Report No. By Benjamin V. Fell Amit M. Kanvinde Gregory G. Deierlein 172 August 2010

279 Pages·2010·3.8 MB·German

Department of Civil and Environmental Engineering
Stanford University

Report No.
The John A. Blume Earthquake Engineering Center was established to promote
research and education in earthquake engineering. Through its activities our
understanding of earthquakes and their effects on mankind’s facilities and structures is
improving. The Center conducts research, provides instruction, publishes reports and
articles, conducts seminar and conferences, and provides financial support for students. The
Center is named for Dr. John A. Blume, a well-known consulting engineer and Stanford alumnus.

Address:

The John A. Blume Earthquake Engineering Center
Department of Civil and Environmental Engineering
Stanford University
Stanford CA 94305-4020

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©2010 The John A. Blume Earthquake Engineering Center
© Copyright by Benjamin V Fell 2008
All Rights Reserved
Abstract

Special Concentrically Braced Frames (SCBFs) are popular lateral load resisting frames due to
their economy, structural efficiency and stiffness. Following the 1994 Northridge earthquake,
braced-frames became increasingly common after brittle fractures were observed at beam-column
connections in Moment Resistant Frames (MRFs). However, braced-frames are also susceptible
to fracture at the middle plastic hinge of the brace, the brace to gusset plate connection, and the
gusset plate to column or beam connection. This research primarily focuses on fracture at the
middle plastic hinge, where the combined effect of global and local buckling during cyclic
loading amplifies the plastic strain at the brace midpoint and initiates fracture. To develop a better
understanding of the localized mechanisms affecting brace fracture, this work combines a large-
scale experimental program with an intensive simulation study to investigate brace behavior
across a wide-range of material types and geometries. The simulations employ continuum-based
modeling techniques to accurately reproduce the stress and strain histories during cyclic loading
while a novel micromechanical fracture model is evaluated as a means to predict the fracture
initiation events. The fracture model operates at the continuum-level and captures the
fundamental mechanisms responsible for ductile fracture unique to Ultra Low Cycle Fatigue
(ULCF) conditions which differ from the well-defined High and Low Cycle Fatigue (HCF and
LCF) mechanisms. From the large-scale brace experiments, cross-section width-thickness and
slenderness ratios are shown to influence the brace axial deformation fracture ductility, such that
a larger width-thickness ratio and a smaller slenderness tend to reduce ductility. Furthermore, the
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experiments are used to evaluate the fracture model at the large-scale where small-scale
calibration tests and a multi-scale modeling procedure is used to connect the steel behavior at the
micromechanical level to the finite element simulation results. The fracture predictions are
encouraging considering the high level of complexity in modeling buckling phenomena and
imperfect constitutive model behavior. The model is used to expand the experimental test matrix
through parametric simulation of square and rectangular bracing components which, along with a
synthesis of experimental results over the last twenty years, informs a general relationship
between brace ductility and geometry.

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Acknowledgements

This research was supported by the National Science Foundation (NSF Grant CMS
0421492), the George E. Brown Jr. Network for Earthquake Engineering Simulation (NEES),
and the Structural Steel Educational Council (SSEC). The advice and guidance of Helmut
Krawinkler and Jack Baker (Stanford University), Stephen Mahin (University of California,
Berkeley), Charles Roeder (University of Washington), Robert Trembly (Polytechnique
Montréal), Patxi Uriz (Exponent Failure Analysis Associates) Walterio López and Mark
Saunders (Rutherford and Chekene) is greatly appreciated. Andy Myers (Stanford
University) has been instrumental to this research by conducting the small-scale calibration
experiments and dedicating his summer during 2005 to setup the large-scale brace tests at the
UC Berkeley Richmond Field Station. The knowledgeable support of the University of
California, Berkeley NEES lab personnel including Shakhzod Takhirov, Donald Patterson,
Donald Clyde, David MacLam, and Jose Robles is gratefully acknowledged. The authors also
acknowledge support from the John A. Blume Earthquake Engineering Center at Stanford
University and the University of California, Davis.

