE 5.2.35 Error message displayed in the STAAD.Pro output file if multiple time history load cases are present

However, within a time history load case, there can be many forcing functions or a forcing function plus a ground motion. In other words, multiple dynamic load items can be part of a single load case. Example 16: Specifying multiple dynamic loads on a structure

5.2.12 Load Combinations for Time History Loading For steel and concrete design, the member forces STAAD.Pro uses from a THA are the absolute maximum values from the duration that the structure was solved for. These are signed values, meaning, they are positive or negative numbers. However, the nature of THA is that, for any member force term, there is also a value with an opposite sign and a magnitude perhaps slightly below this maximum. It is imperative that the member be designed for that value too. For example, if the absolute maximum for a column is 43 kips of axial compression, it is very likely that it also has a tensile force of magnitude slightly below 43 because vibration causes the force to change signs between the two extremities of an oscillation. There is no means available to instruct the program to consider that “second highest” force or moment during the design. Therefore, just like in an RSA, the program can be asked to create pairs of combinations, one with the positive value of the absolute maximum, the other with the negative value of the absolute maximum. This is shown in the next example. Load case 8 is the time history load. LOAD COMB 37 1 1.1 2 1.4 3 1.4 8 0.9 LOAD COMB 38 1 1.1 2 1.4 3 1.4 8 -0.9

This recommendation is for all categories of dynamic loads described in this section.

5.2.13 Resonance Just as the structure has frequencies (which are calculated during eigen extraction), the applied

loads too have one or more frequencies. These are called the excitation frequencies. For a specific harmonic load, this is readily available. It is the value we specify for the term FREQUENCY. For ground acceleration and random excitation, there are probably several frequencies. But without a tool to find them, the frequency content of these loads is not readily available. How do we find out if the applied dynamic loading will cause resonance? For harmonic loading, it is not difficult. As we have seen earlier, the harmonic load command looks like this: AMPLITUDE 3.1 FREQUENCY 80.3 CYCLES 500

In this example, the frequency of the applied loading is 80.3 cps. In the output file, or in the postprocessing mode, STAAD.Pro will list the frequencies for all the modes that it is able to solve for.

FIGURE 5.2.36 Table of frequencies in the post-processing mode

If the frequencies in any of those modes are comparable to the applied frequency, there is a potential for resonance. We use the word “potential” because, in order for resonance to occur, it must be a significant mode, not a localized vibration of just a few members in just a small portion of the structure. If we can perform a frequency analysis of the ground acceleration and random excitation, these frequencies can be compared against the structure’s frequencies. In its absence, only the analysis results can tell us if resonance-type behavior occurs, namely, displacements that keep increasing.

5.2.14 MODE SELECT—Calculating the Response from Just a Few Specific Modes As in the case of an RSA, the structural response obtained from a THA is that resulting from all of the modes calculated by the program. Occasionally, one may wish to examine the response based on just a few specific modes, such as modes 2, 3, and 7. This can be done with the help of an instruction called MODE SELECT. It is described in Section 5.30.2 of the STAAD.Pro

Technical Reference manual. Example 17: Choosing the structure modes to use in a time history analysis

If the selected modes contribute very little to the structural response along the direction of the applied dynamic load, the results from the THA (displacements, reactions, member forces, and plate and solid element stresses) could be zero or very near zero. Hence, while this feature is a good analytical tool, it is best to use all modes for the analysis.

5.2.15 Missing Mass The ability to consider the effect of missing mass, a feature that was described in Section 5.1.3.3.5, is not available for THA at present though it is expected to be available in a future version of the software. Therefore, the only alternative users have is to consider as many modes as possible using CUT OFF MODE SHAPE.

5.2.16 Modal Participation Factor for a Time History Analysis In Section 4.1.7.3, we saw the equation for the calculation of modal participation factors. The term {B} in that equation consists of the weights lumped at the nodes due to which these factors provide a measure of the importance of each mode when the structure is subjected to a 1g acceleration at the base. This is quite useful for an RSA, and for a THA for base excitation. For a random excitation or a harmonic force, because the structure is acted upon by forces above

the base, it would have been useful if {B} were to consist of the forces acting at the various nodes of the structure, and thus provide us the “force” participation factors. Unfortunately, the force participation factor, which is based on a dot product of the mode and the dynamic force distribution in a THA, is calculated but not printed by STAAD.Pro. Hence, even during a THA, the output provided for the command SET PART FACT is the modal participation factors for a 1g ground acceleration. This isn’t of any help in determining how important the individual modes are for the overall response. Related Questions: 1. I am getting negligible displacements for the time history load case. The member forces are also quite small in spite of what I believe is a strong ground acceleration. 2. How can I know whether the number of modes that has been used is sufficient? Answer: A few trial runs may be required with various values of CUT OFF MODE SHAPE n (and CUT OFF FREQUENCY m if frequencies of the higher modes exceed 108 cps), where n is, for example, 30, 40, 50. Compare the displacements, reactions, and member end forces obtained for a 30-mode solution with those for a 40- or 50-mode solution. It will give us a sense of how many modes are needed. On large structures with thousands of nodes and members, the time taken for the analysis may place a limit on how high those cut off values can be.

5.2.17 Member Tension/Compression and Spring Compression/Tension These attributes are solved in STAAD.Pro using an iterative method. However, the THA implementation is a single-iteration approach. Hence, these features are not compatible with THA. Thus, tension-only members can end up with compressive forces, compression-only springs can end up with tensile forces, and so on.

5.2.18 Cables and Multi-linear Springs For these too, STAAD.Pro uses an iterative method to find the forces in cables and spring supports. Hence, cables are treated as ordinary linear truss members, and multi-linear supports are considered to have only a single constant stiffness during THA.

5.2.19 Floor Spectrum This feature has been introduced in STAAD.Pro V8i. It is called floor spectrum and it can be generated for models for which a THA is performed. The program generates a secondary response spectrum dataset of period versus acceleration at a particular node. This topic is not discussed further in this book. Users are urged to refer to Section 5.32.10.3 of the Technical Reference manual.

