toward improved flange bracing requirements for metal building frame systems

369 Pages·2009·11.48 MB·English

by  Quang Dai Tran

TOWARD IMPROVED FLANGE BRACING REQUIREMENTS FOR
METAL BUILDING FRAME SYSTEMS

A Thesis
Presented to
The Academic Faculty

By

Dai Q. Tran

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

Georgia Institute of Technology
May 2009
TOWARD IMPROVED FLANGE BRACING REQUIREMENTS FOR
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: April 6, 2009
To my parents Tran Duc Diep and Nguyen Thi Kieu
ACKNOWLEDGEMENTS

The author would like to express his appreciation to his advisor, Dr. Donald W. White,
for his guidance, patience and encouragement during the course of this study. The
appreciation is also extended to the committee members, Dr. Roberto T. Leon and Dr.
Kenneth M. Will for their comments.

The sponsorship of this research by Metal Building Manufacturers Association (MBMA)
is gratefully acknowledged. In addition, the author would like to thank the following
personnel for their help through the research study: Duane Becker and Carl Glanzman.

I would like to thank Vietnam’s Ministry of Education and Training for supporting my
master study. I want to thank all my friends for all their help, support, interest and valuable
hints.

Greatest thanks to the author’s family, Tran Duc Diep and Nguyen Thi Kieu, Pham Phu
Duc and Nguyen Thi Mai Lan for their unconditional love and support that they provided
throughout the study.

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TABLE OF CONTENTS

ACKNOWLEDGEMENTS ................................................................................................. iv
LIST OF TABLE .................................................................................................................... iv
LIST OF FIGURES ............................................................................................................. xiii