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Table of Contents

Abstract ........................................................................................................................................... ii 
Acknowledgements ....................................................................................................................... iv 
Table of Contents ........................................................................................................................... v 
List of Tables ................................................................................................................................. ix 
List of Figures ................................................................................................................................. x 
Chapter 1  Introduction ............................................................................................................ 1 
1.1 Motivation .................................................................................................................................. 1 
1.2 Objectives and Scope ................................................................................................................. 3 
1.3 Organization and Outline ........................................................................................................... 5 
Chapter 2  Simulating Fracture in SCBF Bracing Components - Background ................ 10 
2.1 Performance Evaluation of SCBF Systems ............................................................................. 12 
2.1.1 SCBF System Behavior .................................................................................................... 12 
2.1.2 Seismic Design Provisions for SCBF Systems ................................................................. 15 
2.1.3 State-of-the-art in SCBF Performance Assessment .......................................................... 17 
2.1.3.1 Studies Examining Seismic Demands in SCBF Systems Through Nonlinear
Dynamic Analysis ................................................................................................................. 19 
2.1.3.1.1 Sabelli (2001) Analyses ..................................................................................... 20 
2.1.3.1.2 Uriz (2005) Analyses ......................................................................................... 21 
2.1.3.1.3 McCormick et al (2007) Analyses ..................................................................... 23 
2.1.3.1.4 Redwood et al (1991) Analyses ......................................................................... 23 
2.1.3.1.5 Tremblay and Poncet (2005) Analyses .............................................................. 24 
2.1.3.1.6 Izvernari et al (2007) Analyses .......................................................................... 25 
2.1.3.2 Shake Table Testing .................................................................................................. 25 
2.1.3.3 Summary of Demand Assessment of SCBF Systems ............................................... 26 
2.1.3.4 Studies Investigating the Capacity of Bracing Members .......................................... 27 
2.1.3.4.1 Square and Rectangular Hollow Steel Structural (HSS) Bracing Components . 30 
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2.1.3.4.2 Round Steel Pipe Bracing Members .................................................................. 32 
2.1.3.4.3 Wide-Flanged Bracing Components .................................................................. 33 
2.1.3.4.4 General Ductility Trends of HSS, Pipe, and Wide-Flanged Steel Braces.......... 34 
2.1.3.4.5 Full-System Braced Frame Tests ....................................................................... 38 
2.2 Modeling Techniques for SCBF Systems ................................................................................ 39 
2.2.1 Demand Characterization ................................................................................................. 40 
2.2.1.1 Techniques for Brace Simulation .............................................................................. 41 
2.2.1.1.1 Rule-Based (or Phenomenological) Brace Models ............................................ 41 
2.2.1.1.2 Concentrated Hinge Brace Models .................................................................... 42 
2.2.1.1.3 Fiber-Element Based Brace Models .................................................................. 42 
2.2.1.1.4 Continuum-Based Brace Models ....................................................................... 43 
2.2.2 Capacity Characterization ................................................................................................ 45 
2.2.2.1 Brace Geometry-Based Fracture Capacity Relationships ......................................... 45 
2.2.2.2 Fiber Element-Based Critical Strain Models ............................................................. 50 
2.2.2.3 Micromechanical Void Growth and Coalescence Models ........................................ 51 
2.3 Summary .................................................................................................................................. 53 
Chapter 3  Large-Scale Brace Component Tests ................................................................. 71 
3.1 Motivation for Large-Scale Brace Tests .................................................................................. 71 
3.2 Experimental Setup .................................................................................................................. 73 
3.3 Test Program Scope ................................................................................................................. 73 
3.3.1 Cyclic Loading Protocols ................................................................................................. 76 
3.3.1.1 Standard Cyclic Loading Protocol ............................................................................ 77 
3.3.1.2 Near-Field Loading Histories .................................................................................... 79 
3.3.1.3 Story Drift and Brace Axial Deformation Relationships .......................................... 80 
3.4 Instrumentation and Miscellaneous Testing Results ................................................................ 81 
3.5 Summary .................................................................................................................................. 84 
Chapter 4  Large-Scale Experimental Results and Design Implications ........................... 98 
4.1 Qualitative Summary of Experimental Response .................................................................... 98 
4.2 Quantitative Summary of Data For All Tests ........................................................................ 100 
4.3 Effect of Test Variables on Cyclic Brace Behavior, Limit States and Design Implications .. 104 
4.3.1 Effect of Width to Thickness Ratios ............................................................................... 104 
4.3.2 Effect of Member Slenderness ....................................................................................... 106 