FIGURE 5.2.37 Floor spectrum pages from the STAAD.Pro Technical Reference manual

FIGURE 5.2.38 Floor spectrum pages from the STAAD.Pro GUI manual

Index A

AASHTO, 163, 174, 420 AASHTO HS20-44, 178 ABS (absolute), 242 Absolute, 422–423. See also ABS (absolute) ABSOLUTE combination, 251, 252 Absolute maximum values, 431 ABSOLUTE method, 250–252 Absolute temperature, 116 Acceleration, 190, 421, 429 ACCIDENTAL torsion, 210 Accidental Torsion, 207–211 multiplying factor for, 208–209 Accidental torsion moments, 219–220 Accuracy, 289 ACI 318-05, 244, 245 ADD LOAD, 186 Advanced analysis engine, 424, 426 Advertising sign, 129 AIJ, 193, 202, 214 AISC, 244 AISC 9th edition, 245 AISC 360-05, 226, 241 AISC 360-10, 241 Algebraic, 249 ALGEBRAIC combination methods, 252 Algorithm floor load, limitations of, 47–53 Alpha, 103, 105 Alpha = coefficient of thermal expansion, 112 Alternate span loading, 26 Ambient temperature, 106, 107, 114 AMPLITUDE, 410, 416, 420 Angles, 144 Animated view, 172 .ANL file, 422 Appurtenances, 129, 146 AREA load, 73 Area load, 73 ARRIVAL TIME, 419 Arrival times, 402–404 ASCE 7, 244 ASCE 7-02, 147, 150, 154, 272 ASCE 7-05, 191, 205, 223, 225, 376 ASCE 7-95, 147 Ascending, 417 Attenuation phase, 427 Automatic load combination, 245, 247–248

Automatic Load Combination generator, 7 Axial compression, 86–87, 431 Axial elongation, 114 Axial forces (P-delta effect), 305 eigensolution, 305 geometric stiffness matrix (Kg), 305 stiffness matrix, 305 Axial loads, 23–24 Axial shortening, 84 Axle. See Specific Axle Axle loads, 160, 169

B

BALANCED, 154 Balanced snow loads, 153 Base acceleration, 219 Base excitation, 434 Base shear, 212, 216, 368–373 direction factor, 368 dynamic weight, 371 linear interpolation, 369 logarithmic interpolation, 369 mass participation factors, 368 SCALE FACTOR, 369 spectral acceleration, 368 Bending capacity, 175 Bending stiffness of slab, 67–69 Bentley Bridge, 190 BETA, 210 Blast loading, 417–420, 418–419, 429 Blasts, 191 Bolts, 198 Boundary beams, 52 Box culvert, 179 Braces, 210 Bracing, 55, 138 Bracing members, 139, 143 Braking, 190, 231 British codes, 244, 245 BS5950-2000, 226 Bucket, 236, 239 BUCKLING, 261 Buckling, 118 Building code, 235, 254 Buried pipes, 212 Buried structures, 212

C

CABLE, 78 Cable axial compression and, 86–87 eccentricity of, 85 large displacement entities, 308 MEMBER TENSION, 308

pre-tensioned, 308 profile, 85 support displacement loads and, 83 Cable analysis, 241 CALCULATE, 328 CALCULATE RAYLEIGH FREQUENCY, 311 Canadian codes, 244 CDAMP (composite damping), 318, 320, 406 ASCE4, 319 ASCE 4-98, 322 CQC, 319 damped strain energy, 322 damping ratio, 319 damping ratio for steel, 324 effective damping ratio, 322 material definition, 324 response spectrum analysis, 323 spring damping, 319 spring supports, 319 strain energy, 319 support spring, 324 time history analysis, 323 total strain energy, 322 Celsius, 103 Celsius/Kelvin, 105 Center of action of the applied loads, 32–34 CG. See Center of gravity (CG) Center of gravity (CG), 21, 133, 316 Center of rigidity, 211 Centrifugal forces, 190 Centroid of the section, 186 Channels, 210 Check Multiple Structures, 142 Circular tank, 90, 100, 146 CLOCKWISE, 209 Closed panels, 133, 150 Closed polygon, 52, 58 Closed structures, 122–133, 135, 136, 143, 149 excluding members for, 143 exposure factor, 129, 133, 134 panel identification for, 124 TYPE command, 129 wind intensity, 129 Closely spaced modes CQC (complete quadratic combination), 313 CSM (closely spaced modes), 313 SRSS (square root of sum of squares), 313 Coarsely meshed, 68 Coarse mesh, 67 Coefficient of thermal expansion (Alpha), 103 Collinear members, 50 Collinear nodes, 212 Combination cases, 234 Combining load cases, 234–252 reference loads, 252–270

repeat loads and load combinations, 235–252 Combining loads, 2 Communication tower, 133, 146 “Component” load cases, 254 Component of that pressure of non-global directions, 144 Component-only load cases, 256 Composite damping, 373 Compression-only floor slab, 116 Compression-only members, 27 Compression-only springs, 241, 261 CON, 21 Concave hull, 47 Concentrated force/moment, 13 Concentrated loads of axles, 184 Concentrated loads on plate elements, 94–95 Concentrated weight, 198 Connectivity, 59 Continuous beam, 210 Contracts, plate, 117 Contraction, temperature, 106 Contributory area, 136 Converge, 259 Conversion of units of temperature, 116–118 Convex hull, 125 Coordinates, joint. See Joint coordinates Coordinates of CG, 34 COSINE function, 412 Cosine function, 409 COUNTER-CLOCKWISE, 209 CQC, 335, 341, 348, 385, 387 Crane, 157 Crane girder, 190 Create combination cases, 229–231 Create New Group, 53 Creating a group, 143 Creep, 87 Crisscrossing members, 59–60 CSM (closely-spaced modes), 376 CSM METHOD, 376 Culverts, 212 Culvert wall, 100 Curved members, 27, 71–73 Curved path, 158 Curved roadway, vehicle in, 178 Curved shape, 146 Curved wall, 100 CUT OFF FREQ, 295 CUT OFF FREQUENCY, 277, 279, 286, 296, 302, 361, 398, 418, 434 CUT OFF MODE, 418 CUT OFF MODES, 289 CUT OFF MODE SHAPE, 276–277, 279, 285, 286, 296, 297, 302, 361, 362, 377, 398, 433, 434 CUT OFF TIME, 400, 401, 411, 423 CUT OFF TIME t5, 418 Cycle of loading, 410 CYCLES, 420