CHAPTER 1. INTRODUCTION ......................................................................................1
1.1 Problem Statement ..............................................................................................................1
1.3 Research Objectives and Goals .........................................................................................5
1.2 Organization ........................................................................................................................9
CHAPTER 2. BACKGROUND ........................................................................................10
2.1 Introduction ........................................................................................................................10
2.2 Bracing Requirements for Columns ...................................................................................11
2.2.1 Bracing Stiffness Requirements ...............................................................................12
2.2.1.1 Exact Buckling Solution for a Column with
a Single Intermediate Brace ..........................................................................15
2.2.1.2 Winter’s Solution ..........................................................................................17
2.2.1.3 Plaut’s Solution .............................................................................................19
2.2.2 Bracing Strength Requirements ...............................................................................20
2.2.2.1 Traditional 2 % Rule .....................................................................................20
2.2.2.2 Winter’s Solution ..........................................................................................21
2.2.2.3 Plaut’s Solution .............................................................................................23
2.2.3 Summary Brace Requirements from the AISC (2005) - Appendix 6 ......................23
2.2.3.1 Relative bracing ............................................................................................23
2.2.3.2 Nodal bracing ................................................................................................24
2.3 Calculation of Column Design Strength from an Eigenvalue Buckling Analysis,
- the AISC Effective Length Method (ELM) .....................................................................26
2.3.1 Elastic Buckling Strength of a Column with Four Equally Spaced
Nodal Braces ............................................................................................................26
2.3.2 Inelastic Buckling Strength Procedure for Determining Column Flexural
Buckling Strength .....................................................................................................31
2.3.3 Example Calculation of Elastic and Inelastic Buckling Strengths for
a Column with Four Equally Spaced Nodal Braces ..................................................33
2.4 Bracing Requirements for Beams ......................................................................................37
2.4.1 Lateral Bracing Requirements .................................................................................37
2.4.2 Torsional Bracing Requirements .............................................................................40
2.4.2.1 Brace Requirements Based on Refined Equations from
Yura and Phillips (1992) ...............................................................................42
2.4.2.2 Brace Requirements Based on the AISC 2005 Appendix 6 .........................44
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CHAPTER 3. REFINED ASSESSMENT OF COLUMN BRACING
REQUIREMENTS – APPLICATION OF THE DIRECT
ANALYSIS AND PLASTIC ZONE ANALYSIS METHODS ...46
3.1 Introduction ........................................................................................................................46
3.2 Overview of Example Column Bracing Problems .............................................................47
3.3 General Geometric Imperfection Modeling Considerations ..............................................51
3.3.1 Types of Imperfections for Assessment of
Column Flexural Buckling Strength ........................................................................51
3.3.2 Appropriate Magnitude of Column Imperfections ..................................................52
3.3.3 Simplified Representation of Out-of-Straightness Imperfections ............................53
3.3.4 Overview of General Considerations Necessary in Selecting an Appropriate
Pattern of Out-of-Straightness and Out-of-Plumbness ............................................54
3.3.5 Specific Procedures for Selecting an Overall Pattern of
Out-of-Straightness and Out-of-Plumbness Imperfections ......................................58
3.3.6 Example Determination of Geometric Imperfection Pattern ...................................63
3.4 Direct Analysis Method (DM) Procedure ..........................................................................69
3.5 DM Example ......................................................................................................................72
3.6 Distributed Plasticity (DP) Procedure ................................................................................78
3.7 DP Example ......................................................................................................................80
3.8 Illustrative Examples - Column Bracing ...........................................................................84
3.8.1 Case 1: Column with Four Intermediate Nodal Braces ..........................................84
3.8.1.1 DM and DP Solutions .................................................................................85
3.8.1.2 Comparison of the Results between the DM, DP, ELM
and the AISC 2005 Appendix 6 Solutions ...................................................91
3.8.1.3 Summary .......................................................................................................96
3.8.2 Case 1b: Column with Single Nodal Brace .............................................................96
3.8.2.1 Bracing Requirements based on the AISC Appendix 6 Commentary ..........97
3.8.2.2 DM and DP Solutions ...................................................................................98
3.8.2.3 Summary .....................................................................................................105
3.8.3 Case 2: Column with Flexible End Supports .........................................................106
3.8.3.1 DM Solution................................................................................................107
3.8.3.2 DP Solution .................................................................................................110
3.8.3.3 Summary .....................................................................................................114
3.8.4 Unequal Brace Spacing ..........................................................................................114
3.8.4.1 Case 3: Unequal Brace Spacing, Multiple Intermediate Nodal Braces ......114
3.8.4.1.1 DM Solution....................................................................................115
3.8.4.1.2 DP Solution .....................................................................................118
3.8.4.1.3 Summary .........................................................................................122
3.8.4.2 Case 3b: Unequal Brace Spacing, Single Intermediate Nodal Braces ........122
3.8.4.2.1 Brace Stiffness Corresponding to the Euler Buckling Load
for the Longer Segment ..................................................................123
3.8.4.2.2 DM Solution: Brace Force Corresponding to the Brace stiffness
to Develop the Euler Buckling Load for the Longer Segment .......124
3.8.4.2.3 DP Solution: Brace Force Corresponding to the Brace stiffness
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to Develop the Euler Buckling Load for the Longer Segment .......125
3.8.5 Case 4: Nonconstant Axial Force ..........................................................................128
3.8.5.1 DM Solution................................................................................................128
3.8.5.2 DP Solution .................................................................................................132
3.8.5.3 Summary .....................................................................................................135
3.8.6 Case 5: Nonprismatic Geometry .............................................................................135
3.8.6.1 DM Solution................................................................................................136
3.8.6.2 DP Solution .................................................................................................139
3.8.6.3 Summary .....................................................................................................142
3.8.7 Hybrid Bracing........................................................................................................142
3.8.7.1 Case 6: Hybrid Bracing (Problem H1)........................................................143
3.8.7.1.1 DM Solution..................................................................................143
3.8.7.1.2 DP Solution ...................................................................................148
3.8.7.2 Case 7: Hybrid Bracing (Problem H2)........................................................151
3.8.7.2.1 DM Solution..................................................................................151
3.8.7.2.2 DP Solution ...................................................................................155
3.8.7.3 Summary .....................................................................................................158
3.9 Summary and Conclusions for Column Bracing .............................................................158