4.3.3 Effect of Cross Sectional Shape ..................................................................................... 107 
4.3.4 Effect of Grout Filling of HSS Specimens ..................................................................... 107 
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4.3.5 Effect of Loading Rate ................................................................................................... 108 
4.3.6 Effect of Unsymmetrical Buckling ................................................................................. 110 
4.4 Brace-Gusset Plate Connection Performance ........................................................................ 110 
4.4.1 Experimental Results ...................................................................................................... 112 
4.5 Comparison of Experimental Data to Commonly Used Formulae for Predicting Strength and
Stiffness of Bracing Members ..................................................................................................... 116 
4.5.1 Elastic Stiffness .............................................................................................................. 116 
4.5.2 Compressive Strengths ................................................................................................... 117 
4.5.3 Maximum Tensile Strength ............................................................................................ 118 
4.6 Summary ................................................................................................................................ 119 
Chapter 5  Application and Evaluation of the CVGM for Large-Scale Components .... 136 
5.1 Development of the Cyclic Void Growth Model (CVGM) ................................................... 139 
5.1.1 Material Behavior, Constitutive Models and Calibration ............................................... 143 
5.1.2 CVGM Calibration ......................................................................................................... 146 
5.1.2.1 Calibration of  ....................................................................................................... 147 
5.1.2.2 Calibration of  ....................................................................................................... 147 
5.1.3 CVGM Application and Validation in Small-Scale Details ........................................... 148 
5.2 Application of CVGM to Large-Scale Bracing Components ................................................ 149 
5.2.1 Material Model Calibration ............................................................................................ 150 
5.2.2 Large-Scale Brace Simulations ...................................................................................... 153 
5.2.2.1 Modeling Global and Local Buckling ..................................................................... 153 
5.2.2.1.1 Imperfections and Buckling Simulations ......................................................... 154 
5.2.2.1.2 Comparison to Experimental Global Buckling ................................................ 155 
5.2.2.1.3 Comparison to Experimental Local Buckling .................................................. 155 
5.2.3 Brace Material CVGM Calibraiton ................................................................................ 156 
5.2.3.1 Brace Material Calibration Results:  ..................................................................... 156 
5.2.3.2 Brace Material Calibration Results:  ..................................................................... 157 
5.2.4 CVGM Fracture Predictions Applied to Large-Scale Brace Components ..................... 162 
5.2.4.1 Application to HSS and Pipe Cross-Sections (Standard Loading) .......................... 163 
5.2.4.2 Application to Near-Field Loading Histories .......................................................... 166 
5.2.4.3 Quasi-Static Versus Earthquake Loading Rates ...................................................... 167 
5.2.4.4 Application to Unsymmetrical Buckling ................................................................. 168 
5.2.4.5 Estimating Uncertainty in the CVGM Fracture Predictions .................................... 169 
5.3 Summary ................................................................................................................................ 171 
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Chapter 6  Parametric Simulation of HSS Bracing Members .......................................... 203 
6.1 Parametric Simulation Matrix ................................................................................................ 204 
6.1.1 Cyclic Loading History .................................................................................................. 205 
6.2 CVGM Fracture Predictions .................................................................................................. 205 
6.2.1 Effect of Width-Thickness Ratio on Brace Ductility ..................................................... 206 
6.2.2 Effect of Slenderness Ratio on Brace Ductility .............................................................. 206 
6.3 Synthesis of Experimental and Simulation Results ............................................................... 208 
6.3.1 A Simplified Approach for Evaluating the Effect of Brace Parameters on Ductility ..... 210 
6.3.1.1 Plastic Hinge Length ............................................................................................... 213 
6.3.1.1.1 Comparison to Fiber-based Brace Simulations ................................................ 216 
6.3.2 Evaluating Brace Axial Deformation Capacities Relative to Earthquake Induced
Interstory Drift Demands ......................................................................................................... 216 
6.4 Summary and Reliability of Parametric Study and Semi-Theoretical Model ........................ 222 
Chapter 7  Summary, Conclusions and Future Work ....................................................... 240 
7.1 Summary and Conclusions .................................................................................................... 241 
7.1.1 Large Scale Brace Experiments ...................................................................................... 241 
7.1.2 CVGM Evaluation in Large Scale Details ..................................................................... 243 
7.1.3 Parametric Simulation of Bracing Members .................................................................. 245 
7.2 Future Work ........................................................................................................................... 246 
References ................................................................................................................................... 249 
Appendix A ................................................................................................................................. 256 
Appendix B ................................................................................................................................. 263 

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