Cyclic frequency, 413

D

DAMP, 318–319, 341, 348 fluid dampers, 319 in time history analysis, 319 DAMPING, 405 Damping, 317–331, 354–358, 422 ABS, 357 ASCE 4 combination methods, 357 ASCE 7-05, 358 CDAMP, 354, 356 composite damping, 356 CQC, 357 CSM, 357 CUT OFF FREQUENCY, 358 CUT OFF MODE SHAPE, 358 DAMP, 354 damping characteristics of soil, 330 damping in frequency calculation, 329–330 DEFINE DAMPING, 355 IBC, 317 IS 1893-2002, 358 MDAMP, 354, 355 modal interaction matrix, 357 modeling shock absorber, 331 response spectrum and time history, 317 spring damping, 356 springs, 356 SRSS, 357 steady-state analysis, 317 strain energy, 356 Ten Percent methods, 357 UBC, 317 Damping and frequencies SET SDAMP, 305 SPRING DAMPING, 305 undamped frequencies, 305 Damping characteristics of soil, 330 CDAMP, 331 laminated rubber bearings, 331 SPRING DAMPING, 331 Damping in frequency calculation, 329–330 CDAMP, 329 DEFINE DAMPING INFO, 330 DEFINE DAMPING table, 329 DEFINE TIME HISTORY, 330 Damping ratio, 317, 319 Damping ratio for individual modes DEFINE DAMPING INFORMATION, 325, 326 EVALUATE, 326 EXPLICIT, 325, 326 maximum permissible damping ratio, 326 MDAMP, 325

modal damping ratios, 325 DEAD, 244 Dead Load, 236 Dead model, 252 Deck, 164–165 Deck level, 185 DEFINE DAMPING INFO, 330 DEFINE DAMPING INFORMATION, 325, 326, 329 DEFINE IBC 2003, 264 DEFINE MOVING LOAD, 254 DEFINE REFERENCE LOADS, 254, 261 DEFINE SEISMIC LOAD, 254 DEFINE SNOW LOAD, 152 DEFINE TIME HISTORY, 330 DEFINE WIND LOAD, 254 Deflection diagram, scale of, 189 Degrees of freedom, 275 Densely meshed, 68 DENSITIES, 335 DENSITY, 279 Density of mesh, 67 Design spectral response acceleration parameter, 223 Destabilizing effects, 226 Diagonal braces, 60 DIRECT ANALYSIS, 261 Direct analysis, 241 Direct Analysis method, 226 Direction, 165 Direction factor, 346–349 ASCE 4-98, 349 ASCE 7-02, 349 displacement, 346 importance factor, 347 IS 1893, 347 SPACE frame, 348 spectral acceleration, 346 spectral displacement, 346 square root of a sum of the squares (SRSS), 347 zone coefficient, 347 Direction of action of loads, 46–47 Direction of loading, 16–21 alternate span loading, 26 axial loads, 23–24 center of action of the applied loads, 32–34 compression-only members, 27 curved members, 27 displaying the loads, 27–28 empty load cases, 30 finding loads on specific member, 38–40 fixed end loads, 30 floating structures, 30 global, 17–18 local, 17 maximum number of load cases, 34 member offsets, 26

member orientation, 26 offshore structures, 30 pre-tension loads, 26 projected, 18 SET NL command, 34–37 singly symmetric cross-sections, 23 tension-only members, 27 trapezoidally varying loads, 29–30 unsymmetric cross-sections, 23 Direction of the movement, 168 Direction of wind, 128 Dish antenna, 129 Disjointed structures, 50, 137 Displaced shape, 117 Displacement history of any node, 423 Displacement mode, 78 Displacements, 408, 429 Displacements at nodes, 249 Display Floor Load Distribution, 42 Displaying (viewing) generated loads, 172–174 Displaying the deflection diagram, 189–190 Displaying the loads, 27–28 Display Wind Load Contributory Area, 125 Distribution of base shear, 211 Distribution of lateral force, 211–212 Dome, 100 Dominant mode, 272 Double root modes, 313, 314 Doubly symmetric structures, 313 Drift, 154 DT, STEP vs., 414 Dummy members, 123 Dummy plate elements, 150 Duplicate beams, 58 Duplicate members, 50. see also Duplicate nodes Duplicate nodes, 50, 58, 137, 138 Duplicate r Members, 58 Duplicate r Nodes, 58 Duration of 1 cycle, 413 Duration of load, 410–411 Duration of loading, 408, 410 Dynamic analysis, 74–76, 238, 265 basics of, 191 Dynamic cases, 242 Dynamic load, 271 direction, 271 magnitude, 271 vibrations, 271 “Dynamic Load Allowance,” 420 Dynamic load cases, 244 Dynamic loading, 272 Dynamic loads, 2, 332 ASCE/SEI 7-05, 332 dynamic analysis, 332 frequencies, 332

ground motion, 332 machine vibration, 332 mode shapes, 332 quasi-static methods, 332 time history analyses, 332 vibration analysis, 332 Dynamic properties damping characteristics, 271 frequencies, 271 mode shapes, 271 of structures, 271 Dynamics-Node Displacement page, 423 Dynamic Weight, 294 Dynamic weight, 282–283 equivalent nodal masses, 283

E

Earthquake, 191, 243, 271 Earthquake analysis, 375 Eccentricity of axial loads, 23 Eccentricity of cable, 85 Eccentric moving load, 186 Editing, reference cases, 258 Edit Input Command File, 243 Effective seismic weight, 73 Eigensolution, 306–307 Eigenvalue analysis, 287–297 CUT OFF MODES, 289 frequencies, 287–290 generalized weight, 290 mass participation factor, 294–297 MODAL CALCULATION REQUESTED, 287 modal mass, 293–294 modal participation factor, 291–293 modal weight, 293–294 periods, 287–290 Eigenvalue extraction advanced solver, 303 check beam plate connectivity, 301 check duplicate nodes, 301 check improperly connected plates, 301 CUT OFF FREQUENCY, 302 CUT OFF MODE SHAPE, 302 FIXED, 302 flexural and torsional deformation, 303 “floating” members and elements, 302 improper connectivity, 301 instabilities and, 300–303 instability warnings, 300, 302 Intersect Selected Members, 302 MEMBER RELEASES, 302 MEMBER TRUSS, 302 monolithic, 301 Multiple Structures, 302

PARTIAL MOMENT RELEASES, 302 PINNED, 302 selfweight, 302 SET SSVECT, 302 singularities, 300 spring supports, 302 spurious mode singularity, 301 subspace iteration method, 301, 302 trial shape vectors, 302 triangular factorization, 301 unstable structure, 301 Eigenvalue frequencies, 309–312 Eigenvalues, 272, 275 ELASTIC MAT, 285 Elastic Mat, 241 Electrical transmission structures, 133 Electrical transmission towers, 156 ELEMENT LOAD, 261, 279, 280 Element Load, 5, 236 ELEMENT MODEL, 59 ELEMENT PROPERTY, 279 Element stresses, 239 ELEMENT WEIGHT, 73, 193, 198, 262 ELFP. See Equivalent lateral force procedure (ELFP) ELFP-based seismic analysis, 73–74, 207 ELFP method, 375 Elongation, 119 Elongation, axial, 114 Empty load cases, 30–32 End actions, 91 ENFORCED, 78 Equilibrium, 249 Equivalent lateral force procedure (ELFP), 73, 192, 210, 212, 214, 225, 265, 269, 272 Equivalent static analysis procedure, 192 EURO 2004, 342 Excitation frequencies, 432 Excluding members, 143 Excluding Slab from the Model, 59 Expand, plate, 117 Expansion, temperature, 106 Expansion joint, 420 EXPLICIT, 325, 326 Explosion, 191, 417–420 Exposed face, 122, 128, 142, 143, 144 Exposure factor, 129, 133, 134, 147, 151 Exterior, 144 External file, 171