CHAPTER 4. ASSESSMENT OF BEAM BRACING REQUIREMENTS
BY SECOND-ORDER ELASTIC ANALYSIS ..........................164
4.1 Introduction .....................................................................................................................164
4.2 Background and Research Approach ..............................................................................165
4.3 Analysis Model ...............................................................................................................168
4.3.1 Equivalent Truss Model .........................................................................................169
4.3.2 Simplified Single-Element Web Plate Model ........................................................172
4.3.3 Refined Web Plate Model ......................................................................................173
4.3.4 Finite Element Modeling (SAP 2000) ...................................................................173
4.3.5 Cantilever Beam Benchmark Tests ........................................................................174
4.4 Geometric Imperfections .................................................................................................178
4.5 Calculation of Brace Requirements by Eigenvalue Buckling Analysis ...........................182
4.5.1 Beam Lateral Bracing Benchmarks .......................................................................184
4.5.1.1 Benchmark Study LB1 ...............................................................................184
4.5.1.2 Benchmark Study LB2 ...............................................................................188
4.5.1.3 Benchmark Study LB3 ...............................................................................192
4.5.1.4 Benchmark Study LB4 ...............................................................................196
4.5.2 Torsional Beam Bracing Benchmarks ..................................................................200
4.5.2.1 Benchmark Study TB1 ...............................................................................201
4.5.2.2 Benchmark Study TB2 ...............................................................................204
4.6 Calculation of Brace Force Requirements by Second-Order
Elastic Load-Deflection Analysis ...................................................................................208
4.6.1 Lateral Beam Bracing ...........................................................................................209
4.6.1.1 Benchmark Study LB1 ...............................................................................209
4.6.1.1.1 Brace Requirements based on the AISC 2005
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Appendix 6 Commentary .............................................................210
4.6.1.1.2 Load-Deflection Results using β = 2β /φ ............................210
iF(SAP)
4.6.1.1.3 Load-Deflection Results using β = 1.9β ...........................213
iF(App6)
4.6.1.1.4 Discussion of Results ...................................................................214
4.6.1.2 Benchmark Study LB2 ...............................................................................215
4.6.1.2.1 Brace Requirements based on the AISC 2005
Appendix 6 Commentary .............................................................215
4.6.1.2.2 Load-Deflection Results using β = 2β /φ ............................216
iF(SAP)
4.6.1.2.3 Load-Deflection Results using β = 1.9β ...........................218
iF(App6)
4.6.1.2.4 Discussion of Results ...................................................................219
4.6.1.3 Benchmark Study LB3 ...............................................................................220
4.6.1.3.1 Brace Requirements based on the AISC 2005
Appendix 6 Commentary .............................................................221
4.6.1.3.2 Load-Deflection Results using β = 2β /φ ............................221
iF(SAP)
4.6.1.3.3 Load-Deflection Results using β = 1.9β ...........................223
iF(App6)
4.6.1.3.4 Discussion of Results ...................................................................224
4.6.1.4 Benchmark Study LB3* .............................................................................225
4.6.1.5 Benchmark Study LB4 ...............................................................................227
4.6.1.5.1 Brace Requirements based on the AISC 2005
Appendix 6 Commentary .............................................................228
4.6.1.5.2 Load-Deflection Results using β = 2β /φ
iF(SAP)
and ∆ = L /500 ..............................................................................229
b
4.6.1.5.3 Load-Deflection Results using β = 2β /φ
iF(SAP)
and β = 1.9β .......................................................................230
iF(App6)
4.6.1.5.4 Discussion of Results ...................................................................232
4.6.2 Torsional Beam Bracing .......................................................................................233
4.6.2.1 Benchmark Study TB1 ...............................................................................233
4.6.2.1.1 Brace Requirements based on the AISC 2005
Appendix 6 Commentary .............................................................233
4.6.2.1.2 Brace Requirements based on the Refined Equations
from Yura and Phillips (1992) .....................................................234
4.6.2.1.3 Load-Deflection Results using β = 2β /φ ............................236
iF(SAP)
4.6.2.1.4 Discussion of Results ...................................................................237
4.6.2.2 Benchmark Study TB2 ...............................................................................238
4.6.2.2.1 Brace Requirements based on the AISC 2005
Appendix 6 Commentary .............................................................239
4.6.2.2.2 Brace Requirements based on the Refined Equations
from Yura and Phillips (1992) .....................................................240
4.6.2.2.3 Load-Deflection Results using β = 2β /φ ............................241
iF(SAP)
4.6.2.2.4 Discussion of Results ...................................................................243
4.7 Combined Lateral and Torsional Bracing .......................................................................244
4.7.1 Calculation Torsional Bracing Stiffness ................................................................245
4.7.2 Calculation Lateral Bracing Stiffness ....................................................................249
4.7.3 Eigenvalue Buckling Analysis ...............................................................................250
4.7.3.1 Benchmark Study CB1 ...............................................................................250
4.7.3.2 Benchmark Study CB2 ...............................................................................254
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4.7.4 Load-Deflection Analysis Results .........................................................................256
4.7.4.1 Benchmark Study CB1 ...............................................................................256
4.7.4.1.1 Load-Deflection Results Using Stiffness Equal
to 2/φ of the Ideal Full Bracing Values .........................................257

