[THESIS TITLE GOES HERE] - Georgia Institute of Technology

377 Pages·2011·4.35 MB·English

FLANGE STABILITY BRACING BEHAVIOR IN METAL
BUILDING FRAME SYSTEMS

A Thesis
Presented to
The Academic Faculty

by

Akhil Sharma

In Partial Fulfillment
of the Requirements for the Degree
Master of Science in the
School of Civil and Environmental Engineering

Georgia Institute of Technology
May 2011
FLANGE STABILITY BRACING BEHAVIOR IN METAL
BUILDING FRAME SYSTEMS

Approved by:

Dr. Donald W. White, Advisor
School of Civil and Environmental Engineering
Georgia Institute of Technology

Dr. Roberto T. Leon
School of Civil and Environmental Engineering
Georgia Institute of Technology

Dr. Kenneth M. Will
School of Civil and Environmental Engineering
Georgia Institute of Technology

Date Approved: November 12, 2010
To my parents, Amrit Lal Sharma and Renu Sharma
for their overwhelming support, patience and love
ACKNOWLEDGEMENTS

I would like to express my deepest gratitude to all those who gave me the
opportunity to complete this thesis. Special thanks are due to my advisor Professor
Donald W. White whose help, stimulating suggestions and encouragement helped me in
all the time of research for and writing of this thesis. I am deeply indebted to my
committee members, Professor Roberto T. Leon and Professor Kenneth M. Will for all
their help and support.

The sponsorship from Metal Building Manufacturers Association (MBMA) for this
research is greatly appreciated. Also, I would like to thank Mr. Duane Becker, Chief
Industries for the suggestions and help that he provided for me.

I want to thank all my friends for all their help, support, interest and valuable hints.
I am obliged to Dr. Yoon Duk Kim for all her assistance and advice on this study.

Special thanks are due to my parents for their support and encouragement that made this
possible.