F

Fa, 195 Factored loads, 239 Factored results, 239 Factoring, 236 Factor term in wind load, 127–128

Fahrenheit, 103, 114 Fahrenheit/Rankine, 105 Falling object, 419 Fictitious member, 64, 179 Finding loads on specific member, 38–40 Fireproofing selfweight and, 13 weight of, 199 wind load and, 146 FIXED, 78 Fixed end actions, 59 Fixed End Load, 5, 30 Flat roof, 150 Flexural stiffness, 314 FLOAD, 42 Floating members, 137 Floating structures, 30 FLOOR GROUP, 44, 48 Floor groups, 53–59, 152 FLOOR LOAD, 150, 280, 281–282 Floor loads, 41–69, 199 algorithm, limitations of, 47–53 assigning floor loads, 44 crisscrossing members and panel identification, 59–60 direction of action of load, 46–47 excluding slab from model, 59 floor groups, 53–58 on inclined planes, 63–67 load distribution principle, 43–44 member offsets, 46 openings on floors, 60–63 XRANGE, YRANGE, and ZRANGE, 44–46 Floor load algorithm, limitations of, 47–53 FLOOR MODAL BASE ACTION, 373 Floor spectrum, 435 FLOOR WEIGHT, 74, 193, 262 Floor weight, 198, 199 Force Amplitude Factor, 415 Force participation factor, 272, 293, 434 FORCING FUNCTION, 417 Forcing function, 392, 419 Foundation mat, 225 .FRC, file with extension, 408 .FRC file, 421, 426 Free vibration, 410 Free-vibration analysis, 272 Free-vibration response, 418 Frequencies, 265, 269. See also Rayleigh frequencies; Eigenvalue frequencies FREQUENCY, 410 Frequency analysis, 266 amplitude of vibration, 313 CALCULATE RAYLEIGH FREQUENCY, 312 dynamic force, 313 dynamic loading, 312 earthquake, 313

free-vibration, 313 free-vibration analysis, 312 and frequencies, 313 member end forces, 312 MODAL CALCULATION REQUESTED, 312 mode shape, 312 node displacements, 312 plate and solid element stresses, 312 psuedostatic, 313 response spectrum, 312, 313 seismic forces, 312 support reactions, 312 time history analysis, 312, 313 Frequency domain, 429–430 Frequency extraction, 265 Frequency of simple beam fundamental mode, 275 Friction, 87 Friction forces, 231 Friction loads on plates, 94 Friction type of load, 90 Front axle, 165, 182 Fundamental frequency, 272 Fundamental mode, 272 Fundamental period, 206, 272 Fv, 195

G

Gable, 153 GABLE UNOBSTRUCTED, 154 Gantry girder, 190 Generalized weight, 290 diagonal mass matrix, 290 generalized mass, 290 Generated loads, viewing, 220–223 Generate seismic weights, 262–265 Geometric imperfections, 226 Global, 17–18 Global axes, 164 Global directions, 90 Global horizontal directions, 144 Gravity analysis, 199, 201, 262 Gravity loads, 55, 254 Ground acceleration, 432 GROUND MOTION, 389 Ground motion (seismic base excitation), 391–392 Ground Motion Loading, 415–417 Gusset plates, 198

H

H15, 163 H20, 163 Harmonic (sinusoidal), 423 Harmonic force, 434

Harmonic load, 408, 411, 427, 432 duration of load for, 410–411 number of cycles of, 424 Harmonic loading, 409–414, 414–415 Heated roofs, 151 Heat transfer analysis, 118 Height, pressure vs., 129–130 Hip, 153 HIPPED, 154 History of displacement at nodes, 425 Horizontal forces, 190 Hotter, 117 HS15, 163 HS20, 163 Hydrostatic load, 29, 97 Hydrostatic pressure, 91, 97

I

IBC, 197, 202, 214, 244, 262–265, 266 IBC 2006, 192, 198, 225, 245, 269, 341 IBC LOAD, 223 Ice, 136 Identify panels, 144 Impact factor, 419 Impact loads, 419–420 Importance factor, 151 Improper beam-plate connectivity, 67 Inclined planes, 63–67, 137, 175. See also Ramps Incomplete panels, 141–142 INCREMENT, 165, 166 Increment, 157 Increment of movement, 180 Influence area, 132, 133, 419 Initial elongation, 26 Initial lack of fit, 87 Initial stress, 87 In-plane stiffness, 59 In-plane stiffness, floor slab, 67 Instability in frames, 210–211 member specifications and, 175 notional loads and, 227 Instability conditions, 253 Instability warnings, 300, 302 Integration step DT, 418 Integration time point, 408 INTENSITY, 147 Interior, 144 International Building Code (IBC), 191 Interpolate, 99 Intersecting members, 138–140, 142 Intersection point, 59, 142 Intersect Selected Members, 59, 139 Inverted stiffness matrix, 238

IS-875 (Indian) code, 147, 245 IS 1893, 193, 197, 202, 214, 262–265, 266, 376 Iterations, 259

J

JACOBI ITERATION, 301 Joint coordinates, 140–141 JOINT COORDINATES CYLINDRICAL REVERSE, 72 Joint displacements, 239, 421 JOINT LOAD, 261, 280, 331 Joint Load, 5, 236 Joint motion plots, 427 JOINT WEIGHT, 73, 193, 262 Joint weight, 198, 265

L

Lane loads, 174 Lanes, 163 Large models, 31, 270 LAT, 195 Lateral analysis, 269 Lateral force, 192, 222, 227 Lateral load analysis, 199 Lateral load interaction, 241 Lateral load reports, 231 Lateral loads, 219–220 Lateral stiffness, 211 Later loads, 55 Latitude, 196–197, 198 Leap Bridge Enterprise, 191 Leeward face, 126 Leeward side, 122 Lever arm, 208 Lifting points, 82–83 Linear, 241 Linear analysis, 242 Linear elastic, 253 Linear interpolation, 408 Linearly varying load, 13, 29 Linear segment, 72 Linear static analysis, 240 Line loads on plate elements, 95 List box, 258 LIVE, 244 Live heading, 5 Live Load, 236, 254 Live load reduction, 5 Live model, 252 Load combining, 2 dynamic, 2 sources of, 2 types, 3–40 Load case number, 4