4.7.4.1.2 Load-Deflection Results using Several Brace Stiffness between
1.0 to 2/φ of the Ideal Full Bracing Values ...................................260

4.7.4.1.3 Discussion of Results .....................................................................263
4.7.4.2 Benchmark Study CB2 ...............................................................................263
4.7.4.2.1 Load-Deflection Results Using Stiffness Equal
to 2/φ of the Ideal Full Bracing Values .........................................264

4.7.4.2.2 Load-Deflection Results using Several Brace Stiffness
between 1.0 to 2/φ of the Ideal Full Bracing Values .....................266

4.7.4.2.3 Discussion of Results .....................................................................269

CHAPTER 5. ASSESSMENT OF BEAM BRACING REQUIREMENTS
BY PLASTIC ZONE ANALYSES ...................................................270
5.1 Introduction ......................................................................................................................270
5.2 Finite Element Modeling ................................................................................................271
5.2.1 Finite Element Discretization ................................................................................271
5.2.2 Load and Displacement Boundary Conditions ......................................................272
5.2.3 Material Stress-Strain Characteristic .....................................................................272
5.2.4 Residual Stress ......................................................................................................276
5.2.5 Geometric Imperfections .......................................................................................279
5.3 Results from Plastic Zone Analyses ...............................................................................280
5.3.1 Lateral Bracing: Benchmark Study LB3 ...............................................................280
5.3.1.1 Results from the AISC 2005 Appendix 6 Commentary
Equations for M=M ..................................................................................281
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5.3.1.2 Results from the Plastic Zone Analyses ....................................................282
5.3.2 Lateral Bracing: Benchmark Study LB3* .............................................................286
5.3.2.1 Results from the Plastic Zone Analyses ....................................................287
5.3.3 Torsional Bracing: Benchmark Study TB1 ...........................................................289
5.3.3.1 Results from the AISC 2005 Appendix 6 Commentary
Equations for M=M ..................................................................................291
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5.3.3.2 Results based on Refined Equations from Yura and Phillips (1992) .........292
5.3.3.3 Results from Plastic Zone Analyses .........................................................293
5.3.4 Combined Lateral and Torsional Bracing: Benchmark Study CB1 ......................298
5.3.5 Lateral Bracing: Richter’s (1998) Test No.6 ........................................................303
5.3.5.1 Results from the AISC 2005 Appendix 6 Commentary
Equations for M=M ..................................................................................304
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5.3.5.2 Results from Plastic Zone Analyses .........................................................305
5.3.6 Torsional Bracing: Richter’s (1998) Test No.6 ....................................................309
5.3.6.1 Results from the AISC 2005 Appendix 6 Commentary
Equations for M=M ..................................................................................309
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5.3.6.2 Results from Plastic Zone Analyses .........................................................310
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5.3.7 Combined Lateral and Torsional Bracing: Richter’s (1998) Test No.6 ...............313
5.3.7.1 Results from Plastic Zone Analyses .........................................................314
5.3.8 Tapered Beam ........................................................................................................317
5.3.9 Summary ...............................................................................................................323
5.4 Summary and Conclusions for Beam Bracing .................................................................324

CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS .......................328
6.1 Summary ........................................................................................................................328
6.2 Findings and Recommendations ....................................................................................329
6.3 Future Work ...................................................................................................................332
REFERENCES .................................................................................................... 336

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