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TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS iv
LIST OF TABLES xiv
LIST OF FIGURES xvi
SUMMARY xxiii
CHAPTER
1 INTRODUCTION 1
1.1 Problem Statement 1
1.2 Research Objectives and Goals 19
1.3 Organization 22
2 BACKGROUND 23
2.1 Bracing Types 24
2.2 Fundamental Column Relative Bracing Requirements 29
2.2.1 Column Relative Bracing Analysis Models 29
2.2.2 Explicit Second-Order Analysis Solution for Relative Bracing 31
2.2.3 Ideal versus Required Relative Bracing Stiffnesses 40
2.2.4 Clarification of Important Attributes of the
AISC Column Relative Bracing Equations 42
2.2.5 Influence of Column Continuity through the Brace Points 44
2.3 Fundamental Column Nodal (Discrete Grounded) Bracing
Requirements 45
2.3.1 Column Nodal Bracing Models 45
2.3.2 Ideal Nodal Bracing Stiffness 47
2.3.3 Full Nodal Bracing Stiffness 47
2.3.4 Partial Nodal Bracing Stiffness 48
v
2.3.5 Nodal Bracing Second-Order Analysis Solutions 54
2.3.5.1 Winter’s Full Bracing Model 55
2.3.5.2 Plaut’s Approximations 62
2.3.5.3 AISC L Approach for Partial Bracing 63
q
2.3.5.4 Lutz and Fisher’s Approximations for Partial Bracing 65
2.3.5.5 Yura’s Solution for the Partially-Braced Column
Buckling Strengths 68
2.3.5.6 General-Purpose Nodal Bracing Model 69
2.4 Key Differences between Column Relative and Nodal Bracing 71
2.5 Fundamental Beam Bracing Requirements 71
2.5.1 Beam Lateral Bracing 71
2.5.2 Beam Torsional Bracing 73
2.6 Overview of 2010 AISC Appendix 6 Bracing Requirements 79
2.6.1 Bracing of Columns 80
2.6.1.1 Relative Bracing 80
2.6.1.2 Nodal Bracing 84
2.6.2 Bracing of Beams 88
2.6.2.1 Lateral Bracing Requirements 89
2.6.2.1.1 Relative Bracing 89
2.6.2.1.2 Nodal Bracing 94
2.6.2.2 Torsional Bracing Requirements 97
2.7 Example Ad Hoc Application of the Current AISC Appendix 6
Requirements to Metal Building Frame Systems 106
2.7.1 Wall Diaphragm Bracing 113
2.7.1.1 Relative (Shear Panel) Bracing Stiffness 114
2.7.1.2 Relative (Shear Panel) Bracing Strength 114
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2.7.2 Torsional Bracing at c3 (Girt Closest to the Top of
the Column 115
2.7.2.1 Torsional Brace Stiffness 116
2.7.2.2 Torsional Brace Strength 121
2.7.2.3 Brace Point Movement at the Strength Condition 121
2.7.3 Roof Diaphragm Bracing Between r1 and r2 122
2.7.3.1 Relative (Shear Panel) Bracing Stiffness 122
2.7.3.2 Relative (Shear Panel) Bracing Strength 123
2.7.4 Roof Diaphragm Bracing Between r7 and r8 123
2.7.4.1 Relative (Shear Panel) Bracing Stiffness 123
2.7.4.2 Relative (Shear Panel) Bracing Strength 125
2.7.5 Torsional Bracing at r1 (Purlin Closest to the Knee) 125
2.7.5.1 Torsional Brace Stiffness 126
2.7.5.2 Torsional Brace Strength 128
2.7.5.3 Brace Point Movement at the Strength Condition 128
2.7.6 Summary 128
2.8 Simplified Brace Strength and Stiffness Requirements 130
2.8.1 Relative Bracing 134
2.8.2 Nodal Lateral Bracing 135
2.8.3 Beam Torsional Bracing 137
2.8.4 Wall Diaphragm Bracing 139
2.8.4.1 Relative (Shear Panel) Bracing Strength Requirement 139
2.8.4.2 Relative (Shear Panel) Bracing Stiffness Requirement 140
2.8.5 Torsional Bracing at c3 (Girt Closest to the Top of
the Column) 140
2.8.5.1 Torsional Brace Strength Requirement 140
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2.8.5.2 Torsional Brace Stiffness Requirement 141
2.8.6 Roof Diaphragm Bracing Between r1 and r2 142
2.8.6.1 Relative (Shear Panel) Bracing Strength Requirement 142
2.8.6.2 Relative (Shear Panel) Bracing Stiffness Requirement 142
2.8.7 Torsional Brace at r1 (Purlin Closest to the Knee) 143
2.8.7.1 Torsional Brace Strength Requirement 143
2.8.7.2 Torsional Brace Stiffness Requirement 143
3 APPLICATION OF VIRTUAL TEST SIMULATION FOR THE
ASSESSMENT OF STABILITY BRACING 146
3.1 Full Nonlinear Shell FEA Modeling of Members and Frames 150
3.1.1 Finite Element Discretization 150
3.1.2 Load and Displacement Boundary Condition 151
3.1.3 Material Properties 153
3.2 Nominal Residual Stresses 155
3.3 Nominal Geometric Imperfections 157
3.3.1 Types and Magnitudes of Critical Imperfections 159
3.3.2 Selection of the Critical Combination of Geometric
Imperfections 161
3.4 FEA representation of the Bracing Components and Systems 169
3.4.1 Model of the Building Longitudinal X Bracing System 171
3.4.2 Modeling of Torsional Braces 172
3.4.3 Modeling of Wall and Roof Shear Diaphragms 173
4 ROOF GIRDER EXAMPLE 174
4.1 Introduction 174
4.2 Geometry and Loading 175
4.3 Bracing Configuration 175
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4.4 AISC Based Bracing Requirements 178
4.4.1 Refined Estimates of the Girder Flexural Resistance for
Full Bracing 178
4.4.2 AISC-Based Torsional Bracing Requirements Using the
Moments from the LRFD Wind Uplift Load Combination 181
4.4.2.1 Required Stiffness 181
4.4.2.2 Required Strength 185
4.4.3 AISC-Based Torsional Bracing Requirements Based on the
AISC LRFD Beam Design Capacity Assuming Full Bracing
Stiffness and Strength 185
4.4.4 AISC-Based Torsional Bracing Requirements Based on the
Maximum Moments from Virtual Test Simulation 187
4.5 Simplified Bracing Requirements 188
4.6 Calculation of the Provided Brace Stiffness and Strength and
Comparison to Required Values 189
4.7 Critical Geometric Imperfections for Virtual Simulation Analysis 194
4.8 Virtual Simulation Results Using AISC-Based Torsional Brace
Stiffness Required to Brace for the LRFD Wind Uplift Loading 197
4.9 Effect of Varying Brace Stiffness 202
4.10 Summary 211
5 SIDEWALL COLUMN EXAMPLE 214
5.1 Introduction 214
5.2 Geometry and Loading 215
5.3 Bracing Configuration 216
5.4 AISC Based Bracing Requirements 219
5.4.1 Refined Estimate of the AISC Flexural Resistance for
Full Bracing 219
5.4.2 AISC-Based Torsional Bracing Design Requirements at
the Top of the Column 224
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5.4.2.1 Required Stiffness to Develop the Specified ASD
Moments in the Column 224
5.4.2.2 Required Stiffness to Develop the Estimated AISC
Load Capacity of the Column 227
5.4.2.3 Required Stiffness to Develop the Virtual Simulation
Capacity of the Column 228
5.4.2.4 Required Strength to Develop the Specified ASD
Moments in the Column 228
5.4.2.5 Required Strength to Develop the Estimated AISC
Load Capacity of the Column 229
5.4.2.6 Required Strength to Develop the Virtual Simulation
Load Capacity of the Column 230
5.4.3 AISC Relative Bracing Design Requirements at the Bottom
of the Column 230
5.4.3.1 Required Stiffness to Develop the Specified ASD
Moments in the Column 230
5.4.3.2 Required Stiffness to Develop the Estimated AISC
Load Capacity of the Column 231
5.4.3.3 Required Stiffness to Develop the Virtual Simulation
Capacity of the Column 232
5.4.3.4 Required Ultimate Strength to Develop the Specified
ASD Moments in the Column 232
5.4.3.5 Required Strength to Develop the Estimated AISC
Load Capacity of the Column 232
5.4.3.6 Required Strength to Develop the Virtual Simulation
Load Capacity of the Column 232
5.5 Simplified Bracing Requirements 233
5.5.1 Required Torsional Brace Strength 233
5.5.2 Required Torsional Brace Stiffness 233
5.5.3 Required Shear Panel Strength 234
5.5.4 Required Shear Panel Stiffness 235
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