LOAD COMBINATION, 34, 205, 235, 239–240, 243, 248, 250, 252, 261, 375 Load combination, 421 Load combination cases, 244 automatic generation of, 244–247 Load combination of combination cases, 243–244 LOAD COMBINATION SRSS, 248 LOAD COMBINATION syntax vs. REFERENCE LOAD syntax, 259 Load-dependent structural conditions, 259–261 Load-dependent structural geometries, 240 Load display icon, 172 Load distribution pattern, 56 Load distribution principle, 43–44 Load factors, 234 LOAD GENERATION, 254 Load generation, 234, 259 overview, 120 snow, 150–157 wind, 120–150 Loading, 1–119 LOAD LIST command, 2–3 loads on plates and solids, 89–102 prestressing load, 83–89 primary load types, 3–40 support displacement loads, 78–83 temperature and strain loads, 102–119 Loading Type, 7–8 Load item, 1 Load item categories, 8–26 LOAD LIST ALL, 3 LOAD LIST command, 2–3 Load mode, 78 Loads along the edge of plate elements, 96–97 Load selection, 258 Loads on frame members, 13–16 Loads on plates and solids, 89–102 Load types, 236 Load Vector, 92, 231, 237, 238 Local, 17 Local coordinate system, 250 LONG, 195 Longitude, 196–197, 198 Longitudinal beams, 55 Longitudinal directions, 190 Lost loads, 227 Lumped masses, 272 Lumped mass method, 296 Lumped weight, 199, 226

M

Machine vibration, 191, 272, 393–394 amplitude, 393 harmonic loading, 393 mechanical vibrations, 393

number of cycles of loading, 393 operating frequency, 393 phase angle, 393 sinusoidal loading, 393 turbines, 393 Macro, 14 Magnification, wind load, 146–147 Margin of tolerance, 45 Masses, for mass matrix, 265 MASS MATRIX earthquake, 278 eigen extraction, 278 mass matrix, 278 member offsets, 278 modulus of elasticity, 278 Poisson’s ratio, 278 response spectrum, 278 stiffness matrix, 278 subspace iteration, 278 time history, 278 Mass matrix, 282 Mass matrix, masses for, 265 Mass modeling, 276, 317, 335–336 directions of vibration, 335 lumped mass method, 276 mass matrix, 335 MODAL CALCULATION REQUESTED, 335 multiple spectrum cases, 336 permanent loads, 335 selfweight, 276 weight of equipment, 335 MASS PARTICIPATION factor, 286, 377 Mass participation factor, 294–297, 295, 361–362 base shear, 294 cumulative participation, 362 CUT OFF FREQ, 295 CUT OFF FREQUENCY, 296, 297 CUT OFF MODE SHAPE, 295, 296, 297 earthquake, 294 eigensolution, 296 high-energy modes, 295 local flutter, 362 lumped mass method, 296 mesh, 296 modal mass, 294 Rayleigh frequency, 296 Rayleigh method, 296 response spectrum analysis, 296 seismic acceleration, 296 SUMM-X, 294, 295 SUMM-Y, 294, 295 SUMM-Z, 294, 295 time history analysis, 296 torsional modes, 295, 362 Mass reference case, 266

Mass reference load cases, 265–270 Mass reference load, 269–270 Master-slave, 67 Master-slave relationship, 59 MATERIAL, 11 Material damping, 320 Material properties vs. temperature, 118 Mathematical model, 117 MAT FOUNDATION, 259 Mat foundation, with compression-only springs, 261 Matrix, 237, 238 Matrix multiplication, 240 Max Global Axis, 99 Maximas, 426 Maximum base shear, 422 Maximum nodal acceleration, 383–384 Maximum number of load cases, 34 MCE, 198 MDAMP, 406 in response spectrum analysis, 329 in time history analysis, 329 MDAMP (modal damping), 318 MDAMP-CALCULATE, 318, 328–329 MDAMP-EVALUATE, 318, 327–328 CALCULATE, 328 damping ratio, 327 Rayleigh damping equation, 327 MDAMP-EXPLICIT, 318 Member initial stress in, 87 temperature loads on, 106–107 MEMBER COMPRESSION, 27, 259 Member compression, 78, 241, 306–307, 434 MEMBER CURVE, 71, 190 Member end forces, 239, 249, 421 Member forces, 241, 408 MEMBER LOAD, 24, 261, 280 Member Load, 5, 236 Member offsets, 26, 46 Member orientation, 26 MEMBER POSTSTRESS, 83, 84–85 MEMBER PRESTRESS, 83, 84–85, 100 Member Prestress, 26 MEMBER PROPERTY, 279 Member Query, 38 MEMBER RELEASES, 175, 302 Member section forces, 249 MEMBER TENSION, 27, 242, 259, 308 Member tension, 78, 434, 306–307 MEMBER TRUSS, 175, 302 MEMBER WEIGHT, 73, 193, 262 Member weight, 198, 265 Mesh density, 92–93 Middle axle, 182 Min Global Axis, 99

Missing Attributes, 135 MISSING MASS, 286, 293, 361 Missing mass, 285–287, 377–378, 433 CUT OFF FREQUENCY, 286 CUT OFF MODE SHAPE, 285, 286 degrees of freedom, 286 ground motion, 286 mass participation, 286 MASS PARTICIPATION factor, 286 MISSING MASS, 286 modes of vibration, 286 response spectrum, 285 response spectrum analysis, 286 SUMM-X, 286 SUMM-Y, 286 SUMM-Z, 286 time history analysis, 285, 286 Missing mass correction, 351–352 ASCE 4-98, 351 ZPA (zero period acceleration), 351 ZPA frequency, 352 Missing Property, 135 Missing Weight, 294, 371–373 Modal analysis, 272, 275 Modal base action, 373–374 MODAL CALC REQ, 304 MODAL CALCULATION REQUESTED, 279, 280, 281, 287, 309, 311 frequency extraction, 277 response spectrum, 277 steady state, 277 time history, 277 Modal combination method, 350 ABSolute, 350 ASCE, 350 closely spaced modes (CSM), 350 CQC (complete quadratic combination), 350 SRSS, 350 TEN Percent method, 350 Modal extraction method, 272, 275–282 mass matrix, 275 mode shapes (eigenvectors), 275 Modal participation factor, 272, 291–293, 433 eigenvector, 291 generalized weight, 291 SET PART FACT, 291, 372, 434 Modal superposition method, 399, 407 Modal weight, 293–294, 371–373 base excitation, 293 base shear, 293 generalized weight, 293 MISSING MASS, 293 modal participation factor, 293 response spectrum analysis, 293 Modeling errors, 253 Mode of vibration, 272

Modes, 269 MODE SELECT, 429, 433 MODE SELECT Command, 385–386 Mode shapes trial vectors, 276 Mode shapes in animation, 299 beam section displacement, 300 Create AVI File, 300 mode shape, 300 node deflection, 300 plate stress contour, 300 Real Player, 300 Windows Media Player, 300 Modes of vibration, 271 Modulus of elasticity, 67 Moment of inertia, 112 Mono, 153 Monolithic prestressing loads, 84 Monolithic connection, 67 Move-Origin, 40 Moving load generator, 157 Moving loads, 157–191 simply supported action, 158 travel straight, 158 curved path, 158 wheel, concentrated load on, 158 Moving vehicle, in skewed direction, 176 Multilinear springs, 78, 382–383, 434 earthquake, 383 ground acceleration, 383 SDOF system, 383 seismograph, 383 time history, 382 Multilinear spring support, 241, 307 nonlinear conditions, 307 Multiple lanes of vehicles, 177 Multiple structures, 137–138 Multiplying factor for accidental torsion, 208–209 MX, 108 MXY, 108 MY, 108

N

NBCC, 202 NBCC 1995 & 2005 (Canadian), 245 NBCC NRC, 198 Nodal displacements, 240, 426 NODAL LOAD, 24 Nodal weights, 226 Node-Displacement page, 189 Node-Reactions page, 53 Non-contiguous areas, 56 Non-global directions, 144

NONLINEAR, 261 Nonlinear, 241 NONLINEAR analysis, 78 NONLINEAR CABLE, 261 Nonlinear analysis, 116 Nonlinear conditions, 240, 241, 242, 253 Nonlinearity, 239, 256 Non-linear situations, 254 Non-load-bearing members, 69 Nonplanar, 140 Normalized, 415 Normalizing mode shapes, 290 generalized mass, 290 mass normalization, 290 Notional load, 233 Notional load factor, 226 Notional Loads, 227, 190, 226–233 NRC, 214 NRC 2005, 266 Number of cycles, of harmonic load, 411, 424–428 Number of modes, 276–277 modes of vibration, 276

O

Obstructed, 153 Occupancy Importance factor, 193 Offset from the shear center, 21–23 Offshore structures, 30 One-way distribution, 155–156 ONEWAY LOAD, 281–282 Oneway load, 69–71, 69–71 TOWARDS option, 70–71 ONEWAY WEIGHT, 74 Opening, 61, 62, 211 Openings on floor, 60–63 Open lattice structures, 133, 136, 146, 156–157 Open panels, 50 OpenSTAAD, 14 Open structures, 133–137 excluding members for, 143 Oscillations, 411, 431 Out-of-plane deformation, 149 Out-of-plane nodes, 143 Overlapping members, 138 Overturning moment, 39

P

Panel, 168 Panel identification, 46, 50, 59–60, 124 Panels floor load, 41 incomplete, 141–142 Parabolically varying load, 14 Partial moment release, 175

PARTIAL MOMENT RELEASES, 302 P-DELTA, 240, 261 PDELTA ANALYSIS, 254 P-DELTA analysis, 243 P-DELTA effect, 241 P-delta effects, 374–375 Peak response, 426 Periods, 205 PINNED, 78 Pinned connection, 210 Planar, 149 Planarity, 64 PLANE, 141, 149 Plate element moments, 249 Plate elements, 89–101, 157 concentrated loads on, 94–95 friction loads on, 94 line loads on, 95 loads along the edge of, 96–97 meshing, 91–93 pressure loading on a partial area, 93–94 prestress load on, 87–89, 100 wind load generation on, 100 Plate element stresses, 249 PLATE MAT, 261, 285 Plate Mat, 241 Plate meshing, 91–92 Plates and solids. See Plate elements; Solid elements Plate stresses, 241 Poisson’s effect, 69 Positive value of pressure, 90 Postprocessing mode, 189, 270, 421 POSTSTRESS, 83 Poststress, 26 Pothole, 420 Precision errors, 45 Pressure, 41 height vs., 129–130 Pressure component. See Component of that pressure Pressure due to liquid, 90 Pressure loading on a partial area, 93–94 Pressure loads, 59, 157 mesh density and, 92–93 on plate elements, 100 on solid elements, 101–102 on surfaces, 100–101 Pressure wave, 419 Prestressing loads, 83–89 issues in, 84 results of, 84 PRESTRESS, 83 Prestress Load, 5, 87–89 Prestress load on plate elements, 100 Pre-tension loads, 26 PRIMARY LOAD CASE, 4

Primary load cases, 234, 236, 237 Primary load types, 3–40 alternate span loading, 26 center of action of applied loads, 32–34 curved members, 27 displaying load, 27–28 empty load cases, 30–32 finding loads on specific member, 38–40 fixed end loads, 30 load heading, 5–7 load item categories, 8–26 loading type, 7–8 maximum number of load cases, 34 offshore and floating structures, 30 pre-tension loads, 26 SET NL command, 34–37 tension-only/compression-only members, 27 total quantity of loads, 38 trapezoidally varying loads, 29–30 Principle of superposition, 240, 253 PRINT CG, selfweight, 12 PRINT LOAD DATA, 171, 219 Print Load Data, 21 PRINT MODE SHAPES, 299 PRINT STATICS CHECK, 38, 218 PRISMATIC, 113 Profile, cable, 85 Property databases, 113 PX, 205 PZ, 205

R

Rain-on-snow, 154 Ramp, 175–176 Random excitation, 191, 392–393, 432, 434 Random excitation load, 417 Rayleigh frequencies, 309–312 displaced shape, 310 eigensolution, 310 Rayleigh frequency, 219, 274 Rayleigh method, 205, 219, 272–275, 284 cantilever, 273 deflected shape, 273, 284, 310 displaced shape, 273 frequency of simple beam, 275 fundamental (lowest) frequency, 273 lateral force, 273 lateral loads, 273 modal extraction, 273 mode shape, 273, 284 vertical loads, 273 Rear axle, 164, 165, 182 REDUCIBLE, 5 Re-entrant corners, 45

Reference cases editing, 258 REFERENCE LOAD, 34, 235, 254, 261, 265 Reference load, 167, 199–205, 252–270 Reference load cases, 262, 270 analysis run-time, 270 post-processing, 270 tension-only members and, 260 Reference load definitions, 256 REFERENCE LOADS, 228–229, 233, 255 Reference loads, 242–243 REFERENCE LOAD syntax LOAD COMBINATION syntax vs., 259 Reference point, 182 Reference wheel, 164 Relative, 422–423 Relative stiffness, 113 REPEAT LOAD, 34, 205, 214, 235, 237, 238–239, 240, 243, 244, 252, 253, 265, 375 Repeat loads, 235–252, 242–243 Reports, lateral load, 231 Reposition the origin, 40 Resonance, 432 Response history, 420, 421–422 Response Modification factors, 193 Response spectrum, 238, 242, 266 Response spectrum analysis (RSA), 265, 333–387 absolute values, 378 ASCE 7-05, 333 base excitation, 333 base shear, 368–373, 379 combination method, 381 compression-only members, 382 compression-only supports, 382 CQC, 379 double root modes, 385 earthquake, 333 eigensolution, 360 ELFP, 380 equivalent lateral force procedure, 333 floor response spectrum, 386 frequencies, 334, 360 ground acceleration, 333 individual modal response, 386 input spectral data, 333 interpolation, 360 linear interpolation, 363 lookup table, 336–543 mass modeling, 335–336 mass participation factor, 361–362 maximum nodal acceleration, 383–384 member forces, 361 missing mass, 377–378 missing weight, 371–373 modal base action, 373–374 modal combination method, 381 modal participation factor, 360

modal weight, 371–373 modes, 334 MODE SELECT Command, 385–386 mode shapes, 360 multilinear springs, 382–383 node displacements, 361 Node-Reactions page, 381 participation factor, 360 P-delta effects, 374–375 peak response, 333 period-acceleration, 334 period-displacement pairs, 334 plate stresses, 361 response spectrum load case, 333 restoring couple, 379 SDOF system, 333 signed results, 386 spectral acceleration, 360 spectral data, 334, 336–543 spectral displacement, 360 spectrum pairs, 336–543 spectrum parameters, 343–360 SRSS, 379 static equilibrium, 379 stiffness matrix, 360 support reactions, 361 symmetrical structures, 385 table of accelerations, 363–367 tension-only members, 382 tension-only supports, 382 time history loading, 386 uplift, 379 weights, 334 RESULT COMBINATION, 240 Results analysis of prestressing loads, 84 Rigid body modes, 312 Rigid diaphragm effect, 59 Rivets, 198 RM Bridge, 190–191 Roof obstruction, 153 Roof slope factor, 153 Roof type, 153 Rotate, 83 Rotational spring, 210 Rotational stiffness, 102 Rotation load, 30 Round-off errors, 140–141 RPM, 410 RSA. See Response spectrum analysis (RSA) RS1, 342 Run-time analysis, 270 Russian code, 147

S

S1, 194–195 SCALE, 348 Scale factor, 343–345, 416 IS 1893 (Part 1):2002, 345 normalization factor, 343, 344 normalized data, 343 site-specific response spectra, 345 soil type, 345 spectral acceleration, 344 spectral displacement, 344 un-normalized data, 343 Scale of deflection diagram, 189 Scales, 28 SD1, 195 SDS, 195 SEISMIC, 244 Seismic, 231 Seismic analysis, 225 Seismic base excitation, 390 Seismic base shear, 192 Seismic definition, 262 Seismic load generation, 191–225 Seismic loads, 191, 254, 271 Seismic model, 252 Seismic response coefficient, 192 Seismic weight, 192 SELFWEIGHT, 261, 262, 279 Selfweight, 5, 8–13, 198, 265 calcualtion of, 11 fireproofing, 13 stage construction, 9 statics check and, 11 Sequence of construction, 84 SET NL command, 34–37 default value of, 37 defined, 36 SET PART FACT, 291, 372, 434 SET SDAMP, 305 SET SHEAR, 315 SET SSVECT, 276, 302 Shear capacity, 175 Shear stiffness cantilever beam, 314 flexural stiffness, 314 lumped weight, 314 SET SHEAR, 315 shear area, 314 Shear walls, 211 Shock absorber modeling, 331 Shrinkage, 87, 116, 119 Sign. See Advertising sign Signed values, 431 Sign of wheel loads, 169 Silo, 100 Simply supported action, 158

Simply supported reactions, 168 SINE function, 412 Sine function, 409 Sine wave, 420 Single angles, 23 Single axle, 169–170 Singly symmetric cross-sections, 23 Sinking supports, 78 Skew, 158, 176 Skewed bridge, 176 Skewed direction, moving vehicle in, 176 Sliding snow, 154 Sloped roof, 150, 152 Sloping bridge, 175 Sloping roadway, 175–176 Sloping roofs, 63 SNiP (Russian), 245 Snow load, 150–157 Soft story checking, 211 SOIL TYPE, 342 Soil Type factors, 193 Solid elements, 101–102, 422. See also Plate elemets applying a moment on, 102 prestress load in, 87–89 pressure loads on, 101–102 temperature loads on, 109–110 Solid element stresses, 249 Solid stresses, 241 Solution time step, 414 Sources, load, 2 Specifying support displacement loads, 80–81 Spectral response acceleration parameter, 198 Spectrum pairs, 336–543 acceleration spectra, 338–340 AIJ, 340 alpha, 342 ASCE 7-05, 340 ascending order, 338 damping ratio, 342 displacement spectra, 338–340 EC8 (1996 and 2004), 340 EC8-2004, 342 equivalent lateral force procedure (ELFP), 340 Eurocode 8 (EC8), 340 external file, 342 IBC, 340 IBC 2006, 340–341 IS 1893, 340, 342 latitude/longitude, 340, 341 linear/logarithmic interpolation technique, 337 lookup table, 337 peak acceleration, 337 peak displacement, 337 period vs. acceleration, 336 period vs. displacement, 336

SDOF system, 337 Ss and S1, 341 unnormalized, 340 zip code, 340, 341 Spectrum parameters, 343–360 damping, 354–358 direction factor, 346–349 graph of spectrum input, viewing, 359 interpolation, linear and logarithmic, 349 mass matrix, 360 missing mass correction, 351–352 modal combination methods, 350 scale factor, 343–345 ZPA (zero period acceleration), 353–354 SPRING COMPRESSION, 242, 254, 259, 260 Spring compression, 78, 241, 307, 434 SPRING DAMPING, 305, 331 Spring damping, 321–322 SET SDAMP, 321–322 SPRING DAMPING, 322 support springs, 322 SPRING TENSION, 259 Spring tension, 241, 307, 434 Square panels, 69 Square root of sum of squares. See SRSS (square root of sum of squares) SQX, 108 SQY, 108 SRSS (square root of sum of squares), 242, 249, 376, 385, 387 SRSS combination method, 250 SRSS Method, 248 Ss, 194–195 STAAD.Offshore, 30 STAAD PLANE, 169 Stage construction, 9 Starting position, 164, 185 Static equilibrium, 249, 251 Static equivalent methods, 262–265 Static load cases, 262–265 Static loads, 1–2 Statics Check, 11, 53, 125 Statics Results Table, 38 Steady state, 411, 427 Steady-State Phase, 423–424, 426 STEP, 412–414 vs. DT, 414 Step-by-step integration, 407 Stiffness matrix, 275 Straight, 158 STRAIN, 118 STRAIN LOAD, 87 Strain load, 118–119 STRAINRATE, 26, 119 Stress, initial, 87 Stress-free temperature, 106. See also Ambient temperature Structure, dynamic properties

fundamental mode, 272 SUBDIV, 412–414 SUBGRADE, 261, 285 Subgrade, 116 Subspace iteration method, 275, 289 SUMM-X, 286, 294, 295, 377 SUMM-Y, 286, 294, 295, 377 SUMM-Z, 286, 294, 295, 377 Superposition, 242 Support displacement loads, 78–83 cables and, 83 inducing a displacement, 81–82 lifting points, 82–83 rigid body movements, 82–83 specifying, 80–81 Support reactions, 239, 241, 249, 251, 408, 421 Supports at different elevations, 211 Support settlements, 78 Surcharge load, 154 Surface entities, 150, 179 Surface Pressure Load, 150 Surfaces, applying pressure loads on, 100–101 Swinging, 190 SX, 108 SXY, 108 SY, 108

T

Table of accelerations, 363–367 extrapolate, 365 linear interpolation, 363, 366 logarithmic interpolation, 363, 366, 367 lookup table, 365 participation factor, 365 spectral acceleration, 365 Temperature conversion of units of, 116–118 heat transfer analysis, 118 vs. material properties, 118 Temperature Differential, 107 Temperature gradient, 106 analysis procedure for, 112–115 example for, 111–112 Temperature Load, 5 Temperature loads, 5, 102–118, 231, 257 buckling and, 118 on solids, 109–110 types of, 106 uniform increase or decrease in, 106 Temperature loads on solids, 109–110 Tensile force, 431 Tension-only members, 27 reference load cases and, 260 Thermal expansion constant, 107

Thermal factor, 151 Time-acceleration pairs, 416 Time-Disp history plots, 426 Time displacement graphs, 411 Time domain, 429 Time-force pairs, 392, 416 Time history, 238, 242, 266 Time history load case, 270 Time history loading, 387–435 arrival times, 400 ASCE 7-05, 387 classical damping, 406 cyclical frequency, 400 damping matrix, 406 diagonal, 406 dynamic analysis, 387 earthquake, 390 explosion, 390 forcing function, 390 free vibration, 401 frequency calculation (mass modeling), 397–398 ground acceleration, 387, 390 ground motion (seismic base excitation), 391–392 harmonic loading, 395 harmonic loads, 401 impact load, 390 machine vibration, 393–394 mass matrix, 398 mass modeling, 394 modal damping, 406 modal superposition method, 399 mode superposition method, 387 multilinear springs, 389 number of time steps, 399 peak response, 387 periodically varying force, 388 random excitation, 390, 392–393 seismic base excitation, 390 sine function, 401 solution time step, 399 spring compression, 389 spring tension, 389 steady state, 388 steady-state phase, 387 steady-state vibration, 401 stiffness matrix, 390 time-force and time-acceleration pairs, 396 time history analysis, 387 time points, 387 time step (DT), 387 transient and steady-state phases, 388 transient phase, 387 turbine generator, 401 Wilson-Theta integration scheme, 399 TIME LOAD, 389, 390, 414, 417

Time period, 410 Time taken, to display wind loads, 144–146 Tires, 163 Tolerance, 290 Top of steel, 55 Torsion, 23, 186 Torsional mode of vibration rotational mass, 315 torsional frequency, 315 Torsional modes, 275, 295 Total quantity of loads, 38 TOWARDS option, 70–71 Tower, 39 Trailer, 168 Transient phase, 423–424 Translation load, 30 Transverse beams, 55 Transverse directions, 190 TRAPEZOIDAL, 99 Trapezoidal load, 44 Trapezoidal load distribution method, 41 Trapezoidally varying loads, 13, 29–30 Trapezoidally varying pressure loads, 90–91 in circular tank, 90 positive value of, 90 pressure due to liquid, 90 Travel, 158 Triangular load, 44 Triangular load distribution method, 41 Tributary area, 125 TRUSS, 210 Truss members, 23, 227 Turbine generator, 191, 271 Two-way distribution, 155–156 TYPE command, 129 Type number, 164

U

UBC, 202, 244, 262–265, 266 UBC 1997, 202, 225, 245 UMOM, 21 UNBALANCED, 154 Unbalanced snow loads, 153 Uncoupled equations, 407 Unheated roofs, 151 UNI, 21 Uniform force/moment, 13 Uniform increase or decrease in temperature, 106 Uniform pressure loads, 90 friction type of load, 90 global directions, 90 Unobstructed, 153 Unstable degree of freedom, 211 Unstressed length, 119

UNSUPPORTED MASSES, 280 Unsymmetric cross-sections, 23

V

Vehicle, 157, 164 configuration (see Vehicle configuration) in curved roadway, 178 on deck, 164–165 definition of, 158–159 description of, 159–164 moving in skewed direction, 176 multiple lanes of, 177 in negative directions, 165 Vehicle configuration, 160 Vehicle definition, 171 Velocities, 421 Velocity, 429 Vertical direction, 144 Vertical load interaction, 241 Vibrating machinery, 2 Vibrating masses, 74 Viewing generated loads, 220–223 Viewing mode shapes, 297–299 inflection points, 299 joint displacements, 299 local modes, 299 PRINT MODE SHAPES, 299 tables for mode shapes and frequencies, post-processing mode, 298 torsional modes, 299 Viewing values (magnitude), 171–172 Viscous damper, 331 JOINT LOAD, 331 truss member, 331

W

Wave loading, 30 Weight. See Specific Weight Weight of fireproofing, 199 Wheel layout, 167 Wheel loads, 168–169 WIDTH parameter, 161–162 Wilson-Theta integration scheme, 399 WIND, 244 Wind, 231 Wind intensity, 129, 134 Wind Load, 236 Wind load generation, 100, 120–150 closed structures, 122–133, 135, 136 directions for, 144 excluding members from, 143 factor term in, 127–128 fire proofing and, 146 magnification, 146–147 magnification of, 146–147

multiple structures, 137–138 open structures, 133–137 out-of-plane nodes, 143 on plane frames, 149 on surface entities, 150 time taken to display, 144–146 types of, 122–136 wind pressure profile, 147–149 Wind loading, 420 Wind load magnification, 146–147 Wind loads, 254 Wind model, 252 Wind pressure, 120 Wind pressure profile, 120, 147–149 Windward face, 126 Windward side, 122, 133

X

XRANGE, 42, 44–46, 125, 130, 142

Y

Young’s modulus, 112 YRANGE, 42, 44–46, 125, 130, 142, 175

Z

Zero density, 67, 179 Zero period acceleration (ZPA), 353–354 mass participation, 354 MIS, 353 MISSING MASS correction, 353 ZERO SPECTRAL ACCELERATION, 364 zip code, 195–196, 198 ZPA. See Zero period acceleration (ZPA) ZRANGE, 42, 44–46, 125, 130, 142